Transformations — Paper 1 · IGCSE Mathematics 0580

18 Examiner's y Use 6 5 A 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 B –2 –3 –4 –5 –6 (a) Describe fully the single transformation which maps flag A onto flag B. Answer(a) [2] (b) Draw, on the grid above, the image of flag A after rotation through 90° clockwise about the origin. [2]

4 marks

Mark scheme: 18 (a) Translation  7  2 W1 cao for translation (allow poor spelling)  −6  or W1 independent for correct vector alone. (b) Correct rotation 2 W1 for (2, 4) missed but other points correct (4, 4), (5, 4), (5, 2) and (2, 4) or SC1 for 90 anti-clockwise rotation or SC1 correct rotation, any other centre

This question in 0580/12 May/June 2010

13 For y Examiner's Use 5 4 3 2 P 1 x –4 –3 –2 –1 0 1 2 3 4 –1 Q –2 The points P ( 3 , 1 ) and Q (−1 , −1) are marked on the grid. (a) Write down the vector .   Answer(a) =   [1]     (b) R and S are two more points. − 2  PR =   and PS = 3 PR .  1  (i) Write down the vector PS .   Answer(b)(i) PS =   [1]     (ii) Mark the point S on the grid. [1]

3 marks

Mark scheme:  4  113 (a)    2  − 6  1 (b) (i)    3  (ii) S plotted at (−3 , 4 ) 1ft ft their PS

This question in 0580/11 Oct/Nov 2010

16 Flags A and B are shown on the grid. For Examiner's y Use 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 B –5 –6 (a) Describe fully the single transformation which maps flag A onto flag B. Answer(a) [3]  5  (b) On the grid, draw the translation of flag A by the vector   . [2]  −3 

5 marks

Mark scheme: 16 (a) Rotation or enlargement 1 Two transformations named, zero for (a) 180° (SF) −1 1 Independent (about or centre) origin oe 1 Independent (b) Correct translation 2 B1 for 5 right or 3 down applied 5 right and 3 down 12 

This question in 0580/12 Oct/Nov 2010

19 (a) For y Examiner's Use 8 7 6 B C 5 4 3 A 2 1 x 0 1 2 3 4 5 6 7 8 Three vertices of the quadrilateral ABCD are shown in the diagram. (i) Write down the co-ordinates of the point B. Answer(a)(i) ( , ) [1] (ii) On the grid, plot and label the point D so that quadrilateral ABCD has rotational symmetry of order 2. [1] (iii) Draw the quadrilateral ABCD. Draw in all the lines of symmetry on your quadrilateral. [1] (b) Write down the mathematical names of these quadrilaterals. P Q Answer(b) P Q [2] Question 20 is printed on the next page.

5 marks

Mark scheme: 19 (a) (i) (1, 5) 1 (ii) D at (5, 2) 1 (iii) Lines x = 3 and y = 3.5 only 1 Dep on (a)(ii) Extra line(s) zero drawn Lines should at least meet the sides (b) Kite Trapezium 1, 1 1 mark for each

This question in 0580/12 Oct/Nov 2011

23 For y Examiner's Use 3 A 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 M –3 –4 –5 The diagram shows two points A (–5, 2) and M (2, –3). (a) B is the point (5, –2). (i) On the grid, mark the point B. [1] (ii) Write as a column vector.     Answer(a)(ii) =   [1]     (b) M is the midpoint of the line BD. Find the co-ordinates of D. Answer(b) ( , ) [2] Question 24 is printed on the next page.

4 marks

Mark scheme: 23 (a) (i) B at (5, −2) 1  10  (ii)   1ft  −4  (b) (–1, –4) 2ft B1, B1 follow through their B plotted 2 2 ( )

This question in 0580/13 Oct/Nov 2011

14 y 11 10 9 B 8 7 6 A 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Describe fully the single transformation that maps shape A onto shape B. Answer … [3] _____________________________________________________________________________________

3 marks

Mark scheme: 14 Enlargement 1 [Centre] (5,4) 1 [Scale factor] 3 1 IGCSE – May/June 2013 0580 12

This question in 0580/12 May/June 2013

21 y 9 8 7 6 5 4 3 2 A B 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 C –2 –3 –4 –5 Three shapes A, B and C are shown on the grid. (a) Describe fully the single transformation that maps shape A onto (i) shape B, Answer(a)(i) … … [2] (ii) shape C. Answer(a)(ii) … … [3] (b) Enlarge shape A by scale factor 2 from the centre (4, 0). [2]

7 marks

Mark scheme: 21 (a) (i) reflection 1 x = 3 1 (ii) rotation 1 [centre] (0,0) oe 1 180 1 (b) correct enlargement 2 B1 for correct scale factor used, wrong centre (−2, 0), (−4, 0), (−2, 6), (−4, 8)

This question in 0580/12 Feb/March 2015

5 A B opposite congruent reflected translated Choose the mathematical word from the list to complete this statement. Pentagon A is … to pentagon B. [1]

1 marks

Mark scheme: 5 Congruent 1

This question in 0580/11 May/June 2017

16 Enlarge the rectangle using a scale factor of 3 and centre of enlargement O. O [2]

2 marks

Mark scheme: 16 Correct enlargement drawn 2 B1 for correct sf but wrong position

This question in 0580/11 May/June 2018

10 Shape A is shown on the grid. A On the grid, enlarge shape A by scale factor 3. [2]

2 marks

Mark scheme: 10 Correct ruled enlargement 2 B1 for two sides correct or for enlargement incorrect scale factor

This question in 0580/11 Oct/Nov 2018

9 Reflect this shape in the line AB. A B [2]

2 marks

Mark scheme: 9 correct reflection 2 B1 for 5 vertices correct

This question in 0580/12 Feb/March 2019

17 X Draw the enlargement of the triangle by scale factor 3, centre X. [2]

2 marks

Mark scheme: 17 correctly enlarged triangle 2 M1 for an enlargement scale factor 3 but incorrect position

This question in 0580/12 Feb/March 2019

20 y 6 A 5 4 B 3 2 1 C 0 1 2 3 4 5 6 7 8 x (a) Write down the co-ordinates of point B. ( … , … ) [1] (b) The quadrilateral ABCD has x = 4 as a line of symmetry. On the grid, plot point D. [1] (c) Write down the mathematical name of quadrilateral ABCD. … [1] (d) Write down the order of rotational symmetry of quadrilateral ABCD. … [1]

4 marks

Mark scheme: 20(a) 7 3 1 20(b) point plotted at (1, 3) 1 20(c) rhombus 1 20(d) 2 1 strict FT their diagram

This question in 0580/13 Oct/Nov 2019

2 A On the grid, draw a shape that is congruent to shape A. [1]

1 marks

Mark scheme: 2 Correct shape drawn 1

This question in 0580/13 May/June 2020

7 (a) Write down the mathematical name of a quadrilateral that has • rotational symmetry of order 1 and • only one line of symmetry. … [1] (b) Reflect the shape in line L. L [2]

3 marks

Mark scheme: 7(a) Kite or isosceles trapezium 1 7(b) Correct shape drawn 2 M1 for 3 sides correctly reflected or 4 correct vertices

This question in 0580/13 May/June 2020

15 y 3 2 1 B x -6 -5 -4 -3-3 -2 -1 0 1 2 3 4 -1 -2 -3 A -4 -5 -6 Describe fully the single transformation that maps shape A onto shape B. … … [3]

3 marks

Mark scheme: 15 Rotation 3 B1 for each clockwise 90° [centre] (0, 0)

This question in 0580/13 May/June 2020

14 y 6 5 4 3 A 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 x – 1 – 2 – 3 – 4 – 5 On the grid, draw the image of (a) triangle A after a reflection in the y-axis, [1] - 3 (b) triangle A after a translation by the vector [2] e- 4o.

3 marks

Mark scheme: 14(a) Triangle at (–1, 1) (–4, 2) (–3, 5) 1 14(b) Triangle at (–2, –3) (1, –2) (0, 1) 2  −3   k  B1 for translation by   or by    k   −4 

This question in 0580/12 Feb/March 2022

23 The diagram shows three shapes, A, B and C, on a 1 cm 2 grid. y 7 6 5 B 4 A 3 2 C 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x Describe fully the single transformation that maps (a) shape A onto shape B … … [3] (b) shape A onto shape C. … … [2]

5 marks

Mark scheme: 23(a) Rotation 3 B1 for each [centre] (–3, 3) 90º clockwise 23(b) Translation 2 B1 for each  7     2 

This question in 0580/13 May/June 2023

18 The diagram shows two shapes, A and B, on a grid. y 4 3 2 A 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 – 5 B – 6 – 7 – 8 (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) On the grid, draw the image of shape A after a reflection in the line x =-1. [2]

5 marks

Mark scheme: 18(a) Rotation 3 B1 for each [centre] (0,0) 90° [anticlockwise] 18(b) Shape drawn correctly 2 M1 for reflection in x = k or in y = −1

This question in 0580/12 Feb/March 2024

18 The diagram shows a rectangle and two points, P and C, on a 1 cm2 grid. y 9 P 8 7 6 C 5 4 3 2 1 0 x 1 2 3 4 5 6 7 8 (a) Write down the coordinates of point C. ( … , … ) [1] (b) The rectangle is enlarged by scale factor 2 with centre of enlargement point C. Find the coordinates of the image of point P. ( … , … ) [2] (c) Find the area of the enlarged rectangle. … cm2 [1]

4 marks

Mark scheme: 18(a) (0, 5) 1 18(b) (14, 11) 2 B1 for each 18(c) 60 1

This question in 0580/11 Oct/Nov 2024

16 The diagram shows a point P and three triangles, A, B and C, on a 1 cm2 grid. y 7 6 5 4 C 3 B 2 1 A x - 4 -3 -2 -1 0 1 2 3 4 5 6 -1 -2 P -3 - 4 - 5 - 6 (a) Find the area of triangle B. … cm2 [1] (b) (i) Write down the coordinates of point P. ( … , … ) [1] - 20 (ii) Work out the coordinates of point P after a translation by the vector e o. 12 ( … , … ) [1] (c) Draw the image of triangle A after a reflection in the line y =-1. [2] (d) Describe fully the single transformation that maps (i) triangle A onto triangle B … … [3] (ii) triangle A onto triangle C. … … [3]

11 marks

Mark scheme: 16(a) 6 1 16(b)(i) 4, –3 1 16(b)(ii) –16, 9 1 FT their (b)(i) 16(c) Triangle drawn with coordinates 2 B1 for reflection in y = k or in x = −1 (1, −2 ) , ( 2, −2 ) and ( 2, −5 ) 16(d)(i) Enlargement 3 B1 for each [scale factor] 2 [centre] ( −1,0 ) 16(d)(ii) Rotation 3 B1 for each 90˚ clockwise [centre] (2,3 )

This question in 0580/12 May/June 2025

21 Shapes A and B are shown on the grid. y 5 4 3 B 2 A 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 (a) Describe fully the single transformation that maps shape A onto shape B. … … [3] (b) Draw the image of shape A after a reflection in the line y =-1. [2]

5 marks

Mark scheme: 21(a) Rotation 3 B1 for rotation 90 anticlockwise oe (0,0) oe B2 for 90 anticlockwise and (0, 0) or for 90 clockwise and (0.5, 3.5) or B1 for 90 anticlockwise or 90 clockwise or (0, 0) or (0.5, 3.5) 21(b) Rectangle with vertices at 2 B1 for reflection in y = k or in x = –1 (1, –3) (3, –3) (3, –4) (1,–4)

This question in 0580/11 Oct/Nov 2025

19 The grid shows two flags, F and A. y 7 6 5 F 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 A – 2 – 3 – 4 – 5 – 6 – 7 (a) On the grid, draw the image of flag F after a reflection in the line x =- 1 . [2] (b) On the grid, draw the image of flag F after a rotation of 180° about (0, 0). [2] (c) Describe fully the single transformation that maps flag F onto flag A. … … [2]

6 marks

Mark scheme: 19(a) Fully correct reflection, points (−4, 5) 2 B1 for a correct reflection in x = k or (−5, 5) (−4, 4) (−5, 4) (−4, 2) y = − 1 19(b) Fully correct rotation, points (−2, −2) 2 B1 for a correct rotation of 180° about (−2, −4) (−2, −5) (−3, −5) (−3, −4) the wrong centre 19(c) Translation 2 B1 for each  2     −6 

This question in 0580/12 Oct/Nov 2025

22 The diagram shows triangles A and B. y 10 9 8 7 B 6 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 10 x Describe fully the single transformation that maps triangle A onto triangle B. … … [3]

3 marks

Mark scheme: 22 Enlargement 3 B1 for each Centre (0,0) [Scale factor] 3

This question in 0580/13 Oct/Nov 2025