IGCSEMaths: ExtendedCIEExam QuestionsCoordinate Geometry & GraphsQuadratic Graphs

Syllabus Edition

First teaching 2023

First exams 2025

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Quadratic Graphs (CIE IGCSE Maths: Extended)

Exam Questions

1 hour16 questions
Medium
Hard
Very Hard
1a
Sme Calculator1 mark

The graph of y equals 10 minus 8 x squared for  negative 1.5 less or equal than x less or equal than 1.5  is drawn on the grid.

cie-igcse-2018-may-jun-1-7

Write down the equation of the line of symmetry of the graph.

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1b
Sme Calculator3 marks

On the grid, draw the tangent to the curve at the point where x equals 0.5.
Find the gradient of this tangent.

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2a
Sme Calculator2 marks

The diagram shows part of the graph of  y space equals space x squared space minus space 2 x space plus space 3

q3-2-14-medium-cie-igcse-maths-extended

By drawing a suitable straight line, use your graph to find estimates for the solutions of x squared space minus space 3 x space minus space 1 space equals space 0

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2b
Sme Calculator3 marks

P is the point on the graph of y space equals space x squared space minus space 2 x space plus space 3 where x space equals space 2

Calculate an estimate for the gradient of the graph at the point P.

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3a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared space minus space x space minus space 6

x -3 -2 -1 0 1 2 3
y 6     -6      

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3b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space minus space x space minus space 6 for values of x from negative 3 to 3

q4b-2-14-medium-cie-igcse-maths-extended

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3c
Sme Calculator2 marks

Use your graph to find estimates of the solutions to the equation x squared space minus space x space minus space 6 space equals space minus 2

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4a
Sme Calculator1 mark

Complete the table of values for y space equals space x squared space – space 5 x space plus space 6

x 0 1 2 3 4 5
y 6   0 0 2  

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4b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space – space 5 x space plus space 6 space for space 0 space less-than or slanted equal to space x space less-than or slanted equal to space 5

q6b-paper1h-jan2019-edexcel-igcse-maths

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4c
Sme Calculator3 marks

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

x squared space – space 5 x space equals space x space – space 7

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5a
Sme Calculator2 marks

Part of the graph ofspace y space equals space 2 x squared minus space 4 x space minus space 1 space is shown on the grid.

q21-4ma1-2h-qp-jan22-paper2-igcse-maths

Use the graph to find estimates for the solutions of the equation 2 x to the power of 2 space end exponent minus space 4 x space minus space 1 space equals space 0

Give your solutions correct to one decimal place.

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5b
Sme Calculator3 marks

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation x to the power of 2 space end exponent minus space x space minus space 1 space equals space 0

Show your working clearly.

Give your solutions correct to one decimal place.

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1
Sme Calculator4 marks

cie-igcse-2020-oct-nov-p4-tz1-q10a

 The diagram shows a sketch of the curve  y space equals space x to the power of 2 space end exponent space plus space 3 x space minus space 4.

Find the coordinates of the points A, B and C.

   

A (.............. , ..............)


B (.............. , ..............)


C (.............. , ..............)

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2
Sme Calculator5 marks
i)
Factorise  24 space plus space 5 x space minus space x squared.
  
[2]
ii)
The diagram shows a sketch of  y space equals space 24 space plus space 5 x space minus space x squared.
 
cie-igcse-2020-oct-nov-p4-tz3-q7a
 
Work out the values of a, b and c.
 
a space equals ................................................     
 
b space equals ................................................     
 
space c space equals space................................................ [3]

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3a
Sme Calculator2 marks
Write  x squared plus 10 x plus 14  in the form  open parentheses x plus a close parentheses squared space plus b.

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3b
Sme Calculator3 marks

Sketch the graph of  y equals x squared plus 10 x plus 14,  indicating the coordinates of the turning point.

cie-igcse-2020-may-june-p4-tz1-q9

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4
Sme Calculator2 marks

cie-igcse-2020-may-jun-p4-tz2-q9ci

On the diagram,

Sketch the graph of space y equals open parentheses x minus 1 close parentheses squared.

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5
Sme Calculator4 marks

Find the turning point of  y space equals space x squared space plus space 4 x space minus space 3  by completing the square.
 

( ...................... , .....................)

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1
Sme Calculator1 mark

The curve  y equals x squared minus 2 x plus 1  is drawn on a grid.
A line is drawn on the same grid.
The points of intersection of the line and the curve are used to solve the equation  x squared minus 7 x plus 5 equals 0.

Find the equation of the line in the form  y equals m x plus c.


y equals ..................................................

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2
Sme Calculator3 marks

The graph of space y equals x squared minus x plus 1 space is shown on the grid.

cie-igcse-2020-may-jun-p4-tz3-q12b

By drawing a suitable line on the grid, solve the equation space x squared minus 2 x minus 2 equals 0.
 

x equals.................... or x equals....................

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3a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared space minus space 2 x

x -2 -1 0 1 2 3 4
y   3 0     3  

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3b
Sme Calculator2 marks

On the grid, draw the graph of y = x2 – 2x for values of x from –2 to 4

q3b-2-14-very-hard-cie-igcse-maths-extended

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3c
Sme Calculator2 marks

Solve x squared space minus space 2 x space minus space 2 space equals space 1

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4a
Sme Calculator3 marks

The diagram shows the graph of y space equals space x squared space minus space 4 x space minus space 2

q4a-2-14-very-hard-cie-igcse-maths-extended

Use the graph to find estimates for the solutions of

i)    x squared space minus space 4 x space minus space 2 space equals space 0

ii)    x squared space minus space 4 x space minus space 6 space equals space 0

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4b
Sme Calculator3 marks

Use the graph to find estimates for the values of x that satisfy the simultaneous equations

space space space space space space space space space y space equals space x squared space minus space 4 x space minus space 2 x space plus space y space equals space 6

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5
Sme Calculator4 marks

The curve bold space bold italic C bold spacehas equation y space equals space 4 left parenthesis x space minus space 1 right parenthesis squared space minus space a space   where a space greater than space 4

Using the axes below, sketch the curve bold italic C.
On your sketch show clearly, in terms of a,

i)
the coordinates of any points of intersection of bold italic C with the coordinate axes,

ii)
the coordinates of the turning point.
q20ii-4ma1-1h-qp-jan20-paper1-igcse-maths

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6
Sme Calculator6 marks

The curve C has equation y space equals space x squared space – space 6 x space plus space 4

Using the axes below, sketch the curve C.
On your sketch show clearly

i)
the exact coordinates of any points of intersection of C with the coordinate axes,

ii)
the coordinates of the turning point.

q21-paper1h-spec2016-edexcel-igcse-maths

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