2 Points A and B are plotted on the grid. – 3 – 2 – 1 1 0 2 3 y x 4 3 2 1 – 1 – 2 – 3 A B (a) Write down the coordinates of point B. ( … , …) [1] (b) Write AB as a vector. f p [1] (c) On the grid, plot point C at (-2, 3). [1]

2(a) (2, 3) 1 2(b) 4 5    1 2(c) C plotted at (–2, 3) 1

7 a 5 7 = - e o b 2 6 = - e o Work out a b - . f p [1]

7 7 13     −   1

10 (a) a 3 4 = - e o b 5 2 = e o Work out. (i) 8b f p [1] (ii) a – b f p [1] (b) Point L has coordinates ( , ) 3 6 - and LM 5 2 = - e o. Find the coordinates of point M. ( … , … ) [1]

10(a)(i) 40 16 1 10(a)(ii) −2 −6 1 10(b) 2 4 1 For (a)(i), you earn the mark by stating 40/16. For (a)(ii), you earn the mark by stating -2/-6. For (b), you earn the mark by correctly identifying the coordinates of point M as (2, 4).

10 C B A – 2 – 2 2 0 4 6 8 10 y x – 4 – 6 – 8 – 10 – 4 – 6 – 8 2 4 6 8 10 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C. … … [3] (b) Draw the image of triangle A after a translation by the vector 2 10 e o. [2]

10(a)(i) Rotation 90° anticlockwise oe (0, − 1) 3 B1 for each 10(a)(ii) enlargement [s.f.] 1 3 (6, 6) 3 B1 for each 10(b) triangle at (− 4, 7) (− 4, 1) (− 1, 1) 2 B1 for translation by 10 k       or 2 k   

10 T A – 8 – 6 – 4 – 2 8 6 4 2 0 – 2 – 4 – 6 – 8 2 4 6 8 x y (a) Describe fully the single transformation that maps triangle T onto triangle A. … … [2] (b) Draw the image of triangle T after an enlargement, scale factor 2 1 - , centre (0, 0). [2]

10(a) Translation 1 8 −     −   2 B1 for each 10(b) Image at (–1, –1), (–4, –1), (–1, –2) 2 B1 for image correct scale factor and orientation but wrong position or for enlargement scale factor 1 2 centre (0, 0)

Cambridge IGCSE Mathematics · 0580

IGCSE Mathematics (0580) Transformations and vectors past paper questions

These questions test transformations — reflection, rotation, enlargement — and vector geometry. Practising them together builds the visual reasoning and the column-vector method the paper rewards.

172 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.