Drawing linear graphs — Paper 3 · IGCSE Mathematics 0580

6 (a) Complete the table below for y = x2 − 2x. For Examiner's x −2 −1 0 1 2 3 4 Use y 8 −1 3 8 [3] (b) On the grid below, draw the graph of y = x2 − 2x for −2 x 4. y 8 7 6 5 4 3 2 y = 2 1 _4 _3 _2 _1 0 1 2 3 4 x _1 _2 [4] (c) The line y = 2 is drawn on the diagram. Use your graph to find the values of x that solve the equation x2 − 2x = 2. Answer(c) x = or x = [2] (d) Complete the table below for y = 4 − x. x −4 0 4 y 8 [2] (e) On the grid above, draw the line y = 4 − x for −4 x 4. [1] (f) Write down the x coordinates of the points of intersection of the graphs of y = x2 − 2x and y = 4 − x. Answer(f) x = or x = [2]

14 marks

Mark scheme: 6 a) 3 0 0 1,1,1 b) 7 correct points plotted P3√ P2√ for 5 or 6 points ± ½ sm. sq. P1√ for 4 points. not strict f.t. smooth curve through all correct points C1 incorrectly plotted points should be ignored for C1. Minimum curved, not pointed c) -0.8 to -0.7 c.a.o. 1 ignore any y values 2.7 to 2.8 c.a.o. 1 IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 3 d) 4 0 1,1 e) correct line drawn through 1 complete line (-4,8) and (4,0) f) -1.7 to -1.4 c.a.o. 1 ignore any y values 2.4 to 2.7 c.a.o. 1 14

This question in 0580/31 Oct/Nov 2004

7 y = 9x – x2. For Examiner's (a) Complete the table of values for this equation. Use x 0 1 2 3 4 5 6 7 8 9 y 8 20 20 8 0 [3] (b) On the grid below, draw the graph of y = 9x – x2 for 0 Y x Y 9. y 22 20 18 16 14 12 10 8 6 4 2 x 0 1 2 3 4 5 6 7 8 9 [4] (c) Write down the values of x and y at the highest point of the curve. For Examiner's Use Answer(c) x = y = [2] (d) (i) On the grid, draw the line y = 6 for 0 Y x Y 9. [1] (ii) Use this line to find the solutions of the equation 9x – x2 = 6. Give your answers correct to one decimal place. Answer(d)(ii) x = or x = [2]

12 marks

Mark scheme: 7 (a) x 0 1 2 3 4 5 6 7 8 9 3 W2 for 4 correct y 0 8 14 18 20 20 18 14 8 0 W1 for 3 correct (b) Their 10 points correctly plotted, within P3ft P2ft for 8 or 9 correct half a square. P1ft for 6 or 7 correct Smooth curve through the 10 correct C1 Shape must be correct and the curve goes above points y = 20. (c) (x =) 4.4 to 4.6 1cao (y =) 20.1 to 20.5 1cao (d) (i) Ruled line y = 6 1 (ii) 8.1 to 8.5 Must be to 1 decimal place 1cao SC1 for both correct but not to 1dp e.g. 8.27 and 0.5 to 0.9 Must be to 1 decimal place 1cao 0.73 IGCSE – May/June 2009 0580, 0581 03

This question in 0580/31 May/June 2009

5 For y Examiner's Use 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 l –3 (a) Find the gradient of the line l. Answer(a) [2] (b) (i) Complete the table below for x + 2y = 6 . x 0 2 y 0 [3] (ii) On the grid, draw the line x + 2y = 6 for −4 Y x Y 6 . [2] (c) The equation of the line l is 4x + 3y = 4. Use your diagram to solve the simultaneous equations 4x + 3y = 4 and x + 2y = 6 . Answer(c) x = y = [2]

9 marks

Mark scheme: − 4 rise 5 (a) oe, –1.2 to –1.4 2 B1 for attempt at 3 run (b) (i) 3, 2, 6 3 B1 for each value (ii) Correct continuous line 2ft Minimum length (0,3) to (6,0) B1 for plotting their 3 points (c) x = −2, y = 4 2ft B1 for their x, B1 for their y from their intersections

This question in 0580/31 Oct/Nov 2011

8 For y Examiner's Use 6 5 4 3 A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 B –4 –5 –6 The diagram shows two shapes A and B. (a) Describe fully the single transformation which maps A onto B. Answer(a) [2] (b) On the grid, draw the line x = 2. [1] (c) On the grid, draw the image of shape A after the following transformations. (i) Reflection in the line x = 2. Label the image C. [1] (ii) Enlargement, scale factor 2, centre (0, 0). Label the image D. [2]

6 marks

Mark scheme:  0  8 (a) Translation   2 B1 for translation B1 for column vector  −6  (b) Correct line drawn 1 Continuous full line. Accept freehand. (c) (i) Correct reflection 1ft Their (b) (ii) Correct enlargement 2 B1 for any other enlargement scale factor 2

This question in 0580/31 Oct/Nov 2011

10 For 4 (a) The table shows some values of y = . Examiner's x Use x –8 –5 –4 –2 –1 1 2 4 5 8 y –1.25 –5 10 2 (i) Complete the table. [2] 10 (ii) On the grid opposite, draw the graph of y = for −8 Y x Y −1 and 1 Y x Y=8 . [4] x (b) (i) On the same grid, draw the straight line through the points (−3, −5) and (1, 3). Extend the line to the edges of the grid. [2] 10 (ii) Find the co-ordinates of the points of intersection of this line with the graph of y = . x Answer(b)(ii) ( , ) and ( , ) [2] (c) For the line in part (b)(i) (i) work out the gradient, Answer(c)(i) [2] (ii) write down the equation in the form y = mx + c . Answer(c)(ii) y = [1] y For Examiner's 10 Use 9 8 7 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 –4 –5 –6 –7 –8 –9 –10

13 marks

Mark scheme: 4 (a) (i) −2, −2.5, −10 2 B1 for 4 or 5 correct 5, 2.5, 1.25 (ii) 10 points correctly plotted 3ft B2ft for 8 or 9 points correctly plotted. B1ft for 6 or 7 points correctly plotted Smooth curve 1 (b) (i) Ruled line through both given points 2 B1 for not ruled but otherwise correct or through just 1 of the points (ii) (−2.5, −4),(2, 5) 2ft B1 for 1 correct. ft their line and their curve. (c) (i) 2 cao 2 M1 for change in y / change in x for 2 correct points (ii) (y =) 2x + 1 1ft Ft (y=) their (c)(i) x + intercept of their line in (b)(i)

This question in 0580/32 May/June 2012

9 (a) Complete the table of values for y = 8 + 3x – x2. For Examiner's Use x –3 –2 –1 0 1 2 3 4 5 6 y –10 8 10 10 –10 [3] (b) On the grid, draw the graph of y = 8 + 3x – x2 for –3 Y x Y 6 . y 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 5 6 –2 –4 –6 –8 –10 [4] (c) Write down the equation of the line of symmetry of the graph. Answer(c) [1] (d) (i) On the grid, draw the graph of y = 6 . [1] (ii) Use your graphs to solve the equation 8 + 3x – x2 = 6 . Answer(d)(ii) x = or x = [2]

11 marks

Mark scheme: 9 (a) y-values –2, 4, 8, 4, –2 3 B2 for 3 or 4 correct B1 for 2 correct (b) 10 correctly plotted points 3ft B2ft for 8 or 9 points B1ft for 6 or 7 points Smooth curve through 10 correct 1 Curve must pass above y = 10 points and correct shape. (c) x = 1.5 oe 1 (d) (i) Line y = 6 drawn 1 (ii) x = 3.5 to 3.7 1ft Ft their curve and their line drawn x = – 0.7 to – 0.5 1ft IGCSE – October/November 2012 0580 31

This question in 0580/31 Oct/Nov 2012

6 Johno travelled from his home on the North Island of New Zealand to Blenheim on the South Island. For He left home at 06 30 and drove 50 km to Wellington where he waited for the 08 20 ferry. Examiner's Use (a) Use information from the travel graph opposite to write down (i) the time Johno arrived at Wellington, Answer(a)(i) [1] (ii) the number of hours and minutes that he waited in Wellington for the 08 20 ferry. Answer(a)(ii) h min [1] (b) The ferry left Wellington at 08 20 and sailed 92 km to Picton on the South Island. The ferry arrived at 11 40. On the travel graph, show the ferry journey. [1] (c) Johno waited 20 minutes to get off the ferry. He then drove for 30 minutes at an average speed of 40 km/h to Blenheim. Complete the travel graph for his journey. [3] (d) Calculate his average speed, in km/h, for the whole journey from his home to Blenheim. Answer(d) km/h [2] (e) Another ferry left Picton at 10 10 and arrived at Wellington at 13 20. (i) On the travel graph, show the journey of this ferry. [2] (ii) How far were the two ferries from Wellington when they passed each other? Answer(e)(ii) km [1] For Examiner's 180 Use 170 160 Distance from home 150 (km) 140 130 120 110 100 90 80 70 60 Wellington 50 40 30 20 10 Home 0 06 00 07 00 08 00 09 00 10 00 11 00 12 00 13 00 14 00 Time

11 marks

Mark scheme: 6 (a) (i) (0)710 1 Accept (0)710 am (ii) 1 (h) 10 (min) 1 (b) Line from (08 20, 50) to 1 (11 40, 142) (c) Correct lines 1ft 1ft for a horizontal line from their (11 40, 142) To (1200, 142) of length two small squares. Then to (12 30, 162) 2ft 2ft is for line from end of their horizontal line 3 small squares across and 10 small squares up. B1 for line from end of their horizontal line 10 small squares up or M1 for 40 × 30 ÷ 60 (implied by 20 kilometres seen) (d) 27 2 M1ft for their total distance ÷ their time in hours SC1 for 36 or 24.9... (e) (i) Line (10 10, their 142) to 2 B1 for one of (10 10, their 142) or (13 20, 50) (13 20, 50) plotted. (ii) 70 to 72 (km) 1ft Ft is their intersection–50, half square accuracy.

This question in 0580/32 Oct/Nov 2012

9 (a) (i) Complete the table of values for y = x2 + x . For Examiner′s Use x –3 –2 –1 0 1 2 3 y 6 0 0 6 [2] (ii) On the grid, draw the graph of y = x2 + x for –3 Ğ x Ğ 3 . y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 [4] (iii) On the grid, draw the line y = 10. [1] (iv) Use both your graphs to solve x2 + x = 10 for –3 Ğ x Ğ 3 . Answer(a)(iv) x = … [1] 2 For (b) Another line, L, has the equation y = 3 x – 5 . Examiner′s Use (i) Write down the gradient of L. Answer(b)(i) … [1] (ii) Write down the equation of a straight line that is parallel to L. Answer(b)(ii) … [1] (c) y 5 K 4 3 2 1 x –2 –1 0 1 2 3 4 –1 –2 –3 –4 –5 –6 –7 Write the equation of the line, K, in the form y = mx + c . Answer(c) y = … [3] _____________________________________________________________________________________

13 marks

Mark scheme: 9 (a) (i) 2 and 2 1 all in the correct places 12 1 (ii) 7 points correctly plotted 3ft P2ft for 5 or 6 points correctly plotted P1ft for 3 or 4 points correctly plotted correct curve through the 7points 1 (iii) correct line 1 Must be ruled and continuous (iv) 2.6 – 2.8 1ft ft their curve and their line (b) (i) 2 1 3 2 (ii) y = x + c 1 c not –5 3 (c) [y =] 2x – 3 3 M2 for y = 2x + p rise or M1 for attempt at gradient i.e. run B1 for y = qx – 3 q≠0

This question in 0580/31 May/June 2013

6 (a) Complete the table of values for y = x2 + 2x – 3 . x –4 –3 –2 –1 0 1 2 3 4 y 0 –3 –4 –3 0 5 21 [2] (b) On the grid, draw the graph of y = x2 + 2x – 3 for –4 Ğ x Ğ 4 . y 25 20 15 10 5 x –4 –3 –2 –1 0 1 2 3 4 –5 [4] (c) On the grid, draw the line y = 10 . [1] (d) Use your graphs to solve the equation x2 + 2x – 3 = 10 for –4 Y x Y 4 . Answer(d) x = … [1] __________________________________________________________________________________________

8 marks

Mark scheme: 6 (a) 5 12 2 B1, B1 (b) 9 points plotted correctly 3FT B2FT for 7 or 8 points correctly plotted B1FT for 5 or 6 points correctly plotted correct smooth curve through all 1 9 correct points (c) correct ruled line 1 minimum length must touch y axis and curve (d) 2.7 to 2.8 1FT FT their curve and ruled line IGCSE – May/June 2014 0580 32

This question in 0580/32 May/June 2014

6 y 6 5 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) On the grid, draw the graphs of (i) y = 5, [1] (ii) x = –3. [1] (b) (i) Write down the co-ordinates of the point of intersection of y = 5 and x = –3. Answer(b)(i) ( … , … ) [1] (ii) Write down the equation of a line parallel to y = 5. Answer(b)(ii) … [1] (c) (i) Complete the table of values for the function y = x2 – 3x . x –2 –1 0 1 2 3 4 5 y 4 0 0 4 [2] (ii) On the grid, draw the graph of y = x2 – 3x for –2 Y x Y 5 . y 11 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 [4] (iii) Write down the co-ordinates of the lowest point of the graph. Answer(c)(iii) ( … , … ) [1] __________________________________________________________________________________________

11 marks

Mark scheme: 6 (a) (i) y = 5 drawn 1 (ii) x = –3 drawn 1 (b) (i) (–3, 5) cao 1 (ii) y = k oe 1 k ≠ 5 (c) (i) 10, –2 –2, 10 2 B1 for 3 correct (ii) 8 correct points plotted 3FT B2 FT for 6 or 7 correctly plotted points or B1 FT for 4 or 5 correctly plotted points correct curve drawn 1 For smooth correct curve, going below y = –2 (iii) (1.5 cao, k ) 1 where –2.5 < k < –2 IGCSE – May/June 2014 0580 33

This question in 0580/33 May/June 2014

6 y 6 4 2 x 0 –5 –4 –3 –2 –1 1 2 –2 –4 –6 –8 –10 (a) On the grid, (i) draw the line y = 3, [1] (ii) draw the line that is perpendicular to the line y = 3 that passes through the point (1, −4). [2] (b) Complete the table of values for y = 2 − 3x − x2. x −5 −4 −3 −2 −1 0 1 2 y −2 2 2 −2 [2] (c) On the grid, draw the graph of y = 2 − 3x − x2 for - 5 G x G 2 . [4] (d) Write down the co-ordinates of the highest point of the graph of y = 2 − 3x − x2. ( … , … ) [1] (e) Use your graphs to solve the equation 2 − 3x − x2 = 3. x = … or x = … [2]

12 marks

Mark scheme: 6 (a) (i) Ruled continuous line y = 3 1 (ii) Ruled continuous line x = 1 2 B1 for (1, –4) plotted or B1 for any line perpendicular to their y = 3 drawn (b) –8, 4, 4, –8 2 B1 for 3 correct (c) Completely correct curve 4 B3FT for 7 or 8 points correctly plotted B2FT for 5 or 6 points correctly plotted B1FT for 3 or 4 points correctly plotted (d) (–1.5, 4.1 to 4.4) 1 (e) –2.5 to –2.7 and –0.3 to –0.5 2FT FT intersection of their (a)(i) with their curve B1FT for one correct

This question in 0580/32 May/June 2016

8 (a) Complete the table of values for y = x 2 - 2x . x - 3 - 2 - 1 0 1 2 3 4 y 3 - 1 3 [3] (b) On the grid, draw the graph of y = x 2 - 2x for - 3 G x G 4 . y 16 14 12 10 8 6 4 2 x 0 –3 –2 –1 1 2 3 4 –2 [4] (c) On the grid, draw the line y = 6 . [1] (d) Use your graph to solve the equation x 2 - 2x = 6 . Give your answers correct to 1 decimal place. x = … or x = … [2] Question 9 is printed on the next page.

10 marks

Mark scheme: 8 (a) 15 8 … 0 … 0 … 8 3 B1 for 8 and 8 in the correct place B1 for 0 and 0 in the correct place B1 for 15 in the correct place (b) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points (c) Correct ruled line 1 (d) –1.8 or –1.7 or –1.6 2FT B1FT for one correct 3.6 or 3.7 or 3.8 or B1FT for both correct answers as co-ordinates or B1FT for both answers correct to more than 1dp

This question in 0580/33 Oct/Nov 2016

127 (a) (i) Complete the table of values for y = . x x –6 –4 –2 –1 1 2 4 6 y –2 –12 12 2 [2] 12 (ii) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 12 10 8 6 4 2 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –2 –4 –6 –8 –10 –12 [4] (iii) On the grid, draw the line y =- 5 . [1] 12 (iv) Use your graph to solve the equation =- 5 . x x = … [1] (b) Line L is drawn on the grid. y 5 4 L 3 2 1 x 0 –4 –3 –2 –1 1 2 3 4 5 –1 (i) Find the gradient of line L. … [2] (ii) Find the equation of line L in the form y = mx + c. y = … [1] (iii) Line M is parallel to line L. Line M passes through the point (0, 3). Write down the equation of line M. y = … [2]

13 marks

Mark scheme: 7(a)(i) –3 –6 6 3 2 B1 for 2 or 3 values correct 7(a)(ii) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 7(a)(iii) Ruled line y = –5 1 7(a)(iv) –2.5 to –2.3 1FT FT intersection of their line with their curve 7(b)(i) –0.5 oe 2 rise M1 for run 7(b)(ii) y = –0.5x + 2 oe 1FT FT their gradient 7(b)(iii) y = –0.5x + 3 oe 2FT B1FT for y = –0.5x + k oe, k ≠ 2 or B1 for y = mx + 3 oe, m ≠ –0.5 or 0

This question in 0580/33 Oct/Nov 2017

66 (a) Complete the table of values for y = , x =Y 0 . x x - 6 - 4 - 3 - 2 - 1 1 2 3 4 6 y - .15 - 3 3 1.5 [3] 6 (b) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 6 5 4 3 2 1 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 1 – 2 – 3 – 4 – 5 – 6 [4] (c) On the grid, draw the line y =- 5 . [1] 6 (d) Use your graph to solve the equation =- 5 . x x = … [1]

9 marks

Mark scheme: 6(a) –1 … –2 … –6 … 6 … 2 … 1 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 6(b) correct smooth curves 4 B3FT for 9 or 10 points plotted correctly B2FT for 7 or 8 points plotted correctly B1FT for 5 or 6 points plotted correctly FT their table 6(c) correct continuous ruled line 1 6(d) –1.2 oe 1 or FT their line and their graph

This question in 0580/33 May/June 2018

8 (a) Complete the table of values for y = 8x - x 2 . x 0 1 2 3 4 5 6 7 8 y 0 12 15 15 12 [3] (b) On the grid, draw the graph of y = 8x - x 2 for 0 G x G 8 . y 18 16 14 12 10 8 6 4 2 0 x 1 2 3 4 5 6 7 8 [4] (c) Write down the equation of the line of symmetry of this graph. … [1] (d) Use the graph to solve 8x - x 2 = 10 . x = … or x = … [2]

10 marks

Mark scheme: 8(a) 7 16 7 0 3 B2 for 2 or 3 correct B1 for 1 correct 8(b) Correct curve 4 B3FT for 8 or 9 points plotted correctly or B2FT for 6 or 7 points plotted correctly or B1FT for 4 or 5 points plotted correctly 8(c) x = 4 1 8(d) 1.45 to 1.65 and 6.35 to 6.55 2 B1 for each or both correct as co-ordinates

This question in 0580/32 Oct/Nov 2018

67 (a) Complete the table of values for y = . x x –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 y –1 –2 –3 –6 6 3 2 1.2 1 [2] 6 (b) On the grid, draw the graph of y = for -6 G x G -1 and 1 G x G 6 . x y 6 5 4 3 2 1 0 x –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 [4] 6 (c) Use your graph to solve the equation = 4. 5 . x x = … [1] (d) (i) On the grid, draw the line y = x. [1] 6 (ii) Write down the co-ordinates of the points of intersection of y = and y = x. x ( … , … ) and ( … , … ) [2]

10 marks

Mark scheme: 7(a) −1.2, −1.5, 1.5 2 B1 for 2 correct 7(b) Correct curve 4 B3FT for 11 or 12 points correctly plotted or B2FT for 9 or 10 points correctly plotted or B1FT for 6, 7 or 8 points correctly plotted 7(c) 1.2 to 1.4 1 FT their (b) 7(d)(i) Correct ruled line 1 7(d)(ii) (−2.6 to −2.3, −2.6 to −2.3,) and 2 FT y = x drawn and their curve (2.3 to 2.6, 2.3 to 2.6) B1FT for one correct, or both x values correct or both y values correct

This question in 0580/33 Oct/Nov 2018

8 (a) Complete the table of values for y = - x 2 + x + 5 . x -3 -2 -1 0 1 2 3 4 y -1 3 3 [3] (b) On the grid, draw the graph of y = - x 2 + x + 5 for - 3 G x G 4 . y 6 5 4 3 2 1 -3 -2 -1 0 1 2 3 4 x -1 -2 -3 -4 -5 -6 -7 -8 [4] (c) Write down the coordinates of the highest point of the graph. ( … , … ) [1] (d) Write down the equation of the line of symmetry of the graph. … [1] (e) (i) On the grid, draw the line y = x for - 3 G x G 4 . [1] (ii) Write down the values of x where the line y = x crosses the curve y =- x 2 + x + 5 . x = … and x = … [2] Question 9 is printed on the next page.

12 marks

Mark scheme: 8(a) −7, 5, 5, −1, −7 3 B2 for 3 or 4 correct B1 for 2 correct 8(b) Correct curve 4 B3FT for 7 or 8 correct plots or B2FT for 5 or 6 correct plots or B1FT for 3 or 4 correct plots. 8(c) (0.5, k) where 5 < k < 6 1 8(d) x = 0.5 oe 1 8(e)(i) y = x ruled from 1 ( −3, −3) to (4, 4) 8(e)(ii) −2.2, 2.2 2 B1 for each accept −2.4 to −2.1 and 2.1 to 2.4

This question in 0580/33 May/June 2020

159 (a) Complete the table of values for y = . x x - 5 - 3 - 2 - 1 1 2 3 5 y - 15 15 [3] 15 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 16 14 12 10 8 6 4 2 0 x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 – 2 – 4 – 6 – 8 – 10 – 12 – 14 – 16 [4] (c) On the grid, draw the line y = 6 . [1] 15 (d) Use your graph to solve = 6 . x x = … [1]

9 marks

Mark scheme: 9(a) −3 −5 −7.5 7.5 5 3 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 9(b) Correct curve 4 B3FT for 7 or 8 points plotted correctly or B2FT for 5 or 6 points plotted correctly or B1FT for 3 or 4 points plotted correctly 9(c) Correct ruled line 1 9(d) 2.5 or 2.4 to 2.6 1 FT their line (y = k) and their curve

This question in 0580/31 Oct/Nov 2020

10 (a) Complete the table of values for y = x 2 - 5x - 2 . x - 2 - 1 0 1 2 3 4 5 6 y 4 - 2 - 8 - 8 - 2 4 [2] (b) On the grid, draw the graph of y = x 2 - 5x - 2 for - 2 G x G 6 . y 14 12 10 8 6 4 2 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 – 6 – 8 – 10 [4] (c) On the grid, draw the line y = 2 . [1] (d) Use your graph to solve the equation x 2 - 5 x - 2 = 2 . x = … or x = … [2]

9 marks

Mark scheme: 10(a) 12 −6 −6 2 B1 for 1 or 2 correct 10(b) Correct curve 4 B3FT for 8 or 9 points correctly plotted or B2FT for 6 or 7 points correctly plotted or B1FT for 4 or 5 points correctly plotted 10(c) Ruled line y = 2 drawn 1 10(d) −0.9 to −0.5 2 FT y = 2 and their curve B1 for each 5.5 to 5.9

This question in 0580/32 Oct/Nov 2021

129 (a) Complete the table of values for y = , x ! 0 . x x -6 -4 -3 -2 -1 1 2 3 4 6 y -3 -6 6 3 [3] 12 (b) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 12 10 8 6 4 2 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 – 6 – 8 – 10 – 12 [4] (c) On the grid, draw the line y = 5 . [1] 12 (d) Use your graph to solve the equation = 5 . x x = … [1]

9 marks

Mark scheme: 9(a) −2 … −4 … −12 12 … 4 … 2 3 B2 for 4 or 5 correct B1 for 2 or 3 correct 9(b) Correct curve 4 B3FT for 9 or 10 points plotted correctly B2FT for 7 or 8 points plotted correctly B1FT for 5 or 6 points plotted correctly 9(c) Correct ruled line drawn 1 9(d) 2.4 1 FT their graph and y = 5

This question in 0580/31 May/June 2022

- 62 (a) (i) Complete the table of values for y = . x x -6 -4 -3 -2 -1.5 -1 1 1.5 2 3 5 6 y 1 2 3 6 -6 -3 -2 -1 [3] - 6 (ii) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 6 5 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 – 5 – 6 [4] (iii) Write down the order of rotational symmetry of the graph. … [1] (iv) Write down the equation of each line of symmetry of the graph. … and … [2] (v) On the grid, draw the line y = 2.5 . [1] - 6 (vi) Use your graph to solve the equation = 2 .5 . x x = … [1] (b) L P Draw a line that passes through the point P and is perpendicular to line L. [1] (c) Find the equation of the straight line that • is parallel to the line y = 3x + 5 and • passes through the point (1, 7). Give your answer in the form y = mx + c . y = … [2]

15 marks

Mark scheme: 2(a)(i) 1.5 4 –4 –1.2 3 B2 for 3 correct or B1 for 1 or 2 correct 2(a)(ii) Correct graph drawn 4 B3FT for 12 or 11 correct plots B2FT for 10 or 9 correct plots B1FT for 8,7 or 6 correct plots 2(a)(iii) 2 1 2(a)(iv) y  x oe y  x oe 2 B1 for each 2(a)(v) Correct ruled line 1 2(a)(vi) 2.4 1 FT their graph and y  2.5 2(b) Correct ruled line 1 2(c)  y  3 x  4 cao 2 B1 for final answer  y   3 x  k , k  5 or  y   jx  4 , j ≠ 0

This question in 0580/32 May/June 2022

6 y 10 L 9 8 7 6 5 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 x – 1 – 2 – 3 – 4 (a) Find the equation of line L in the form y = mx + c. y = … [2] (b) Write down the coordinates of the point where line L crosses the x-axis. ( … , … ) [1] (c) (i) Complete the table of values for y = x 2 + 5x + 3 . x −6 −5 −4 −3 −2 −1 0 1 y 9 −1 −1 [3] (ii) On the grid, draw the graph of y = x 2 + 5x + 3 for -6 G x G 1. [4] (d) (i) On the grid, draw the line y = 6 . [1] (ii) Use your graphs to solve the equation x 2 + 5x + 3 = 6 . x = … or x = … [2]

13 marks

Mark scheme: 6(a)  y = 2 x + 7 2 B1 for 2 x + c, c  7 or B1 for mx + 7 where m is their gradient and m  2 6(b) ( −3.5, 0 ) 1 6(c)(i) 3, −3, −,3 3, 9 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 6(c)(ii) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 6(d)(i) Correct ruled line drawn 1 6(d)(ii) 0.4 to 0.7, −5.7 to −5.4 2 FT their graph and their line B1FT for each

This question in 0580/32 Feb/March 2023

7 (a) y 6 L 5 4 3 2 1 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 – 4 – 5 – 6 (i) Find the equation of line L. Give your answer in the form y = mx + c . y = … [2] (ii) On the grid, draw the line y = 1. [1] (iii) Write down the coordinates of the point where the two lines intersect. ( … , … ) [1] (b) (i) Complete the table of values for y = x 2 + x - 8 . x - 4 - 3 - 2 - 1 0 1 2 3 4 y 4 - 2 - 8 - 8 - 2 4 [2] (ii) On the grid, draw the graph of y = x 2 + x - 8 for - 4 G x G 4 . y 12 10 8 6 4 2 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 2 – 4 – 6 – 8 – 10 [4] (iii) Write down the equation of the line of symmetry of the graph. … [1] (iv) Use your graph to solve the equation x 2 + x - 8 = 0 . x = … or x = … [2]

13 marks

Mark scheme: 7(a)(i) [y =] 1.5x – 2 final answer 2 B1 for 1.5x + c as final answer or B1 for mx − 2, m ≠ 0, as final answer 7(a)(ii) Correct ruled line 1 7(a)(iii) (2, 1) 1 FT their (a)(ii) 7(b)(i) −6 −6 12 2 B1 for one or two correct 7(b)(ii) Correct and accurate curve 4 B3FT for 8 or 9 points accurately plotted or B2FT for 6 or 7 points accurately plotted or B1FT for 4 or 5 points accurately plotted 7(b)(iii) x = −12 oe 1 7(b)(iv) −3.5 to −3.3 2.3 to 2.5 2 B1FT for each

This question in 0580/32 May/June 2023

8 y L 6 5 4 3 2 1 x - 3 - 2 - 1 0 1 2 3 4 5 6 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 (a) Find the equation of line L in the form y = mx + c . y = … [2] (b) (i) On the grid, draw the line y = x . [1] (ii) Write down the coordinates of the point where the line y = x intersects line L. ( … , … ) [1] 8(c) (i) Complete the table of values for y = . x x −5 −4 −3 −2 −1 1 2 3 4 5 y −1.6 −2.7 2.7 1.6 [3] 8 (ii) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 8 7 6 5 4 3 2 1 x - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 [4]

11 marks

Mark scheme: 8(a) [y =] 2x − 5 final answer 2 B1 for answer of 2x + c or mx – 5 (m ≠ 0) 8(b)(i) Correct ruled line 1 8(b)(ii) (5, 5) 1 FT their ruled y = x 8(c)(i) −2 −4 −8 8 4 2 3 B2 for 3, 4 or 5 correct or B1 for 1 or 2 correct 8(c)(ii) Correct curve 4 B3FT for 9 or 10 points correctly plotted or B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted

This question in 0580/31 Oct/Nov 2023

15 A B C y y y 3 3 x xx xx NOT TO SCALE D E F y y y 3 x 3 xx 3 x 3 Write down the letter of the graph that shows these lines. (a) x = 3 … [1] (b) y = 3 x … [1]

2 marks

Mark scheme: 15(a) E 1 15(b) B 1

This question in 0580/31 May/June 2025

15 The equation of a line is y =- 5x + 7 . (a) Write down the gradient of this line. … [1] (b) Find the coordinates of the point where this line crosses the y-axis. ( … , … ) [1]

2 marks

Mark scheme: 15(a) −5 1 15(b) 0 , 7 1

This question in 0580/32 May/June 2025

4 y 4 P 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 – 4 (a) Write down the coordinates of point P. ( … , … ) [1] (b) On the grid, draw the line y = x . [1] (c) On the grid, draw the line that goes through point P and is perpendicular to the line y = x . [1]

3 marks

Mark scheme: 4(a) –2, 3 1 4(b) correct ruled line y = x 1 4(c) correct ruled line y =−+x 1 1 FT their straight y = x

This question in 0580/32 Oct/Nov 2025