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![71
Math Student's Copy Book
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
AL KAMAL AZHARIAN INSTITUTES Primary Six First Term
Volumes
Definition:
The solid: Any object that occupies a room in the space.
Notice that:
The solid are two kinds
Solids
We will study two solids only:
1) Cuboid:
His irregular solid its properties:
1- It has 6 faces, each of them is rectangle.
2- It has 12 edges, 8 vertices and 3 dimensions (length, width, and height).
3- Each two opposite faces are equal in area (congruent and they are parallel)
4- Each two adjacent faces intersect at a line segment,which is called an edge.
2) Cube:
It is cuboid with equal dimensions it's properties:
1- It has 6 faces, each of them is a square.
2- All the faces are equal in area [congruent].
3- Each two opposite faces are parallel.
4- It has 8 vertices and 12 edges.
5- All the edges are equal in length.
6- It has 3 dimensions.
A geometrical shape Hasn't geometrical shape](https://image.slidesharecdn.com/mathprimary6-151208094416-lva1-app6892/85/slide-71-320.jpg)
![72
Math Student's Copy Book
AL KAMAL AZHARIAN INSTITUTES Primary Six First Term
Volumes
Definition: the number of units which a solid consists of.
The units of volumes:
1) The cubic decimeter [dm3
]:
It is the volume of cube of edge length 1dm
1dm = 10 cm
2) The cubic meter [m3
]:
It is the volume of cube of edge length 1m
1m = 100 cm = 10 dm
3) The cubic millimeter [mm3
]:
It is the volume of cube of edge length 1mm
Converting units
Complete:
1) 5 cm3
= ………….. mm3
2) 1500 mm3
= ………….. cm3
3) 0.001 cm3
= ………….. mm3
4) 300 000 cm3
= ………….. mm3
5) 7000 000 cm3
= ………….. m3
6) 85000 000 000 mm3
= ………….. cm3
7) 24000 dm3
= ………….. m3
8) 15 dm3
= ………….. mm3
Arrange discerningly:
500 000 cm3
, 50 000 dm3
, 5m3
……………………………………………………………………….
……………………………………………………………………….
cm3
1000×
1000
m3
dm3
mm3
1000× 1000×
1000 1000](https://image.slidesharecdn.com/mathprimary6-151208094416-lva1-app6892/85/slide-72-320.jpg)
![73
Math Student's Copy Book
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
AL KAMAL AZHARIAN INSTITUTES Primary Six First Term
The volume of the cuboid
Remember:
Cuboid has 12 edges, [4 length, 4 width , 4 height]
The dimensions is [length, width, height]
The volume of cuboid = length × width × height
The volume of cuboid = the product of its dimensions
The volume of cuboid = Area of one base × height
Example (1):
A cuboid its length 5cm, its width = 3cm, its height = 2cm.
Find the volume of cuboid.
Solution: Volume of cuboid = length × width× height
= 5 × 3 × 2 = 30 cm3
Example (2):
A cuboid its dimensions 30cm, 2dm , 9cm. Find its volume.
Solution: Convert = 2dm = 2 × 10 = 20 cm
The volume of cuboid = the product of its dimensions =30×20×9= 5400cm3
Drill (1):
A cuboid the area of its base 9cm2
and its length 3cm. Find the volume.
Solution
…………………………………………………………………………..…
…………………………………………………………………………..…
…………………………………………………………………………..…
Drill (2):
A cuboid its length 7dm, its width 2m and its height 3cm. Find the volume.
Solution
…………………………………………………………………………..…
…………………………………………………………………………..…
…………………………………………………………………………..…
…………………………………………………………………………..…
…………………………………………………………………………..…
V
HWL
V
HB.A
Length
width
height](https://image.slidesharecdn.com/mathprimary6-151208094416-lva1-app6892/85/slide-73-320.jpg)
![101
Math Student's Copy Book
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
AL KAMAL AZHARIAN INSTITUTES Primary Six First Term
Exercises on representing
data by the frequency curve
Drill (1):
1) If the marks of pupils is between [20 , 52]. Find the range of these marks.
…………………………………………………………………………..
2) If the marks of 6 pupils in one exam is 29 , 33 , 57 , 40 , 36 , 49 . Find
the range of these marks.
Solution
The greatest mark = …………….
The smallest mark = ……………
Range = …………………………
Drill (2):
The following table represents the marks of 50 pupils in one exam.
2) Represent the data by frequency curve then answer the following:
d) The number of students who have less than 30 marks.
e) The number of students who have 40 degree or more and what the
percentage.
f) The number of students that have 10 marks and less than 30 marks.
Sets 0 – 10 – 20 – 30 – 40 – 50 – Total
Frequency 4 7 8 14 11 6 50](https://image.slidesharecdn.com/mathprimary6-151208094416-lva1-app6892/85/slide-101-320.jpg)
Uploaded byأمنية وجدى
المراجعة النهائية فى الماث للشهادة الابتدائية الترم الأول لمدرسة الكمال
This document contains notes from a math student's copy book covering ratios and fractions. It includes examples and exercises on simplifying fractions, writing numbers divisible by certain numbers, finding ratios between quantities, and properties of ratios. Key concepts covered are ratios comparing two quantities, reducing ratios to simplest form, ratio properties such as keeping the same units and order, and using ratios to solve word problems involving quantities in a given ratio. Worked examples demonstrate finding ratios and using them to determine unknown values. Exercises provide practice applying these ratio and fraction skills.
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المراجعة النهائية فى الماث للشهادة الابتدائية الترم الأول لمدرسة الكمال
- 1. 1 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Revision on Simplifying the fraction and divisibility Example (1): Write a number formed from two digits and divisible by two ………………………………………………………………… Example (2): Put a circle around the number that divisible by two and underline on the number divisible by 3 1324 , 231 , 324 , 380 ………………………………………………………………… Drill: Write three whole number divisible by 5 ……………… , ……………… , ……………… Example (3): Simplify into simplest form: a) = b) = = c) = d) = Remember 1) The numbers that divisible by 2 is the numbers that its unite is (0, 2, 4, 6, 8). 2) The numbers that divisible by 5 is the numbers that unite is (0 , 5) 3) The numbers that divisible by 3 is the numbers that its sum is divisible by 3 (from the multiples of 3) 18 27 ….. ….. 420 490 ….. ….. 13 12 ….. ….. 41 205 ….. ….. Remembe r The prime numbers that numbers have two factors 288 120
- 2. 2 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Write the prime numbers between 1 , 50 The prime numbers is: .................................................................................................................................................................................................. .................................................................................................................................................................................................. .................................................................................................................................................................................................. .................................................................................................................................................................................................. .................................................................................................................................................................................................. Evaluation: 1) Simplify: a) = b) = 2) Write 5 numbers divisible by 2 of 5 together: ………… , ………… , ………… , ………… , ………… Drill: 1) Write 3 number divisible by 2 of 3 together: ……………… , ……………… , ……………… 2) Write number divisible by 2 of 3 together: ………………………… 3) Simplify: a) = b) = a) = Think 72 84 ….. ….. 5 10 ….. ….. 7 21 ….. ….. 16 32 ….. ….. 18 27 ….. ….. 150 450 ….. …..
- 3. 3 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit (1) Lesson (1) The meaning of ratio Ratio: Is comparing between two quantities or numbers as the same type and same unite. Example (1): Huda has 20 pound and Yasmin has 40 pounds compare between them. Solution: = = = and we write it 1 : 2 and we read it 1 to Z Example (2): Find the ration between two numbers in simplest form 64 , 48 Solution: 1st number : 2nd number 48 : 64 ( 2) 24 : 32 ( 4) 6 : 8 ( 2) 3 : 4 another solution: = = = = = and we write it 1 : 2 and we read it 1 to Z Example: Complete: The ration between two numbers = Drill: Find the ratio between two numbers of the following: a) 16 , 32 b) 150 , 450 c) 34 , 102 : ............: 2nd number1st number:2nd number1st number : ............: ............: 3216 : ............: ............: ............ : ............: ............: ............ H.W: P.B P.5 no. 1 , 2 , 3 Definitions: What with Huda What with Yasmin 205 20 40 2 4 1 2 Simplest form 1st number 2nd number What with Yasmin 205 48 64 24 32 6 8 3 4 1st term (antecedent) (consequent) ….... …....
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- 5. 5 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The meaning of ratio Example: Find the ratio between two numbers 16 , 40 then determine antecedent and the consequent. Solution: ............................................................................................................................................................................................................. ............................................................................................................................................................................................................. ............................................................................................................................................................................................................. Example (1): In one of the classes of the first grade primary the number of boys is 15 pupils and the number of girls is 20 pupils. Calculate: 1) The ratio between the number of boys and the number of girls. 2) The ratio between the number of girls and the number of all pupils in the class. Solution: - Number of girls = 25 girl - Number of boy = 15 boy - The number of pupils = 25 + 15 = 40 pupils 1) Number of boys : number of girls .................................................:............................................. .................................................:............................................. 2) Number of boys : number of pupils .................................................:............................................. .................................................:............................................. Example (2): Find the ration between 2.3 , 5.75 Solution: 1st number : 2nd number 2.3 : 5.75 ……………. : ..…………… ……………. : ..…………… ……………. : ..…………… ……………. : ..…………… Example (3): If the number of sum pupils in school is 540 pupil, the number of boys is 405 pupil. Find: 1) The ratio between the number of boys 2) The ratio between number of boys and the number of girls in two ways: and the number of pupils: …………………………………………..…. ……………………………..…………… …………………………………………..…. ……………………………..…………… …………………………………………..…. ……………………………..…………… H.W: P.B P.5 no. 4 , 5 , 6 , 7
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- 7. 7 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (2) The properties of ratio - Ton = 1000 kgm - Pound = 100 piasters - Kg = 1000 gm - metre = 100 cm - (feddan – kirate – sahm) are units of cultivated lands. feddan = 24 Kirat kirat = 24 sahm Properties of ratio: - Property 1: The ratio has the same properties of the fraction as reduction, simplifying and comparison. - Property 2: in its simplest form, the two terms of the ratio should be two whole numbers. - Property 3: At comparing two quantities of the same type to form the ratio between them, they must have the same unit. - Property 4: The ratio between two quantities of the same kind doesn't have any units. - Property 5: The ratio keeps the order. Example (1) : Find the ratio between: a) 1 : 2.2 (convert into decimal number) 1.6 : 2.2 ( × 10 the two terms) 16 : 22 ( ) …….. : ……… b) Two areas 0.75 kirats, 16 sahm convert 0.75 kirats = 0.75 × 24 = 18 sahm 1st area : 2nd area 18 : 16 (2) 9 : 8 c) : 3 5 Definitions: Remember 1 2 3 4
- 8. 8 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 4 : 6 (2) 2 : 3 Example (2) A rectangle its length 30 cm and width is 18 cm. Find the ratio between perimeter of rectangle and its length. Solution: Perimeter of rectangle = (length + width) × 2 = (30 + 18) × 2 = 48 × 2 = 96 cm Perimeter of rectangle : length 96 : 30 ……... : …….. ……... : …….. Drill: Find the ratio between two amounts: 250 P.T : 7 pounds Solution: ………….…. : …………….. ………….…. : …………….. ………….…. : …………….. ………….…. : …………….. H.W: P.B P.9 no. 1 , 2 , 3 1 2
- 9. 9 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
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- 11. 11 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on Properties of ratio 1) Circumference of the circle = 2r 2) Perimeter of equilateral triangle = side length. Complete: a) Perimeter of square = ……………… b) The diameter of circle = …………… Example 1: Find the ratio between the perimeter of square and its length. Solution: perimeter : side length side length × 4 : side length 4 : 1 Drill 1:Find the ratio between the perimeter of equilateral triangle and its side length. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Example 2: Find the ratio between the circumference of the circle and its radius. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill 2: Find the ratio between the circumference of the circle and its diameter. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Example 3: A rectangle its area is 32 cm2 and its width is 4cm find: 1) Length of rectangle. 2) The ratio between the length and width of rectangle. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill 3: Complete: 1) The ratio between side length of square and its perimeter = …….... : …....… 2) The ratio between the two side lengths of square = ………. : ………. 3) The ratio between the radius of circle and its circumference = …….. : ….... H.W: P.B P.9 no. 4 , 5 / P.10 no. 6 , 7 , 8 Remember
- 12. 12 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 13. 13 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (3) Miscellaneous exercises on ratio and its properties Example (1): Find the ratio between 1 , 3 Solution: 1 : 3 : = = × = = = 1 : 2 Example (2): If the ratio between the weight of Hani to the weight of Ahmed is 5 : 6 and the weight of Ahmed is 72 kgm. Find the weight of Hani. Solution: Hani weight : Ahmed weight 5 : 6 parts ……. : 72 real value The value of one part = 72 6 = 12 kg. The weight of Hani = 12 × 5 = 50 kg. Example (2): A primary school has 540 pupils, if the ration between the number of boys to the number of girls is 4 : 5 Calculate the number of each boys and girls. Solution: Number of boys : number of girls : sum 4 : 5 : 9 ……. : ……… : 540 The value of one part = 540 9 = 60 pupils The number of boys = 4 × 60 = 240 boys. The number of boys = 5 × 60 = 300 girls Chick the solution: Sum = 240 + 300 = 540 pupils. Drill (2): If the ratio between the weight of (Samia) to the weight of (Seham) is 7 : 5 and the difference between the weights is 9.6 kg. Find the weight of each of them. Solution: Samia weight : Seham weight : ………………. …………….. : ……………... : ……………..... …………….. : ……………... : ……………..... …………….. : ……………... : ……………..... H.W: P.B P.14 no. 1 , 2 , 5 To convert the mixed number into improper fraction 1 = (1×4)+3= 4+3= 7 7 4 3 4 3 4 1 2 3 4 1 2 7 4 7 2 7 4 7 2 7 4 7 2 14 28 1 2
- 14. 14 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 15. 15 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The ratio and its proprrties Complete: a) One hour = …………... minutes. b) One day = ……………. hours. c) Perimeter of rectangle = ………….. Drill (1): Find the ratio between: a) 8 hours , 2 days b) 18 : 6.3 Solution Solution ............................................................................................................................................................................................ ............................................... ............................................................................................................................................. ....................................................................................................................................... ..................................................... ............................................................................................................................................................................................ ............................................... ............................................................................................................................................. Drill (2): A piece of land is a shape of rectangle the ratio between its dimension 4 : 7 and its perimeter is 44 meter. Find the area of land. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill (3): The ration between the heights of two buildings in a town is 4 : 7 if the difference between their in 9 meters. Find the height of each of them. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. H.W: P.B P.14 no. 3 , 4 , 6
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- 17. 17 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (4) Ratio among three numbers Complete: 1) If A is half B then A : B = ……… : ……….. 2) If A is double B then A : B = ……… : ……….. Example (1): Three persons start commerce the first paid 400 pounds, the second paid 600 pounds and the third paid 1000 pounds. Find the ration between them. Solution 1st : 2nd : 3rd 400 : 600 : 1000 (100) 4 : 6 : 10 (100) 2 : 3 : 5 Example (2): a , b and c are three numbers such that the ration a : b = 4 : 3 and the ratio b : c = 2 : 3 Find the ratio among the three numbers a , b and c. Solution: A : B : C 4 : 3 : ….. …. : 2 : 3 …. : ….. : …… Drill (1): Find the ratio between 0.5 , , 0.125 Solution: 0.5 : : 0.125 0.5 : 0.25 : 0.125 ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… Drill (2): If A : B = 2 : 3 , B : C = 6 : 5 , Find A : B : C Solution: A : B : C ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… H.W: P.B P.18 no. 2 , 5 1 4
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- 19. 19 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The ratio among three numbers Complete: a) If A is third B then A : B = ……… : ……….. b) If A : B = 5 : 6 , B : C = 8 : 9 then A : B : C = ……….. : ……… : …….. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… Drill (1): Amount of money distributes between (Ahmed) , (Ali) and (Tarek) as the ratio 2 : 5 : 3 if the money with Ali more than the money with (Ahmed) by 45 pounds. Find the money with each of them and the total money. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….…………
- 20. 20 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Remember The sum of interior angles of triangle is 180 Drill (2): If the ratio between the measures of the angles of triangle is 5 : 6 : 7 and the measure. Find the measure of each of angle and find the type of triangle according to its angles. Solution …………………………………………………… …………….……………………………………… …………………………………….……………… …………………………………………………… ……….………………………………………….. ……….………………………………………….. Drill (3): If A, B , C are three numbers if A = B , and A = C Find the ratio between A : B : C. Solution: A : B : C ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… Drill (4): The ratio between the side lengths of triangle is 2 : 3 : 4 if the perimeter is 54 cm. Find the lengths of each of side. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… 5 3 10 7
- 21. 21 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.18 no. 1 , 3 , 4 , 6 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
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- 23. 23 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (5) Ratio Applications (Rates) The rate is: The ratio between two quantities of different kinds and the unit of rate is the unit of the first quantity per each unit of the second quantity. Example (1): A factory produces 3000 lamps in 4 hours. Find the rate of production. Solution Rate = = 750 lamp / hour (we read it 750 lamps per hour) Drill (1): A car consumes 20 liters of petrol to cover a distance 350 km. Calculate: the rate of consumption of the car to benzene. Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (2): Two machines the first produces 3000 meters of cloth in 4 hours and the second produces 2520 meter in three hours and half. What is more efficient? Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (3): A factory produces 5000 cans in 8 hours. Find the rate. Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (4): A car covers a distance 250 km in 5 hours. Find the velocity (speed) Solution ………………………………………………………………….………… ………………………………………………………………….………… 3000 lamp 4 hours 3
- 24. 24 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.20 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 25. 25 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term General Revision on Unit (1) Drill (1): Find the ration between: a) 1 : 2.2 b) 0.75 kirat , 16 sahm, ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ c) 250 p.t : 7 pounds d) 5 : 14.5 ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ Drill (2): Find the ration between: Divide 150 pounds between two persons such that the share of the first = the share of the second. Find the share of each of them. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Drill (3): Find the ration between: If the weight of (Aya) = (Mona) weight, and (Mona) weight = (Arwa) weight. Find the weight of each of them If Arwa weight more than (Aya) weight by 24.1 kgm. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. Drill (4): A piece of land in a shape of rectangle the ration between its length to width is 5 : 3, If the perimeter is 64 meter. Find the area of land. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 3 5 9 4 2 3 4 3 4 4 2 3 4
- 26. 26 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.24 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 27. 27 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit (2) Lesson (1) The meaning of proportion The proportion is: The equality of two ratios or more. Complete: 1) = = 2) = = Example (1): Complete the table: a) × = = 6 b) 8 = 8 × = = 12 From the table we deduce = = We consider the number 3 , 2 , 9 , 16 , 12 , 8 proportional numbers Drill (1): a) = = = b) = = 27 ….. 3 2 …. 6 16 ….. 4 3 …. 21 2 3 1 9 1 1 18 3 2 3 1 3 2 24 2 ….. 8 9 ….. 3 2 18 4 3 12 9 ….. 3 12 …. 4 20 39...15... 2...8...12 ÷ 2 3 × 2 3
- 28. 28 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.28 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 29. 29 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (2) The properties of proportion Properties of proportion: Property (1): If we multiply (or divide) each of the two terms of ratio by the same non-zero number, then resultant ratio is equal to the first ratio and they together form a proportion. Property (2): The product of extremes = the product of means. Example (1): Complete: 1) = 2) = Solution 1) = 2) = Example (2): Complete: = Notice that: 3 , 5 , 12 , 20 3 × 20 = 60 (the product of extremes) 5 × 12 = 60 (the product of means) Example (3): Find the value of X in the following proportion: a) = b) X , 7 , 24 , 56 = X = X = = 3 X = 120 Example (4): Find the 3rd proportion of the following 1.8 , 1.5 , 3 1.8 , 1.5 , X , 3 = X = = = 3.6 means Extremes 12 ….. 3 5 3 21 1 ….. 4× 3 5 12 20 114× 3 3 21 1 7 11 3 12 20 3 5 3 24 15 X X 7 24 56 7 × 24 56 24 × 15 3 1.8 1.5 X 3 1.8 × 3 1.5 5.4 1.5
- 30. 30 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (1): Find the fourth proportion for the following 6 , 4 , 8 , 15 Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.B P.33 no.1 , 2 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 31. 31 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Lesson (2) The properties of proportion Example (1): Find the value of X in the following proportion: 1) = 0.8 Solution = X + 3 = X + 3 = 4 X = 4 – 3 X = 1 Example (2): To make fig jam we need 4.8 kgm from sugar to 6 kgm from fig. Find: 1) How many kilograms of sugar added to 15 kgm of fig? 2) How many kilograms of fig added to 14.4 kgm of sugar? 1) Solution 2) The weight of sugar X = = 12 kgm The weight of fig = X = = 18 kgm Drill (1): A car needs 14 liter of benzene to cover a distance 175 km. How many kilometers a care covered if it uses 20 liters? Solution Drill (2): Find the value of X in the following proportion = Solution: ------------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------- Weight of fig 6 15 Weight of sugar 4.8 X Weight of fig 6 X Weight of sugar 4.8 14.4 distance 175 ……….. liters ………. ………. 8 10 X + 3 5 4.8 × 15 6 X + 3 5 5 × 8 10 14.4 × 6 4.8 2 X 12 5 2 The distance = …………………… ………………………………………
- 32. 32 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (3): A primary school, its building height is 14 meter and the shade of this building at a certain moment is 5 m length. What is the height of a tree in the same moment if its shade length is 3 meters? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.B P.33 no.3 , 4 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 33. 33 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (3) Drawing Scale Drawing Scale = Kilometer = 1000 meter Meter = 100 cm Kilometer = 100000 cm Example (1): The height of Cairo tower in image 12 cm and the real height 180 meter. Find the ratio between the height of tower in image and the real height Solution Convert = 180 × 100 = 18000 cm The height in image: The height in real 12 : 18000 ( 6) 2 : 3000 ( 2) 1 : 1500 Then = and this is drawing scale The case of drawing scale: 1) If the drawing scale > 1 this expresses enlargement – (magnification) 2) If the drawing scale < 1 this expresses (minimization) – (reduction). Example (2): If the distance between two cities is 75 km and the distance between them on a map is 15 cm. Find the drawing scale and what is mean? Solution Remember Drawing length Real length 5 The height in image The real height Real length 5 1 1500
- 34. 34 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term The real length in cm = 75 × 100 000 = 7500 000 cm Drawing scale = = = and this mean that every 1 cm in drawing represent 500 000 cm real. Note that: The important converts in drawing scale: km cm m cm m cm Drill (1): If the distance between Aswan and Comompo 40 km, and the distance between them on a map is 10 cm. Find the drawing scale to this map and what is mean? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Complete: a) 3.5 km = ………….. m b) Drawing scale = ………… Drawing length Real length 5 15 7500 000 1500 1 500 000 1500 × 100 000 × 100 10
- 35. 35 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Lesson (3) Drawing Scale Complete: 1) If drawing scale < this express ----------------------------------------------------------------- 2) If drawing scale > 1 this express ------------------------------------------------------------------ 3) 15 km = --------------------------------------------- cm Drill (1): A road its length 2.5 km, appear on a map with length 14 cm. Find the drawing scale and its mean what. Solution Real length = ------------------------------------------------------------------------ Drawing scale = ------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (1): Adel took a magnified picture with a camera if the length of an insect in the picture is 6 cm and its real length is 4 mm. Find the ratio of magnification (Drawing scale) Solution The real length in cm = 4 10 = 0.4 cm Drawing scale = = = = 15 : 1 Drill (2): If the distance between Cairo and Alex on a map is 3.5 cm. Find the drawing scale if the distance between them 210 km. Drawing length Real length 5 6 0.4 1500 60 4 15 00 15 1
- 36. 36 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: 1) A magnified of an insect its real length 5 mm and its length after enlargement 10 cm. Find the ratio of magnification. Solution --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- 2) A map drawn to Suize Qanal and its length on a map is 8.6 cm, and real length 172 km. Find the drawing scale. Solution --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------
- 37. 37 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Finding the real length Drill: If the distance between two cities 45 km and if the distance between them on a map 3 cm. Find the drawing scale. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (1): A map with drawing scale 1 : 1000 000 and the distance between two cities on this map is 35 cm. Find the real length by kilometer. Solution Drawing scale = Drawing length : Real length 1 : 1000 000 35 cm : ………… Real length = = 35000 000 cm Real length in km = 35000 000 100 000 = 350 km Drill (1): A map was drawn for Suiz Qanal in drawing scale 1 : 500 000, if the drawing length is 34.6 cm. Find the real length by kilometer. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): 35 × 1000 000 1
- 38. 38 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term A drawing scale of a building was 1 : 1000 , if the height of a building in a picture is 3 cm. Then what's the real length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: 1) Area department drawn by drawing scale 1 : 20 000 if a street appears in Minia on one of maps by 7 cm. Find the length of this street by meters. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 2) A map was drawing scale 3 : 800000 If the distance between them on a map is 12 cm. Find the real distance by kilometer between this cities. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 39. 39 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Finding the drawing length Example (1): A magnified picture of an insect was taken with enlargement ratio 50 : 1. If the length of the insect on the picture is 30 cm. What is real length of the insect? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (2): If the drawing scale on a map 1 : 5000000 and the real length between two cities 150 km. Find the length between this cities on a map. Solution The real length in cm = 150 × 100 000 = 15000 000 D.S = D.L : R.L 1 : 5000 000 ……… : 1500 000 D.L = = 3 cm Drill (1): 1 × 15000 000 5000 000
- 40. 40 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term If the distance between Cairo and Tanta is 85 Km and the drawing scale is 3 : 5000000. Find the distance between them on this map. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): Ahmed draw a picture for his brother Osama in drawing scale 1 : 40 If the real length of Osama is 150 cm. What his drawing length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: The distance between Ismailia and Eltal Elkebeer is 45 km and the drawing scale is 1 : 3000 000. Find the distance between them ob this map. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 41. 41 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term General Exercises on drawing scale From the opposite figure: 1- Drawing scale = ………………………….. 2- Drawing length = ………………………… 3- Real length = …………………………….. Drill (1): If the distance between two cities on a map is 5 cm and the drawing scale is 1 : 1000 000 Find: 1- The real length between cities in km. 2- The distance between them on another map it drawing scale 1 : 500 000 Solution 1- Drawing scale = D.L : R.L 1 : 1000 000 5 : ………… R.L = = 5000 000 cm R.L by km = 5000 000 100 000 = 50 km 2- D.S = D.L : R.L 1 : 500 000 ..………. : 5000 000 D.L = = 10 cm Drill (2): 5 × 1000 000 1 D.L R.LD.S ÷ ÷ × 5000 000 × 1 500 000
- 42. 42 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term A magnified picture of an insect was taken with enlargement ratio 100 : 1 if the length of the insect is 0.6 mm then what is the length of insect after magnification. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (3): A If the distance between two cities is 75 km and the distance between them on a map is 15 cm. Find the drawing scale and what is mean? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: Exercises on drawing scale: 1) A map was drawn for Suiz Qanal and the length of map was 8.6 cm and real length 172 km. Find the drawing scale. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 43. 43 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 2) A distance between Aswan and Comompo 40 km and the distance between them on a map 10 cm. Find the drawing scale. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 3) Ahmed is length is 1.5 m. Find his length in picture which its drawing scale is 1 : 25 Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 4) A map drawn with drawing scale 1 : 500 000 if the real length between two cities 45 km. Find the drawing length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------- 5) A map drawn with drawing scale 1 : 20000 if a street appear in this map with length 7 cm. What is the real length of the street by meters? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 44. 44 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 6) A map with drawing scale 1 : 250000 if the distance between two cities is 8.2 cm. Find the real distance between cities by km. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 7) The distance between Ismailia and Eltall Elkibeer is 45 km If the drawing length is 1.5 cm. Find the drawing scale. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 8) A map drawn with drawing scale 3 : 800 000 if the real distance between two cities is 12cm. Find the real length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------- 9) An insect with real length 0.5 cm after magnification by ratio 8 : 1. What its drawing length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 45. 45 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (4) The proportional division Proportional division: Is to divide anything (money , land , weights, ……) according to given ratio. Example (1): Distribute L.E 50 between two persons in a ratio . Find the share of each of them. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (2): Three persons start a commerce the first bayed 35000 pounds and the second bayed 25000 pounds and the third bayed 20000 pounds and the end of the year the profit was 16000 pounds. Find the Share of each of them from the profit. Solution 1st : 2nd : 3rd : Sum 35000 : 25000 : 20000 (100) 35 : 25 : 20 (5) 7 : 5 : 4 : 16 50 ……. : …..… : ……… : 16000 The share of the first = = 7000 pounds. The share of the second = = 7000 pounds. The share of the third= = 7000 pounds. Example (3): Divide 6600 pounds among Samir, Samy and Sameh, the share of Samy the share of Samir, and the share of Sameh the share of Samy. Find the share of each of them. -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 2 3 1 16000 × 7 16 16000 × 5 16 16000 × 4 16 1 2 1 2 3 1
- 46. 46 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.42 no. 4 & 5 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 47. 47 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Lesson (4) The proportional division Drill (1): If the number of pupiles in a primary school are 540 pupiles, if of the number of pupils is girls. Find the number of girls. Solution The number of girls = × 540 = 450 girl Example (1): A man distributed amount of money is 225 pounds among his three sons, if the share of the first is third money and the ration between the second to third is 2 : 3. Find the share of each of them. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (2): A man die and leave a piece of land its area 96 feddan distributed on his wife and two sons, and one daughter, if the share of wife is the capital. And the share of boy is double the share of daughter. Find the share of each of them. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill: Divide amount of money between two persons in ratio 3 : 5. If the share of the second is more than the first by 30 pounds. Find the share of each of first. -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 5 6 1 5 6 1 1 8
- 48. 48 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.42 no. 1 & 2 & 3 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 49. 49 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (5) Percentage The percentage is: A ratio its second term is 100 and it is denoted by % The whole percentage = 100 % = 1 1st : converting a percentage into common fraction or adecimal. Example (1):Put the following in form of fraction in the simplest form: 1) 75 % = = = 2) 12.5% = = = = = Drill (1): Convert to fraction: 1) 45 % = …………………… 2) 37.5 % = …………………. Example (2):Put the following percentage in a decimal form: 1) 75 % = = 0.75 2) 12.5% = = 0.125 Drill (2): Convert to fraction: 1) 35 % = …………………… 2) 62.5 % = …………………. 2nd – converting a common fraction or a decimal in to percentage Example (3):Put the following percentage in a decimal form: 1) = × 100 % = 20 % 2) 0.625 = 0.625 × 100 % = 62.5 % 75 100 15 20 3 4 5 5 5 5 12.5 100 125 1000 25 200 5 5 5 5 5 40 1 8 75 100 12.5 100 1 5 1 5
- 50. 50 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (3): Convert to fraction: 1) 0.45 = ……………………% 2) = ………………….% H.W: Convert in to percentage: 1) = ……………………% 2) = …………………. 3) = …………………… 4) 56. 42 = …………………. 5) 0.352 = …………………… 6) 0.008 = …………………. 7) 2.05 = …………………… Convert in to proper fraction: 1) 2.5 % = ……………………… 2) 90 %= ………………………. 3) 12 % = …………………… Convert in to decimal number: 1) 16 % = ……………..……… 2) 25 %= ………………..……. 3) 12.5 % = …………………… 3 4 3 4 17 50 5 8 1 2
- 51. 51 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Percentage Remember: The whole percentage = 100 % = 1 Put the following in form of fraction in the simplest form: 1) 1 – 35 % = ……………. 2) 75 % = 3) 10 10 = ………… % Example (1): If the component of cloth cotton, linen, and silk, the percentage of silk is 15 % and the percentage of cotton is 55%. Find the percentage of linen. Solution The percentage of linen = 100 % - (15% + 55%) = 100% - 70 % = 30 % Drill (1): Magid bought a T-shirt, labeled on a small card on it (made of cotton and synthetic) the percentage of the synthetic 40 % only. Calculate the percentage of cotton then find the equivalent fraction to each percentage. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (2): A school the number of pupils is 200, if the number of succeeds 175 pupils. Find the percentage of succeeds. Solution Number of succeeds = 175 pupil The percentage of succeeds = × 100% = × 100% = 87.5 % Example (3): …... ….. Famous ratios = 50 % = 12.5 % = 25 % 1 = 100 % = 75 % 1 2 1 8 1 4 3 4 Number of succeeds Number of pupils 5175 200
- 52. 52 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Samir bought a box of oranges the number of oranges is 150 orange, and he founded that 24 oranges is damaged.Find the percentage of undamaged oranges. Solution The number of undamaged oranges = ………………………………….. The percentage of undamaged oranges = ………………………………. Drill (1): A primary school has 400 pupils, and the number of girls was 150 girl. Find the percentage of number of boys. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.B P.47 no. 1 & 5 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 53. 53 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on Percentage Complete: 1) × = ……………. % 2) = …………. % Example (1): Find: 1) 40 % of 120 pounds. Solution × 120 = 48 pounds 2) If 30% of amount is 150 pound. Find the total money. Solution The amount = 150 × = 500 pound Drill (1): Find: 1) 15 % from 160 kgm = ……………………… 2) If 25 % from amount of money is 400 pounds. Find the amount of money. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): Complete: 1) 40 % + 25 % + ……………… = 1 2) 15 % from 160 = ……………. 3) 0.74 = ……………. % 4) 30 % – 0.30 = ………………………… H.W: Complete: 2 5 ….. 5 2 …..4 5 ….. 40 100 5 ….. 100 30 13 20 30
- 54. 54 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 1) = ……………% 2) If = 9 % then X = ………… 3) 1 = ………… % 4) 62.5 % = ……………… 5) = 10 % then X = …………… 6) 20% + = ……………% 7) 12 % from 2500 pounds = ………….. pounds 8) 40% + 25 % + …………… = 1 9) 15% from 160 = …………… 10) The percentage is …………….. 11) 0.74 = = ………… % 12) 1 = …………… % X 5 303 5 30 X 18 5 30 2 5 30 74 .… … … 30
- 55. 55 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (6) Applications on the percentage Complete: 1) 5 % – 0.05 = ……………. 2) If 30 % of amount of money is 150 pounds then the amount of money is = ………………….. 3) 40% + 25 % + ………… = 1 Example (1): Mona deposit L.E 3000 in a bank.The percentage of interest is 10.5% peryear What is the amount of this sum after one year. Solution Before interest : interest : After interest 100 : 10.5 : 110.5 300 : …... : X The amount after interest = = 3315 pounds Example (2): A mixture its 480 pounds the discount is 10 % find the price after discount. Solution Before interest : interest : After interest 100 : 10 : 90 480 : …... : X The price after descount = = 432 pounds Drill (1): If the price of a car 8000 pounds and the discount is 20% Find the price after discount, and the value of discount. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 3000 × 110.5 100 90 × 480 100
- 56. 56 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (2): If the number of pupils in a primary school is 300 pupils and if the percentage of successes is 97% . Find the number of failed. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.51 no. 1 & 2 & 3 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 57. 57 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on Percentage Example (1): A shopkeeper bought goods with price 1640 pounds and sold it for a profit 15% Find the selling price. Solution Cost price : Profit : Selling price 100% : 15% : 115% 1640 : …... : X Silling price = = 1886 pounds Drill (1): A man bought a refrigerator by 960 pound. And he spends 20 pounds for transporting then he sold it by a loss 25%. Find the selling price and the value of loss. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): Find the buying price of goods sold for L.E 21520 and the percentage of profit is 15% and find the profit. -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 1640 × 115 100
- 58. 58 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: 1) Nariman bought a washing machine for 2185 pound after the salesman gave her a discount 5%. Find the price before discount. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 2) If the cost price of a set of electric appliances is L.E 72000 and it is solt at 12 % profit, calculate the selling price. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 59. 59 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Finding the percentage Of the profit or loss Rules: Profit = selling price – buying price Loss = buying price and spending – selling price Example (1): A man bought goods with price 1200 pounds and sold it by 1488 pounds. Find the percentage of profit. Solution Profit = selling price – buying price = 1488 – 1200 = 288 pounds Percentage of profit = × 100% = × 100 % = 24% Drill (2): A man bought a car for 26250 pounds and he spends for repairing 3750 pounds then he sold it for 25500 pounds. Find the percentage of loss. Solution The buying price and spending = 26250 + 3750 = 30000 L.E Loss = 30000 – 25500 = 4500 pounds The percentage of loss = × 100% = 10% Drill (3): A man bought a car for 68000 pounds and spend for repairing 4000 pounds then sold it by 82800. Find the percentage of profit. -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (4): profit buying price and spending 100 profit buying price and spending 100 288 1200 4500 30000 1200
- 60. 60 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term A man bought a pace of land by 100 000 pounds and sold it after three years by 130000 pounds. Find the percentage of profit. -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.54 unit test from 1 to 75 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 61. 61 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit three Geometry and measurement Lesson (1): The relations between the geometrical shapes The relation between the geometrical shapes: 1) Two intersecting straight line its two lines form 4 angles. 2) Two perpendicular straight lines it's two lines form 4 right angles. 3) Two parallel straight lines its straight lines never intersecting. Parallelogram: 1) A quadiratelar each opposite sides are parallel and equal in length. 2) Each opposite angles is equal in measure. 3) The sum of two adjacent angles equal 180 4) The diagonals bisect each other. 5) The diagonals are not equal in length. 6) The diagonals not perpendicular. A BC D M
- 62. 62 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Rectangle Rectangle: Is a parallelogram one of its angle is right. Properties: 1) Two diagonal are equal in length. 2) The diagonals not perpendicular. Rhombus Rhombus: It is a parallelogram each two adjacent sides are equal in length. Properties: 1) The diagonals are not equal in length. 2) The diagonals are perpendicular. Square Aquare: It is a parallelogram in which one of each angle is right and two adjacent sides are equal. Properties: 1) The diagonals are equal in length. 2) The diagonals are perpendicular. A BC D M X YL Z M A BC D M
- 63. 63 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Relations between geometrical shapes Complete: 1) Four sides are equal in …………….. , …….…………. 2) Two diagonals are equal in …………….. , …….…………. 3) Two diagonals are perpendicular in …………….. , …….…………. 4) Four angles are right in …………….. , …….…………. 5) Two opposite angle are equal in measure in …………….. , …….……… , …………….. , …….…………. 6) The diagonals bisect each other in ………. , ….….. , ………... , ……….. 7) The sum of two adjacent angles equal 180 in …………….. , …….……… , …………….. , …….…………. 8) If one of angles in parallelogram is right then it's called …………. 9) If two adjacent sides are equal in parallelogram and its diagonals are perpendicular then it's called ……………. 10) The number of quadrilaterals in which its diagonals bisect each other = ………… Parallelogram Rectangle Rhombus Square two adjacent sides are equal or two diagonals are perpendicular
- 64. 64 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.59 no.1 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 65. 65 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Follow Lesson (1) The relations between the geometrical shapes 1) How many angles in the following shape the number of angles is …………. and it is ………….. , ………………………… ….…………………………………….... 2) Complete: a) The parallelogram in which its diagonals are perpendicular is …………………. b) Two diagonals are equal and perpendicular in ……………………… Example (1): ABCD is parallelogram m(<A) = 50 , AB = 4cm , AD = 6cm m(<DBC) = 30 Find: 1) m(<C) , m(<ABD) , m(<ADC), m(<ADB) 2) The perimeter of parallelogram ABCD. Solution 1) m(<C) = m (<A) = 50 (Apposite angles) m (<ABD) = 180 – (50 + 30) = 180 – 80 = 100 (Adjacent angles) m (<ADC) = 180 – 50 = 130 (Adjacent angles) m(<ADB) = 180 – (50 + 100) = 180 – 150 = 30 (The sum of two adjacent sides) × 2 2) Perimeter of parallelogram = (the sum of two adjacent sides) × 2 = (4 + 6) × 2 = 20 cm AB C D H Remember The perimeter of parallelogram = (the sum of two adjacent sides) × 2 Remember C A B 50 30 B D A
- 66. 66 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill: In the opposite figure ABCD is parallelogram Find m(<D), m(<BAC) , m(<ACD) Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.59 no 3 , P.60 no 4 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Trapezium is: Quadrilateral in which two sides only are parallel C B D C A B 100 35
- 67. 67 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on geometrical shapes Drill (1): ABCD is parallelogram MD = 4cm, AD = 7cm AB = 6 cm, m (<CAD) = 50 m (< ABC) = 65 Find: 1) M(<ADC), m(BAC) 2) Length of BD 3) Perimeter of ABD Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): In the opposite figure: Find: m(<BAC) , m(<ADC) Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- D C A B M 110 D C A B 45
- 68. 68 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.82 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 69. 69 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (2) The visual patterns The visual pattern: Is a consequence of shapes or symbols according to a certain rule Complete: 1) X X Z X X Z X X Z , ……………. , ……..…….. 2) ……………………………………………………… The description of the pattern is repetition of 3) ……………………………………………………… Drill: Discover the pattern in the following, then write its description 1) ………………………..……..…….. The description of the pattern …………….…………. 2) ..………………………..……..…….. The description of the pattern …………….………….
- 70. 70 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.63 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 71. 71 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Volumes Definition: The solid: Any object that occupies a room in the space. Notice that: The solid are two kinds Solids We will study two solids only: 1) Cuboid: His irregular solid its properties: 1- It has 6 faces, each of them is rectangle. 2- It has 12 edges, 8 vertices and 3 dimensions (length, width, and height). 3- Each two opposite faces are equal in area (congruent and they are parallel) 4- Each two adjacent faces intersect at a line segment,which is called an edge. 2) Cube: It is cuboid with equal dimensions it's properties: 1- It has 6 faces, each of them is a square. 2- All the faces are equal in area [congruent]. 3- Each two opposite faces are parallel. 4- It has 8 vertices and 12 edges. 5- All the edges are equal in length. 6- It has 3 dimensions. A geometrical shape Hasn't geometrical shape
- 72. 72 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Volumes Definition: the number of units which a solid consists of. The units of volumes: 1) The cubic decimeter [dm3 ]: It is the volume of cube of edge length 1dm 1dm = 10 cm 2) The cubic meter [m3 ]: It is the volume of cube of edge length 1m 1m = 100 cm = 10 dm 3) The cubic millimeter [mm3 ]: It is the volume of cube of edge length 1mm Converting units Complete: 1) 5 cm3 = ………….. mm3 2) 1500 mm3 = ………….. cm3 3) 0.001 cm3 = ………….. mm3 4) 300 000 cm3 = ………….. mm3 5) 7000 000 cm3 = ………….. m3 6) 85000 000 000 mm3 = ………….. cm3 7) 24000 dm3 = ………….. m3 8) 15 dm3 = ………….. mm3 Arrange discerningly: 500 000 cm3 , 50 000 dm3 , 5m3 ………………………………………………………………………. ………………………………………………………………………. cm3 1000× 1000 m3 dm3 mm3 1000× 1000× 1000 1000
- 73. 73 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term The volume of the cuboid Remember: Cuboid has 12 edges, [4 length, 4 width , 4 height] The dimensions is [length, width, height] The volume of cuboid = length × width × height The volume of cuboid = the product of its dimensions The volume of cuboid = Area of one base × height Example (1): A cuboid its length 5cm, its width = 3cm, its height = 2cm. Find the volume of cuboid. Solution: Volume of cuboid = length × width× height = 5 × 3 × 2 = 30 cm3 Example (2): A cuboid its dimensions 30cm, 2dm , 9cm. Find its volume. Solution: Convert = 2dm = 2 × 10 = 20 cm The volume of cuboid = the product of its dimensions =30×20×9= 5400cm3 Drill (1): A cuboid the area of its base 9cm2 and its length 3cm. Find the volume. Solution …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Drill (2): A cuboid its length 7dm, its width 2m and its height 3cm. Find the volume. Solution …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… V HWL V HB.A Length width height
- 74. 74 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: 1 to 4 P.B P.75 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 75. 75 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) The volume of the cuboid In the opposite figure: B.A = B.A = L × W H = V B.A L = W = Example (1): A cuboid its base in a shape of square its length 5 cm and its height 3cm. Find the volume. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Example (2): A cuboid its volume 810 cm3, and its height 15 cm, and its width 6 cm. Find: 1) Area of one base. 2) The length of a cuboid. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Example (3): A box in a shape of cuboid its dimension 60 cm, 48 cm, 24 cm, it wanted to put a pieces of soap in it in a shape of cuboid its dimensions 10 cm, 4cm, 3 cm Find the number of soap and the price of the box by pounds if the price of one soap 50 P.T Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… V H 1200 V H × W 1200V H × L 1200 V H B.A W×L
- 76. 76 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.75 no. 5 , 6 , 7 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 77. 77 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (5) The volume of the cube The cube: Is the cuboid with equal dimension? Volume of cube = the edge × it self × it self Finding the edge of cube: The edge = the sum of edges 12 The edge = perimeter of base 4 The edge = √ for check The edge = √ for check Example (1): A cube its edge 5 cm. Find the volume. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (2): A cube the sum of its edge is 108 cm. Find the volume. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (3): A cube the area of one of its face is 36 cm2 . Find the volume. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (4): A cube the base perimeter is 28 cm. Find its volume. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (5): A cube its volume 216 cm3 . Find the length of edge. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..…
- 78. 78 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.78 no. 1 , 2 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 79. 79 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) The volume of a cube Example (1): A cube the sum of 7 edges from its edges is 48 cm. Find the volume. Solution …………….……………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (2): A cube its volume 1728 cm3 . Find its volume. Solution …………….……………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… Example (2): A box in a shape of a cube the length of one edge 8 cm it fills with perfume. Find the price of 3 boxes. If the price of 1cm3 is 0.25 pounds. Solution ………………………………………………………………….. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Drill (1): 8400 cm3 of water is poured into a vessel in the shape of a cuboid with internal dimensions 20 , 35 , 45 cm. Find: 1) The height of water in the vessel. 2) The volume of water needed to be added for the vessel becomes filled with water completely. Solution …………………………………………………………………. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Drill (2): A box of cartoon in a shape of a cube its external edge length 50 cm. An antique made of glass is put inside it. And for protecting it from damage the box is put inside other box of carton in the shape of cube its internal edge length is 60 cm the empty part between the two boxes is filled with sponge form all over sides. Calculate the volume of sponge. Solution ………………………………………………………………….
- 80. 80 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… H.W: P.B P.78 no. 3 , 4 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 81. 81 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on volume The external edge = internal edge + (2 × thickness) The internal edge = external edge – (2 × thickness) Example (1): A cube the sum of it surf use area of faces 54 cm2 . Find its volume. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… Example (2): An aquarium for fish is cube shaped it has a lid. The internal edge length of the aquarium is 65 cm. The aquarium is made of glass. Find the volume of the glass given now that the thickness of the glass is 50 mm. Solution Convert = 50 100 = 0.5 cm The external edge = internal edge + (2 × thickness) = 65 + (2 × 0.5) = ……………………. The external edge = …………………………………………………. The internal edge = …………………………………………………. The volume of glass = external volume – internal volume = …………………………………………………. = ………………………………………………….
- 82. 82 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.78 no. 5 , 6 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 83. 83 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (6) The capacity The capacity:- Is the volume of the inner space for any hollow solid? The capacity of the vessel:- It is the volume of the liquid which fills the vessel completely. The unit of capacity is litre The units of capacity: Example (1): Complete: 1) 5600 cm3 = ………………. l 2) 0.23 m3 = ……..…………l 3) 9.25 dm3 = ………………. l 4) 4.63 L = ……..…………cm3 Drill (1): Complete: 1) 55 ml = …………….…….cm3 2) 0.66 m3 = ……..…………l 3) 3.25m3 = ………………. dm3 4) 5700 mm3 = ……..…….…ml Drill (2): A cube shaped vessel. Its internal edge length is 30 cm. it is filled with food oil 1) Calculate the capacity of the vessel. 2) If the price of one litres of food oil is 9.5 pounds. Calculate the price of all oil. Solution ………………………………………………………………….. …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… …………………………………………………………………………..… metre3 = m3 dm3 = litre cm3 = ml mm3
- 84. 84 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.81 no. 1 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------
- 85. 85 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) The capacity Example (1): A container has 12 litre of honey. It is wanted to put them in smaller vessels (bottles) the capacity of each of them is 400 cm3 . Calculate the number of bottles which is needed for that. Solution The capacity of container by cm3 = 12 × 1000 = 12000 cm3 The number of bottles = 12000 400 = 30 bottles. Drill (1): A swimming pool, a cuboid shape its internal dimensions are 40m, 30m, 1.8m. Find the capacity by litres. Solution ………………………………………………………………….. …………………………………………………………………………..… …………………………………………………………………………..… Drill (2): A container in the shape of a cuboid, its internal dimensions are length 25 cm, 30cm , the height = 42 cm. an amount of solar is put in it, its height = 1/3 the height of the container. Solution The height of solar = …………………………….. Volume of solar = …………………………….….. Volume of solar by litre = ……………………….. The price of solar = ……………………………… H.W: P.86 all -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 86. 86 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 87. 87 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit (4) Lesson (1) The kinds of statistics data Descriptive data: They are data written in the form of description to the case of the persons in the society as: the favourite colour, favorite food, the birth place ……. Etc Quantative data: They are data written in the form of numbers to express a certain phenomenon as: age, height, weight, the shoes size ………etc. The data requisition sheet: Is a sheet contains a set of data some of them is descriptive and the other is quantitative belong to a certain person or a thing. Data base: Is some quantitative and descriptive data of number of persons or establishments? Example (1): A class contains 36 pupils. The superior of pupils to register the hobbies which each of them prefers selecting it from five hobbies (singing, drawing, acting, reading, playing music) for making a competition concerned with these hobbies. The data were as follows: drawing – reading – playing music – singing – acting – reading – playing music – drawing – acting – reading – playing music – acting – singing – reading – drawing – acting – drawing – singing – playing music – drawing – acting – drawing – reading– reading – drawing – acting – reading – drawing – singing – drawing – reading – singing – acting – drawing – playing music. How can you deal with these data?
- 88. 88 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Solution The tally frequency data table From the previous table: 1) What is the hobby which the most pupils prefer? And what is its percentage? …………………………………………………………………………… …………………………………………………………………………… 2) What is the hoppy which is the least preferable? And what is the percentage? …………………………………………………………………………… …………………………………………………………………………… The hobby Tallies Frequency Singing …………. …………. Drawing …………. …………. Acting …………. …………. Reading …………. …………. Playing music …………. …………. Total …………. …………. The hobby Singing Drawing ………. ……….. ………. ………. Number of pupils ………. ……….. ………. ……….. ………. ……….
- 89. 89 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Math Student's Copy Book H.W: P.93 no. 1 & 2
- 90. 90 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 91. 91 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 2nd : Collecting the statistics quantative data The range = the maximum value – minimum value The number of sets = Example: The scores of the pupils of a class of sixth grade in mathematics at the end of the year had been collected for 42 pupils their marks were as follows give the fall mark is 60 36 – 32 – 42 – 38 – 45 – 28 – 42 – 57 – 20 – 41 – 59 – 49 – 48 – 46 – 40 – 48 – 51 – 53 – 54 – 55 – 36 – 33 – 44 – 57 – 54 – 46 – 52 – 26 – 37 – 30 – 34 – 47 – 35 – 44 – 29 – 49 – 49 – 50 – 23 – 43 – 39 – 43. From the frequency table then answer the following: 1) What is the number of excellent pupils? 2) What is the number of pupils of low level? Solution 1) Determine the highest and the lowest value : The maximum mark = 59 The minimum mark = 20 2) Determine the range: Range = 59 – 20 = 39 3) Determine the suitable length of set = 5 marks. The number of sets = = = 7 8 sets The range The length of set 100 range The length of set 100 39 5 4 5
- 92. 92 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Frequency data table Sets Tallies Frequency 20 – 25 – 30 – 35 – 40 – 45 – 50 – 55 – Total Sets 20 – 25 – Total Frequency
- 93. 93 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Math Student's Copy Book H.W: P.97 no. 1 & 2
- 94. 94 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 95. 95 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Representing the quantative statistics data by the frequency curve Centre of the set = Example (1): The following table represents the frequency of marks of 70 pupils: 1) Represent the data by frequency curve then answer the following: a) The number of pupils that has less than 30 marks. b) The number of pupils that has 40 marks or more. c) The percentage of the pupils that have 20 marks and less than 40 marks Solution a) Number of students = ……………. b) Number of pupils = ……………… c) Number of pupils = ……………… Frequency data table Sets 10 – 20 – 30 – 40 – 50 – 60 – Total Frequency 6 8 12 15 10 19 70 Sets Tallies Frequency Point 10 – 20 – …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. …….. Lower limit + upper limit 2
- 96. 96 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Representing data -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
- 97. 97 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Math Student's Copy Book
- 98. 98 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Math Student's Copy Book H.W: P.100 no. 1 & 2
- 99. 99 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Math Student's Copy Book
- 100. 100 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term
- 101. 101 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on representing data by the frequency curve Drill (1): 1) If the marks of pupils is between [20 , 52]. Find the range of these marks. ………………………………………………………………………….. 2) If the marks of 6 pupils in one exam is 29 , 33 , 57 , 40 , 36 , 49 . Find the range of these marks. Solution The greatest mark = ……………. The smallest mark = …………… Range = ………………………… Drill (2): The following table represents the marks of 50 pupils in one exam. 2) Represent the data by frequency curve then answer the following: d) The number of students who have less than 30 marks. e) The number of students who have 40 degree or more and what the percentage. f) The number of students that have 10 marks and less than 30 marks. Sets 0 – 10 – 20 – 30 – 40 – 50 – Total Frequency 4 7 8 14 11 6 50
- 102. 102 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Solution
- 103. 103 Math Student's CopyBook Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Math Student's Copy Book
- 104. 104 Math Student's CopyBook AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.100 no. 3