Mathematics 0580 · syllabus C7.1, E7.1
Cambridge IGCSE Mathematics 0580 — Transformations topical past papers
Drawing and fully describing reflections, rotations, enlargements and translations on a grid, and on the Extended route combining transformations.
- Questions
- 232
- Years
- 2009–2026
- With mark scheme
- 94%
- Questions 2022–2026
- 68
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Transformations covers
A transformation moves or resizes a shape. A reflection flips it in a mirror line; a rotation turns it about a centre through an angle; an enlargement changes its size by a scale factor, measured from a centre; a translation slides it by a column vector, whose top number is the move to the right and bottom number the move up. Reflections, rotations and translations keep the shape's size; an enlargement keeps its angles but multiplies its lengths.
You draw images on a grid and describe given transformations fully, which means stating the type and every detail: the equation of the mirror line, the centre, angle and direction of a rotation, the centre and scale factor of an enlargement, or the column vector of a translation. Core reflections are in vertical or horizontal lines, rotations are through multiples of 90° about the origin, a vertex or the midpoint of an edge, scale factors are positive or fractional, and each question uses a single transformation. Extended uses any straight mirror line, such as y = x or y = −x, any centre of rotation, negative scale factors, and combinations of transformations.
Transformations are Core content, so they can be set on all four papers, with the wider cases on Papers 2 and 4 only. An enlargement creates similar shapes, so the topic links to similarity and scale factors; a translation is a vector, which leads into the Extended vectors topic; and lines of symmetry are mirror lines. Equations of lines such as x = 2, y = −1 and y = x come from coordinate geometry.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C7.1 Transformations
- E7.1 Transformations
What you should be able to do
- Reflect a shape in a given line, and find the equation of a mirror line
- Rotate a shape through 90°, 180° or 270° about a given centre, clockwise or anticlockwise
- Enlarge a shape about a given centre with a positive or fractional scale factor, or a negative one on the Extended route
- Translate a shape by a column vector, and find the vector of a given translation
- Describe a single transformation fully, with every detail it needs
- Carry out and describe combinations of transformations (Extended)
Key ideas
- A reflection needs the equation of its mirror line
- A rotation needs its centre, its angle and its direction
- An enlargement needs its centre and scale factor; a factor between 0 and 1 makes the shape smaller, and a negative factor puts the image on the other side of the centre
- A translation needs its column vector, whose top number is the move to the right and bottom number the move up
- Reflections, rotations and translations give congruent images; enlargements give similar ones
How Transformations has been examined
From 2022 to 2026, Transformations was on Paper 3 · Calculator (Core) in 11 of 14 exam series, worth about 8% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 13 | 4% | 8 of 14 |
| Paper 2 · Non-calculator (Extended) | 16 | 3% | 10 of 14 |
| Paper 3 · Calculator (Core) | 23 | 8% | 11 of 14 |
| Paper 4 · Calculator (Extended) | 16 | 4% | 9 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 7.
Filed in Momentum under: Transformation.
A worked example
Triangle T has vertices (1, 1), (3, 1) and (1, 2). Find the vertices of its image after (a) a rotation of 90° anticlockwise about the origin and (b) an enlargement with scale factor −2, centre the origin.
- (a) A rotation of 90° anticlockwise about the origin sends the point (x, y) to (−y, x).
- So (1, 1) goes to (−1, 1), (3, 1) to (−1, 3) and (1, 2) to (−2, 1).
- (b) An enlargement with scale factor −2 from the origin multiplies each coordinate by −2, so the image is twice as large and on the opposite side of the centre.
- So (1, 1) goes to (−2, −2), (3, 1) to (−6, −2) and (1, 2) to (−2, −4).
- Check: the side from (1, 1) to (3, 1) has length 2, and its image, from (−2, −2) to (−6, −2), has length 4.
Answer: (a) (−1, 1), (−1, 3) and (−2, 1); (b) (−2, −2), (−6, −2) and (−2, −4)
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Describing two transformations when one is asked for: 'the single transformation' needs one type with all its details, and a pair of transformations earns nothing.
- Leaving out a detail: a rotation without its centre or direction, or an enlargement without its centre, loses marks even if the rest is right.
- Confusing x = 2 with y = 2 as a mirror line: x = 2 is vertical and y = 2 is horizontal.
- Writing a translation vector upside down or with the wrong signs: the top number is the move right (negative for left), the bottom number the move up (negative for down).
- Calling a fractional enlargement a 'reduction', or giving its factor as 2 instead of ½: describe it as an enlargement with scale factor ½.
Exam technique
- Use tracing paper, which is allowed in every paper, to check rotations: trace the shape, hold the centre with a pencil point and turn.
- To find a centre of enlargement, draw straight lines through corresponding vertices of the object and the image; they meet at the centre.
- Check an enlargement by measuring one side: the image side divided by the object side is the scale factor.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.