CHAPTER 01 Operations with Integers

Calculate the followings.

(a) 3 – 7 = (b) – 4 – 5 = (c) – 8 + 3 = (d) – 2 × – 7 =

(e) 21 ÷ – 3 = (f) – 100 ÷ –25 = (g) 8 × – 4 = (h) 12 + – 3 =

(i) 7 – – 4 = (j) – 2 + – 3 = (k) – 6 – – 8 = (l) 5 – 8 + 1 =

(m) 7 – 9 – 2 = (n) – 10 + 3 + 13 = (o) –15 + 15 =

 CHAPTER 01 Rational & Irrational Numbers

Rational Numbers: Irrational Numbers:

1. Fractions 1. π

2. Terminating Decimals: 0.4, 0.73, 1.8, 2.89 2. Surds: √5 , √19 , √28 , √34 , √109
. . .. . .
3. Recurring Decimals: 0.7, 0.9, 0.23, 0.621

4. Intergers: ..….-3, -2, -1, 0, 1, 2, 3……

5. Whole Numbers: 0, 1, 2, 3, 4…..

6. Natural Numbers: 1, 2, 3, 4……

1. Sort the following numbers into the correct section of the table.

Rational Numbers:

Integers:

Whole Numbers:

Natural Numbers:

Irrational Numbers:

Not Rational or
Irrational Number:
2.
 CHAPTER 01 Estimating Square Roots & Cube Roots

1. Draw a ring around the number that is nearest in 4. (a) Write down the value of √225
value to the square root of 74.

8.1 5500 8.6 4900 9

(b) Draw a ring around the best estimate to the

cube root of 100
3.2 4.6 10 33

2. Find ∛ 32

5.

3.

6. The number 12.25 has two square roots.

Find them both.
 CHAPTER 01 Power and Indices

1. Simplify each of the followings. 3. Find the value of n.

93 × 9
(a) 74 × 7 × 73 = 9ⁿ
9⁶

(b) 4⁴ × 4³ ÷ 4¹⁰

(c) 6⁻² × 6⁻³

(d) 8⁻⁵ ÷ 8⁻² 4.

(e) 5⁻⁷ × 5⁵

(f) 4⁶ × 4⁻³

(g) 9⁴ ÷ 9⁻¹

(h) (12⁴)⁵

920
(o)
(9 × 9⁹)² 5.

2
(84 × 85 )
(p)
(8²⁰ ÷ 8²)

2. Write the followings as a fraction.

(a) 5⁻²

(b) 3⁻³

(c) 7⁻⁵

(d) 4⁻¹
 CHAPTER 02 Simplifying Expressions

1. Simplify the following expressions.

(a) 3x – 2y + 4x + 5y

(b) 6x – 3y – 5x – 5y (m) −3 × 7y

(c) 6 – 2x – 3y – 5x (n) 3a × 2a × a

(d) 3b³ − 2b + b³ − 4b (0) (−6r) × (−10w)

(e) 5x² − x² (p) (y³)⁹

(q) (2m³)⁴
(f) y⁴ × y⁶

(r) (5w y³)²

(g) a⁸ ÷ a⁴

(h) 7x⁴ × 3x⁵ 9𝑥 9

(s)
3𝑥³

(i) 5x4 × 3x5 × 2x

𝑥3𝑦5
(j) 18x⁷ ÷ 6x (t)
𝑥𝑦

8m5
(k)
2m⁷ 15𝑦 5 + 5𝑦 5
(u)
2𝑦²

3𝑟 9
(l)
6𝑟³
 CHAPTER 02 Expanding Brackets & Factorizing

2. Expand and simplify the following expressions. 3. Factorize the following expressions.

(a) 12x + 8
(a) (x − 2) (x + 8)

(b) 28xy − 7x

(b) (c) 24x² − 10x

(d) 18x²y + 24xy³

(c) (x − 8)²

(e)

(d) 4 (5d + 1) − 3 (d − 2)

(f)
 CHAPTER 02 Checkpoint Exam - Past Paper Questions

1. 4.

5.

2.

3.
6.
7. 10.

8.

11. Angelique is n years old.

Jamila says,

‘To get my age, start with Angelique’s age, add one

and then double.’

Write an expression, in terms of n, for Jamila’s age.

9.
12.

(b)

13.
14. Rajiv takes four suitcases on holiday.

Suitcase A has mass x kg.

Suitcase B has a mass that is 6 kg less than suitcase A.
Suitcase C has a mass that is twice the mass of suitcase B.
The total mass of all four suitcases is (6x – 20) kg.
Find an expression, in terms of x, for the mass of suitcase D.
Give your answer in its simplest form.
 CHAPTER 03 Constructions

1. Construct a perpendicular bisector from point C to the line AB.

. C

A B

2. Construct a perpendicular bisector on the line AB passing through point X.

A . X
B
 3. Construct a line perpendicular to the line segment AB passing through the point C.

4. (a) Construct a 60⁰ angle from point X

(b) Construct a 30⁰ angle by bisecting the 60⁰ angle

.
X

Note: the word ″Bisect″ means to divide a shape or an angle into two equal parts.
5.

6. Construct an inscribed square, with a pair of compasses and a straight edge.

7. Construct an inscribed regular hexagon with side length 4 cm.

8. Inscribe an equilateral triangle in a circle using a ruler and pair of compasses only.
 CHAPTER 03 2D and Isometric Drawings

(Plan): What you see on top.

(Front Elevation): What you see in the front view.
(Side Elevation): What you see in the side view.

1. (a) Draw the plans and elevations for the following shapes.

(b)
(c)

2. (a) The diagrams show the plan view and elevations of a 3D shape. Draw the 3D shape.
 CHAPTER 03 Symmetry

Rotational Symmetry:
(The number of times a shape can “fit into itself”
when it is rotated 360 degrees.)

Trapezium
Isosceles Trapezium

Regular Pentagon Regular Hexagon Regular Octagon

5 lines of symmetry 6 lines of symmetry 8 lines of symmetry

Notes: Notes:

 Line of symmetry is also called line of reflection symmetry.  A shape with rotational symmetry (order 1) doesn’t have
rotational symmetry.
 Number of lines of symmetry in a regular shape is the same
as its number of sides.  Order of rotational symmetry in a regular shape is the
same as its number of sides.
For example:
For example:
A square has 4 sides equal in length, therefore it has 4 lines
of symmetry. A square has 4 sides equal in length, therefore it has
rotational symmetry order 4
An equilateral triangle has 3 sides equal in length, therefore
it has 3 lines of symmetry. An equilateral triangle has 3 sides equal in length,
therefore it has rotational symmetry order 3
A regular hexagon has 6 sides equal in length, therefore it
has 6 lines of symmetry A regular hexagon has 6 sides equal in length, therefore
it has rotational symmetry order 6
 Plane of Symmetry (Plane of Reflection Symmetry): cuts a 3D shape into 2 equal halves.

Cuboid (rectangular faces only) Cube

(This cuboid has 3 planes of symmetry)

(A cube has 9 planes of symmetry)

Cuboid (rectangular and square faces)

Isosceles Triangular Prism

(This cuboid has 5 planes of symmetry) (An isosceles triangular prism has 2 planes of symmetry)

Square based pyramid Equilateral Triangular Prism

A square based pyramid has 4 planes of symmetry (An equilateral triangular prism has 4 planes of symmetry)
 Note: the number of planes of symmetry in a regular prism = number of sides of the base +1
For example:
An equilateral triangular prism: 3 + 1 = 4 planes of symmetry
A regular octagonal prism: 8 + 1 = 9 planes of symmetry

1. Write down the number of planes of (g)

symmetry for each shape below.

(a) Regular pentagonal prism (d) Trapezoidal prism

2. What is the order of the rotational

symmetry for this shape?
(b) Regular hexagonal prism

(e)

(c) Isosceles trapezoidal prism

 CHAPTER 03 Bearings & Scale Drawings

Note: Bearings are always measured clockwise from North. 2. (a) What is the bearing of B from A?

(b) What is the bearing of A from B?

1. A ship travels from A to B on a bearing of 210° for 120 km.

(a) Draw a scale drawing of the ship’s journey.
Use the scale 1 cm = 20 km.

3. (a) What is the bearing of A from B?

(b) What is the bearing of B from A?

(b) Use the scale drawing to work out how many kilometers
the ship is from lighthouse at point C.
4. The diagram shows the position of two towns, A and B. 5. Here is a map of an island

A third town, C, is one a bearing of 070⁰ from A and on a

bearing of 310⁰ from B.
Find the position of the town C on the diagram.

10 km

A helicopter flies in a straight line from

Leek to Donhampton.

(a) How far does the helicopter fly?

(b) Write down the bearing of

Donhampton from Leek.
 CHAPTER 03 Checkpoint Exam – Past Paper Questions

1.

(b)
2. The diagram shows a sketch of a kite. 3. The diagram shows the position of two mountains, A and B.

Use a ruler and compasses to construct the

kite in the shape below.
The diagonal AB has been drawn for you.
Leave in your construction lines.

A third mountain, C, is on a bearing of 145⁰ from A

and on a bearing of 270⁰ from B.
Mark the position of C on the diagram

4.
 5. Hassan makes a scale drawing of his bedroom. 7. The diagram shows an object made from 5 cubes.
He uses the scale 1:40 It has been drawn on isometric paper.
Hassan’s bed is represented by a rectangle
4.5cm long on his drawing.
Work out the actual length of Hassan’s bed.

Draw the plan and the front elevation

of the object on the grids below.

6. The diagram shows a cuboid.

The length, width and height of the cuboid are
all different.

Write down the number of planes of symmetry

of this cuboid.
8.

9.
 CHAPTER 04 Multiplying & Dividing by a Power of 10

1. Work out:

0.036 × 10⁵ =

470 × 10⁻² =

2 ÷ 10⁻⁴ =

2.

3. Draw a line to match each calculation to its correct answer.

 CHAPTER 04 Standard Form

Numbers in standard form are written in this format: a × 10ⁿ

a is: 1 ≤ a < 10
CHAPTERThe
04 value ofStandard Form

Standard
1. Write form isform:
in standard a way of writing very large or2.very small numbers
Classify by into the correct column in the table.
these numbers
using the powers of ten.
(a) 8000
Numbers in standard form are written in this format: a × 10ⁿ
10⁶ 9 × 10⁻⁰⋅⁵ 1 × 10⁻¹⁵
The value of a is: 1 ≤ a < 10

(b) 7236 2.3 × 10⁻⁶ 0.4 × 10⁸ 10 × 10⁴

26.4 × 10⁷ 4.6 ÷ 10³

(c) 0.038
In standard form Not in standard form

(d) 183 000

(e) 0.000062

(f) 0.03

(g) 0.00005
 CHAPTER 04 Rounding

2. Round each of these numbers as indicated.

(a) 135 901 (to 3 s.f)
CHAPTER 04 Standard Form

(b) 15.0343 (to 3 s.f.)

1. Round each of these numbers as indicated.

(a) 43.281 (to 1 d.p.)

(c) 0.002094 (to 1 s.f.)

(b) 0.0723 (to 2 d.p.)

(d) 3.954 (to 2 s.f.)

(c) 4.5703 (to 3 d.p.)

(e) 0.007019 (to 2 s.f.)

(d) 7.999 (to 2 d.p.)

(e) 0.9999 (to 3 d.p.)

 CHAPTER 04 Upper and Lower Bounds

1. Complete the table. 3. A number rounded correct to the nearest 10 is 240.

Number, Rounded Bounds Nova writes this inequality to show the bounds of
n CHAPTER
correct to
04 Standard Form
the original number, x:
340 Nearest 10 ≤n< 239.5 ≤ x ≤ 245

Write down 2 mistakes Nova has made.

4500 Nearest 100 ≤n<

7000 Nearest 1000 ≤n<

0.7 1 d.p. ≤n<

3.78 2 d.p. ≤n<

4000 1 s.f. ≤n<

3400 2 s.f. ≤n<

Nearest 4. A number rounded correct to the nearest 10 is 5200.

17 whole ≤n<
number Sami thinks that the number lies within the bounds
5150 ≤ n < 5250`
Is he correct? Explain your answer.
F2. Find the lower bound and upper bound for the followings:
(a) A car has a mass of m kg. The mass of the car correct to
the nearest 100 kg is 1200 kg.

(b) A pencil has length p cm. The length of the pencil correct
to the nearest cm is 14 cm.
 CHAPTER 04 Checkpoint Exam – Past Paper Questions

1. Complete the table to show equivalent numbers. 4.

The first row is done for you.

CHAPTER 04 Standard Form

Power of 10 Ordinary number

10² 100
10 000
10⁵

2.

5.

3.

6.
 CHAPTER 05 Collecting Data & Frequency Tables

 Primary data: the data you have collected yourself.

Advantage: you know how reliable the data is.
Disadvantage: It is time consuming.

 Secondary data: is the data collected by someone else or from the internet.
Advantage: It is quicker to collect as someone else has done all the work.
Disadvantage: it may not be reliable.

 Numerical data (Quantitative data): data that is related to numbers and has 2 types.

a. Discrete data: the numbers are integers only, because you count it.
For example: number of children in a family: 1, 2, 3…etc. You cannot have 3.4 children.

b. Continuous data: can be any value or decimal number.

For example: height, weight, length, width…etc.

 Categorical data (Qualitative data): is about the characteristics of the data and is not related to numbers.
For example hair color, favourite fruit, gender…etc.

1.

2. State whether each data is discrete, continuous, or categorical.

(a) Speed of a train (g) Volume of water in a bath

(b) Number of pets (h) Favourite singer

(c) Mass of a baby (i) Length of a football field

(d) Time to run 100 m (j) Eye color

(e) Distance between two towns (k) Marks out of 10 on a test

(f) Gender (l) Height of a tree

 5. Chen rolls a dice and records the score each
3. Lily wants to count the number of cars of
time. The results are shown in the table.
different colours that drive past her school.
Calculate his mean score.
Design a data collection sheet that Lily could use.

6. The table shows the heights of some plants

4. Here are the heights, h metres, of 15 students in
Mia’s class. Height (cm) Frequency
0≤h<5 4
1.56 1.49 1.05 1.75 1.63 1.47 5 ≤ h < 10 7
10 ≤ h < 15 12
1.25 1.93 1.16 1.45 1.29 1.40 15 ≤ h < 20 16
20 ≤ h < 25 8
1.02 1.67 1.72 25 ≤ h < 30 3

Use the data to complete the group, tally and

frequency columns in the table.

(a) Work out the mean plant height.

(b) What is the modal class?

(c) Find an estimate of the range.

(d) Find the class interval where the median lies.

 CHAPTER 05 Checkpoint Exam – Past Paper Questions

1. 3. The table shows the ages of a group of boys

and girls

Tick (✓) to show if these statements are

true or false.

There are more girls aged 12 years than boys

aged 12 years.

2. Anastasia collects information to investigate this statement.

Older teachers pay more for their cars than younger teachers.
The range of ages for the boys is higher than the
range of ages for the girls.
Tick (✓) the two items that are most relevant to her investigation.

if the teacher is male or female

the age of the teacher

the subject the teacher teaches

the price the teacher paid for their car

 Note: More RANGE means More Variable
Greater Spread
Less Consistent

4. The table shows the mean and range of the 6. A set of data has fewer than 6 values.
number of customers at a restaurant on The median of the set of data is 5 but none of the
Mondays and Thursdays. values is 5.
Write down a set of possible values for this data.

The restaurant manager says,

‘The number of customers on Mondays is less
variable than on Thursdays.’
Explain why the manager is correct. 7. Mia wants to investigate if older students have
more money than younger students. She
surveys students at her school.

Identify two pieces of data that Mia must

collect from each of the students.

5. Draw a ring around all the statements that are

examples of discrete data.
…………………… and …………………..

 mark out of 10 on a test

8. Carlos carries out a survey on clubs at school.

 time taken to run a marathon This is one of the questions in his survey.

 mass of a bag of oranges

 average speed of a journey

Write down one reason why this is not a good question

 number of books sold

9. The table shows data about the life of two types of battery. 11. The table shows some statistics for the number
of words per page in two different books.

Use the median and the range to compare Book …………… has a more consistent
the two types of battery. number of words per page.

Median: We know this by comparing the ……………

12. Hassan plays cricket. The table shows the

Range:
number of catches he makes in 50 games.

(a) Write down the modal number of catches

10. Angelique wants to find out how students in her class
travel to school.
Design a question for her to find this data. Include
response boxes.
(b) Find the median number of catches.
 13. Here are the spelling test results for the 25 (c) Tick (✓) the class that has the better results
students in Class A. overall.

Explain your answer.

(a) Complete the table for Class A.

14. Safia wants to find out whether people like a new airport.

She surveys 20 people who work at the airport one

morning in March to find their opinion of the airport.

Write down two ways Safia could improve her data

collection method.

(b) Here is some information about Class B for the 1.

same test.

2.

Draw a ring around the two best measures for

comparing which class did better.

M Mean Mode Median Range

15. Youssef says,

Youssef does an experiment to see if this is true.

He shows 80 people six numbers and asks them to remember them.
He records if they can or cannot.
Here are the results.

Tick (✓) to show whether this evidence supports what Youssef says.

Give a reason for your answer.

 CHAPTER 06 Pythagoras’s Theorem

Note: Hypotenuse is the longest side of a triangle and it is always opposite to the 90⁰.

1. Find the value of x

2. Find the value of y

 CHAPTER 06 Area, Perimeter, Volume

(Triangle) (Trapezium) (Parallelogram)

1 1
A= ×b×h A= × (a + b) × h A= b×h
2 2

(Circle) (Semi - Circle) (A Quarter - Circle)

1 1
A = π × r² A= × π × r² A= × π × r²
2 4

1 1
C= π×d C= ×π×d C = ×π×d
2 4

Note:
 To find the perimeter of any shape, add up all the sides outside.
h

w
l

Volume of cuboid = l × w × h Volume of cylinder = π × r² × h

Notes:
 Volume of any prism = base area × height

 Base area is the part that is repeated on both ends of a 3D shape.

 To find the surface area of any 3D shape, find the area of each face and then add them up.
1. Calculate the area of this compound shape. 3. Find the volume of this shape.

11 cm
3 cm

4. Find the volume of this shape.

2. Find the volume of this cylinder.

3
5. Find the volume of this shape. 7. The diagram shows a cuboid with a volume of 240 cm³.

(a) Find the height of the cuboid.

(b) Find the surface area of the cuboid.

6. The diagram shows a prism.

The area of the cross-section of this prism is 20 cm².

Work out the volume of the prism.
 8. Find the surface area of this prism 10. Find the surface area of this cylinder.

11. Find the total surface area of this triangular prism.

9. Find the total surface area of this square based pyramid.

 CHAPTER 06 Checkpoint Exam – Past Paper Questions

1. Here is a drawing of the net of a cube. 3. The diagram shows a prism.

The cross-section can be divided into three identical
rectangles.
Each rectangle measures 7cm by 4 cm.
The prism is 10 cm long.

Work out the surface area of the cube.

2. Here is the net of a cuboid.

Work out the volume of the prism.

Work out the surface area of the cuboid

4. The diagram shows a trapezium. 6. Cubes with side length 3 cm are packed into a
larger cuboid box.

Work out how many of the cubes fit inside this box.

The area of the trapezium is 30 cm².

a and b are both whole numbers with a < b.
Work out one possible pair of values for a and b.

7. The diagram shows a semicircle.

5. A circle has diameter 8 cm.

The diameter of the semicircle is 12cm.

Calculate the perimeter of the semicircle.

Calculate the circumference of the circle.

8. Here are two rectangles. 9.

The second rectangle is cut in half and joined to the

first rectangle to make a new shape.

Write down the length of the hypotenuse of triangle BCE.

Calculate the perimeter of the new shape.

10. A fish tank in the shape of a cuboid has

length 60cm, depth 30 cm and height 30 cm.

Find the capacity of the fish tank in liters.

11. Carlos builds a wooden frame. 12. The diagram shows two cuboids.

He needs two 45 cm lengths of wood and

two 60 cm lengths of wood.
Carlos has a 2 meter length of wood.
The cuboids have equal volume.
Find the height, h, of cuboid B.
Tick (✓) to show if Carlos has enough
wood to build the frame.

Show your working.

13. The diagram shows a shape made from two 14. Here is a cylinder.
identical parallelograms and a triangle.

(a) The diameter of the top of the cylinder is 12cm.

Calculate the area of the top of the cylinder.

Calculate the total area of the shape.

(b) The volume of the cylinder is 1700 cm³.

Calculate the height of the cylinder.
 CHAPTER 7 Fractions

1. Work out the followings. 4 3 1

(e) 1 +2 ×1
Give your answer in the simplest form. 5 4 3

3 1
(a) 2 + 1
5 3

3 5
(b) 3 –2
4 6
1 5
(f) (1 − ) × (1 + )
4 6

3 2
(c) 1 ×3
5 11

3
3 5
(g) (1 + 0.25) +
4 8

2 24
(d) 2 ÷
5 25

2
1 1
(h) ( + 5.5) − 2
2 2
2. Here is a multiplication with a mixed number missing. 4.

Work out the missing mixed number.

3.
5. Write these as a single fraction. 7.

2𝑑 3𝑑
(a) +
3 4

3 1 8.
(b) –
𝑚 2𝑚

3
(c) 2 +
ℎ

9.

6. Simplify these fractions.

27𝑥+3
(a)
9
10.

25𝑥+15𝑦−5𝑧
(b)
10
 CHAPTER 7 Checkpoint Exam Questions

1. Here are some number cards. 4. In a traffic survey of 495 vehicles, 390 are cars.
Work out the fraction of the vehicles that are not cars.
Give your answer as a fraction in its simplest form.

Use two of the cards to make a fraction which is

1
less than
2

5. Work out the fraction that is halfway between

1 1
and 1
3 2
2. There are 30 days in November.
3
It rains on of them.
5
Work out the number of days when it does not rain.

Write your answer in its simplest form.

43
3. Write as a mixed number.
7
 2
2 8. A hamster eats of a bag of carrots each day.
6. Convert 4 to a decimal. 7
7
Work out how many days it takes the hamster
Give your answer correct to 2 decimal places.
to eat 8 whole bags of carrots.

9. Simplify.

7. (a) Here is a calculation.

87 ÷ 14 = 6 remainder 3

Draw a ring around the correct fraction for the

answer to this calculation.

(b) Use two whole numbers to complete this

calculation.

10. Draw a ring around the fraction that is the largest.

11. 13. Complete these fraction calculations.
(a)

(b)

12. Write each of these as a single fraction.

Give each answer in its simplest form.
(c)
 CHAPTER 8 Equations, Inequalities, Formulas

8 2
6. Solve =
1. Solve 5x – 2 = 3 (x + 4) 𝑥+6 5

7. Solve –3x ≤ 9
2. Solve 8x – 5 > 6x − 13

Note: Flip the inequality sign when dividing or

multiplying by a negative number.

8. (a) Solve the inequality.

3. Solve 5 ≤ 2x – 3 < 17

19 ≤ 7 − 3x

24
4. Solve =6
𝑥

(b) Represent the range of values for x on the number line.

50
5. Solve = 25
𝑥−5
 11. Solve these simultaneous equations.
9. (a) Solve 4x + 10 ≥ x + 25
3x + y = 19
2x – y = 6

(b) Show your answer to part (a) on the number line.

(c) Using your answer to part (a), write down the

smallest number that x can be.
12. Solve these simultaneous equations.
6x + 2y = 10
2x + 3y = 1
10. (a) Solve –2 < x + 2 ≤ 3

(b) Represent the solution to the inequality on the

number line

(c) Using your answer to part (a), write down all the 13. Jane is 3 years older than her sister sue.
integers that x can be from smallest to largest.
Their combined age is 19.
Write an equation to show this information.
 𝑦−ℎ
14. Students must get at least 50 out of 100 in order 18. Make h the subject of the formula p=
8
to pass the math exam. Using m to represent the
students’ marks, write an inequality to show this.

15. I am thinking of a number.

I subtract 13 from my number.
I divide 350 by this result.
19. Make m the subject of the formula v = m² + s
The answer is 14.
Write an equation to show this.

16. Make r the subject of the formula h = 2 (r − 4) 20. Make x the subject of the formula y = √ x + c

21. Write an inequality represented by each of these

number lines.

5
17. Make T the subject of the formula v= +y
𝑇
 CHAPTER 8 Checkpoint Exam – Past Paper Questions

1. Some trees are planted in rows of 10 4. These two lines are the same length.

Complete the formula to find the total number All measurements are in centimeters.
of trees, t, in r rows.

t = ……………...

(a) Write down an equation to show that the two

lines are the same length.
2. Blessy thinks of a number and multiplies it by 3
She then subtracts 6
Her final answer is 15
Work out the number Blessy started with.
(b) Work out the length of one line.

3. Anastasia is a years old, Blessy is b years old 5. The cost to hire a hall is $20 plus $15 per hour.
and Manjit is m years old.
(a) Write down a formula for the cost $C to hire the hall
(a) Blessy is older than Manjit. for h hours.
Draw a ring around the correct inequality.
C = …………………………..

(b) Anastasia is less than half the age of Blessy. (b) Use the formula to work out the cost to hire the hall
Write this statement as an inequality. for 6 hours.

$ ………………….
6. Ahmed has a rod 2 meters long. 7. Solve these simultaneous equations.
5x + 2y = 26
10x – y = 37
Use an algebraic method to work out your answer.

He cuts the rod into four pieces and uses them to make a
rectangle.

The length of the rectangle is 3 times the width.

Calculate the area of the rectangle in square centimeters.
 CHAPTER 09 Interior & Exterior Angles

 The sum of interior angles of a polygon = (n – 2) × 180⁰

 The sum of exterior angles of a polygon = 360⁰
360⁰
 The measure of one exterior angle of a regular polygon = 𝑛
 One exterior angle + one interior angle = 180⁰

1. The diagram shows a hexagon. Find the value of x. 3. The diagram shows a pentagon with the
exterior angles marked.
Find the value of y.

2. What is the measure of each interior angle of a 4. What is the exterior angle of a regular octagon?
regular pentagon?
5. The diagram shows a pentagon with three of 7. Can a regular polygon have an interior angle of 110°?
its sides extended. Work out the value of x and y. Show your work.

6. Find the number of sides of a regular polygon 8.

with an exterior angle of 40°.
 CHAPTER 09 Types of Angles

Corresponding Angles

(Angles that add up to 90°)

(Angles that add up to 180°)

Alternate Angles

Vertically opposite Angles

1. Find the missing angles 2. Sandy says she has drawn a kite with angles
70°, 90°, 120°, 80°.
a.
Is she correct? Explain your answer.

3. Work out the size of the missing angles (a,b,c)

4. Find the values of a and b

b.
5. Find the lettered angles.

(a) (d)

(b)

(e)

(c)
 CHAPTER 09 Tessellations

A pattern made by fitting shapes together, with no gaps and overlapping, is called a tessellation.

1. Tick (✓) the regular polygons that will tessellate.

- Hexagon

- Quadrilateral

- Heptagon

- Triangle

- Octagon

2. Will a regular pentagon tessellate?

Explain how you know.
 Chapter 09 Finding a point between two other points

1. A is the point (4, 2)

B is the point (22, - 13)

2
Find the coordinates of the point that is
3
of the way along AB from A.
 CHAPTER 09 Checkpoint Exam – Past Paper Questions

1. Triangle A is shown in the diagram. 2. The diagram shows a triangle on a grid.

On the grid, draw 6 more of the same triangle to
show how it tessellates.

Draw a ring around the triangles below

that are congruent to Triangle A.

3. Calculate the size of each exterior angle of a

regular 10-sided polygon.
4. The coordinates of point A are (3, 8) and the 6. The diagram shows an isosceles triangle ABE and a
coordinates of point B are (9, 15). quadrilateral BCDE. AD is a straight line.

Find the coordinates of the midpoint of AB.

(a) Calculate the value of p and the value of q.

5. AB is a line segment.
M is the midpoint of AB.

A is the point (7, 2). (b) Hassan says that the quadrilateral BCDE is a kite.
M is the point (5, 6). Tick (✓) to show if Hassan is correct or not
correct.

Work out the coordinates of point B.

Give a reason for your answer.

7. The grid shows the positions of three points, 9. The diagram shows triangle XYZ.
A, B and C.
XY is parallel to ZV.
XZW is a straight line.

Jamila proves that the angles of triangle XYZ

add up to 180°. Complete her proof.

ABCD is a square. Angles a and e are equal because they are

Write down the coordinates of D. ……………………… angles.

Angles b and ………… are equal because they

are alternate angles.

8. Naomi draws a tessellation using only one Angles c, d and e add up to 180° because
type of regular polygon.
Three of these polygons meet at one point
in her tessellation. ……………………………………………

Name the regular polygon Naomi uses.

……………………………………………

So the angles in triangle XYZ add up to 180.

 10. A square and a regular hexagon are joined 12. The diagram shows a pair of parallel lines,
together along one edge. GH and JK.

Find angle BAC

EF is a straight line that crosses GH at X and

crosses JK at Y.
On the diagram,

• label with the letter A the angle that is

alternate to angle GXY,

11. A quadrilateral is drawn on the grid below.

• label with the letter C the angle that is
corresponding to angle GXY.

Show how the quadrilateral tessellates.

Draw 5 more of these quadrilaterals.
13. 15. The diagram shows a regular pentagon and a
regular hexagon.

Choose one of these words to complete each sentence

about the angles in the diagram.

reflex corresponding alternate

opposite right A, B and E are vertices of the pentagon.
C, D and E are vertices of the hexagon.
ABCD is a straight line.
Calculate the size of angle BEC.

14. The diagram shows a straight line crossing two

parallel lines. There are no right angles in the diagram.
16. Here is a grid. 18. Line AB is shown on the grid.

(a) A = (1,–1), B = (–5,–2) and C = (–3,2) (a) Plot the point (0, –3) on the grid. Label it C.
Plot points A, B and C on the grid.

(b) ABCD is a rectangle.

(b) ABCD is a parallelogram.
Find the coordinates of point D. Write down the coordinates of D.

17. Draw a ring around all the shapes that are congruent
to triangle A.

A
 19. Write the letter of each shape in the 21.
correct position in the table.

One has been done for you.

ABC is a straight line.

Triangle ABD is isosceles.
Find angle x.

20. A pattern is made by tessellating shape A on the grid.

Draw shape A three more times to continue the tessellation.

22. Two points A and B have coordinates

(–1, 4) and (3, 6).
Find the coordinates of the midpoint of AB.
 CHAPTER 10 Graphs, Charts and Diagrams

1. 2. Write the type of correlation shown in each

scatter diagram below.

(a) (b)

(a) What is the largest screw made by Machine A?

(c) (d)

(b) What is the modal screw length for Machine B?

(c) What is the range of screw lengths for Machine A?

(e)
(d) Find the median screw length for Machine B.
3.
4. Find the average speed of an object that 7. Here is a distance - time graph for an aeroplane journey.
travels 180 km in 2 hours and 15 min.

5. A car travels for five hours at a constant speed a. How long was the flight?
of 80 km / h. How far did the car travel?

b. What was the speed of the aeroplane between the

first and third hour of the flight?

6. A car travels 210 km at a speed of 70 km / h.

Work out how long this takes. c. What was the average speed for the entire flight
time? (Do not include the time when the
aeroplane had stopped.)
8.

9.
10. Write a reason why each of the following graphs could be misleading.

(a) (b)

(c)
 CHAPTER 10 Checkpoint Exam – Past Paper Questions

1. The scatter graph shows the value (thousands of dollars) 2. Angelique leaves home at 8.30am.
and the age (years) of eight cars.
She walks at a constant speed to a shop which is 3
kilometers from her home.
She arrives at the shop at 9.10 am and stays there
for 15 minutes.
She then walks at a constant speed back home,
arriving there at 10.10 am.

Draw a travel graph to show Angelique’s journey.

A ninth car has a value of 11 thousand dollars and is 5

years old.

(a) Plot the information for the ninth car on the grid.

(b) Find the median age of the nine cars.

3. A car travels at 72 km/h.

Work out the number of meters the car
travels in one second.

(c) Describe the relationship between the value of a car

and its age.
4. The cost of a visit by a plumber is in two parts. 5. Fifty children take a mathematics test.
Three weeks later they take a second
mathematics test.
The graph shows their scores, out of 10,
in both tests.
(a) Complete this formula for the cost, y dollars, of a
visit that lasts x hours.

(b) Draw a graph to show the costs of visits lasting up

to 5 hours.

Write a statement to compare the scores of

the children in the two tests.

(c) A visit costs 115 dollars.

Use your graph to estimate the length of the visit,
in hours.
6. Rajiv measures the lengths of 40 birds. 7. Write down the temperature shown on this scale.

(a) Draw a frequency diagram to show these lengths.

8. Write down the speed shown on the diagram.

(b) Rajiv says that the median length is in the interval

18 ≤ L < 19

Tick (✓) to show if Rajiv is correct or not.

9. Write down the mass shown by the arrow
on the diagram.

Give a reason for your answer.

 11. Some cars are surveyed to compare engine size, in
10. Two coffee shops record the different types
liters, with the time taken to reach a speed of 100 km/h.
of coffee they sell in a day.
The results are shown on the scatter graph.

The pie charts show their results.

The coffee shop at the train station sells more

cups of Americano than the coffee shop at the
park.

(a) Another car has an engine size of 1.8 litres and takes
Work out how many more cups of Americano 9.5 seconds to reach 100 km/h.
are sold.
Add this data to the scatter graph.

(b) Use the graph to estimate the time taken by a car with
engine size 1.7 litres.

………………. seconds
12. Oliver draws two pie charts that show the favourite 13. Angelique leaves home at 09:30 to go for a walk.
subjects of students from two different schools. The graph shows information about her walk.

School A has 200 students.

School B has 120 students.

She walks 8km, stops for a rest and then returns

home the same way.
(a) Work out her speed on the return part of her
journey.

Oliver says that the same number of students in School

A and in School B said maths is their favourite subject.

Tick (✓) to show if Oliver is correct or not correct.

(b) Carlos is Angelique’s brother.

He leaves home at 10:00
You must show your working.
He walks at 6 km/h in the same direction as
Angelique.
He walks for 90 minutes.
Draw a line on the graph to show his walk.

(c) Estimate the time when Angelique and

Carlos meet.
14. This graph shows the number of drinks that are 15. The bar chart shows how students in
sold in one week. Class 7 travel to school.

Tick (✓) to show if these statements are

true or false.
(a) Work out how many more drinks of lemonade
than water are sold. One has been done for you.

There are 40 students in Class 7

(b) Write down the modal drink.

50% of the students travel by car or bus.

A quarter of the students walk to school.

16. Students can choose to take part in a club after school. 17. This frequency diagram shows the number of
visits to the gym by 155 people in September.
Lily draws a pie chart to show the clubs chosen by girls.
Yuri draws a pictogram to show the clubs chosen by boys.

Work out how many people went to the gym

more than 20 times.

Tick (✓) to show if each of these statements is true or false

or you cannot tell.

Ten more boys choose football than choose music.

Work out the class interval that contains the

median number of visits.

The modal club is the same for both girls and boys.

A larger proportion of girls than boys choose art.

A larger number of boys than girls choose football.

18. Mike conducts an experiment to find 19. Trains travel between two stations.
out if cars drive at different speeds on
The distance between the two stations is 200 km
different days.
The average speed of two trains is shown in the table.
He collects data about the speed of cars
on the road between 12pm and 1pm on
two different days.
His data is shown in the back to back
stem-and-leaf diagram.

Calculate the difference between the journey times

of the two trains.
Give your answer in minutes.

(a) Work out the difference in speed

between the fastest car on Monday
and the fastest car on Thursday.

………………. km/h
(b) Mike concludes that the speed of
cars is lower when there are more cars
on the road. Explain how the data
supports Mike’s conclusion.
20. The graph shows that the cost of electrical wire 21. Samira owns a bookshop.
is proportional to the length of the wire. She makes money from the café in the shop as well as
from selling books.
The bar chart shows Samira’s profits between 2019
and 2021

(a) Use the graph to find a formula for the cost, c

dollars, of a length of wire, x meters.
Samira says,
‘My total profits have increased between 2019 and 2021’

Write down one other comment to describe how her

profits have changed between 2019 and 2021
c = ………………….........

(b) Calculate the cost of 23.4m of wire.

22. The table shows the resting pulse rate of eight people and 23. The chart shows information about the
how many kilometres they run per week. number of minutes 85 runners take to run
ten kilometers.

Frequency
(a) Draw a scatter graph to show this information.

Time (minutes)

Find the percentage of the runners that take

less than one hour.

(b) Write down the type of correlation between

kilometres run per week and resting pulse rate.

(c) Mike runs 14 kilometres per week. Draw a ring

around the most likely resting pulse rate for
Mike.

46 57 68 75
24. Yuri and Chen live in the same house. 25. A group of people each complete two
puzzles, A and B.
They both go for a walk along the same path and return
back home again. The time taken for each person to complete
the puzzles is recorded.
The travel graph shows some information about Yuri’s
and Chen’s walks. The results are shown on the graphs. The
scales on each graph are the same.

(a) Write down the time when Chen passes Yuri.

(b) Chen does not walk as far as Yuri.

He stops for 30 minutes when he is 10 km from home.
He then walks back home at a constant speed, arriving
home 45 minutes before Yuri.
Complete the travel graph for Chen. Complete the sentence.

The graphs show that puzzle ……… is more

difficult because ……………………………...

…………………………………………………

…………………………………………………
 CHAPTER 11 Ratio & Proportion

4. x and y are directly proportional

1. Work out the largest share when $350
is divided in the ratio 3 : 2 : 5 x 3 10

y 51 68

Find the missing numbers in the table.

2. Divide 6.3 km in the ratio 1: 5: 3 5. x and y are directly proportional

x 4 8 16

y 10 20 40

Write an equation connecting x and y.

3. Simplify:

6. m is inversely proportional to b.
a. 48 : 72 Use the table to find the value of x.

m 20 15
b 36 x
b. 28 : 35

c. 60 : 15 : 45
7. A box contains pink, red, and green sweets. 9. Write each of these as a ratio in its simplest
The ratio of pink to red sweets is 2 : 3. whole number form.
The ratio of red to green sweets is 5 : 14.
(a) 2.8 : 7
Find the ratio of pink to green sweets in the simplest form.
1
0

(b) 2 : 3.5 : 0.5

8. Leela and Pavarti share some money in the ratio 5 : 9. 1

(c) 60 % : 2.4 : 1
Pavarti gets $252 more than Leela. 4

How much money does Leela get?

2 4
(d) :
3 5
10. The angles in A, B, and C in this triangle are 12.
in the ratio 3 : 4 : 3.
Work out the size of each angle.
What type of triangle is this?

13. It takes 12 builders 30 days to complete a building.

(a) How long would it take 4 builders to complete

the building?

11. A map is drawn to a scale of 1 : 30 000.

Find the actual distance in meters between two
towns that are 3.8 cm apart on the map.

(b) How many builders would it take to complete the

building in 20 days?
 CHAPTER 11 Checkpoint Exam – Past Paper Questions

1. The ratio of boys to girls in a school is 3. Pink paint is made by mixing 9 parts of white
paint with 5 parts of red paint.
Boys : girls = 4 : 3
Find the number of parts of red paint needed to
One day, 18 girls are absent from school.
mix with 54 parts of white paint.
This represents 5% of all the girls in the school.

Calculate the total number of students in the school.

4. Gabriella’s book has 348 pages.

She has read 163 of the pages.
Safia’s book has 562 pages.
She has read 225 of the pages.

2. Carlos has some toy bricks.

Tick (✓) to show who has read the
Each brick is either red or blue. greater proportion of their book.
Show all your working.
The ratio of red bricks to blue bricks is 3:4

Draw a ring around the fraction of the bricks that are blue.
5. The exchange rate from euros (€) to dollars ($) is 7. Gabriella is 110 cm tall.
€1 = $1.2 Pierre is 154 cm tall.
This is the ratio of their masses.
Complete these conversions. Gabriella’s mass : Pierre’s mass
3:8
€160 to dollars. 1
The value of their total mass, in kg, is of the
4
value of their total height, in cm.

Complete the table.

$76.80 to euros.

6. Here are some currency exchange rates.

1 US dollar = 7.76 HK dollars

1 US dollar = 1.47 NZ dollars

Work out the value of 1000 HK dollars in NZ dollars.

8. Ari has r red flowers, w white flowers and y yellow flowers. 10. Here is part of a recipe.

r:w=3:2
w:y =4:3

Ari has 12 yellow flowers.

Work out how many flowers he has in total. (a) Write the ratio amount of flour : amount of water
in its simplest form.

(b) Naomi makes the recipe using 5 cups of flour.

Find how much water she uses.

9. Draw a ring around each of the two ratios that are equivalent.

2:3 4:3 3:2 6:8 15 : 10

11. 13. A cinema records the ratio of children to
adults in the audiences of two films
shown last week.

Which film has the greater proportion of

children in the audience?
Show how you worked out your answer.

12. Write the ratio 75 cm : 1.8 m in its simplest form.

14. The table shows the ratio of the number of (b) A dance class needs a ratio of 1 teacher for every
teachers to the number of students needed for 16 students.
each class.
There are 5 dance teachers.

72 students choose dance.

Calculate how many more students can attend the

dance class.

(a) Students are asked to choose from the three

classes.

14 choose swimming, 22 choose volleyball

and 27 choose football.

All the classes happen at the same time.

15. The diagram shows a postcard with a width of 10cm.
Calculate the number of teachers needed in The ratio of width to length of the postcard is 4 : 5
total.

(a) Work out the length of the postcard.

(b) Work out the area of the postcard.

 CHAPTER 12 Sequences and Functions

1. What is the term to term rule of the 4. Write down the nth term for the following
following sequences? sequences.

a. 7, 16, 25, 34, 43 (a) 4, 11, 18, 25, 32

b. 10, 20, 40, 80, 160

(b) 20, 15, 10, 5, 0

2. The third term of a sequence is 20.
The term to term rule is add 12.

Write down the first four terms of the sequence.

(c) 7, 10, 15, 22, 31

3. The position to term rule of a sequence is

cube then add 1.
Write down the first five terms of the sequence.
 𝑛 8.
5. A sequence has nth term
10

Find the 50th term in the sequence.

6. Find the nth term of the sequence

1, 8, 27, 64, 125…

Use three different numbers to complete

7. (a) Find the 40th term for the arithmetic sequence the mapping diagram.

4, 11, 18, 25, 32

9. Here is a function.

Fill in the missing numbers.

(b) Which term in the sequence is 172?

 CHAPTER 12 Straight lines

Equation of a line: y = mx + c Gradient of a line from two points:

m is the gradient and c is the y-intercept

1. Find the gradient of the line joining: 4. A straight line L is shown on the grid.
(a) (2, 7) and (5, 1)

(b) (2, -3) and (0, 5)

Find the:
(a) gradient
2. What is the gradient and y-intercept of the line

y = 5x + 2

3. What is the gradient and y-intercept of the line

(b) y-intercept
5y + 10x = 4

(c) x-intercept
5. The equations of two straight lines are 7. Work out the equation of a line that
passes through (0, 2) and (1, 5)

y = 5x + 4 and y – 5x = 3

Are these two lines parallel? Explain how you know.

6. Write the equation of a line parallel to y = 4x – 5

with y-intercept of (0, 7)?
8. Draw a ring around the point which does not lie on
the line y = 3x + 2

(2, 8) (0, 4) (100, 302) (9, 29)

 CHAPTER 12 Graphs of Linear and Quadratic Functions

1. (a) Complete the table of values for y = 2x + 3 2. (a) Complete the table for the quadratic function
y = x² + 3

x -2 -1 0 1 2

y
(b) Draw the graph of y = 2x + 3

(b) Use the table to draw the graph of y = x² + 3

 CHAPTER 12 Checkpoint Exam – Past Paper Questions

1. The term-to-term rule of a sequence is multiply by 3. 3. Write each of these lines in the correct position
The fourth term of the sequence is 54. in the table.
Work out the first term of the sequence.
y = 4x + 1

y = –1

y = – 6x

x + y = 11
2. Here are the coordinates of five points.
Cross ( × ) the point that is not on the line y = 3x – 5
with equation y = 5x – 3

The first one has been written in for you.

4. Draw a ring around the function that corresponds

to the rule in the box.
 5. Temperature can be measured in degrees Celsius 7. The graph shows four straight lines.
(°C) or degrees Fahrenheit (°F).
Here is a function to change degrees Celsius to
degrees Fahrenheit.

(a) Use the function to change 25°C to °F.

(b) Complete the inverse function.

(a) Draw a ring around the equations of the two lines
that do not intersect each other.

y = 2x + 1 y = 0.5x – 2 y=5–x x+y=1

6. A sequence begins
(b) Write down the solution to these simultaneous
equations.
3, – 6, 12, – 24, 48, …

y = 2x + 1
(a) Write down the term-to-term rule for this sequence.
y = 0.5x – 2

x = ……………

(b) Write down the next two terms.

y = …………….
8. (a) Complete the function machine for the 10. (a) Complete the table of values for y – 2x = 6
statement below.

(b) The line 4y – x = 7 is shown on the grid below.

Draw the line y – 2x = 6 on the same grid.

(b) Work out the number Hassan was

thinking of in part (a).

9. Angelique finds coordinates on the

straight line y = 2x + 4
She finds the x-coordinate from a given
y-coordinate.
Draw a ring around the correct function
to find x.

x = 2y + 4 x = (y − 4) ÷ 2

(c) Use the graph to solve the simultaneous equations

x = (y ÷ 2) − 4 x = (y + 4) ÷ 2
4y – x = 7 and y – 2x = 6

x = ………….

y = .................
11. The grid shows a straight line. 12. Here is a sequence of numbers.

80, 40, 20, 10…

Find the term-to-term rule for this sequence.

13. Here is a mapping.

(a) Draw a ring around the equation of the line.

y=x+2 y = 2x + 2 y = –2 Write a value in each box to make the mappings correct.
The first one has been done for you.
y=x–2 y = 2x – 2

(b) A different equation is 2x + y = 4

Complete the table of values for 2x + y = 4

(c) Draw the line 2x + y = 4 on the same grid.

14. The diagram shows the first three patterns of
a sequence made from rods.

(a) Draw Pattern 4 in the sequence

(b) Complete the statement.

When the pattern number increases by 1,

the number of rods increases by ………..

(c) Work out how many rods will be used for

Pattern 7

15. The first three terms of the sequence 3n² − 7n are

– 4, – 2, 6

Write down the first three terms of the sequence

3n² − 7n + 3
 CHAPTER 13 Transformations

Note:
- To describe a translation – give the vector.

- To describe a rotation – give the angle (90⁰, 180⁰, 270⁰ or 360⁰), direction (clockwise or anti-clockwise), and
the center of rotation.

- To describe a reflection – give the equation of the mirror line.

- To describe an enlargement – give the scale factor and center of enlargement.

1. 2.
 5. Triangle ABC is enlarged by a scale factor of 2 to
3.
give triangle XYZ.

(a) Find the vector that transforms D to C.

(a) Side YZ is 9 cm. Find the length of side BC.

(b) Find the vector that transforms D to O.

(b) Angle BAC is 35° .Find angle YXZ.

4. The diagram shows a shape drawn on a square grid.

6.

Reflect the shape in the mirror line

7. 8. Triangle B is drawn on the grid.

Q is the reflection of P in the line x = 2

Work out the coordinates of Q.

Triangle A is translated 3 right and 5 down

to give triangle B.
Draw and label triangle A on the grid.
9. The diagram shows shape A and shape B 11. Here is a rectangle on a coordinate grid.
drawn on a grid.

Describe fully the single transformation that

transforms shape A to shape B.
The rectangle is rotated 90° clockwise about vertex A.
Work out the coordinates of the image of vertex B.

10.
12. The diagram shows an object A and an image B. 13.

A can be mapped onto B using a rotation center (0, 0)

followed by a different type of transformation.
Complete the descriptions of the two transformations.

First transformation:

Rotation, ………………………………………………...
…………………………………………… , center (0,0).

Followed by second transformation:

………………………………………………………….
14. 16. (a) The perimeter of a triangle is 12 cm.

What is the perimeter of the image of

this triangle after enlargement with scale
factor of 3?

(b) The area of a triangle is 6 cm².

What is the area of the image of this

triangle after enlargement with scale
factor of 3?

15. Shape A is enlarged by a scale factor of 2 to make shape B.

Shape B is then rotated to make shape C.
Shape C is then translated to make shape D. 17. A hexagon has area 21 cm².
Tick (✓) to show if each pair of shapes are congruent or
It is enlarged by scale factor k.
not congruent

The image has an area of 525 cm².

Find the value of k.

18. 19. Two shapes are shown on the grid.

Describe the single transformation that maps

shape A onto shape B.
20. Draw an enlargement of Pentagon P using the center of enlargement (2, 1) and scale factor of 3.
21. The diagram shows triangle A drawn on a grid.

(a) Reflect triangle A in the line y = 2

Label the reflection B.

(b) Reflect triangle B in the line x = 1

Label the reflection C.

(c) A rotation will map triangle C back onto triangle A.

Find the coordinates of the center of this rotation

(………. , ……..)
 CHAPTER 14 Fractions, Percentages, and Decimals

1. Write each fraction as a percentage. 2. Write these as a percentage.

3 (a) 0.6
(a)
5

(b) 0.02

11
(b) (c) 0.79
25

(d) 0.237

141 (e) 1.14

(c)
50

(f) 3.8

9
(d) (g) 5
15

Note: to change any number into a percentage,

Multiply by 100
32
(e) 3. Change each percentage to a number.
80

(a) 10 %
55
(f)
500
(b) 37 %

(c) 54.5 %

9
(g)
1000 (d) 100 %

(e) 600 %
131
(h)
200
(f) 247 %

Note: to change any percentage into a number,

5
(i)
8 Divide by 100
 CHAPTER 14 Finding the percentage of an amount

1. Work out:
2. Write the missing numbers in the boxes.
(a) 37% of $200

(b) 15% of 60 children

3. Write $126 as a percentage of $200

(c) 20% of 7.50 m

4. The table shows the favourite colors of a class of children.

(d) 30% of $3.40

What percentage like yellow?

 CHAPTER 14 Discount, Tax, Percentage Increase, Percentage Decrease

1. What is the selling price of a $400 television if a 5. A bag had an original price of $110.
sales tax of 20% is charged? In the sale it is reduced to $82.50.
What percentage discount was given on
the bag?

2. What is the selling price of a $120 jacket after a

15% discount?

6. Layla buys a bicycle for $230.

She sells the bicycle for. $322.
What percentage profit does Layla make?

3. Rozya bought a mobile phone for $260.

What is her percentage loss if she sells the
phone for $228.80?

7. (a) Increase $350 by 20%

4. Last week there were 1400 visitors to a museum.

This week there are 1470.
What is the percentage increase in the number (b) Decrease $60 by 5%
of visitors?
 CHAPTER 14 Simple Interest & Compound Interest, Compound percentages

1. A bank has a simple interest rate of 4%. 5. Amir buys a painting for $2500.
What will be the value of a $300 investment
after 5 years? At the end of the first year the value of the
painting increases by 24%.
At the end of second year the value of the
painting decreases by 17%.
Work out the value of the painting at the
end of the second year.

2. John invests $450 at a rate of 2% per year

simple interest.
Calculate the interest John earns after 6 years.

+++++++++++++++++++++++++
6. A shop normally sells coats for $200 each.
One week, the shop reduces the price of the
3. Harry invests $9500 in a bank paying coats by 20%.
compound interest of 3% each year for 4 years. The following week, the shop reduces the
Work out the value of his investment after 4
years. sale price by a further 10%.

What is the cost of the coat now?

4. Kate invests $7000 in a bank offering 2.3%

compound interest. Calculate the value of her
investment after 6 years.
 CHAPTER 14 Checkpoint Exam – Past Paper Questions

1. Here are two books. 3. Mia buys 50 coats at $28 each.

She sells 38 of these coats at $49 each.
She sells the rest of the coats at $40 each.
Find the overall percentage profit Mia has
made on these coats.

Lily reads 32% of Book A.

Safia reads 40% of Book B.

Tick (✓) to show who reads the most pages.

You must show all your working.

2. Work out the missing amount in this statement.

4. Draw a line to match each fraction to its percentage equivalent. 5. A hotel has 250 rooms.
The first one has been done for you. 175 rooms are occupied.
Calculate the percentage of the rooms
that are occupied.

6. 40% of a number is 80
Find 55% of this number.

5. Here is a shape that has been divided into equal parts.

(a) Write down the fraction of the shape that is shaded.

Give your answer in its simplest form.

(b) Find the percentage of the shape that is unshaded.

 3
7. Write 8 as a percentage of 32 11. Write as a decimal
5

8. The original price of a television is reduced by 25%.

This new price is then increased by 25%.
Calculate the price of the television now as a
percentage of the original price.
12. Mia buys a car for $12500
She sells it to Chen for $16000

(a) Calculate Mia’s percentage profit.

9. The diagram shows a square split into congruent triangles.

(b) Chen sells the car to Gabriella.
He makes a loss of 5%.
Calculate the price Gabriella pays
for the car.

Work out the percentage of the square that is shaded.

10. Write 0.285 as a fraction in its simplest form.

13. 52% of the students in a school are girls. 15. Here are the costs of buying theatre tickets from a
booking agency.
50% of the girls play a musical instrument.
25% of the boys play a musical instrument.
Work out the percentage of students in the
whole school that play a musical instrument.

Hassam buys two adult tickets and two child tickets.

The booking agency charges an extra 5% of the total cost
as a booking fee.
Work out how much Hassam pays altogether.

14. (a) Work out 45% of $285

16. In 1975, the population of lions in Africa

was 250 000
In 2015, the population of lions in Africa
(b) Eva buys a book for $5 was 30000
She sells it for $6.50 Calculate the percentage decrease in the
African lion population between 1975
Work out the percentage profit.
and 2015.
 CHAPTER 15 Probability
Or +
Note:

And ×

1. The diagram shows a fair 8-sided spinner. 3. The table shows the shoe size of 23 students.

(a) The spinner is spun once.

A student is picked at random.
Write down the probability that the spinner
lands on the number 7. (a) Work out the probability that the student has a
shoe size of 8.

(b) The spinner is spun 160 times. (b) Work out the probability that the student has a
shoe size of 7 or smaller.
Work out the expected number of times the
spinner lands on the number 7

4. Megan has a fair 6 sided spinner.

The spinner has the letters A, B and C on it.
1
The probability that the spinner will land on an A is
2
1
7 The probability that the spinner will land on a C is
3
2. The probability that David will win a game is
10
Write the letters on the spinner.
What is the probability that he will not win the
game?
5. Elliott has eight numbered cards. 7. The probability of Jane spinning a 10 on a
spinner is 0.8
Work out the number of times she is
expected to spin a 10 if she spins the
One of the cards is chosen at random. spinner 60 times.

Elliott says:
1
The probability of an 8 is
4
The range of the numbers is 5.
The probability of a number greater than 10 is 0.
8. Sarah rolls a dice and flips a coin together.
1
The probability of a 7 is What is the probability of rolling a 6 on the
2
dice and getting a tails on the coin?
Fill in the six missing numbers.

6.

9. Here is a four - sided spinner.

0 1
Bag A Bag B

1 3

(a) What number is the spinner most likely

Toby says, to land on?
“You are more likely to pick a black marble at
random from bag B than from bag A because
bag B has more black marbles.” (b) Alex spins the spinner twice.

Is Toby Correct? Explain your answer. Find the probability that it lands on the
number 1 both times.
 Note:
10. Jayne rolls two fair dice together. - Two events are mutually exclusive if they cannot
Find the probability that she rolls two sixes. happen at the same time.
For example, when you flip a coin it is
impossible to get heads and tails at the same time.

- Two events are independent when the outcome

of one event has no effect on the outcome of the
other.
For example when you roll a dice and flip a coin
together, the probability of getting a 6 on the dice
11. Leo has 4 blue pencils and 6 red pencils in his does not change the probability of getting a head
pencil case. on the coin.

He takes a pencil at random and uses it.

Leo replaces the pencil and takes a second pencil
13. Here are some pairs of events.
at random.
State whether each pair of events is independent or
not independent.
Find the probability that both pencils are red.
Pick a disk from a box at Pick another disk from
random and replaces it. the same box at random.

Pick a disk from a box at Pick another disk from

random and do not the same box at random.
12. There are 20 sweets in a box. replace it.

The probability that a chocolate is picked at

random from the box is 0.6
How many chocolates are in the box?
Pick a disk from a box at Roll a dice
random and do not
replace it.
14. Here is a spinner with 2 white, 1 black and 2 grey sections: 15. David and Becky want to estimate how many
yellow jelly beans are in a tub of 500 jelly beans.
A trial consists of taking a jelly bean at random,
noting the color and replacing the jelly bean in
the tub.

The spinner was spun 200 times and the results shown in
the table below.

(a) Write down the relative frequency of David

taking a yellow jelly bean.

(b) Write down the relative frequency of Becky

taking a yellow jelly bean.
Complete the table by writing down the experimental and
theoretical probabilities.

(c) Whose experiment gives the more reliable

estimate of the number of yellow jelly beans
in the tub?
Give a reason for your answer.
 CHAPTER 15 Checkpoint Exam – Past Paper Questions

3. Anastasia has four coins A, B, C and D.

1. Complete these sentences. One of these coins is a fair coin and the other
three are biased coins.
The probability that a football team wins a match is She throws each coin 200 times and records
0.6 and the probability it does not win is the number of times she gets a head.

………..... Tick (✓) the coin that is most likely to be the

fair coin.
The probability that a player scores a goal is ………..
and the probability that the player does not score a
3
goal is
8

The probability that a fan supports a team is 72% and

the probability that the fan does not support the team

is …………... %.

2. Yuri rolls a six-sided dice 200 times.

Lily rolls the same dice 250 times.
The table shows their relative frequencies for a
score of six.
4. Mike has six cards each labelled with a letter.
He selects a card at random and records the
letter on it.

Work out how many sixes they rolled altogether. (a) Write down a list of all the possible outcomes.

(b) Write down the probability that Mike selects a

card that is labelled with the letter C.
5. The diagram shows a fair six-sided spinner. 6. Hassan travels by bus to work every
morning.
Each section is numbered.
The bus is either green or blue or yellow.
The numbers on four of the sections are shown.
The table shows information about the
probabilities of each color.

Color of bus Green Blue Yellow

Probability 2x 2x x

Ahmed spins the spinner twice and the scores are added.
The sample space diagram shows some of the total scores. (a) Calculate the value of x.

(b) Work out the probability that Hassan’s bus is

either blue or yellow.

Calculate the probability that the total score is 10 or more.

7. Mike throws a fair six-sided dice. 8. (a) Chen throws a coin 120 times.
He gets 54 heads.
Write down the relative frequency
that Chen gets a head.

(a) The scale shows the probability of an event.

(b) Jamila also throws a coin 120 times.

Tick (✓) all the events that could be represented
by the arrow. The relative frequency that she gets
a head is 0.575
Work out how many more heads
Getting an odd number on the dice. Jamila gets than Chen gets.

Getting the number 3 on the dice.

Getting a number less than 4 on the dice

(b) Draw an arrow (↑) on the scale to show the

probability of getting a 4 or a 5 on the dice.
 11. Pierre rolls a dice with four sides,
9. William plays a game.
numbered 1 to 4
He throws two fair dice.
He also throws a coin with two outcomes,
His score is the higher of the two numbers shown H or T.
on the dice.
List all the possible outcomes.
The sample space diagram shows some of his
One has been done for you.
possible scores.
You may not need to use all the rows.

(a) Complete the sample space diagram.

(b) Work out the probability that his score is greater

than 4

10. Mike throws an ordinary six-sided dice and flips a

coin at the same time.
One possible outcome is a 4 and a tail.
Work out the total number of possible outcomes.
 14. A bag contains some counters.
12. Hassan plays cricket.
Each counter is either red or green or yellow or blue.
The table shows the number of catches he makes in 50 games.
A counter is taken from the bag at random.
The table shows the probabilities of taking a red
counter, a green counter and a yellow counter.

Color Red Green Yellow Blue

Probability 0.25 0.5 0.15

Use the table to estimate the probability that he makes exactly

one catch in the next game he plays.
Tick (✓) to show if each of these statements is true,
false or whether you cannot tell.

One quarter of the counters in the bag are red.

13. A box contains pens of different colors.

Yuri takes a pen from the box at random.
The probabilities of him taking a pen colored red or blue or
green are shown in the table.

Color of pen Red Blue Green The bag contains 100 counters altogether.
Probability 0.4 0.15 0.25

Yuri says,
‘There must be more than three different colours of pen in
the box.’
Explain how the probabilities show Yuri is correct.
The bag contains more blue counters than yellow.
15. Lily has two bags. Each bag contains four 16. Babies born at a hospital are described as having
counters, as shown in the diagram. Low or Medium or High mass at birth.
The table shows some information about 200
babies born at the hospital last month.

(a) Fill in the missing values in the table.

She picks one counter from each bag and

adds together the numbers on the counters.
Work out the probability that the total of
her numbers is more than 3
You may find the table useful.

(b) One of the male babies is chosen at random.

Find the probability he has a Medium mass.

 Other Important Topics

NUMBER FACTS

1. Here is a number fact. 3. Here is a number fact.

148 × 76 = 11248 5478 × 64 = 350592

Use this fact to work out the calculations. Use this to work out

14.8 × 76 54.78 × 6.4

149 × 76 3505.92 ÷ 64

4. Here is a number fact.

2.

13442  47 = 286

Use this to work out

13.442  4.7

2.86 × 94
MULTIPLES, FACTORS, PRIMES

1. Write down the factors of 36. 4. Write down the prime factors of 250

5. Find the HCF of 126 and 180

2. Write down all the prime numbers between
60 and 70

3. Write 72 as a product of prime factors

6. Find the LCM of 60 and 72

CONVERTING UNITS

2 2 2

2 2 2 2

2 2 2

3 3 3

3 3 3 3

3 3 3
 Tera (T) 10¹²

Giga (G) 10⁹

Mega (M) 10⁶

Kilo (K) 10³

Base Unit 10⁰

centi (c) 10⁻²

milli (m) 10⁻³

micro (µ) 10⁻⁶

nano (n) 10⁻⁹

1 mile = 1.6 km

1 hectare (ha) = 10 000 m²

1 L = 1000 cm³

1 ml = 1 cm³
 Q. Complete these conversions.

1. (a) 0.7 μm = nm

2. (b) 300 MB = GB

3. (c) 70 000 μL = L

4. 400 000 000 kg = Tg

(d) 2.89 TB = KB

(e) 25 mg = g

(f) 2000 nm = m

(g) 4.71 ha = m²

(h) 30 000 m² = ha