## Exam-Style Questions on Transformations## Problems on Transformations adapted from questions set in previous Mathematics exams. |

## 1. | 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.

- Sally uses a reflection in the line y = 7 followed by a rotation of 90
^{o}anticlockwise about the point (9,9). - Eddie transforms shape A first with a reflection in the line \(y = x\) followed by his favourite transformation.

(a) Draw and label shape B.

(b) Describe fully Eddie's favourite transformation.

## 2. | 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.

## 3. | 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 \(b\).

## 4. | GCSE Higher |

Plot the following points in order then join them up in order to make an irregular hexagon.

$$(-3,-1), (-2,-2), (-1,-2), (0,-1), (-1,-4), (-2,-4)$$Enlarge the hexagon by a scale factor of \(2\frac12 \), centre (-3,-4).

## 5. | IB Standard |

\(f\) and \(g\) are two functions such that \(g(x)=3f(x+2)+7\).

The graph of \(f\) is mapped to the graph of \(g\) under the following transformations:

A vertical stretch by a factor of \(a\) , followed by a translation \(\begin{pmatrix}b \\c \\ \end{pmatrix}\)

Find the values of

(a) \(a\);

(b) \(b\);

(c) \(c\).

(d) Consider two other functions \(h\) and \(j\). Let \(h(x)=-j(2x)\). The point A(8, 7) on the graph of \(j\) is mapped to the point B on the graph of \(h\). Find the coordinates of B.

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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