IGCSEMaths: ExtendedCIEExam Questions2. Algebra & Graphs2.14 Quadratic Graphs

Syllabus Edition

First teaching 2021

Last exams 2024

|

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.

How did you do?

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.

How did you do?

Did this page help you?

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

How did you do?

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.

How did you do?

Did this page help you?

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      

How did you do?

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

How did you do?

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

How did you do?

Did this page help you?

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  

How did you do?

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

How did you do?

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

How did you do?

Did this page help you?

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.

How did you do?

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.

How did you do?

Did this page help you?

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

How did you do?

Did this page help you?

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]

How did you do?

Did this page help you?

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.

How did you do?

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

How did you do?

Did this page help you?

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.

How did you do?

Did this page help you?

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.
 

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

How did you do?

Did this page help you?

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 ..................................................

How did you do?

Did this page help you?

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....................

How did you do?

Did this page help you?

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  

How did you do?

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

How did you do?

3c
Sme Calculator2 marks

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

How did you do?

Did this page help you?

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

How did you do?

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

How did you do?

Did this page help you?

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

How did you do?

Did this page help you?

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

How did you do?

Did this page help you?