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GCSEMathsOCRHigherExam Questions7. Graphs of Equations & FunctionsGraphs of Functions

Graphs of Functions (OCR GCSE Maths: Higher)

Exam Questions

3 hours49 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.

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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

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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

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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

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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

 

 

 

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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

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6
Sme Calculator2 marks

Sketch the graph of y = 3x

Give the value of the y-intercept.

q17-paper4-nov2019-ocr-gcse-maths

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7
Sme Calculator2 marks

Shirley is asked to sketch a graph of  y = 5x for x > 0

She produces the following.

q13-paper5-june2019-ocr-gcse-maths

The graph has two errors.

How should they be corrected?

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8
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 = ...................................................

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9
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 = ................

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10
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 y equals x cubed

q4aii-paper4-spec2015-ocr-gcse-maths

[2]

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11a
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

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11b
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

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12
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

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

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13a
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

ii) the point Q

[2]

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13b
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

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14a
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?

14b
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

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15
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)

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16
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)

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1a
Sme Calculator2 marks

Complete the table of values for y space equals space 2 to the power of x

x

negative 2

negative 1

0

1

2

3

y

0.25

 

 

2

 

 

How did you do?

1b
Sme Calculator2 marks

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

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

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2a
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?

2b
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?

2c
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

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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.

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3b
Sme Calculator1 mark

Write down the coordinates of the point Q.

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4
Sme Calculator3 marks

Here are some graphs.

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

In the table below, match each equation with the letter of its graph.

Equation 

Graph

y space equals space sin space x

 

y space equals space x cubed space plus space 4 x

 

y space equals space 2 to the power of x

 

y space equals space 4 over x

 

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5a
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?

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 2 for values of x from long dash 1 space to space 5

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

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5c
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

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6a
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?

6b
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

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6c
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

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7a
Sme Calculator2 marks
q7-medium-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, draw the graph of space x squared space plus y squared space equals space 4

How did you do?

7b
Sme Calculator2 marks
Ox~7ekor_q7b-medium-2-17-graph-of-equation-edexcel-gcse-maths

On the grid, sketch the graph of y space equals space cos space x space for space 0 to the power of degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 to the power of degree

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8
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

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9
Sme Calculator2 marks

Sketch the graph of y space equals sin space x for 0 degree less than x less than 360 degree

q13a-paper5-nov2020-ocr-gcse-maths

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10a
Sme Calculator2 marks

The number of gannets on an island is assumed to follow this exponential growth model.

N = 0.45 × 1.07x

N is the number of gannets, in thousands.
x is the number of years after 1st January 2010.

Complete the table for N = 0.45 × 1.07x.

x

0

5

10

15

20

N

0.45

0.63

 

1.24

 

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10b
Sme Calculator2 marks

Draw the graph of straight N space equals space 0.45 space cross times 1.07 to the power of straight x

q21b-paper4-nov2018-ocr-gcse-maths

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10c
Sme Calculator2 marks

Use the graph to find the year when the gannet population is predicted to reach 1000.

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11a
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?

11b
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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12a
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?

12b
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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12c
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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13a
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

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13b
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.

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14
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)

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15a
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

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15b
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

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1a
Sme Calculator2 marks

On the grid, construct the graph of x squared space plus space y squared space equals space 16

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

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1b
Sme Calculator3 marks

Find estimates for the solutions of the simultaneous equations

table row cell x squared space plus space y squared space end cell equals cell space 16 end cell row cell y space end cell equals cell space 2 x plus 1 end cell end table

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2a
Sme Calculator2 marks

On the grid, draw the graph of x squared space plus space y squared space equals space 12.25

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

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2b
Sme Calculator3 marks

Hence find estimates for the solutions of the simultaneous equations

table row cell x squared space plus space y squared space end cell equals cell space 12.25 end cell row cell 2 x plus y end cell equals 1 end table

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3a
Sme Calculator2 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?

3b
Sme Calculator2 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

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3c
Sme Calculator2 marks

Solve  x squared minus 2 x minus 2 equals 1

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4a
Sme Calculator2 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?

4b
Sme Calculator2 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?

4c
Sme Calculator2 marks

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

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5a
Sme Calculator3 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?

5b
Sme Calculator3 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

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6a
Sme Calculator2 marks

Construct the graph of space x squared space plus space y squared space equals space 9

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

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6b
Sme Calculator3 marks

By drawing the line x space plus space y space equals space 1 on the grid, solve the equations x squared space plus space y squared space equals space 9 x space plus space y space equals 1

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7a
Sme Calculator2 marks
q8-hard-2-17-graph-of-equation-edexcel-gcse-maths

The graph of y space equals space k to the power of x, where k is a positive constant, is shown above.

Find the value of k.

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7b
Sme Calculator2 marks
q8b-hard-2-17-graph-of-equation-edexcel-gcse-maths

The graph of space y equals space sin space x degree space for values of x from space long dash 270 space to space plus 270 space is shown above.

On the same axes, draw the graph of y space equals space 1 space long dash space sin space x degree for values of x from long dash 270 space to space plus 270

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8a
Sme Calculator3 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?

8b
Sme Calculator4 marks

Sketch the graph of begin mathsize 16px style y equals x squared minus 10 x plus 22 end style .

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

q19b-paper5-nov2020-ocr-gcse-maths

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9a
Sme Calculator2 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............................ space

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9b
Sme Calculator2 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.............................. space left square bracket 2 right square bracket end cell end table

ii)table row blank row blank end tableHence use the graph to solve the equation 2x2 + x − 4 = 0. x = ............................ or x = ............................[3]

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10a
Sme Calculator3 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

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10b
Sme Calculator5 marks

The sketch shows part of a graph which has equation y equals a x squared plus b x plus c.

q19b-paper5-june2017-ocr-gcse-maths

Find the values of space a comma space b spaceand c.

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

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11a
Sme Calculator3 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.

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11b
Sme Calculator3 marks

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

q18b-paper5-nov2018-ocr-gcse-maths

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12
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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13a
Sme Calculator3 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?

13b
Sme Calculator1 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

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14a
Sme Calculator2 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?

14b
Sme Calculator2 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?

14c
Sme Calculator4 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.

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15a
Sme Calculator2 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?

15b
Sme Calculator2 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?

15c
Sme Calculator2 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............................................

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16
Sme Calculator1 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.

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17
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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18
Sme Calculator1 mark

y is an obtuse angle.

Which statement is true? Tick one box.

square

sin space y space greater than space 0 and cos space y space greater than space 0

size 26px square

sin space y space greater than space 0 spaceand cos space y space less than space 0

size 26px square

sin space y space less than space 0 space andspace cos space y space greater than space 0

size 26px square

sin space y space less than space 0 and cos space y space less than space 0

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