IGCSEMaths: CoreCIEExam QuestionsAlgebra & SequencesLinear Equations

Syllabus Edition

First teaching 2021

Last exams 2024

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Linear Equations (CIE IGCSE Maths: Core)

Exam Questions

2 hours28 questions
Easy
Medium
Hard
1
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Solve the equation  12 x minus 7 equals 23

x space equals.....................................

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2
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Solve.

7 x minus 5 space equals space 16

x space equals .................................. 

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3
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Solve.

3 w space minus space 7 space equals space 32

 w space equals ........................... 

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4
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Solve the equation 8 x space minus space 5 space equals space 7.

x space equals .............................

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5a
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Complete these statements.

When w space equals.............................. , 10 w space equals space 70.

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5b
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When 5 x space equals space 15 comma space 12 x space equals.........................

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6
Sme Calculator4 marks

Solve these equations.

i)
x plus 7 equals 15
x = .............................................. [1]
ii)
5 left parenthesis 3 x space plus space 8 right parenthesis space equals space 10
x = .............................................. [3]

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7
Sme Calculator2 marks

Solve.

8 open parentheses w plus 11 close parentheses equals 120

w = ................................................... 

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8
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Solve.

fraction numerator x minus 2 over denominator 3 end fraction equals 3

x = ................................................... 

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1
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Solve the equation.

6 minus 2 x equals 3 x

x space= .............................................

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2
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Solve.

fraction numerator 1 minus p over denominator 3 end fraction space equals space 4

p equals.......................

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3
Sme Calculator5 marks

Solve these equations.

i)
x over 3 equals 18
x equals............................[1]
ii)
5 x plus 18 equals 8
x equals...............................[2]
iii)
12 x minus 3 equals 4 x plus 21
x equals............................[2]

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4
Sme Calculator3 marks

Solve.

5 open parentheses 2 x plus 4 close parentheses equals 85

x = .................................................

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5
Sme Calculator6 marks

Solve these equations.

i)
5 x equals negative 30
x space equals space................................................. space left square bracket 1 right square bracket
ii)
4 x minus 2 equals 28
x space equals space................................................. space left square bracket 2 right square bracket
iii)
3 open parentheses 2 x plus 7 close parentheses equals 12
x space equals space................................................. space left square bracket 3 right square bracket

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6
Sme Calculator6 marks

Solve.

i)
10 x equals 5
x = ................................................... [1]
ii)
7 x minus 3 equals 2 x plus 11
x space= ................................................... [2]
iii)
3 open parentheses 2 x minus 1 close parentheses equals 27
x = ................................................... [3]

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7
Sme Calculator6 marks

Solve these equations.

i)
x over 4 equals 20
x = .............................................. [1]
ii)
3 x space minus space 5 space equals space 16
x = .............................................. [2]
iii)
5 left parenthesis 2 x space plus space 1 right parenthesis space equals space 27
x space= .............................................. [3]

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8
Sme Calculator2 marks

Solve.

3 x space minus space 2 space equals space 5 x space plus space 1

x space equals space.............................. 

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9
Sme Calculator3 marks

4 left parenthesis 5 x space plus space 7 right parenthesis space equals space 42

x space equals .............................. 

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10
Sme Calculator3 marks

Solve these equations.

i)
3 space x space equals space 18

x space equals......................... [1]

ii)
8 x minus 15 equals space 6 x plus 2

x space equals......................... [2]

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1
Sme Calculator4 marks

q6-0580-0980-w20-oct-nov-2020-cie-igcse-maths

The diagram shows a shape made from rectangles.
The shape has a total area of 517m2.

Find the value of x.

x equals.....................

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2
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Rovers, United and City are football teams.

Rovers scoredspace x spacegoals.
United scored 8 goals more than Rovers.
City scored 3 goals less than twice the number of goals scored by Rovers.

The three teams scored a total of 117 goals.

Write down and solve an equation to find the value of x.

x = ................................................. 

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3
Sme Calculator6 marks

In this part, all angles are in degrees.

qp7d-0580-33-paper-3-may-2020-cie-igcse-maths

i)
Use the information in the triangle to write down an equation in terms of x.

[1]

ii)
Solve this equation to find the value of x.
x space= ................................................. [3]
iii)
Work out the size of the smallest angle in the triangle.
[2]

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4
Sme Calculator5 marks
i)
Navja weighs a parcel with mass wkg on her scales.
She uses the masses shown to balance the scales.
qp1bi-0580-32-paper-3-march-2020-cie-igcse-maths
Work out the value of w.
w = ................................................. [3]
ii)
Sometimes Navja uses an electronic weighing machine.
The machine gives the mass, p kg, of a parcel as 12.4kg, correct to the nearest 100g.

Complete this statement about the value of p.
.................. less-than or slanted equal to p less than ................... [2]

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5
Sme Calculator2 marks

Esme buys 8 magazines at $2.45 each and y cards at $3.15 each.
Esme spends $60.55 in total.

How many cards does she buy?

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6
Sme Calculator4 marks

Cara has n pencils.
Alice has twice as many pencils as Cara.
Leon has three more pencils than Alice.
The three children have a total of 58 pencils.

Use this information to write down an equation and solve it to find the value of n.

n = ................................................... 

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7
Sme Calculator3 marks

Solve the equation 3 left parenthesis 2 x space minus space 4 right parenthesis space equals space 4 left parenthesis x space plus space 7 right parenthesis.

x space equals ...........................

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8
Sme Calculator3 marks

Neelum hires a machine to clean carpets.
It costs $25 to hire the machine for the first day and $9 for each extra day after the first day.
Neelum pays a total of $88 to hire the machine.

Work out the total number of days she hires the machine for.

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9
Sme Calculator5 marks

In this part, all measurements are in centimetres.

qp7f-0580-33-paper-3-nov-2020-cie-igcse-maths

The diagram shows a kite with sides open parentheses 2 x plus 5 close parentheses and open parentheses 3 x minus 1 close parentheses.
The perimeter of the kite is 33 cm.

Work out the length of a shorter side.

............................................ cm 

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10
Sme Calculator5 marks

A club is arranging transport for its members.

Speedy Coaches charge $625 plus $15 per member.

The total cost, in dollars, for x members is given by the expression 15 x space plus space 625.

i)
Sporty Coaches charge $117 plus $19 per member.
Write an expression for the total cost, in dollars, for xmembers.
[2]
ii)
The total cost is the same for both Speedy Coaches and Sporty Coaches.

Write down an equation and solve it to find x.
x space= .............................................. [3]

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