IGCSEMathsEdexcelMaths AHigherExam QuestionsSequences, Functions & GraphsGraphs of Functions

Graphs of Functions (Edexcel IGCSE Maths A: Higher): Exam Questions

Exam code: 4MA1

3 hours46 questions
Easy
Medium
Hard
1
Sme Calculator1 mark

Brogan needs to draw the graph of y space equals space x squared space plus space 1

Here is her graph.

q1-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down one thing that is wrong with Brogan's graph.

How did you do?

2a
Sme Calculator2 marks

Complete the table of values for  y space equals space x cubed space long dash space 4 x

x

negative 3

negative 2

negative 1

0

1

2

3

y

 

 

3

0

 

 

15

How did you do?

2b
Sme Calculator2 marks

On the grid, draw the graph of space y space equals space x cubed space long dash space 4 x space from x space equals space minus 3 space to space x space equals 3

q2-easy-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

3a
Sme Calculator2 marks

Complete the table of values for y space equals space x cubed space long dash space 3 x space plus space 1

x

negative 2

negative 1

0

1

2

y

 

3

 

 

3

How did you do?

3b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x cubed space long dash space 3 x space plus space 1 for values of x from long dash 2 space to space 2

q3-easy-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

4a
Sme Calculator2 marks

Complete the table of values for y equals space 6 over x

x

0.5

1

2

3

4

5

6

y

 

6

3

 

1.5

 

1

How did you do?

4b
Sme Calculator2 marks
q4-easy-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, draw the graph of y space equals space 6 over x space for space space 0.5 space less-than or slanted equal to space x space less-than or slanted equal to space 6

How did you do?

5a
Sme Calculator2 marks

Complete the table of values for y space equals space 4 over x

x

0.5

1

2

4

5

8

y

 

4

2

 

 

 

How did you do?

5b
Sme Calculator2 marks

On the grid, draw the graph of space y space equals space 4 over x for 0.5 space less-than or slanted equal to space x space less-than or slanted equal to space 8

q5b-easy-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

6a
Sme Calculator1 mark

The graph of y space equals space straight f left parenthesis x right parenthesis is drawn on the grid.

q6a-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the turning point of the graph.

How did you do?

6b
Sme Calculator1 mark

Write down the roots of straight f left parenthesis x right parenthesis space equals space 2

How did you do?

6c
Sme Calculator1 mark

Write down the value of space straight f left parenthesis 0.5 right parenthesis

How did you do?

7a
Sme Calculator1 mark

The graph of y space equals space straight f left parenthesis x right parenthesis is drawn on the grid.

q7a-easy-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the turning point of the graph.

How did you do?

7b
Sme Calculator1 mark

Write down estimates for the roots of space straight f left parenthesis x right parenthesis equals 0

How did you do?

7c
Sme Calculator1 mark

Use the graph to find an estimate for straight f left parenthesis 1.5 right parenthesis

How did you do?

8a
Sme Calculator2 marks

Complete the table of values for  y equals 1 over x open parentheses x squared plus 4 close parentheses

x

0.25

0.5

1

2

4

8

y

16.25

 

 

 

 

8.5

How did you do?

8b
Sme Calculator2 marks

On the grid, draw the graph of  y equals 1 over x open parentheses x squared plus 4 close parentheses for 0.25 less-than or slanted equal to x less-than or slanted equal to 8

q15b-4ma1-2h-qp-june21-paper2-igcse-maths

How did you do?

9
Sme Calculator3 marks

Here are six graphs.

q15-4ma1-2h-qp-jan20-paper2-igcse-maths

Complete the table below with the letter of the graph that could represent each given equation. Write your answers on the dotted lines.

Equation

Graph

y space equals space 2 over x squared

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

y space equals space minus space 1 half x cubed

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

y space equals space minus 5 over x

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

How did you do?

10a
Sme Calculator2 marks

The diagram shows part of a sketch of the curve space y space equals space sin space x degree

q16-paper2h-spec2016-edexcel-igcse-maths

Write down the coordinates of

(i) the point P

[1]

(ii) the point Q

[1]

How did you do?

10b
Sme Calculator2 marks

Sketch the graph of y space equals space tan space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

Show the coordinates of any points of intersection with the coordinate axes.

q16b-paper2h-spec2016-edexcel-igcse-maths

How did you do?

11a
Sme Calculator2 marks

Complete the table of values for y equals 6 over x

x

0.5

1

2

3

4

5

6

y

 

6

 

2

 

 

1

How did you do?

11b
Sme Calculator2 marks

On the grid, draw the graph of  y equals 6 over x  for 0.5 less-than or slanted equal to x less-than or slanted equal to 6

q11b-4ma1-2hr-qp-jan22-paper2-igcse-maths

How did you do?

12
Sme Calculator1 mark

Circle the point that is on the graph of y space equals space 1 over x

(–1, 1)

 (0.3, 3)

(0.8, 0.2)

(2.5, 0.4)

 

How did you do?

13
Sme Calculator1 mark

The equation of a curve is space y space equals space left parenthesis x space – space 1 right parenthesis squared space – space 6 space

Circle the coordinates of the turning point.

(–1, –6)

(1, 6)

(–1, 6)

(1, –6)

How did you do?

14
Sme Calculator1 mark

The graph of y = x3 − x2 − 2 is drawn on the grid.

q19-paper5-june2019-ocr-gcse-maths

Use the graph to solve x3 − x2 − 2 = 0.

Give your answer correct to 1 decimal place.

x = ................................................... 

How did you do?

15
Sme Calculator2 marks

Here is the graph of   y = x2 + x − 6.

q10-paper4-nov2018-ocr-gcse-maths

Use the graph to solve the equation  x2 + x − 6  = 0.

x = ................. or x = ................ 

How did you do?

16
Sme Calculator2 marks

(i) Sketch a graph on the axes that shows that y is directly proportional to x.

q4ai-paper4-spec2015-ocr-gcse-maths

[2]

(ii) Sketch a graph on the axes that shows begin mathsize 16px style y equals x cubed end style

q4aii-paper4-spec2015-ocr-gcse-maths

[2]

How did you do?

1a
Sme Calculator2 marks

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

x

negative 3

negative 2

negative 1

0

1

2

3

y

6

 

 

negative 6

 

 

 

How did you do?

1b
Sme Calculator2 marks

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

q2-medium-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

1c
Sme Calculator2 marks

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

How did you do?

2
Sme Calculator2 marks

Sketch the graph of y space equals space cos space x to the power of degree space end exponent space for space 0 space less-than or slanted equal to space x space less-than or slanted equal to space 360

q8-medium-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

3a
Sme Calculator1 mark

The diagram shows part of a sketch of the curve y space equals space sin space x to the power of ring operator.

q3-medium-2-17-graph-of-equation-edexcel-gcse-maths

Write down the coordinates of the point P.

How did you do?

3b
Sme Calculator1 mark

Write down the coordinates of the point Q.

How did you do?

4a
Sme Calculator2 marks

Complete the table of values for space y space equals space x squared minus 3 x space plus space 2

bold italic x

negative 1

0

1

2

3

4

5

bold italic y

6

 

 

 

2

 

12

How did you do?

4b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space long dash space 3 x space plus space 2 for values of x from long dash 1 space to space 5

q5-medium-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

4c
Sme Calculator2 marks

Find estimates for the solutions of the equation x squared space minus space 3 x space plus space 2 space equals space 4

How did you do?

5a
Sme Calculator2 marks

Complete the table of values for y space equals space x squared space minus space 3 x space plus 1

x

negative 2

negative 1

0

1

2

3

4

y

11

 

1

negative 1

 

1

 

How did you do?

5b
Sme Calculator2 marks

On the grid, draw the graph of y space equals space x squared space long dash space 3 x space plus space 1 for values of x spacefrom long dash 2 space to space 4

q6-medium-2-17-graph-of-equation-edexcel-gcse-maths

How did you do?

5c
Sme Calculator2 marks

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

x squared space minus space 3 x space plus 1 space equals space 3

How did you do?

6a
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?

6b
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?

6c
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?

7a
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?

7b
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?

8
Sme Calculator2 marks

The diagram shows the graph of y space equals space straight f space left parenthesis x right parenthesis for negative 4 space less-than or slanted equal to space x space less-than or slanted equal to space 12

jc9uPwkM_q18-4ma1-1hr-qp-jan20-paper1-igcse-maths

Note: Point P in the graph is from the previous question. It is not required for this question.

The equation straight f space left parenthesis x right parenthesis space equals space k has exactly two different solutions for negative 4 space less-than or slanted equal to space x space less-than or slanted equal to space 12

Use the graph to find the two possible values of k.

How did you do?

9a
Sme Calculator3 marks

Write 3 x squared space minus space 12 x space plus space 7 in the form a left parenthesis x space plus space b right parenthesis squared space plus space c

How did you do?

9b
Sme Calculator1 mark

The line bold L is the line of symmetry of the curve with equation y space equals space 3 x squared space minus space 12 x space plus space 7

Using your answer to part (a) or otherwise, write down an equation of bold L.

How did you do?

10
Sme Calculator1 mark

Circle the point that lies on the curve  y space equals space x squared space – space 4 x space plus space 1

(–1, 4)

(–1, –4)

(–1, –2)

(–1, 6)

How did you do?

11a
Sme Calculator1 mark

Here is a sketch of space y space equals space cos space x spacefor values of x from 0° to 360°

q27-paper-1h-nov-2018-aqa-gcse-maths

alpha degree is an acute angle.

cos space alpha degree space equals space k

Circle the value of cos space left parenthesis 180 degree space – space alpha degree right parenthesis

1 space – space k

k

– k

– 1 space – space k

How did you do?

11b
Sme Calculator1 mark

Circle the value of cos spaceleft parenthesis 360 degree space plus space alpha degree right parenthesis

k space – space 1

k space plus space 1

– k

k

How did you do?

12a2 marks

Complete the table of values for y space equals space x squared space space – space x space – space 4

x

-3

-2

-1

0

1

2

3

y

2

-4

How did you do?

12b2 marks

On the grid below, draw the graph ofy space equals space x squared space space – space x space – space 4 for values of x from –3 to 3

Grid graph with x and y axes ranging from -5 to 10 vertically and -3 to 3 horizontally, with labelled integer increments and positive arrows.

How did you do?

13a
Sme Calculator2 marks

Complete the table of values for y equals x cubed minus 3 x plus 1

x

-2

-1

0

1

2

y

-1

How did you do?

13b2 marks

On the grid, draw the graph of y equals x cubed minus 3 x plus 1 for values of x from − 2 to 2

A graph with x-axis and y-axis ranging from -4 to 6, featuring a grid with labelled increments, used for plotting mathematical data.

How did you do?

13c1 mark

Here are four graphs.

Four graphs labeled A, B, C, and D show hyperbolic functions on xy-axes. Each has an origin marked O; curves shift across quadrants differently.

Write down the letter of the graph that could have the equation y equals negative 1 over x squared

    Choose your answer

    1a
    Sme Calculator    2 marks

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

    x

    negative 2

    negative 1

    0

    1

    2

    3

    4

    y

     

    3

    0

     

     

    3

     

    How did you do?

    1b
    Sme Calculator    2 marks

    On the grid, draw the graph of space y equals space x squared long dash space 2 x spacefor values of x from long dash 2 space to space 4

    q3-hard-2-17-graph-of-equation-edexcel-gcse-maths

    How did you do?

    1c
    Sme Calculator    2 marks

    Solve  x squared minus 2 x minus 2 equals 1

    How did you do?

    2a
    Sme Calculator    2 marks

    Complete the table of values for y space equals space x squared long dash space 2 x long dash space 1

    x

    negative 2

    negative 1

    0

    1

    2

    3

    4

    y

    7

     

     

    negative 2

    negative 1

     

     

    How did you do?

    2b
    Sme Calculator    2 marks

    On the grid, draw the graph of  y space equals space x squared long dash space 2 x long dash space 1 for values of x from long dash 2 space to space 4

    q4-hard-2-17-graph-of-equation-edexcel-gcse-maths

    How did you do?

    2c
    Sme Calculator    2 marks

    Solve   x squared space minus space 2 x space minus 1 space equals x plus 3

    How did you do?

    3a
    Sme Calculator    3 marks

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

    q5-hard-2-17-graph-of-equation-edexcel-gcse-maths

    Use the graph to find estimates for the solutions of

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

    [1]

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

    [2]

    How did you do?

    3b
    Sme Calculator    3 marks

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

    table row cell y space end cell equals cell space x squared space long dash space 4 x space long dash space 2 end cell row blank blank blank row cell x space plus space y space end cell equals 6 end table

    How did you do?

    4a
    Sme Calculator    2 marks

    Complete the table of values for y space equals space x cubed – space 2 x squared – space 3 x space plus space 4

    x

    -2

    -1

    -0.5

    0

    1

    1.5

    2

    3

    y

     

     

    4.875

    4

     

    -1.625

     

     

    How did you do?

    4b
    Sme Calculator    2 marks

    On the grid, draw the graph of y space equals space x cubed – space 2 x squared – space 3 x space plus space 4  for values of x from –2 to 3

    q14b-paper2h-june2018-edexcel-igcse-maths

    How did you do?

    4c
    Sme Calculator    4 marks

    By drawing a suitable straight line on the grid, find estimates for the solutions of the equation x to the power of 3 space end exponent – space 2 x squared space – space x space plus space 1 space equals space 0

    Give your solutions correct to 1 decimal place.

    How did you do?

    5
    Sme Calculator    4 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?

    6a
    Sme Calculator    3 marks

    Express 7 space plus space 12 x space – space 3 x squared in the form a space plus space b left parenthesis x space plus space c right parenthesis squared where a comma space b andspace c spaceare integers.

    How did you do?

    6b
    Sme Calculator    1 mark

    bold C is the curve with equationspace y space equals space 7 space plus space 12 x space – space 3 x squared space

    The point A is the maximum point on bold C

    Use your answer to part (a) to write down the coordinates of A

    How did you do?

    7a
    Sme Calculator    2 marks

    Complete the table of values for y space equals space 1 half space x cubed space – space 2 x space plus space 3

    x

    – 3

    –2

    – 1

    0

    1

    2

    3

    y

    – 4.5

     

     

    3

     

    3

     

    How did you do?

    7b
    Sme Calculator    2 marks

    On the grid, draw the graph of y space equals space 1 half space x cubed space – space 2 x space plus space 3 space for space – 3 space less-than or slanted equal to space x space less-than or slanted equal to space 3

    q18b-paper2hr-nov2020-edexcel-igcse-maths

    How did you do?

    7c
    Sme Calculator    2 marks

    By drawing a suitable straight line on the grid, find an estimate for the solution of the equation 1 half space x cubed space – space x space plus space 4 space equals space 0

    x space equals............................................ 

    How did you do?

    8
    Sme Calculator    1 mark

    The curve bold C has equation y space equals space 3 space – space 5 left parenthesis x space plus space 1 right parenthesis squared
    The point A is the maximum point on bold C.

    Write down the coordinates of A.

    How did you do?

    9
    Sme Calculator    6 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?

    10a
    Sme Calculator    1 mark

    The curve C has equation y space equals space straight f left parenthesis x right parenthesis where straight f left parenthesis x right parenthesis space equals space 9 space – space 3 left parenthesis x space plus space 2 right parenthesis squared

    The point A is the maximum point on bold C.

    Write down the coordinates of A.

    How did you do?

    10b
    Sme Calculator    1 mark

    The curve bold C is transformed to the curve bold S by a translation of open parentheses table row 4 row 0 end table close parentheses Find an equation for the curve bold S.

    How did you do?

    10c
    Sme Calculator    1 mark

    The curve bold C is transformed to the curve bold T.

    The curve bold T has equation y space equals space 3 left parenthesis x space plus space 2 right parenthesis squared – space 9

    Describe fully the transformation that maps curve bold C onto curve bold T.

    How did you do?

    11a
    Sme Calculator    3 marks

    Write x squared space plus space 4 x space minus space 16 in the form open parentheses x space plus space a close parentheses squared space minus space b.

    How did you do?

    11b
    Sme Calculator    3 marks

    Sketch the graph of begin mathsize 16px style y space equals space x squared space plus space 4 x space minus space 16 end style , showing clearly the coordinates of any turning points.

    q18b-paper5-nov2018-ocr-gcse-maths

    How did you do?

    12a
    Sme Calculator    3 marks

    Write  begin mathsize 16px style x squared minus 10 x plus 22 end style  in the form  open parentheses x minus a close parentheses squared minus b.

    How did you do?

    12b
    Sme Calculator    4 marks

    Sketch the graph of y equals x squared minus 10 x plus 22 .

    Show clearly the coordinates of any turning points and the value of the y-intercept.

    q19b-paper5-nov2020-ocr-gcse-maths

    How did you do?

    13a
    Sme Calculator    2 marks

    The graph of y space equals space 2 x squared space plus space 3 x space minus space 9 is drawn below.

    q19-paper6-nov2020-ocr-gcse-maths

    Use the graph to solve 2 x squared space plus space 3 x space minus space 9 space equals space 0.

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

    How did you do?

    13b
    Sme Calculator    2 marks

    The equation 2x2 + x − 4 = 0 can be solved by finding the intersection of the graph of y = 2x2 + 3x − 9  and the line y = ax + b.

    (i) Find the value of a and the value of b.

    table row a equals cell space............................. space space end cell row b equals cell.............................. open square brackets 2 close square brackets end cell end table

    (ii) Hence use the graph to solve the equation 2x2 + x − 4 = 0.

    x = ............................ or x = ............................[3]

    How did you do?

    14a
    Sme Calculator    3 marks

    Sketch the graph of begin mathsize 16px style y equals open parentheses x minus 2 close parentheses squared minus 3 end style. Show the coordinates of any turning points.

    q19a-paper5-june2017-ocr-gcse-maths

    How did you do?

    14b
    Sme Calculator    5 marks

    The sketch shows part of a graph which has equation begin mathsize 16px style y equals a x squared plus b x plus c end style.

    q19b-paper5-june2017-ocr-gcse-maths

    Find the values of space a comma space b spaceand begin mathsize 16px style c end style.

    a space equals space....................................... space b space equals space....................................... c space equals space....................................... space

    How did you do?

    156 marks

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

    Cartesian coordinate plane with horizontal x-axis and vertical y-axis intersecting at origin O. Axes are labelled with arrows pointing right and up.

    How did you do?

    16a2 marks

    The diagram shows part of a sketch of the curve y equals sin space x degree

    Graph of a wave-like curve intersecting the x-axis at points P and Q, with axes labelled x and y, starting at origin O.

    Write down the coordinates of
    (i) the point P

    (ii) the point Q

    How did you do?

    16b2 marks

    Sketch the graph of y space equals space tan space x spacefor 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

    Show the coordinates of any points of intersection with the coordinate axes.

    Cartesian coordinate plane with horizontal x-axis and vertical y-axis intersecting at origin O, labelled with x and y.

    How did you do?

    173 marks

    Here are 6 graphs

    Grid with six graphs labelled A to F. Graphs depict various functions, each with x and y axes. Functions vary from smooth curves to discontinuous forms.

    Complete the table below with the letter of the graph that could represent each given equation.

    Write your answers on the dotted lines.

    Equation

    Graph

    y equals sin x

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

    y equals negative 3 over x

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

    y equals 4 x cubed minus 5 x

    ...........

    How did you do?