Transformations of Graphs (Edexcel GCSE Maths)

Exam Questions

2 hours36 questions
1
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2 marks

q1-easy-2-23-transformation-of-graphs-edexcel-gcse-maths

The curve with equation space y space equals space straight f left parenthesis x right parenthesis space is translated so that the point at (0, 0) is mapped onto the point (4, 0).

Find an equation of the translated curve.

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2
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2 marks

The graph of y space equals space straight f left parenthesis x right parenthesis is shown on both grids below.

i)
On this grid, draw the graph of y space equals space minus straight f left parenthesis x right parenthesis

q2i-easy-2-23-transformation-of-graphs-edexcel-gcse-maths
[1]
ii)
On the grid below, draw the graph of y space equals space straight f left parenthesis x space minus space 3 right parenthesis
q2ii-easy-2-23-transformation-of-graphs-edexcel-gcse-maths
[1]

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3
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3 marks

q3-easy-2-23-transformation-of-graphs-edexcel-gcse-maths

The diagram shows part of the curve with equation y space equals space straight f left parenthesis x right parenthesis.
The coordinates of the minimum point of this curve are left parenthesis 3 comma space minus 4 right parenthesis

Write down the coordinates of the minimum point of the curve with equation

i)
y equals straight f open parentheses x close parentheses plus 3

[1]

ii)
y equals straight f open parentheses x plus 2 close parentheses

[1]

iii)
y equals straight f open parentheses negative x close parentheses

[1]

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4a
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1 mark

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

q4a-easy-2-23-transformation-of-graphs-edexcel-gcse-maths

The graph G is a translation of the graph of y space equals space straight f left parenthesis x right parenthesis.

Write down, in terms of f, the equation of graph G.

4b
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2 marks

The graph of y space equals space straight f left parenthesis x right parenthesis has a maximum point at (-4, 3).

Write down the coordinates of the maximum point of the graph of y space equals space straight f left parenthesis negative x right parenthesis.

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5
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2 marks

The diagram shows a sketch of the curve with equation y space equals space straight f left parenthesis x right parenthesis

q23-january-2022-1h-edexcel-igcse-maths

There is only one maximum point on the curve.
The coordinates of this maximum point are (5, 7)

Write down the coordinates of the maximum point on the curve with equation

i)
y space equals space straight f left parenthesis x space plus space 9 right parenthesis
[1]

ii)
y space equals space straight f left parenthesis x right parenthesis space plus space 3
[1]

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6
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2 marks

Here is the graph of y space equals space straight f left parenthesis x right parenthesis

q21b-paper2hr-june2018-edexcel-igcse-maths

On the grid above, draw the graph of y space equals space straight f left parenthesis – x right parenthesis

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7
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1 mark

The curve with equation y space equals space g left parenthesis x right parenthesis is transformed to the curve with equation y space equals space minus g left parenthesis x right parenthesis by the single transformation bold T bold.

Describe fully the transformation bold T bold.

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8
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2 marks

On the axes, sketch the curve  y equals x cubed minus 2

You must show the coordinates of the y-intercept.

q8-paper-2h-june-2019-aqa-gcse-maths

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9
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1 mark

One of these is the graph of y space equals space 1 space plus space sin space x for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

Circle the letter above the correct graph.

q22-paper-2h-nov-2020-aqa-gcse-maths

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10
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1 mark

(7, 28) is a point on the graph y space equals space straight f left parenthesis x right parenthesis

Circle the point which must be on the graph y space equals space straight f left parenthesis x right parenthesis space plus space 2

(7, 26) (7, 30) (5, 28) (9, 28)

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1a
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3 marks

q1a-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

The diagram shows part of the curve with equation y space equals space straight f left parenthesis x right parenthesis.
The coordinates of the maximum point of the curve are (3, 5).

Write down the coordinates of the maximum point of the curve with equation

i)
y space equals space straight f open parentheses x plus 3 close parentheses
[1]
ii)
[1]
iii)
Error converting from MathML to accessible text.
[1]
1b
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1 mark

The curve with equation y space equals space straight f left parenthesis x right parenthesis is transformed to give the curve with equation y space equals space straight f left parenthesis x right parenthesis minus 4

Describe the transformation.

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2a
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1 mark

The diagram shows a sketch of the graph of y space equals space cos space x.

q2-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

Write down the coordinates of the point A.

2b
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1 mark

On the same diagram, draw a sketch of the graph of y space equals space minus cos space x.

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3
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2 marks

Here is the graph of y equals space sin space x to the power of ring operator space for  negative 180 space less-than or slanted equal to x less-than or slanted equal to 180

q3-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

On the grid, sketch the graph of y space equals space sin space x to the power of ring operator minus 2 for long dash 180 space less-than or slanted equal to space x space less-than or slanted equal to space 180

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4a
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2 marks

Here is the graph of y equals space sin space x to the power of ring operator space for  negative 180 space less-than or slanted equal to x less-than or slanted equal to 180

q4-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

On the grid above, sketch the graph of y space equals space sin space x to the power of ring operator plus 2 for long dash 180 space less-than or slanted equal to space x space less-than or slanted equal to space 180

4b
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2 marks

Here is the graph of y equals space cos space x to the power of ring operator space for  negative 180 space less-than or slanted equal to x less-than or slanted equal to 180

q4b-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

On the grid above, sketch the graph of y space equals space minus space cos space x to the power of ring operator for long dash 180 space less-than or slanted equal to space x space less-than or slanted equal to space 180

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5a
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1 mark

The equation of a curve is y space equals space a to the power of x
A is the point where the curve intersects the y-axis.

State the coordinates of A.

5b
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3 marks

The equation of circle bold C is x squared space plus space y squared space equals space 16

The circle bold C is translated by the vector open parentheses table row 3 row 0 end table close parentheses to give circle bold B.

Draw a sketch of circle bold B.


Label with coordinates
   the centre of circle bold B
   and any points of intersection with the x-axis.

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6a
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2 marks

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

On this grid, sketch the graph of y space equals space straight f open parentheses x minus 3 close parentheses

q6a-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

6b
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2 marks

On this grid, sketch the graph of y space equals space long dash space straight f left parenthesis x right parenthesis

q6b-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

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7a
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2 marks

y space equals space straight f left parenthesis x right parenthesis

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

q7a-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

On the grid above, sketch the graph of space y space equals negative space straight f left parenthesis x right parenthesis.

7b
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1 mark

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

q7b-medium-2-23-transformation-of-graphs-edexcel-gcse-maths

The graph G is a translation of the graph of y space equals space straight f left parenthesis x right parenthesis.

Write down the equation of graph G.

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8a
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1 mark

Here is the graph of space y space equals space cos space x spacefor 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

q28-paper-1h-nov-2021-aqa-gcse-maths-1

In parts (a) and (b) the graph of y space equals space cos space x is shown as a dashed line.

On the grid below, draw the graph of y space equals space cos space left parenthesis x space – space 90 degree right parenthesis for 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

q28a-paper-1h-nov-2021-aqa-gcse-maths

8b
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1 mark

On the grid below, draw the graph of y equals 1 plus cos space x space space for space space 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

q28b-paper-1h-nov-2021-aqa-gcse-maths

8c
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1 mark

Rita tries to draw the graph ofspace y space equals space cos space left parenthesis – x right parenthesis space forspace 0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree
Here is her graph.

q28c-paper-1h-nov-2021-aqa-gcse-maths

Give a reason why Rita’s graph is incorrect.

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9
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2 marks

Here is a sketch of    y space equals space straight f left parenthesis x right parenthesis

The curve passes through the points

   (–2, –10)  (–1, –3)  (0, –2)  (1, –1)  (2, 6)

q24-paper-2h-nov-2018-aqa-gcse-maths

On the grid, sketch the curve y space equals space straight f left parenthesis x space plus space 2 right parenthesis

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10
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1 mark

The curve with equation   y space equals space x squared space minus space 5 x space plus space 2 is reflected in the x-axis.

Circle the equation of the reflected curve.

y space equals space x squared space minus space 5 x space minus space 2 y space equals negative space x squared space plus space 5 x space plus space 2
y space equals negative x squared space plus space 5 x space minus space 2 y space equals space x squared space plus space 5 x space plus space 2

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11
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2 marks

The graph of begin mathsize 16px style y equals cos open parentheses x minus 30 close parentheses end style for  0 degree less-than or slanted equal to x less-than or slanted equal to 360 degree crosses the x-axis in two places.

Write down the values of begin mathsize 16px style x end style where this occurs.

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

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12
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3 marks

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

q16-paper6-june2019-ocr-gcse-maths

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1a
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2 marks

The graph of y space equals space straight f left parenthesis x right parenthesis is shown on each of the grids.

On this grid, sketch the graph of y space equals space straight f left parenthesis x minus 3 right parenthesis

q1a-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

1b
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2 marks

On this grid, sketch the graph of y space equals space straight f left parenthesis negative x right parenthesis space plus space 2

q1b-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

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2a
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1 mark

The graph of space y space equals space straight f left parenthesis x right parenthesis space is shown on both grids below

q2a-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

On the grid above, sketch the graph of y space equals space straight f open parentheses negative x close parentheses

2b
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1 mark

q2b-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

On this grid, sketch the graph of y space equals negative straight f open parentheses x close parentheses plus 3

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3a
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2 marks

This is a sketch of the curve with the equation y space equals space straight f left parenthesis x right parenthesis.

The only minimum point of the curve is at P left parenthesis 3 comma space long dash 4 right parenthesis.

q3a-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

Write down the coordinates of the minimum point of the curve with the equation y space equals space straight f open parentheses x minus 2 close parentheses

3b
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2 marks

Write down the coordinates of the minimum point of the curve with the equation  y space equals space straight f open parentheses x plus 5 close parentheses plus 6

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4a
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2 marks

q4a-hard-2-23-transformation-of-graphs-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.

4b
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2 marks

q4b-hard-2-23-transformation-of-graphs-edexcel-gcse-maths

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

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

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5
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2 marks

The graph of y space equals space straight f left parenthesis x right parenthesis is transformed to give the graph of y space equals space long dash straight f left parenthesis x space plus space 3 right parenthesis
The point A on the graph of y space equals space straight f left parenthesis x right parenthesis is mapped to the point P on the graph of y space equals space long dash straight f left parenthesis x space plus space 3 right parenthesis

The coordinates of point A are left parenthesis 9 comma space 1 right parenthesis
Find the coordinates of point P.

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6
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2 marks

The graph of the curve straight C with equation y space equals space straight f left parenthesis x right parenthesis is transformed to give the graph of the curve straight S with equation y space equals space straight f left parenthesis negative x right parenthesis minus space 3

The point on straight C with coordinates left parenthesis 7 comma space 2 right parenthesis is mapped to the point Q on straight S.

Find the coordinates of Q.

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7
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2 marks

The graph of y space equals space h left parenthesis x right parenthesis intersects the x-axis at two points.
The coordinates of the two points are (–1, 0) and (6, 0)

The graph of y space equals space h left parenthesis x space plus space a right parenthesis passes through the point with coordinates (2, 0), where a is a constant.

Find the two possible values of a.

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8
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4 marks

The curve bold S has equationspace y space equals space straight f left parenthesis x right parenthesis spacewherespace straight f left parenthesis x right parenthesis space equals space x squared space
The curve bold T has equation space y space equals space straight g left parenthesis x right parenthesis spacewhere straight g left parenthesis x right parenthesis space equals space 2 x squared – space 12 x space plus space 13

By writing straight g left parenthesis x right parenthesis in the form a left parenthesis x space – space b right parenthesis squared – space c, where a comma space b and c are constants,
describe fully a series of transformations that map the curve bold S onto the curve bold T.

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9a
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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.

9b
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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.

9c
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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.

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10
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3 marks

The graph ofspace y space equals space a cos space left parenthesis x space – space b right parenthesis degree space plus space c space for space minus 180 space less-than or slanted equal to space x space less-than or slanted equal to space 360 spaceis drawn on the grid below.

q21c-4ma1-2h-qp-nov21-paper2-igcse-maths

Find the value of a, the value of b and the value of c.

a = .......................................................       
b = .......................................................       
   c = .......................................................       

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11
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2 marks

The equation of a curve space bold C bold spaceis y space equals space x squared plus space 3 x space plus space 4
The curve bold C bold spaceis transformed to curve bold Sunder the translation open parentheses table row 4 row 6 end table close parentheses

Find an equation of curve bold S.

You do need to simplify the equation.

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12
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4 marks

The graph of y space equals space x cubed space plus space 6 is translated 4 units to the right.

The translated graph has equation y space equals space straight f left parenthesis x right parenthesis

Work out straight f left parenthesis x right parenthesis.

Give your answer in the form x cubed space plus space a x squared space plus space b x space plus space c where a comma space b and c are integers.

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13
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3 marks

Curve P has equation y space equals space 2 left parenthesis x space – space 1 right parenthesis squared space – space 5

Curve Q is a reflection in the y-axis of curve P.

Work out the equation of curve straight Q.

Give your answer in the form    space y space equals space a x squared space plus space b x space plus space c space     where a comma space b and c are integers.

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14
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2 marks

For all values of x

straight f left parenthesis x right parenthesis space equals space sin space x
straight g left parenthesis x right parenthesis space equals space x space plus space 90

On the grid, draw the graph of the composite function  y equals fg open parentheses x close parentheses  for  0 degree space less-than or slanted equal to space x space less-than or slanted equal to space 360 degree

q27b-paper2h-june2017-aqa-gcse-maths

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