Geometry, trigonometry & vectors
Vectors — IGCSE 0580 Paper 2
Paper 2 (non-calculator) style practice and an exam-style test.
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Transformations · revision guide
How to describe a transformation fully
Translation, reflection, rotation and enlargement: exactly what to write to get every mark, with four worked examples for IGCSE 0580 and GCSE.
“Describe fully the single transformation that maps shape A onto shape B” is one of the most reliable questions in IGCSE and GCSE maths. It appears in 32 of the 63 Cambridge IGCSE 0580 mark schemes from June 2024 to June 2026 that we checked, on Core and Extended papers. It is usually worth 2 or 3 marks.
Those marks are not for the drawing. In the mark schemes each mark is for one detail, “B1 for each”, so students who name the transformation but leave out the centre or the direction lose marks they could easily have had. Learn what each transformation needs and you can collect every mark.
What each transformation needs
| Transformation | Write down | Marks |
|---|---|---|
| Translation | the word translation + the column vector, e.g. 6−3 | 2 |
| Reflection | the word reflection + the equation of the mirror line, e.g. x = 1 | 2 |
| Rotation | the word rotation + the angle + the direction + the centre, e.g. 90° clockwise, centre (2, 1) | 3 |
| Enlargement | the word enlargement + the scale factor + the centre, e.g. scale factor 2, centre (1, 1) | 3 |
For a 180° rotation you do not need a direction, because clockwise and anticlockwise give the same image.
Only ever give one transformation
The question says single transformation. Cambridge mark schemes state that more than one transformation scores 0. “A rotation followed by a translation” gets no marks, even if it works. If you think you need two moves, look again: a reflection followed by another reflection, for example, is always a single translation or rotation.
Translation
Every point moves the same distance in the same direction. Pick one corner of A, find the matching corner of B and count: across first, then up or down. The top number of the vector is the move right (positive) or left (negative). The bottom number is the move up (positive) or down (negative).
Example 1 · Core and Foundation
Describe fully the single transformation that maps triangle A onto triangle B.
- The corner (−5, 1) of A moves to (1, −2) on B.
- Across: −5 to 1 is 6 to the right, so the top number is 6.
- Down: 1 to −2 is 3 down, so the bottom number is −3.
- Check another corner: (−3, 1) + 6 across and 3 down = (3, −2). ✓
Answer: Translation by the vector 6−3
Reflection
The shape flips over a mirror line, so B is a mirror image of A and each point on B is the same distance from the line as its matching point on A. The mirror line is exactly halfway between matching points. Give the line as an equation: a vertical line is x = number, a horizontal line is y = number. Extended and Higher papers also use the diagonal lines y = x and y = −x.
Example 2 · Core and Foundation
Describe fully the single transformation that maps triangle A onto triangle B.
- B is a mirror image of A, so this is a reflection.
- Matching corners: (−1, 1) on A and (3, 1) on B. Halfway between x = −1 and x = 3 is x = 1.
- Check another pair: (−3, 1) and (5, 1). Halfway between −3 and 5 is 1. ✓
- The mirror line is vertical, so its equation is x = 1.
Answer: Reflection in the line x = 1
A common slip is to write “reflection in the y-axis” when the mirror line is x = 1. The y-axis is the line x = 0.
Rotation
The shape turns about a fixed point, the centre. You need three things:
- The angle. At IGCSE it is always a multiple of 90°. Compare one edge of A with the matching edge of B: a horizontal edge that becomes vertical means 90°.
- The direction. Clockwise or anticlockwise (not needed for 180°).
- The centre. Use tracing paper: the front of every 0580 paper says “You may use tracing paper”, so ask for it. Trace A, put your pencil point on a guess for the centre and turn the paper through the angle. If the tracing lands on B, the guess is right. Good guesses are the origin, a corner of the shape, or a point the same distance from matching corners.
Example 3 · Extended and Higher
Describe fully the single transformation that maps triangle A onto triangle B.
- The horizontal edge of A, from (3, 2) to (6, 2), matches the vertical edge of B, from (3, 0) to (3, −3). So the angle is 90°.
- The edge pointing right on A points down on B: that is a quarter turn clockwise.
- Try the centre (2, 1). The corner (3, 2) is 1 right and 1 up from it. After a quarter turn clockwise it should be 1 right and 1 down: (3, 0). ✓
- Check (6, 2): 4 right and 1 up becomes 1 right and 4 down: (3, −3). ✓
Answer: Rotation, 90° clockwise, centre (2, 1)
At Core, the centre is the origin, a corner of the shape or the midpoint of one of its edges. At Extended it can be any point.
Enlargement
The shape changes size but keeps its shape. You need two things:
- The scale factor = length on B ÷ matching length on A. If B is smaller, the scale factor is a fraction, such as ½. Still call it an enlargement.
- The centre. Draw straight lines through matching corners of A and B and extend them. They all cross at the centre of enlargement.
Example 4 · Core and Foundation
Describe fully the single transformation that maps triangle A onto triangle B.
- B is the same shape but bigger, so this is an enlargement.
- The base of A is 2 squares long. The base of B is 4 squares long. Scale factor = 4 ÷ 2 = 2.
- Draw lines through matching corners: (2, 2) to (3, 3), (4, 2) to (7, 3) and (2, 3) to (3, 5). They meet at (1, 1).
- Check: (4, 2) is 3 right and 1 up from (1, 1). Doubled, that is 6 right and 2 up: (7, 3). ✓
Answer: Enlargement, scale factor 2, centre (1, 1)
The reverse transformation, B onto A, is an enlargement with scale factor ½ and the same centre, (1, 1).
Negative scale factors (Extended and Higher only). The image is on the opposite side of the centre and upside down. The lines through matching corners still meet at the centre, but now the centre lies between A and B.
Words that lose marks
- “Flip”, “turn”, “move”, “slide”. Use the mathematical names: reflection, rotation, translation, enlargement.
- “Rotational symmetry”. Mark schemes say this is not accepted for rotation. Rotational symmetry describes one shape, not a transformation.
- Coordinates instead of a vector. A translation needs a column vector, 6−3, not (6, −3).
- A mirror line without an equation. “Reflection in the dotted line” is not enough. Write x = 1.
- Missing the direction. “Rotation 90°, centre (2, 1)” loses a mark. Mark schemes do accept equivalents such as 270° anticlockwise or −90° for 90° clockwise, but 90° clockwise is clearest.
What is on your syllabus
| Topic | IGCSE 0580 Core (C7.1) | IGCSE 0580 Extended (E7.1) | GCSE (AQA and Edexcel G7, G8) |
|---|---|---|---|
| Reflection | Vertical and horizontal lines | Any straight line, including y = x and y = −x | Foundation and Higher |
| Rotation | Multiples of 90° about the origin, a vertex or the midpoint of an edge | Multiples of 90° about any centre | Foundation and Higher |
| Enlargement | Positive and fractional scale factors | Also negative scale factors | Fractional: Foundation. Negative: Higher only |
| Translation | By a column vector | By a column vector | Foundation and Higher |
| Combined transformations | Not tested | Can be tested | Higher only (G8) |
Quick checklist for the exam
- Name the transformation with its proper word.
- Add the details: vector; mirror line; angle, direction and centre; scale factor and centre.
- Give one transformation only.
- Check your answer on one more corner.
Practise this in Transformation Station
Draw the image on the grid and describe fully the single transformation, exactly as on IGCSE 0580 and GCSE papers. Free, no sign-up.
Frequently asked questions
How many marks is “describe fully the single transformation” worth?
Usually 2 marks for a translation or reflection and 3 marks for a rotation or enlargement: one mark for the name and one for each detail.
Do I need to say clockwise for a 180° rotation?
No. A half turn gives the same image in either direction, so the angle and the centre are enough.
Can I use tracing paper in the IGCSE exam?
Yes. Cambridge IGCSE 0580 papers state “You may use tracing paper”. Ask the invigilator for it; it is the quickest way to find a centre of rotation.
What if the image is smaller than the object?
It is still an enlargement, with a fractional scale factor such as ½ or ⅓. Give the scale factor and the centre.
Are combined transformations on IGCSE Core?
No. The 0580 syllabus says Core questions will not involve combinations of transformations. They can appear on Extended papers and GCSE Higher.
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