This document contains a mid-term exam with multiple choice and short answer questions testing mathematical concepts like ratios, proportions, scales, percentages, and word problems. The exam has 5 questions covering topics such as rate calculations, sharing amounts proportionally, and solving for unknown values. The answers provided give the step-by-step work and solutions to the questions posed in the exam.

1. (1)
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Model Exam (1)
Question 1:
 Complete the following
(1) The ratio between 18 hours and one day (in the simplest form)
is …………… : ……………
(2) If the tallness of a pupil in the picture is 12 cm and its real tallness is
1.2 meter then the drawing scale is 1 : ……………
(3) A machine produces 600 meter of clothes regularly in one hour and
Half. So, the rate of production in meter per hour = ……………
(4) If a : b = 2 : 3 , b : c = 6 : 7 then a : c = ……………
(5) If X , 18 , 6 , 9 are proportional quantities then X = ……………
(6) The ratio between the side length of the square and its perimeter
= …………… : ……………
(7) 39% + + 0.1 = …………………. %
Question 2:
 Choose the correct answer:
(1) An agricultural machine ploughs 14 Fadden in 3.5 hours then the rate of performance of the machine in Fadden per hour is ……………
a- b- 4 c- 8 d- 49

2. (2)
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(2) If 100 gram from food stuff gives 300 calories. How many calories will be given from 30 gram of this food?
a- 90 b- 100 c- 900 d- 9 000
(3) : 3 = ……………
a- 1 : 2 b- 2 : 5 c- 1 : 10 d- 1 : 5
(4) = , then x = ……………
a- 3 b- 5 c- 15 d- 27
(5) The ratio between the two numbers 3 , 9.6 = ……………
a- b- c- d-
Question 3:
(a) A lens was used to enlarge an insect of real length 0.4 mm and its length after enlargement is 4.8 cm. calculate the ratio of enlargement.
(b) Three persons set up a company. At the end of the year the profit has been divided.
The share of the first = the share of the second.
The share of the second = the share of the third. If the share of the first is more than the share of the third by 8 250 pounds, what is the share of each of them?

3. (3)
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Question 4:
(a) The ratio between the length of a rectangle to its width equals
7 : 4 , its perimeter is 44 meters. Find the length and the width of the rectangle and calculate its area.
(b) A man distributed 6300 pounds between his three sons, if the share of the first was third of the money and the ratio between the share of the second and the third is equals 3 : 2. Calculate the share of each of them.
Question 5:
(a) Two machines for the manufacture of cloth, the first produce 500 meters of cloth in two hours and the second produces 600 meters of cloth in 2 hours and half. Which of the two machines is more efficient?
(b) A man owns a piece of land its area is 48 kirats. He recommended the half of the area is specialized for building a school. And the other half is divided among his two sons and his two daughters such that the share of the boy is twice the share of the girl. Calculate the share of each of them.

4. (4)
Mid-Term First
Term
Model Exam (2)
Question 1:
 Chose the correct answer:
(1) 300 gm : 1 kg = ………
a- 1 : 2 b- 1 : 5 c- 1 : 10 d- 1 : 30
(2) If the numbers 4 , X , 12 , 18 were in proportionate,
then the value of X = ……..
a- 2 b- 3 c- 6 d-54
(3) = ………%
a- 40 b- 45 c- 60 d- 90
(4) The length of a rectangle whose its area equals 24 cm2 is 6 cm then the ratio between its perimeter and its length equals ………
a- 4 : 1 b- 10 : 3 c- 12 : 5 d-3 : 2
(5) 1 = ……… %
a- 175 b- 150 c- 125 d- 225
(6) …….. + 35% = 1
a- 65% b- 34% c- 100% d-35%

5. (5)
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Question 2:
 Complete the following:
(1) If the real length of an insect is 0.3 mm and its length in a picture
is 4.5 cm then the drawing scale = ……… : 1
(2) If = 4 , X = ………
(3) 18 kirat : 2 Fadden = ……… : ………
(4) 5 kg : 3000 gm = ……… : ……… (in the simplest form)
(5) If = 9 % , then x = ………
Question 3:
(a) The ratio between the measurements of angles in a triangle is
2 : 3 : 4 Find the measure for each angle in this triangle.
(b) The height of a minaret is 85 meters and the length of its shadow in a moment equals 34 m. what is the height of a tree in front of this minaret if the length of its shadow equals 17 meters in the same moment.
Question 4:
(a) A photo was taken for one of the very delicate insects by enlargement ratio 100 : 1 If the actual length of the insect length is 0.8 mm. Find the length of the insect in the picture.

6. (6)
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(b) Three persons involved in a business. The first paid 60000 pounds, the second paid 80000 pounds and the third paid 90000 pounds, at the end of the year the net profit was 20700 pounds. Calculate the share of each of them.
Question 5:
(a) An agricultural machine ploughs 6 Fadden at 3 hours. Find the rate of performance of this machine. If another machine ploughed 6 kirat in 6 minutes which of two machines is the best in performance.
(b) Atlas of a number of cities drawn at a scale of 1 : 100000 if the real distance between the two cities is 36 km. Find the drawing distance between them in the atlas.

7. (7)
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Model Exam (3)
Question 1:
 Complete the following:
(1) If the drawing length = 2 cm and the real length = 6 meters, then the drawing scale equals …………
(2) A class contains 40 pupils. 32 pupils are present in a day, then the percentage of the absentees = …………
(3) 62.5 % =
(4) The ratio between two numbers = ………
(5) If a : b = 2 : 3 , b : c = 3 : 5 then a : c = ……………
(6) The ratio between the diameter of acircle to its circumference is ……… : ………
Question 2:
 Choose the correct answer:
(1) 30 % of a number equals ………
a- Its third b- its three tenth
c-its three fifth d- its three seventh
(2) = 10 % , then x = ………
a- b- c- d-

8. (8)
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(3) If the drawing length of an object is 2 cm and its real length equals 20 meter, then the drawing scale equal ………
a- 1 : 10 b- 1 : 100 c- 1 : 1000 d- 1 : 10000
(4) If = , then x = ………
a- 6 b- 21 c- 12 d- 7
(5) The ratio between 18 kirats , 2 feddan in its simplest form is ………
a- 9 : 1 b- 1 : 9 c- 8 : 3 d- 3 : 8
(6) 30% of 450 L.E. = ………
a- 30 L.E. b- 45 L.E. c- 13.5 L.E. d- 135 L.E.
Question 3:
(a) Three persons set up a commercial business, the first paid what the second paid, the second paid what the third paid at the end of the year the profit became L.E 6240. Calculate the share of each of them from profit.
(b) A minaret of height 22 m, the length of its shade at a moment is 6 meter. How height is a house neighbor to the minaret if the length of its shade = 3 m at the same moment.

9. (9)
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Question 4:
(a) If the ratio among the prices of three electric sets ( TV , Oven , Refrigerator ) is 4 : 5 : 8 and if the price of TV is L.E 1200. Calculate the price of each of the oven and the refrigerator.
(b) A computer color printer prints 12 papers each 4 minutes.find the rate of work of this printer
Question 5:
(a) If the distance between two cities is 180 km and the drawing scale is 1 : 9 000 000
How long is the distance between the two cities on the map?
(b) A primary school has 300 pupils in grade six. If 60 pupils of them failed. Find the percentage of success in this school.

10. (10)
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Model Exam (4)
Question 1:
 Complete the following
(1) The ratio between any two numbers = …… : ……
(2) If the tallness of Ahmed in the picture is 7 cm and its real tallness is 1.4 meter then the drawing scale is 1 : ……………
(3) A machine produces 90 meter of clothes regularly in one hour So, the rate of production in meter per minut = ……………
(4) If a: b = 1: 4, b: c =3: 2 then a: c = ……………
(5) The second proportional of the numbers 7,14,4 is …….
(6) The ratio between the side length of the rhombus and its perimeter = ……………: ……………
Question 2:
 Choose the correct answer:
(1) An agricultural machine ploughs 24 Fadden in 4 hours then the rate of performance of the machine in Fadden per hour is ……………
b- b- 6 c- 8 d- 49
(2) The length of an insect in the picture is 4 cm and its real length is 2 millimeter, then the drawing scale is ……..
b- 20:1 b- 1:20 c- 2:1 d- 1:2

11. (11)
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(3) : = ……………
b- 2:15 b- 15:2 c- 6:5 d- 5:6
(4) = , then x = ……………
b- 3 b- 5 c- 15 d- 21
(5) 1 - 0.4 = ……………%
b- b- c- d-
Question 3:
(a) A lens was used to enlarge an insect of real length 5 mm and its length after enlargement is 4.5 cm. calculate the ratio of enlargement.
(b) Three persons set up a company. At the end of the year the profit has been divided.
The share of the first = the share of the second.
The share of the second = the share of the third. If the share of the first is more than the share of the third by92000 pounds, what is the share of each of them?
Question 4:
(a) The ratio between the length of a rectangle to its width equals
3:5 , its perimeter is 80 meters. Find the length and the width of the rectangle and calculate its area.

12. (12)
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(b) A man died and left a capital of L.E 96000 to be divided among his wife , 3 boys and 2 girls the wife should take 1/8 of the capital , and each boy should take twice as much as each girl calculate the share of the wife and each boy and girl.
Question 5:
(a) A worker paints a wall of area 100 m2 at 5 hours , find the area of painting at 8 hours and How many hours does the worker need to paint 50 m2
(b) A machine produces 250 m of cloth in 2 hours , another machine produces 300 m of the same cloth in 2 and half hours. Which one is better?

13. (13)
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Answers
Model Exam (1)
Question1:
(1) One day = 24 hours
18 : 24 ÷(6)
3 : 4
(2) 1 : 10
(3) The rate of production per hour = = 400 m/h
(4) a : b : c
2 : 3 3
6 : 6 : 7
12 : 18 : 21
So, a : c = 12 : 21 = 4 : 7
(5)
X = = 12
(6) 1 : 4
(7) 39% + 50 % + 10% = 99%
Question 2:
(1) = 4
(2)
Gram
100
30
Calories
300
x
X = = 90
2
×
×
×

14. (14)
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(3) : 3 = : = 2 : 10÷ (2)
= 1 : 5
(4) X = = 27
(5) 3 : 9.6
3.2 : 9.6 10
32 : 96 ÷ (16)
2 : 6 = 1 : 3 =
Question 3:
(a) The real length = 0.4 mm
The drawing length = 4.8 cm × 10 = 48 mm
The drawing scale = drawing length :real length
48 : 0.4 × (10)
480 : 4 ÷ (4)
120 : 1
3

15. (15)
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(b) 1st : 2nd : 3rd: diffrence
5 : 3 : 3
4 : 4 : 3
20 : 12 : 9 : 11
X : Y : Z : 8250
The value of one part = 8250 ÷ 11 = 750
The share of the 1st = 750 × 20 = 15000 L.E
The share of the 2nd = 750 × 12 = 9000 L.E
The share of the 3rd = 750 × 9 = 6750 L.E
Question 4:
(a) Length : Width : Perimeter [ ( L + W )× 2 ]
7 : 4 : 22
? : ? : 44
The value of one part = 44 ÷ 22 = 2 meters
Lengh = 7 × 2 = 14 meters
Width = 4 × 2 = 8 meters
Area = L × W = 14 × 8 = 112 m2

16. (16)
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(b) The share of the 1st = × 6300 = 2100 pounds
The money left = 6300 – 2100 = 4200 pounds
2nd : 3rd : Sum
3 : 2 : 5
? : ? : 4200
The value of one part = 4200 ÷ 5 = 840 pounds
The share of the 2nd = 840 × 3 = 2520 pounds
The share of the 3rd = 840 × 2 = 1680 pounds
Question 5:
(a) The rate of the 1st machine = 500 ÷ 2 = 250 m/h
The rate of the 2nd machine = 600 ÷ 2.5 = 240 m/h
The first machine is more efficient.
(b) The area of the school = 48 ÷ 2 = 24 kirats
The remainder = 48 – 24 = 24 kirats
Son : Son : daughter : daughter : Sum
2 : 2 : 1 : 1 : 6
? : ? : ? : ? : 24
The value of one part = 24 ÷ 6 = 4 kirats
The share of the son = 2 × 4 = 8 kirats
The value of the daughter = 1 × 4 = 4 kirats

17. (17)
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Model Exam (2)
Question 1:
(1) 300 gm : 1 kg
300 gm : kg × 1000
300 gm : 1500 gm ÷ (300)
1 : 5
(2) = , then x = = 6
(3) × 100% = 45 %
(4) A = W × L
Width × 6 = 24 cm2
W = 4 cm
P = (L + W) × 2
= ( 6 + 4 ) × 2 = 20 cm
The ratio between the Perimeter and the Length = 20 : 6 = 10 : 3
(5) 1 × 100% = 175 %
(6) 1 = 100%
100 % – 35% = 65 %

18. (18)
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Question 2:
(1) Drawing scale = drawing length : real length
4.5 cm× 10 : 0.3 mm
45 mm : 0.3 mm
450 mm : 3 mm ÷ (3)
150 : 1
(2) x + 12 = 24, then x = 12
(3) 18 kirats : 2 Fadden × 24
18 kirats : 48 kirats ÷ (6)
3 : 8
(4) 5 kg : 3000 gm ÷ 1000
5 kg : 3 kg = 5 : 3
(5) =
= = 0.27
Question 3:

19. (19)
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(a) A1 : A2 : A3 : sum
2 : 3 : 4 : 9
? : ? : ? : 180º
A1 = = 40 º
A2 = = 60º
A3 = = 80º
(b)
Real length
85 m
X
Shadow
34 m
17 m
The tree length = = 42.5 m
Question 4:
(a) D.L. : R.L.
100 : 1
X : 0.8 mm
X = = 80 mm = 8 cm
(b) 1st : 2nd : 3rd
60000 : 80000 : 90000
6 : 8 : 9

20. (20)
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1st : 2nd : 3rd : sum
6 : 8 : 9 : 23
? : ? : ? : 20700 LE
Value of one part = = 900 LE
1st share = 6 900 = 5400 LE
2nd share = 8 900 = 7200 LE
3rd share = 9 900 = 8100 LE
Question 5:
(a) 6 feddan = 6 × 24 =144 kirat
3 hours = 180 min
The rate of the first machine = 144 ÷180 = 0.8 kirat min
The rate of the second machine = = 1 kirat/min
So The second machine is better
(b) D.S. =D.L. : R.L.
1 : 100000
? : 36 km
D.L. = = 0.00036 km = 36 cm

21. (21)
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Model Exam (3)
Question 1:
(1) The drawing scale = drawing length : real length
2 cm : 6 m × 100
2 cm : 600 cm ÷ (2)
1 : 300
The drawing scale = 1 : 300
(2) The percentage of present = × 100 = 80 %
Then the percentage of the absentees = 100 % – 80 % = 20 %
(3) 62.5 % = = =
(4) The first number : The second number
(5) a : b : c
2 : 3 : 3
3 : 3 : 5
6 : 9 : 15 ÷ (3)
2 : 3 : 5
Then, a : c = 2 : 5
(6) 1 :

22. (22)
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Question2:
(1) 30 % = = = three tenths
(2) = 10 % = =
=
X = = =
(3) Drawing scale = drawing length : real length
2 cm : 20 m × 100
2 cm : 2000 cm
2 : 2000 ÷ (2)
1 : 1000
(4) =
X = = 6
(5) 18 K : 48 K ÷6
3 : 8
(6) × 450 = 135 L.E.

23. (23)
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Question 3:
(a) First : second : third
3 : 4 : 4
2 : 2 : 3
6 : 8 : 12 ÷ (2)
3 : 4 : 6
First : second : third : sum
3 : 4 : 6 : 13
? : ? : ? : 6240
First = = 1440 L.E
Second = = 1920 L.E
Third = = 2880 L.E
(b)
Height
22
?
Shade
6
3
The height of the house = = 11 m

24. (24)
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Question 4:
(a) TV : Oven : Refrigerator
4 : 5 : 8
1200 : ? : ?
The price of the oven = = 1500 L.E
The price of the refrigerator = = 2400 L.E
(b) Rate = = 3 paper / minutes
Question 5:
(a) Drawing length : real length
1 : 9 000 000
? : 180 × 100 000
The distance on the map = = 2 cm
(b) The percentage of failed = × 100 = 20 %
Then, the percentage of success = 100 % – 20 % = 80 %

25. (25)
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Model Exam (4)
Question1
(1) First number :second number
(2) D.l : R.l
7 CM:1.4M
7CM:140CM (÷7)
1:20
(3) r
(4)
1 : 4 : 4
3 : 3 : 2
3 :12:8
Then, a:c=3:8
(5) then x = = 2
(6)
Question2
(1) 6
(2) 20 : 1
(3) 6:5
(4) 21
(5) 60

26. (26)
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Question3
(a) D.S. = D.L. : R.L.
4.5 cm : 5 mm ÷ 5
45 mm : 5 mm
9 : 1
(b) 1st : 2nd : 3rd : sum
2 : 5 : 5
3 : 3 : 5
6 : 15 : 25 : 46
X : Y : Z : 92 000
The value of one part = 92000 ÷ 46 = 2000 l.E
The share of the 1st = 2000×6= 12000 L.E
The share of the 2nd = 2000 × 15 = 30000 L.E
The share of the 3rd = 2000 × 25 =50000 L.E
Question4
(a) L : w : P
3 : 5 : 16
: 80
Value of 1 part= =5 cm
L =5
W= cm

27. (27)
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(b) The share of the wife = 96000=12000 LE
The rest= 96000-12000=84000LE
B : B : B : G : G: SUM
2 : 2 : 2 : 1 : 1: 8
84000
The value of 1 part =84000÷8=10500 L.E
Boy = 10500 ×2 = 21000LE
Girl= 10500 × 1 = 10500 LE
Question 5:
(a) Rate = m2 / hr
M2
100
x
Hr
5
8
Then x= 2
(b) Rate 1 = m2 hr
Rate 2 = =120 m2/hr
The first machine is better