Further Graphs (Cambridge (CIE) IGCSE Maths: Core)

Exam Questions

2 hours15 questions
1a
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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

1b
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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
1c
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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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2a
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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

2b
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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
2c
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1 mark

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

2d
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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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3a
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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

 

3b
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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
3c
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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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4
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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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5
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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.

q11bii-058032-march2018-cie-igcse-maths-core

[4]

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

[1]

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1a
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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

1b
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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
1c
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3 marks

i) On the grid, draw the line y = 3.

[1]

ii) Use your line to solve the equation 1 plus 5 x minus x squared equals 3

x space= .................... orspace x space= .................... [2]

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2a
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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 = .............................................. 

2b
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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]

2c
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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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3a
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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

3b
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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
3c
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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]

3d
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2 marks

Use your graph to find the solutions of the equation 5 plus 2 x minus x squared equals 4.

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

3e
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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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4
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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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5
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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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1a
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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

 

 

 

1b
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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
1c
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1 mark

On the grid, draw the line y = 6.

1d
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1 mark

Use your graph to solve 15 over x equals 6.

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

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2a
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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

2b
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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
2c
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1 mark

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

2d
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2 marks

Use your graph to solve the equation 7 plus 2 x minus x squared equals 0

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

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3a
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3 marks

Complete 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

 

 

3b
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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
3c
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1 mark

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

3d
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1 mark

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

3e
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3 marks

i) On the grid, draw the line y equals x for negative 3 less-than or slanted equal to x less-than or slanted equal to 4

[1]

ii) Write down the values of x where the line y equals x crosses the curve y equals negative x squared plus x plus 5

x = ...................... and x = ...................... [2]

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4a
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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

 

 

4b
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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.

mxTZWD6J_ms24b-0580-11-paper-1-oct-nov-2019-cie-igcse-maths

[4]

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5
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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]

iii) On the grid, draw the line y space equals space 8.

[1]

iv) Use your graph to solve 12 over x equals 8.

x = .............................................. [1]

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