GCSEMathsEdexcelHigherExam Questions2. AlgebraSolving Inequalities

Solving Inequalities (Edexcel GCSE Maths: Higher)

Exam Questions

3 hours51 questions
Easy
Medium
Hard
1a
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Solve 14 n space greater than space 11 n space plus space 6

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1b
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On the number line below, show the set of values of x for which negative 2 space less than space x space plus space 3 space less-than or slanted equal to space 4

q1b-easy-2-21-solving-inequalities-edexcel-gcse-maths

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2a
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n is an integer.

   negative 1 space less-than or slanted equal to n less than 4 List the possible values of n.

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2b
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uLKgU9wj_q2b-easy-2-21-solving-inequalities-edexcel-gcse-maths

Write down the inequality shown in the diagram.

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2c
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Solve        space space y space minus 2 space greater than space 5

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3a
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negative 3 space less than space n space less-than or slanted equal to space 1

n is an integer.

Write down all the possible values of n.

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3b
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Solve the inequality space 3 p minus 7 greater than 11

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4
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Solve    3 x minus 5 space less than space 16

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5a
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Show the inequality x space less than space 3 on the number line below

q5a-easy-2-21-solving-inequalities-edexcel-gcse-maths

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5b
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Solve the inequality     4 x space minus 7 space greater-than or slanted equal to 13

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6a
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Solve the inequality  6 y space plus space 5 space greater than space 8

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6b
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Here is an inequality, in x, shown on a number line.

q6b-easy-2-21-solving-inequalities-edexcel-gcse-maths

Write down the inequality.

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7
Sme Calculator2 marks

negative 4 space less-than or slanted equal to space 2 y space less than space 6

y is an integer.

Write down all the possible values of y.

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8a
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Solve the inequalities  – 7 space less-than or slanted equal to space 2 x space – space 3 space less than space 5

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8b
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On the number line, represent the solution set to part a).

q9ii-4ma1-1h-qp-nov21-paper1-igcse-maths

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9
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Solve the inequality      5 x minus 7 less-than or slanted equal to 2

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10a
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n is an integer. Write down all the values of n such thatspace – 2 space less-than or slanted equal to space n space less than space 3

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10b
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On the number line, represent the inequality y space less-than or slanted equal to space 1

q1b-4ma1-1hr-qp-jan22-paper1-igcse-maths

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11
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Solve 5 left parenthesis x space plus space 3 right parenthesis space less than space 60

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12
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Solve  – 3 x space greater than space 6

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13
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Circle the inequality shown by the diagram.

q1-paper3h-nov2017-aqa-gcse-maths

– 4 space less-than or slanted equal to space x space less than space 5

– 4 space less-than or slanted equal to space x space less-than or slanted equal to space 5

– 4 space less than space x space less than space 5

– 4 space less than space x space less-than or slanted equal to space 5

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14
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Here is a sketch of y space equals space straight f left parenthesis x right parenthesis where space straight f left parenthesis x right parenthesis spaceis a quadratic function. The graph intersects the x-axis where space x space equals space – 2.5 spaceand x space equals space 1

q21-paper3h-june2017-aqa-gcse-maths

Circle the solution of straight f left parenthesis x right parenthesis space greater than space 0

x space less than space – 2.5 space or space x space greater than space 1

x space greater than space – 2.5 space or space x space greater than space 1

– 2.5 space less than space x space less than space 1

x space greater than space – 2.5 space or space x space less than space 1

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15
Sme Calculator2 marks

Solve the inequality.

3 x minus 2 greater than 10

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16
Sme Calculator1 mark

Write down the largest integer that satisfies 5 x space minus space 1 space less than space 10.

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1a
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negative 2 space less than space n space less-than or slanted equal to 3

Represent this inequality on the number line.

q1a-medium-2-21-solving-inequalities-edexcel-gcse-maths

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1b
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Solve the inequality 8 x minus 3 space greater-than or slanted equal to space 6 x space plus space 4

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2a
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negative 5 space less than space y space less-than or slanted equal to 0

y is an integer.

Write down all the possible values of y.

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2b
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Solve    6 open parentheses x minus 2 close parentheses space greater than 15

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3a
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m is an integer such that  long dash 2 space less than space m space less-than or slanted equal to space 3

Write down all the possible values of m.

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3b
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Solve   7 x space minus 9 space less than space 3 x plus 4

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4a
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Solve 6 x space plus space 4 space greater than space x plus 17

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4b
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n is an integer with long dash 5 space less than space 2 n space less-than or slanted equal to space 6

Write down all the values of n

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5a
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On the number line, show the inequality – 2 space less-than or slanted equal to space y space less than space 1

q3a-4ma1-1hr-qp-jan21-paper1-igcse-maths

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5b
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n is an integer.

Write down all the values of n that satisfy – 3.4 space less than space n space less-than or slanted equal to space 2

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6a
Sme Calculator1 mark
q1a-paper2hr-june2019-edexcel-igcse-maths

Write down the inequality shown on the number line.

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6b
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Solve the inequality 4 y space minus space 13 space less-than or slanted equal to space y space plus space 8

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7a
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Solve the inequality  7 t space minus 8 less or equal than space 2 t plus 7

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7b
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On the number line below, represent the solution set of the inequality solved in part (a).

q5cii-4ma1-2h-qp-jan21-paper2-igcse-maths

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8
Sme Calculator2 marks

Solve the inequality 7 t space – space 3 space less-than or slanted equal to space 2 t space plus space 31

Show your working clearly.

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9
Sme Calculator3 marks

Solve the inequality 3 x space plus space 15 space less than space 8 x space plus space 3

Show clear algebraic working.

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10
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Solve the inequality 2 q space greater-than or slanted equal to space 31 space – space 3 q

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11
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Solve  4 greater than 11 minus x over 3

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12
Sme Calculator3 marks

x is an integer.

– 4 space less than space x space less-than or slanted equal to space 2

and

2 space less-than or slanted equal to space x space plus space 3 space less than space 9

Work out all the possible values of x.

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13
Sme Calculator2 marks

Solve  8 space greater than space 3 space minus space 1 half x

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14
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Solve 7 x space plus space 6 space greater than space 1 space plus space 2 x

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15
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Here is the graph of space y space equals space straight f left parenthesis x right parenthesis space where straight f left parenthesis x right parenthesis is a quadratic function.

q29-paper3h-nov2017-aqa-gcse-maths

Write down all the integer solutions of f left parenthesis x right parenthesis space greater-than or slanted equal to space 0

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16a
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Solve  5 x plus 6 greater than 3 x plus 15

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16b
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Write down the inequality represented by the number line.

q8b-paper-1h-nov-2021-aqa-gcse-maths

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17
Sme Calculator1 mark

m to the power of 2 space end exponent greater than space 9

Circle the possible value of m.

2 begin inline style 7 over 8 end style

2.8

3

negative 7 over 2

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18
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Solve  3 x plus 4 less than 19.

Show your solution on the number line.

q2-paper6-nov2020-ocr-gcse-maths

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19
Sme Calculator4 marks

Solve 3 x minus 5 greater-than or slanted equal to 10

Show your solution on the number line.

q1-paper6-nov2019-ocr-gcse-maths

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20
Sme Calculator3 marks

Gemma’s solution to the inequality 3 x space plus space 1 space greater than space minus space 5

q2-paper5-june2018-ocr-gcse-maths

Is Gemma’s solution correct?
Explain your reasoning.

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21
Sme Calculator3 marks

Solve.

   5 x space plus space 1 space greater than space x space plus space 13

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1
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Solve the inequality x squared space greater than space 3 left parenthesis x space plus space 6 right parenthesis

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2
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Solve   x squared space greater than space 3 x plus 4

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3
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Solve   2 x squared space plus space 3 x minus space 2 space greater than space 0

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4
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n is an integer such that 3 n plus 2 less-than or slanted equal to space 14 space and space fraction numerator 6 n over denominator n squared plus 5 end fraction space greater than 1

Find all the possible values of n.

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5
Sme Calculator4 marks

Solve the inequality 4 x squared space – space 5 x space – space 6 space greater than space 0

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6a
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Solve x squared space space plus space 2 x space greater than space 6 x space plus space 5

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6b
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Represent your solution set to part (a) on the number line below.

q17b-paper1h-spec2016-edexcel-igcse-maths

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7
Sme Calculator5 marks

Here is a rectangle.

q22-4ma1-2h-qp-jan22-paper2-igcse-maths

Given that the area of the rectangle is less than 75 space cm squared
find the range of possible values of x

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8
Sme Calculator3 marks

Solve the inequality 5 y squared space minus space 17 y space less-than or slanted equal to space 40

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9
Sme Calculator5 marks

The diagram shows a rectangle.

q17-paper2h-nov2020-edexcel-igcse-maths

The area of the rectangle is A cm squared
Given that A less than space 3 x plus 27
find the range of possible values for x.

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10
Sme Calculator3 marks

Here is a sketch of the curve    y equals x squared plus 4 x minus 12

q24-paper-2h-june-2019-aqa-gcse-maths

Work out the values of x for which    x squared space plus space 4 x space – space 12 space less than space 0

Give your answer as an inequality.

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11
Sme Calculator3 marks

Here are two inequalities.

– 2 space less-than or slanted equal to space x space less-than or slanted equal to space 3
9 space less-than or slanted equal to space x space plus space y space less-than or slanted equal to space 11

x and y are integers.
Work out the greatest possible value of y space – space x

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12
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Martha’s solution to the inequality 8 x plus 5 less-than or slanted equal to 3 x minus 10 is shown on the number line.

q9-paper6-june2019-ocr-gcse-maths

Is her solution correct?
Explain your reasoning.

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13
Sme Calculator4 marks

Solve the inequality.

   x squared minus space 5 x space minus space 6 less-than or slanted equal to 0

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14
Sme Calculator3 marks

Find the interval for which x squared space minus space 7 x space plus space 10 space less-than or slanted equal to space 0.

.......................... less-than or slanted equal to space x space less-than or slanted equal to ..........................

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