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Term pack

Year 7 Maths

Name: ________________________

Skills in this pack

  • Multiplying and dividing fractions and decimals
  • Rational numbers
  • The unitary method
  • Profit and loss
  • Powers and exponents
  • Squares and square roots
  • Ratio and proportion
  • Algebraic expressions
  • Solving equations
  • Letters for numbers
  • Area of triangles and parallelograms
  • Circles: centre, radius and diameter
  • Volume with unit cubes
  • Lines and angles
  • Properties of triangles
  • Visualising solid shapes
  • Proving angle facts
  • Understanding elementary shapes
  • Data handling
  • Mean, median and mode
  • Averages
  • Probability

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Year 7 Maths · 1 of 22

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

    Mark the line with an X.

    0.00.51.01.52.0

  2. 2.1/2 × 1/3 = ? Write your answer as a fraction.

  3. 3.7.5 ÷ 0.5 = ?

  4. 4.Put these amounts in order, smallest first.

    • 0.4
    • 1/2
    • 0.75
    • 1/3
    • 0.25

  5. 5.0.36 ÷ 4 = ?

  6. 6.1/2 ÷ 1/4 = ?

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

  8. 8.2/5 ÷ 1/10 = ?

Multiplying and dividing fractions and decimals · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 2 of 22

Rational numbers

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

  1. 1.1/2 - 3/4 = ? Write your answer as a fraction.

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

  3. 3.Tap where -5/4 sits.

    Mark the line with an X.

    -2.00-1.000.001.002.00

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

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

  5. 5.Tap where -1/2 sits.

    Mark the line with an X.

    -2.0-1.5-1.0-0.50.00.51.01.52.0

  6. 6.-2/5 × 10 = ?

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

    Groups: Left of zero · Right of zero

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

  8. 8.Put these rational numbers in order, smallest first.

    • 0
    • -1/4
    • -3/2
    • 1
    • -1
    • 2/5

Rational numbers · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 3 of 22

The unitary method

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

  1. 1.12 identical bricks weigh 30 kg. What do 20 of those bricks weigh, in kilograms?

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

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

  3. 3.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 pens bought and the total cost
    • c) The number of taps filling a tank and the time it takes
    • d) The number of workers and the days needed to finish a job

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

    Groups: Direct proportion · Inverse proportion

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

  5. 5.If 5 notebooks cost $150, what do 8 notebooks cost? Give just the number.

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

  7. 7.A machine fills 350 bottles in 5 minutes. How many bottles does it fill in 8 minutes?

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

The unitary method · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 4 of 22

Profit and loss

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

  1. 1.An item is sold for exactly what it cost. What is the profit per cent?

    • a) 100
    • b) 50
    • c) 0
    • d) There is no way to tell

  2. 2.A shopkeeper buys a chair for $600 and sells it for $750. What is the profit? Give just the number.

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

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

  5. 5.Put these sales in order of profit per cent, smallest first.

    • Bought for $100, sold for $105
    • Bought for $40, sold for $60
    • Bought for $200, sold for $220
    • Bought for $50, sold for $60
    • Bought for $80, sold for $100

  6. 6.Every one of these was bought for $400. Match each selling price to its profit per cent, using a minus sign for a loss.

    • Sold for $500
    • Sold for $300
    • Sold for $440
    • Sold for $360
    • Sold for $600
    • -25
    • 25
    • 10
    • -10
    • 50

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

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

Profit and loss · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 5 of 22

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

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

  2. 2.81 is 3 to some power. What is that power?

  3. 3.100000 is 10 to some power. What is that power?

  4. 4.7⁴ × 7³ is the same as which single power?

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

  5. 5.Work out each power, then sort it by whether its value is less than 100 or more than 100.

    Groups: Less than 100 · More than 100

    • 2⁷
    • 3⁴
    • 3⁵
    • 6²
    • 2⁵
    • 5³

  6. 6.Which is larger: 2⁵ or 5²?

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

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

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

  8. 8.What is 2⁴?

Powers and exponents · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 6 of 22

Squares and square roots

Square whole numbers and find the square roots of perfect squares.

Before you start

Every whole number from zero to twenty-five sits on this line. Find 1, 4, 9, 16 and 25 on it, and look at the gaps between them.

0510152025

The gaps go 3, then 5, then 7, then 9 — the perfect squares spread out as you go, which is why so few numbers have a whole square root.

  1. 1.17² = ?

  2. 2.√576 = ?

  3. 3.A square garden has an area of 169 square metres. How long is each side, in metres?

  4. 4.Work each one out, then put them in order, smallest first.

    • √196
    • √49
    • √144
    • √16
    • √81

  5. 5.Sort each number by whether it is a perfect square.

    Groups: Perfect square · Not a perfect square

    • 70
    • 50
    • 99
    • 64
    • 49
    • 81

  6. 6.What is the smallest whole number, apart from zero, you can multiply 18 by to get a perfect square?

  7. 7.Match each number to its square root.

    • 36
    • 100
    • 121
    • 400
    • 625
    • 6
    • 10
    • 25
    • 11
    • 20

  8. 8.13² = ?

Squares and square roots · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 7 of 22

Ratio and proportion

Write and simplify ratios, and use them to share amounts and scale recipes.

  1. 1.Which ratio is equivalent to 3:4?

    • a) 4:3
    • b) 9:16
    • c) 6:8
    • d) 7:8

  2. 2.These ratios are all written as first:second. Put them in order, smallest first.

    • 2:3
    • 5:4
    • 1:2
    • 3:4
    • 1:4

  3. 3.Share 40 sweets between two children in the ratio 3:5. How many does the second child get?

  4. 4.The ratio of boys to girls in a class is 5:4. There are 20 boys. How many girls are there?

  5. 5.Are 2:3 and 8:12 in proportion?

    • a) No
    • b) Only if you swap them round
    • c) Yes
    • d) There is not enough information

  6. 6.A recipe uses 2 cups of rice to 5 cups of water. How many cups of water are needed for 6 cups of rice?

  7. 7.Share 40 sweets between two children in the ratio 3:5. How many does the first child get?

  8. 8.Match each ratio to its simplest form.

    • 8:12
    • 10:4
    • 9:27
    • 16:20
    • 18:24
    • 4:5
    • 5:2
    • 1:3
    • 2:3
    • 3:4

Ratio and proportion · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 8 of 22

Algebraic expressions

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

  1. 1.Which of these is a like term of 5pq?

    • a) 5p + q
    • b) q
    • c) -2pq
    • d) 5p

  2. 2.Simplify 5x + 3y - 2x + y.

    • a) 7x + 4y
    • b) 3x + 4y
    • c) 3x + 2y
    • d) 7xy

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

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

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

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

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

  6. 6.Simplify 7a - 2a.

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

  7. 7.Simplify 3x + 5x.

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

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

Algebraic expressions · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 9 of 22

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

  2. 2.x ÷ 4 = 5. What is x?

  3. 3.3x - 4 = 2x + 6. What is x?

  4. 4.4(x + 2) = 20. What is x?

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

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

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

  7. 7.5x - 7 = 18. What is x?

  8. 8.2x + 1 = x + 9. What is x?

Solving equations · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 10 of 22

Letters for numbers

Write simple algebraic expressions and work out their value.

Before you start

The scale is level. Move the weights about and see what keeps it that way.

38

Take the same amount off both sides and it stays level. Take it off one side only and the scale says so at once — which is the whole rule for solving an equation, felt before it is written down.

  1. 1.If a = 6, what is the value of a × a?

  2. 2.The scale is level and every box holds the same. What does one box weigh?

    The scale is balanced. Write what one box weighs.

    353

  3. 3.If y = 9, what is the value of 2y - 4?

  4. 4.If x = 4 and y = 3, what is the value of x + 2y?

  5. 5.Which expression means '5 more than x'?

    • a) x + 5
    • b) 5 - x
    • c) x - 5
    • d) 5x

  6. 6.Match each description to the expression that says the same thing.

    • 7 less than m
    • m shared equally between 7
    • 7 times m
    • 7 more than m
    • m + 7
    • 7m
    • m - 7
    • m ÷ 7

  7. 7.Add weights from the shelf until both sides are equal.

    Circle weights from the tray to make the scale level.

    127532

  8. 8.If x = 5, what is the value of x + 12?

Letters for numbers · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 11 of 22

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.A triangle has a base of 10 cm and a height of 6 cm. What is its area, in square centimetres?

  2. 2.The height of a parallelogram is measured...

    • a) at right angles to the base
    • b) from one corner to the opposite corner
    • c) along the slanting side
    • d) all the way round the outside

  3. 3.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
    • 12
    • 30
    • 24

  4. 4.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) impossible to compare
    • c) the same as the parallelogram's area
    • d) half the parallelogram's area

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

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

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

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

Area of triangles and parallelograms · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 12 of 22

Circles: centre, radius and diameter

Name the centre, radius and diameter of a circle, and use the fact that the diameter is twice the radius.

Before you start

Three parts are marked on these two equal circles. Find the point in the middle of the first, the line that reaches from its middle to the edge, and the line that crosses the whole of the second, and see what each one is called.

123
  1. 1. The radius
  2. 2. The diameter
  3. 3. The centre

Lay two of the shorter line end to end and they cover the longer one exactly. That is the whole relationship between a radius and a diameter, in one picture.

  1. 1.A circle has a radius of 6 cm. What is its diameter, in centimetres?

    • a) 36
    • b) 3
    • c) 12
    • d) 6

  2. 2.A circle has a diameter of 20 cm. What is its radius, in centimetres?

    • a) 20
    • b) 40
    • c) 10
    • d) 5

  3. 3.The diameter of a circle is always...

    • a) three times the radius
    • b) half the radius
    • c) twice the radius
    • d) the same as the radius

  4. 4.Every measurement here is in centimetres. Sort each circle by whether its diameter is below 20 or above 20.

    Groups: Diameter below 20 · Diameter above 20

    • radius 8
    • radius 15
    • radius 6
    • radius 12
    • diameter 26
    • diameter 15

  5. 5.Match each circle's radius to the diameter of the same circle.

    • radius 3
    • radius 5
    • radius 8
    • radius 11
    • 10
    • 22
    • 16
    • 6

  6. 6.Tap the radius.

    Write the number of the part.

    123

  7. 7.What is the name for the point exactly in the middle of a circle?

  8. 8.A round table top has a diameter of 90 cm. How far is it from the middle of the table to its edge, in centimetres?

    • a) 90
    • b) 180
    • c) 45
    • d) 30

Circles: centre, radius and diameter · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 13 of 22

Volume with unit cubes

Find the volume of a box by counting the unit cubes that fill it.

  1. 1.Match each box to the number of unit cubes that fill it.

    • 2 by 2 by 2
    • 2 by 3 by 2
    • 3 by 3 by 2
    • 4 by 3 by 2
    • 5 by 4 by 2
    • 12
    • 18
    • 24
    • 8
    • 40

  2. 2.A cuboid is built from 2 layers. Each layer is 6 cubes long and 2 cubes wide. How many cubes are there altogether?

  3. 3.Which of these boxes holds the most unit cubes?

    • a) 1 by 5 by 5
    • b) 2 by 3 by 4
    • c) 3 by 3 by 3
    • d) 2 by 2 by 6

  4. 4.A cuboid is built from 36 unit cubes in 3 equal layers. How many cubes are in each layer?

  5. 5.A box is 4 cubes long, 3 cubes wide and 2 cubes tall. How many unit cubes fill it?

  6. 6.A tower is built from 3 layers, and each layer holds 4 cubes. How many cubes is that altogether?

  7. 7.A cube measures 3 unit cubes along every edge. How many unit cubes is it built from?

    • a) 27
    • b) 9
    • c) 81
    • d) 18

  8. 8.A cuboid is 6 cm long, 3 cm wide and 2 cm tall. What is its volume, in cubic centimetres? Give just the number.

Volume with unit cubes · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 14 of 22

Lines and angles

Use complementary, supplementary, vertically opposite and parallel-line angle facts.

Before you start

Two straight lines cross, and only one of the four angles they make has been given to you. Find out how big each of the others is.

1234
  1. 1. 70° — given
  2. 2. 110° — supplementary
  3. 3. 70° — opposite
  4. 4. 110° — also opposite

Going round the crossing the angles read 70, 110, 70, 110. Each neighbouring pair sits on a straight line and adds to 180°, and each opposite pair is equal — which is the same fact told twice.

  1. 1.Sort each angle as acute or obtuse.

    Groups: Acute · Obtuse

    • 92°
    • 145°
    • 12°
    • 35°
    • 78°
    • 170°

  2. 2.Parallel lines are cut by a transversal. One co-interior angle is 115°. What is the other, in degrees?

  3. 3.Angles round a point add up to how many degrees?

  4. 4.Three angles sit side by side on a straight line. Two of them are 45° and 85°. What is the third, in degrees?

  5. 5.Two straight lines cross. One of the four angles is 130°. What is the angle next to it, in degrees?

  6. 6.Two angles are complementary. One of them is 65°. What is the other, in degrees?

  7. 7.Two angles sit on a straight line, and one is three times the other. How big is the smaller one, in degrees?

  8. 8.When two straight lines cross, the two angles directly opposite each other are always...

    • a) equal
    • b) complementary
    • c) supplementary
    • d) right angles

Lines and angles · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 15 of 22

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

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

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

  3. 3.Every angle of an equilateral triangle is the same size. How big is each one, in degrees?

  4. 4.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

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

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

  6. 6.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?

  7. 7.In an isosceles triangle the two base angles are always...

    • a) supplementary
    • b) right angles
    • c) equal
    • d) 60° each

  8. 8.Two angles of a triangle are 50° and 60°. What is the third, in degrees?

Properties of triangles · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 16 of 22

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.How many edges does a square pyramid have?

  2. 2.How many faces does a cube have?

  3. 3.How many vertices does a cuboid have?

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

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

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

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

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

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

  8. 8.How many vertices does a triangular pyramid have?

Visualising solid shapes · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 17 of 22

Proving angle facts

Use the linear-pair axiom to prove vertically opposite angles equal, and apply the angle-sum and exterior-angle theorems.

Before you start

One side of this triangle has been carried straight on past the corner B. Find out what each of the four angles here is called.

1234
  1. 1. The interior angle at A
  2. 2. The interior angle at B
  3. 3. The interior angle at C
  4. 4. The exterior angle at B

The exterior angle at B equals the two interior angles it does not touch — the ones at A and C — added together. That is the exterior angle theorem, and it follows straight from the angle sum.

  1. 1.An exterior angle of a triangle is 110°, and one of the two interior angles opposite it is 45°. What is the other one, in degrees?

  2. 2.The exterior angle theorem says an exterior angle of a triangle is equal to...

    • a) half of 180°
    • b) the largest interior angle
    • c) the two interior angles opposite it, added together
    • d) the interior angle next to it

  3. 3.Two angles of a triangle are 55° and 65°. What is the third, in degrees?

  4. 4.Parallel lines are cut by a transversal, and one of a pair of alternate interior angles is 73°. What is the other, in degrees?

  5. 5.Sort each set of angles by whether they must be equal or must add up to 180°.

    Groups: Must be equal · Must add up to 180°

    • Alternate interior angles on parallel lines
    • Co-interior angles on parallel lines
    • Corresponding angles on parallel lines
    • Vertically opposite angles
    • A linear pair
    • The three angles of a triangle

  6. 6.Parallel lines are cut by a transversal. Two co-interior angles measure 2x degrees and x degrees. What is x?

  7. 7.Two angles form a linear pair. One of them is 118°. What is the other, in degrees?

  8. 8.Two straight lines cross. One of the four angles is 47°. What is the angle vertically opposite it, in degrees?

Proving angle facts · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 18 of 22

Understanding elementary shapes

Classify angles by size, triangles by their sides and their angles, and tell flat shapes from solid ones.

Before you start

Four angles, drawn side by side and getting wider as you go. Find out what each one is called.

1234
  1. 1. Acute
  2. 2. Right angle
  3. 3. Obtuse
  4. 4. Straight

Acute is under 90°, obtuse is over it, and the straight one is a half turn — 180°, which is why it stopped looking like a corner at all.

  1. 1.This triangle has one right angle. Tap the corner where it is.

    Write the number of the part.

    123

  2. 2.The angles of a triangle add up to 180°. Two of them are 55° and 65°. How big is the third, in degrees?

  3. 3.Two right angles side by side make a straight angle. How many degrees is a straight angle?

  4. 4.Match each angle to the name for its size.

    • 45°
    • 90°
    • 120°
    • 180°
    • 300°
    • Obtuse
    • Right
    • Acute
    • Straight
    • Reflex

  5. 5.An angle of 200° is which kind of angle?

    • a) Obtuse
    • b) Straight
    • c) Acute
    • d) Reflex

  6. 6.A triangle has sides of 5 cm, 5 cm and 8 cm. How many of its sides are equal in length?

  7. 7.A full turn is 360° and splits into four equal right angles. How many degrees is one right angle?

  8. 8.An angle of 145° is which kind of angle?

    • a) Obtuse
    • b) Acute
    • c) Reflex
    • d) Right

Understanding elementary shapes · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 19 of 22

Data handling

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

  1. 1.Which average is the value that appears most often?

    • a) The mode
    • b) The range
    • c) The mean
    • d) The median

  2. 2.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

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

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

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

  6. 6.Find the mean of 12, 15, 18 and 15.

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

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

    Write the number of the part.

    1234

Data handling · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 20 of 22

Mean, median and mode

Find the mean, median, mode and range of a small set of numbers.

  1. 1.Find the mode of 5, 8, 8, 2, 9, 8 and 1.

  2. 2.Find the range of 12, 4, 9 and 20.

  3. 3.Which average is the middle value once the data has been put in order?

    • a) The mode
    • b) The median
    • c) The range
    • d) The mean

  4. 4.Find the median of 12, 5, 9, 3 and 7.

  5. 5.Five children scored 6, 7, 8, 9 and 10. What is the mean score?

  6. 6.Match each word to what it tells you about a set of numbers.

    • Mean
    • Median
    • Mode
    • Range
    • The middle value, once in order
    • The value that turns up most often
    • The gap between the largest and the smallest
    • The total shared out equally

  7. 7.Find the median of 2, 4, 6 and 8.

  8. 8.Find the mode of 2, 3, 3, 5, 7 and 3.

Mean, median and mode · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 21 of 22

Averages

Find the average of a small set of numbers by sharing the total out equally.

  1. 1.Three parcels weigh 2 kg, 5 kg and 8 kg. What is their average mass, in kilograms? Give just the number.

  2. 2.Three children have 5, 8 and 11 stickers. They share them all out equally. How many does each child end up with?

  3. 3.Work out each average, then put the sets in order, smallest average first.

    • 8, 10, 12
    • 1, 2, 3
    • 2, 4, 6
    • 5, 6, 7

  4. 4.Find the average of 4, 6 and 8.

  5. 5.Find the average of 10, 12, 14 and 16.

  6. 6.Two numbers have an average of 9. One of them is 6. What is the other?

  7. 7.The average of four numbers is 7. What do the four numbers add up to?

  8. 8.Work out each average, then sort it by size.

    Groups: Average is less than 10 · Average is 10 or more

    • 8, 10, 12
    • 9, 11, 13
    • 5, 6, 7
    • 2, 4, 6
    • 1, 2, 3
    • 14, 16, 18

Averages · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 22 of 22

Probability

Work out the probability of a simple event and of it not happening.

  1. 1.What is the probability of an event that is certain to happen?

    • a) It depends on the event
    • b) 0
    • c) 1
    • d) 0.5

  2. 2.The probability that it rains tomorrow is 0.3. What is the probability that it does not rain?

  3. 3.A fair die is rolled. What is the probability of getting a number greater than 4? Give your answer as a fraction.

  4. 4.A bag holds 3 red balls and 5 blue balls. One is taken out without looking. What is the probability it is red? Give your answer as a fraction.

  5. 5.A fair coin is tossed. What is the probability of getting a head? Give your answer as a fraction.

  6. 6.A fair die is rolled. What is the probability of getting a 4? Give your answer as a fraction.

  7. 7.A card is drawn from a full pack of 52. What is the probability it is red? Give your answer as a fraction.

  8. 8.A bag holds 3 red balls and 5 blue balls. One is taken out without looking. What is the probability it is blue? Give your answer as a fraction.

Probability · Year 7 Maths · www.arenapublications.com/learn

Answer keys — Year 7 Maths

In the same order as the worksheets.

Multiplying and dividing fractions and decimals

  1. 1. 0.7
  2. 2. 1/6
  3. 3. 15
  4. 4. 1. 0.25 2. 1/3 3. 0.4 4. 1/2 5. 0.75
  5. 5. 0.09
  6. 6. 2
  7. 7. 3/8
  8. 8. 4

Rational numbers

  1. 1. -1/4
  2. 2. -5/3
  3. 3. -1.25
  4. 4. b) Because it can be written as a fraction with 1 on the bottom
  5. 5. -0.5
  6. 6. -4
  7. 7. -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
  8. 8. 1. -3/2 2. -1 3. -1/4 4. 0 5. 2/5 6. 1

The unitary method

  1. 1. 50
  2. 2. d) inverse proportion
  3. 3. b) The number of pens bought and the total cost
  4. 4. 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
  5. 5. 240
  6. 6. 8
  7. 7. 560
  8. 8. 60

Profit and loss

  1. 1. c) 0
  2. 2. 150
  3. 3. 200
  4. 4. 600
  5. 5. 1. Bought for $100, sold for $105 2. Bought for $200, sold for $220 3. Bought for $50, sold for $60 4. Bought for $80, sold for $100 5. Bought for $40, sold for $60
  6. 6. Sold for $500 → 25; Sold for $300 → -25; Sold for $440 → 10; Sold for $360 → -10; Sold for $600 → 50
  7. 7. 1700
  8. 8. 20

Powers and exponents

  1. 1. b) 3⁴
  2. 2. 4
  3. 3. 5
  4. 4. c) 7⁷
  5. 5. 2⁵ → Less than 100; 3⁴ → Less than 100; 6² → Less than 100; 5³ → More than 100; 2⁷ → More than 100; 3⁵ → More than 100
  6. 6. c) 2⁵
  7. 7. 1 → 10⁰; 10 → 10¹; 100 → 10²; 1000 → 10³; 10000 → 10⁴
  8. 8. 16

Squares and square roots

  1. 1. 289
  2. 2. 24
  3. 3. 13
  4. 4. 1. √16 2. √49 3. √81 4. √144 5. √196
  5. 5. 49 → Perfect square; 64 → Perfect square; 81 → Perfect square; 50 → Not a perfect square; 70 → Not a perfect square; 99 → Not a perfect square
  6. 6. 2
  7. 7. 36 → 6; 100 → 10; 121 → 11; 400 → 20; 625 → 25
  8. 8. 169

Ratio and proportion

  1. 1. c) 6:8
  2. 2. 1. 1:4 2. 1:2 3. 2:3 4. 3:4 5. 5:4
  3. 3. 25
  4. 4. 16
  5. 5. c) Yes
  6. 6. 15
  7. 7. 15
  8. 8. 8:12 → 2:3; 10:4 → 5:2; 9:27 → 1:3; 16:20 → 4:5; 18:24 → 3:4

Algebraic expressions

  1. 1. c) -2pq
  2. 2. b) 3x + 4y
  3. 3. 11
  4. 4. 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
  5. 5. 3
  6. 6. d) 5a
  7. 7. c) 8x
  8. 8. 11

Solving equations

  1. 1. b) Divide both sides by 7
  2. 2. 20
  3. 3. 10
  4. 4. 3
  5. 5. 1. Subtract 4 from both sides 2. 3x = 15 3. Divide both sides by 3 4. x = 5
  6. 6. 7
  7. 7. 5
  8. 8. 8

Letters for numbers

  1. 1. 36
  2. 2. box = 5
  3. 3. 14
  4. 4. 10
  5. 5. a) x + 5
  6. 6. 7 less than m → m - 7; m shared equally between 7 → m ÷ 7; 7 times m → 7m; 7 more than m → m + 7
  7. 7. 5 on the right pan
  8. 8. 17

Area of triangles and parallelograms

  1. 1. 30
  2. 2. a) at right angles to the base
  3. 3. base 4 cm → 12; base 5 cm → 15; base 8 cm → 24; base 10 cm → 30
  4. 4. d) half the parallelogram's area
  5. 5. 18
  6. 6. 40
  7. 7. 6
  8. 8. 6

Circles: centre, radius and diameter

  1. 1. c) 12
  2. 2. c) 10
  3. 3. c) twice the radius
  4. 4. radius 6 → Diameter below 20; radius 12 → Diameter above 20; diameter 15 → Diameter below 20; diameter 26 → Diameter above 20; radius 8 → Diameter below 20; radius 15 → Diameter above 20
  5. 5. radius 3 → 6; radius 5 → 10; radius 8 → 16; radius 11 → 22
  6. 6. 1 — The radius
  7. 7. centre
  8. 8. c) 45

Volume with unit cubes

  1. 1. 2 by 2 by 2 → 8; 2 by 3 by 2 → 12; 3 by 3 by 2 → 18; 4 by 3 by 2 → 24; 5 by 4 by 2 → 40
  2. 2. 24
  3. 3. c) 3 by 3 by 3
  4. 4. 12
  5. 5. 24
  6. 6. 12
  7. 7. a) 27
  8. 8. 36

Lines and angles

  1. 1. 35° → Acute; 92° → Obtuse; 78° → Acute; 145° → Obtuse; 12° → Acute; 170° → Obtuse
  2. 2. 65
  3. 3. 360
  4. 4. 50
  5. 5. 50
  6. 6. 25
  7. 7. 45
  8. 8. a) equal

Properties of triangles

  1. 1. c) No — 2 and 3 together are shorter than 7
  2. 2. 10
  3. 3. 60
  4. 4. 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
  5. 5. 55
  6. 6. 12
  7. 7. c) equal
  8. 8. 70

Visualising solid shapes

  1. 1. 8
  2. 2. 6
  3. 3. 8
  4. 4. 12
  5. 5. d) A circle
  6. 6. 5
  7. 7. Triangular pyramid → 4; Triangular prism → 5; Cube → 6; Pentagonal prism → 7; Hexagonal prism → 8
  8. 8. 4

Proving angle facts

  1. 1. 65
  2. 2. c) the two interior angles opposite it, added together
  3. 3. 60
  4. 4. 73
  5. 5. Vertically opposite angles → Must be equal; A linear pair → Must add up to 180°; Alternate interior angles on parallel lines → Must be equal; Co-interior angles on parallel lines → Must add up to 180°; Corresponding angles on parallel lines → Must be equal; The three angles of a triangle → Must add up to 180°
  6. 6. 60
  7. 7. 62
  8. 8. 47

Understanding elementary shapes

  1. 1. 2 — the bottom left corner
  2. 2. 60
  3. 3. 180
  4. 4. 45° → Acute; 90° → Right; 120° → Obtuse; 180° → Straight; 300° → Reflex
  5. 5. d) Reflex
  6. 6. 2
  7. 7. 90
  8. 8. a) Obtuse

Data handling

  1. 1. a) The mode
  2. 2. 2 — Tuesday
  3. 3. 20
  4. 4. 2
  5. 5. 7
  6. 6. 15
  7. 7. 70
  8. 8. 3 — Wednesday

Mean, median and mode

  1. 1. 8
  2. 2. 16
  3. 3. b) The median
  4. 4. 7
  5. 5. 8
  6. 6. Mean → The total shared out equally; Median → The middle value, once in order; Mode → The value that turns up most often; Range → The gap between the largest and the smallest
  7. 7. 5
  8. 8. 3

Averages

  1. 1. 5
  2. 2. 8
  3. 3. 1. 1, 2, 3 2. 2, 4, 6 3. 5, 6, 7 4. 8, 10, 12
  4. 4. 6
  5. 5. 13
  6. 6. 12
  7. 7. 28
  8. 8. 2, 4, 6 → Average is less than 10; 8, 10, 12 → Average is 10 or more; 1, 2, 3 → Average is less than 10; 9, 11, 13 → Average is 10 or more; 5, 6, 7 → Average is less than 10; 14, 16, 18 → Average is 10 or more

Probability

  1. 1. c) 1
  2. 2. 0.7
  3. 3. 1/3
  4. 4. 3/8
  5. 5. 1/2
  6. 6. 1/6
  7. 7. 1/2
  8. 8. 5/8

Year 7 Maths · www.arenapublications.com/learn