Graphs of Functions (Edexcel GCSE Maths: Foundation)

Exam Questions

2 hours20 questions
1
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2 marks

The diagram shows four graphs.

Four graphs labelled Graph, A, Graph B, Grraph C and Graph D

Each of the equations in the table is the equation of one of the graphs.

Complete the table.

Equation Letter of Graph
table row blank row blank end table y equals negative x squared table row blank row blank end table  
table row blank row blank end table y equals 1 over x table row blank row blank end table  
table row blank row blank end table y equals x squared table row blank row blank end table  
table row blank row blank end table y equals x cubed table row blank row blank end table  

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2
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2 marks

Here is the graph of  y equals x squared minus 5 x plus 3

Graph of the equation y=x^2-6x+5

Use your graph to find the solutions to  0 equals x squared minus 6 x plus 5 

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3a
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2 marks

Complete the table of values for  y equals 1 over x

x negative 4 negative 3 negative 2 negative 1 0 1 2 3 4
y negative 0.25         1 0.5    
3b
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4 marks

On the grid, draw the graph  y equals 1 over x  for  negative 4 less or equal than x less or equal than 4.

Blank coordinate grid with both axes going from -4 to +4

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4a
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2 marks

Complete the table of values for y equals x squared minus 4 x minus 3

x -2 -1 0 1 2 3 4 5
y   2 -3 -6   -6 -3 2

4b
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4 marks

On the grid, draw the graph of y equals x squared minus 4 x minus 3 for negative 2 less-than or slanted equal to x less-than or slanted equal to 5.

qp10b-0580-32-paper-3-nov-2020-cie-igcse-maths

4c
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2 marks

Use your graph to solve the equation x squared minus 4 x minus 3 equals 0.

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

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5a
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3 marks

Complete the table of values for y equals x squared minus 3 x minus 6

x -3 -2 -1 0 1 2 3 4 5 6
y 12   -2         -2   12

5b
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4 marks

On the grid, draw the graph of  y equals x squared minus 3 x minus 6 for  -3 less-than or slanted equal to x less-than or slanted equal to 6.

qp9b-0580-32-paper-3-may-2020-cie-igcse-maths

5c
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1 mark
Write down the equation of the line of symmetry of the graph.
5d
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2 marks
Use your graph to solve the equation  x squared minus 3 x minus 6 equals 0
x = ............................ or x = ............................ 

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6a
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2 marks

Complete the table of values for y equals x squared minus 5 x plus 3.

x -1 0 1 2 3 4 5 6
y     -1 -3 -3 -1 3  

6b
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4 marks

On the grid, draw the graph of y equals x squared minus 5 x plus 3 for negative 1 less-than or slanted equal to x less-than or slanted equal to 6.

qp6b-0580-32-paper-3-oct-nov-2019-cie-igcse-maths

 

6c
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2 marks

Use your graph to solve the equation x squared minus 5 x plus 3 equals 0

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

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7
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5 marks
i)
Complete the table of values for y equals x squared minus 2 x
x -2 -1 0 1 2 3 4
y 8   0 -1 0   8

ii)
On the grid, draw the graph of y equals x squared minus 2 x space for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.
qp8aii-0580-33-paper-3-oct-nov-2019-cie-igcse-maths
[4]

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8
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8 marks
i)
Complete the table of values for y equals x squared minus 10 x.

x negative 6 negative 3 0 3 6 9 12 15
y 96     negative 21 negative 24   24 75

[3]

ii)
On the grid, draw the graph of y space equals space x squared minus 10 x space for space space minus 6 space less or equal than space x space less or equal than space 15.
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[4]

iii)
Write down the co-ordinates of the lowest point of the graph.
[1]

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1
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2 marks

Here is the graph of  y equals x squared minus 5 x plus 3

Graph of the equation y=x^2-5x+3

Use your graph to find estimates of the solutions to  0 equals x squared minus 5 x plus 3 

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2a
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2 marks

Complete the table of values for y equals 1 plus 5 x minus x squared

x -1 0 1 2 3 4 5
y   1 5   7   1

2b
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4 marks

On the grid, draw the graph of y equals 1 plus 5 x minus x squared for negative 1 less-than or slanted equal to x less-than or slanted equal to 5.

qp3b-0580-33-paper-3-nov-2020-cie-igcse-maths

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3a
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3 marks

qp7-0580-03-paper-3-specimen-2020-cie-igcse-maths

The line L is shown on the grid.
Find the equation of the line in the form y space equals space m x space plus space c.
y = .............................................. 
3b
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6 marks
i)
Complete the table of values for y equals x squared plus 2 x plus 4.

x -2 -1 0 1 2 3
y 4   4 7   19

[2]

ii)
On the grid opposite, draw the graph of y space equals space x squared space plus space 2 x space plus space 4 for – 2 space less-than or slanted equal to space x space less-than or slanted equal to space 3.
[4]
3c
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1 mark

For – 2 space less-than or slanted equal to space x space less-than or slanted equal to space 3 comma write down the x-coordinate of the point of intersection of the line L with the curvey space equals space x squared space plus space 2 x space plus space 4.

x equals...............................

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4a
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2 marks

Complete the table of values for y equals 5 plus 2 x minus x squared.

x negative 2 negative 1 0 1 2 3 4
y   2 5 6     negative 3

4b
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4 marks

On the grid, draw the graph of y equals 5 plus 2 x minus x squared for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.

q4b-058033-mayjune2019-cie-igcse-maths-core

4c
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2 marks
i)
On the grid, draw the line of symmetry.

[1]

ii)
Write down the equation of the line of symmetry.

[1]

4d
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4 marks
i)
On the grid, draw a line from left parenthesis negative 1 comma space 2 right parenthesis space to space left parenthesis space 1 comma space 6 right parenthesis.
[1]
ii)
Find the equation of this line in the form y equals m x plus c.
y space equals ............................ [3]

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5
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8 marks
i)
Complete the table of values for y equals x open parentheses 3 minus x close parentheses.

x negative 4 negative 2 negative 1 0 1 2 4
y   negative 10   0 2   negative 4

[3]

ii)
On the grid, draw the graph of y equals x open parentheses 3 minus x close parentheses for negative 4 less-than or slanted equal to x less-than or slanted equal to 4.

q8cii-058032-march2019-cie-igcse-maths-core

[4]

iii)
Write down the co-ordinates of the highest point of the graph for negative 4 less-than or slanted equal to x less-than or slanted equal to 4.

[1]

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6
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10 marks
i)
Complete the table of values for y space equals space x squared space minus space x space minus space 5.

x -3 -2 -1 0 1 2 3 4
y 7   -3   -5      

[3]

ii)
On the grid, draw the graph of y space equals space x squared space minus space x space minus space 5 space for space minus 3 space less-than or slanted equal to space x italic space italic less-than or slanted equal to italic space 4.
q10bii-058031-mayjune2018-cie-igcse-maths-core
[4]
iii)
Write down the co-ordinates of the lowest point on the graph.
[1]

iv)

a)
On the grid, draw the line of symmetry of the graph.
[1]
b)
Write down the equation of this line.
[1]

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1
Sme Calculator
2 marks

Here is the graph of  y equals x squared minus 5 x plus 3

Graph of the equation y=x^2-6x+5

Use your graph to find the solutions to  x squared minus 6 x plus 5 equals negative 3 

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2a
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3 marks

Complete the table of values for y equals 15 over x

x -5 -3 -2 -1   1 2 3 5
y       -15   15      

2b
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4 marks

On the grid, draw the graph of y equals 15 over x for negative 5 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 5.

q9b-0580-31-paper-3-nov-2020-cie-igcse-maths

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3a
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2 marks

Complete the table of values for y equals 7 plus 2 x minus x squared

x -2 -1 0 1 2 3 4
y -1     8 7   -1

3b
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4 marks

On the grid, draw the graph of y equals 7 plus 2 x minus x squared for negative 2 less-than or slanted equal to x less-than or slanted equal to 4.

qp4b-0580-31-paper-3-may-2020-cie-igcse-maths

3c
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1 mark

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

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4a
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3 marks

omplete the table of values for y equals negative x squared plus x plus 5

x -3 -2 -1 0 1 2 3 4
y   -1 3     3    

4b
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4 marks

On the grid, draw the graph of y equals negative x squared plus x plus 5 for negative 3 less-than or slanted equal to x less-than or slanted equal to 4.

qp8b-0580-33-paper-3-may-2020-cie-igcse-maths

4c
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1 mark

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

4d
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1 mark

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

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5a
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2 marks

Complete the table of values for y equals 8 over x.

x -5 -4 -3 -2 -1   1 2 3 4 5
y   -2 -2.7 -4 -8   8 4 2.7    

5b
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4 marks

On the grid, draw the graph of y equals 8 over x spacefor negative 5 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 5.

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]

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6
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9 marks
i)
Complete the table of values for y equals 12 over x comma space x not equal to 0.
x -6 -4 -3 -2 -1   1 2 3 4 6
y -2 -3         12       2

[3]

ii)

On the grid, draw the graph of y equals 12 over x for negative 6 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 6.

q5cii-058031-mayjune2019-cie-igcse-maths-core

[4]

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