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O LevelAdditional MathsCambridgeExam QuestionsAlgebra & FunctionsEquations, Inequalities & Graphs

Equations, Inequalities & Graphs (Cambridge O Level Additional Maths)

Exam Questions

1 hour16 questions
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1
Sme Calculator3 marks

Solve the equation space 5 vertical line 5 x space – space 2 vertical line space – space 1 space equals space 14 space.

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2
Sme Calculator3 marks

q1b-2025-specimen-paper-2-cie-igcse-additional-maths

The diagram shows the graph of y space equals space straight f left parenthesis x right parenthesis space comma space where space straight f left parenthesis x right parenthesis space equals space 2 left parenthesis x space plus space 1 right parenthesis squared left parenthesis x space – space 1 right parenthesis .
Use the graph to solve the inequality space straight f left parenthesis x right parenthesis space less-than or slanted equal to space – 1 space.

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3a
Sme Calculator3 marks

On the axes, sketch the graph of y space equals space 5 open parentheses x plus 1 close parentheses open parentheses 3 x minus 2 close parentheses open parentheses x minus 2 close parentheses, stating the intercepts with the coordinate axes. 

q1a-june-2021-cie-igcse-additional-maths

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3b
Sme Calculator2 marks

Hence find the values of x for which 5 open parentheses x plus 1 close parentheses open parentheses 3 x minus 2 close parentheses open parentheses x minus 2 close parentheses greater than 0.

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4a
Sme Calculator3 marks

On the axes below sketch the graph of y space equals negative 3 left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis left parenthesis x plus 1 right parenthesis, showing the coordinates of the points where the curve intersects the coordinate axes.

q1-0606-m20-qp-12-additional-maths

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4b
Sme Calculator2 marks

Hence find the values of x for which negative 3 left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis left parenthesis x plus 1 right parenthesis space greater than space 0.

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5a
Sme Calculator3 marks

On the axes below, sketch the graph of y space equals space open vertical bar 5 x minus 7 close vertical bar, showing the coordinates of the points where the graph meets the coordinate axes.

q5-0606-m20-qp-22-additional-maths

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5b
Sme Calculator3 marks

Solve 5 open vertical bar space 5 x minus 7 close vertical bar space minus 1 space equals space 14.

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6a
Sme Calculator2 marks

On the axes below, sketch the graph of y space equals negative left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x minus 6 right parenthesis, showing the coordinates of the points where the graph meets the coordinate axes.

q3-0606-s20-qp-23-additional-maths

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6b
Sme Calculator2 marks

Hence solve negative left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis x minus 6 right parenthesis space less or equal than space 0.

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1
Sme Calculator3 marks

Solve the inequality open vertical bar 4 x minus 1 close vertical bar space greater than space 9.

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2
Sme Calculator3 marks

On the axes below, sketch the graph of space y space equals space open vertical bar left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis close vertical bar spaceshowing the coordinates of the points where the curve meets the axes.

q1-0606-s20-qp-12-additional-maths

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3a
Sme Calculator3 marks

q2-0606-w20-qp-12-additional-maths

The diagram shows the graph of y space equals space straight f left parenthesis x right parenthesis, where straight f left parenthesis x right parenthesis is a cubic polynomial.

Find space straight f left parenthesis x right parenthesis.

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3b
Sme Calculator2 marks

Write down the values of x such that straight f left parenthesis x right parenthesis less than 0.

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4a
Sme Calculator3 marks

On the axes below, sketch the graph of y space equals space left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis left parenthesis 3 minus x right parenthesis, stating the intercepts on the coordinate axes.

q1-0606-w20-qp-13-additional-maths

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4b
Sme Calculator2 marks

Hence write down the values of x such that left parenthesis x minus 2 right parenthesis left parenthesis x plus 1 right parenthesis left parenthesis 3 minus x right parenthesis space greater than space 0.

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5
Sme Calculator1 mark

Solve open vertical bar 3 x minus 2 close vertical bar space equals space 4 plus x .

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1
Sme Calculator3 marks

q1-2025-specimen-paper-1-cie-igcse-additional-maths

The diagram shows the graph of y space equals space vertical line straight f left parenthesis x right parenthesis vertical line, where straight f left parenthesis x right parenthesis is a cubic function.
Find the possible expressions for straight f left parenthesis x right parenthesis in factorised form.

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2a
Sme Calculator2 marks

The diagram shows the graph of a cubic curve .

q1-0606-s20-qp-11-additional-maths

Find an expression for straight f open parentheses x close parentheses.

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2b
Sme Calculator2 marks

Solve straight f left parenthesis x right parenthesis space less or equal than space 0.

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3a
Sme Calculator3 marks

Write 2 x squared space plus 3 x minus 4 in the form a left parenthesis x plus b right parenthesis squared space plus c, where a comma space b and c are constants.

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3b
Sme Calculator2 marks

Hence write down the coordinates of the stationary point on the curve y space equals space 2 x squared space plus 3 x minus 4.

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3c
Sme Calculator3 marks

On the axes below, sketch the graph of y space equals space open vertical bar 2 x squared space plus 3 x minus space 4 close vertical bar, showing the exact values of the intercepts of the curve with the coordinate axes.

q4c-0606-s20-qp-13-additional-maths

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3d
Sme Calculator1 mark

Find the value of k for which open vertical bar 2 x squared space plus 3 x minus space 4 close vertical bar equals space k has exactly 3 values of x.

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4
Sme Calculator3 marks

q1-0606-w20-qp-11-additional-maths

The diagram shows the graph of y space equals space open vertical bar straight p open parentheses x close parentheses close vertical bar , where straight p left parenthesis x right parenthesis is a cubic function. Find the two possible expressions for straight p left parenthesis x right parenthesis.

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5
Sme Calculator3 marks

Solve the inequality open vertical bar 3 x plus 2 close vertical bar space greater than space 8 plus x.

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