Transformations — Paper 4 · IGCSE Mathematics 0580

2 y 12 10 P 8 6 4 2 S Q x –10 –8 –6 –4 –2 0 2 4 6 8 10 –2 –4 R –6 –8 (a) Describe fully the single transformation that maps (i) shape P onto shape Q, … … [3] (ii) shape P onto shape R, … … [2] (iii) shape P onto shape S. … … [3] (b) (i) Draw the reflection of shape S in the line y = x . [2] (ii) Write down the matrix that represents the transformation in part (b)(i). [2] f p

12 marks

This question in 0580/42 Feb/March 2017

3 y 8 7 B 6 5 4 3 2 A 1 x 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 (a) (i) Draw the image of triangle A after reflection in the line x = 4 . [2] (ii) Draw the image of triangle A after rotation of 90° anticlockwise about (0, 0). [2] 1 (iii) Draw the image of triangle A after translation by the vector [2] c- 5m. (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (c) Find the matrix that represents the transformation in part (a)(ii). [2] f p (d) Point P has co-ordinates (4, 1). - 1 0 1 0 F = and G = represent transformations. c 0 1m c 0 2m (i) Find G(P), the image of P after the transformation represented by G. ( … , … ) [2] (ii) Find GF(P). ( … , … ) [3] (iii) Find the matrix Q such that GQ (P) = P . [3] f p

19 marks

Mark scheme: 3(a)(i) Image at (5, 1), (7, 1), (7, 4) 2 B1 reflection in y = 4 or x = k 3(a)(ii) Image at (–1, 1), (–4, 1), (–1, 3) 2 B1 correct size and correct orientation wrong position or for rotation 90° clockwise around (0, 0) 3(a)(iii) Image at (2, – 4), (4, – 4), (2, – 1) 2 § 1 · § k · B1 for translation by ¨ ¸ or ¨ ¸ © k ¹ © −5 ¹ 3(b) Enlargement 1 [sf] – 0.5 oe 1 (5, 5) 1 3(c) § 0 −1 · 2 B1 for one correct column or row ¨ ¸ © 1 0 ¹ 3(d)(i) (4, 2) 2 § 1 0 ·§ 4 · M1 for ¨ ¸¨ ¸ oe © 0 2 ¹© 1 ¹ 3(d)(ii) (– 4, 2) 3 § −1 0 · § 1 0 ·§ −4 · M2 for ¨ ¸ or ¨ ¸¨ ¸ © 0 2 ¹ © 0 2 ¹© 1 ¹ § 1 0 ·§ − 1 0 · ª § 4 · º or M1 for ¨ ¸¨ ¸ « ¨ ¸ » © 0 2 ¹© 0 1 ¹ ¬ © 1 ¹ ¼ § −4 · or ¨ ¸ © 1 ¹ 3 2 0 ·3(d)(iii) 1 § ¨ ¸ oe isw M2 for det = 2 soi or k§¨ 2 0 ·¸ soi 2 © 0 1 ¹ © 0 1 ¹ or M1 for recognition that Q is inverse matrix of G or GQ = I or QG = I

This question in 0580/41 May/June 2017

2 (a) y 12 11 10 9 T 8 7 6 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 On the grid, draw the image of 6 (i) triangle T after translation by the vector , [2] c- 5m (ii) triangle T after rotation through 90° anticlockwise with centre (4, 10), [2] 1 (iii) triangle T after enlargement with scale factor , centre (10, 0). [2] 2 0 - 1 (b) Describe fully the single transformation that is represented by the matrix . c- 1 0m … … [2] 2 3 2 (c) M = N = P = ( 1 5) c 2 4 m c 3 m (i) Find (a) MN, MN = [2] (b) NP, NP = [2] (c) M -1 . M -1 = [2] f p (ii) Write down a product of two of the matrices M, N and P which it is not possible to work out. … [1]

15 marks

Mark scheme: 2(a)(i) Image at (8, 1), (10, 5), (8, 5) 2 6  k  B1 for translation  or   k  −5  or 3 correct points not joined 2(a)(ii) Image at (4, 10), (4, 8), (8, 8) 2 B1 for rotation 90˚ anticlockwise but different centre or for rotation 90˚ clockwise about (4, 10) or 3 correct points not joined 2(a)(iii) Image at (6, 3), (6, 5), (7, 5) 2 1 B1 for enlargement factor but incorrect centre 2 or 3 correct points not joined 2(b) Reflection 1 y = − x oe 1 If zero scored, M1 for correct use of matrix product 2(c)(i)(a)  13  2 B1 for each in a 2 by 1 matrix   or SC1 for (13 [,] 16)  16  2(c)(i)(b)  2 10  2 B1 for answer any 2 by 2 matrix    3 15  2(c)(i)(c) 1  4 −3  2  4 − 3    oe isw B1 for k   oe soi (k ≠ 0 ) 2  −2 2   − 2 2  or for determinant = 2 oe soi 2(c)(ii) NM or MP or N² oe or P² oe 1

This question in 0580/42 May/June 2017

6 y 12 10 8 6 A 4 2 x –10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 –2 –4 –6 C –8 B –10 –12 (a) Describe fully the single transformation that maps shape A onto (i) shape B, … … [2] (ii) shape C. … … [3] (b) Draw the image of shape A after rotation through 90° anticlockwise about the point (3, -1). [2] (c) Draw the image of shape A after reflection in y = 1. [2] 3 0 (d) Describe fully the single transformation represented by the matrix f0 3p. … … [3]

12 marks

Mark scheme: 6(a)(i) Translation 1  3  1   oe  − 13  6(a)(ii) Enlargement 1 1 [sf ] −1 oe 2 ( 0, −4 ) 1 6(b) Image at 2 B1 for rotation of 90º anticlockwise about ( 0, 0 ) ( 0, 6 ) ( −4, 6 ) ( −4, 2 ) the wrong centre or 90º clockwise about (3, −1) or 4 points correct but not joined. 6(c) Image at 2 B1 for reflection in y = k or in x = 1 ( 4, 0 ) ( 10, 0 ) ( 10, −4 ) ( 6, −4 ) or 4 points correct but not joined 6(d) Enlargement 1 [sf ] 3 1 Origin oe 1

This question in 0580/43 May/June 2017

11 (a) A = 1 4 Find (i) A2, [2] f p (ii) A–1, the inverse of A. [2] f p - 1 0 (b) Describe fully the single transformation represented by the matrix . c 0 1 m … … [2] (c) Find the matrix that represents a clockwise rotation of 90º about the origin. [2] f p (d) C A NOT TO P a SCALE O B b In the diagram, O is the origin and P lies on AB such that AP : PB = 3 : 4. OA = a and OB = b . (i) Find OP, in terms of a and b, in its simplest form. OP = … [3] (ii) The line OP is extended to C such that OC = m OP and BC = ka. Find the value of m and the value of k. m = … k = … [2]

13 marks

Mark scheme: 11(a)(i)  1 −18  2   M1 for two or three correct elements  6 13  11(a)(ii) 1  4 3  2  4 3    or better isw M1 for det = 11 or [k]   isw 11  −1 2   −1 2  11(b) Reflection 1 y-axis oe 1 11(c)  0 1  2   B1 for one correct column or row  −1 0  11(d)(i) 1 4 3 3 M2 for correct unsimplified answer seen (4a + 3b) or a + b JJJG 3 JJJG 4 7 7 7 or AP = (b – a) oe or BP = (a – b) oe 7 7 JJJG JJJG or M1 for AB = b – a or BA = a – b or correct JJJG route for OP 11(d)(ii) 7 2 B1 for each value [m =] 3 m or M1 for (4a + 3b) = b + ka oe 4 7 [k =] 3

This question in 0580/41 Oct/Nov 2017

4 (a) y 6 5 4 3 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 F –2 –3 –4 –5 –6 –7 Draw the image of 6 (i) flag F after translation by the vector [2] f- 2p, (ii) flag F after rotation through 180° about (– 2, 0), [2] (iii) flag F after reflection in the line y = x. [2] (b) y 5 4 P 3 2 Q 1 x 0 1 2 3 4 5 (i) Describe fully the single transformation that maps triangle P onto triangle Q. … … [3] (ii) Find the matrix that represents this transformation. [2] f p 4u (c) The point A is translated to the point B by the vector . f3up AB = 12.5 Find u. u = … [3]

14 marks

Mark scheme: 4(a)(i) Correct translation 2 6  k  B1 for translation  or   k  − 2  4(a)(ii) Correct rotation 2 B1 for rotation 180˚ but other centre 4(a)(iii) Correct reflection 2 B1 for reflection in y = − x 4(b)(i) Enlargement 3 B1 for each 1 [factor] or 0.5 2 [centre] (0, 0) oe 4(b)(ii)  1  2  k 0   0  B1 for matrix of form   oe, k ≠ 0 or 1 2   oe  0 k   1   0   2  4(c) ± 2.5 3 B2 for 25u 2 = 156.25 or 5u = [±]12.5 or M1 for (4u ) 2 + (3u ) 2

This question in 0580/42 Oct/Nov 2017

5 y 8 7 6 5 4 3 B 2 A 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 (a) Draw the image of (i) triangle A after a reflection in the line x = 0, [2] (ii) triangle A after an enlargement, scale factor 2, centre (0, 4), [2] -5 (iii) triangle A after a translation by the vector [2] f 3p. (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] 0 -1 3 1 (c) T = U = f1 0p f0 2p Point P has co-ordinates (1, -4). (i) Find T(P). ( … , … ) [2] (ii) Find TU(P). ( … , … ) [2] (iii) Describe the single transformation represented by the matrix T. … … [3]

16 marks

Mark scheme: 5(a)(i) Image at (0, 1), (0, 2), (–3, 1) 2 B1 for reflection in y = 0 or x = k 5(a)(ii) Image at (0, 0), (0, –2), (6, –2) 2 B1 for correct size and correct orientation wrong position or for 2 correct vertices plotted 5(a)(iii) Image at (–5, 4), (–5, 5), (–2, 4) 2  − 5  k B1 for translation by   or   k  3 5(b) Rotation 3 B1 for each 90° clockwise oe (4, –1) 5(c)(i) (4, 1) 2  0 − 1  1  M1 for     1 0  − 4  5(c)(ii) (8, –1) 2  0 − 1  3 1  1  M1 for      1 0  0 2  − 4   0 − 2  1  or     3 1  − 4   0 − 1  − 1  or     1 0  − 8  5(c)(iii) Rotation 3 B1 for each 90° anti-clockwise oe Origin oe

This question in 0580/43 Oct/Nov 2017

4 y 8 7 6 5 B 4 3 A 2 C 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 D –5 –6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [2] (ii) triangle A onto triangle C, … … [3] (iii) triangle A onto triangle D. … … [3] (b) On the grid, draw the image of triangle A after an enlargement by scale factor 2, centre ,7 3 [2] ^ h.

10 marks

Mark scheme: 4(a)(i) Translation 2 B1 for each  − 8    oe  2  4(a)(ii) Enlargement 3 B1 for each 1 [sf = ] oe 2 ( −4, 0 ) 4(a)(iii) Rotation 3 B1 for each 90° clockwise oe (1, − 1) 4(b) Triangle with (1, –1), (5, –1), (1,7) 2 B1 for correct size and orientation in wrong position or for 3 correct points not joined

This question in 0580/41 May/June 2018

3 y 6 5 4 3 B 2 1 x 0 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 –2 –3 A –4 –5 –6 (a) (i) Draw the image of triangle A after a reflection in the line x = 2. [2] - 2 (ii) Draw the image of triangle A after a translation by the vector [2] c 4 m. 1 (iii) Draw the image of triangle A after an enlargement by scale factor - , centre (3, 1). [3] 2 (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] 0 - 1 (c) Describe fully the single transformation represented by the matrix c- 1 0m. … … [2]

12 marks

Mark scheme: 3(a)(i) Image at (3, – 3), (7, – 3), (7, – 5) 2 B1 for reflection in any x = k or if 3 correct points not joined 3(a)(ii) Image at (– 5, 1), (– 1, 1), (– 5, – 1) 2  −2  k B1 for translation by   or   k  4 or if 3 correct points not joined 3(a)(iii) Image at (6, 3), (6, 4), (4, 3) 3 B2 for correct size and orientation but wrong position or if 3 correct points not joined B1 for enlargement SF ½ with centre (3, 1) 3(b) Rotation 3 B1 for each 90° [anticlockwise]oe (– 6, – 2) 3(c) Reflection 2 B1 for each y = – x oe k

This question in 0580/42 May/June 2018

8 (a) M = N = 1 2 P = 4 3 1 (i) For the following calculations, put a tick (ü) if it is possible or put a cross (û) if it is not possible. There is no need to carry out any of the calculations. Calculation ü or û N + P NP M2 N2 MN NM [4] 1 (ii) Work out + P . f 2 p … [1] (iii) Work out PN. … [2] (iv) Work out M -1 . … [2] 0 - 1 (b) Describe fully the single transformation represented by the matrix f1 0p. … … [3]

12 marks

Mark scheme: 8(a)(i) × 4 B3 for 5 correct 9 B2 for 4 correct 9 B1 for 3 correct × × 9 8(a)(ii) 5 1 Fraction line and/or missing brackets scores 0  3 8(a)(iii)  4 8  2 B1 for 2 or 3 correct elements (dep on 2 × 2 matrix)    1 2  8(a)(iv) 1  3 −1  2  3 −1    oe isw B1 for k   or determinant = 2 soi 2  −4 2   −4 2  8(b) Rotation 3 B1 for each Origin oe 90 [anticlockwise] oe

This question in 0580/43 May/June 2018

2 y 8 6 4 B 2 –8 –6 –4 –2 0 2 4 6 8 10 x –2 –4 A C –6 D –8 –10 (a) Describe fully the single transformation that maps (i) flag A onto flag B, … … [2] (ii) flag A onto flag C, … … [3] (iii) flag A onto flag D. … … [3] (b) Draw the reflection of flag A in the line y =- 1. [2]

10 marks

Mark scheme: 2(a)(i) Translation 2 B1 for each  5  Accept 5 right and 8 up    8  2(a)(ii) Enlargement 3 B1 for each [sf] 0.5 oe [centre] (0, −7) 2(a)(iii) Rotation 3 B1 for each 90 [anticlockwise] oe Origin oe 2(b) Image at (−8, 1) (−8, 5) (−8, 7) 2 B1 for reflection of flag A in the line (−4, 1) x = −1 or y = k or for vertices of triangle in correct place but not joined

This question in 0580/41 Oct/Nov 2018

1 (a) y 7 6 5 4 3 T 2 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x –1 –2 –3 –4 P –5 –6 –7 (i) Describe fully the single transformation that maps triangle T onto triangle P. … … [2] - 2 (ii) Translate triangle T by the vector [2] e - 5o. (iii) Rotate triangle T through 90° anticlockwise about (0, 0). [2] 1 (iv) Enlarge triangle T by scale factor - with centre (0, 0). [2] 2 (b) y B (5, 6) NOT TO SCALE A (3, 2) O x (i) Find the column vector AB. AB = [1] f p (ii) Find AB . AB = … [2] (iii) B is the mid-point of the line AC. Find the co-ordinates of C. ( … , … ) [2] (iv) Find the equation of the straight line that passes through A and B. … [3] (v) The straight line that passes through A and B cuts the y-axis at D. Write down the co-ordinates of D. ( … , … ) [1]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Reflection 2 B1 for each y = –1 1(a)(ii) Triangle at 2 − 2   k  (0, –3), (4, –1), (4, –3) B1 for translation   or    k   −5  or for three correct vertices 1(a)(iii) Triangle at 2 B1 for rotation about (0, 0) 90° clockwise (–2, 2), (–2, 6), (–4, 6) or 90° anticlockwise with wrong centre or for three correct vertices 1(a)(iv) Triangle at (–3, –1), (–3, –2), 2 1 B1 for scale factor − with wrong centre (–1, –1) 2 1 or scale factor with centre (0, 0) 2 or for three correct vertices 1(b)(i)  2  1   cao  4  1(b)(ii) 4.47 or 4.472… 2 M1 for (their 2) 2 + (their 4) 2 1(b)(iii) (7, 10) 2 B1 for each 1(b)(iv) y = 2 x − 4 oe 3 6 − 2 M1 for gradient = oe or answer y = mx – 4 5 − 3 M1 for substituting (3, 2) or (5, 6) into y = their mx + c or into y – k = their m(x – h) or into their y = mx – 4 1(b)(v) (0, –4) 1 FT their (b)(iv)

This question in 0580/43 Oct/Nov 2018

2 y 8 7 6 5 4 A B 3 2 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x –1 –2 –3 C –4 –5 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [2] (ii) triangle A onto triangle C. … … [3] (b) On the grid, draw the image of 1 (i) triangle A after an enlargement, scale factor - , centre (3, 0), [2] 2 - 3 (ii) triangle A after a translation by the vector , [2] e 1o 0 1 (iii) triangle A after the transformation that is represented by the matrix . e1 0o [3]

12 marks

Mark scheme: 2(a)(i) Reflection 2 B1 for each x = 1.5 2(a)(ii) Rotation 3 B1 for each (0, −1) 90° [anticlockwise] oe 2(b)(i) Image at (5, −1) (6, −1) (6, −3) 2 B1 for correct size and orientation but wrong position 1 If 0 scored, SC1 for enlargement SF 2 with centre (3, 0) 2(b)(ii) Image at (−6, 3) (−4, 3) (−6, 7) 2  − 3  k B1 for translation   or   k  1 2(b)(iii) Image at (2, −1) (2, −3) (6, −3) 3 M2 for 3 correct coordinates soi  0 1  − 1 − 3 − 3  or M1 for     1 0  2 2 6  or B1 for stating reflection in y = x

This question in 0580/42 Feb/March 2019

1 y 10 9 8 7 6 5 4 3 T 2 1 0 x 1 2 3 4 5 6 7 8 9 10 - 1 (a) (i) Translate shape T by the vector . c 6 m Label the image A. [2] (ii) Rotate shape T about the point (5, 3) through 180°. Label the image B. [2] (iii) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) (i) Reflect shape T in the line y = x. [2] (ii) Find the matrix that represents the transformation in part (b)(i). [2] f p

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Image at (1, 7), (4, 7), (4, 9), (3, 9) 2  −1  k B1 for translation by   or   k  6 1(a)(ii) Image at (5, 3), (6, 3), (8, 5), (5, 5) 2 B1 for 180° rotation with wrong centre 1(a)(iii) Rotation 3 B1 for rotation 180˚ B1 for 180° (4.5, 6) B1FT for centre from their (a)(i) OR Enlargement, B1 for enlargement [factor] – 1 B1 for – 1 (4.5, 6) B1FT for centre from their (a)(i) 1(b)(i) Image at (1, 2), (1, 5), (3, 5), (3, 4) 2 B1 for y = x drawn or for 3 correct points 1(b)(ii)  0 1  2 B1 for one correct row or one column   within a 2 by 2 matrix  1 0 

This question in 0580/41 May/June 2019

3 y 7 6 5 4 3 A 2 1 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 B –3 –4 –5 (a) On the grid, draw the image of - 3 (i) triangle A after a translation by the vector [2] e 2o, (ii) triangle A after a reflection in the line y = x. [2] (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (c) (i) Find the matrix that represents an enlargement, scale factor - 2, centre (0, 0). [2] f p (ii) Calculate the determinant of the matrix in part (c)(i). … [1]

10 marks

Mark scheme: 3(a)(i) Image at (–5, 4), (–2, 4), (–4, 6) 2  − 3  k B1 for translation by   or   k  2 3(a)(ii) Image at (2, 1), (4, –1), (2, –2) 2 B1 for reflection in y = –x or y = x drawn 3(b) Rotation 3 B1 for each 90°[ anticlockwise] oe (1, –1) 3(c)(i)  − 2 0  2 B1 for 2 by 2 matrix with one correct row or   column  0 − 2  3(c)(ii) Strict FT their (c)(i) 1 Answer not equal to zero FT their (c)(i) only if 2 by 2

This question in 0580/43 May/June 2019

3 A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB. ( … , … ) [2] (ii) Find the equation of the line AB. Give your answer in the form y = mx + c . y = … [3] (b) The line AB is transformed to the line PQ. Find the co-ordinates of P and the co-ordinates of Q after AB is transformed by 5 (i) a translation by the vector e- 2o, P ( … , … ) Q ( … , … ) [2] (ii) a rotation through 90° anticlockwise about the origin, P ( … , … ) Q ( … , … ) [2] (iii) a reflection in the line x = 2 , P ( … , … ) Q ( … , … ) [2] - 1 2 (iv) a transformation by the matrix e 0 - 1o. P ( … , … ) Q ( … , … ) [2] (c) Describe fully the single transformation that maps the line AB onto the line PQ where P is the point (-2, -6) and Q is the point (-10, -16). … … [3]

16 marks

Mark scheme: 3(a)(i) (3, 5.5) 2 B1 for either value correct 3(a)(ii) 5 7 3 5 x + final answer B2 for answer x + c oe or for correct 4 4 4 equation in different form 8 − 3 or M1 for oe 5 − 1 and M1 for correct substitution shown of (1, 3) or (5, 8) or their (a)(i) into y = (their m)x + c oe 3(b)(i) (6, 1) 2 B1 for 2 or 3 values correct (10, 6) 3(b)(ii) (–3, 1) 2 B1 for 2 or 3 values correct (–8, 5) If 0 scored, SC1 for (3, –1) and (8, –5) 3(b)(iii) (3, 3) 2 B1 for 2 or 3 values correct but not for (–1, 8) (1, 3) and (5, 8) 3(b)(iv) (5, –3) 2 B1 for either (11, –8)  − 1 2  1   − 1 2  5  or M1 for    or     0 − 1  3   0 − 1  8  3(c) Enlargement 3 B1 for each –2 Origin oe

This question in 0580/42 Oct/Nov 2019

7 y 8 7 6 5 4 3 2 A 1 x - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 - 1 - 2 - 3 B - 4 - 5 - 6 (a) Describe fully the single transformation that maps shape A onto shape B. … … [2] (b) On the grid, draw the image of - 3 (i) shape A after a translation by the vector [2] e 4o, (ii) shape A after a rotation through 180° about (0, 0), [2] (iii) shape A after an enlargement, scale factor 2, centre (-7, 0). [2]

8 marks

Mark scheme: 7(a) Reflection 2 B1 for each y = –1 7(b)(i) Image at 2  −3  k (–6, 5) (–6, 7) (–5, 7) (–4, 5) B1 for translation by   or   k  4 7(b)(ii) Image at 2 B1 for shape correct size and orientation (1, –1) (3, –1) (3, –3) (2, –3) but wrong position 7(b)(iii) Image at 2 B1 for shape correct size and orientation, (1, 2) (1, 6) (3, 6) (5, 2) wrong position

This question in 0580/43 Oct/Nov 2019

4 y 6 5 4 3 2 T 1 0 x – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 – 1 – 2 – 3 – 4 A – 5 – 6 (a) Draw the image of triangle T after a reflection in the line y =- 1. [2] (b) Draw the image of triangle T after a rotation through 90° clockwise about (0, 0). [2] (c) Describe fully the single transformation that maps triangle T onto triangle A. … … [2]

6 marks

Mark scheme: 4(a) Triangle at (–4, –4) (–1, –3) 2 B1 for correct points not joined or for reflection (–4, –3) in any y = k or for reflection in x = –1 4(b) Triangle at (1, 1) (1, 4) (2, 4) 2 B1 for correct points not joined or rotation 90 clockwise around any point or rotation 90 anticlockwise around (0, 0) 4(c)  5  2 B1 for translation or correct vector oe Translation    − 6 

This question in 0580/41 May/June 2020

2 y 10 9 8 7 6 B 5 A 4 3 2 1 – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 – 2 C – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 (a) (i) Draw the image of triangle A after a reflection in the line y =- x . [2] - 2 (ii) Draw the image of triangle A after a translation by the vector [2] e- 9o. (b) Describe fully the single transformation that maps (i) triangle A onto triangle B, … … [3] (ii) triangle A onto triangle C. … … [3]

10 marks

Mark scheme: 2(a)(i) triangle with vertices at 2 B1 for correct reflection in y = x (−2, −1) (−8, −1) (−2, −5) 2(a)(ii) triangle with vertices at 2  k   − 2  B1 for translation by   or   (−1, −1) (−1, −7) (3, −7)  − 9   k  2(b)(i) Enlargement 3 B1 for each [centre] (−7, 8) [sf] ½ 2(b)(ii) Rotation 3 B1 for each [centre] (0, 0) 90° clockwise oe

This question in 0580/43 May/June 2020

1 y 7 6 C 5 4 3 A 2 1 0 x – 7 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 – 1 – 2 B – 3 – 4 – 5 – 6 – 7 – 8 8 (a) Draw the image of shape A after a translation by the vector [2] e- 6o. (b) Draw the image of shape A after a reflection in the line y =- 1. [2] (c) Describe fully the single transformation that maps shape A onto shape B. … … [3] (d) Describe fully the single transformation that maps shape A onto shape C. … … [3]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Image at 2 8  k  (4, –1) (4, –4) (5, –4) B1 for translation by  or   or for k  −6  correct vertices not joined 1(b) Image at 2 B1 for reflection in x = –1 or y = k or for (–4, –4) (–4, –7) (–3, –4) correct vertices not joined 1(c) Enlargement 3 B1 for each 3 (–5, 5) 1(d) Rotation 3 B1 for each 90º clockwise oe (1, 1)

This question in 0580/41 Oct/Nov 2020

2 y 8 7 6 5 4 3 2 T 1 x – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 – 1 – 2 – 3 – 4 P – 5 – 6 – 7 – 8 (a) Describe fully the single transformation that maps triangle T onto triangle P. … … [2] (b) (i) Reflect triangle T in the line x = 1. [2] (ii) Rotate triangle T through 90° anticlockwise about (6, 0). [2] (iii) Enlarge triangle T by a scale factor of -2, centre (1, 0). [2]

8 marks

Mark scheme: 2(a) Translation 2 B1 for each  1     − 6  2(b)(i) Image at (0, 1), (–3, 1), (–3, 2) 2 B1 for reflection in x = k or y = 1 2(b)(ii) Image at (5, –4), (5, –1), (4, –1) 2 B1 for rotation 90° anticlockwise with other centre or for rotation 90° clockwise about (6, 0) 2(b)(iii) Image at (–1, –2), (–7, –2), (–7, –4) 2 B1 for enlargement, factor –2 with other centre

This question in 0580/42 Oct/Nov 2020

2 y 8 7 6 5 4 A B 3 2 1 0 x – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 – 1 – 2 – 3 – 4 – 5 – 6 (a) On the grid, draw the image of (i) triangle A after a rotation of 90° anticlockwise about (0, 0), [2] 3 (ii) triangle A after a translation by the vector [2] e- 5o. (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

7 marks

Mark scheme: 2(a)(i) Triangle at (–3, 2) (–3, 3) (–5, 2) 2 B1 for correct rotation about incorrect point or for rotation 90 clockwise around (0, 0) 2(a)(ii) Triangle at (5, –2) (6, –2) (5, 0) 2 3  k  B1 for translation by  or   k  −5  2(b) Enlargement 3 B1 for each [SF] 3 [Centre] (1, 4)

This question in 0580/43 Oct/Nov 2020

2 y 14 12 10 B 8 A 6 4 2 – 14 – 12 – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 x – 2 – 4 C – 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] - 5 (b) Draw the image of triangle A after a translation by the vector [2] e- 10o. (c) Draw the image of triangle A after a reflection in the line y = 4 . [2]

10 marks

Mark scheme: 2(a)(i) rotation 3 B1 for each 90 anticlockwise oe (–3, 2) 2(a)(ii) enlargement 3 B1 for each 1 − 2 ( −2, − 1) 2(b) Image at (– 3, – 5) (1, − 5) (1, 3) 2  − 5   k  B1 for translation by   or    k   −10  2(c) Image at (2, 3) (6, 3) (6, − 5) 2 B1 for reflection in y = k or x = 4

This question in 0580/42 Feb/March 2021

7 y 6 5 4 T 3 2 1 –– 66 –– 55 –– 44 –– 33 –– 22 –– 11 0 1 2 3 4 5 6 7 x –– 11 –– 22 A –– 33 –– 44 –– 55 –– 66 (a) On the grid, draw the image of 2 (i) triangle T after a translation by the vector [2] e- 1o, (ii) triangle T after a rotation, 90° clockwise, about the origin, [2] 1 (iii) triangle T after an enlargement, scale factor - , centre (-2, 3). [2] 2 (b) Describe fully the single transformation that maps triangle T onto triangle A. … … [2]

8 marks

Mark scheme: 7(a)(i) Triangle at (4, 0) (4, 3) (6, 3) 2 2  k  B1 for translation by  or   k  −1  If 0 scored SC1 for triangle at (3, 0.5) (3, 3.5) (5, 3.5) 7(a)(ii) Triangle at (1, –2) (4, –4) (4, –2) 2 B1 for rotation 90 clockwise wrong centre or for rotation 90 anticlockwise about the origin 7(a)(iii) Triangle at (–4, 4) (–4, 2.5) 2 1 B1 for enlargement SF − with wrong (–5, 2.5) 2 centre 1 or for enlargement SF with centre 2 (–2, 3) 7(b) Reflection 2 B1 for each y = – x oe

This question in 0580/42 May/June 2021

7 (a) y 8 7 6 5 4 3 A 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 B – 2 – 3 – 4 (i) On the grid, draw the image of (a) shape A after an enlargement, scale factor 2, centre (0, 1), [2] (b) shape A after a reflection in the line y = x - 1. [3] (ii) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) C B NOT TO q M SCALE O A p OABC is a trapezium and O is the origin. M is the midpoint of AB. OA = p , OC = q and OA = 2CB. Find, in terms of p and q, the position vector of M. Give your answer in its simplest form. … [3]

11 marks

Mark scheme: 7(a)(i)(a) Shape at (–2, 1) ( –4, 1) ( –4, 7) (0, 7) 2 B1 for 3 correct points or for enlargement SF2 from any centre 7(a)(i)(b) Shape at (2, –2) (2, –3) (5, –1) (5, –3) 3 B2 for correct orientation but wrong position or for 3 correct points or B1 for y = x – 1 drawn 7(a)(ii) Rotation 3 B1 for each 90 [anticlockwise] oe (0, 0) oe 7(b) 3 1 1 3 p + 2q 3  1  1  p + q or ( 3p + 2q ) or M2 for AM = AM =  - p + q + p  oe 4 2 4 4 2  2   final answer or M1 for correct route for AB oe soi by –½ p + q  or for OM soi

This question in 0580/41 Oct/Nov 2021

4 y 9 8 7 6 5 4 3 A 2 B 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 (a) On the grid, draw the image of triangle A after - 4 (i) a translation by the vector [2] e 5o, (ii) a reflection in the line x = 1, [2] (iii) an enlargement, scale factor 2 and centre ( - 5 , - 2 ). [2] (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

9 marks

Mark scheme: 4(a)(i) Image at (–5, 6) (–5, 8) (–6, 7) 2  − 4  k B1 for translation by   or   k  5 4(a)(ii) Image at (3, 1) (3, 3) (4, 2) 2 B1 for reflection in y = 1 or x = k 4(a)(iii) Image at (3, 4) (3, 8) (1, 6) 2 B1 for enlargement, sf 2, in wrong position 4(b) Rotation 3 B1 for each 90º [anticlockwise] oe (–3, 0)

This question in 0580/42 Oct/Nov 2021

1 The diagram shows three triangles, T, A, and B, drawn on a 1 cm2 grid. y 8 7 B 6 5 4 A 3 T 2 1 0 1 2 3 4 5 6 7 8 x (a) Describe fully the single transformation that maps triangle T onto triangle A. … … [3] (b) (i) Describe fully the single transformation that maps triangle T onto triangle B. … … [2] (ii) Calculate the distance that each point of triangle T moves when it is mapped onto triangle B. … cm [2]

7 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) Rotation 3 B1 for each 90° clockwise oe [centre] (5, 2) 1(b)(i) Translation 2 B1 for each  −1     4  1(b)(ii) 4.12 or 4.123... 2 M1 for (their (–1))2 + (their 4)2

This question in 0580/43 Oct/Nov 2021

5 (a) Draw the lines of symmetry of the rectangle. [2] (b) y 8 7 6 5 4 3 B 2 1 0 x – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 – 1 A – 2 – 3 C – 4 – 5 – 6 – 7 (i) Describe fully the single transformation that maps (a) triangle A onto triangle B, … … [2] (b) triangle A onto triangle C. … … [3] (ii) (a) Draw the image of triangle A after reflection in y = 2 . [2] (b) Draw the image of triangle A after enlargement by scale factor - 2, centre (- 1, 1). [2]

11 marks

Mark scheme: 5(a) Correct lines drawn 2 B1 for one correct with no incorrect lines 5(b)(i)(a) Translation or translate 2 B1 for each   1    oe  4  5(b)(i)(b) Rotation or rotate 3 B1 for each 90 [anticlockwise] oe [centre] (2, 1) 5(b)(ii)(a) Triangle at (– 5, 6) (– 2, 6) (– 2, 5) 2 B1 for reflection in y = k 5(b)(ii)(b) Triangle at (1, 5) (1, 7) (7, 7) 2 B1 for correct size and orientation, wrong position

This question in 0580/42 May/June 2022

2 (a) y 7 6 5 4 A 3 T 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 – 2 – 3 – 4 – 5 (i) Draw the image of triangle T after a reflection in the line y = x . [2] - 1 (ii) Draw the image of triangle T after a translation by the vector [2] e 3o. (iii) Describe fully the single transformation that maps triangle T onto triangle A. … … [3] (b) A quadrilateral P is enlarged by a scale factor of 1.2 to give quadrilateral Q. The area of quadrilateral P is 20 cm2. Calculate the area of quadrilateral Q. … cm2 [2]

9 marks

Mark scheme: 2(a)(i) Triangle drawn at (2, – 1), 2 B1 for two correct points (2, – 4), (3, – 4) If 0 scored, SC1 for reflection of triangle T in y = – x 2(a)(ii) Triangle drawn at (– 5, 6), 2  1  k (– 2, 5), (– 5, 5) B1 for translation by   or by   k  3 If 0 scored SC1 for triangle drawn at (–4.5, 3.5), (–4.5, 4.5) and (–1.5, 3.5) 2(a)(iii) Enlargement 3 B1 for each [SF] – 1.5 oe [centre] (0, 3) 2(b) 8 4 2 M1 for 1.2² oe 28.8, 28 , 28 10 5

This question in 0580/43 May/June 2022

4 y 8 7 6 A 5 4 C 3 2 1 D – 8 – 7 – 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) shape A onto shape B, … … [2] (ii) shape A onto shape C, … … [3] (iii) shape A onto shape D. … … [3] (b) On the grid, draw the image of shape A after a reflection in the line y = x + 8 . [2]

10 marks

Mark scheme: 4(a)(i) Translation 2 B1 for each  7    oe  −8  4(a)(ii) Rotation 3 B1 for each 90º [anticlockwise] oe (0, 8) 4(a)(iii) Enlargement 3 B1 for each 1 [sf] oe 2 [centre] (–1, –4) 4(b) Image at 2 (–4, 4) (–3, 4) (–2, 5) (–2, 3) (–4, 3) B1 for the line y = x + 8 drawn soi long enough to be fit for purpose or correct size and orientation but wrong position

This question in 0580/42 Oct/Nov 2022

4 y 6 5 4 A 3 2 T 1 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 (a) Draw the reflection of triangle T in the line y =- 2 . [2] 1 (b) Draw the enlargement of triangle T with scale factor and centre of enlargement ( - 5 , - 3 ). [2] 2 (c) Describe fully the single transformation that maps triangle T onto triangle A. … … [3]

7 marks

Mark scheme: 4(a) Triangle drawn at (1, – 5), 2 B1 for reflection in any horizontal line (1, – 7), (5, – 5) If 0 scored, SC1 for reflection in x = – 2 4(b) Triangle drawn at (– 2, 0), 2 B1 for correct size and orientation but wrong position (– 2, – 1), (0, – 1) 4(c) Rotation 3 B1 for each 90 [anticlockwise] oe [centre] (– 1, 0)

This question in 0580/43 Oct/Nov 2022

4 (a) y 6 5 4 3 2 T 1 0 x 1 2 3 4 5 6 7 8 9 10 – 1 – 2 (i) Enlarge triangle T by scale factor 3, centre (0, 2). [2] (ii) (a) Rotate triangle T about (4, 2) by 90˚ clockwise. Label the image P. [2] (b) Reflect triangle T in the line x + y = 6 . Label the image Q. [3] (c) Describe fully the single transformation that maps triangle P onto triangle Q. … … [2] (b) a H O Z NOT TO SCALE b K The diagram shows triangle OHK, where O is the origin. The position vector of H is a and the position vector of K is b. Z is the point on HK such that HZ : ZK = 2 : 5. Find the position vector of Z, in terms of a and b. Give your answer in its simplest form. … [3]

12 marks

Mark scheme: 4(a)(i) Triangle at (3, –1), (9, –1), (9, 2) 2 B1 for correct shape, size and orientation or for correct plots but no triangle 4(a)(ii)(a) Triangle at (3, 3), (4, 3), (3, 5) 2 B1 for correct shape size and orientation or for rotation about (4, 2) 90˚ anticlockwise or for correct plots but no triangle 4(a)(ii)(b) Triangle at (4, 3), (5, 3), (5, 5) 3 B2 for correct shape size and orientation or for correct plots but no triangle or M1 for x + y = 6 drawn 4(a)(ii)(c) Reflection 2 B1 for each x = 4 4(b) 5 2 3 a + b final answer 7 7 B2 for correct unsimplified answer OR 2 5 M2 for HZ = ( b − a ) or KZ = ( a − b ) oe 7 7 or M1 for HK = –a + b or KH = –b + a or for a correct route

This question in 0580/42 Feb/March 2023

1 y 9 8 7 6 5 4 C 3 2 1 x -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 A -3 B -4 -5 (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 (i) shape A after a reflection in the line y = 2 [2] (ii) shape A after an enlargement, scale factor - 2 , centre (0, 0). [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Translation 2 B1 for each  −7    oe  −1  1(a)(ii) Rotation 3 B1 for each 90º clockwise oe (5, 1) 1(b)(i) Image at 2 B1 for reflection in y = k, k  2 (2, 6) (3, 6) (3, 8) or for reflection in x = 2 1(b)(ii) Image at 2 B1 for an enlargement, sf –2 in the wrong position (–4, 4) (–6, 4) (–6, 8)

This question in 0580/41 Oct/Nov 2023

1 y 7 6 5 4 3 T 2 1 x -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 - 7 (a) (i) Translate triangle T by the vector Label the image K. [2] e 1o. (ii) Describe fully the single transformation that maps triangle K onto triangle T. … … [1] (b) Reflect triangle T in the line y = 4 . [2] (c) Rotate triangle T through 90° clockwise about (0, 0). [2] 1 (d) (i) Enlarge triangle T by scale factor - , centre (0, 0). Label the image P. [2] 2 (ii) Describe fully the single transformation that maps triangle P onto triangle T. … … [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Image at (–5, 3), (–1, 3), (–1, 5) 2  −7  k B1 for translation   or   k  1 1(a)(ii)  7  1 Translation   cao  −1 1(b) Image at (6, 4), (6, 6), (2, 6) 2 B1 for reflection in line x = 4 or for reflection in line y = k 1(c) Image at (2, –2), (2, –6), (4, –6) 2 B1 for correct size and orientation or for rotation 90˚ anticlockwise about (0, 0) 1(d)(i) Image at (–1, –1), (–3, –1), (–3, –2) 2 B1 for correct size and orientation 1 or for enlargement SF , centre (0, 0) 2 1(d)(ii) Enlargement and [centre] (0, 0) 2 B1 for Enlargement and [centre] (0, 0) [factor] –2 B1 for [factor] –2

This question in 0580/42 Oct/Nov 2023

3 y 8 7 6 5 4 A 3 2 B 1 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 x - 1 - 2 - 3 - 4 - 5 - 6 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) Draw the image of triangle A after (i) a reflection in the line y = 1 [2] 5 (ii) a translation by the vector [2] b - 7 l (iii) an enlargement, scale factor 2, centre ( - 4 , 5) . [2]

9 marks

Mark scheme: 3(a) Rotation 3 B1 for each 90° [anticlockwise] oe (2, 7) 3(b)(i) Image at (–4, –1), (–3, –1), (–4, –4) 2 B1 for reflection in y = k or x = 1 3(b)(ii) Image at (2, –4), (1, –4), (1, –1) 2 5  k  B1 for translation by  or   k  −7  3(b)(iii) Image at ( –4, 7), ( –4, 1), (–2, 1) 2 B1 for enlargement, factor 2 with other centre

This question in 0580/43 Oct/Nov 2023

2 y 6 5 4 B 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 A -3 -4 -5 (a) On the grid, draw (i) the image of triangle A after a reflection in the line x = 1 [2] 1 (ii) the image of triangle A after an enlargement by scale factor with centre (5, 1). [2] 2 (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (c) The point (a, b) is reflected in the line y = k where k is an integer and b 1 k . Write the coordinates of the image of point (a, b) in terms of a, b and k. ( … , … ) [2]

9 marks

Mark scheme: 2(a)(i) Triangle at (1, –1) ( 1, –3) (–3, –3) 2 B1 for reflection in x = k or for reflection in y = 1 2(a)(ii) Triangle at (3, –1) (5, –1) (3, 0) 2 B1 for correct size and orientation but wrong position 2(b) Rotation 3 B1 for each 90 clockwise oe [centre] (2, 4) oe 2(c) (a, 2k –b) oe isw 2 B1 for each coordinate

This question in 0580/41 Oct/Nov 2024

2 (a) A is the point (3, 7) and B is the point (-1, 5). (i) Find the coordinates of the midpoint of the line AB. ( … , … ) [2] (ii) Write AB as a column vector. f p [1] (iii) AC = 3BA Find the coordinates of C. ( … , … ) [2] (b) y 7 6 5 4 Q 3 P 2 1 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 – 2 (i) Rotate shape P through 180° about the point (4, 1). [2] (ii) Reflect shape P in the line y = x + 2 . [2] (iii) Describe fully the single transformation that maps shape P onto shape Q. … … [3]

12 marks

Mark scheme: 2(a)(i) (1, 6) 2 B1 for each 2(a)(ii)  −4  1    −2  2(a)(iii) (15, 13) 2 FT their (a)(ii)  12   −12  M1 for   or   seen  6   −6  or for –1 + 16 and 5 + 8 seen 2(b)(i) Image at (4, 1), (5, –1), (7, –1), (7, 1) 2 B1 for rotation 180° but incorrect position 2(b)(ii) Image at (1, 3), (–1, 3), (–1, 6), (1, 5) 2 B1 for correct orientation but incorrect position or for drawing line y = x + 2 2(b)(iii) Enlargement 3 B1 for each [centre] (3, 3) 1 [factor] − 2

This question in 0580/43 Oct/Nov 2024

10 y 7 6 5 4 A 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 B -3 -4 -5 (a) Draw the image of (i) triangle A after a reflection in the line y = 1 [2] - 6 (ii) triangle A after a translation by the vector b l . [2] 1 (b) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

7 marks

Mark scheme: 10(a)(i) Triangle drawn at (2, 0), (1, –1) 2 B1 for reflection in y = k and (3, –3) or for reflection in x = 1 10(a)(ii) Triangle drawn at (–4, 3), (–5, 4) and 2  −6   k  B1 for translation by or by (–3, 6)      k   1  10(b) Rotation 3 B1 for each 90° anticlockwise oe [centre] (3, –1)

This question in 0580/42 Feb/March 2025

8 y 7 6 5 A B 4 3 2 1 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 1 – 2 – 3 – 4 – 5 (a) On the diagram, draw the image of 1 (i) shape A after a translation by the vector e o [2] - 7 (ii) shape A after a reflection in the line y = x + 1. [3] (b) Describe fully the single transformation that maps shape A onto shape B. … … [3]

8 marks

Mark scheme: 8(a)(i) Image drawn at (–2, –3), 2 1  k  B1 for translation by  or by   (–3, –2), (–4, –2) and k  −7  (–3, –4) 8(a)(ii) Image drawn at (2, –3), 3 B2 for correct size and orientation but wrong position (3, –2), (4, –3) and (4, –4) or for quadrilateral with 3 correct vertices or B1 for y = x + 1 drawn soi long enough to be recognised 8(b) Rotation 3 B1 for each 90° anticlockwise oe (–2, 6)

This question in 0580/42 Oct/Nov 2025

7 y 12 11 10 9 8 D 7 6 5 4 F 3 2 1 x 0 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 – 1 E – 2 – 3 – 4 – 5 – 6 – 7 – 8 (a) Describe fully the single transformation that maps triangle D onto triangle E. … … [2] (b) Describe fully the single transformation that maps triangle D onto triangle F. … … [3]

5 marks

Mark scheme: 7(a) Translation 2 B1 for translation  2   2    B1 for    −8   −8  7(b) Enlargement 3 B1 for each 1 [scale factor] − 3 [centre] (–3, 4)

This question in 0580/43 Oct/Nov 2025