OCR GCSE Maths

Topic Questions

GCSEMathsOCRTopic Questions7. Graphs of Equations & FunctionsTransformations of Graphs

Transformations of Graphs

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1
Sme Calculator2 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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2
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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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3
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The graph of y equals x squared is translated to give the graph of y equals open parentheses x minus 3 close parentheses squared plus 5.

Write down the vector that represents this transformation.
 

open parentheses table row cell space space space end cell row cell space space space space end cell end table close parentheses 

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4
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The graph of y equals 4 open parentheses negative x close parentheses cubed plus 1 is a reflection of the graph of y equals 4 x cubed plus 1.

Write down the equation of the mirror line.

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5
Sme Calculator1 mark

The graph of y equals 1 over x is translated by the vector open parentheses table row 7 row 0 end table close parentheses.

Write down the equation of the translated graph.

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1a
Sme Calculator2 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.

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1b
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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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2a
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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.

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2b
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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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3a
Sme Calculator1 mark

The curve C has equation  y 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.

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3b
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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.

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3c
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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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4
Sme Calculator3 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 = ....................................................... 

= ....................................................... 

   c = ....................................................... 

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5
Sme Calculator2 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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6
Sme Calculator3 marks

Curve straight 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 straight 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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1a
Sme Calculator1 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.

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1b
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On the same diagram, draw a sketch of the graph of y space equals space minus cos space x.

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2
Sme Calculator2 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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3a
Sme Calculator2 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

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3b
Sme Calculator2 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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4
Sme Calculator2 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 begin mathsize 16px style x end style-axis in two places.

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

begin mathsize 16px style x equals end style...........................

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5
Sme Calculator3 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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6a
Sme Calculator1 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

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6b
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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

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6c
Sme Calculator1 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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7
Sme Calculator1 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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