Transformations — Paper 4 · IGCSE Mathematics - International 0607

4 y 9 8 7 A 6 5 4 3 2 1 x 0 –9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 –7 –8 –9 J N 0 (a) Translate triangle A with vector KK OO. Label the image B. [2] - 4 L P (b) Rotate triangle A through 90° anticlockwise about (0, 0). Label the image C. [2] (c) Describe fully the single transformation that maps triangle C onto triangle A. … … [2] (d) Reflect triangle A in the line y =- x . Label the image D. [3] (e) Describe fully the single transformation that maps triangle C onto triangle D. … … [2]

11 marks

Mark scheme: 4(a) Correct triangle (2, 1) (3, 1) (2, 4) 2  k  0 B1 for translation   or   − 4  k 4(b) Correct triangle 2 B1 for correct rotation, incorrect centre (–5, 2) (–5, 3) (–8, 2) or for rotation 90° clockwise, correct centre 4(c) Rotation [Centre] (0, 0) 2 B1 for each 90° clockwise oe 4(d) Correct triangle 3 B1 for y = – x soi (–5, –2) (–5, –3) (–8, –2) M1 for correct shape, incorrect location 4(e) Reflection 2 B1 for each x-axis oe

This question in 0607/41 May/June 2017

2 (a) (i) Reflection in the line y = x maps triangle A onto triangle B. Describe fully the single transformation that maps triangle B onto triangle A. … … [1] (ii) Enlargement, with centre (2, 1) and scale factor 4, maps triangle C onto triangle D. Describe fully the single transformation that maps triangle D onto triangle C. … … [2] J N - 3 (iii) Translation by the vector KK OO maps triangle E onto triangle F. 5 L P Describe fully the single transformation that maps triangle F onto triangle E. … … [2] (b) y 4 3 2 1 P x 0 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4 (i) Rotate triangle P through 90° anticlockwise about (0, 0). Label the image Q. [2] (ii) Stretch triangle P with stretch factor 2 and the y-axis invariant. Label the image R. [2]

9 marks

Mark scheme: 2(a)(i) Reflection, y = x 1 2(a)(ii) Enlargement [with centre] (2, 1) 2 B1 for each 1 [scale factor] oe 4 2(a)(iii) Translation 2 B1 for each  3     −5  2(b)(i) Correct triangle 2 SC1 for rotation 90° clockwise about (0, 0) (0, 0), (0, 2), (–2, 3) or rotation 90° anti-clockwise about different centre 2(b)(ii) Correct triangle 2 SC1 for stretch with s.f. = 2, x-axis invariant or (0, 0), (4, 0), (6, 2) stretch with y-axis invariant with different scale factor.

This question in 0607/42 May/June 2017

1 y 10 9 8 7 6 5 4 3 2 1 x –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 T –3 –4 –5 U –6 –7 –8 –9 –10 J N - 2 (a) Translate triangle T by the vector KK OO. [2] 7 L P (b) (i) Reflect triangle T in the x-axis. Label the image P. [1] (ii) Reflect triangle T in the line x =- 1. Label the image Q. [1] (iii) Describe fully the single transformation that maps triangle P onto triangle Q. … … [3] (c) Describe fully the single transformation that maps triangle T onto triangle U. … … [3]

10 marks

Mark scheme: Question Answer Marks Part Marks 1(a) Image at (0, 5), (3, 5), (3, 3) 2  −2  k SC1 for translation   or   k  7 1(b)(i) Image at (2, 2), (5, 2), (5, 4) 1 1(b)(ii) Image at (– 4, – 2), (– 7, – 2), (– 7, – 4) 1 1(b)(iii) Rotation 3 B1 for each 180 [centre] (– 1 , 0) 1(c) Stretch 3 B1 for each [factor]2 x-axis oe invariant

This question in 0607/43 May/June 2017

3 y 6 5 4 3 2 Q 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 P –3 –4 –5 –6 –7 –8 (a) (i) Reflect shape P in the line y = 1. Label the image A. [2] (ii) Rotate shape P through 90° clockwise about (- 1, 1) . Label the image B. [2] (iii) Describe fully the single transformation that maps shape A onto shape B. … … [2] (b) Describe fully the single transformation that maps shape P onto shape Q. … … [3] (c) Stretch shape P with the x-axis invariant and factor 2. [2]

11 marks

Mark scheme: 3(a)(i) Image at (2, 4), (3, 6), (6, 6), (6, 4) 2 SC1 for reflection in other horizontal line or in the line x = 1 3(a)(ii) Image at (– 4, – 2), (– 6, – 3), 2 SC1 for correct orientation but wrong (– 6, – 6), (– 4, – 6) centre 3(a)(iii) Reflection 2 B1 for each y = – x oe 3(b) Enlargement 3 B1 for each [centre] (0, 0) oe [factor] – 0.5 oe 3(c) Image at (2, – 4), (6, – 4), (6, – 8), 2 SC1 for stretch with x-axis invariant with (3, – 8) other factor or stretch with y = k invariant with stretch factor 2

This question in 0607/42 Oct/Nov 2017

8 You may use the grid to help you in answering this question. The transformation P is a rotation through 90° anti-clockwise about the origin. The transformation Q is a reflection in the line y =- x . (a) Find the image of the point (5, 1) under the transformation P. ( … , … ) [2] (b) Find the image of the point (5, 1) under the transformation Q. ( … , … ) [2] (c) Describe fully the single transformation equivalent to the transformation P followed by the transformation Q. … … [2]

6 marks

Mark scheme: 8(a) (–1, 5) 2 B1 for each 8(b) (–1, –5) 2 B1 for each 8(c) Reflection 2 B1 for each y-axis oe

This question in 0607/43 Oct/Nov 2017

1 y 10 9 A 8 7 6 5 4 3 2 B T 1 x −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 (a) Describe fully the single transformation that maps (i) triangle T onto triangle A, … … [2] (ii) triangle T onto triangle B. … … [2] (b) Enlarge triangle T with centre (5, 0) and scale factor 2. [2] (c) Stretch triangle T with the y-axis invariant and factor 2. [2]

8 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Translation 2 B1 for each 1  7 1(a)(ii) Reflection 2 B1 for each 1 x = – oe 2 1(b) Triangle drawn at 2 B1 for enlargement factor 2 with wrong (3, 2), (3, 4), (–3, 2) centre, or correct centre with wrong positive factor (not 1) 1(c) Triangle drawn at 2 B1 for stretch factor 2 with x-axis invariant. (2, 1), (8, 1), (8, 2) or stretch factor 2 translated horizontally

This question in 0607/41 May/June 2018

6 y 10 8 6 4 A 2 x −8 −6 −4 −2 0 2 4 6 8 −2 −4 −6 −8 −10 - 7 (a) Translate triangle A with vector Label the image B. [2] e- 3o. (b) Rotate triangle A through 90° anti-clockwise about (-1, 2). Label the image C. [2] (c) Describe fully the single transformation that maps triangle C onto triangle B. … … [3] (d) Enlarge triangle A scale factor -2 with centre (3, 1). Label the image D. [2] (e) Describe fully the single transformation that maps triangle D onto triangle A. … … [2]

11 marks

Mark scheme: 6(a) Correct triangle. 2  − 7   k  (–6, –1), (–4, –1), (–6, 3) B1 for   or    k   − 3  6(b) Correct triangle. 2 B1 for correct rotation about any centre (–1, 4), (–1, 6), (–5, 4) or for correct centre but 90o clockwise 6(c) Rotation 3 B1 for each 90o clockwise oe [Centre] (–6, 4) 6(d) Correct triangle. 2 B1 for correct enlargement with wrong centre (3, –1), (7, –1), (7, –9) 6(e) Enlargement [centre] (3, 1) 2 B1 for each [SF] –0.5

This question in 0607/42 May/June 2018

3 y 10 9 8 7 6 5 4 3 A 2 1 B x –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 –3 –4 –5 –6 –7 3 (a) Draw the image of triangle A after a translation by the vector [2] c- 7m. (b) Draw the image of triangle B after a stretch, factor 3 and the x-axis invariant. [2] (c) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

7 marks

Mark scheme: 3(a) Triangle at (4, –4), (5, –4), (5, –6) 2 3  k  B1 for translation  or   k  −1  3(b) Triangle at (5, 0), (7, 0), (7, 3) 2 B1 for any stretch in with x-axis invariant or correct stretch translated vertically 3(c) Rotation 3 90° clockwise oe B1 for each (3, –1)

This question in 0607/43 May/June 2018

6 y 9 8 7 6 5 4 A 3 2 1 x 0 –9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 –7 –8 –9 (a) Reflect triangle A in the line x =- 2 . Label the image B. [2] (b) Rotate triangle A through 180° about (-2, -1). Label the image C. [2] (c) Describe fully the single transformation that maps triangle C onto triangle B. … … [2] (d) Enlarge triangle A with centre of enlargement (1, 2) and scale factor 2. Label the image D. [2]

8 marks

Mark scheme: 6(a) Vertices (–5, 3) (–8, 3) (–8, 5) 2 B1 for reflection in x = k , k ≠−2 or B1 for reflection in y = –2 6(b) Vertices (–5, –5) (–8, –5) (–8, –7) 2 B1 for correct rotation with incorrect centre of rotation. 6(c) Reflection 2 B1 for each y = –1 cao 6(d) Vertices (1, 4) (7, 4) (7, 8) 2 M1 for enlargement SF2 different centre or for enlargement different SF, correct centre

This question in 0607/41 Oct/Nov 2018

3 y 7 6 B 5 4 3 2 1 A x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 –3 –4 –5 -5 (a) Translate triangle A by the vector . [2] e 3o (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (c) Describe fully the single transformation that is equivalent to a reflection in y = -x followed by a reflection in the y-axis. You may use the grid below to help you. … … [3]

8 marks

Mark scheme: 3(a) Triangle at (–5, 3), (–1, 3), (–1, 5) 2  − 5  k B1 translation   or   k  3 3(b) Enlargement 3 B1 for each 1 [Scale factor] − 2 [Centre] (6, 4) 3(c) Rotation 3 B1 for each 90° clockwise oe (0, 0)

This question in 0607/42 Oct/Nov 2018

2 y 11 10 9 8 C 7 6 5 4 3 2 1 A 0 x 1 2 3 4 5 6 7 8 9 10 11 12 – 1 – 2 B – 3 – 4 – 5 (a) Describe fully the single transformation that maps triangle A onto triangle B. … [2] 6 (b) Translate triangle A by the vector . [2] e- 3o (c) Triangle A can be mapped onto triangle C by a rotation followed by an enlargement. (i) Use trigonometry to calculate the angle of rotation. … [3] (ii) The scale factor of the enlargement is a where a is an integer. Find the value of a. a = … [3]

10 marks

Mark scheme: 2(a) Reflection 2 B1 for each y = –1 2(b) Triangle at (6, –3), (11, –3), 2  k  6 B1 for translation   or  (10, –1)  −3  k 2(c)(i) 63.4 or 63.43 to 63.44 3 4 B2 for tan [θ ] = oe 2 or B1 for correct angle clearly identified and no other angle seen. 2(c)(ii) 5 3 125 10 5 M2 for or or 5 20 5 or M1 for 10 2 + 5 2 or 4 2 + 2 2 or 12 + 2 2 or 125 or 20 or 5

This question in 0607/41 May/June 2019

6 y 6 5 Q 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 P – 2 – 3 – 4 – 5 – 6 (a) Reflect shape P in the y-axis. [1] 6 (b) Translate shape P by the vector [2] e- 3o. (c) Describe fully the single transformation that maps shape P onto shape Q. … … [3] (d) Stretch shape P with stretch factor 2 and the x-axis invariant. [2]

8 marks

Mark scheme: 6(a) Correct reflection at (1, –1), 1 (4, –1), (4, –3), (3, –3) 6(b) Correct translation at (5, – 4), 2  6   k  (2, – 4), (2, – 6), (3, – 6) B1 for translation   or    k   −3  6(c) Rotation 3 B1 for each 90[º] clockwise oe (0, 1) 6(d) Correct stretch at (–1, –2), 2 B1 for stretch factor 2 displaced vertically (– 4, –2), (– 4, – 6), (–3, – 6)

This question in 0607/42 May/June 2019

6 You may use this grid to help you answer this question. y 0 x The transformation P is a reflection in the line y = x. The transformation Q is a rotation of 180° about the origin. The transformation R is a stretch, scale factor 2 with x-axis invariant. The transformation S is a stretch, scale factor 2 with y-axis invariant. (a) (i) Find the co-ordinates of the image of the point (5, 1) under the transformation P. ( … , … ) [1] (ii) Find the co-ordinates of the image of the point (x, y) under the transformation P followed by the transformation Q. ( … , … ) [2] (iii) Describe fully the single transformation equivalent to P followed by Q. … … [2] (b) Describe fully the single transformation equivalent to R followed by S. … … [3] (c) Describe fully the single transformation equivalent to the inverse of R. … … [2]

10 marks

Mark scheme: 6(a)(i) (1, 5) 1 6(a)(ii) (–y, –x) 2 B1 for each co-ordinate 6(a)(iii) Reflection 2 B1 for each y = –x 6(b) Enlargement 3 B1 for each Scale factor 2 Centre (0, 0) 6(c) Stretch x-axis invariant 2 B1 for each SF 0.5

This question in 0607/43 May/June 2019

4 y 10 9 8 A 7 6 C 5 4 3 2 T 1 0 x 1 2 3 4 5 6 7 8 9 10 –1 B –2 –3 (a) Describe fully the single transformation that maps triangle T onto (i) triangle A, … … [2] (ii) triangle B, … … [3] (iii) triangle C. … … [3] (b) Stretch triangle T by a factor of 2 with the y–axis invariant. [2]

10 marks

Mark scheme: 4(a)(i) Translation 2 B1 for each  −1     6  4(a)(ii) Rotation 3 B1 for each [centre] (2, 1) 90 clockwise oe 4(a)(iii) Enlargement 3 B1 for each [centre] (3, 0) [factor] 3 4(b) Correct stretch at 2 B1 for stretch factor 2 with x-axis invariant (4, 1) (10, 1), (10, 3) or for stretch with x = k invariant with stretch factor 2

This question in 0607/41 Oct/Nov 2019

11 y 4 x 0 180 –4 f (x) = 3 sin (3 x°) (a) On the diagram, sketch the graph of y = f ( x) for 0 G x G 180. [2] (b) Write down the amplitude and the period of f (x). Amplitude = … Period = … [2] (c) Solve the inequality f (x) 1- 1.5 for 0 G x G 180. … [2] (d) g (x) = 3 sin ( x°) (i) On the same diagram, sketch the graph of y = g (x) for 0 G x G 180. [1] (ii) On the diagram, shade the regions where f (x) H g (x ). [1] (iii) Describe fully the single transformation that maps the graph of y = g (x) onto the graph of y = f (x). … … [3]

11 marks

Mark scheme: 11(a) Correct4444 sketch 2 B1 for sine graph with incorrect amplitude and/or incorrect period, passing through (0, 0). 2222 0000 0000 50505050 100100100100 150150150150 -2-2-2-2 -4-4-4-4 11(b) 3 2 B1 for each 120 11(c) 70 < x < 110 2 B1 for 70 and 110 seen 11(d)(i) Correct4444 sketch 1 2222 0000 0000 50505050 100100100100 150150150150 -2-2-2-2 -4-4-4-4 11(d)(ii) Two areas shaded, which are below 1 graph of y = f(x) and above graph of y = g(x) 11(d)(iii) Stretch 3 B1 for each 1 [factor] 3 invariant line y-axis oe

This question in 0607/41 Oct/Nov 2019

1 y 6 5 A 4 3 2 1 x – 6 –5 – 4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 – 4 –5 – 6 (a) Reflect triangle A in the x-axis. Label the image B. [1] 0 (b) Translate triangle A by the vector Label the image C. [1] e- 3o. (c) Describe fully the single transformation that maps triangle B onto triangle C. … … [2] (d) Rotate triangle A through 90° anti-clockwise, about the origin. Label the image D. [2] (e) Describe fully the single transformation that maps triangle B onto triangle D. … … [2]

8 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Correct triangle with vertices 1 (3, –5), (5, –5), (5, –4) 1(b) Correct triangle with vertices 1 (3, 2), (5, 2), (5, 1) 1(c) Reflection 2 B1 for each y = –1.5 oe 1(d) Correct triangle with vertices 2 B1 for correct rotation with incorrect centre of (–5, 3), (–5, 5), (–4, 5) rotation. or B1 for clockwise rotation with correct centre of rotation. 1(e) Reflection 2 B1 for each y = x oe

This question in 0607/42 Oct/Nov 2019

5 y 7 6 5 A 4 3 2 1 x –7 – 6 – 5 – 4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 C B –3 – 4 –5 – 6 –7 (a) Reflect triangle A in the line y = 1. [2] (b) Rotate triangle B through 90° clockwise about (1, 0). [3] (c) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (d) Describe fully the single transformation that maps triangle B onto triangle C. … … [3]

11 marks

Mark scheme: 5(a) Triangle at (2, 0), (2, –4), (4, –4) 2 B1 for reflection in y = k or x = 1 5(b) Triangle at (0, 2), (–2, 2), (–2, 3) 3 B2 for Rotation 90° anti-clockwise about (1, 0) or B1 for Rotation 90° clockwise about any centre. 5(c) Enlargement 3 B1 for each 1 [Scale factor] − oe 2 [Centre] (0, 0) oe 5(d) Stretch 3 B1 for each [Stretch factor] 3 Invariant [line] y-axis oe

This question in 0607/43 Oct/Nov 2019

1 y 5 4 3 2 T 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 – 2 Q – 3 – 4 P – 5 – 6 (a) (i) Reflect shape T in the y-axis. [1] - 5 (ii) Translate shape T by the vector [2] e 3o. (iii) Enlarge shape T by scale factor 2, centre (2, 0). [2] (b) Describe fully the single transformation that maps shape T onto (i) shape P, … … [3] (ii) shape Q. … … [3]

11 marks

This question in 0607/41 May/June 2020

2 (a) y 10 9 8 7 6 A 5 4 3 C 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 B – 5 – 6 (i) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (ii) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (b) You may use the grid to help you in answering this question. The transformation P is a rotation of 90° clockwise about the origin. The transformation Q is a reflection in the line y =- x . (i) Find the image of the point ( 5, - 2) under the transformation P. ( … , … ) [1] (ii) Find the image of the point ( 5, - 2) under the transformation Q. ( … , … ) [1] (iii) Describe fully the single transformation equivalent to P followed by Q. … … [2] (iv) Describe fully the single transformation equivalent to Q followed by P. … … [2]

11 marks

Mark scheme: 2(a)(i) Translation 2 B1 for each  − 6     − 10  2(a)(ii) Enlargement 3 B1 for each SF 2 Centre (0, 9) 2(b)(i) (–2, –5) 1 2(b)(ii) (2, –5) 1 2(b)(iii) Reflection 2 B1 for each x-axis oe 2(b)(iv) Reflection 2 B1 for each y-axis oe

This question in 0607/42 May/June 2020

5 (a) (i) A reflection in the line y = 3 maps triangle A onto triangle B. Describe fully the single transformation that maps triangle B onto triangle A. … … [1] 5 (ii) A translation using the vector maps triangle C onto triangle D. e- 4o Describe fully the single transformation that maps triangle D onto triangle C. … … [2] (iii) An enlargement, centre ( 2, - 1) , scale factor 3, maps triangle G onto triangle H. Describe fully the single transformation that maps triangle H onto triangle G. … … [2] (b) y 6 5 4 3 D A 2 1 x – 11 – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 1 – 2 – 3 – 4 (i) Rotate triangle A through 90° anticlockwise, centre (-1, 0). Label the image B. [2] 1 (ii) Enlarge triangle A with scale factor - , centre (1, 3). 2 Label the image C. [2] (iii) Describe fully the single transformation that maps triangle A onto triangle D. … … [3]

12 marks

Mark scheme: 5(a)(i) Reflection in the line y = 3 1 5(a)(ii) Translation 2 B1 for each  − 5     4  5(a)(iii) Enlargement [centre] (2, –1) 2 B1 for each 1 [scale factor] 3 5(b)(i) Triangle at (–6, 0), (–2, 0), (–2, – 2) 2 B1 for rotation 90° clockwise about (–1, 0) or 90° anticlockwise about another centre 5(b)(ii) Triangle at (2, 2), (2, 4), (3, 4) 2 1 B1 for enlargement scale factor – , 2 wrong centre 1 or scale factor , centre (1, 3) 2 5(b)(iii) Stretch 3 B1 for each [Stretch factor] 3 Invariant line y-axis oe 6a)(i) 74 1

This question in 0607/43 May/June 2020

9 y A NOT TO SCALE B O x C A is the point (-2, 6), B is the point (3, 2) and C is the point (3, -4). (a) Write down the equation of BC. … [1] (b) Find the coordinates of the point M, the mid-point of AC. ( … , … ) [1] (c) The quadrilateral ABCD has rotational symmetry of order 2 about the point M. Find the coordinates of the point D. ( … , … ) [2] (d) Find the equation of the perpendicular bisector of AC. … [4]

8 marks

Mark scheme: 9(a) x = 3 oe 1 9(b)  1  1  , 1  oe  2  9(c) (–2, 0) 2 B1 for each coordinate 9(d) 1 3 4 3 term equivalent y = x + oe −−4 6 2 4 M1 for gradient of AC = 3 −−( 2) −1 M1 for m = theirgradient M1 for substituting their (b) into their y = mx + c

This question in 0607/43 May/June 2020

4 (a) y 8 7 6 5 4 C 3 B 2 A 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 (i) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (ii) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (iii) On the grid, draw the stretch of triangle A, scale factor 2, y-axis invariant. [2] (b) Describe fully the single transformation that is the inverse of (i) a reflection in y = 2 , … … [1] - 5 (ii) a translation with vector . e 2o … … [2]

11 marks

Mark scheme: 4(a)(i) Rotation, 3 B1 for each [Centre] (0, 0) [Anticlockwise] 90 or clockwise 270 4(a)(ii) Enlargement 3 B1 for each [Scale factor] 2 [Centre] (–1, –1) 4(a)(iii) Correct triangle 2 B1 for correct stretch with x-axis (2, 1) (6, 1) (6, 2) invariant or B1 for correct SF in wrong position 4(b)(i) Reflect 1 y = 2 4(b)(ii) Translation 2 B1 for each  5     − 2 

This question in 0607/41 Oct/Nov 2020

9 p = q = 3 - 1 A is the point (3, 4). (a) Find p - q . [1] f p (b) A is translated onto H by the vector p. Find the coordinates of H. ( … , … ) [1] (c) J is translated onto A by the vector q. Find the coordinates of J. ( … , … ) [1] (d) Find the coordinates of the mid-point of HJ. ( … , … ) [1] (e) Find the length of HJ. HJ = … [3] 1 (f) A line L, parallel to the vector q, has gradient - . 2 Find the equation of the line perpendicular to the line L that passes through the point A. … [3]

10 marks

Mark scheme: 9(a)  − 3  1    4  9(b) (2, 7) 1 9(c) (1, 5) 1 9(d) (1.5, 6) 1 FT their (b) and (c). 9(e) 2.24 or 2.236... 3 FT their (b) and (c). M2 for (their 2 – their 1)2 + (their 7 – their 5)2 oe or M1 for (their 2 – their 1) and (their 7 – their 5) seen 9(f) y = 2x – 2 oe 3 − 1 M1 for gradient = oe soi 2 1 − 2 M1 for substituting (3, 4) in y = their m x + c Answer 2x – 2 implies M1 M1

This question in 0607/43 Oct/Nov 2020

10 (a) y 6 5 4 3 V 2 T 1 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 1 – 2 – 3 – 4 – 5 – 6 (i) Describe fully the single transformation that maps shape T onto shape V. … … [3] (ii) Reflect shape T in the line y =- 2 . [2] (iii) Stretch shape T by a factor of 2 with the x-axis invariant. [2] (b) f ( x) = log ( x) g ( x) = log ( x3 ) Describe fully the single transformation that maps the graph of y = f ( x) onto the graph of y = g ( x) . … … [3] Question 11 is printed on the next page.

10 marks

Mark scheme: 10(a)(i) Rotation 3 B1 for each 90 [anticlockwise] oe (0, 0) oe 10(a)(ii) Image at 2 B1 for reflection in y = k (1, –5), (2, –6), (4, –6), (4, –5) 10(a)(iii) Image at (1, 2), (2, 4), (4, 2), (4, 4) 2 B1 for other stretch, factor 2, y = k invariant or y-axis invariant 10(b) Stretch 3 B1 for each [factor] 3 x-axis oe invariant If 0 scored M1 for [g(x)] = 3log x

This question in 0607/43 Oct/Nov 2020

1 (a) y 10 8 6 4 2 A – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 x – 2 – 4 – 6 (i) Rotate triangle A through 90° anticlockwise about (0, 0). Label the image B. [2] (ii) Reflect triangle A in the y-axis. Label the image C. [1] (iii) Describe fully the single transformation that maps triangle B onto triangle C. … … [2] (b) y 6 E E 4 2 DD 0 2 4 6 8 10 12 x Describe fully the single transformation that maps trapezium D onto trapezium E. … … [3]

8 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) correct triangle B 2 B1 for 90° rotation about wrong centre (0, 3) (0, 8) (−3, 3) 1(a)(ii) correct triangle C 1 (−3, 0) (−8, 0) (−3, 3) 1(a)(iii) reflection 2 B1 for each 𝑥+ 𝑦= 0 oe 1(b) enlargement 3 B1 for each [scale factor] 3 [centre] (0, 0) oe

This question in 0607/42 Feb/March 2021

2 y 9 8 7 6 A 5 4 3 2 1 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 x – 1 – 2 – 3 – 4 – 5 – 6 - 3 (a) Translate triangle A with vector Label the image B. [2] b - 5 l. (b) Describe fully the single transformation that maps triangle B onto triangle A. … … [2] (c) Rotate triangle A through 90° clockwise about (0, 0). Label the image C. [2] (d) Reflect triangle A in the line y = x . Label the image D. [2] (e) Describe fully the single transformation that maps triangle C onto triangle D. … … [2]

10 marks

Mark scheme: 2(a) Correct triangle 2 B1 for correct translation in y or for (–8, –1) (–7, –1) (–8, 3) correct translation in x 2(b) Translation 2 B1 for each 3  5 2(c) Correct triangle 2 M1 for correct rotation, wrong centre (4, 4) (4, 5) (8, 5) or for rotation anticlockwise 90°, about O 2(d) Correct triangle 2 M1 for correct orientation, incorrect (4, –4) (4, –5) (8, –5) position or for reflection in y = –x 2(e) Reflection 2 B1 for each y = 0 oe

This question in 0607/41 May/June 2021

2 (a) y 9 8 7 6 5 B 4 3 2 A 1 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 (i) Rotate triangle A 90° anticlockwise about (-1, 2). [2] (ii) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) Describe fully the single transformation that is equivalent to reflection in x = 3 followed by reflection in x = 7. You may use the grid below to help you. … … [2]

7 marks

Mark scheme: 2(a)(i) Triangle at (–2, 4), (0, 4), (0, 5) 2 B1 for rotation 90° clockwise about (–1, 2) or rotation anticlockwise 90° about wrong centre 2(a)(ii) Stretch 3 B1 for each [Factor] 2 Invariant [line] y = –1 oe 2(b) Translation 2 B1 for each 8  0

This question in 0607/42 May/June 2021

2 You may use this grid to help you answer this question. y O x Transformation P is a rotation of 180° about the origin. Transformation Q is a reflection in the line y = x . (a) Find the coordinates of the image of the point (5, 2) under transformation P. ( … , … ) [1] (b) Find the coordinates of the image of the point (5, 2) under transformation Q. ( … , … ) [1] (c) Find the coordinates of the image of the point (x, y) under transformation P followed by transformation Q. ( … , … ) [2] (d) Describe fully the single transformation that is equivalent to transformation Q followed by transformation P. … … [2]

6 marks

Mark scheme: 2(a) (–5, –2) 1 2(b) (2, 5) 1 2(c) (–y, –x) 2 B1 for each. If 0 scored SC1 for answer (–2, –5) 2(d) Reflection 2 B1 for each y = − x

This question in 0607/43 Oct/Nov 2021

1 y 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x T – 1 – 2 P – 3 - 2 (a) Translate triangle T by the vector [2] e 2o. (b) Reflect triangle T in the line y = 0 .5 . [2] (c) Describe fully the single transformation that maps triangle P onto triangle T. … … [3] (d) Enlarge triangle P with scale factor - 2 , centre ( 3, - 1) . [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) correct triangle 2 k  2  (−4, 1) (−3, 1) (−3, 1.5) B1 for translation  or   or 2  k   1  translation through    1  1(b) correct triangle 2 B1 for reflection in either y = k or (−1, 1.5) (−1, 2) (−2, 2) x = 0.5 1(c) Rotation 3 B1 for each 180⁰ (1, −1.5) 1(d) correct triangle 2 B1 for any enlargement scale factor −2 (3, 1) (3, 2) (1, 1)

This question in 0607/41 May/June 2022

1 y 8 7 6 5 A B 4 3 2 1 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Rotate triangle B through 90° clockwise with centre of rotation (1, 0). Draw this triangle and label it C. [2] (c) Describe fully the single transformation that maps triangle C onto triangle A. … … [2]

6 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Reflection 2 B1 for each x = 1 oe 1(b) Correct triangle 2 B1 for correct rotation with incorrect centre (5, –4) (5, –7) (7, –7) or 90 rotation anticlockwise about correct centre 1(c) Reflection 2 B1 for each y = x – 1 oe

This question in 0607/42 May/June 2022

3 y 10 9 8 D 7 6 5 4 B 3 2 A 1 0 x – 6 –5 – 4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 C –1 –2 –3 – 4 The diagram shows triangles A, B, C and D and the line with equation x + y = 9 . (a) Enlarge triangle A with centre (4, 3) and scale factor 3. [2] (b) Describe fully the single transformation that maps triangle A onto (i) triangle B, … … [2] (ii) triangle C. … … [3] (c) Triangle A can be mapped onto triangle D by a rotation of 90° clockwise about a point on the line x + y = 9 followed by a reflection. Find one possible centre of rotation and the equation of the corresponding mirror line. Centre ( … , … ) Equation of mirror line … [2]

9 marks

Mark scheme: 3(a) Triangle at (1, 0), (–5, 0), (–5, –3) 2 B1 for enlargement with centre (4, 3) wrong scale factor or enlargement scale factor 3 with wrong centre. 3(b)(i) Translation 2 B1 for each  5     2  3(b)(ii) Stretch 3 B1 for each Invariant line y = 4 [Factor] 2 3(c) e.g. 2 B1 for point on x + y = 9 and x = k (7, 2) x = 5.5 (6, 3) x = 4.5 (8, 1) x = 6.5 (9, 0) x = 7.5 (5, 4) x = 3.5 (4, 5) x = 2.5 (3, 6) x = 1.5

This question in 0607/43 May/June 2022

1 y 10 9 8 7 6 B 5 A 4 3 2 1 0 x –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] 3 (b) Translate triangle A by vector Label the image C. [2] e- 6o. (c) Rotate triangle B through 90° clockwise about (3, 6). Label the image D. [2] (d) Reflect triangle B in the line y = 1. Label the image E. [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Rotation 3 B1 for each 180 Centre (0, 5) 1(b) Correct triangle 2 3  k  (–3, 0) (–3, –2) (0, –2) B1 for translation  or   k  −6  1(c) Correct triangle 2 B1 for correct rotation with incorrect centre (3, 6) (3, 3) (1, 3) or for rotation 90 anticlockwise with correct centre 1(d) Correct triangle 2 B1 for reflection in y = k , or x = 1 (6, –4) (6, –2) (3, –4)

This question in 0607/41 Oct/Nov 2022

1 y 12 11 10 9 8 P 7 6 5 Q T 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 x (a) Rotate triangle T through 90° clockwise about the point (9, 6). [2] (b) Enlarge triangle T with scale factor 1, centre (0, 0). [2] 2 (c) Describe fully the single transformation that maps triangle T onto triangle P. … … [2] (d) Describe fully the single transformation that maps triangle T onto triangle Q. … … [3]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Triangle at (7, 7), (9, 7), (7, 11) 2 B1 for correct orientation but incorrect position or for 90° anticlockwise rotation 1(b) Triangle at (2, 2), (4, 2), (4, 3) 2 B1 for correct size and orientation but incorrect position 1(c) Translation 2 B1 for each  −3     3  1(d) Stretch 3 B1 for each 1 2 x = 1 invariant

This question in 0607/43 Oct/Nov 2022

2 y 10 9 8 C A 7 6 5 4 3 2 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 – 4 – 5 B – 6 – 7 (a) Describe the single transformation that maps triangle A onto triangle B. … … [2] (b) Describe the single transformation that maps triangle A onto triangle C. … … [3] (c) Reflect triangle B in the line y = 1. Label the image D. [2] (d) Enlarge triangle B scale factor 2, centre (-6, -6). Label the image E. [2]

9 marks

Mark scheme: 2(a) Translation 2 B1 for each  −11     −13  2(b) Rotation 3 B1 for each 90 clockwise oe [Centre] (4, 9) 2(c) Correct triangle 2 B1 for correct reflection in y = k , (–6, 8) (–6, 7) (–3, 7) 2(d) Correct triangle 2 B1 for correct SF enlargement, incorrect (–6, –6) (–6, –4) (0, –4) position

This question in 0607/42 Feb/March 2023

3 y 9 8 7 6 5 C 4 3 B A 2 1 x 0 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 – 1 – 2 – 3 – 4 – 5 – 6 – 7 (a) Reflect triangle A in the line y =- 1. [2] - 5 (b) Translate triangle A by the vector [2] e 3o. (c) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (d) Describe fully the single transformation that maps triangle A onto triangle C. … … [3]

10 marks

Mark scheme: 3(a) Triangle at (1, –6), (2, –4), (4, –4) 2 B1 for reflection in x = – 1 or y = k 3(b) Triangle at (–4, 7), (–3, 5), (– 1, 5) 2   5  k B1 for translation   or   k  3 3(c) Rotation 3 B1 for each 90˚ [anticlockwise] oe [Centre] origin or (0, 0) 3(d) Stretch 3 B1 for each [Factor] 2 x-axis (or y = 0) invariant

This question in 0607/42 May/June 2023

7 A is the point ( - 8 , 2) and C is the point (8, 10). y C NOT TO SCALE A x O (a) Find the equation of the line AC. … [3] (b) N is the point (4, 8). Show that N lies on AC. [1] (c) Find the equation of the line that is perpendicular to AC and passes through N. … [3] (d) A and C are two vertices of a quadrilateral ABCD. B is the point (2, 12). D is the reflection of B in the line AC. (i) Find the coordinates of D. ( … , … ) [2] (ii) Write down the name of the special quadrilateral ABCD. … [1] (iii) Find the length AC. … [2] (iv) Find the area of the quadrilateral ABCD. … [3]

15 marks

Mark scheme: 7(a) 1 3 1 y = x + 6 oe final answer B2 for x + 6 2 2 OR 10  2 M1 for oe 8 ( 8) M1 for substituting (–8, 2) or (8, 10) into y = (their m)x + c oe 7(b) 1 1 × 4 + 6 = 8 oe 2 7(c) y = –2x + 16 oe final answer 3 B2 for –2x + 16 OR 1 M1 for grad =  1 their 2 M1 for substituting (4, 8) into y = (their m)x + c 1 oe, their m ≠ their 2 7(d)(i) (6, 4) 2 B1 for each coordinate 7(d)(ii) Kite 1 7(d)(iii) 2 M1 for (8 – (–8))2 + (10 – 2)2 17.9 or 17.88 to 17.89 or 8 5 oe 7(d)(iv) 80 or 79.5 to 80.5 3 1 M2 for × their (d)(iii) × their BD 2 1 or 2 × × their (d)(iii) × their BN oe 2 i.e. a correct method for the area of ABCD. or B1for [BN =] 4.47 or 4.472... or 2 5 oe or [BD =] 8.94 or 8.944... or 4 5 oe or M1 for a correct method for the area of one of the triangles in ABCD.

This question in 0607/42 May/June 2023

1 y 8 7 6 5 4 3 A 2 B 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 - 6 (a) Translate triangle A by Label the image C. [2] e 4o. (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (c) Reflect triangle A in the line x =- 2 . Label the image D. [2] (d) Enlarge triangle A by scale factor - 1, centre (0, 0). Label the image E. [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Correct triangle 2  6  k B1 for translation by   or  (–5, 5) (–5, 7) (–6, 7)  k  4 1(b) Rotation 3 B1 for each 90 clockwise oe Centre (2, 0) 1(c) Correct triangle 2 B1 for correct reflection in x = k or in y (–5, 1) (–5, 3) (–4, 3) = –2 1(d) Correct triangle 2 B1 for correct enlargement, incorrect (–1, –1) (0, –3) (–1, –3) centre

This question in 0607/43 May/June 2023

4 (a) p = q = - 2 1 (i) Work out p + 2q . [2] f p (ii) A is the point (2, 6) and B is the image of point A after a translation by the vector p. Find the coordinates of B. ( … , … ) [1] (iii) Find the magnitude of q. … [2] (b) Find the vector that translates the point (1, 5) to the point ( - 1, 7). [2] f p (c) y 6 5 4 B 3 2 T 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -1 -2 -3 A -4 -5 -6 (i) Describe fully the single transformation that maps triangle T onto triangle A. … … [2] (ii) Describe fully the single transformation that maps triangle T onto triangle B. … … [3] (iii) Reflect triangle T in the y-axis. [1] (iv) Stretch triangle T with factor 3 and invariant line y = 3 . [2]

15 marks

Mark scheme: 4(a)(i)  −7  2 B1 for each    −10   0  or for   seen  2  4(a)(ii) (5, 4) 1 4(a)(iii) 5.1[0] or 5.099... 2 M1 for (–5)2 + 12 oe 4(b)  −2  2 B1 for each    2  4(c)(i) Translation 2 B1 for each  2     −5  4(c)(ii) Rotation 3 B1 for each 90˚ [anticlockwise] oe (0, 2) 4(c)(iii) Image at (–1, 1) (–3, 1), (–1, 2) 1 4(c)(iv) Image at (1, 0), (1, –3), (3, –3) 2 B1 for stretch factor 3 in y = k or in x = 3

This question in 0607/41 Oct/Nov 2023

1 y 6 5 4 V 3 2 1 x – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 1 – 2 T – 3 – 4 – 5 – 6 (a) Reflect triangle T in the line x =- 1. Label the image A. [2] 1 (b) Translate triangle T using the vector Label the image B. [2] e4o. (c) Describe fully the single transformation that maps triangle T onto triangle V. … … [3] 1 (d) Stretch triangle V with factor and invariant line x = 2 . Label the image C. [2] 2

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) triangle (–6, –2) (–4, –2) (–4, –5) 2 B1 for reflection in y = −1 or reflection in x = k 1(b) triangle (3, 2) (5, 2) (3, −1) 2 1 k B1 for translation  or  k 4 1(c) rotation 3 B1 for each 180⁰ [centre] (0, 0) oe OR enlargement [centre] (0, 0) oe [sf] –1 1(d) triangle (−1, 2) (0, 5) (0, 2) 2 B1 for correct shape but translated horizontally from correct position.

This question in 0607/42 Oct/Nov 2023

3 y 8 7 6 C 5 4 3 2 A 1 0 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 - 5 (a) Translate triangle A by the vector . Label the image B. [2] e 2o (b) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (c) (i) Triangle D is the image of triangle A after a reflection in the line y =-1 followed by a rotation, 90° clockwise, about the point ( 1, -1) . Draw and label triangle D. [4] (ii) Describe fully the single transformation that maps triangle A onto triangle D. … … [2]

11 marks

Mark scheme: 3(a) Triangle at (–4, 4), (–2, 4), (–4, 3) 2  − 5   k  B1 for translation through   or    k   2  3(b) Enlargement 3 B1 for each [Scale Factor] –2 [Centre] (2, 3) 3(c)(i) Triangle at (–2, –1), (–1, –1), (–2, –3) 4 B2 for triangle at (1, –3), (1, –4), (3, –4) or B1 for reflection in y = k or x = –1 dep B1 for rotation of their first image 90˚ clockwise or anticlockwise about (1, – 1) or rotation 90˚ clockwise about wrong centre. If 0 scored, SC1 for correct triangle translated 3(c)(ii) Reflection 2 B1 for each y = –x oe

This question in 0607/43 Oct/Nov 2023

3 y 8 7 6 5 B 4 C 3 A 2 1 0 x -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 -7 -8 (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) (i) Rotate triangle A through 90° clockwise about ( - 1 , - 1) . Label the image D. [2] (ii) Reflect triangle D in the line x = - 1. Label the image E. [2] (iii) Describe fully the single transformation that maps triangle A onto triangle E. … … [2]

11 marks

Mark scheme: 3(a) Translation 2 B1 for each  −7     2  3(b) Enlargement 3 B1 for each 1 [sf] − 2 [centre] (–1, 3) 3(c)(i) Triangle at (1, –3), (5, –3), (1, –5) 2 B1 for rotation 90˚ anticlockwise about (–1, –1) or for rotation 90˚ clockwise about wrong centre 3(c)(ii) Triangle at (–3, –3), (–7, –3), 2 FT their (c)(i) (–3, –5) B1 for reflection in x = k or y = –1 3(c)(iii) Reflection 2 B1 for each y = –x – 2 oe

This question in 0607/42 Feb/March 2024

3 y 9 8 7 6 5 4 A 3 2 1 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 2 (a) Translate triangle A with vector Label the image B. [2] e- 6o. (b) Describe fully the single transformation that maps triangle B onto triangle A. … … [2] (c) Rotate triangle A through 90° clockwise about (0, 0). Label the image C. [2] (d) Reflect triangle A in the line y = x . Label the image D. [2] (e) Describe fully the single transformation that maps triangle C onto triangle B. … … [3]

11 marks

Mark scheme: 3(a) Correct triangle 2  2   k  (–5, 0), (–5, –3), (–4, –3) B1 for translation   or    k   6  3(b) Translation 2 B1 for each  2     6  3(c) Correct triangle 2 B1 for correct rotation, incorrect centre or for (3, 6), (3, 7), (6, 7) correct rotation 90 anticlockwise 3(d) Correct triangle 2 B1 for correct size and orientation, wrong (3, –6), (3, –7), (6, –7) position or reflection in y = –x 3(e) Rotation 3 B1 for each 90 anticlockwise oe [Centre] (4, –2)

This question in 0607/41 May/June 2024

8 (a) y 6 5 4 A 3 2 T B 1 – 2 – 1 0 1 2 3 4 5 6 x Describe fully the single transformation that maps (i) triangle T onto triangle A … … [2] (ii) triangle T onto triangle B. … … [3] (b) P is the point (-3, 2). 5 The vector from P to Q is e o. - 7 (i) Find the coordinates of Q. ( … , … ) [1] 5 (ii) Find the magnitude of the vector e o. - 7 … [2] (c) Find the equation of the line that passes through the points (-3, -1) and (1, 11). Give your answer in the form y = mx + c . y = … [3]

11 marks

Mark scheme: 8(a)(i) Translation 2 B1 for each 3  2 8(a)(ii) Enlargement (or reduction) 3 B1 for each 1 [scale factor] oe 2 [centre] (5, 1) 8(b)(i) (2, –5) 1 8(b)(ii) 8.6[0] or 8.602... 2 M1 for 5 2 ( 7) 2 or 5 2  7 2 or better 8(c) [y=] 3x + 8 3 11 1 M1 for (m) oe 1 3 M1 for substituting (–3, –1) or (1, 11) into y = (their m)x + c oe

This question in 0607/42 May/June 2024

6 (a) y 9 8 B 7 6 5 4 C 3 A 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 – 3 – 4 (i) Reflect triangle A in the line y = x . [2] (ii) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (iii) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (b) Write down the inverse of each of these transformations. - 3 (i) Translation with the vector e 4o … … [2] (ii) Stretch with the line y = 1 invariant and stretch factor 3 … … [3]

13 marks

Mark scheme: 6(a)(i) Triangle at (1, –2), (4, –2) , (3, –3) 2 B1 for reflection in y = –x or correct size and orientation 6(a)(ii) Rotation 3 B1 for each 90˚ clockwise oe [centre] (4, 1) 6(a)(iii) Enlargement 3 B1 for each [Scale factor] –2 [centre] (–1, 3) 6(b)(i) Translation 2 B1 for each  3      4  6(b)(ii) Stretch 3 B1 for each y = 1 [invariant] 1 factor 3

This question in 0607/43 May/June 2024

6 (a) y 9 8 7 A 6 5 4 3 2 1 x – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 (i) Draw the image of triangle A after a reflection in the line y =- x . Label the image B. [2] (ii) Draw the image of triangle B after a reflection in the y-axis. Label the image C. [1] (iii) Describe fully the single transformation that maps triangle C onto triangle A. … … [3] -1 (b) The transformation P is a translation with vector e o. 3 The transformation Q is a stretch, factor 3 with invariant line y = 2 . (i) Describe the transformation that is the inverse of P. … [2] (ii) Describe the transformation that is the inverse of Q. … [2]

10 marks

Mark scheme: 6(a)(i) Correct triangle 2 B1 for correct orientation, incorrect position (–7, –6) (–7, –3) (–6, –3) 6(a)(ii) Correct triangle 1FT (7, –6) (7, –3) (6, –3) 6(a)(iii) Rotation 3 B1 for each Centre (0, 0) oe 90o [anticlockwise] oe 6(b)(i) Translation 2 B1 for each  1  Vector   .  − 3  6(b)(ii) Stretch and [invariant line] y = 2 2 B1 for each 1 [factor] 3

This question in 0607/41 Oct/Nov 2024

5 (a) Describe fully the single transformation that is the inverse of an enlargement with scale factor 3 and centre (2, 2). … … [2] (b) y 10 8 A 6 4 2 -10 -8 -6 -4 -2 0 2 4 6 8 10 x -2 -4 -6 -8 -10 (i) Draw the image of shape A after a rotation of 90° anticlockwise with centre (0, 0). [2] - 5 (ii) Draw the image of shape A after a translation with vector e o followed by an enlargement - 4 with scale factor -2 and centre (0, 0). [4] (c) y 10 8 A 6 4 B 2 0 x 2 4 6 8 10 -2 -4 -6 Describe fully the single transformation that maps shape A onto shape B. … … [3]

11 marks

Mark scheme: 5(a) enlargement 2 B1 for scale factor 1 B1 enlargement and centre [sf] oe 3 [centre] (2, 2) 5(b)(i) image at (–5,7) (–5,8) 2 B1 for rotation 90° clockwise or for correct angle (–7,8) (–7,9) (–8,9) (–8,7) with wrong centre 5(b)(ii) image at (–4,–2) (–4,–8) 4 B2 for correct translation (–6,–2) (–8,–6) (–6,–6)  −5   k  or B1 for translation   or   (–8,–8)  k   −4  B2 for correct enlargement of their translated image or B1 for enlargement SF –2 incorrectly placed 5(c) stretch 3 B1 for each correct [sf] 3 [Invariant line] y = 10

This question in 0607/43 Oct/Nov 2024

9 y 9 8 7 B A 6 5 4 3 2 1 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 0 (a) Translate triangle A with vector e o. Label the image C. [2] - 8 (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (c) Rotate triangle B through 90° clockwise with centre of rotation (-6, 2). Label the image D. [2]

6 marks

Mark scheme: 9(a) Correct triangle 2 0  k  M1 for translation or (2, 0), (2, –3), (4, –3)    k  −8  9(b) Reflection 2 B1 for each x = –2 oe 9(c) Correct triangle 2 M1 for rotation 90 clockwise, incorrect centre (–3, 2), (–3, 4), (0, 2)

This question in 0607/42 May/June 2025

12 Transformation A is a rotation 90° clockwise about the origin. 3 Transformation B is a translation by the vector e o. - 1 Describe fully the single transformation equivalent to transformation A followed by transformation B. You may use the grid to help you. … … [3]

3 marks

Mark scheme: 12 Rotation 3 B1 for each 90˚ clockwise oe [Centre] (1, –2)

This question in 0607/41 Oct/Nov 2025