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Term pack

Class 7 Maths

Name: ________________________

Skills in this pack

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

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Class 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.-6 × 4 = ?

  2. 2.-45 ÷ (-5) = ?

  3. 3.-36 ÷ 9 = ?

  4. 4.-7 × (-3) = ?

  5. 5.-3 × (-4) × (-2) = ?

  6. 6.Match each calculation to its answer.

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

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

  8. 8.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

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

Class 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.Put these amounts in order, smallest first.

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

  2. 2.Multiply a whole number by a fraction smaller than 1. The answer is always...

    • a) exactly the same as the whole number
    • b) smaller than the whole number you started with
    • c) bigger than the whole number you started with
    • d) a whole number too

  3. 3.0.4 × 0.3 = ?

  4. 4.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

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

  5. 5.3/5 × 10 = ?

  6. 6.1/2 ÷ 1/4 = ?

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

  8. 8.7.5 ÷ 0.5 = ?

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

Class 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.Match each rational number to its opposite — the number the same distance from zero on the other side.

    • 3/4
    • -2/5
    • 1/2
    • -7
    • 5/6
    • -5/6
    • -1/2
    • 7
    • -3/4
    • 2/5

  4. 4.-2/3 - 1/6 = ? Write your answer as a fraction.

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

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

  6. 6.-3/4 + 1/4 = ? Write your answer as a fraction.

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

    Mark the line with an X.

    -2.00-1.000.001.002.00

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

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

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

Class 7 Maths · 4 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.The mean of five numbers is 14. What do the five numbers add up to?

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

  3. 3.Find the mode of 4, 6, 4, 9, 4 and 6.

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

  5. 5.Match each set of numbers to its mean.

    • 2, 4, 6
    • 10, 20, 30, 40
    • 5, 5, 5, 5
    • 1, 2, 3, 4, 5
    • 8, 12
    • 10
    • 3
    • 4
    • 5
    • 25

  6. 6.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

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

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

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

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

Class 7 Maths · 5 of 17

Algebraic expressions

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

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

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

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

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

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

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

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

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

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

  6. 6.Simplify 7a - 2a.

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

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

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

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

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

Class 7 Maths · 6 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. 1.2x + 1 = x + 9. What is x?

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

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

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

  4. 4.3x = 21. What is x?

  5. 5.3x - 4 = 2x + 6. What is x?

  6. 6.5x - 7 = 18. What is x?

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

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

  8. 8.I think of a number, double it and add 5. The answer is 17. What was my number?

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

Class 7 Maths · 7 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.Parallel lines are cut by a transversal. One co-interior angle is 115°. What is the other, in degrees?

  2. 2.Two angles are supplementary. One of them is 110°. What is the other, in degrees?

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

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

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

    Groups: Acute · Obtuse

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

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

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

  7. 7.A pair of parallel lines is cut by a transversal. Alternate angles are always...

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

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

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

Class 7 Maths · 8 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.In an isosceles triangle the two base angles are always...

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

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

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

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

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

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

  6. 6.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
    • 9, 12, 15
    • 4, 5, 6
    • 8, 15, 17

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

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

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

Class 7 Maths · 9 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.Triangle PQR is congruent to triangle XYZ. Angle X is 40° and angle Y is 65°. How big is angle R, in degrees?

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

  3. 3.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
    • angle X
    • side XZ
    • side XY
    • side YZ
    • angle Z

  4. 4.Triangle ABC is congruent to triangle PQR, with A matching P, B matching Q and C matching R. Tap the side of triangle PQR that matches side AB.

    Write the number of the part.

    123

  5. 5.Two angles are congruent when...

    • a) they are the same size
    • b) they are drawn the same way up
    • c) their arms are the same length
    • d) they are both acute

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

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

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

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

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

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

Class 7 Maths · 10 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 10% of 250?

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

  3. 3.A shopkeeper buys a bag for ₹400 and sells it for ₹500. What is the profit as a percentage of the cost? Give just the number.

  4. 4.What is 20% of 45?

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

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

  6. 6.A shirt costs ₹500 and is reduced by 20% in a sale. What is the sale price? Give just the number.

  7. 7.Match each percentage to the same amount written as a fraction.

    • 50%
    • 25%
    • 20%
    • 75%
    • 10%
    • 1/10
    • 1/4
    • 1/2
    • 3/4
    • 1/5

  8. 8.What is 25% of 80?

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

Class 7 Maths · 11 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.If 5 notebooks cost ₹150, what do 8 notebooks cost? Give just the number.

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

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

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

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

  5. 5.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
    • 120
    • 36
    • 84
    • 60

  6. 6.A car travels 240 km in 4 hours. At the same speed, how far does it travel in 7 hours, in kilometres?

  7. 7.12 identical bricks weigh 30 kg. What do 20 of those bricks weigh, in kilograms?

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

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

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

Class 7 Maths · 12 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.A cycle is bought for ₹4000 and sold for ₹3600. What is the loss per cent? Give just the number.

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

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

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

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

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

  7. 7.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

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

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

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

Class 7 Maths · 13 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.The simple interest on ₹2500 for 4 years is ₹500. What is the rate per cent per year? 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.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 halves
    • b) It doubles
    • c) It is multiplied by itself
    • d) It stays the same

  4. 4.₹4000 is borrowed at 6% per year for 3 years. What is the total amount to be paid back? Give just the number.

  5. 5.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
    • 500
    • 100
    • 300
    • 200

  6. 6.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

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

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

  8. 8.Find the simple interest on ₹3000 at 7% per year for 6 months. Give just the number.

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

Class 7 Maths · 14 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 parallelogram has a base of 8 cm and a height of 5 cm. What is its area, in square centimetres?

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

  3. 3.A square field has a side of 25 m. What is its perimeter, in metres?

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

    Groups: Area · Perimeter

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

  5. 5.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

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

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

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

  8. 8.A path runs all the way round a rectangular garden 20 m long and 15 m wide. How far is it once round the garden, in metres?

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

Class 7 Maths · 15 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.What is 2⁴?

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

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

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

  4. 4.What is 6²?

  5. 5.81 is 3 to some power. What is that power?

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

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

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

  8. 8.What is 10³?

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

Class 7 Maths · 16 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.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

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

  3. 3.Which of these has rotational symmetry of order 2 but no line of symmetry at all?

    • a) A square
    • b) The letter A
    • c) The letter S
    • d) An equilateral triangle

  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
    • 0
    • 4
    • 3
    • 2
    • 1

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

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

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

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

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

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

Class 7 Maths · 17 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.Match each solid to the number of faces it has.

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

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

    Groups: Every surface is flat · Has a curved surface

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

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

  4. 4.Which solid has exactly one flat face and one curved surface?

    • a) A cone
    • b) A cube
    • c) A cylinder
    • d) A sphere

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

  6. 6.A solid has 6 faces and 8 vertices. Using the rule faces + vertices - edges = 2, how many edges does it have?

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

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

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

Answer keys — Class 7 Maths

In the same order as the worksheets.

Multiplying and dividing integers

  1. 1. -24
  2. 2. 9
  3. 3. -4
  4. 4. 21
  5. 5. -24
  6. 6. -6 × 5 → -30; -6 × (-5) → 30; -42 ÷ 7 → -6; -42 ÷ (-6) → 7; 9 × (-2) → -18
  7. 7. -8
  8. 8. -3

Multiplying and dividing fractions and decimals

  1. 1. 1. 0.25 2. 1/3 3. 0.4 4. 1/2 5. 0.75
  2. 2. b) smaller than the whole number you started with
  3. 3. 0.12
  4. 4. 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
  5. 5. 6
  6. 6. 2
  7. 7. 3/8
  8. 8. 15

Rational numbers

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

Data handling

  1. 1. 70
  2. 2. 29
  3. 3. 4
  4. 4. 20
  5. 5. 2, 4, 6 → 4; 10, 20, 30, 40 → 25; 5, 5, 5, 5 → 5; 1, 2, 3, 4, 5 → 3; 8, 12 → 10
  6. 6. 3 — Wednesday
  7. 7. 7
  8. 8. b) The mode

Algebraic expressions

  1. 1. 11
  2. 2. 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
  3. 3. c) 3x + 4y
  4. 4. m + 4 → 10; 2m → 12; m - 1 → 5; 3m → 18; m ÷ 2 → 3
  5. 5. 3
  6. 6. c) 5a
  7. 7. d) -2pq
  8. 8. 11

Solving equations

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

Lines and angles

  1. 1. 65
  2. 2. 70
  3. 3. c) equal
  4. 4. 35° → Acute; 92° → Obtuse; 78° → Acute; 145° → Obtuse; 12° → Acute; 170° → Obtuse
  5. 5. 25
  6. 6. 360
  7. 7. a) equal
  8. 8. 45

Properties of triangles

  1. 1. c) equal
  2. 2. 70
  3. 3. 60
  4. 4. b) No — 2 and 3 together are shorter than 7
  5. 5. 10
  6. 6. 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
  7. 7. 75
  8. 8. 55

Congruence

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

Percentages

  1. 1. 25
  2. 2. 220
  3. 3. 25
  4. 4. 9
  5. 5. 1. 1/5 2. 30% 3. 0.4 4. 1/2 5. 60%
  6. 6. 400
  7. 7. 50% → 1/2; 25% → 1/4; 20% → 1/5; 75% → 3/4; 10% → 1/10
  8. 8. 20

The unitary method

  1. 1. 240
  2. 2. c) inverse proportion
  3. 3. 560
  4. 4. 60
  5. 5. 3 pens → 36; 5 pens → 60; 7 pens → 84; 10 pens → 120
  6. 6. 420
  7. 7. 50
  8. 8. a) The number of pens bought and the total cost

Profit and loss

  1. 1. 10
  2. 2. 150
  3. 3. 20
  4. 4. 1700
  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. 1000
  7. 7. c) 0
  8. 8. b) the cost price

Simple interest

  1. 1. 5
  2. 2. 120
  3. 3. b) It doubles
  4. 4. 4720
  5. 5. 1 year → 100; 2 years → 200; 3 years → 300; 5 years → 500
  6. 6. ₹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
  7. 7. 800
  8. 8. 105

Area of triangles and parallelograms

  1. 1. 40
  2. 2. 6
  3. 3. 100
  4. 4. base × height → Area; 1/2 × base × height → Area; 2 × (length + width) → Perimeter; 4 × side → Perimeter; length × width → Area; all the sides added together → Perimeter
  5. 5. b) half the parallelogram's area
  6. 6. 6
  7. 7. a) at right angles to the base
  8. 8. 70

Powers and exponents

  1. 1. 16
  2. 2. d) 3⁴
  3. 3. 5
  4. 4. 36
  5. 5. 4
  6. 6. 1 → 10⁰; 10 → 10¹; 100 → 10²; 1000 → 10³; 10000 → 10⁴
  7. 7. 25
  8. 8. 1000

Symmetry

  1. 1. 3
  2. 2. 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
  3. 3. c) The letter S
  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. b) A
  7. 7. 2
  8. 8. 72

Visualising solid shapes

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

Class 7 Maths · www.arenapublications.com/learn