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Term pack

Year 8 Maths

Name: ________________________

Skills in this pack

  • The unitary method
  • Profit and loss
  • Simple interest
  • Algebraic expressions
  • Solving equations
  • Exponents and powers
  • Multiplying and dividing integers
  • Multiplying and dividing fractions and decimals
  • Rational numbers
  • Powers and exponents
  • Properties of triangles
  • Congruence
  • Symmetry
  • Visualising solid shapes
  • Area of triangles and parallelograms
  • Data handling

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Year 8 Maths · 1 of 16

The unitary method

Find the value of one thing first, then scale it to any number — and tell direct proportion from inverse.

  1. 1.A store of food lasts 20 cows for 6 days. How long would the same store last 15 cows, in days?

  2. 2.More workers finish the same job in less time. That relationship is called...

    • a) a ratio in its simplest form
    • b) inverse proportion
    • c) direct proportion
    • d) no proportion at all

  3. 3.If 5 notebooks cost £150, what does 1 notebook cost? Give just the number.

  4. 4.One pen costs £12. Match each number of pens to what they cost. Give the cost as a plain number.

    • 3 pens
    • 5 pens
    • 7 pens
    • 10 pens
    • 36
    • 60
    • 84
    • 120

  5. 5.A car travels 240 km in 4 hours. How far does it travel in 1 hour, in kilometres?

  6. 6.Sort each pair of quantities by the way they vary together.

    Groups: Direct proportion · Inverse proportion

    • Weight of rice bought and its cost
    • Speed of a car and the time for a fixed journey
    • Number of taps filling a tank and the time taken
    • Distance travelled and time taken at a steady speed
    • Number of workers and the days to finish a job
    • Number of books bought and the total cost

  7. 7.Which of these pairs are in direct proportion?

    • a) The speed of a car and the time it takes on a fixed journey
    • b) The number of taps filling a tank and the time it takes
    • c) The number of workers and the days needed to finish a job
    • d) The number of pens bought and the total cost

  8. 8.7 workers build a wall in 12 days. Working at the same rate, how long would 14 workers take, in days?

The unitary method · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 2 of 16

Profit and loss

Work out profit, loss and discount, and give a profit or loss as a percentage of the cost price.

  1. 1.A trader buys a bag for £800 and sells it at a profit of 25%. What is the selling price? Give just the number.

  2. 2.Profit per cent is always worked out as a percentage of...

    • a) the discount
    • b) the selling price
    • c) the cost price
    • d) the profit

  3. 3.A toy costs £450 and is sold at a profit of £90. What is the profit per cent? Give just the number.

  4. 4.A shopkeeper buys a fan for £1200 and sells it for £1000. What is the loss? Give just the number.

  5. 5.A watch marked at £2000 is sold with a discount of 15%. What is the selling price? Give just the number.

  6. 6.A cycle is bought for £4000 and sold for £3600. What is the loss per cent? Give just the number.

  7. 7.A shirt is sold for £540 at a loss of 10%. What was the cost price? Give just the number.

  8. 8.Sort each sale by whether it made a profit or a loss.

    Groups: Profit · Loss

    • Bought for £1000, sold for £950
    • Bought for £200, sold for £250
    • Bought for £500, sold for £450
    • Bought for £75, sold for £60
    • Bought for £40, sold for £44
    • Bought for £90, sold for £120

Profit and loss · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 3 of 16

Simple interest

Work out simple interest and the total amount, and find the rate or the time when the interest is known.

  1. 1.In a simple interest question, what does the rate tell you?

    • a) The number of years the money is kept for
    • b) The amount borrowed at the start
    • c) The total interest over the whole time
    • d) The interest earned on every 100 of the principal in one year

  2. 2.The principal and the rate stay the same, but the money is left for twice as long. What happens to the simple interest?

    • a) It stays the same
    • b) It doubles
    • c) It is multiplied by itself
    • d) It halves

  3. 3.Find the simple interest on £5000 at 8% per year for 2 years. Give just the number.

  4. 4.The simple interest on £2500 for 4 years is £500. What is the rate per cent per year? Give just the number.

  5. 5.Find the simple interest on £1200 at 10% per year for 1 year. Give just the number.

  6. 6.The simple interest on £800 at 5% per year is £200. For how many years was the money invested?

  7. 7.Each of these is left for 2 years. Sort them by whether the simple interest comes to less or more than £500.

    Groups: Less than £500 · More than £500

    • £2000 at 10% per year
    • £3000 at 5% per year
    • £5000 at 8% per year
    • £1000 at 20% per year
    • £5000 at 6% per year
    • £4000 at 8% per year

  8. 8.Find the simple interest on £600 at 12% per year for 5 years. Give just the number.

Simple interest · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 4 of 16

Algebraic expressions

Identify terms and coefficients, collect like terms and evaluate an expression.

  1. 1.Sort each term by whether it is a like term of 4x.

    Groups: Like term of 4x · Not a like term of 4x

    • -9x
    • 7x
    • x
    • 4y
    • 9
    • 4xy

  2. 2.What is the coefficient of x in the expression 4x - 9?

  3. 3.Find the value of 2x + 3 when x = 4.

  4. 4.Find the value of a × a + 2 when a = 3.

  5. 5.Take m = 6. Match each expression to its value.

    • m + 4
    • 2m
    • m - 1
    • 3m
    • m ÷ 2
    • 3
    • 10
    • 5
    • 12
    • 18

  6. 6.Simplify 3x + 5x.

    • a) 2x
    • b) 8
    • c) 8x
    • d) 15x

  7. 7.How many terms are there in the expression 3x + 2y - 7?

  8. 8.Simplify 7a - 2a.

    • a) 14a
    • b) 5
    • c) 5a
    • d) 9a

Algebraic expressions · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 5 of 16

Solving equations

Solve a linear equation in one variable by keeping both sides balanced.

Before you start

Two mystery boxes and some weights, and the beam is level. See how much you can take away without it moving.

517

Take the 5 off both sides and the two boxes stand against what is left; one box is half of that. The scale has just walked you through the whole solution without a line of working.

  1. 1.What is the right first move to solve 7x = 56?

    • a) Subtract 7 from both sides
    • b) Multiply both sides by 7
    • c) Add 7 to both sides
    • d) Divide both sides by 7

  2. 2.x + 5 = 12. What is x?

  3. 3.2x + 3 = 11. What is x?

  4. 4.x - 9 = -2. What is x?

  5. 5.2x + 1 = x + 9. What is x?

  6. 6.3x - 4 = 2x + 6. What is x?

  7. 7.Put these steps in the right order to solve 3x + 4 = 19.

    • 3x = 15
    • Subtract 4 from both sides
    • x = 5
    • Divide both sides by 3

  8. 8.4(x + 2) = 20. What is x?

Solving equations · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 6 of 16

Exponents and powers

Work out powers and use the laws of exponents to simplify them.

  1. 1.Write 2⁵ ÷ 2³ as a power of 2.

    • a) 2⁸
    • b) 2¹⁵
    • c) 2
    • d) 2²

  2. 2.Work out 2⁵ ÷ 2³ as an ordinary number.

  3. 3.Work out each one, then sort it by its value.

    Groups: Equals 8 · Equals 16

    • 4²
    • 8¹
    • 2³
    • 2 × 4
    • 2⁴
    • 16¹

  4. 4.Simplify a⁵ × a³.

    • a) a¹⁵
    • b) 2a⁸
    • c) a⁸
    • d) a²

  5. 5.What is 3⁰?

  6. 6.What is 10⁴?

  7. 7.Simplify (2³)².

    • a) 2⁶
    • b) 2¹
    • c) 2⁵
    • d) 2⁹

  8. 8.What is 2³ (two to the power 3)?

Exponents and powers · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 7 of 16

Multiplying and dividing integers

Multiply and divide positive and negative whole numbers, and get the sign right every time.

Before you start

This line runs from twelve below zero to twelve above it, in twos. Move along it and see how the two halves mirror each other.

-12-60612

Every step to the right adds 2 and every step to the left takes 2 away, so multiplying by a negative is the same jumps walked the other way. That is the whole sign rule, in one picture.

  1. 1.Match each calculation to its answer.

    • -6 × 5
    • -6 × (-5)
    • -42 ÷ 7
    • -42 ÷ (-6)
    • 9 × (-2)
    • 7
    • -6
    • 30
    • -30
    • -18

  2. 2.A negative number multiplied by another negative number always gives...

    • a) a positive number
    • b) zero
    • c) a negative number
    • d) whichever sign the bigger number has

  3. 3.The product of two integers is -48. One of them is 6. What is the other?

  4. 4.-7 × (-3) = ?

  5. 5.Tap the integer that is exactly halfway between -8 and 2.

    Mark the line with an X.

    -10-9-8-7-6-5-4-3-2-1012345678910

  6. 6.56 ÷ (-7) = ?

  7. 7.8 × (-5) = ?

  8. 8.-45 ÷ (-5) = ?

Multiplying and dividing integers · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 8 of 16

Multiplying and dividing fractions and decimals

Multiply and divide fractions and decimals, and know when the answer will be smaller than what you started with.

  1. 1.1/2 × 1/3 = ? Write your answer as a fraction.

  2. 2.1/2 ÷ 1/4 = ?

  3. 3.Work out 0.5 × 1.4, then tap where the answer sits.

    Mark the line with an X.

    0.00.51.01.52.0

  4. 4.7.5 ÷ 0.5 = ?

  5. 5.0.4 × 0.3 = ?

  6. 6.Work out each one, then sort it by whether the answer is less than 1 or more than 1.

    Groups: Less than 1 · More than 1

    • 3/4 × 2
    • 2/3 ÷ 1/3
    • 0.5 × 0.8
    • 1/4 ÷ 2
    • 1/3 × 1/2
    • 0.9 ÷ 0.3

  7. 7.3/4 ÷ 2 = ? Write your answer as a fraction.

  8. 8.2/5 ÷ 1/10 = ?

Multiplying and dividing fractions and decimals · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 9 of 16

Rational numbers

Place, compare, add and subtract numbers that can be written as one whole number over another.

  1. 1.What is the reciprocal of -3/5? Write your answer as a fraction.

  2. 2.Write a rational number that lies exactly halfway between 1/2 and 3/4.

  3. 3.Sort each rational number by which side of zero it sits on.

    Groups: Left of zero · Right of zero

    • -4/3
    • 5/6
    • 9/2
    • -7/8
    • -1/10
    • -2.5

  4. 4.-2/5 × 10 = ?

  5. 5.Every whole number is also a rational number. Why?

    • a) Because it is always positive
    • b) Because it never has a decimal point
    • c) Because it can be written as a fraction with 1 on the bottom
    • d) Because it is always bigger than a fraction

  6. 6.1/2 - 3/4 = ? Write your answer as a fraction.

  7. 7.Which is greater: -3/4 or -2/3?

    • a) They are equal
    • b) -2/3
    • c) -3/4
    • d) Negative fractions cannot be compared

  8. 8.-2/3 - 1/6 = ? Write your answer as a fraction.

Rational numbers · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 10 of 16

Powers and exponents

Read and write a power, work out its value, and use the laws for multiplying and dividing powers of the same base.

Before you start

This line runs to thirty-two in twos. Find 2, 4, 8, 16 and 32 on it, and see how far apart they get.

08162432

Each of those is double the one before, so every jump is as long as the whole walk that came before it. A power grows far faster than the small numbers writing it suggest.

  1. 1.100000 is 10 to some power. What is that power?

  2. 2.Which is larger: 2⁵ or 5²?

    • a) They are equal
    • b) 5²
    • c) There is no way to tell
    • d) 2⁵

  3. 3.Which power means the same as 3 × 3 × 3 × 3?

    • a) 3⁵
    • b) 3⁴
    • c) 3 × 4
    • d) 4³

  4. 4.Match each number to the power of 10 it is equal to.

    • 1
    • 10
    • 100
    • 1000
    • 10000
    • 10⁰
    • 10⁴
    • 10³
    • 10²
    • 10¹

  5. 5.Work out 5⁶ ÷ 5⁴ as an ordinary number.

  6. 6.7⁴ × 7³ is the same as which single power?

    • a) 7¹²
    • b) 7¹
    • c) 49⁷
    • d) 7⁷

  7. 7.What is 6²?

  8. 8.What is 10³?

Powers and exponents · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 11 of 16

Properties of triangles

Use the angle sum, the exterior angle rule and Pythagoras' theorem in a triangle.

Before you start

A right-angled triangle, with the corner that makes it one marked. Find out what each of its three sides is called.

1234
  1. 1. A short side
  2. 2. The other short side
  3. 3. Hypotenuse — the longest
  4. 4. The right angle

Square the two short sides, add them, and you land on the square of the hypotenuse — 60² + 80² = 100². Swapping which short side you call which changes nothing, because addition does not care about order.

  1. 1.An exterior angle of a triangle is 120°. One of the two opposite interior angles is 45°. What is the other, in degrees?

  2. 2.A right-angled triangle has shorter sides of 3 cm and 4 cm. How long is the hypotenuse, in centimetres?

  3. 3.An isosceles triangle has an apex angle of 40°. How big is each base angle, in degrees?

  4. 4.Can a triangle have sides of 2 cm, 3 cm and 7 cm?

    • a) Yes
    • b) Only if it is isosceles
    • c) Only if it is right-angled
    • d) No — 2 and 3 together are shorter than 7

  5. 5.A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. How long is the other short side, in centimetres?

  6. 6.A right-angled triangle has an angle of 35° besides the right angle. What is the third angle, in degrees?

  7. 7.Each row gives the three side lengths of a triangle. Sort them by whether the triangle is right-angled.

    Groups: Right-angled · Not right-angled

    • 3, 4, 5
    • 2, 3, 4
    • 5, 12, 13
    • 4, 5, 6
    • 9, 12, 15
    • 8, 15, 17

  8. 8.A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse, in centimetres?

Properties of triangles · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 12 of 16

Congruence

Say when two figures are congruent, read a congruence statement in the right order, and use it to find matching sides and angles.

  1. 1.Triangle ABC is congruent to triangle DEF. BC is 9 cm long. How long is EF, in centimetres?

  2. 2.Sort each pair of figures by whether they have to be congruent.

    Groups: Must be congruent · Need not be congruent

    • Two rectangles with the same area
    • Two line segments 7 cm long
    • Two triangles with the same three angles
    • Two rectangles with the same perimeter
    • Two squares with sides of 4 cm
    • Two equilateral triangles with sides of 5 cm

  3. 3.Triangle ABC is congruent to triangle PQR. The perimeter of ABC is 26 cm. What is the perimeter of PQR, in centimetres?

  4. 4.In the statement 'triangle ABC is congruent to triangle PQR', which side matches AB?

    • a) PQ
    • b) QR
    • c) AP
    • d) PR

  5. 5.Two figures are congruent when they...

    • a) have exactly the same shape and exactly the same size
    • b) have the same area as each other
    • c) have the same number of sides as each other
    • d) have the same shape, but may be different sizes

  6. 6.A square tile is lifted up and put back down turned a quarter turn. Is it congruent to the way it was before?

    • a) Only if it is turned back first
    • b) No, because it is facing a different way
    • c) Yes — turning a shape changes neither its shape nor its size
    • d) Only if it was the right way up to begin with

  7. 7.Triangle ABC is congruent to triangle DEF. Angle C is 72°. How big is angle F, in degrees?

  8. 8.Two line segments are congruent when...

    • a) they are both perfectly straight
    • b) they point in the same direction
    • c) they meet at a point
    • d) they are the same length

Congruence · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 13 of 16

Symmetry

Count lines of symmetry, find the order of rotational symmetry, and work out the smallest turn that leaves a shape looking the same.

  1. 1.A shape has rotational symmetry of order 5. What is the smallest turn that leaves it looking the same, in degrees?

  2. 2.Which capital letter has exactly one line of symmetry?

    • a) N
    • b) S
    • c) H
    • d) A

  3. 3.Put these regular shapes in order by how many lines of symmetry they have, fewest first.

    • Square
    • Regular pentagon
    • Regular octagon
    • Regular hexagon
    • Equilateral triangle

  4. 4.How many lines of symmetry does a square have?

  5. 5.How many lines of symmetry does a regular hexagon have?

  6. 6.This triangle has two equal sides. Three lines have been drawn on it. Tap the one that is a line of symmetry.

    Write the number of the part.

    123

  7. 7.What is the order of rotational symmetry of an equilateral triangle?

  8. 8.How many lines of symmetry does a rectangle that is not a square have?

Symmetry · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 14 of 16

Visualising solid shapes

Count the faces, edges and vertices of a solid, tell flat surfaces from curved ones, and say what a solid looks like from another direction.

Before you start

A cube, drawn on flat paper. Find out what each part of it is called.

1234
  1. 1. The top face
  2. 2. The front face
  3. 3. An edge
  4. 4. A vertex

A cube has 6 faces, 12 edges and 8 vertices — and you can only find some of them on the drawing, because three faces and three edges are hidden round the back.

  1. 1.You look straight down on a cylinder standing upright on a table. What shape do you see?

    • a) A circle
    • b) A square
    • c) A rectangle
    • d) A triangle

  2. 2.How many edges does a square pyramid have?

  3. 3.Tap one of this cuboid's vertices.

    Write the number of the part.

    123

  4. 4.Match each solid to the number of faces it has.

    • Triangular pyramid
    • Triangular prism
    • Cube
    • Pentagonal prism
    • Hexagonal prism
    • 4
    • 6
    • 7
    • 8
    • 5

  5. 5.How many edges does a cube have?

  6. 6.How many faces does a triangular prism have?

  7. 7.How many flat faces does a cylinder have?

    • a) 1
    • b) 3
    • c) 0
    • d) 2

  8. 8.Sort each solid by whether every one of its surfaces is flat.

    Groups: Every surface is flat · Has a curved surface

    • Square pyramid
    • Cylinder
    • Triangular prism
    • Cone
    • Sphere
    • Cube

Visualising solid shapes · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 15 of 16

Area of triangles and parallelograms

Find the area of a parallelogram, a triangle and a rhombus, and the perimeter of a straight-sided shape.

  1. 1.Sort each rule by what it works out.

    Groups: Area · Perimeter

    • base × height
    • 1/2 × base × height
    • 4 × side
    • all the sides added together
    • 2 × (length + width)
    • length × width

  2. 2.A triangle and a parallelogram share the same base and the same height. The triangle's area is...

    • a) twice the parallelogram's area
    • b) half the parallelogram's area
    • c) impossible to compare
    • d) the same as the parallelogram's area

  3. 3.A triangle has a base of 9 cm and a height of 4 cm. What is its area, in square centimetres?

  4. 4.A parallelogram has an area of 60 square centimetres and a base of 10 cm. What is its height, in centimetres?

  5. 5.A triangle has an area of 24 square centimetres and a base of 8 cm. What is its height, in centimetres?

  6. 6.Every one of these triangles has a height of 6 cm. Match each base to the triangle's area in square centimetres.

    • base 4 cm
    • base 5 cm
    • base 8 cm
    • base 10 cm
    • 15
    • 30
    • 24
    • 12

  7. 7.A rectangle 14 cm by 9 cm has a triangle of base 14 cm and height 9 cm cut out of it. What area is left, in square centimetres?

  8. 8.A rhombus has diagonals of 8 cm and 6 cm. What is its area, in square centimetres?

Area of triangles and parallelograms · Year 8 Maths · www.arenapublications.com/learn

Year 8 Maths · 16 of 16

Data handling

Find the mean, median, mode and range of a set of data, and read information off a bar chart.

  1. 1.Seven children scored 3, 5, 5, 7, 8, 9 and 12. What is the median score?

  2. 2.A bar graph shows 7 blue cars and 5 white cars. How many more blue cars are there than white ones?

  3. 3.Find the range of 33, 18, 47 and 22.

  4. 4.This bar chart shows how many books a library lent out on four days. Tap the bar for the day it lent the most.

    Write the number of the part.

    1234

  5. 5.The mean of five numbers is 14. What do the five numbers add up to?

  6. 6.Sort each statement by whether it describes the mean or the mode.

    Groups: The mean · The mode

    • It is always a value taken from the list itself
    • A list can have more than one of them
    • Every value in the list changes it
    • The value that appears most often
    • One unusually large value pulls it upwards
    • Add every value up and divide by how many there are

  7. 7.A bar graph shows 4 red cars, 7 blue cars, 5 white cars and 4 black cars. How many cars are there altogether?

  8. 8.Find the median of 21, 8, 14, 30 and 11.

Data handling · Year 8 Maths · www.arenapublications.com/learn

Answer keys — Year 8 Maths

In the same order as the worksheets.

The unitary method

  1. 1. 8
  2. 2. b) inverse proportion
  3. 3. 30
  4. 4. 3 pens → 36; 5 pens → 60; 7 pens → 84; 10 pens → 120
  5. 5. 60
  6. 6. Number of books bought and the total cost → Direct proportion; Number of taps filling a tank and the time taken → Inverse proportion; Distance travelled and time taken at a steady speed → Direct proportion; Speed of a car and the time for a fixed journey → Inverse proportion; Number of workers and the days to finish a job → Inverse proportion; Weight of rice bought and its cost → Direct proportion
  7. 7. d) The number of pens bought and the total cost
  8. 8. 6

Profit and loss

  1. 1. 1000
  2. 2. c) the cost price
  3. 3. 20
  4. 4. 200
  5. 5. 1700
  6. 6. 10
  7. 7. 600
  8. 8. Bought for £200, sold for £250 → Profit; Bought for £500, sold for £450 → Loss; Bought for £90, sold for £120 → Profit; Bought for £1000, sold for £950 → Loss; Bought for £75, sold for £60 → Loss; Bought for £40, sold for £44 → Profit

Simple interest

  1. 1. d) The interest earned on every 100 of the principal in one year
  2. 2. b) It doubles
  3. 3. 800
  4. 4. 5
  5. 5. 120
  6. 6. 5
  7. 7. £2000 at 10% per year → Less than £500; £5000 at 6% per year → More than £500; £1000 at 20% per year → Less than £500; £4000 at 8% per year → More than £500; £3000 at 5% per year → Less than £500; £5000 at 8% per year → More than £500
  8. 8. 360

Algebraic expressions

  1. 1. 7x → Like term of 4x; x → Like term of 4x; -9x → Like term of 4x; 4y → Not a like term of 4x; 4xy → Not a like term of 4x; 9 → Not a like term of 4x
  2. 2. 4
  3. 3. 11
  4. 4. 11
  5. 5. m + 4 → 10; 2m → 12; m - 1 → 5; 3m → 18; m ÷ 2 → 3
  6. 6. c) 8x
  7. 7. 3
  8. 8. c) 5a

Solving equations

  1. 1. d) Divide both sides by 7
  2. 2. 7
  3. 3. 4
  4. 4. 7
  5. 5. 8
  6. 6. 10
  7. 7. 1. Subtract 4 from both sides 2. 3x = 15 3. Divide both sides by 3 4. x = 5
  8. 8. 3

Exponents and powers

  1. 1. d) 2²
  2. 2. 4
  3. 3. 2³ → Equals 8; 2⁴ → Equals 16; 8¹ → Equals 8; 4² → Equals 16; 2 × 4 → Equals 8; 16¹ → Equals 16
  4. 4. c) a⁸
  5. 5. 1
  6. 6. 10000
  7. 7. a) 2⁶
  8. 8. 8

Multiplying and dividing integers

  1. 1. -6 × 5 → -30; -6 × (-5) → 30; -42 ÷ 7 → -6; -42 ÷ (-6) → 7; 9 × (-2) → -18
  2. 2. a) a positive number
  3. 3. -8
  4. 4. 21
  5. 5. -3
  6. 6. -8
  7. 7. -40
  8. 8. 9

Multiplying and dividing fractions and decimals

  1. 1. 1/6
  2. 2. 2
  3. 3. 0.7
  4. 4. 15
  5. 5. 0.12
  6. 6. 1/3 × 1/2 → Less than 1; 3/4 × 2 → More than 1; 2/3 ÷ 1/3 → More than 1; 0.5 × 0.8 → Less than 1; 0.9 ÷ 0.3 → More than 1; 1/4 ÷ 2 → Less than 1
  7. 7. 3/8
  8. 8. 4

Rational numbers

  1. 1. -5/3
  2. 2. 5/8
  3. 3. -7/8 → Left of zero; 5/6 → Right of zero; -4/3 → Left of zero; 9/2 → Right of zero; -1/10 → Left of zero; -2.5 → Left of zero
  4. 4. -4
  5. 5. c) Because it can be written as a fraction with 1 on the bottom
  6. 6. -1/4
  7. 7. b) -2/3
  8. 8. -5/6

Powers and exponents

  1. 1. 5
  2. 2. d) 2⁵
  3. 3. b) 3⁴
  4. 4. 1 → 10⁰; 10 → 10¹; 100 → 10²; 1000 → 10³; 10000 → 10⁴
  5. 5. 25
  6. 6. d) 7⁷
  7. 7. 36
  8. 8. 1000

Properties of triangles

  1. 1. 75
  2. 2. 5
  3. 3. 70
  4. 4. d) No — 2 and 3 together are shorter than 7
  5. 5. 12
  6. 6. 55
  7. 7. 3, 4, 5 → Right-angled; 5, 12, 13 → Right-angled; 9, 12, 15 → Right-angled; 8, 15, 17 → Right-angled; 2, 3, 4 → Not right-angled; 4, 5, 6 → Not right-angled
  8. 8. 10

Congruence

  1. 1. 9
  2. 2. Two squares with sides of 4 cm → Must be congruent; Two rectangles with the same area → Need not be congruent; Two equilateral triangles with sides of 5 cm → Must be congruent; Two triangles with the same three angles → Need not be congruent; Two line segments 7 cm long → Must be congruent; Two rectangles with the same perimeter → Need not be congruent
  3. 3. 26
  4. 4. a) PQ
  5. 5. a) have exactly the same shape and exactly the same size
  6. 6. c) Yes — turning a shape changes neither its shape nor its size
  7. 7. 72
  8. 8. d) they are the same length

Symmetry

  1. 1. 72
  2. 2. d) A
  3. 3. 1. Equilateral triangle 2. Square 3. Regular pentagon 4. Regular hexagon 5. Regular octagon
  4. 4. 4
  5. 5. 6
  6. 6. 1 — the line from the top
  7. 7. 3
  8. 8. 2

Visualising solid shapes

  1. 1. a) A circle
  2. 2. 8
  3. 3. 3 — a vertex
  4. 4. Triangular pyramid → 4; Triangular prism → 5; Cube → 6; Pentagonal prism → 7; Hexagonal prism → 8
  5. 5. 12
  6. 6. 5
  7. 7. d) 2
  8. 8. Cube → Every surface is flat; Cone → Has a curved surface; Triangular prism → Every surface is flat; Sphere → Has a curved surface; Square pyramid → Every surface is flat; Cylinder → Has a curved surface

Area of triangles and parallelograms

  1. 1. base × height → Area; 1/2 × base × height → Area; 2 × (length + width) → Perimeter; 4 × side → Perimeter; length × width → Area; all the sides added together → Perimeter
  2. 2. b) half the parallelogram's area
  3. 3. 18
  4. 4. 6
  5. 5. 6
  6. 6. base 4 cm → 12; base 5 cm → 15; base 8 cm → 24; base 10 cm → 30
  7. 7. 63
  8. 8. 24

Data handling

  1. 1. 7
  2. 2. 2
  3. 3. 29
  4. 4. 2 — Tuesday
  5. 5. 70
  6. 6. Add every value up and divide by how many there are → The mean; The value that appears most often → The mode; Every value in the list changes it → The mean; A list can have more than one of them → The mode; One unusually large value pulls it upwards → The mean; It is always a value taken from the list itself → The mode
  7. 7. 20
  8. 8. 14

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