Questions as text
Q1 · Answer the whole of this question on one sheet of graph paper 0580/41 Oct/Nov 2005
2 Answer the whole of this question on one sheet of graph paper. (a) Draw and label x and y axes from –8 to +8, using a scale of 1 cm to 1 unit on each axis. [1] (b) Draw and label triangle ABC with A (2, 2), B (5, 2) and C (5, 4). [1] (c) On your grid: 3 (i) translate triangle ABC by the vector and label this image A1B1C1; [2] −9 (ii) reflect triangle ABC in the line x = −1 and label this image A2B2C2; [2] (iii) rotate triangle ABC by 180° about (0, 0) and label this image A3B3C3. [2] 1.5 0 (d) A stretch is represented by the matrix . 0 1 (i) Draw the image of triangle ABC under this transformation. Label this image A4B4C4. [3] 1.5 0 (ii) Work out the inverse of the matrix . [2] 0 1 (iii) Describe fully the single transformation represented by this inverse. [3]
16 marks
Mark scheme: 2 (a) Correct Scales S1 Accuracy 2 mm throughout question. From –8 to 8 for x and y possible. (b) Correct triangle ABC T1 (c) (i) Correct translation with vertices at TR2ft SC1ft for any translation (5, –7), (8, –7), (8, –5) (ii) Correct reflection with vertices at FR2ft SC1ft for two points correct or reflection in (–4, 2), (–7, 2), (–7, 4) x = 1 or y = –1 (iii) Correct rotation with vertices at RN2ft SC1ft for 2 points correct (–2, –2), (–5, –2), (–5, –4) (d) (i) Correct image drawn with vertices at B3 B2 for 3 correct points shown in working. B1 (3, 2), (7.5, 2), (7.5, 4) for 2 correct vertices s.o.i. B2 (ii) 1 1 0 1 1 0 o.e. SC1 for or 15 0 1 . 5 1 . 5 0 1 . 5 (iii) Stretch B1 y-axis invariant o.e. B1 B1 factor 2 3 [16] IGCSE – NOVEMBER 2005 0580/0581 4
This question in 0580/41 Oct/Nov 2005
Q2 · 3 7 Transformation T is translation by the vector 0580/41 May/June 2006
3 7 Transformation T is translation by the vector . 2 Transformation M is reflection in the line y = x. (a) The point A has co-ordinates (2, 1). Find the co-ordinates of (i) T(A), [1] (ii) MT(A). [2] (b) Find the 2 by 2 matrix M, which represents the transformation M. [2] (c) Show that, for any value of k, the point Q (k – 2, k – 3) maps onto a point on the line y = x following the transformation TM(Q). [3] (d) Find M-1, the inverse of the matrix M. [2] 0 3 0 4 (e) N is the matrix such that N + = . 1 0 0 0 (i) Write down the matrix N. [2] (ii) Describe completely the single transformation represented by N. [3]
15 marks
Mark scheme: 7 (a) (i) (5 , 3) B1 (ii) (3, 5) 1+1 ft from (a)(i) (b) 0 1 B2 SC1 for a correct column 1 0 (c) M(Q) = (k – 3 , k – 2) seen M1 SC2 if a numerical value of k is TM(Q) = (k – 3 + 3 , k – 2 + 2) seen M1 chosen and full working leads to (k , k) = (k , k) so y = x E1 (k , k) (d) 0 1 B2 SC1 for determinant = –1 or for “self-inverse” 1 0 (e) (i) 0 1 B2 SC1 for 3 correct numbers. − 1 0 (ii) Rotation B1 Centre (0 , 0) B1 270° or clockwise 90° B1 15 2
This question in 0580/41 May/June 2006
Q3 · Answer the whole of this question on a sheet of graph paper 0580/41 May/June 2007
2 Answer the whole of this question on a sheet of graph paper. (a) Draw and label x and y axes from −6 to 6, using a scale of 1 cm to 1 unit. [1] (b) Draw triangle ABC with A (2,1), B (3,3) and C (5,1). [1] (c) Draw the reflection of triangle ABC in the line y = x. Label this A1B1C1. [2] (d) Rotate triangle A1B1C1 about (0,0) through 90° anti-clockwise. Label this A2B2C2. [2] (e) Describe fully the single transformation which maps triangle ABC onto triangle A2B2C2. [2] 1 0 (f) A transformation is represented by the matrix . −1 1 (i) Draw the image of triangle ABC under this transformation. Label this A3B3C3. [3] 1 0 (ii) Describe fully the single transformation represented by the matrix . [2] − 1 1 (iii) Find the matrix which represents the transformation that maps triangle A3B3C3 onto triangle ABC. [2]
15 marks
Mark scheme: 2 (a) Axes to correct scale S1 Accept 2mm accuracy throughout (b) Correct triangle A(2,1)B(3,3)C(5,1) B1 Condone absence of labels (c) A1(1,2), C1(1,5), B1(3,3) B2 B1 for 2 correct points ft their ABC Condone absence of labels and sides but not incorrect suffices (d) A2(–2,1), C2(–5,1), B2(–3,3) B2 B1 for 2 correct points ft their A1B1C1 Condone absence of labels and sides but not incorrect suffices SC1 for rotation of their A1B1C1 90° clockwise about the origin If triangle ABC is rotated correctly treat as mis-read (e) Reflection B1 Indep (Only possible answer) y-axis oe cso B1 (f) (i) A3(2, –1), C3(5, –4), B3(3,0) B3 B2 for 2 correct points plotted Condone absence of labels and sides If B0, M1 for any set up of matrix multiplication seen for at least one point and A1 for correct result (If correct triangle A2B2C2 used treat as MR, and the co-ords are (–2, 3), (–5, 6), (–3, 6)) (ii) Shear, y-axis invariant oe B1,B1 Allow factor of either +1 or –1 if invariant line omitted, but dependent on shear or stretch (iii) 1 0 B2 B1 for the left hand column 1 1 [15] IGCSE – May/June 2007 0580 and 0581 04
This question in 0580/41 May/June 2007
Q4 · Answer the whole of this question on a sheet of graph paper 0580/41 Oct/Nov 2007
7 Answer the whole of this question on a sheet of graph paper. (a) Draw x and y axes from 0 to 12 using a scale of 1 cm to 1 unit on each axis. [1] (b) Draw and label triangle T with vertices (8, 6), (6, 10) and (10, 12). [1] (c) Triangle T is reflected in the line y = x. (i) Draw the image of triangle T. Label this image P. [2] (ii) Write down the matrix which represents this reflection. [2] 1 0 (d) A transformation is represented by the matrix 2 1 0 2 (i) Draw the image of triangle T under this transformation. Label this image Q. [2] (ii) Describe fully this single transformation. [3] (e) Triangle T is stretched with the y-axis invariant and a stretch factor of 1 . 2 Draw the image of triangle T. Label this image R. [2]
13 marks
Mark scheme: 7 (a) Correct axes S1 must fit on paper 2mm acc throughout Ignore labels on triangles throughout (b) Correct triangle drawn (T) T1 vertices at (8, 6), (6, 10) and (10, 12) (c) (i) Correct reflection in y = x drawn (P) P2ft ft their T, P1 for two correct vertices drawn (6, 8), (10, 6), (12, 10) or line y = x correctly drawn (within 2mm of (12,12) if extended) (ii) B2 B1 for a correct column 0 1 1 0 (d) (i) Correct enlargement, scale factor 0.5, Q2ft (4, 3), (3, 5), (5, 6) centre (0,0) drawn (Q) Q1 for any enlargement s.f. ½ or 2 correct vertices drawn SC1 for 3 points within 5 mm if rays method used or for correct enlargement but of P (ii) Enlargement only B1 (scale factor) 0.5 B1 indep (centre) (0, 0) o.e. B1 indep (e) Correct stretch drawn (R) R2ft R1 for two correct vertices ft (4, 6), (3, 10), (5, 12) [13]
This question in 0580/41 Oct/Nov 2007
Q5 · Y C 5 B 4 3 2 1 D A x –4 –3 –2 –1 O 1 2 3 4 –1 The pentagon OABCD is shown on the grid… 0580/41 May/June 2008
6 y C 5 B 4 3 2 1 D A x –4 –3 –2 –1 O 1 2 3 4 –1 The pentagon OABCD is shown on the grid above. (a) Write as column vectors (i) , [1] (ii) BC . [1] (b) Describe fully the single transformation which maps the side BC onto the side OD. [2] (c) The shaded area inside the pentagon is defined by 5 inequalities. 1 One of these inequalities is y Y x + 4. 2 Find the other 4 inequalities. [5]
9 marks
Mark scheme: 6 (a) (i) 2 Allow (2 1), condone omission of B1 brackets 1 (ii) 2 Allow (2 1), condone omission of ft B1ft brackets 1 ft their (i) if a vector (b) 0 Allow (0 –4), condone omission of Translation o.e. B1, B1 brackets, allow in words −4 Any extra transformation spoils both marks (c) y > 0 o.e. B1 For all four, condone strict inequalities x < 2 o.e. B1 and only penalise first incorrect sign, 1 B1 which may be = or an inequality sign y > x o.e. 2 B2 If B0, B1 for 2x or for 4 if other y < 2x + 4 o.e. co-efficient is not zero 1 y < x + 4 gets zero [9] 2
This question in 0580/41 May/June 2008
Q6 · Examiner's y Use 8 7 T 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 P… 0580/41 May/June 2010
3 Examiner's y Use 8 7 T 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 P –4 –5 –6 Q –7 –8 (a) On the grid, draw the enlargement of the triangle T, centre (0, 0), scale factor 12 . [2] For − 1 0 Examiner's (b) The matrix represents a transformation. Use 0 1 − 1 0 8 8 2 (i) Calculate the matrix product . 0 1 4 8 8 Answer(b)(i) [2] (ii) On the grid, draw the image of the triangle T under this transformation. [2] (iii) Describe fully this single transformation. Answer(b)(iii) [2] (c) Describe fully the single transformation which maps (i) triangle T onto triangle P, Answer(c)(i) [2] (ii) triangle T onto triangle Q. Answer(c)(ii) [3] (d) Find the 2 by 2 matrix which represents the transformation in part (c)(ii). Answer(d) [2]
15 marks
Mark scheme: 3 (a) Triangle drawn with co-ords at (1, 4), 2 SC1 for 2 correct vertices or an enlargement sf (4, 2), (4, 4) 1 with wrong centre 2 − 8 − 8 − 2 (b) (i) 4 8 8 2 B1 each row (ii) Triangle drawn at (–8, 4), (–8, 8), (–2, 8) 2ft SC1 for 2 correct ft vertices. Can also be ft (i) correct regardless of (i) (iii) Reflection cao B1 Independent of (i) or (ii) Extra transformations lose all marks y – axis or x = 0 cao 2 B1 Independent of (i) or (ii) (c) (i) Translation B1 Extra transformations lose all marks − 10 − 10 o.e. 2 B1 (ii) Rotation 3 B1 Extra transformations lose all marks (0, 0) B1 Allow word origin for (0, 0) 90° clockwise oe B1 Allow – 90° or 270° (anti-clockwise) 0 1 (d) − 1 0 2 B1 each column IGCSE – May/June 2010 0580 41
This question in 0580/41 May/June 2010
Q7 · Examiner's y Use 9 8 7 6 5 V 4 3 2 T 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 U… 0580/42 May/June 2010
4 Examiner's y Use 9 8 7 6 5 V 4 3 2 T 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 U –6 (a) On the grid, draw −7 (i) the translation of triangle T by the vector , [2] 3 (ii) the rotation of triangle T about (0, 0), through 90° clockwise. [2] (b) Describe fully the single transformation that maps (i) triangle T onto triangle U, Answer(b)(i) [2] (ii) triangle T onto triangle V. Answer(b)(ii) [3] For (c) Find the 2 by 2 matrix which represents the transformation that maps Examiner's Use (i) triangle T onto triangle U, Answer(c)(i) [2] (ii) triangle T onto triangle V, Answer(c)(ii) [2] (iii) triangle V onto triangle T. Answer(c)(iii) [1]
14 marks
Mark scheme: 7 k 4 (a) (i) Triangle with vertices (–4, 4), (–1, 4), 2 SC1 for translation k or 3 (–1, 6) (ii) Triangle with vertices (1, –3), (1, –6), 2 SC1 two correct vertices or 90° anticlockwise (3, –6) about (0, 0) (b) (i) Reflection only 1 Marks independent but must be single y = –x oe 1 transformation to score any marks (ii) Stretch only 1 Marks independent but must be single x-axis oe invariant 1 transformation to score any marks (factor) 3 1 IGCSE – May/June 2010 0580 42 0 − 1 (c) (i) − 1 0 2 B1 each column 1 0 (ii) 0 3 ft 2ft ft factor in (b)(ii) only if stretch and can recover to correct matrix SC1ft for right-hand column 1 1 0 n 0 0 1 0 1 0 n (iii) 1 ft to 1 0 3 0 0 n ft 1ft n to 1 or 1 0 0 n ≠ 0, ± 1 1 for , allow 0.33 or better 3 180 2 + 115 2 − 90 2 2
This question in 0580/42 May/June 2010
Q8 · For y Examiner's Use 8 6 4 A A 2 x –8 –6 –4 –2 0 2 4 6 8 –2 –4 –6 –8 Draw the images of… 0580/42 Oct/Nov 2010
8 (a) For y Examiner's Use 8 6 4 A A 2 x –8 –6 –4 –2 0 2 4 6 8 –2 –4 –6 –8 Draw the images of the following transformations on the grid above. 3 (i) Translation of triangle A by the vector . Label the image B. [2] −7 (ii) Reflection of triangle A in the line x = 3. Label the image C. [2] (iii) Rotation of triangle A through 90° anticlockwise around the point (0, 0). Label the image D. [2] (iv) Enlargement of triangle A by scale factor –4, with centre (0, 1). Label the image E. [2] (b) The area of triangle E is k × area of triangle A. For Write down the value of k. Examiner's Use Answer(b) k = [1] (c) y 5 4 3 2 1 F x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 –5 (i) Draw the image of triangle F under the transformation represented by the 1 3 matrix M = . [3] 0 1 (ii) Describe fully this single transformation. Answer(c)(ii) [3] (iii) Find M–1, the inverse of the matrix M. Answer(c)(iii) [2]
17 marks
Mark scheme: 8 (a) (i) Correct translation to (3, –5), 2 SC1 for translation of 3 or k or vertices k −7 (5, –6) and (4, –4) only (ii) Correct reflection to (4, 1), (5, 3) 2 SC1 for reflection in y = 3 or vertices only and (6, 2) (iii) Correct rotation to (–2, 0), (–1, 2) 2 SC1 for rotation 90 clockwise around (0, 0) and (–3, 1) or vertices only (iv) Correct enlargement to (0, –3), 2 SC1 for two correct points or vertices only (–8, 1) and (–4, –7) (b) 16 cao 1 (c) (i) Correct transformation to 3 B2 for 3 correct points shown in working but not (–4, 0), (5, 3) and (–2, 0) plotted or B1 for incorrect shear drawn with x-axis invariant or two correct points shown (ii) Shear only 1 If more than one transformation given – no marks available x-axis oe invariant 1 Accept fixed, constant oe for invariant (factor) 3 1 1 − 3 (iii) oe 2 B1 for determinant = 1 or k 1 − 3 oe 0 1 0 1 IGCSE – October/November 2010 0580 42 4 4
This question in 0580/42 Oct/Nov 2010
Q9 · For y Examiner's Use 4 A B 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 C –2 –3 –4 –5 –6 (a)… 0580/41 May/June 2011
5 For y Examiner's Use 4 A B 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 C –2 –3 –4 –5 –6 (a) On the grid above, draw the image of − 3 (i) shape A after translation by the vector , [2] − 2 (ii) shape A after reflection in the line x = −1 . [2] (b) Describe fully the single transformation which maps (i) shape A onto shape B, Answer(b)(i) [3] (ii) shape A onto shape C. Answer(b)(ii) [3] (c) Find the matrix representing the transformation which maps shape A onto shape B. Answer(c) [2] − 1 0 (d) Describe fully the single transformation represented by the matrix . 0 − 1 Answer(d) [3]
15 marks
Mark scheme: − 3 k 5 (a) (i) Correct translation (see diagram) 2 SC1 for translation by or by k −2 (ii) Correct reflection (see diagram) 2 SC1 for reflection in y = −1 (b) (i) Stretch, 1 (factor) 3, 1 y-axis or x = 0 invariant 1 (ii) Rotation 1 90° clockwise 1 Accept −90° (1, − 1) 1 3 0 1 0 k 0 (c) (i) ft from (b)(i) 2 ft SC1 for (ft from (b)(i)) or 0 1 0 3 0 1 with k algebraic or numeric but ≠ 1 or 0 (ii) Rotation, 1 180° 1 Origin 1 Accept O or (0,0)
This question in 0580/41 May/June 2011
Q10 · For Examiner's Use A P Draw the enlargement of triangle P with centre A and scale factor 2 0580/42 May/June 2011
8 (a) For Examiner's Use A P Draw the enlargement of triangle P with centre A and scale factor 2. [2] (b) y Q R x 0 (i) Describe fully the single transformation which maps shape Q onto shape R. Answer(b)(i) [3] (ii) Find the matrix which represents this transformation. Answer(b)(ii) [2] (c) y S T x 0 Describe fully the single transformation which maps shape S onto shape T. Answer(c) [3]
10 marks
Mark scheme: 8 (a) Correct enlargement 2 B1 for any enlargement of 2 in correct orientation (b) (i) Stretch only 1 y- axis oe invariant 1 (factor) 4 1 4 0 (ii) 2ft Ft their factor 4 0 1 k 0 1 0 SC1 for k ≠ 0, ≠ 1 or ft their 0 1 0 4 factor 4 (c) Shear only 1 x-axis oe invariant 1 (factor) 2 1 IGCSE – May/June 2011 0580 42
This question in 0580/42 May/June 2011
Q11 · For y Examiner's Use 6 5 X 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6… 0580/43 May/June 2011
2 For y Examiner's Use 6 5 X 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) (i) Draw the reflection of shape X in the x-axis. Label the image Y. [2] (ii) Draw the rotation of shape Y, 90° clockwise about (0, 0). Label the image Z. [2] (iii) Describe fully the single transformation that maps shape Z onto shape X. Answer(a)(iii) [2] 1 (b) (i) Draw the enlargement of shape X, centre (0, 0), scale factor . [2] 2 1 (ii) Find the matrix which represents an enlargement, centre (0, 0), scale factor . 2 Answer(b)(ii) [2] (c) (i) Draw the shear of shape X with the x-axis invariant and shear factor –1. [2] (ii) Find the matrix which represents a shear with the x-axis invariant and shear factor –1. Answer(c)(ii) [2]
14 marks
Mark scheme: 2 (a) (i) Image at (4, –4), (6, –4), (6, –6), 2 SC1 for reflection in y-axis (2, –6) (ii) Image at (–4, –4), (–4, –6), (–6, –6), 2 ft SC1 ft if rotated 90° anti-clockwise about (0, 0) (–6, –2) (iii) Reflection 1 ft ft their Z (name of transformation) y = –x 1 ft independent (full details) (b) (i) Image at (2, 2), (3, 2), (3, 3), (1, 3) 2 SC1 for enlargement s.f. 0.5 with correct orientation, different centre or sf – 0.5, centre (0, 0) 5.0 0 (ii) cao 2 B1 B1 each column 0 5.0 (c) (i) Image at (0, 4), (2, 4), (0, 6), (–4, 6) 2 SC1 if 3 vertices correct 1 − 1 1 k (ii) 2 SC1 for , k ≠ 0 but can be algebraic or 0 1 0 1 1 0 numeric or for − 1 1 IGCSE – May/June 2011 0580 43
This question in 0580/43 May/June 2011
Q12 · For y Examiner's Use 8 6 4 B 2 x –8 –6 –4 –2 0 2 4 6 8 C –2 –4 D –6 A –8 (a) Describe… 0580/41 Oct/Nov 2011
7 For y Examiner's Use 8 6 4 B 2 x –8 –6 –4 –2 0 2 4 6 8 C –2 –4 D –6 A –8 (a) Describe fully the single transformation which maps (i) triangle A onto triangle B, Answer(a)(i) [2] (ii) triangle A onto triangle C, Answer(a)(ii) [3] (iii) triangle A onto triangle D. Answer(a)(iii) [3] (b) Draw the image of For − 5 Examiner's (i) triangle B after a translation of , [2] Use 2 1 0 (ii) triangle B after a transformation by the matrix . [3] 0 2 1 0 (c) Describe fully the single transformation represented by the matrix . 0 2 Answer(c) [3]
16 marks
Mark scheme: 7 (a) (a) (i) Reflection only B1 Spoilt if extras y = –2 B1 (ii) Enlargement only B1 Spoilt if extras 1 B1 2 (1, 4) B1 (iii) Rotation only B1 Spoilt if extras 90° clockwise oe B1 Accept –90° or (+)270° Around (1, –3) B1 − 5 k (b) (i) Triangle at (–4, 4), (–1, 4), (–1, 5) 2 B1 for translation of or k 2 After B0, SC1 for translation of 5 small squares to the left and 2 small squares up (ii) Triangle at (4, 4), (1, 4), (4, 6) 3 B1 for each of (4, 4) or (4, 6) plotted If no/wrong plots allow SC2 for 3 correct coordinates shown in working or SC1 for any 2 correct coordinates shown 1 0 1 4 4 or M1 for shown 0 2 2 2 3 (c) Stretch only B1 Spoilt if extras (Factor) 2 B1 x-axis oe invariant B1 IGCSE – October/November 2011 0580 41
This question in 0580/41 Oct/Nov 2011
Q13 · For y Examiner's Use 6 4 P 2 W x –6 –4 –2 0 2 4 6 –2 –4 –6 (a) Draw the reflection of… 0580/43 Oct/Nov 2011
4 For y Examiner's Use 6 4 P 2 W x –6 –4 –2 0 2 4 6 –2 –4 –6 (a) Draw the reflection of shape P in the line y = x. [2] − 2 (b) Draw the translation of shape P by the vector . [2] 1 (c) (i) Describe fully the single transformation that maps shape P onto shape W. Answer(c)(i) [3] (ii) Find the 2 by 2 matrix which represents this transformation. Answer(c)(ii) [2] 1 0 (d) Describe fully the single transformation represented by the matrix . 0 2 Answer(d) [3]
12 marks
Mark scheme: 4 (a) Image (1, –1), (1, –2), (4, –2), (3, –1) 2 B1 if vertices plotted only or reflects in y = –x − 2 k (b) Image (–3, 2), (–4, 2), (–4, 5), (–3, 4) 2 B1 for translation by or k 1 (c) (i) Rotation only, 1 Spoilt if extras 90 clockwise oe, 1 (Centre) (0, 0) oe 1 0 1 (ii) 2 B1 for one row or one column correct − 1 0 (d) Stretch only, 1 Spoilt if extras (Factor) 2, 1 x-axis oe invariant 1
This question in 0580/43 Oct/Nov 2011
Q14 · For y Examiner's Use 10 9 8 7 6 5 4 P 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 R –2… 0580/41 May/June 2012
7 For y Examiner's Use 10 9 8 7 6 5 4 P 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 R –2 –3 Q –4 –5 –6 (a) Describe fully (i) the single transformation which maps triangle P onto triangle Q, Answer(a)(i) [3] (ii) the single transformation which maps triangle Q onto triangle R, Answer(a)(ii) [3] (iii) the single transformation which maps triangle R onto triangle P. Answer(a)(iii) [3] (b) On the grid, draw the image of For Examiner's Use − 4 (i) triangle P after translation by , [2] − 5 (ii) triangle P after reflection in the line x = −1 . [2] (c) (i) On the grid, draw the image of triangle P after a stretch, scale factor 2 and the y-axis as the invariant line. [2] (ii) Find the matrix which represents this stretch. Answer(c)(ii) [2]
17 marks
Mark scheme: 7 In any part of part (a) all marks are independent but mention of a second transformation scores 0 out of 3 (a) (i) Rotation 1 accept R (centre/about) origin (O) (0,0) 1 180° 1 SC3 for all of enlargement, sf – 1, (0, 0) (ii) Enlargement 1 accept E (centre/about) (0,− 3) 1 SF − 3 1 (iii) Enlargement 1 accept E (centre/about) (0, 6) 1 1 1 SF 3 − 4 k (b) (i) image at (−4, −2) (−2, −2) and (−1, 0) 2 SC1 for translation by or , k ≠ 0 k −5 (ii) image at (− 2, 3) (− 4, 3) and (− 5, 5) 2 SC1 for reflection in y = − 1 (c) (i) image at (0, 3) (4, 3) and (6, 5) 2 SC1 for stretch sf 2 with x-axis invariant ie at (0,6) (2,6) (3,10) (ii) 2 0 2 ft ft their stretch factor only ft 1 0 0 1 SC1 for correct left hand column ft or ft 0 2
This question in 0580/41 May/June 2012
Q15 · For y Examiner's Use 8 7 X 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2… 0580/43 Oct/Nov 2012
2 (a) For y Examiner's Use 8 7 X 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 Y –3 –4 –5 –6 –7 –8 –9 − 11 (i) Draw the translation of triangle X by the vector . [2] − 1 1 (ii) Draw the enlargement of triangle Y with centre (–6, – 4) and scale factor . [2] 2 (b) For y Examiner's Use 8 7 W X 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 Y –3 –4 Z –5 –6 –7 –8 –9 Describe fully the single transformation that maps (i) triangle X onto triangle Z, Answer(b)(i) [2] (ii) triangle X onto triangle Y, Answer(b)(ii) [3] (iii) triangle X onto triangle W. Answer(b)(iii) [3] (c) Find the matrix that represents the transformation in part (b)(iii). Answer(c) [2]
14 marks
Mark scheme: − 11 k 2 (a) (i) Image at (– 3, 1), (– 7, 7), 2 SC1 for translation or k −1 (– 3, 7) (ii) Image at (– 4, – 1), (– 4, – 4), 2 SC1 for enlargement factor 0.5 and correct (– 2, – 4) orientation In each part of (b) must be one transformation only – if more then lose all marks for that part (b) (i) Reflection, y = 1 2 B1 B1 independent (ii) Rotation, (3, 2), 180 oe 3 B1 B1 B1 independent or enlargement, (3, 2), (factor) – 1 (iii) Stretch, (factor) 0.5, 3 B1 B1 B1 independent – must be clear on invariant Invariant line y-axis or x = 0 line IGCSE – October/November 2012 0580 43 5.0 0 (c) 2 ft ft their factor in (b)(iii) only if stretch not 0 or 1 0 1 k 0 SC1 for [k ≠ 0 or 1] or 0 1 1 0 ft their factor only if stretch in (b)(iii) 0 5.0
This question in 0580/43 Oct/Nov 2012
Q16 · For Examiner′s y Use 9 8 7 6 5 4 3 2 Q 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1… 0580/41 May/June 2013
4 For Examiner′s y Use 9 8 7 6 5 4 3 2 Q 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 R –4 –5 –6 (a) Describe fully the single transformation that maps shape Q onto shape R. Answer(a) … [3] 5 (b) (i) Draw the image when shape Q is translated by the vector [2] 4 e o. (ii) Draw the image when shape Q is refl ected in the line x = 2. [2] (iii) Draw the image when shape Q is stretched, factor 3, x-axis invariant. [2] (iv) Find the 2 × 2 matrix that represents a stretch of factor 3, x-axis invariant. Answer(b)(iv) [2] e o 0 1 (c) Describe fully the single transformation represented by the matrix 1 0 e o. Answer(c) … [2] _____________________________________________________________________________________
13 marks
Mark scheme: 4 (a) Enlargement 1 [centre] (–3, 4) 1 Do not allow column vector for coordinates [scale factor] 3 1 5 k (b) (i) Image at (1 5), (4, 5), (4, 6), (1, 7) 2 SC1 for translation by or 4 k (ii) Image at (5, 1), (8, 1), (8, 3), (5, 2) 2 SC1 for reflection in y = 2 (iii) Image at 2 SC1 for three correct vertices or shape with vertices at (–4, 1) (– 4, 3), (– 1, 3), (– 1, 6), (– 4, 9) and (–1, 1), (–1, 4) and (–4, 7) 1 0 1 0 3 0 (iv) 2 SC1 for , k ≠ ± 1 or 0 3 0 k 0 1 (c) Reflection 2 B1 B1 independent y = x oe
This question in 0580/41 May/June 2013
Q17 · For Examiner′s y Use 10 9 8 7 6 5 4 3 2 A B 1 x 0 1 2 3 4 5 6 7 8 (a) (i) Draw the image… 0580/43 May/June 2013
7 For Examiner′s y Use 10 9 8 7 6 5 4 3 2 A B 1 x 0 1 2 3 4 5 6 7 8 (a) (i) Draw the image of shape A after a stretch, factor 3, x-axis invariant. [2] (ii) Write down the matrix representing a stretch, factor 3, x-axis invariant. Answer(a)(ii) [2] e o (b) (i) Describe fully the single transformation which maps shape A onto shape B. Answer(b)(i) … [3] (ii) Write down the matrix representing the transformation which maps shape A onto shape B. Answer(b)(ii) [2] e o _____________________________________________________________________________________
9 marks
Mark scheme: 7 (a) (i) Triangle at (1, 3) (1, 9) (3, 3) 2 SC1 for correct vertices not joined or triangle(1, 1) (3, 1) (1, 7) 1 0 1 0 (ii) 2 SC1 for , k ≠ ± 1 or 0 0 3 0 k 3 0 or 0 1 (b) (i) Shear 1 x-axis oe invariant 1 [factor] 2 1 (ii) 1 2 2FT FT from their 2 in (b)(i) 1 k 0 1 SC1 for , k ≠ 0 0 1 1 0 or 2 FT 1
This question in 0580/43 May/June 2013
Q18 · For Examiner′s y Use 10 9 8 7 6 5 4 3 2 T U 1 x 0 1 2 3 4 5 6 7 8 9 10 (i) Draw the refl… 0580/41 Oct/Nov 2013
5 (a) For Examiner′s y Use 10 9 8 7 6 5 4 3 2 T U 1 x 0 1 2 3 4 5 6 7 8 9 10 (i) Draw the refl ection of triangle T in the line y = 5. [2] (ii) Draw the rotation of triangle T about the point (4, 2) through 180°. [2] (iii) Describe fully the single transformation that maps triangle T onto triangle U. Answer(a)(iii) … [3] (iv) Find the 2 × 2 matrix which represents the transformation in part (a)(iii). Answer(a)(iv) [2] f p (b) For Examiner′s P Q Use NOT TO SCALE p R O s S In the pentagon OPQRS, OP is parallel to RQ and OS is parallel to PQ. PQ = 2OS and OP = 2RQ. O is the origin, = p and = s. Find, in terms of p and s, in their simplest form, (i) the position vector of Q, Answer(b)(i) … [2] (ii) . Answer(b)(ii) = … [2] (c) Explain what your answers in part (b) tell you about the lines OQ and SR. Answer(c) … [1] _____________________________________________________________________________________
14 marks
Mark scheme: 5 (a) (i) Correct reflection to (4, 8) 2 SC1 for reflection in line x = 5 (2, 9) (4, 9) or reflection in y = k Ignore additional triangles (ii) Correct rotation to (4, 2), (4, 3) 2 SC1 for rotation 180˚ with incorrect centre (6, 3) Ignore additional triangles (iii) Shear, x-axis oe invariant, 3 B1 each (independent) [factor] 2 1 2 (iv) 2FT FT their shear factor 0 1 B1FT for one correct column or row in 2 by 2 matrix but not identity matrix 1 0 or SC1FT for 2 1 (b) (i) p + 2s final answer 2 M1 for recognising OQ as position vector soi 1 1 (ii) s + p final answer 2 B1 for s + kp or ks + p 2 2 or correct route (k ≠ 0) (c) parallel and OQ = 2SR oe 1
This question in 0580/41 Oct/Nov 2013
Q19 · For Examiner′s y Use 8 7 6 5 4 D C 3 2 B A 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8… 0580/42 Oct/Nov 2013
9 For Examiner′s y Use 8 7 6 5 4 D C 3 2 B A 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 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 (i) triangle B, Answer(a)(i) … [2] (ii) triangle C, Answer(a)(ii) … [2] (iii) triangle D. Answer(a)(iii) … [3] (b) On the grid, draw For Examiner′s Use (i) the rotation of triangle A about (6, 0) through 90° clockwise, [2] (ii) the enlargement of triangle A by scale factor –2 with centre (0, –1), [2] (iii) the shear of triangle A by shear factor –2 with the y-axis invariant. [2] (c) Find the matrix that represents the transformation in part (b)(iii). Answer(c) [2] f p _____________________________________________________________________________________ Question 10 is printed on the next page.
15 marks
Mark scheme: 9 (a) (i) Reflection x = –2 oe 2 B1 for either (ii) Translation − 7 oe 2 2 B1 for either (iii) Stretch x-axis oe invariant [factor] 3 3 B1 for each (b) (i) Triangle with coords at (8, 2) 2 B1 for rotation about (6, 0) but 90° (7, 3) and (7, 5) anticlockwise Or for rotation 90° clockwise around any point (ii) Triangle with coords at 2 B1 for 2 correct points or for enlargement of (–2, –5) (–6, –5) and (–8, –7) SF –2 any centre (iii) Triangle with coords at (1, –1) 2 B1 for 2 correct points or coordinates of (4, –6) and (3, –5) 2 points shown 1 0 (c) 2 B1 for one row or one column correct but not − 2 1 identity matrix. 1 − 2 Or SC1 for 0 1
This question in 0580/42 Oct/Nov 2013
Q20 · S North Scale: 2 cm to 3 km P L In the scale drawing, P is a port, L is a lighthouse and… 0580/41 May/June 2014
5 S North Scale: 2 cm to 3 km P L In the scale drawing, P is a port, L is a lighthouse and S is a ship. The scale is 2 centimetres represents 3 kilometres. (a) Measure the bearing of S from P. Answer(a) … [1] (b) Find the actual distance of S from L. Answer(b) … km [2] (c) The bearing of L from S is 160°. Calculate the bearing of S from L. Answer(c) … [1] (d) Work out the scale of the map in the form 1 : n. Answer(d) 1 : … [2] (e) A boat B is ● equidistant from S and L and ● equidistant from the lines PS and SL. On the diagram, using a straight edge and compasses only, construct the position of B. [5] (f) The lighthouse stands on an island of area 1.5 cm2 on the scale drawing. Work out the actual area of the island. Answer(f) … km2 [2] __________________________________________________________________________________________
13 marks
Mark scheme: 5 (a) [0]44 to [0]48 1 (b) 12.6 to 13.2 2 B1 for 8.4 to 8.8 seen (c) 340 1 (d) 1 : 150 000 2 M1 for × 100 000 soi (e) Arcs for perp bisector of SL 1 Two pairs of correct arcs Ruled perp bisector of SL 1 Within tolerance of overlay Arcs for bisector of angle PSL 1 Marks on PS and SL plus one pair of correct arcs Ruled bisector of angle PSL 1 Within tolerance of overlay B marked within accuracy 1 Within tolerance of overlay Dep on two correct bisectors drawn (f) 3.375 2 M1 for 1.5 × 1.52 or (2/3)2 seen
This question in 0580/41 May/June 2014
Q21 · Y 4 3 A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 (a) On the grid, -5 (i) draw… 0580/41 May/June 2014
7 y 4 3 A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 (a) On the grid, -5 (i) draw the image of shape A after a translation by the vector [2] e-4 o, (ii) draw the image of shape A after a rotation through 90° clockwise about the origin. [2] 2 0 (b) (i) On the grid, draw the image of shape A after the transformation represented by the matrix 0 1 f p. [3] 2 0 (ii) Describe fully the single transformation represented by the matrix 0 1 f p. Answer(b)(ii) … … [3] __________________________________________________________________________________________
10 marks
Mark scheme: − 5 k 7 (a) (i) Image: (–4, –3), (–4, –1), (–3, –1) 2 SC1 for translation or k −4 (ii) Image: (1, –1), (3, –1), (3, –2) 2 SC1 for rotation about the origin but 90º anticlockwise (b) (i) Image: (2, 1), (2, 3), (4, 3) 3 B2 for 2 correct vertices plotted or SC2 for 3 vertices shown in working or SC1 for 2 vertices shown in working or 2 0 1 1 2 M1 × 0 1 1 3 3 (ii) Stretch 1 [factor] 2 1 Invariant line y-axis oe 1 Accept x = 0, stays the same
This question in 0580/41 May/June 2014
Q22 · Y 8 7 6 5 4 3 Q 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8… 0580/42 May/June 2014
4 y 8 7 6 5 4 3 Q 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 (a) Draw the refl ection of shape Q in the line x = –1 . [2] (b) (i) Draw the enlargement of shape Q, centre (0, 0), scale factor –2 . [2] (ii) Find the 2 × 2 matrix that represents an enlargement, centre (0, 0), scale factor –2 . Answer(b)(ii) [2] f p (c) (i) Draw the stretch of shape Q, factor 2, x-axis invariant. [2] (ii) Find the 2 × 2 matrix that represents a stretch, factor 2, x-axis invariant. Answer(c)(ii) [2] f p (iii) Find the inverse of the matrix in part (c)(ii). Answer(c)(iii) [2] f p (iv) Describe fully the single transformation represented by the matrix in part (c)(iii). Answer(c)(iv) … … [3] __________________________________________________________________________________________
15 marks
Mark scheme: 4 (a) Image at (–3, 2), (–5, 2), (–5, 4), (–3, 3) 2 SC1 reflection in y = – 1 or x = k or 4 correct points not joined (b) (i) Image at (–2, –4), (–6, –4), (–6, –8), 2 SC1 other enlargement of scale factor -2, (–2, –6) correct size and correct orientation or 4 correct points not joined − 2 0 k 0 (ii) 2 SC1 for , k may be algebraic or 0 − 2 0 k numeric but not 0 or 1 (c) (i) Image at (1, 4), (3, 4), (3, 8), (1, 6) 2 SC1 for trapezium with vertices at (1, 6) and (3, 8) or correct stretch with y-axis invariant or 4 correct points not joined 1 0 1 0 (ii) 2 SC1 for k may be algebraic or 0 2 0 k 2 0 numeric but not 0 or 1 or for 0 1 1 2 0 (iii) oe isw 2FT FT inverse of their (c)(ii) (algebraic or 2 0 1 numeric) 1 a c or B1FT their (c)(ii) for b d 2 2 0 p 0 1 ie FT their correct fraction or their transposed matrix FT for 2 and 1 mark dependent on det ≠ 0 (iv) Stretch, 3 B1 B1 B1 each independent cao 1 [factor ] , 2 invariant [line] x-axis oe IGCSE – May/June 2014 0580 42 Qu Answers Mark Part Marks
This question in 0580/42 May/June 2014
Q23 · 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 7 8 –1 –2 –3 B –4 –5 –6 –7 –8… 0580/41 Oct/Nov 2014
3 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 7 8 –1 –2 –3 B –4 –5 –6 –7 –8 (a) Draw the image when triangle A is refl ected in the line x = 0. [1] (b) Draw the image when triangle A is rotated through 90° anticlockwise about (–4, 0). [2] (c) (i) Describe fully the single transformation that maps triangle A onto triangle B. Answer(c)(i) … … [3] (ii) Complete the following statement. Area of triangle A : Area of triangle B = … : … [2] (d) Write down the matrix that represents a stretch, factor 4 with the y-axis invariant. Answer(d) [2] f p (e) (i) On the grid, draw the image of triangle A after the transformation represented by the 1 0 matrix . e 2 1 o [3] (ii) Describe fully this single transformation. Answer(e)(ii) … … [3] 1 0 (iii) Find the inverse of the matrix . e 2 1 o Answer(e)(iii) [2] f p __________________________________________________________________________________________
18 marks
Mark scheme: 3 (a) Correct reflection 1 (0, 1) (3, 1) (3, 3) (b) Correct rotation 2 SC1 for rotation of 90º anticlockwise about the wrong (–5, 1) (–7, 1) (–5, 4) centre or 90º clockwise about (–4, 0) or for 3 correct points plotted but not joined (c) (i) Enlargement 3 B1 for each [scale factor] 2 [centre] (–7, 7) (ii) 1 : 4 or 3 : 12 or ¼ : 1 2 M1 for 1 : 22 oe, e.g. (3 × 2)/2 : (6 × 4)/2 or SC1 for 4 : 1 or 12 : 3 or 1 : ¼ 4 0 k 0 (d) 2 B1 for , k may be algebraic or numeric 0 1 0 1 but ≠ 0 or 1 1 0 or SC1 for 0 4 (e) (i) Correct shear drawn 3 B2 for two correct points plotted or if not plotted (0, 1) (–3, –5) (–3, –3) correctly shown in working or 1 0 − 3 1 0 − 3 1 0 0 B1 for or or or 2 1 3 2 1 1 2 1 1 better (ii) Shear 3 B1 for each y-axis or x = 0 invariant [factor] 2 (iii) 1 0 2 B1 for [determinant =] 1 shown or stated oe − 2 1 1 0 or k soi, k ≠ 0 − 2 1 Qu Answers Mark Part Marks
This question in 0580/41 Oct/Nov 2014
Q24 · 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 8 –1 –2 –3 –4 B –5 –6 C –7 –8… 0580/42 Feb/March 2015
7 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 8 –1 –2 –3 –4 B –5 –6 C –7 –8 (a) Describe fully the single transformation that maps (i) flag A onto flag B, Answer(a)(i) … … [3] (ii) flag A onto flag C. Answer(a)(ii) … … [3] 2 (b) Draw the image of flag A after a translation by the vector [2] e 1 o. (c) Draw the image of flag A after a reflection in the line x = 1. [2] 1 0 (d) Describe fully the single transformation represented by the matrix e 0 - 1 o. Answer(d) … … [2] __________________________________________________________________________________________
12 marks
Mark scheme: 7 (a) (i) Rotation 1 [centre] (0, 0) or origin 1 90° [anticlockwise] oe 1 (ii) Enlargement 1 1 [centre] (−2, 1) 1 [s.f.] − 2 2 k (b) vertices at (−3, 4) (−3, 5) (−3, 6) 2 SC1 for translation by or k 1 (−2, 6) (c) vertices at (7, 3) (7, 4) (7, 5) (6, 5) 2 SC1 for reflection in y = 1 or reflection in any vertical line (d) reflection 1 x-axis oe 1
This question in 0580/42 Feb/March 2015
Q25 · Y 7 6 5 4 3 C 2 A 1 x –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 B… 0580/41 May/June 2015
3 y 7 6 5 4 3 C 2 A 1 x –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 B –5 –6 –7 (a) Draw the image of - 1 (i) shape A after a translation by , [2] 3 f p (ii) shape A after a rotation through 180° about the point (0, 0), [2] 1 0 (iii) shape A after the transformation represented by the matrix [3] 0 - 1 f p. (b) Describe fully the single transformation that maps shape A onto shape B. Answer(b) … … [3] (c) Find the matrix which represents the transformation that maps shape A onto shape C. Answer(c) [2] f p
12 marks
Mark scheme: 1 k 3 (a) (i) image at (1, 4) (1, 5) (2, 5) (4, 4) 2 SC1 for translation by or k 3 or 4 correct vertices plotted but not joined (ii) image at (−2, −1 ) (−5, −1) (−2, −2) 2 SC1 for correct size and orientation, wrong (−3, −2) position or 4 correct vertices plotted but not joined (iii) image at (2, −1) (2, −2) (3 ,−2) 3 B2 for 3 correct vertices plotted (5, −1) or if no / wrong plots allow SC2 for 4 correct coordinates in column matrix or shown in working or SC1 for any 3 correct coordinates or 1 0 2 2 3 5 M1 for oe 0 − 1 1 2 2 1 (b) enlargement B1 [centre] (1, 0) B1 not as column vector [scale factor] − 3 B1 (c) 0 − 1 2 B1 for one correct row or column or 0 1 1 0 − 1 0
This question in 0580/41 May/June 2015
Q26 · Y 9 8 7 6 B A 5 4 3 2 1 x 0 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 D –3 C –4 –5 –6… 0580/42 Oct/Nov 2015
7 y 9 8 7 6 B A 5 4 3 2 1 x 0 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 D –3 C –4 –5 –6 –7 (a) Describe fully the single transformation that maps (i) shape A onto shape B, Answer(a)(i) … … [3] (ii) shape A onto shape C, Answer(a)(ii) … … [2] (iii) shape A onto shape D. Answer(a)(iii) … … [3] (b) Find the 2 × 2 matrix that represents the transformation in part (a)(iii). Answer(b) [2] f p 2 (c) On the grid, draw the image of shape A after a translation by the vector . [2] e- 3 o 0 1 (d) Describe fully the single transformation represented by the matrix . e 1 0 o Answer(d) … … [2]
14 marks
Mark scheme: 7 (a) (i) Rotation 1 [+]90 or 90 anticlockwise oe 1 ( 0 , 2 ) 1 Not as column vector (ii) Reflection 1 y = 1 oe 1 (iii) Enlargement 1 1 1 [s f ] −2 oe 1 Origin oe (b) 1 2FT FT their s f from (a)(iii) − 0 2 oe SC1 for k 0 , k ≠ 1 or 0 1 0 − 0 k 2 (c) Image at (4 , 1) (6, 1) (6 , 5) 2 ruled or good freehand (4 , 3) 2 SC1 for translation k k or or for 4 correct vertices not joined −3 (d) Reflection 1 y = x oe 1
This question in 0580/42 Oct/Nov 2015
Q27 · 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 –1 U –2 –3 –4 W –5 –6 (a) On… 0580/43 Oct/Nov 2015
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 –1 U –2 –3 –4 W –5 –6 (a) On the grid, draw the image of - 4 (i) triangle T after a translation by the vector [2] e 4 o, (ii) triangle T after a reflection in the line y = – 1. [2] (b) Describe fully the single transformation that maps triangle T onto triangle U. Answer(b) … … [3] (c) (i) Describe fully the single transformation that maps triangle T onto triangle W. Answer(c)(i) … … [2] (ii) Find the 2 × 2 matrix that represents the transformation in part (c)(i). Answer(c)(ii) [2] f p __________________________________________________________________________________________
11 marks
Mark scheme: 4 k 2 (a) (i) Image at (–2, 5), (1, 5), (1, 7) 2 SC1 for translation or k 4 or 3 correct vertices plotted but not joined (ii) Image at (2, –3), (5, –3), (5, –5) 2 SC1 for a reflection in a horizontal line or in the line x = − 1 or 3 correct vertices plotted but not joined (b) Rotation 1 Alt Enlargement SF –1 (–1, 0) 180 oe 1 (–1, 0) 1 Not as column vector (c) (i) Reflection 1 y = –x oe 1 (ii) 0 − 1 2 SC1 for a correct row or column − 1 0
This question in 0580/43 Oct/Nov 2015
Q28 · Y 8 7 6 Z 5 4 X Y 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 (a) Describe fully the… 0580/42 Feb/March 2016
6 y 8 7 6 Z 5 4 X Y 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 (a) Describe fully the single transformation that maps (i) triangle X onto triangle Y, … … [3] (ii) triangle X onto triangle Z. … … [3] - 5 (b) (i) Draw the image of triangle X after a translation by the vector c 3 m. Label this triangle P. [2] (ii) Draw the reflection of triangle P in the line y = 3. [2] 0 –1 (c) Draw the image of triangle X after the transformation represented by the matrix [3] c 1 0 m.
13 marks
Mark scheme: 6 (a) (i) Rotation 1 90° [anticlockwise] oe 1 ( 4 , 4 ) 1 (ii) Enlargement 1 [centre] ( 5 , 1 ) 1 [scale factor] 2 1 − 5 k (b) (i) Image at (−2, 5) (−2, 7) (−1, 7) 2 B1 for translation by or k 3 (ii) Image at (−2, 1) (−2, −1) (−1, −1) 2FT FT their triangle P reflected in line y = 3 B1 for reflection of triangle P in the line x = 3 or y = k (c) Image at (−2, 3) (−4, 3) (−4, 4) 3 B2 for 2 vertices correct in triangle or 3 correct co-ordinates soi in working or B1 for 1 vertex in triangle correct soi 0 − 1 3 3 4 or M1 for shown 1 0 2 4 4 or statement rotation 90° [ anticlockwise] about (0, 0)
This question in 0580/42 Feb/March 2016
Q29 · Y 6 5 4 3 Q 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 T –3 –4 –5 –6 5 (i)… 0580/41 May/June 2016
2 (a) y 6 5 4 3 Q 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 T –3 –4 –5 –6 5 (i) Draw the image of triangle T after a translation by the vector [2] c- 2m. (ii) Draw the image of triangle T after a reflection in the line y = 1. [2] (iii) Describe fully the single transformation that maps triangle T onto triangle Q. … … [3] 1 2 4 3 1 3 (b) M = N = P = 0 6m c3 4m c1 k m c (i) Work out M + P. [1] f p (ii) Work out PM. [2] f p (iii) M = N Find the value of k. k = … [3] 0 - 1 (c) (i) Describe fully the single transformation represented by the matrix c1 0m. … … [3] (ii) Find the matrix which represents a reflection in the line y = x. [2] f p
18 marks
Mark scheme: 5 k 2 (a) (i) Triangle drawn, 2 SC1 for translation or vertices (2, – 4), (2, – 5), (4, – 4) k − 2 or correct points not joined (ii) Triangle drawn, 2 SC1 for reflection in line y = k vertices (– 3, 4), (– 3, 5), (– 1, 4) or line x = 1 or correct points not joined (iii) Enlargement 1 [factor] 3 1 [centre] (– 6, – 5) 1 2 5 (b) (i) 1 3 10
This question in 0580/41 May/June 2016
Q30 · Y 5 4 3 A 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 On the grid, draw the image… 0580/42 May/June 2016
3 (a) y 5 4 3 A 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 7 –1 –2 –3 –4 –5 –6 On the grid, draw the image of (i) shape A after a reflection in the line x = 1, [2] (ii) shape A after an enlargement with scale factor –2, centre (0, 1), [2] 0 -1 (iii) shape A after the transformation represented by the matrix . [3] c m 1 0 3 0 (b) Describe fully the single transformation represented by the matrix c m. 0 3 … … [3]
10 marks
Mark scheme: 3 (a) (i) Image at (3, 1), (5, 1), (5, 4), (4, 4), 2 SC1 reflection in y = 1 or x = k (4, 2), (3, 2) or 6 correct points not joined (ii) Image at (2, 1), (6, 1), (6, – 5), (4, – 5), 2 SC1 for other enlargement of scale factor –2, (4, – 1), (2, – 1) correct size and correct orientation or 6 correct points but not joined (iii) Image at (– 1, – 1), (– 2, – 1), 3 M2 for 6 correct points shown in working or (– 2, – 2), (– 4, – 2), (– 4, – 3), plotted correctly but not joined (– 1, – 3) or M1 for 0 −1 −1 −1 −2 −2 −3 −3 1 0 1 2 2 4 4 1 or for rotation 90° [anticlockwise] centre (0, 0) stated (b) Enlargement 3 B1 for each [sf] 3 origin oe
This question in 0580/42 May/June 2016
Q31 · Y 8 6 U 4 V 2 x –8 –6 –4 –2 0 2 4 6 8 –2 T –4 –6 (a) (i) Draw the image of triangle T… 0580/43 May/June 2016
6 y 8 6 U 4 V 2 x –8 –6 –4 –2 0 2 4 6 8 –2 T –4 –6 (a) (i) Draw the image of triangle T after a reflection in the line x = 0. [2] (ii) Draw the image of triangle T after a rotation through 90° clockwise about (–2, –1). [2] (iii) Describe fully the single transformation that maps triangle T onto triangle U. … … [2] (iv) Describe fully the single transformation that maps triangle T onto triangle V. … … [3] (b) (i) Find the matrix that represents the transformation in part (a)(i). [2] f p (ii) Describe fully the single transformation represented by the inverse of the matrix in part (b)(i). … … [2]
13 marks
Mark scheme: 6 (a) (i) Correct image (2, –5) (4, –5) (4, –1) 2 SC1 for reflection in y = 0 or 3 correct points not joined (ii) Correct image (–2, 1) (–6, 1) (–6, –1) 2 SC1 for rotation 90 clockwise any centre or 3 correct points not joined 1 (iii) Translation by 2 B1 for each 9 (iv) Enlargement 1 [SF] – ½ oe 1 [Centre] (2, 1) 1 −1 0 (b) (i) 2 B1 for one correct row or column but not the 0 1 identity matrix (ii) Reflection 1 x = 0 oe 1
This question in 0580/43 May/June 2016
Q32 · Y 8 7 6 A 5 4 3 B 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8… 0580/41 Oct/Nov 2016
5 y 8 7 6 A 5 4 3 B 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 - 4 (a) v = c- 8m (i) Draw the image of triangle A after the translation by vector v. [2] (ii) Calculate v . … [2] (b) (i) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (ii) Find the matrix that represents the transformation that maps triangle A onto triangle B. [2] f p (iii) Calculate the determinant of the matrix in part (b)(ii). … [1]
10 marks
Mark scheme: 4 k 5 (a) (i) Image at (–2, – 4), (4, – 4), (4, 0) 2 SC1 for translation or k −8 (ii) 8.94 or 8.944… 2 M1 for ( − 4) 2 + ( − 8) 2 or 4 2 + 8 2 (b) (i) Enlargement 1 [factor] 0.5 oe 1 [centre] (0, 0) oe 1 0.5 0 (ii) oe 2FT FT their scale factor from (b)(i) dep on 0 0.5 enlargement and centre (0, 0) B1FT for one row or column (iii) 1 1FT Strict FT their matrix but not for identity 0.25 or 4 matrix 2 2
This question in 0580/41 Oct/Nov 2016
Q33 · Y 8 B 7 6 5 4 A 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 (a) Draw the image… 0580/43 Oct/Nov 2016
4 y 8 B 7 6 5 4 A 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 (a) Draw the image when triangle A is reflected in the line x = 1. [2] -2 (b) Draw the image when triangle A is translated by the vector [2] c 3 m. (c) Draw the image when triangle A is enlarged by scale factor 2 with centre (4, 5). [2] (d) Describe fully the single transformation that maps triangle A onto triangle B. … … [3]
9 marks
Mark scheme: 4 (a) Triangle drawn at 2 SC1 for correct reflection in x = k or y = 1 (–4, 3), (–1, 3), (–1, 4) −2 k (b) Triangle drawn at 2 SC1 for translation by or (1, 7), (1, 6), (4, 6) k 3 (c) Triangle drawn at 2 M1 for two correct vertices (2, 3), (2, 1), (8, 1) or SC1 for correct enlargement about the wrong centre (d) Rotation 1 90º clockwise oe 1 Accept –90° (7, 4) 1
This question in 0580/43 Oct/Nov 2016
Q34 · 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… 0580/42 Feb/March 2017
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
Mark scheme: 2 (a) (i) Rotation 1 90° [anticlockwise] oe 1 (9, 5) 1 (ii) Translation 1 −8 oe 1 −14 (iii) Enlargement 1 1 [sf] 1 3 (− 8, − 2) 1 (b) (i) Image at (1, − 3) (2, − 3) (2, − 5) 2 M1 for triangle correct size and orientation, wrong position or SC1 for correct reflection in y = –x 0 1 (ii) 2 B1 for 1 correct column or row 1 0
This question in 0580/42 Feb/March 2017
Q35 · 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)… 0580/41 May/June 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
Q36 · 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… 0580/42 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
Q37 · 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)… 0580/43 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
Q38 · - 3 11 (a) A = c1 4 m Find (i) A2, [2] f p (ii) A–1, the inverse of A 0580/41 Oct/Nov 2017
2 - 3 11 (a) A = c1 4 m 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
Q39 · 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… 0580/42 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
Q40 · 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… 0580/43 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
Q41 · 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)… 0580/41 May/June 2018
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
Q42 · 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… 0580/42 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
Q43 · 1 4 8 (a) M = N = 1 2 P = c4 3m ^ h f 1 p (i) For the following calculations, put a tick… 0580/43 May/June 2018
2 1 4 8 (a) M = N = 1 2 P = c4 3m ^ h f 1 p (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
Q44 · 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… 0580/41 Oct/Nov 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
Q45 · Y 7 6 5 4 A B 3 2 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 –3 –4 –5 (a) Describe… 0580/42 Oct/Nov 2018
3 y 7 6 5 4 A B 3 2 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x –1 –2 –3 –4 –5 (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [3] (b) On the grid, draw the image of (i) triangle A after a reflection in the x-axis, [1] 7 (ii) triangle A after a translation by the vector [2] e- 5o, 0.5 0 (iii) triangle A after the transformation represented by the matrix . [3] e 0 0.5o
9 marks
Mark scheme: 3(a) Rotation 3 B1 for each 90[°] clockwise oe Origin oe 3(b)(i) Image at (–4, –1) (–4, –4) (–2, –4) 1 3(b)(ii) Image at (3, –1) (5, –1) (3, –4) 2 7 k B1 for translation by or k − 5 or for 3 correct points not joined 3(b)(iii) Image at (–2, ½) (–2, 2) (–1, 2) 3 B2 for 3 correct co-ordinates soi in working or correct size and orientation in wrong position 0.5 0 −4 −4 −2 or M1 for shown 0 0.5 1 4 4 or for statement: enlargement, sf 0.5, (0, 0)
This question in 0580/42 Oct/Nov 2018
Q46 · 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)… 0580/43 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
Q47 · 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)… 0580/42 Feb/March 2019
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
Q48 · 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… 0580/41 May/June 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
Q49 · 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… 0580/43 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
Q50 · A line joins A (1, 3) to B (5, 8) 0580/42 Oct/Nov 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
Q51 · 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… 0580/43 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
Q52 · 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)… 0580/41 May/June 2020
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
Q53 · 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… 0580/43 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
Q54 · 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… 0580/41 Oct/Nov 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
Q55 · 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… 0580/42 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
Q56 · 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… 0580/43 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
Q57 · 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… 0580/42 Feb/March 2021
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
Q58 · 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… 0580/42 May/June 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
Q59 · 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… 0580/41 Oct/Nov 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
Q60 · 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… 0580/42 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
Q61 · The diagram shows three triangles, T, A, and B, drawn on a 1 cm2 grid 0580/43 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
Q62 · Draw the lines of symmetry of the rectangle 0580/42 May/June 2022
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
Q63 · 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)… 0580/43 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
Q64 · 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… 0580/42 Oct/Nov 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
Q65 · 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… 0580/43 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
Q66 · 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… 0580/42 Feb/March 2023
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
Q67 · 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)… 0580/41 Oct/Nov 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
Q68 · 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)… 0580/42 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
Q69 · 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… 0580/43 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
Q70 · Y 6 4 2 x – 6 – 4 – 2 0 2 4 6 – 2 T – 4 – 6 On the grid, draw the image of (i) triangle T… 0580/41 May/June 2024
2 (a) y 6 4 2 x – 6 – 4 – 2 0 2 4 6 – 2 T – 4 – 6 On the grid, draw the image of (i) triangle T after a reflection in the x-axis [1] - 5 (ii) triangle T after a translation by the vector [2] e- 2o 1 (iii) triangle T after an enlargement by scale factor - with centre - ,1 1 [2] 2 ` j. (b) A shape P is enlarged by scale factor 3 to give shape Q. 2 Shape Q is then enlarged by scale factor to give shape R. 5 The area of shape P is 10 cm2. Calculate the area of shape R. … cm 2 [3]
8 marks
Mark scheme: 2(a)(i) Triangle at (2, 1) (1, 3) (5, 3) 1 2(a)(ii) Triangle at (–4, –5) (–3, –3) 2 5 k B1 for translation by or (0, –5) k 2 2(a)(iii) Triangle at (–2.5, 2) (–4, 3) 2 (–2, 3) 1 B1 for enlargement by sf with any 2 centre 2(b) 14.4 3 2 2 M2 for [10 ×] 32 × oe 5 2 2 or M1 for 32 or soi 5
This question in 0580/41 May/June 2024
Q71 · 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… 0580/41 Oct/Nov 2024
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
Q72 · A is the point (3, 7) and B is the point (-1, 5) 0580/43 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
Q73 · 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… 0580/42 Feb/March 2025
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
Q74 · 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… 0580/42 Oct/Nov 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
Q75 · 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… 0580/43 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
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3 / 93![Question 5: y C 5 B 4 3 2 1 D A x –4 –3 –2 –1 O 1 2 3 4 –1 The pentagon OABCD is shown on the grid above. (a) Write as column vectors (i) , [1] (ii) BC…](https://img.pastlit.com/crops/8f864f26-a345-4525-88eb-53e1a582dfcb/q6.webp)
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11 / 93![Question 10: (a) For Examiner's Use A P Draw the enlargement of triangle P with centre A and scale factor 2. [2] (b) y Q R x 0 (i) Describe fully the si…](https://img.pastlit.com/crops/3a923785-0d64-4881-aea6-23006d8195ff/q8.webp)
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![Question 13: For y Examiner's Use 6 4 P 2 W x –6 –4 –2 0 2 4 6 –2 –4 –6 (a) Draw the reflection of shape P in the line y = x. [2] − 2 (b) Draw the tr…](https://img.pastlit.com/crops/f07ad104-2a6b-49d0-ad7d-955a4a8e93a4/q4.webp)
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22 / 93![Question 18: (a) For Examiner′s y Use 10 9 8 7 6 5 4 3 2 T U 1 x 0 1 2 3 4 5 6 7 8 9 10 (i) Draw the refl ection of triangle T in the line y = 5. [2] (ii…](https://img.pastlit.com/crops/6edfb182-13f4-4c35-a225-c0cdb2339a65/q5.webp)
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41 / 93![Question 31: y 8 6 U 4 V 2 x –8 –6 –4 –2 0 2 4 6 8 –2 T –4 –6 (a) (i) Draw the image of triangle T after a reflection in the line x = 0. [2] (ii) Draw t…](https://img.pastlit.com/crops/43738981-b3f4-4a42-91b3-f87151fea968/q6.webp)
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![Question 33: y 8 B 7 6 5 4 A 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 (a) Draw the image when triangle A is reflected in the line x = 1. [2] …](https://img.pastlit.com/crops/49a97ea4-6968-4402-8883-cdd1c9afca05/q4.webp)
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50 / 93![Question 38: - 3 11 (a) A = c1 4 m Find (i) A2, [2] f p (ii) A–1, the inverse of A. [2] f p - 1 0 (b) Describe fully the single transformation represent…](https://img.pastlit.com/crops/c82e024e-4f88-4bfc-9d37-d77907d26617/q11.webp)
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63 / 93![Question 48: 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 sh…](https://img.pastlit.com/crops/0732adac-11f9-4383-a080-60fb5f249b36/q1.webp)
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65 / 93![Question 50: A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB. ( ........................ , ........................) [2] (ii) Find th…](https://img.pastlit.com/crops/81aa6d77-6dc1-4c2d-8c9f-d820bd22f28e/q3.webp)
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79 / 93![Question 62: (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 – …](https://img.pastlit.com/crops/29ef37e9-dd2c-4fce-91ee-a10d2f60d3a3/q5.webp)
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83 / 93![Question 66: (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 …](https://img.pastlit.com/crops/9d161d62-f49c-47ff-8188-f324767206b1/q4.webp)
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87 / 93![Question 70: (a) y 6 4 2 x – 6 – 4 – 2 0 2 4 6 – 2 T – 4 – 6 On the grid, draw the image of (i) triangle T after a reflection in the x-axis [1] - 5 (ii)…](https://img.pastlit.com/crops/e5ff309b-ed41-4d46-8528-b18db26bf32a/q2.webp)
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