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Exam-Style Questions on Transformations

Problems on Transformations adapted from questions set in previous Mathematics exams.


GCSE Higher

Shape A can be transformed to shape B by a reflection in the y-axis followed by a translation \( {c \choose d} \) Transformation

Find the value of \(c\) and the value of \(d\).


GCSE Higher

The shape A is drawn on the coordinate grid as shown below.


Sally and Eddie each transform the shape A onto shape B.

(a) Draw and label shape B.

(b) Describe fully Eddie's favourite transformation.


GCSE Higher

The diagram shows a red trapezium drawn on a grid.


The trapezium is subjected to two transformations, one after the other.

One transformation is a reflection in the line \(y=x\).

The other transformation is a reflection y-axis.

Does it matter in which order these transformations are made? Explain your answer.


GCSE Higher

(a) Shape \(A\) is translated to shape \(B\) using the vector \( \begin{pmatrix}m\\n\\ \end{pmatrix}\). What are the values of \(m\) and \(n\)?


(b) Vectors \(a, b, c, d\) and \(e\) are drawn on an isometric grid. Write each of the vectors \(c, d\) and \(e\) in terms of \(a\) and/or \(b\).



GCSE Higher

The diagram shows a trapezium A on a grid.


Trapezium A is reflected in the line \(x=10\) to give trapezium B.

Trapezium B is translated by \(\begin{pmatrix} -6 \\ -3 \\ \end{pmatrix} \) to give trapezium C.

(a) Draw the trapezia B and C on the grid above.

(b) Trapezium C is reflected in the line \(y=5\) to give trapezium D. What are the coordinates of the centre of a 180° rotation that would map trapezium D onto trapezium A?


GCSE Higher

The following points have been plotted then joined up in order to make an irregular hexagon.

$$(-3,-1), (-2,-2), (-1,-2), (0,-1), (-1,-4), (-2,-4)$$ Irregular hexagon

Enlarge the hexagon by a scale factor of \(2\frac12 \), centre (-3,-4).


GCSE Higher

Describe fully the single transformation that maps trapezium A onto trapezium B.

Two Trapezia


GCSE Higher

The graph of the curve with equation y = \(f(x)\) is shown on the grid below.

First graph

(a) On the grid above, sketch the graph of the curve with equation \(y = f(–x)\)

The red curve with equation \(y = x^2-5x+4\) is transformed by a translation to give the blue curve such that the point (2.5, -2.25) on the red curve is mapped to the point (-2.5, -2.25) on the blue curve.

Other graphs

(b) Find an equation for the blue curve.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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