Edexcel International GCSE Maths Transformations Past Paper Questions and Solutions (4MA1 Higher)

By /
Edexcel International GCSE Maths A (4MA1) · Higher · Vectors and Transformation Geometry

Transformations: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every transformations question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 3 questions worth 12 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

18 marksHigherJune 2023 · Paper 1H (4MA1/1H) · Q4

The diagram shows a sketch of triangle A and triangle B on a coordinate grid. Triangle A has vertices (−7, 2), (−11, −5) and (f, −3). Triangle B has vertices (6, 12), (2, d) and (9, e).

(a) Given that triangle A has been translated to give triangle B, work out the value of d, the value of e and the value of f. (3)

The diagram also shows shape P with vertices (2, 5), (2, 3), (3, 2), (3, 3) and shape Q with vertices (6, 11), (6, 5), (9, 2), (9, 5).

01234567891011120123456789101112xyPQ

(b) Describe fully the single transformation that maps shape P onto shape Q. (3)

(c) Rotate shape P 90° clockwise about (3, 5). Label your shape R. (2)

Show solution

Part (a)

  1. The top vertex (−7, 2) moves to (6, 12). That is 13 right and 10 up, so the translation is 13 units right and 10 units up.
  2. (−11, −5) moves to (−11 + 13, −5 + 10) = (2, 5), so d = 5
  3. (f, −3) moves to (9, e): f + 13 = 9 gives f = −4, and −3 + 10 = 7 gives e = 7

Answer: d = 5, e = 7, f = −4

Part (b)

  1. Q is bigger than P, so it is an enlargement.
  2. The vertical side of P from (2, 3) to (2, 5) is 2 long. The matching side of Q from (6, 5) to (6, 11) is 6 long.
  3. Scale factor = 6 ÷ 2 = 3
  4. To find the centre, draw lines through matching vertices, for example (2, 5) to (6, 11) and (3, 2) to (9, 2). They meet at (0, 2).
  5. Check: from (0, 2) to (3, 2) is 3 across; × 3 = 9 across, giving (9, 2) ✓

Answer: Enlargement, scale factor 3, centre (0, 2)

Part (c)

  1. For a 90° clockwise turn about (3, 5), each point’s position relative to the centre changes from (across, up) to (up, −across).
  2. (2, 5) → (3, 6), (2, 3) → (1, 6), (3, 2) → (0, 5), (3, 3) → (1, 5)
01234567801234567xy(3, 5)PR

Answer: R has vertices (3, 6), (1, 6), (0, 5) and (1, 5)

Tip: Tracing paper helps: trace P, put your pencil point on (3, 5) and turn the paper a quarter turn clockwise.
22 marksHigherJanuary 2020 · Paper 1H (4MA1/1H) · Q8

The shaded shape has vertices (7, 10), (15, 10), (15, 4) and (11, 4). On the grid, enlarge the shaded shape with scale factor 1⁄2 and centre (1, 2).

01234567891011121314151601234567891011xy(1, 2)
Show solution
  1. For each vertex, halve its distance from the centre (1, 2).
  2. (7, 10) is 6 right and 8 up from (1, 2). Half: 3 right and 4 up, giving (4, 6).
  3. (15, 10) is 14 right and 8 up. Half: 7 right and 4 up, giving (8, 6).
  4. (15, 4) is 14 right and 2 up. Half: 7 right and 1 up, giving (8, 3).
  5. (11, 4) is 10 right and 2 up. Half: 5 right and 1 up, giving (6, 3).
01234567891011121314151601234567891011xy(1, 2)

Answer: Shape with vertices (4, 6), (8, 6), (8, 3) and (6, 3)

32 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q10

The shaded triangle has vertices (7, 4), (13, 4) and (7, 13). On the grid, enlarge the shaded shape with scale factor 1⁄3 and centre (1, 7).

0123456789101112131401234567891011121314xy(1, 7)
Show solution
  1. For each vertex, find how far it is from the centre (1, 7), multiply that distance by 1⁄3, and measure it from the centre again.
  2. (7, 4) is 6 right and 3 down from (1, 7). A third of that is 2 right and 1 down, giving (3, 6).
  3. (13, 4) is 12 right and 3 down. A third: 4 right and 1 down, giving (5, 6).
  4. (7, 13) is 6 right and 6 up. A third: 2 right and 2 up, giving (3, 9).
0123456789101112131401234567891011121314xy(1, 7)

Answer: Triangle with vertices (3, 6), (5, 6) and (3, 9)

Tip: A fractional scale factor makes the shape smaller and moves it closer to the centre.

More Vectors and Transformation Geometry questions

Need help with Edexcel International GCSE Maths? The Vector Academy runs small-batch online classes for 4MA1 Higher, taught by experienced tutors. Book a free demo class.

Book a free trial class

Tell us a little about your requirement.