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Term pack

Year 7 Maths

Name: ________________________

Skills in this pack

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

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Year 7 Maths · 1 of 17

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

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

  2. 2.Match each calculation to its answer.

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

  3. 3.-3 × (-4) × (-2) = ?

  4. 4.-36 ÷ 9 = ?

  5. 5.56 ÷ (-7) = ?

  6. 6.-45 ÷ (-5) = ?

  7. 7.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

  8. 8.Work out -2 × 4, then tap where the answer sits.

    Mark the line with an X.

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

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

Year 7 Maths · 2 of 17

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 · 3 of 17

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 · 4 of 17

Percentages

Find a percentage of an amount, and change between fractions and percentages.

Before you start

This line is the whole of something, split into a hundred. Move along it and read the percentages off.

020406080100

50 sits exactly halfway, 25 is halfway again, and 10 is a tenth of the way along. Those three are worth knowing by sight, because nearly every other percentage is built out of them.

  1. 1.What is 25% of 80?

  2. 2.What is 10% of 250?

  3. 3.A pupil scored 15 marks out of 20. What percentage is that? Give just the number.

  4. 4.What is 3/4 written as a percentage?

    • a) 34%
    • b) 75%
    • c) 25%
    • d) 43%

  5. 5.What is 50% of 96?

  6. 6.What is 20% of 45?

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

    • 60%
    • 1/5
    • 1/2
    • 30%
    • 0.4

  8. 8.A book costs $200. The price goes up by 10%. What is the new price? Give just the number.

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

Year 7 Maths · 5 of 17

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 · 6 of 17

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 · 7 of 17

Simple interest

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

  1. 1.Find the simple interest on $2000 at 5% per year for 3 years. Give just the number.

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

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

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

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

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

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

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

  8. 8.In every row the principal is $1000 and the rate is 10% per year. Match each length of time to the simple interest it earns.

    • 1 year
    • 2 years
    • 3 years
    • 5 years
    • 300
    • 500
    • 200
    • 100

Simple interest · Year 7 Maths · www.arenapublications.com/learn

Year 7 Maths · 8 of 17

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 · 9 of 17

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 · 10 of 17

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 · 11 of 17

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 17

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 · 13 of 17

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 · 14 of 17

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

    Groups: Must be congruent · Need not be congruent

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

  2. 2.Two figures are congruent when they...

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

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

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

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

  6. 6.Triangle PQR is congruent to triangle XYZ. Angle X is 40° and angle Y is 65°. How big is angle R, in degrees?

  7. 7.Triangle LMN is congruent to triangle XYZ. Match each part of LMN to the part of XYZ that matches it.

    • side LM
    • side MN
    • side LN
    • angle L
    • angle N
    • side XY
    • side XZ
    • angle X
    • side YZ
    • angle Z

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

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

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

Year 7 Maths · 15 of 17

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.How many lines of symmetry does an equilateral triangle have?

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

  3. 3.What is the order of rotational symmetry of a square?

  4. 4.Match each shape to the number of lines of symmetry it has.

    • Scalene triangle
    • Isosceles triangle
    • Rectangle that is not a square
    • Equilateral triangle
    • Square
    • 3
    • 1
    • 2
    • 4
    • 0

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

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

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

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

  8. 8.Sort each shape by whether it has any line of symmetry at all.

    Groups: Has at least one line of symmetry · Has no line of symmetry

    • Rhombus
    • The letter Z
    • Regular pentagon
    • Square
    • Scalene triangle
    • Parallelogram that is not a rhombus or a rectangle

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

Year 7 Maths · 16 of 17

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 17

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

Answer keys — Year 7 Maths

In the same order as the worksheets.

Multiplying and dividing integers

  1. 1. d) a positive number
  2. 2. -6 × 5 → -30; -6 × (-5) → 30; -42 ÷ 7 → -6; -42 ÷ (-6) → 7; 9 × (-2) → -18
  3. 3. -24
  4. 4. -4
  5. 5. -8
  6. 6. 9
  7. 7. -3
  8. 8. -8

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

Percentages

  1. 1. 20
  2. 2. 25
  3. 3. 75
  4. 4. b) 75%
  5. 5. 48
  6. 6. 9
  7. 7. 1. 1/5 2. 30% 3. 0.4 4. 1/2 5. 60%
  8. 8. 220

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

Simple interest

  1. 1. 300
  2. 2. 120
  3. 3. 360
  4. 4. b) It doubles
  5. 5. 5
  6. 6. 5
  7. 7. b) The interest earned on every 100 of the principal in one year
  8. 8. 1 year → 100; 2 years → 200; 3 years → 300; 5 years → 500

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

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

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

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

Congruence

  1. 1. 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
  2. 2. c) have exactly the same shape and exactly the same size
  3. 3. 9
  4. 4. b) Yes — turning a shape changes neither its shape nor its size
  5. 5. 72
  6. 6. 75
  7. 7. side LM → side XY; side MN → side YZ; side LN → side XZ; angle L → angle X; angle N → angle Z
  8. 8. a) they are the same length

Symmetry

  1. 1. 3
  2. 2. 2
  3. 3. 4
  4. 4. Scalene triangle → 0; Isosceles triangle → 1; Rectangle that is not a square → 2; Equilateral triangle → 3; Square → 4
  5. 5. 4
  6. 6. d) A
  7. 7. 72
  8. 8. Square → Has at least one line of symmetry; Scalene triangle → Has no line of symmetry; Rhombus → Has at least one line of symmetry; Parallelogram that is not a rhombus or a rectangle → Has no line of symmetry; Regular pentagon → Has at least one line of symmetry; The letter Z → Has no line of symmetry

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

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

Year 7 Maths · www.arenapublications.com/learn