Transformations — Paper 3 · IGCSE Mathematics (9-1) 0980

5 The diagram shows four shapes A, B, C and D and a point P on a 1 cm2 grid. y 12 11 10 A 9 C 8 D 7 6 5 B 4 3 P 2 1 0 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 x (a) Find (i) the perimeter of shape A, … cm [1] (ii) the area of shape A. … cm2 [1] (b) (i) Write down the co-ordinates of point P. ( … , … ) [1] (ii) Find the co-ordinates of the image of point P when (a) P is reflected in the y-axis, ( … , … ) [1] (b) P is reflected in the line y = 6 . ( … , … ) [2] (iii) Find the vector that translates point P to the point (49, - 12) . [2] f p (c) Describe fully the single transformation that maps (i) shape A onto shape B, … … [3] (ii) shape C onto shape D. … … [3]

14 marks

Mark scheme: 5(a)(i) 16 1 5(a)(ii) 12 1 5(b)(i) (5, 2) 1 5(b)(ii)(a) (−5, 2) 1 5(b)(ii)(b) (5, 10) 2 B1 for (5, k) or (7, 2) 5(b)(iii)  44  2 FT their (b)(i)    −14   44   49 − their 5  B1 for   or    k   k   k   k  or   or    −14   −12 − their 2  5(c)(i) Enlargement 3 B1 for each (SF) 0.5 oe (centre) (−3, 1) 5(c)(ii) Rotation 3 B1 for each 180° (centre) (4, 8)

This question in 0980/32 May/June 2019

5 Triangles A, B and C are shown on the grid. y 8 7 6 5 A B 4 C 3 2 1 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 – 1 – 2 – 3 – 4 – 5 – 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C. … … [3] (b) On the grid, 6 (i) translate triangle A by the vector [2] e- 2o, (ii) reflect triangle A in the line y = 1. [2]

10 marks

Mark scheme: 5(a)(i) Rotation 3 B1 for each 90° clockwise oe [centre] (0, 0) oe 5(a)(ii) Enlargement 3 B1 for each [sf] 0.5 oe [centre] (1, 2) 5(b)(i) Triangle at (3, 2) (1, 5) (1, 2) 2 6  k  B1 for translation of  or   k  − 2  5(b)(ii) Triangle at (–3, –2) (–5, –2) (–5, –5) 2 B1 for reflection in y = k or x = 1

This question in 0980/31 Oct/Nov 2019

8 y 6 5 4 3 B 2 A 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -1 C -2 -3 D -4 -5 -6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C, … … [2] (iii) triangle A onto triangle D. … … [3] (b) On the grid, draw the image of triangle A after a reflection in the line y =- 1. [2]

10 marks

Mark scheme: 8(a)(i) Rotation 3 B1 for each [centre] (0, 0) oe 90° [anticlockwise] oe 8(a)(ii) Translation 2 B1 for each  − 6     − 3  8(a)(iii) Enlargement 3 B1 for each [centre] (6, 4) [sf] 3 8(b) Correct reflection 2 B1 for correct reflection in y = k (2, −3), (2, −4), (5, −3)

This question in 0980/32 May/June 2020

8 y 6 5 4 3 D 2 C 1 0 x – 6 – 5 – 4 – 3 – 2 – 11 1 2 3 4 5 6 ––11 A ––22 – 3 – 4 B – 5 – 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C, … … [2] (iii) triangle A onto triangle D. … … [3] (b) On the grid, draw the image of triangle A after a reflection in the line x =- 2 . [2]

10 marks

Mark scheme: 8(a)(i) Rotation 3 B1 for each [centre] (2, −2) 90° [anticlockwise] oe 8(a)(ii) Translation 2 B1 for each  − 4     3  8(a)(iii) Enlargement 3 B1 for each [centre] (−2, −5) [sf] 2 8(b) Correct reflection of triangle 2 B1 for correct reflection in lines x = k points at (−3, 0) (−3, −2) (−6, −2) or y = −2

This question in 0980/31 Oct/Nov 2020

id. C (a) Write down the mathematical name of the shaded polygon. … [1] (b) Find the area of the shaded polygon. … cm2 [2] (c) Describe fully the single transformation that maps (i) the shaded polygon onto polygon A, … … [2] (ii) the shaded polygon onto polygon B, … … [3] (iii) the shaded polygon onto polygon C. … … [3] (d) On the grid, draw the image of the shaded polygon after a reflection in the line y = 0 . [2]

13 marks

Mark scheme: 2(a) Pentagon 1 2(b) 12 2 B1 for 10 to 14 2(c)(i) Translation 2 B1 for each 7  4 2(c)(ii) Rotation 3 B1 for each [centre] (0, 0) oe 180° 2(c)(iii) Enlargement 3 B1 for each [centre] (4, 2) [scale factor] 0.5 oe 2(d) Correct reflection 2 B1 for a correct reflection in x = 0 or in (−2, −2), (−1, −4), (−2, −6), (−4, −6) y = k k ≠ 0 or for 4 correct points (−6, −4)

This question in 0980/32 May/June 2021

9 y 8 7 B 6 5 A 4 3 2 1 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 x - 1 - 2 - 3 - 4 (a) On the grid, draw the image of (i) triangle A after a rotation of 90° clockwise about the origin, [2] (ii) triangle A after a reflection in the line x = 5 , [2] (iii) triangle A after an enlargement, scale factor 2, centre (7, 7). [2] (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [2]

8 marks

Mark scheme: 9(a)(i) Triangle at (2, –3), (5, –3), (5, –2) 2 B1 for correct size and orientation but wrong position or for correct 90° anticlockwise about the origin 9(a)(ii) Triangle at (7, 2), (7, 5), (8, 5) 2 B1 for reflection in y = 5 or x = k (k ≠ 5) 9(a)(iii) Triangle at (–3, 3), (–1, 3), (–1, –3) 2 B1 for correct size and orientation but wrong centre 9(b) Translation 2 B1 for each  − 7    oe  2 

This question in 0980/31 Oct/Nov 2021

9 The grid shows three shapes, A, B and C. y 4 3 2 1 0 x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 – 1 – 2 A – 3 – 4 – 5 C – 6 B – 7 – 8 – 9 – 10 (a) Describe fully the single transformation that maps (i) shape A onto shape B, … … [2] (ii) shape A onto shape C. … … [3] (b) On the grid, draw the image of shape A after a rotation, 90° clockwise, centre (6, -3). [2]

7 marks

Mark scheme: 9(a)(i) Translation 2 B1 for each   7      4  9(a)(ii) Enlargement 3 B1 for each [centre] ( 1,0) [scale factor] 2 9(b) Shape correctly drawn 2 B1 for correct 90° anticlockwise rotation about (6,  3) at (6, –3) (7, –3) (7, 1) (4, 1) or correct orientation but rotated about the wrong centre (4, –1) (5, –1) (5, 0) (6, 0)

This question in 0980/32 May/June 2022

2 Triangles A, B and C are shown on the grid. y 6 5 4 3 A 2 C 1 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 x - 1 - 2 B - 3 - 4 - 5 - 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C. … … [3] (b) On the grid, (i) reflect triangle A in the line y = 0 , [2] - 7 (ii) translate triangle A by the vector [2] e 1o.

10 marks

Mark scheme: 2(a)(i) Rotation 3 B1 for each 180° (0, 0) 2(a)(ii) Enlargement 3 B1 for each 0.5 oe (–1, 1) 2(b)(i) Shape drawn at (3, –1), (5, –1), (3, –5) 2 B1 for reflection in x = 0 or y = k 2(b)(ii) Shape drawn at (–4, 2), (–2, 2), (–4, 6) 2  −7  k B1 for a translation by   or   k  1

This question in 0980/31 Oct/Nov 2022

6 (a) For each quadrilateral, draw any lines of symmetry and write down its mathematical name. (i) Name … [3] (ii) Name … [2] (b) The diagram shows three triangles A, B and C, on a grid. y 7 6 5 4 3 A 2 1 – 7 – 6 – 5 –– 44 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 C – 2 – 3 B – 4 – 5 – 6 – 7 (i) Describe fully the single transformation that maps (a) triangle A onto triangle B … … [3] (b) triangle A onto triangle C. … … [3] (ii) On the grid, reflect triangle A in the line x =- 1. [2]

13 marks

Mark scheme: 6(a)(i) Two correct diagonals 2 B1 for one accurate diagonal and no extra or two correct and one extra rhombus 1 6(a)(ii) 1 correct diagonal 1 kite 1 6(b)(i)(a) Enlargement 3 B1 for each (sf=) 3 oe (centre) (4, 6) oe 6(b)(i)(b) Rotation 3 B1 for each 90° clockwise oe (centre) (0, 0) oe 6(b)(ii) Correct reflection, points (–3, 2) 2 B1 for a correct reflection in y = −1 (–6, 2) (–3, 4) or in x = k

This question in 0980/32 May/June 2023

6 y 10 9 8 7 6 5 4 A 3 2 1 B x - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 - 1 C - 2 - 3 - 4 - 5 - 6 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (c) On the grid, draw the image of triangle A after a reflection in the line y = 6 . [2]

7 marks

Mark scheme: 6(a) Translation 2 B1 for each  2     −3  6(b) Enlargement 3 B1 for each (sf = ) 3 (centre = ) (4, 6) 6(c) Correct reflection 2 B1 for correct reflection in line y = k points (1, 7), (1, 9), (5, 9)

This question in 0980/31 Oct/Nov 2023

nd D (a) Write down the mathematical name of quadrilateral A. … [1] (b) (i) Find the area of quadrilateral A. … cm2 [1] (ii) Measure the perimeter of quadrilateral A. … cm [1] (c) Describe fully the single transformation that maps (i) quadrilateral A onto quadrilateral B … … [2] (ii) quadrilateral A onto quadrilateral C … … [2] (iii) quadrilateral A onto quadrilateral D. … … [3] (d) On the grid, enlarge quadrilateral A by scale factor 2, centre ( - 3, - 3) . [2]

12 marks

Mark scheme: 3(a) Trapezium 1 3(b)(i) 7.5 1 3(b)(ii) 11 to 11.4 1 3(c)(i) Translation 2 B1 for each  9     7  3(c)(ii) Reflection 2 B1 for each y = −3 oe 3(c)(iii) Rotation 3 B1 for each (0, 0) 90° clockwise 3(d) Trapezium drawn at 2 B1 for correct enlargement, scale factor (−1, 5),(−7, 5),(−7, 11),(−3, 11) 2, but in the wrong position.

This question in 0980/32 May/June 2024

4 (a) A parallelogram ABCD has sides 8 cm and 6 cm. Lines AB and BC have been drawn. By constructing triangle ACD, complete the parallelogram. Use a ruler and compasses only and leave in your construction arcs. A 6 cm B 8 cm C [2] (b) y 7 6 5 B 4 3 A 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 – 4 – 5 – 6 (i) Describe fully the single transformation that maps shape A onto shape B. … … [2] (ii) On the grid, draw the image of shape A after a rotation, 90° anticlockwise, centre (5, 1). [2]

6 marks

Mark scheme: 4(a) Correct parallelogram 2 B1 for triangle constructed onto given pair of lines with one correct and one incorrect arc or correct triangle with no arcs or for no triangle but two correct arcs only. If 0 scored SC1 for triangle constructed onto given pair of lines with arcs but lines interchanged 4(b)(i) Translation 2 B1 for each  −6     2  4(b)(ii) Correct shape with coordinates 2 B1 for correct 90 clockwise rotation (5, 1) (5, –3) (2, –3) (2, –1) (4, –1) (4, 1) about (5, 1) or correct orientation, wrong centre

This question in 0980/31 Oct/Nov 2024

15 Shapes A and B are shown on the grid. y 5 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 B – 3 A – 4 – 5 – 6 (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] 6 (b) On the grid, draw the image of shape A after a translation by the vector e o. [2] 7

5 marks

Mark scheme: 15(a) Enlargement 3 B1 for each [centre] (0,0) [scale factor] 0.5 15(b) Triangle at (2,2) (4,2) (2,5) 2  k   6  B1 for translation by   or    7   k 

This question in 0980/31 Oct/Nov 2025