This document contains a tutorial on various topics for Grade 10 mathematics, including number patterns and sequences, functions and graphs, algebra and equations, finance, analytical geometry, transformations, trigonometry, mensuration, and data handling. It provides examples and multi-part questions to practice each topic, with explanations and step-by-step workings. The document is designed to help students review and reinforce key concepts covered in Grade 10 math.
The cubic diophantine equation with four unknowns given by 3 3 2 2 x y x y x y 16zw is
analyzed for its non-zero distinct integer points on it. Different patterns of integer points for the equation
under consideration are obtained. A few interesting relations between the solutions and special number
patterns namely Polygonal number, Gnomonic number, Star number and Pronic number are presented.
The cubic diophantine equation with four unknowns given by 3 3 2 2 x y x y x y 16zw is
analyzed for its non-zero distinct integer points on it. Different patterns of integer points for the equation
under consideration are obtained. A few interesting relations between the solutions and special number
patterns namely Polygonal number, Gnomonic number, Star number and Pronic number are presented.
Happy Math Humans (group h) of 8 - St. Basil
3 students of 8 - St. Basil representing the group Happy Math Humans, will show you how to factor different types of polynomials.
Randić Index of Some Class of Trees with an AlgorithmEditor IJCATR
The Randić index R(G) of a graph G is defined as the sum of the weights (dG(u)dG(v))-1/2 over all edges e = uv of G. In this
paper we have obtained the Randić index of some class of trees and of their complements. Also further developed an algorithmic
technique to find Randić index of a graph.
Pedagogy of Mathematics (Part II) - Set language introduction and ex.1.2, Set Language, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This quiz is open book and open notes/tutorialoutletBeardmore
FOR MORE CLASSES VISIT
tutorialoutletdotcom
Math 107 Quiz 2 Spring 2017 OL4
Professor: Dr. Katiraie Name________________________________ Instructions: The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
will be posted in your Portfolio with comments.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This learner's module discusses about the topic of Radical Expressions. It also discusses the definition of Rational Exponents. It also teaches about writing an expression in a radical or exponential form. It also teaches about how to simplify expressions involving rational exponents.
Happy Math Humans (group h) of 8 - St. Basil
3 students of 8 - St. Basil representing the group Happy Math Humans, will show you how to factor different types of polynomials.
Randić Index of Some Class of Trees with an AlgorithmEditor IJCATR
The Randić index R(G) of a graph G is defined as the sum of the weights (dG(u)dG(v))-1/2 over all edges e = uv of G. In this
paper we have obtained the Randić index of some class of trees and of their complements. Also further developed an algorithmic
technique to find Randić index of a graph.
Pedagogy of Mathematics (Part II) - Set language introduction and ex.1.2, Set Language, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This quiz is open book and open notes/tutorialoutletBeardmore
FOR MORE CLASSES VISIT
tutorialoutletdotcom
Math 107 Quiz 2 Spring 2017 OL4
Professor: Dr. Katiraie Name________________________________ Instructions: The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
will be posted in your Portfolio with comments.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
This learner's module discusses about the topic of Radical Expressions. It also discusses the definition of Rational Exponents. It also teaches about writing an expression in a radical or exponential form. It also teaches about how to simplify expressions involving rational exponents.
Directions Please show all of your work for each problem. If app.docxduketjoy27252
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. The option of hand writing your work and scanning it is acceptable.
1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 5
22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
23. Identify the property that is illustrated by the following statement.
10 (3 + 11) = 10 3 + 10 11
24. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)
25. Add. 14 + (–6)
26. Subtract. –17 – 6
27. Evaluate. 3 – (–3) – 13 – (–5)
28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
31. Evaluate. (–9)(0) + 13
32. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?
33. Write the following phrase using symbols: 2 times the sum of v and p
34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 4
35. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?
36. Write the following geometric expression using the given symbols.
times the Area of the base (A) times the height(h)
37. Evaluate if x = 12, y = , and z = .
38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
39. If the circumference of a circle whose radius is r is given by C = 2πr, in which π ≈ 3.14, find the circumference when r = 15 meters (m).
40. Combine like terms: 9v + 6w + 4v
41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.
42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.
43. Use the distributive property to remove the p.
Q1Perform the two basic operations of multiplication and divisio.docxamrit47
Q1
Perform the two basic operations of multiplication and division to a complex number in both rectangular and polar form, to demonstrate the different techniques.
· Dividing complex numbers in rectangular and polar forms.
· Converting complex numbers between polar and rectangular forms and vice versa.
Q2
Calculate the mean, standard deviation and variance for a set of ungrouped data
· Completing a tabular approach to processing ungrouped data.
Q3
Calculate the mean, standard deviation and variance for a set of grouped data
· Completing a tabular approach to processing grouped data having selected an appropriate group size.
Q4
Sketch the graph of a sinusoidal trig function and use it to explain and describe amplitude, period and frequency.
· Calculate various features and coordinates of a waveform and sketch a plot accordingly.
· Explain basic elements of a waveform.
Q5
Use two of the compound angle formulae and verify their results.
· Simplify trigonometric terms and calculate complete values using compound formulae.
Q6
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules
· Use the chain, product and quotient rule to solve given differentiation tasks.
Q7
Use integral calculus to solve two simple engineering problems involving the definite and indefinite integral.
· Complete 3 tasks; one to practise integration with no definite integrals, the second to use definite integrals, the third to plot a graph and identify the area that relates to the definite integrals with a calculated answer for the area within such.
Q8
Use the laws of logarithms to reduce an engineering law of the type y = axn to a straight line form, then using logarithmic graph paper, plot the graph and obtain the values for the constants a and n.
· See Task.
Q9
Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form
· See Task.
Q10
Use differential calculus to find the maximum/minimum for an engineering problem.
· See Task.
Q11
Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.
· See Task.
Q12
Use numerical integration and integral calculus to analyse the results of a complex engineering problem
· See Task.
Level of Detail in
Solution
s: Need to show work leading to final answer
Need
Question 1
(a) Find:
(4 + i2)
(1 + i3)
Use the rules for multiplication and division of complex numbers in rectangular form.
(b) Convert the answer in rectangular form to polar form
(c) Repeat Q1a by first converting the complex numbers to polar form and then using the rules for multiplication and division of complex numbers in polar form.
(d) Convert the answer in polar form to rectangular form.
Question 2
The following data within the working area consists of measurements of resistor values from a producti ...
EVALUATING INTEGRALS.Evaluate the integral shown below. (H.docxgitagrimston
EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative shown below.
3)
d
dx
x5
0
sin t dt
For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2
Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.
9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east
at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is discontinuous.
18)
Solve the "composite function ...
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Grade 10 - 2 - Tutorials
GRADE 10 TUTORIALS
LO Topic Page
1 Number patterns and sequences 3
2 Functions and graphs 6
2 Algebra and equations 8
1 Finance 12
3 Analytical Geometry 14
3 Transformation 16
3 Trig / Mensuration 21
4 Data handling 26
3. Grade 10 - 3 - Tutorials
Grade 10 Tutorial Number Patterns and Sequences
Question 1
Add the next three terms to each number pattern and explain how you calculated these terms:
1.1 2; 7; 12; 17; … 1.2 10; 8; 6; 4; …
1.3 ;...
2
`1
3;
4
3
2;2;
4
1
1 1.4 1; 3; 9; 27; …
1.5 1; 1; 2; 3; 5; 8; 13; …
Question 2
Write down the next three terms and the general (or nth term) of each pattern:
2.1 2; 4; 6; 8; … 2.2 1; 7; 13; 19; …
2.3 1; 4; 9; 16; … 2.4 25; 21; 17; 13; …
2.5 ;...44;33;22;1 −−−− xxxx 2.6 ;...
5
1
;
4
1
;
3
1
;
2
1
2.7 ;...2;
2
3
;1;
2
1
2.8 ;...3;
4
1
3;
2
1
3;
4
3
3
Question 3
3.1
3.1.1 How many blocks in the next T?
3.1.2 How many blocks in the nth T?
3.1.3 Which T has 69 blocks?
4. Grade 10 - 4 - Tutorials
3.2 ☺☺☺☺
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☺☺☺☺ ☺☺☺☺ ☺☺☺☺
☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺ ☺☺☺☺
☺☺☺☺ ☺☺☺☺ ☺☺☺☺
☺☺☺☺ ☺☺☺☺
☺☺☺☺
3.2.1 How many faces in the next pattern?
3.2.2 How many faces in the nth pattern?
3.2.2 In which pattern are there 84 faces?
3.3
3.3.1 How many lines in the pattern with 4 triangles?
3.3.2 How many lines are needed for n triangles?
3.3.3 How many triangles are formed with 46 lines?
Question 4
Figure 1 Figure 2 Figure 3
4.1 How many flowers would be used in the 4th figure?
4.2 How many flowers would be used in the 10th figure?
4.3 How many flowers would be used in the n-th figure?
5. Grade 10 - 5 - Tutorials
Question 5
When two people meet, they shake hands, resulting in 1 handshake. If three people met and all shook hands,
there would be three handshakes.
5.1 How many handshakes would there be if 4 people
met and shook hands?
5.2 How many handshakes would there be if 5 people
met?
5.3 Can you generalize this result?
Question 6
Your mother has chosen a base pattern for your bathroom floor. The figure below illustrates the pattern she
chose. As shown, the pattern is made up of 16 squares, 8 of which are shaded and 8 which are not.
Step 1: Base Pattern
Duplicates of the same pattern are then added to create Step 2.
6.1 How many base patterns were added to the
original in order to complete Step 2?
6.2 How many shaded unit squares would you
need for Step 2?
6.3 Each step is accomplished by surrounding the
existing figure with copies of the base
pattern. How many of the base patterns need
to be added to complete Step 3?
6.4 How many shaded unit squares would you
need for Step 3?
6.5 How many shaded unit squares would you need for Step 6?
6.6 Write a generalization or rule for determining the number of shaded unit squares that are
added in Step n.
6. Grade 10 - 6 - Tutorials
Grade 10 Tutorial Functions and Graphs
Question 1
If x
xf 2)( = and
x
xg
1
)( = and 2
)( xxh −= , answer the following questions;
1.1 Determine the values of the following;
1.1.1 )1(−f 1.1.2 )2(f
1.1.3 x if 0)( =xf 1.1.4 )1(−g
1.1.5 )2(g 1.1.6 x if 2)( =xg
1.1.7 )2(−h 1.1.8 )2(h
1.2 Describe the type of function that is defined in each case.
1.3 Draw a sketch graph of each of the functions showing all critical points,
asymptotes, axes of symmetry and intercepts with the axes. You can use the
values in question 1.1 to assist you if necessary. Each function must be
sketched on a separate set of axes.
1.4 Determine the domain and range of the functions f , g and h .
Question 2
Consider the functions 9)( 2
−= xxs and 62)( −= xxt
2.1 Sketch the graphs of s and t on the same system of axes, showing ALL
intercepts with the axes and relevant turning points
2.2 Use your sketch to find the values of x if;
2.2.1 )()( xtxs =
2.2.2 0)( >xs
2.3 Write down the equation of q if )(xq results from shifting )(xs 2 units up.
7. Grade 10 - 7 - Tutorials
2
1
-1
-2
-2 2
A ( 1 ; 1 )
h
g
x
y
-90 -60 -30 0 30 60 90 120 150 180
-2
-1
1
2 g
f
Question 3
Sketched below are the functions cbxg x
+=)( and
x
k
xh =)( and A, the point of intersection, is ( 1 ; 1 )
3.1 Find the values of k , c and b
3.2 What is the equation of the
asymptote of g
3.3 What is the range of g
3.4 What is the equation of f if )(xf
is the reflection of )(xg in the y-axis
Question 4
Below is a sketch of qxxf += cos)( and xaxg sin)( =
4.1 Write down the amplitude of f and g
4.2 What is the range of f
4.3 What is the period of f
4.4 Determine the values of a and q
4..5 What is the equation of h if )(xh is the reflection of )(xg in the x-axis?
8. Grade 10 - 8 - Tutorials
Grade 10 Tutorial Algebra and Equations
Question 1
1.1 Use the laws of exponents to simplify the following expressions:
1.1.1 226
xxx ÷× −
1.1.2 ( ) 2
33 pp
q
×
1.1.3 320
3126 ×÷ 1.1.4 13
22
)(
)(
−
−
−
−
xy
yx
1.2 When working with computers, data is measured in powers of 2 as given below:
1 Kilobyte (KB) = 210 bytes , 1 Megabyte (MB) = 210 KB , I Gigabyte (GB) = 210 MB
1.2.1 How many bytes are there in a Megabyte? Give your answer as a power of 2.
1.2.2 A memory stick holds 512MB of data. How many bytes is this? Express your
answer as a power of 2.
1.2.3 If a digital photograph contains 524 288 bytes of data, how many photographs
can be stored on a CD? Work in powers of 2 and show all your work.
Question 2
Remove brackets and simplify the following expressions:
2.1 )3(5 −aa 2.2 )13()4(2 +−+ xxx
2.3 )23)(14( +− mm 2.4 2
)42( yx +
2.5 2
)2(3 −− x 2.6 )56)(56( −+ pp
2.7 )35)(7( 2
−++ yyy
Question 3
Factorise the following expressions:
3.1 yxy 315 − 3.2 252
4
1
−m
3.3 483 2
+− xx 3.4 6112 2
−− rr
3.5 )2(2)2(6 +−+ rrs 3.6 qqxx 55 +++
3.7 yxkykx −−+
9. Grade 10 - 9 - Tutorials
Question 4
Simplify the following expressions:
4.1
ba
ba
2
23
6
24
−
4.2 2
24
2
35
2
3
6
2
4
18
x
yx
x
y
xy
x
÷× 4.3 2
5
1
10
3
mm
+
4.4
x
x
x
x
3
25
5
3 −
−
−
4.5
a
ba
a
ba
2
+
+
−
Question 5
Check, by substitution, whether or not 1−=x is a solution to each of the following equations: (Show all your
work)
5.1 xx 43)1(27 −=−+ 5.2 0)1)(1( =+− xx
5.3 0)1(3 2
=−xx 5.4 )4(
3
1
3
4
x
x
−=
−
5.5 8
1
8 =x
Question 6
Solve for x in each of the following equations:
6.1 2787 =−x 6.2 )7(3183 +−=− xx
6.3
5
4
5
2
3
=−
xx
6.4
24
5
3
1
8
12
=
−
−
+ xx
6.5 034 2
=− xx 6.6 025 2
=− x
6.7 051612 2
=+− xx 6.8 255 1
=+x
6.9 543.2 2
=−x
Question 7
Solve the following inequalities and represent the solution on a number line:
7.1 153 ≥−x 7.2 xx 53)1(2 >+−
10. Grade 10 - 10 - Tutorials
Question 8
Use your calculator and the trial and error method to find an approximate solution (correct to one decimal place)
to the following equations.
8.1 3013 2
=−− xx 8.2 444 =x
Question 9
Solve the following simultaneous equations:
9.1 5−= xy and 32 += xy 9.2
53
03
=+
=−
yx
yx
Question 10
The area of the rectangle in the diagram is
32 2
−− xx 2
cm .
10.1 Find the length and breadth of the
rectangle in terms of x.
10.2 For which value(s) of x will the rectangle be
a square?
Question 11
11.1 The cost of operating a taxi includes the wage paid to the driver as well as the cost per
kilometre to run the taxi. If a taxi owner pays his drivers R250 per day and the per km cost of
running the taxi is R3.50, write an equation for the daily cost of operating the taxi. Let C be the
daily cost and x be the km travelled in a day.
11.2 If the taxi travel 234km in one day, what is the cost of operating the taxi for that day?
11.3 If the cost of taxi operation for a day is R684, how many kilometres did the taxi cover in
the day?
32 2
−− xx
11. Grade 10 - 11 - Tutorials
Question 12
12.1 Set up two equations to represent the following statements:
12.1.1 The sum of two numbers is 12.
12.1.2 The difference of the two numbers is 7.
12.2 Draw graphs of these two equations on graph paper and on the same set of axes.
12.3 Solve the two simultaneous equations using the graphs and write down your solution.
12.4 Check your answer by substituting your solution into both equations.
Question 13
An engineer is testing the emergency stopping time of a lift that is being installed in a high-rise building. The
time that the lift takes to stop after the emergency brakes have been applied is given by the equation:
kxx =− 42
, where x is the time in seconds and k is the number of the floor where the brakes were applied.
Calculate how long it will take the lift to stop if the brakes are applied on the 12th floor.
12. Grade 10 - 12 - Tutorials
Grade 10 Tutorial Finance
1 Erin invests R5000 in a financial institution.
1.1 Calculate the amount she would receive if she invests at simple interest rate of 10% p.a. for
five years.
1.2 Calculate the amount she would receive if she invests at compound interest rate of
10% p.a. for five years.
1.3 Calculate the amount she would receive if she invests at compound interest rate of
10% p.a compounded monthly for five years.
2 Determine through calculation which of the following investments will be more profitable:
(a) R10 000 at 9 % p.a compound interest for 3 years.
(b) R10 000 at 11 % p.a simple interest for 3 years.
3. How much must you invest in order to receive R1 250 interest at a simple interest rate of 8%
over three years?
4 At what interest rate must you invest R12 500 to receive R18 000 in total after 4 years?
5 Thandi made a loan of R42 000 which she settled after 5 years at a rate of 17,5% compounded
annually. Calculate :
5.1 the total amount that she repaid
5.2 the monthly instalments over the five years.
6 The inflation rate over the past two years was 5,6% and 6,1%. What are the current prices of the
following articles if they cost the following amounts two years ago:
CD player: R 195 DVD player: R595, Music Center: R2 495
13. Grade 10 - 13 - Tutorials
7 Jane would like to buy a refrigerator. The local furniture store is advertising refrigerators as
shown below.
7.1 Decide which refrigerator Jane should buy. Show all calculations you used to make your
decision.
7.2 Jane decides that she will rather save R350 per month and buy Refrigerator A cash.
How long will it take her to save enough money? Is this a wise decision? Explain
your reasoning.
8 Peter invested R 6 500 into a savings account offering 8,5 % interest compounded annually.
After 3 years Peter deposits a further R 2 800 into the account. What is the total amount of
money in the account at the end of the fifth year, assuming Peter has made no withdrawals
from the account?
9 R5000 is deposited into a savings account. The money is doubled after a period of 8 years.
Calculate the interest rate at which this would happen if the interest is calculated as:
9.1 simple interest
9.2 compound interest
10 Use the table below to answer the questions that follows:
Country Currency Value of Unit
(in Rand)
United States of America Dollar 7,081
Switzerland Franc 5,892
United Kingdom Pound 13.982
10.1 You have R5000 to spend in Switzerland. How much Francs can you buy?
10.2 What will it cost you in Rands to purchase 4500 dollars?
10.3 If you exchange 600 pounds how much Rands will you get?
Now only R4999
Cash
OR
R500 deposit and
R425 x 18 months
Now only
R5489 or R550
deposit and R259 x 24
months
WAS
R599
A B
14. Grade 10 - 14 - Tutorials
Grade 10 Tutorial Analytical Geometry
Question 1
1. In each case below, decide whether the triangle is:
a. right-angled or not and whether it is
b. scalene, isosceles or equilateral
1.1 in which A is the point , B is the point and C is
1.2 with vertices P , and
1.3 in which X is the point , Y is the point and Z is .
1.4 with vertices and .
1.5 where O is the origin, P is and Q is .
Question 2
Sketched below is . The co-ordinates of the vertices are as indicated on the sketch.
2.1 Calculate the co-ordinates of the mid-points D and E of AB and AC respectively.
2.2 Show that
2.3 Show that
2.4 Determine the co-ordinates of F, the mid-point of CB
2.5 Is ? Explain.
15. Grade 10 - 15 - Tutorials
Question 3
Given the points and , show that:
3.1 PARM is a parallelogram by proving both pairs of opposite sides parallel.
3.2 Prove that PA = MR
Question 4
The vertices of a quadrilateral are , . Prove that:
4.1 RHOM is a rhombus;
4.2 the diagonals RO and HM bisect each other.
Question 5
Show that SQRE with vertices and , is a square.
Question 6
Quadrilateral RECT with vertices , E and is a rectangle.
6.1 Determine the value of .
6.2 Determine the co-ordinates of the mid-point of the diagonal RC and show that this point
is also the mid-point of the diagonal ET.
6.3 Show that the diagonals of the rectangle are equal in length.
Question 7
Given the co-ordinates of the four vertices, A, B, C and D, determine by calculation the type of quadrilateral and
hence fill in the table. Notice that more than one column might need to be filled
in. For example a square is also a rhombus, a rectangle and a parallelogram.
A B C D
Rectangle
Square
Rhombus
Trapezium
Parallelogram
Kite
7.1
7.2
7.3
7.4
7.5
7.6
16. Grade 10 - 16 - Tutorials
Grade 10 Tutorial Transformation Geometry
Question 1
1.1 Describe the translations in each of the following. Use and ordered pair to describe the translation.)
1.1.1 From A to B 1.1.2 From C to J 1.1.3 From F to H
1.1.4 From I to J 1.1.5 From K to L 1.1.6 From J to E
1.1.7 From G to H
1.2 A is the point (4;1). Use the grid on your answer sheet to plot each of the following points under the
given transformations. Give the co-ordinates of the points you have plotted.
1.2.1 B is the reflection of A in the x-axis.
1.2.2 C is the reflection of A in the y-axis.
1.2.3 D is the reflection of B in the line x=0.
1.2.4 E is the reflection of C is the line y=0.
1.2.5 F is the reflection of A in the line y= x
1.2.6 G is the reflection of D in the line y=x.
4
2
-2
-4
-6
-5 5
L
K
JIH
G
F
E
D
C B
A
17. Grade 10 - 17 - Tutorials
Question 2
Complete the table on the answer sheet provided.
Point Image Transformation
(-2;3)
(3;5) (5;3)
(2;-4) Reflection in the line x=0
(-1;1) Reflection in the line y=0
(-6;-4)
A translation according to the mapping )4;3();( −+→ yxyx , following
by a reflection in the x-axis.
(2;7) A reflection in the line y=x, followed by a reflection in the y-axis.
Question 3
In the diagram, B, C and D are images of polygon A. In each case, the transformation that has been applied to
obtain the image involves a reflection and a translation of A. Write down the letter of each image and describe
the transformation applied to A in order to obtain the image.
6
4
2
-2
-4
-6
-8
-10
-5 5 10
D
C
B
A
)4;3();( −+→ yxyx
18. Grade 10 - 18 - Tutorials
6
4
2
-10 -5
B
A
Question 4
The design in the diagram has been constructed using
various transformations of quadrilateral OEFG.
4.1 Describe any reflections of OEFG that you
can see in the design.
4.2 Describe any translations of OEFG that
you can see in the design.
4.3 OKLM is an image of OEFG. Describe the
transformation that has been applied to OEFG.
4.4 Give the equations of the lines of symmetry
in the design.
4.5 In each of the following describe the transformation
required to generate the second design:
4.5.1 4.5.2
Question 5
In the diagram, A is the point (-6;1) and B is the point (0;3).
5.1 Find the equation of line AB
5.2 Calculate the length of AB
5.3 A’ is the image of A and B’ is
the image of B. Both these images
are obtain by applying the following
transformation:
( ) ( )1;4; −−→ yxyx
Give the coordinates of both A’
and B’
5.4 Find the equation of A’B’
5.5 Calculate the length of A’B’
5.6 Can you state with certainty that AA'B'B is a parallelogram? Justify your answer.
4
2
-2
-4
-5 5
G
O
F
E
K
L
M
4
2
-2
-4
-5 5 10 15
G
O
F
E
4
2
-2
-4
-6
-8
-10
-12
-5 5 10
G
O
F
E
19. Grade 10 - 19 - Tutorials
Question 6
The vertices of triangle PQR have co-ordinates as shown in the diagram.
6.1 Give the co-ordinates of P', Q' and R', the
images of P, Q and R when P, Q and R are
reflected in the line y=x.
6.2 Determine the area of triangle PQR.
8
6
4
2
-2
-5 5 10
R(4;2)
P(2;-1) Q(8;-1)
20. Grade 10 - 20 - Tutorials
Diagram Sheet
Question 1.2
6
4
2
-2
-4
-6
-5 5
A ( 4 ; 1 )
Question 2
Point Image Transformation
(-2;3)
(3;5) (5;3)
(2;-4) Reflection in the line x=0
(-1;1) Reflection in the line y=0
(-6;-4)
A translation according to the mapping )4;3();( −+→ yxyx , following
by a reflection in the x-axis.
(2;7) A reflection in the line y=x, followed by a reflection in the y-axis.
)4;3();( −+→ yxyx
21. Grade 10 - 21 - Tutorials
Grade 10 Tutorial Trig / Mensuration
Section A - Trigonometry
1 Complete the following statements with reference to the diagram alongside so that they are correct:
1.1 the definition of =θsin ---------------------
1.2 the definition of =θcos ---------------------
1.3 the definition of =θtan ---------------------
2 Complete the following statements with reference to the diagram alongside so that they are correct:
2.1 the definition of =θsin ---------------------
2.2 the definition of =θcos ---------------------
2.3 the definition of =θtan ---------------------
3.1 Consider the diagram alongside and write down all possible ratios for sine, cosine and tangent
of the following angles:
3.1.1 Rˆ 3.1.2 Nˆ
3.1.3 1
ˆK 3.1.4 2
ˆK
3.1.5 1
ˆT 3.1.6 2
ˆT
3.1.7 1
ˆP 3.1.8 2
ˆP
3.2 List all pairs of complementary angles in the diagram above.
3.3 Make a conjecture about the sine and cosine trigonometric ratios for complementary angles.
P
R K M
T
N
1 2
1
1
2
2
θ
adjacent
oppositehypotenuse
P(x ; y)
x
θ
y
r
0
22. Grade 10 - 22 - Tutorials
k
24
26
k
17
8
θθθθ
θθθθ
θθθθ
k
3
4
72°°°°
d
12d
17
31°°°°
53°°°°
d
7
4.1 In each of the following first calculate k and then find the value of:
sin θ ; cos θ ; tan θ ;
θ
θ
cos
sin
; sin 2θ + cos 2θ
4.1.1 4.1.2 4.1.3
4.2 Calculate d in each of the following:
4.2.1 4.2.2 4.2.3
4.3 If sin θ =
13
5
, determine each of the following without the use of a calculator:
(Hint: Use a sketch) (θ < 90o)
4.3.1 cos θ 4.3.2 tan θ 4.3.3
θ
θ
cos
sin
4.3.4 sin 2θ 4.3.5 cos 2θ 4.3.6 sin 2θ + cos 2θ
4.4 If cosθ = t =
1
t
, express each of the following in terms of t: (Hint: Use a sketch)
4.4.1 sin θ 4.4.2
θ
θ
cos
sin
4.4.3 sin 2θ + cos 2θ
4.4.4 Make a conjecture about
a)
θ
θ
cos
sin
and b) sin 2θ + cos 2θ
23. Grade 10 - 23 - Tutorials
5 Use a calculator to determine θ (correct to ONE decimal place) in each of the following:
5.1 sin θ =
25
12
5.2 cos θ =
17
5
5.3 tan θ =
7
24
5.4 3 cos θ = 5 5.5 7 sin θ = 3 5.6 3 tan θ = 5
5.7 tan θ = 0,536 5.8 2 cos θ = 1,754 5.9 sin 3θ = 0,894
5.10 tan (θ - 50o) = 2, 182 5.11 5 sin (2θ + 10o) – 4 = 0
6 In ∆PQR, PT ⊥ QR, ∠Q = x, QT = 15 units and QP = 27 units.
6.1 Calculate the numerical value of PQ.
6.2 Calculate the numerical value of x
7 In ∆ABC, CD ⊥ AB, CD = h units, AC = b units and BC = a units.
7.1 Write down sin A in terms of h and b.
7.2 Write down sin B in terms of h and a.
7.3 Hence show that
b
B
a
A sinsin
=
7.4 Now calculate ∠B if ∠A = 63o, a = 11,4 cm and b = 9,7 cm.
8 With reference to the figure alongside:
8.1 Write down two ratios for cos 34°.
8.2 If CD = 8,3 cm, calculate the value of BD
8.3 Write down a trigonometric definition for
AB
BD
.
9 In the figure alongside MN ⊥ NR, ∠MRN = 42o, MN = 8 units, PR = 5 units and PR ⊥ NR.
9.1 Calculate NR.
9.2 Calculate MR
9.3 Calculate PN
P
Q R
T
x
A B
C
D
a
b
h
B
A
D
C
34°
42o
M
N
P
R
24. Grade 10 - 24 - Tutorials
10 From a point on the ground the angle of elevation
to the top of a building is 52°.
The distance to the base of the building is 45 m.
Calculate the height of the building.
(Correct to ONE decimal place)
11 The angles of elevation of the top of a cellular phone
pylon RS from two points P and Q, 12 m apart are
0
40 and 0
55 respectively as shown in the figure.
Determine the height of the cellular phone pylon.
Section B - Mensuration
1 Consider the figures below and in each case determine:
1.1 the surface area 1.2 the volume
(a) (b)
1.3 Determine the surface area if the edge of the base in (a) is doubled.
1.4 Determine the volume in (b) if the radius is doubled.
h
_Building
_ 45 m
52o
18 cm
18 cm
30 cm
15 cm
24 cm
P Q
R
0
40
0
55
12 m x S
25. Grade 10 - 25 - Tutorials
120cm
54cm
25cm
2 The diagram below represents three identical cylindrical logs stacked together.
The diameter of a log is 20 cm and the length of the logs are 150 cm each.
2.1 Determine the total volume of the three logs.
2.2 Determine the surface area of a single
log if the length is multiplied by a
factor of 3.
3 The municipality uses gutters as shown below to channel water away from buildings. The gutters are
solid and in the shape of semi-cylinders. The inner radius is 23 cm and 5cm less than the outer
radius. The gutter is 2 m long and is made of concrete.
3.1 Calculate the volume of the solid gutter
3.2 How much water in litre can the gutter hold.
4 The open cardboard box below have length, 120 cm, width, 54 cm and height, 25 cm. The box
contains 18 cans of jam. The height of the jam can is 25 cm.
4.1 Calculate the total surface area of the box.
4.2 What is the radius of each can? Show ALL
calculations.
4.3 What volume of the box do the cans occupy?
4.4 Hence, determine the unused volume of the
box.
26. Grade 10 - 26 - Tutorials
Grade 10 Tutorial Data Handling
In the appendix you will find two tables. Table 1 indicates the meals offered at the local fast food outlet, All Day
Burger, together with the ingredients for each menu item. Table 2 shows daily intake guidelines for Boys and
Girls between 15 and 18. Use the two tables to assist you in answering the following questions.
Question 1
1.1 Samuel orders a Burger Special with super onion rings, a packet of large chips and a large
Coke. What percentage of his daily intake of calories is he consuming in this one meal?
1.2 Taking all menu items into consideration;
1.2.1 Determine the mean, median and mode grams of protein on the menu
1.2.2 Which of the measures of central tendency calculated in 1.2.1 are most
appropriate to describe this fast food menu. Give reasons for your answer.
1.3 Consider the carbohydrate content of the menu items.
1.3.1 Determine the mean, median and mode grams of carbohydrate on
the menu
1.3.2 Discuss the relevance of these averages.
1.4 Discuss how coffee, tea and Diet Coke affect the mean calorie content of fast food.
1.5 1.5.1 Calculate the range and inter quartile range of sugar content amongst the
menu items
1.5.2 What are the items most heavily weighted with respect to sugar and how
does this affect the range?
Question 2
Most foods eaten consist of a combination of different nutrients. Some nutrients we need more than others. All
foods also have a measurement of energy (calories) which we should try to limit. In Table 2 we see what the
recommended daily allowance is for boys and girls between the ages of 15 and 18. Draw a pie chart to
represent the Guideline Daily Amount of nutrients (i.e. exclude calories) for Girls. Be sure to use a suitable
heading and a key. All calculations must be shown.
27. Grade 10 - 27 - Tutorials
Question 3
A group of 10 boys put in different orders as follows;
Boy Fast Food Order
David Chicken burger with medium chips
Ian Hamburger with super onion rings and a large Coke
Samuel Bacon double cheese burger with a Diet Coke
Adnaan Chicken and cheese burger with medium Coke
Thembi Cheese burger with medium chips
Matthew Cheese burger with super onion rings and large chips
Lyle Bacon cheese burger with coffee
Chuck Burger special with onion rings and a medium Coke
Clinton Hamburger with super onion rings and large chips
Mvuyo Large chips and large Coke
3.1 Sum up the number of calories, grams of carbohydrate and grams of
protein for each boy placing an order.
3.2 Represent the boys’ intake of these two nutrients together with their calories using a
compound (sectional) bar graph.
3.3 Referring to you bar graph, comment on their choice of meal
Question 4
All Day Burger is open 24 hours a day, 7 days a week. They work with a staff of 12 for most of the day. Between
3 pm and 9 pm, an extra 3 people are on duty. The staff feel that management should arrange their shifts better
according to the times when they are busiest. They record the number of items they sell on a Saturday and then
present the graph below to their management team. Write a motivation, to accompany this graph, explaining
how you would organize the shifts at All Day Burger, if you were the manager.
130
120
100
80
60
40
FrequencyofItemssold
20
1-2:59
3-5:59
6-8:59
9-11:59
12-2:59
3-5:59
6-8:59
9-11:59
am pm