GCSEFurther MathsAQAExam Questions2. Algebra & FunctionsSolving Inequalities

Solving Inequalities (AQA GCSE Further Maths): Exam Questions

Exam code: 8365

41 mins13 questions
Medium
Hard
Very Hard
1a
Sme Calculator1 mark

Circle the solution of – 3 x less than – 18

x greater than – space 6 space space space space space space space space space space space space space space space space space x less than – space 6 space space space space space space space space space space space space space space space space space space x greater than 6 space space space space space space space space space space space space space space space space space space x less than 6

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1b
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Circle the solution of x squared greater or equal than 16

x greater or equal than – 4 space or space x less or equal than 4 space space space space space space space space space space space space space space space space space space space space x less or equal than – 4 space or space x greater or equal than 4

x greater or equal than – 4 space or space x greater or equal than 4 space space space space space space space space space space space space space space space space space space space space x less or equal than – 4 space or space x less or equal than 4

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2
Sme Calculator3 marks

Solve 2 x squared plus 4 greater than left parenthesis 2 x – 3 right parenthesis left parenthesis x plus 1 right parenthesis

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3
Sme Calculator2 marks

Work out the smallest integer value of x that satisfies the inequality 8 – 5 x less than 26

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4
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Write down the range of values for x for which left parenthesis 2 x plus 3 right parenthesis left parenthesis x – 2 right parenthesis less than 0

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5
Sme Calculator3 marks

Work out all the integer values of x for which

– 5 less than 4 x plus 3 less or equal than 13

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1
Sme Calculator3 marks

Work out the integer values of x for which x squared minus 20 x plus 96 less than 0

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2
Sme Calculator3 marks

Work out the range of values of x for which 25 x squared greater or equal than 16

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3
Sme Calculator3 marks

Work out the range of values of x for which

x squared – 11 plus 28 greater than 0

You must show your working.

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4
Sme Calculator4 marks

Work out the range of values of m for which

3 m open parentheses 4 m plus 1 close parentheses less or equal than 5 m plus 2

You must show your working.

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5
Sme Calculator3 marks

The graph of y equals open parentheses 4 minus x close parentheses open parentheses 1 plus x close parentheses is shown below.

The graph of y = (4-x)(1+x). The points of intersection of the graph with the x-axis are labelled A and B.

Use this graph to work out the range of values of x for which

4 plus 3 x less than x squared

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1
Sme Calculator4 marks

A small stone is kicked off the ground and flies through the air.

The vertical movement of the stone is given by the equation

h equals 12 t minus 5 t squared

where h is the vertical height of the stone above the ground (in metres) and t is the time after being kicked (in seconds).

By forming and solving a suitable inequality, find the range of time, t, for which the stone is above a vertical height of 4 metres.

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2
Sme Calculator6 marks

A rectangular picture frame has a height of x cm and a width of y cm.

The total perimeter of the frame is 120 cm.

If the area of the frame must be less than 800 cm2, form and solve an inequality in terms of x to find the range of values the height can take.

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3
Sme Calculator4 marks

Work out the range of values of p for which

open parentheses p plus 2 close parentheses cubed greater or equal than 17 plus p open parentheses p plus square root of 3 close parentheses open parentheses p minus square root of 3 close parentheses

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