Rates — Paper 3 · IGCSE Mathematics 0580

1 (a) Two friends, Hatab and Yasin, went on a cycle ride. For Part of the distance-time graph for their journey is shown below. Examiner's Use 18 16 14 12 Distance 10 from home Yasin (km) 8 Hatab 6 Hatab and Yasin 4 2 0 10 00 11 00 12 00 13 00 14 00 15 00 Time of day For the first part of the journey they cycled at the same speed. (i) Find their speed for the first part of the journey. Answer(a)(i) km/h [1] (ii) At 11 00 they stopped for half an hour. Show this on the graph. [1] (iii) They continued on their ride and at 12 45 they were 16 kilometres from home. Show this part of the journey on the graph. [1] (iv) They stopped again and then had a race going home. (a) For how long did they stop? Answer(a)(iv)(a) min [1] (b) Who won the race? Answer(a)(iv)(b) [1] (v) What was the total length of their journey? Answer(a)(v) km [1] (b) On a certain day the conversion rate between dollars ($) and Indian rupees was For Examiner's $1 = 45 rupees. Use (i) How many rupees were equivalent to $10? Answer(b)(i) rupees [1] (ii) Use this information to draw a conversion graph on the axes below. 500 400 300 Rupees 200 100 0 1 2 3 4 5 6 7 8 9 10 11 Dollars ($) [2] (iii) Use your graph to find (a) how many rupees were equivalent to $6.80, Answer(b)(iii)(a) rupees [1] (b) how many dollars were equivalent to 480 rupees. Answer(b)(iii)(b) $ [1]

11 marks

Mark scheme: number Marks Total 1 a) i) 10 1 ii) straight line from 1 (11,10) to (11 30,10) iii) straight line from 1√ allow +2 mm in length by (11 30,10) to (12 45,16) eye but must go through the correct points. f.t. from their (1130,10) iv) a) 15 1 allow ¼ hour b) Hatab 1 v) 32 1 b) i) 450 1 ii) straight line ruled from 2 SC1 for freehand or (1,45) to (10,450) broken line or any straight line through the origin ± ½ small square at both points iii) a) 306 ± 4 1 b) 10 60 to 10.80 1 allow 10.6 etc. 11

This question in 0580/31 Oct/Nov 2004

3 (a) Kinetic energy, E, is related to mass, m, and velocity, v, by the formula For Examiner's 1 Use E = mv2. 2 (i) Calculate E when m = 5 and v = 12. Answer(a)(i) E= [2] (ii) Calculate v when m = 8 and E = 225. Answer(a)(ii) v = [2] (iii) Make m the subject of the formula. Answer(a)(iii) m = [2] (b) Factorise completely xy2 – x2y. Answer(b) [2] (c) Solve the equation 3(x – 5) + 2(14 – 3x) = 7. Answer(c) x = [3] (d) Solve the simultaneous equations 4x + y = 13, 2x + 3y = 9. Answer(d) x = y = [3]

14 marks

Mark scheme: 1 3 (a) (i) 360 B2 M1 for × 5 × 122oe 2 (ii) 7.5oe B2 M1 for 225 /4 oe (implied by 56.25) 2 E 1 2 1 (iii) or E v B2 B1 for 2E or E or division by v2 2 v 2 2 (b) xy( y – x) final answer B2 B1 for x(y2 – xy) or y(xy – x2) SC1 for xy(y + x) (c) 3x – 15 + 28 – 6x (= 7) MA1 13 – 3x (= 7) M1ft Independent ax + b (=7) from their expansion x= 2 A1cao www 3 (d) Equating coefficients of x or y, or M1 equivalent method. or a correctly substituted substitution. E.g. 5y = 5 oe or 10x = 30 oe A1 y = 13 – 4x ⇒ 2x + 3(13 – 4x) = 9 x = 3, y = 1 A1 www 3 [14]

This question in 0580/31 May/June 2007

5 Aminata and her brother live 18 kilometres from a shopping centre. For (a) Aminata leaves home at 09 00 and runs 3 kilometres to a bus stop. Examiner'sUse She arrives there at 09 30. Write down her average speed, in kilometres per hour. Answer(a) km / h [1] (b) She waits 15 minutes for the bus. The bus travels the remaining 15 kilometres to the shopping centre at an average speed of 20 km / h. (i) At what time does she arrive at the shopping centre? Answer(b)(i) [2] (ii) On the grid below, complete the travel graph showing her journey to the shopping centre. 20 Shopping Centre 18 16 14 12 Distance 10 from home (km) 8 6 4 2 Home 0 09 00 10 00 11 00 12 00 13 00 Time [2] (c) Her brother leaves home at 11 15. For He travels to the shopping centre by car at an average speed of 54 km / h. Examiner's Use (i) Work out how long, in minutes, he takes to travel to the shopping centre. Answer(c)(i) minutes [1] (ii) Show his journey on the grid. [1] (d) Aminata and her brother leave the shopping centre at 12 00. They travel home by car and arrive at 12 45. (i) Show their journey home on the grid. [1] (ii) Calculate the average speed of their journey home. Answer(d)(ii) km / h [2]

10 marks

Mark scheme: 5 (a) 6 W1 (b) (i) 10 30 W2 M1 for 1520 SC1 for 10 15 (ii) Line from 09 30 to 0945 W1 accuracy ± 1mm Line to (‘10 30’, 18) W1ft (c) (i) 20 W1 (ii) Line (11 15, 0) to W1ft ft their time in (c)(i) provided in minutes and Y 45 ( their 11 35, 18) Line (11 15, 0) to (11 [15 + ‘20’], 18) (d) (i) Line (12 00,18) to (12 45,0) W1 (ii) 24 W2 M1 for 18 ÷ 0.75 Allow 18 ÷ 45 × 60 for method

This question in 0580/31 Oct/Nov 2008

5 A shopkeeper buys cheese for $3.75 per kilogram and sells it for $5.10 per kilogram. For Examiner's (a) Calculate his percentage profit. Use Answer(a) % [3] (b) Mrs Garcia buys cheese from the shopkeeper. Calculate the number of grams of cheese she can buy for $2.04 . Answer(b) g [2] (c) The shopkeeper sells 7 kg of cheese and has 3 kg left. (i) He reduces his selling price of $5.10 per kilogram by 70%. Calculate the reduced price. Answer(c)(i) $ [2] (ii) He sells the 3kg of cheese at the reduced price. Calculate the total amount of money he receives by selling all the cheese. Answer(c)(ii) $ [2]

9 marks

Mark scheme: 1.5 − .375 5 (a) 36 (%) 3 M2 for × 100 .375 1.5 M1 for or 136% or 1.36 or .375 5.1 – 3.75 implied by 1.35 (b) 400 2 M1 for 2.04 ÷ 5.1 implied by figs 4 (c) (i) 1.53 2 M1 for (1 – 0.7) × 5.1 oe or 5.10 – (5.10 × 0.70) (ii) 40.29 cao 2 M1 for 7 × 5.1 + 3 × their (c)(i) or 35.7 + (3 × their (c)(i) evaluated)

This question in 0580/31 Oct/Nov 2010

11 Roberto earns a total of $p per week. For He works for t hours each week and is paid a fixed amount per hour. Examiner's He also receives a bonus of $k every week. Use The formula for p is p = 8t + k. (a) Write down how much Roberto is paid per hour. Answer(a) $ [1] (b) (i) Find how much Roberto earns in a week when he works for 40 hours and his bonus is $35. Answer(b)(i) $ [2] (ii) Find how many hours Roberto works in a week when he earns $288 and his bonus is $24. Answer(b)(ii) h [3] (c) Make t the subject of the formula. Answer(c) t = [2]

8 marks

Mark scheme: 11 (a) 8 1 (b) (i) 355 2 M1 for 8 × 40 + 35 seen or better ( 288 − 24) (ii) 33 3 M2 for 8 or B1 for 264 seen p − k (c) t = 2 B1 mark for a correct step 8

This question in 0580/31 Oct/Nov 2010

6 (a) The formula for finding the interior angle of a regular polygon with n sides is given below. For Examiner's 180( n − 2) Use Interior angle = n (i) Find the size of the interior angle of a regular polygon with 9 sides. Answer(a)(i) [2] (ii) Multiply out the brackets. 180(n – 2) Answer(a)(ii) [1] (iii) A regular polygon has an interior angle of 156°. How many sides does this polygon have? Answer(a)(iii) [3] (b) Solve the simultaneous equations. 3x + 5y = 9 x + 2y = 4 Answer(b) x = y = [3]

9 marks

Mark scheme: 6 (a) (i) 140 2 M1 for 180 × (9 – 2) ÷ 9 or better (ii) 180n – 360 1 (iii) 15 3 M2 for 360 ÷ (180 – 156) or M1 for 156n = their (a)(ii) and M1dep for pn = q from their linear expression (b) (x =) –2, (y =) 3 3 M1 for equating coefficients of x or y and adding or subtracting, allow 1 error A1 for 1 correct

This question in 0580/32 Oct/Nov 2010

2 Eduardo lives in Argentina and travels to Uruguay for a holiday. For Examiner's (a) His flight from Buenos Aires to Montevideo takes 55 minutes. Use The plane departs at 17 35. (i) Write down the arrival time. Answer(a)(i) [1] (ii) The distance between Buenos Aires and Montevideo is 230 km. Calculate the average speed of the plane. Answer(a)(ii) km/h [3] (b) At the airport, Eduardo changed some Argentine pesos (ARS). He received 9121 Uruguay pesos (UYU). (i) The exchange rate was ARS 1 = UYU 6.515. Calculate how many Argentine pesos Eduardo changed. Answer(b)(i) ARS [2] (ii) Eduardo spent 1890 Uruguay pesos on meals. Calculate this as a percentage of the UYU 9121. Answer(b)(ii) % [1] (iii) At the end of his holiday, Eduardo has UYU 610 remaining. He changes this into Argentine pesos when the exchange rate is UYU 1 = ARS 0.149. Calculate how much Eduardo receives in Argentine pesos. Give your answer to the nearest whole number. Answer(b)(iii) ARS [2]

9 marks

Mark scheme: 2 (a) (i) 18 30 oe 1 (ii) 251 (250.9…) 3 M1 for distance ÷ time (any units) and M1 for 55 ÷ 60 oe (b) (i) 1400 2 M1 for 9121 ÷ 6.515 (ii) 20.7(2…) 1 (iii) 91 2 B1 for 90.89 or 90.9 or 90.8 or 610 × 0.149 or B1 (indep) for correct rounding to integer if from a decimal −5 

This question in 0580/33 Oct/Nov 2010

4 (a) An electrician is paid a fixed amount of $12 and then $6.50 for each hour she works. For Examiner's (i) The electrician works for 7 hours. Use Calculate how much she is paid for this work. Answer(a)(i) $ [2] (ii) The electrician works for n hours. Write down an expression, in terms of n, for how much she is paid. Answer(a)(ii) [1] (iii) The electrician is paid $44.50 for her work. Calculate the number of hours she worked. Answer(a)(iii) [2] (b) Solve the simultaneous equations. 3x O y = 22 5x + 3y = 4 Answer(b) x = y = [3]

8 marks

Mark scheme: 4 (a) (i) ($)57.5(0) 2 M1 for 12 + 6.5 × 7 (ii) 12 + 6.5(0) n oe 1 (iii) 5 2ft M1 for (44.5(0) − their 12) ÷ their 6.5 soi (b) (x =) 5, (y =) −7 3 ww both correct B3 ww one correct B0 M1 for consistent multiplication and add/subtract or by substitution M1 for 5x + 3(3x − 22) = 4 oe A1 for 1 correct answer

This question in 0580/32 May/June 2011

2 The distance between Geneva and Gstaad is 150 km. For Examiner's (a) Write 150 in standard form. Use Answer(a) [1] 1 (b) A car took 1 hours to travel from Geneva to Gstaad. 2 Calculate the average speed of the car. Answer(b) km/h [1] (c) A bus left Gstaad at 10 15. It arrived in Geneva at 12 30. Calculate the time, in hours and minutes, that the bus took for the journey. Answer(c) h min [1] (d) Another bus left Geneva at 13 55. It travelled at an average speed of 60 km/h. Find the time it arrived in Gstaad. Answer(d) [2] (e) The distance of 150 km is correct to the nearest 10 km. Complete the statement for the distance, d km, from Geneva to Gstaad. Answer(e) Y d I [2]

7 marks

Mark scheme: 2 (a) 1.5(0) × 102 cao 1 (b) 100 cao 1 (c) 2 hours 15 minutes cao 1 (d) 16(:) 25 (pm) or (0)425 pm 2 M1 for 2.5 (oe), 2hrs 30 min (e) 145 ≤ d < 155 2 B1 for each value in correct place

This question in 0580/31 Oct/Nov 2011

5 (a) An aeroplane takes off 140 metres before reaching the end of the runway. For It climbs at an angle of 22° to the horizontal ground. Examiner's Use NOT TO SCALE h 22° 140 m Calculate the height of the aeroplane, h, when it is vertically above the end of the runway. Answer(a) h = m [2] (b) After 3 hours 30 minutes the aeroplane has travelled 1850 km. Calculate the average speed of the aeroplane. Answer(b) km/h [2] (c) A B NOT TO SCALE 15 km C The aeroplane descends from A, at a height of 12 000 metres, to C, at a height of 8 300 metres. (i) Work out the vertical distance, BC, that the aeroplane descends. Answer(c)(i) m [1] (ii) The distance AC is 15 kilometres. Calculate angle BAC. Answer(c)(ii) Angle BAC = [2]

7 marks

Mark scheme: h 5 (a) 56.6 or 56.56… 2 M1 for tan 22 =140 or better 140 or M1 for tan(90–22) = or better h (1850) (b) 529 (km/h) or 528.6 or 528.57… 2 M1 for or better. 5.3 (c) (i) 3700(m) 1 their (c)(i) (ii) 14.3 or 14.2(8…) 2ft M1 for sin (BAC) = 15000 IGCSE – October/November 2011 0580 32

This question in 0580/32 Oct/Nov 2011

3 For Park 600 Examiner's Use 550 500 450 400 350 Distance from Bruce’s home 300 (metres) 250 200 Jason’s home 150 100 50 Bruce’s home 0 09 00 09 10 09 20 09 30 09 40 09 50 10 00 10 10 Time One morning, Bruce walked from his home to Jason’s home and the two boys walked to the park. The distance-time graph shows Bruce’s journey. (a) How many minutes was Bruce at Jason’s home? Answer(a) min [1] (b) How far from the park were Bruce and Jason at 09 20? Answer(b) m [2] (c) Work out the speed at which Bruce and Jason walked to the park. Give your answer in km/h. Answer(c) km/h [3] (d) Bruce stayed at the park for 35 minutes. He then walked home at a speed of 60 metres per minute. Complete the graph to show Bruce’s time at the park and his journey home. [3]

9 marks

Mark scheme: 3 (a) 5 1 (b) 150 2 B1 for 450 seen or implied .045 (c) 1.8 3 M2 for oe .025 (M1 for correct distance ÷ correct time) (d) Straight line (09 25, 600) to 1 (10 00, 600) Straight line (10 00, 600 to 10 10, 0) ft 2ft M1 for 600 ÷ 60 oe ft their graph 10 mins to time axis IGCSE – October/November 2011 0580 33

This question in 0580/33 Oct/Nov 2011

9 For P Examiner's Use 5 cm NOT TO SCALE Q 12 cm R 25 cm The diagram shows a solid triangular prism of length 25 cm. The cross-section of the prism is triangle PQR. PQ = 5 cm, QR = 12 cm and angle PQR = 90°. (a) (i) Calculate the volume of the prism. Answer(a)(i) cm3 [3] (ii) The prism is made from wood. The mass of 1 cm3 of the wood is 0.96 g. Calculate the mass of the prism. Give your answer in kilograms. Answer(a)(ii) kg [2] (b) (i) Show that PR = 13 cm. For Examiner's Answer(b)(i) Use [2] (ii) The prism is completely covered with plastic at a cost of $0.08 per square centimetre. By finding the total area of the two triangles and the three rectangles, calculate the total cost of the plastic used. Answer(b)(ii) $ [4]

11 marks

Mark scheme: 9 (a) (i) 750 3 M2 for 0.5 × 12 × 5 × 25 seen or implied (M1 for 0.5 × 12 × 5 or M1 for their area of cross-section × 25) (ii) 0.72 2ft ft their (i) × 0.00096 SC1 for 720 (or ft their (i) × 0.96) (b) (i) 52 + 122 M1 169 M1 1 (ii) 64.8(0) www4 4 M2 for 2 × × 12 × 5 + 25 × 13 + 25 × 12 + 25 × 5 2 (M1 for any three correct) M1 for their area × 0.08

This question in 0580/33 Oct/Nov 2011

10 (a) Tatiana goes for a walk. For Examiner's (i) She walks for 15 minutes at a speed of 80 metres per minute. Use Calculate the distance she walks. Answer(a)(i) m [1] (ii) She then walks for a further p minutes at w metres per minute. Write down an expression, in terms of p and w, for the total distance Tatiana walks. Answer(a)(ii) m [1] (iii) Write down an expression, in terms of p and w, for Tatiana’s average speed, in metres per minute. Answer(a)(iii) m/min [2] (b) The volume, V, of a solid is given by the following formula. For Examiner's Use V = 3b(t + 12 m) (i) Find V when b = 4, t = 5 and m = 6 . Answer(b)(i) V = [2] (ii) Find b when t =3, m = 2 and V = 84. Answer(b)(ii) b = [3] Question 11 is printed on the next page.

9 marks

Mark scheme: 10 (a) (i) 1200 1 (ii) 1200 + pw 1ft ft their (i) + pw 1200 + pw (iii) 2ft ft their (ii)/(15 + p) 15 + p M1 for ÷ (15 + p) 1 (b) (i) 96 2 M1 for 3 (4)(5 + ×6) or better 2 1 (ii) 7 3 M1 for 84 = 3b(3 + ×2) or better 2 A1 for equation 12b = 84 oe correct kb = l IGCSE – October/November 2011 0580 33

This question in 0580/33 Oct/Nov 2011

6 James and Wei have a car. For Each year James drives 3 600 km and Wei drives 4 800 km. Examiner's Use (a) Write 3 600 : 4 800 as a ratio in its simplest form. Answer(a) : [1] (b) A garage charges $420 to service the car. James and Wei share the $420 in the ratio James : Wei = 2 : 3 . Find the amount that James pays. Answer(b) $ [2] (c) On a 268 km journey the car uses 22.8 litres of fuel. By writing these numbers to 1 significant figure, estimate the distance travelled using one litre of fuel. Show all your working. Answer(c) km [2] (d) On another journey the car uses 46.3 litres of fuel. Fuel costs $1.48 per litre. Work out the cost of the fuel for this journey. Answer(d) $ [2] (e) The table shows some information about the car. For Examiner's Use Fuel tank capacity 64 litres (to the nearest litre) Width 1810 mm (to 3 significant figures) (i) Write down the upper bound of the fuel tank capacity. Answer(e)(i) litres [1] (ii) Write down the minimum width of the car. Answer(e)(ii) mm [1]

9 marks

Mark scheme: 6 (a) 3 : 4 cao 1 (b) 168 2 M1 420 ÷ (2 + 3) or 84 seen (c) 300 ÷ 20 = 15 2 250 / 260 / 270 / 300 if 0 scored SC1 for 20 / 23 / 25 or 15 ww (d) 68.5(2) 2 M1 for 46.3 × 1.48, 68.53 or 68.524 (e) (i) 64.5 1 (ii) 1805 1

This question in 0580/33 May/June 2012

2 (a) Luka earns $475 each week. For Examiner's Use (i) He works for 38 hours each week. How much does he earn for each hour he works? Answer(a)(i) $ [1] (ii) Luka pays $175 in rent each week. Write the amount he pays in rent as a fraction of his weekly earnings. Give your answer in its lowest terms. Answer(a)(ii) [2] 7 (iii) He spends of his weekly earnings on bills. 20 How much money does he have left after paying rent and bills? Answer(a)(iii) $ [2] (b) Luka’s weekly earnings of $475 are increased by 6%. Calculate his new weekly earnings. Answer(b) $ [2] (c) Luka has saved $350. He invests this for 2 years at a rate of 4% per year compound interest. How much interest does he receive after 2 years? Answer(c) $ [3]

10 marks

Mark scheme: 2 (a) (i) 12.5(0) 1 7 175 (ii) 2 B1 for oe seen 19 475 7 (iii) 133.75 2 M1 for × 475 20 (b) 503.5(0) 2 M1 for 106 ÷ 100 × 475 Or 475 + (6 ÷ 100 × 475) (c) 28.56 3 M1 for 350 × 1.042 oe dep M1 for ‘their 378.56’ – 350 Or M1 for (350 × 0.04) (imp by 14) and (350 + ‘their 14’) × 0.04 (imp by 14.56) dep M1 ‘their 14’ + ‘their 14.56’ IGCSE – October/November 2012 0580 31

This question in 0580/31 Oct/Nov 2012

7 (a) The cost, $C, of hiring a meeting room for n people is calculated using the formula For Examiner's Use C = 80 + 5n. (i) Calculate C when n = 12. Answer(a)(i) [2] (ii) Maria pays $230 to hire the meeting room. Work out the number of people at the meeting. Answer(a)(ii) [2] (iii) Make n the subject of the formula C = 80 + 5n. Answer(a)(iii) n = [2] (b) Expand and simplify 2(3x + 4) – 3(2 – x) . Answer(b) [2] (c) Solve the simultaneous equations. 3x + y = 13 2x + 3y = 18 Answer(c) x = y = [3]

11 marks

Mark scheme: 7 (a) (i) 140 2 M1 for 80 + 5 × 12 or better (ii) 30 2 M1 for (230 – 80) ÷ 5 or 150 seen C − 80 C 80 −C (iii) or − 16 or 2 M1 for C – 80 = 5n 5 5 − 5 C 80 5n final answer Or M1 for = + or better 5 5 5 (b) 9x + 2 final answer 2 M1 for 9x + k or mx + 2 or 6x + 8 or – 6 + 3x or 9x + 2 spoilt (c) x = 3, y = 4 3 M1 for correct method to eliminate one variable A1 x = 3 A1 y = 4

This question in 0580/31 Oct/Nov 2012

8 (a) A water tank in the shape of a cuboid measures 55 cm by 40 cm by 75 cm. For Examiner's Use (i) Find the volume of the tank. Answer(a)(i) cm3 [2] (ii) Write down the volume of the tank in litres. Answer(a)(ii) litres [1] (b) Another water tank contains 260 litres. (i) The tank is emptied at a rate of 25 litres per minute. Work out the time taken to completely empty the tank. Give your answer in minutes and seconds. Answer(b)(i) minutes seconds [2] (ii) 260 litres is given correct to the nearest 10 litres. Write down the lower bound of this amount. Answer(b)(ii) litres [1] (c) A different tank is in the shape of a cube. It has a volume of 27 000 cm3. Find the height of this tank. Answer(c) cm [2]

8 marks

Mark scheme: 8 (a) (i) 165 000 2 M1 for figs 165 or 55 × 40 × 75 seen (ii) 165 1ft ‘their (a)(i)’ ÷ 1000 (b) (i) 10 minutes 24 seconds 2 M1 for 260 ÷ 25 or 10.4 seen or 624 seen (ii) 255 1 3 27000 (c) 30 2 M1 for

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

2 (a) The travel graph shows Helva’s journey from her home to the airport. For Examiner's Use 200 airport 180 160 140 120 Distance from home 100 (km) 80 60 40 20 home 0 08 00 10 00 12 00 14 00 16 00 Time (i) What happened at 09 30? Answer(a)(i) [1] (ii) Work out the time taken to travel from home to the airport. Give your answer in hours and minutes Answer(a)(ii) hours minutes [1] (iii) Calculate Helva’s average speed for the whole journey from home to the airport. Answer(a)(iii) km/h [2] (iv) Between which two times was Helva travelling fastest? Answer(a)(iv) and [1] (v) Helva’s husband left their home at 11 00 and travelled directly to the airport. He arrived at 15 30. Complete the travel graph for his journey. [1] (b) (i) Helva and her husband are flying from Finland to India. For Their plane takes off at 17 00 and arrives in India 7 hours 25 minutes later. Examiner's Use 1 The time in India is 3 hours ahead of the time in Finland. 2 What is the local time in India when the plane arrives? Answer(b)(i) [2] (ii) The temperature is O3°C in Finland and 23°C in India. Write down the difference between these two temperatures. Answer(b)(ii) °C [1] (c) Helva exchanged 7584 rupees for euros (€). The exchange rate was 1€ = 56 rupees. How many euros did Helva receive? Give your answer correct to 2 decimal places. Answer(c) € [2]

11 marks

Mark scheme: 2 (a) (i) stopped 1 (ii) 5 hours 30 mins or 5 ½ hours 1 (iii) 32.72 – 32.73 or 32.7 2 ft M1 180 ÷ their (a)(ii) ft correct to 3 sig figs (iv) 10(00) and 12(00) 1 (v) Line or curve from 1100,0 to 1530,180 1 (b) (i) (0)355 or 3.55 am 2 B1 0025 or 2030 seen SC1 2055 as answer or 3.55 pm as answer (ii) 26° or –26° 1 (c) 135.43 cao 2 M1 135 or 135.4 or 7854 ÷ 56, implied by 135.(428…) IGCSE – October/November 2012 0580 33

This question in 0580/33 Oct/Nov 2012

1 (a) On a map, the height of Hillibar Station is 1047 m and the height of Sular Junction is 297 m. For Examiner′s Use (i) Calculate the difference in these heights. Answer(a)(i) … m [1] (ii) The temperature falls by 1°C for every 100 m increase in height. One day the temperature in Sular Junction is 19°C. Work out the temperature at Hillibar Station. Answer(a)(ii) … °C [1] (iii) Write 297 correct to the nearest ten. Answer(a)(iii) … [1] (iv) Write 1047 correct to the nearest hundred. Answer(a)(iv) … [1] (b) (i) Kim arrives at Hillibar Station at 12 35. The taxi to her hotel takes 27 minutes. Work out the time Kim arrives at her hotel. Answer(b)(i) … [1] (ii) Henry takes 17 minutes to walk from his home to Sular Junction. He must arrive there by 10 43. Work out the latest time he can leave home. Answer(b)(ii) … [1] (c) Here is part of a train timetable. For Examiner′s Each journey from Sular Junction to Hillibar Station takes the same time. Use Sular Junction departs 10 59 12 32 14 48 Hillibar Station arrives 12 35 14 08 (i) Complete the timetable. [2] (ii) The distance between Sular Junction and Hillibar Station is 64 km. Calculate the average speed, in kilometres per hour, of a train between these two stations. Answer(c)(ii) … km/h [2] (iii) Joel arrives at Sular Junction at 11 48. At what time is the next train to Hillibar Station due to depart? Answer(c)(iii) … [1] _____________________________________________________________________________________

11 marks

Mark scheme: Qu. Answers Mark Part Answers 1 (a) (i) 750 1 (ii) 11, 11.5 or 12 1ft (iii) 300 1 (iv) 1000 1 (b) (i) 13 02 1 (ii) 10 26 1 (c) (i) 16 24 2 B1 for 1 (h) 36 or 2 (h) 16 or 3 (h) 49 or 96 or 136 or 229 or 4.24(pm) soi. (ii) 40 cao 2 M1 for 64 ÷ their time (e.g. 1(h) 36(m) ) (iii) 12 32 1

This question in 0580/31 May/June 2013

8 Ben and Ruth own a company. For Examiner′s Use (a) The company’s profi ts of $43 680 are shared in the ratio Ben : Ruth = 2 : 5 . Calculate Ruth’s share of the profi ts. Answer(a) $ … [2] (b) Ruth invests $15 000 at a rate of 4% per year simple interest. Calculate how much her investment is worth at the end of 3 years. Answer(b) $ … [3] (c) The company employs 450 people. 14% of these people work in sales. Calculate the number of people who work in sales. Answer(c) … [2] (d) Every year Ben travels 32 000 km on business. For Examiner′s Use (i) Car-rent Cost ($) = 600 + 0.35d where d is the distance travelled in kilometres Calculate the cost of hiring a car from Car-rent to travel 32 000 km. Answer(d)(i) $ … [2] (ii) Drive-easy Cost = $100 plus $4 for every 10 km travelled Calculate the cost of hiring a car from Drive-easy to travel 32 000 km. Answer(d)(ii) $ … [2] _____________________________________________________________________________________

11 marks

Mark scheme: 8 (a) 31 200 2 M1 for (43 680 ÷ 7) × 5 or 6240 × 5 (b) 16 800 3 M2 for 15 000 + 15 000 × 0.04 × 3 oe or M1 for 15 000 × 0.04 × 3 oe, imp by 1800 (c) 63 2 M1 for 450 × [0].14 oe (d) (i) 11 800 2 M1 for 600 + 0.35 × 32 000 or better (ii) 12 900 2 M1 for 100 + 4 × 32 000 ÷ 10 or better IGCSE – May/June 2013 0580 31

This question in 0580/31 May/June 2013

8 For Examiner′s Use 5 Sweet 4 shop 3 Distance (km) 2 1 Home 0 14 10 14 20 14 30 14 40 14 50 15 00 15 10 15 20 15 30 15 40 Time (a) Jono walked from his home to a sweet shop. Use the travel graph to calculate his walking speed in kilometres per hour. Answer(a) … km/h [2] (b) Jono stayed in the sweet shop for 20 minutes. He then ran home at a steady speed of 12 km/h. (i) On the grid above, complete the travel graph for Jono. [2] (ii) Write down the time Jono arrived home. Answer(b)(ii) … [1] (c) The sweet shop owner records how much time and how much money children spend in his shop. For Examiner′s Use Time in shop (min) 3 6 7 9 10 11 12 14 15 15 20 Money spent ($) 0.50 1.20 1.10 1.60 2.00 1.70 2.00 2.80 2.30 2.90 3.00 3 2 Money spent ($) 1 0 5 10 15 20 25 Time in shop (min) (i) Complete the scatter diagram. The fi rst seven points have been plotted for you. [2] (ii) What type of correlation does this scatter diagram show? Answer(c)(ii) … [1] (iii) On the grid, draw the line of best fi t. [1] (iv) A child spent $2.50 in the shop. Use your line of best fi t to estimate how long the child was in the shop. Answer(c)(iv) … min [1] _____________________________________________________________________________________

10 marks

Mark scheme: 4 8 (a) 6 2 M1 for [× 60] oe 40 (b) (i) Line from (1450,4) to (1510,4) 1 Line from (1510,4) to (1530,0) 1ft Ft is (their 1510,4) to (their 1510 + 20,0) (b) (ii) 1530 1ft (c) (i) 4 points plotted correctly 2 P1 for 3 correct (ii) Positive 1 (iii) Correct ruled line 1 (iv) 12< Ans <16 1ft IGCSE – May/June 2013 0580 32

This question in 0580/32 May/June 2013

5 (a) For Examiner′s North Use C B D North A Scale: 1 cm to 12 km The diagram shows four towns, A, B, C and D, joined by straight roads AB, BC and BD. The scale is 1 centimetre represents 12 kilometres. (i) Measure the bearing of B from A. Answer(a)(i) … [1] (ii) Work out the distance in kilometres from A to B. Answer(a)(ii) … km [2] (iii) Saraswati takes 1 hour 30 minutes to drive from A to B. Calculate her average speed, in kilometres per hour, for this journey. Answer(a)(iii) … km/h [1] (b) At B, Saraswati follows another straight road which is equidistant from BC and BD. For Examiner′s Use Using a straight edge and compasses only and leaving in all your construction lines, construct the line of this road on the diagram. [2] (c) Another motorist, Leah, leaves C and drives on a bearing of 165° to meet Saraswati at town E. Town E is on the road in part (b). Show Leah’s journey on the diagram and mark the town E. [1] (d) Saraswati travelled from B to E at an average speed of 55 km/h. Calculate the time, in hours and minutes, that she took. Answer(d) … h … min [4] (e) There is a speed limit of 50 km/h on all roads within 30 km of town D. On the diagram, show the boundary of the region where this speed limit applies. [2] _____________________________________________________________________________________

13 marks

Mark scheme: 5 (a) (i) (0)35 to (0)39 1 (ii) 117.6 to 122.4 [km] 2 B1 for (10 ± 0.2) cm seen (iii) 80 or 78.4 to 81.6 1ft ft their (a)(ii) ÷ 1.5 (b) Bisector of angle CBD with 2 2 B1 correct line (±2°), some or all arcs absent correct pairs of arcs. (c) Ruled line from C to BD on a 1 bearing of 165° (d) 1 [h] 18 [min] to 1 [h] 26 [min] 4 B1ft measure BE www M1 change to kilometres. M1 for their distance ÷ 55 (e) Circle, centre D, with radius 2 M1 for 2.5 ± 0.2 soi. 2.5 ± 0.2 cm SC1 for circle, centre D, incorrect radius or freehand ‘correct’ circle IGCSE – May/June 2013 0580 33

This question in 0580/33 May/June 2013

4 (a) For Examiner′s Use North Sea B North A The scale drawing shows the position of two airfi elds, A and B. The scale is 1 cm represents 50 km. (i) Find the actual distance between A and B. Give your answer in kilometres. Answer(a)(i) … km [2] (ii) Measure the bearing of B from A. Answer(a)(ii) … [1] (iii) A third airfi eld, C, is 525 km from airfi eld A and 350 km from airfi eld B. On the scale drawing, construct the position of airfi eld C. [2] (iv) Measure the bearing of B from C. Answer(a)(iv) … [1] (b) A plane is at airfi eld C at 10 40. For Examiner′s It fl ies 525 km to airfi eld A at a speed of 700 km/h. Use Work out the time when the plane reaches airfi eld A. Answer(b) … [3] (c) This plane has a maximum take-off weight of 4173 kg. Write 4173 kg correct to the nearest hundred kilograms. Answer(c) … kg [1] (d) The plane can fl y at a maximum height of 13 107 m. Write 13 107 m in kilometres, correct to 3 signifi cant fi gures. Answer(d) … km [2] (e) In one week, the plane fl ies a total distance of 8520 km, correct to the nearest ten kilometres. Write down the lower bound of this distance. Answer(e) … km [1] _____________________________________________________________________________________

13 marks

Mark scheme: 4 (a) (i) 370 to 380 2 B1 for 7.4 to 7.6 seen (ii) [0]36 to [0]40 1 (iii) Intersecting arcs: 2 Arc centre A radius 10.5 cm B1 for one correct arc Arc centre B radius 7 cm or C correct with no arcs (iv) 300 to 310 1FT (b) 11 25 3 M2 for 525 ÷ 700 × 60 or better soi Or M1 for 525 ÷ 700 soi by 0.75 (c) 4200 1 (d) 13.1 2 B1 for 13 100 or 13.107 or 13.100 Or B1FT their conversion to 4 or more sig figs seen and then correctly rounded to 3 sig figs (e) 8515 1

This question in 0580/32 Oct/Nov 2013

3 The Wong family spend the day at the zoo. (a) The Wong family has 2 adults and 3 children aged 2, 5 and 11 years old. Admission Adults $8.50 Children 11-16 years $6.00 Children 3-10 years $4.50 Children under 3 years FREE Mr Wong pays for his family to go into the zoo using a $50 note. Work out the change he receives. Answer(a) $ … [3] (b) The dolphin show fi nishes at 11 05. It lasts for 1 hour and 20 minutes. Write down the time the dolphin show starts. Answer(b) … [1] (c) Torty the tortoise was born on 27 December 1898. Work out how many years old she was on 3 January 2003. Answer(c) … years [1] (d) Last year, the ratio snakes : lizards = 3 : 5 . There were 45 lizards. (i) Work out how many snakes there were last year. Answer(d)(i) … [2] (ii) This year, there are 3 more snakes and the same number of lizards. Write down the new ratio snakes : lizards. Give your answer in its simplest form. Answer(d)(ii) … : … [2] (e) Mr Wong hires a vehicle to drive around the zoo. The cost is $25 for the fi rst hour and $7.50 for every extra half hour. He pays $85 altogether. For how long does he hire the vehicle? Answer(e) … hours [3] (f) Mrs Wong wants to buy some food for the giraffes. Small Bag Medium Bag Large Bag 225g 250g 325g 60 cents 70 cents 90 cents Work out which bag is the best value for money. Show how you decide. Answer(f) … [3] (g) The diagram shows a map of the zoo. The scale is 1 centimetre represents 50 metres. North Entrance Scale: 1 cm to 50 m Flamingos North Exit (i) Measure the bearing of the fl amingos from the entrance. Answer(g)(i) … [1] (ii) Xanthe looks after all the animals within 200 m of the exit. Draw accurately the locus of points inside the zoo which are 200 m from the exit. [2] (iii) A shop, S, is on a bearing of 212° from the entrance and a bearing of 293° from the exit. Mark the point S on the map. [3] __________________________________________________________________________________________

21 marks

Mark scheme: 3 (a) 22.5[0] 3 M1 for (2 × 8.5 + 6 + 4.50) M1 for 50 – their total (b) [0]9 45 1 (c) 104 1 45 (d) (i) 27 2 M1 for × 3 5 (ii) 2 : 3 cao 2 M1 for (their 27 + 3) : 45 or better If zero SC1 for 3 : 2 85− 25 (e) 5 3 M1 for soi by 8 7.50 their 8 M1 for + 1 2 (f) 3.75, 3.57... 3.61... [g / c] 3 M1 for 1 correct division, not evaluated small [bag] M1 for 2 further consistent correct divisions, not evaluated (g) (i) 105 1 (ii) correct locus drawn 2 M1 for any arc centre exit (iii) S marked correctly 3 B1 for indication of bearing of 212° B1 for indication of bearing of 293°

This question in 0580/33 May/June 2014

4 600 550 500 Seville 450 400 Distance from Madrid (km) 350 Cordoba 300 250 200 150 100 50 Madrid 0 07 00 07 30 08 00 08 30 09 00 09 30 10 00 10 30 11 00 Time (a) A train leaves Madrid at 07 00. It arrives at Cordoba at 08 40 and stays at the station for 10 minutes. It then continues to Seville arriving at 09 40. (i) Show this journey on the grid opposite. [3] (ii) Write down, in hours and minutes, the total time for this journey. Answer(a)(ii) … h … min [1] (iii) Calculate, in kilometres per hour, the average speed for the whole journey. Answer(a)(iii) … km/h [2] (b) Another train leaves Seville at 07 45. It travels to Madrid without stopping at an average speed of 200 km/h. (i) Calculate, in hours and minutes, the time taken for this journey. Answer(b)(i) … h … min [2] (ii) Show this journey on the grid. [2] (c) How far from Madrid were the trains when they passed each other? Answer(c) … km [1] __________________________________________________________________________________________

11 marks

Mark scheme: 4 (a) (i) Line (0700, 0) to (08 40, 310) 1 Lines need not be ruled and could be curves Horizontal line 2 squares 1FT with positive gradients throughout. Line their (08 50, 310) to (09 40, 470) 1FT (ii) 2[h]40[min] 1 (iii) 176.25 2 M1FT for 470 ÷ their (a)(ii) (b) (i) 2[h]21[min] 2 M1 for 470 ÷ 200 soi (ii) Line from (07 45, 470) to (their 10 06, 2FT B1 for (07 45, 470) correctly plotted 0) or B1FT for (their 10 06, 0) correctly plotted (c) 290 to 300 1FT (Correct or follow through) FT from intersection on their graph.

This question in 0580/32 Oct/Nov 2014

9 Adriano hires a car. The cost of hiring the car is $36 per day plus 24 cents for each kilometre travelled. He hires the car for 5 days and travels a total of 660 km. (a) (i) Calculate the cost to hire the car. Answer(a)(i) $ … [3] (ii) 15% tax is then added to this cost. Calculate the total cost of hiring the car including tax. Answer(a)(ii) $ … [2] (b) The car uses one litre of fuel to travel 11 km. Fuel costs $1.80 per litre. (i) Work out the number of litres used to travel the 660 km. Answer(b)(i) … litres [1] (ii) Work out the cost of this fuel. Answer(b)(ii) $ … [1] (iii) Find the total cost of hiring the car including tax and the fuel used. Answer(b)(iii) $ … [1] (c) During the 5 days Adriano earns $1600. What percentage of his earnings is your answer to part (b)(iii)? Give your answer correct to the nearest whole number. Answer(c) … % [2]

10 marks

Mark scheme: 9 (a) (i) 338.4[0] 3 M2 for 5 × 36 + 660 × 0.24 or better or M1 for 5 × 36 or 660 × 0.24 or better (ii) 389.16 2FT M1FT for 1.15 × their (a)(i) oe (b) (i) 60 1 (ii) 108 1FT 1.8 × their (b)(i) (iii) 497.16 1FT FT their (a)(ii) + their (b)(ii) their (b)(iii) (c) 31 nfww 2FT M1FT for × 100 1600

This question in 0580/32 Oct/Nov 2014

4 The diagram shows the positions of two villages Dormouth, D, and Greenton, G. The scale is 1 centimetre represents 20 kilometres. North G North Scale: 1 cm to 20 km D (a) Find the distance, in kilometres, from Dormouth to Greenton. Answer(a) … km [1] (b) Measure the bearing of Dormouth from Greenton. Answer(b) … [1] (c) Foxhill is 84 km from Dormouth. The bearing of Foxhill from Dormouth is 105°. Mark the position of Foxhill on the diagram. Label it F. [2] (d) A straight road joins Dormouth to Foxhill. A car drives from Dormouth to Foxhill at a constant speed of 54 km/h. Calculate the time it takes to complete the 84 km journey. Give your answer to the nearest minute. Answer(d) … h … min [3] (e) Change 54 km/h to m/s . Answer(e) … m/s [2] __________________________________________________________________________________________

9 marks

Mark scheme: 4 (a) 126 1 Accept 122 to 130 (b) 240 1 (c) Correct position on diagram 2 B1 for angle 103° to 107° B1 for distance 4.0 cm to 4.4 cm (d) 1 hour and 33 min 3 84 M2 for × 60 oe 54 84 30 or M1 for or × 60 54 54 54 × 1000 (e) 15 2 M1 for or better 60 × 60

This question in 0580/32 Feb/March 2015

3 Sonia works in a toy shop. (a) (i) One week she works for 30 hours and is paid $180. Calculate the amount she is paid per hour. Answer(a)(i) $ … [1] (ii) The next week Sonia works for 38 hours and is paid $220. Find the difference in her pay per hour for these two weeks. Answer(a)(ii) $ … [2] (b) The shop sells bags of 40 marbles. One bag has marbles in the ratio red : blue : green = 1 : 3 : 4. (i) Calculate the number of marbles of each colour. Answer(b)(i) Red = … , blue = … , green = … [2] (ii) A second bag of 40 marbles contains 11 red marbles, 9 blue marbles and 20 green marbles. All the marbles from the two bags are mixed together. Write down the ratio of marbles red : blue : green. Give your answer in its simplest form. Answer(b)(ii) … : … : … [2] (c) Thilo and Toby buy some boats and trains from the toy shop. The cost of one boat is b cents and the cost of one train is t cents. (i) Toby buys 3 boats and 4 trains for $5.70 . Complete this equation. 3b + 4t = … [1] (ii) Thilo buys 1 boat and 2 trains for $2.40 . Write this information as an equation. … = … [2] (iii) Solve your two equations to find the cost of a boat and the cost of a train. You must show all your working. Answer(c)(iii) Cost of a boat = … cents Cost of a train = … cents [3] (d) Train track costs 99 cents per 20 cm. Calculate the cost of buying 3.4 metres of train track. Answer(d) $ … [3] __________________________________________________________________________________________

16 marks

Mark scheme: 3 (a) (i) 6 1 220 (ii) 0.21 2 M1 for or better 38 (b) (i) 5, 15, 20 2 B1 for 1 correct answer in the right place or M1 for 40 ÷ (1 + 3 + 4) [×k] soi where k is 1 or 3 or 4 (ii) 2 : 3 : 5 2 M1 for (16,24,40) or better or M1FT for ‘their (5,15,20)’ + (11,9,20) or better (c) (i) 570 1 (ii) b + 2t = 240 2 B1 for b + 2t seen (iii) [b] 90 3 M1FT for correct elimination of one [t] 75 variable Working must be shown A1 for b = 90 A1 for t = 75 If zero is scored SC1 for 2 values satisfying one of their equations (ft) SC1 if no working shown, but 2 correct answers given (d) 16.83 3 B1 for 340 or 0.2 or 5 seen M1 for figs 340 ÷ figs 20 × figs 99 or figs 340 × figs 5 × figs 99

This question in 0580/31 May/June 2015

4 The Patel family flies from their home town, H, to Kiruna, K, in Lapland. (a) The scale drawing shows their journey. The scale is 1 centimetre represents 40 kilometres. North K North Scale: 1 cm to 40 km H (i) Measure the bearing of K from H. Answer(a)(i) … [1] (ii) Work out the distance in kilometres from H to K. Answer(a)(ii) … km [2] (iii) The average speed of the plane is 450 km/h. Find the average speed in m/s. Answer(a)(iii) … m/s [2] (b) The probability that the plane arrives on time is 0.15 . (i) Write down the probability that the plane does not arrive on time. Answer(b)(i) … [1] (ii) Every year there are 240 flights from H to K. Calculate the expected number of flights that arrive on time. Answer(b)(ii) … [1] (c) The Patel family has six suitcases. The number of items in each suitcase is shown below. 15 16 16 18 19 21 (i) Find the range. Answer(c)(i) … [1] (ii) Write down the mode. Answer(c)(ii) … [1] (iii) Work out the median. Answer(c)(iii) … [1] (iv) Calculate the mean. Answer(c)(iv) … [2] (v) Find the probability that a suitcase chosen at random has more than 18 items. Answer(c)(v) … [1] (d) Mr Patel buys a bag of sweets. The bag of sweets costs $3.25 . (i) Calculate the cost of the sweets in euros (€) when the exchange rate is €1 = $1.24 . Answer(d)(i) € … [2] (ii) The weight, w grams, of the bag of sweets is 250 g correct to the nearest 10 g. Complete this statement about the value of w. Answer(d)(ii) …  w < … [2] __________________________________________________________________________________________

17 marks

Mark scheme: 4 (a) (i) 292 1 (ii) 380 2 B1 for ( 9.5 ± 0.2 ) If zero scored, SC1 for figs ‘372 to 388’ 450 × 1000 (iii) 125 2 M1 for or better 60 × 60 (b) (i) 0.85 1 (ii) 36 1 (c) (i) 6 1 (ii) 16 1 (iii) 17 1 (iv) 17.5 2 M1 for (15+16+16+18+19+21) ÷ 6

This question in 0580/31 May/June 2015

7 40 Cawley 35 30 25 Distance from 20 Audley (km) 15 Brookland 10 5 Audley 0 09 00 09 30 10 00 10 30 11 00 Time The grid shows the travel graph for a train travelling from Audley to Cawley, stopping at Brookland. (a) (i) Between which two towns is the train journey fastest? Give a reason for your answer. Answer(a)(i) From … to … is fastest because … [1] (ii) Calculate the speed of the train, in kilometres per hour, between Brookland and Cawley. Answer(a)(ii) … km/h [2] (b) When the train reaches Cawley, it waits for 10 minutes. It then returns to Audley without stopping at Brookland. The return speed of the train is 70 km/h. (i) Complete the travel graph for this train. [2] (ii) Write down the time this train arrives at Audley. Answer(b)(ii) … [1] (c) Trains leave Audley for Cawley every 100 minutes. The first train of the day is the 09 00 train. Write down the time that the fourth train leaves Audley for Cawley. Answer(c) … [2] __________________________________________________________________________________________

8 marks

Mark scheme: 7 (a) (i) Brookland to Cawley 1 and [gradient is] steeper oe 35 − 10 (ii) 100 2 M1 for oe time (b) (i) correct graph 2 B1 for horizontal line (0940, Cawley) to (0950, Cawley) B1FT for line (their 0950, Cawley) to (their 0950 + 30, Audley) (ii) 10 20 1FT (c) 1400 2 B1 for 300 or 5 h or 2:00 or 2 o’clock or any 2 of 10:40, 12:20(FT) or 14:00(FT)/2:00(FT) If zero scored, SC1 for 1540 or 3:40pm

This question in 0580/31 May/June 2015

9 Nina is going on a holiday to Dubai from her home in Mumbai. (a) At the airport she buys 2 packets of sandwiches and 3 magazines. Complete her shopping bill in Indian rupees. 2 packets of sandwiches at 325 rupees per packet = … rupees 3 magazines at 75 rupees per magazine = … rupees Total = … rupees [3] (b) She changed 10 000 rupees to dirhams when the exchange rate was 18.3 rupees = 1 dirham. How much did she receive? Answer(b) … dirhams [2] (c) The flight from Mumbai to Dubai takes 2 hours 50 minutes. The distance from Mumbai to Dubai is 1937 km. (i) Show that the average speed of the flight is 684 km / h, correct to the nearest whole number. Answer(c)(i) [2] (ii) Nina’s flight leaves Mumbai at 13 15. 1 The local time in Mumbai is 1 2 hours ahead of the local time in Dubai. Find the time of arrival in Dubai. Give your answer in the 24-hour clock. Answer(c)(ii) … [2]

9 marks

Mark scheme: 9 (a) 650 1 225 1 875 1FT (b) 546 or 546.4 or 546.44 or 546.45 2 M1 for 10 000 ÷ 18.3 (c) (i) 1937 ÷ 2.83[3…] or M1 1937 ÷ 170 × 60 683.6 to 684.4 … A1 but not 684 (ii) 14 35 2 B1 for 16 05 [time in Mumbai on arrival] or B1 for 11 45 [time in Dubai on departure from Mumbai] or M1 for 2 hours 50 mins – 1 hour 30 mins + 1315 or SC1 for answer 2 35pm

This question in 0580/32 May/June 2015

6 The travel graph shows a journey of a train from A to C, stopping at B. C 125 100 75 Distance from A (km) 50 25 A 0 09 00 10 00 11 00 12 00 Time (a) Write down the time that the train leaves A. Answer(a) … [1] (b) Write down the time that the train stops at B. Answer(b) … [1] (c) For how many minutes did the train stop at B? Answer(c) … min [1] (d) Work out the average speed of the train between A and C. Answer(d) … km/h [3] (e) Another train leaves C at 09 50 and arrives at A at 11 40 without stopping. It travels at a constant speed. (i) On the grid, draw the travel graph for this train. [1] (ii) At what time do the two trains pass each other? Answer(e)(ii) … [1] (f) A ticket from A to C costs 2345 rupees. The exchange rate is 1 rupee = $0.024 . Calculate the cost of the ticket in dollars. Answer(f) $ … [1]

9 marks

Mark scheme: 6 (a) 09 20 1 (b) 10 00 1 (c) 20 1 (d) 50 3 M1 for use of 125 ÷ their time B1 for time = 2.5 (e) (i) points (09 50, 125) and (11 40, 0) 1 plotted and joined with a ruled continuous line (ii) 10 40 to 10 50 1FT FT their line (f) 56.28 final answer cao 1

This question in 0580/33 May/June 2015

7 Fintown 16 14 12 Emley 10 Distance 8 from Dexford (km) 6 4 2 Dexford 0 09 00 09 10 09 20 09 30 09 40 Time The grid shows the travel graph for a train travelling from Dexford to Fintown, stopping at Emley. (a) (i) Write down the distance the train travels in the first 8 minutes. Answer(a)(i) … km [1] (ii) Calculate the average speed, in kilometres per hour, for the journey from Dexford to Fintown. Answer(a)(ii) … km/h [3] (b) The train waits at Fintown for 4 minutes. The train then returns to Dexford without stopping at Emley. The return speed of the train is 80 km/h. (i) Complete the travel graph. [2] (ii) Change 80 km/h to metres per second. Answer(b)(ii) … m/s [2] (c) Trains leave Dexford for Fintown every 75 minutes. The train that leaves Dexford at 09 00 is the first train of the day. Write down the time that the fourth train leaves Dexford for Fintown. Answer(c) … [2]

10 marks

Mark scheme: 7 (a) (i) 10 1 (ii) 48 3 16 M2 for × 60 oe 20 16 or M1 for oe 20 16 If zero scored SC1 for × 60 or 53.3… 18 (b) (i) Straight line 1 (09 20, 16) to (09 24, 16) Straight line from (their 09 24, 16) to (their 09 24 + 12, 0) 1FT (ii) 22.2 or 22.22… 2 80 × 1000 M1 for oe 60 × 60 figs 8 If zero scored SC1 for or figs 222 figs 36 (c) 12 45 [pm] 2 M1 for 3 × 75 soi or SC1 for answer 14 00 or 2 pm

This question in 0580/32 Oct/Nov 2015

6 Swimming pool Shop Distance from home (km) Cinema Home 0 10 00 10 10 10 20 10 30 10 40 10 50 11 00 Time Abjit cycles from his home to the swimming pool. The travel graph for his journey is drawn on the grid. On his journey he passes the cinema and the shop. (a) Write down where Abjit stops on his journey to the swimming pool. … [1] (b) Abjit is cycling fastest between the shop and the swimming pool. Explain how you know this from looking at the graph. … [1] (c) Abjit cycles at 20 km/h from his home to the cinema. This part of the journey takes 12 minutes. (i) Show that the distance from Abjit’s home to the cinema is 4 km. [2] (ii) Complete the scale on the vertical axis of the grid by showing at least two other values. [1] (d) Calculate the speed, in km/h, that Abjit cycles from the cinema to the shop. … km/h [2] (e) When Abjit arrives at the swimming pool it is closed. Without stopping at the swimming pool he cycles home at a constant speed. It takes him 24 minutes to cycle home. Complete the travel graph for his journey home. [1] (f) Calculate the average speed, in km/h, for the whole journey. … km/h [3] (g) Abjit’s bicycle wheel has a radius of 29 cm. (i) Calculate the circumference of the wheel. Give your answer correct to 1 decimal place. … cm [3] (ii) Calculate the number of complete turns the wheel makes when travelling 500 m. … [2]

16 marks

Mark scheme: 6 (a) shop 1 (b) [graph] steepest oe 1 1 (c) (i) 0.2 × 20 or 12 × oe M2 M1 for 12×20 3 (ii) distance axis numbered correctly 1 with at least 2 more numbers 3 3 (d) 12 2 M1 for or [ 60 ] 0.25 15× (e) ruled line from (1034, 8) to 1 (1058, 0) their swimming pool distance × 2 (f) 16.6 or 16.55… 3 M2 for ×60 their 1058 − 1000 dist or M1 for a timeinterval (g) (i) 182.2 3 M1 for 2π × 29 A1 for 182.2 to 182.24 A1FT for their A1 rounded correctly to 1dp 50000 500 (ii) 274 2FT M1FT or their ( g )( i ) their ( g )( i ) ÷ 100 If zero scored SC1 for figs 27[44…] 1732

This question in 0580/32 Feb/March 2016

3 Paul and Mary go on a 14 night cruise in the Mediterranean. (a) The price of the cruise is $237 per person per night. A tax of 6% is added to this price. Find the total amount Paul and Mary pay for this cruise. $ … [3] (b) At a port Mary buys 2 bottles of sun cream. Each bottle costs $7.89 . Work out the change she receives from $20. $ … [2] (c) Paul and Mary leave the ship at 09 23 to tour Pisa. 3 The tour lasts for 6 hours. 4 Find the time when the tour finishes. … [2] (d) The ship leaves at 18 40 to sail to the next port. It sails 270 km at an average speed of 32.4 km/h. Find the time when the ship arrives. … [3] (e) There are 1800 passengers on the ship. They are in the ratio males : females = 5 : 4. Work out the number of male passengers. … [2]

12 marks

Mark scheme: 3 (a) 7034.16 3 M2 for 14 × 237 × 2 × 1.06 oe or M1 for 14 × 237 × 2 oe or 237 × 1.06 oe or 237 × 2 × 1.06 oe or 237 × 1.06 × 14 oe (b) 4.22 2 M1 for 20 – 2 × 7.89 (c) 16 08 or 4 08 pm 2 B1 for 45 min soi (d) 03 00 or 3 am 3 M1 for 270 ÷ 32.4 or 8.33[…] or 8 (h) 20 (min) M1dep for 18 40 + their 8.33 (e) 1000 2 M1 for 18004 + 5 [×5] oe

This question in 0580/31 May/June 2016

7 The scale drawing shows a park, ABCDE. The scale is 1 centimetre represents 20 metres. B North A C D Scale: 1 cm to 20 m E (a) Measure the bearing of B from A. … [1] All constructions in the following parts must be completed using a straight edge and compasses only. All construction arcs must be clearly shown. (b) A straight cycle path crosses the park from E to BC. The path bisects angle AED. (i) Construct the cycle path. [2] (ii) Work out the actual length, in metres, of the cycle path. … m [2] (iii) Alice cycles from E to BC along the path at a constant speed of 9 km/h. (a) Show that 9 km/h is equivalent to 2.5 m/s. [1] (b) Find the time she takes to cycle from E to BC. Give your answer in seconds. … s [2] (c) A straight footpath, equidistant from D and E, crosses the park from DE to AB. Construct the footpath. [2] (d) (i) Construct the locus of points 150 metres from A and inside the park. [2] (ii) A region for sports activities is less than 150 metres from A and closer to E than to D. Shade this region. [1]

13 marks

Mark scheme: 7 (a) 48 to 52 1 (b) (i) Correct ruled angle bisector with 2 B1 for accurate with no / one pair of arcs 2 pairs of correct arcs or M1 for 2 pairs of correct arcs with no / wrong line (ii) 270 to 278 2FT B1 for 13.5 ± 0.2 [cm] seen in working or B1FT for their line from E ± 0.2cm to outside (iii)(a) 9 × 1000 ÷ ( 60 × 60 ) 1 (iii)(b) 108 to 111.2 2FT M1FT for their (b)(ii) ÷ 2.5 (c) Correct ruled perpendicular 2 B1 for accurate with no / one pair of arcs bisector of DE with 2 pairs of or arcs M1 for correct intersecting arcs with no / wrong line (d) (i) Arc centre A, radius 7.5 2 B1 for centre A, incorrect radius from AB to AE or correct arc too short (ii) Correct region shaded 1FT follow through provided an area is possible

This question in 0580/33 May/June 2016

5 (a) This graph shows Gianna’s journey to work. 20 Work 15 Distance from home 10 (km) 5 Home 0 07 00 07 30 08 00 08 30 09 00 Time (i) How far did Gianna travel to work? … km [1] (ii) Explain what happened at 07 10. … [1] (iii) Calculate the average speed for Gianna’s journey to work. … km/h [2] (b) Gianna earns $1320 each month. She divides her money in the ratio Bills : Leisure : Other = 12 : 5 : 7. Work out how much she spends on each. Bills = $ … Leisure = $ … Other = $ … [3] (c) Gianna invests $5000 for 3 years at a rate of 2.1% per year compound interest. Calculate the amount she will have at the end of the 3 years. Give your answer correct to 2 decimal places. $ … [4]

11 marks

Mark scheme: 5 (a) (i) 17.5 1 (ii) She stopped oe 1 (iii) 8.75 2 M1FT for their (a)(i) ÷ 2 soi (b) 660 3 M2 for one correct value in correct place 275 1320 385 or × k where k is 5, 12 or 7 ( 5 + 12 + 7 ) or better in working 1320 or M1 for or better ( 5 + 12 + 7 ) If zero scored, SC1 for all correct answers in incorrect order (c) 5321.66 cao 4 M2 for 5000 × 1.0213 oe or M1 for 5000 × 1.021 × 1.021 oe A1 for 5321.661….. B1 indep for their answer corrected to 2 d.p. if their unrounded answer is shown to at least 3 d.p.

This question in 0580/31 Oct/Nov 2016

1 (a) Juan takes his car to a garage for repairs. Complete his bill. Item Price ($) Service 475.00 3 tyres at $86 each … 4.5 litres of oil at $5.68 per litre … __________________________ Total … [3] (b) Juan buys a van costing $4400. He pays a deposit of $3740. (i) Work out $3740 as a percentage of $4400. … % [1] (ii) He borrows the rest of the money for one year at a rate of 12% per year simple interest. Work out how much he pays back at the end of one year. $ … [3] (c) Juan pays $321 for insurance. He makes 12 equal payments. Work out each payment. $ … [1] (d) Juan’s car travels 12.4 km and uses 1 litre of fuel. His van travels 1 km and uses 0.0792 litres of fuel. Using 1 litre of fuel, which vehicle travels further? Explain how you decide. … travels further because … … [2] (e) In 2015 the total cost of repairs and fuel for his van was $4200. These costs are in the ratio repairs : fuel = 1 : 2. Find the cost of the fuel. $ … [2]

12 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 258[.00] 1 25.56 1 758.56 1FT FT 475 + their two previous answers (b) (i) 85 1 (ii) 739.2[0] 3 M1 for 4400 – 3740 or soi by 660 M1 for their 660 × 1.12 oe (c) 26.75 cao 1 (d) Van and 12.6 > 12.4 oe 2 B1 for 12.6[…] or 0.0806[…] or 0.982[…] or 0.0792 < 0.0806 or 0.982 < 1 (e) 2800 2 M1 for [2×] 4200 ÷ (1 + 2) oe or soi by 1400

This question in 0580/33 Oct/Nov 2016

5 A train departs from Green Hill, stops at Deep Valley for 5 minutes and then goes on to Clear Lake. The train timetable shows the times. Station Arrive Depart Green Hill - 10 30 Deep Valley 10 45 10 50 Clear Lake 11 14 - (a) (i) Complete this statement. The journey from Green Hill to Deep Valley takes … minutes. [1] (ii) Write your answer to part (a)(i) as a fraction of an hour. … [1] (b) The train travels the 18 km between Green Hill and Deep Valley at a constant speed. Calculate the speed, in km/h, for the train on this part of the journey. … km/h [1] (c) The train travels at a constant speed of 85 km/h between Deep Valley and Clear Lake. Work out the distance between Deep Valley and Clear Lake. … km [2] (d) Work out the total distance between Green Hill and Clear Lake. … km [1] (e) Complete the travel graph to show the whole journey from Green Hill to Clear Lake. 60 56 52 48 44 40 36 32 Distance (km) 28 24 20 Deep Valley 16 12 8 4 Green Hill 0 10 30 10 40 10 50 11 00 11 10 11 20 Time [3]

9 marks

Mark scheme: 5 (a) (i) 15 1 1 (ii) oe 1FT FT their (a)(i) / 60 4 (b) 72 1FT FT 18 / their (a)(ii) or 18 / their (a)(i) × 60 24 (c) 34 2 M1 for [ 85] × or 85 × 24 [ ÷60 ] or 60 85 ÷ 60 × [ 24 ] (d) 52 1FT FT is 18 + their 34 (e) ruled line from (10 30, 0) to 1 (10 45, 18) ruled line from (10 45, 18) to 1 (10 50, 18) ruled line from (10 50, 18) to 1FT FT (10 50, 18) to (11 14, their 52) (11 14, 52) 6

This question in 0580/32 Feb/March 2017

2 (a) The diameter of the Earth is 12 756 km. Write 12 756 km in metres. … m [1] (b) The distance from the Earth to the Moon is 384 000 km. Work out the time it would take a car travelling at 100 km/h to travel 384 000 km. Give your answer in days. … days [2] (c) The distance from the Sun to the Earth is 149.6 million kilometres. Write 149.6 million in standard form. … [2] (d) The diameter of a grain of salt is 1 × 10−4 metres. (i) Write 1 × 10−4 as an ordinary number. … [1] (ii) Write 1 × 10−4 metres in millimetres. … mm [1]

7 marks

Mark scheme: 2(a) 12 756 000 1 2(b) 160 2 384000 M1 for 100 2(c) 1.496 × 108 2 M1 for 1.496 × 10k or 149 600 000 oe If zero scored, SC1 for 1.496 × 102 million 2(d)(i) 0.0001 1 2(d)(ii) 0.1 oe 1

This question in 0580/33 May/June 2017

3 The McVay family go to the cinema. (a) The cinema has 510 seats. (i) The first 6 rows each have 18 seats. The next 8 rows each have 20 seats. All the other rows each have 22 seats. Work out the total number of rows of seats in the cinema. … [3] (ii) 70% of the 510 seats are occupied. Work out how many seats are occupied. … [1] (b) The McVay family has 2 adults and 2 children. Ticket Prices Adult $7.95 Child $5.95 Family Ticket (2 Adults and 2 Children) $24 Work out how much they save by buying a family ticket rather than a ticket for each person. $ … [2] (c) The film starts at 14 15 and lasts for 116 minutes. Work out the time that the film ends. … [2] (d) Popcorn is sold in tubs. Large Medium Small 135g 100g 70g $3.15 $2.30 $1.60 Work out which tub of popcorn is the best value for money. You must show your working. … [3]

11 marks

Mark scheme: 3(a)(i) 25 3 510 − ( 6 × 18 + 8 × 20 ) M2 for soi 22 or M1 for 6 × 18 + 8 × 20 soi 3(a)(ii) 357 1 3(b) 3.8[0] 2 M1 for 2 × 7.95 + 2 × 5.95 or better 3(c) 16 11 or 4.11 pm 2 M1 for conversion to 1 hour and 56 mins or a complete correct method 3(d) Complete correct method M2 M2 for 2.28… or 2.29, 2.3, 2.33… [c/g] oe or 43.75, 43.47… or 43.48, 42.85… or 42.86 [g/$] oe or M1 for one correct calculation small A1

This question in 0580/33 May/June 2017

7 36 Wegmouth 32 28 Distance (km) 24 20 Tyneland 16 12 8 4 Seatown 0 11 00 11 30 12 00 12 30 13 00 Time The diagram shows the travel graph for a bus travelling between three towns. (a) (i) For how many minutes does the bus stop at Wegmouth? … minutes [1] (ii) Write down the time the bus leaves Wegmouth. … [1] (iii) The speed of the bus from Tyneland to Wegmouth is 96 km/h. Change 96 km/h to metres per second. … m/s [2] (b) On the journey back from Wegmouth, the bus stops for 15 minutes in Tyneland. It then travels at a constant speed of 64 km/h to Seatown. Complete the travel graph. [3] (c) A cyclist leaves Seatown at 11 15 and travels at a constant speed to Wegmouth. She arrives in Wegmouth at 12 30. (i) On the travel graph, draw this journey. [1] (ii) Write down the time when the cyclist meets the bus. … [1] (iii) How far is the cyclist from Wegmouth when she meets the bus? … km [1] (d) Mrs Jones travels on the bus to Wegmouth. The probability that she stands on the bus is 0.4 . (i) Write down the probability that she does not stand on the bus. … [1] (ii) Mrs Jones travels on the bus 85 times. Work out the expected number of times that she stands on the bus. … [1] (e) In one week, a bus driver works five days. On four days he works from 9 am to 5 pm. On one day he works from 3 pm to 10 pm. (i) Find the total number of hours he works in this week. … hours [2] (ii) Each day he is paid $18 per hour before 7 pm. After 7 pm he is paid 25% extra per hour. Calculate how much the bus driver is paid for this week. $ … [3]

17 marks

Mark scheme: 7(a)(i) 20 1 7(a)(ii) 11 55 1 7(a)(iii) 2 2 96 26 or 26.7 or 26.66 to 26.67 M1 for 96 × 1000 or oe 3 3600 or B1 for figs 267 or better 7(b) Ruled horizontal line from 1 (12 20, 16) to (12 35,16) Ruled line from 2 16 M1 for [ × 60 ] (their 12 35, 16) to 64 (their 12 35+15, 0) 7(c)(i) Ruled line from 1 (11 15, 0) to (12 30, 32) 7(c)(ii) 12 09 1FT FT their graph 7(c)(iii) 9 1FT FT their graph 7(d)(i) 0.6 oe 1 7(d)(ii) 34 1 7(e)(i) 39 2 B1 for 32 or 7 and 8 seen 7(e)(ii) 715.5[0] 3 M2 for (their e(i) – 3) × 18 + 3 × 18 × 1.25 oe or M1 for (their e(i) – 3) × 18 or [3] × 18 × 1.25 or [3] × 18 × 0.25 oe

This question in 0580/33 May/June 2017

5 The scale drawing shows the positions of three towns A, B and C. The scale is 1 centimetre represents 12 kilometres. North North B North C A Scale: 1 cm to 12 km (a) Find the actual distance between town A and town B. … km [2] (b) Measure the bearing of town B from town A. … [1] (c) Measure the bearing of town B from town C. … [1] (d) Town D is 84 km from town A and 42 km from town C. (i) In this part, use a ruler and compasses only and show your construction arcs. On the diagram, construct a possible position for town D. [3] (ii) A plane takes 10 minutes to fly the 84 km from town A to town D. Work out the average speed of the plane in kilometres per hour. … km/h [2] (e) The bearing of town E from town A is 118°. Work out the bearing of town A from town E. … [2]

11 marks

Mark scheme: 5(a) 51.6 2 B1 for 4.3[cm] 5(b) [0]47 1 5(c) 292 1 5(d)(i) Arc centre A radius 7 cm 1 Arc centre C radius 3.5 cm 1 One point marked at intersection 1 If zero scored, SC1 for any arc centred on A or C, of correct arcs or correct point marked with no arcs 5(d)(ii) 504 2 M1 for 84 ÷ their time or 84 × 6 5(e) 298 2 M1 for 118 + 180 oe

This question in 0580/31 Oct/Nov 2017

8 Three children from the same family travel from their home to the same school. Caroline cycles to school. Rob runs to school. William walks to school. School Caroline Rob 8 6 Distance (km) 4 2 Home 0 07 00 07 30 08 00 08 30 09 00 Time The travel graph shows the journeys to school for Caroline and Rob. Rob leaves home before Caroline. (a) Explain what is happening when the two lines intersect on the travel graph. … … [1] (b) Work out Rob’s speed in km/h. … km/h [2] (c) William leaves home at 07 25. He walks to school at a constant speed of 6 km/h. On the grid, draw William’s journey. [1] (d) At what time is the distance between Rob and William greatest? … [1] (e) Complete this list of names in the order they arrive at school. First … Second … Third … [1]

6 marks

Mark scheme: 8(a) Caroline cycles past Rob oe 1 8(b) 9.6 2 8 M1 for [× 60 ] 50 8(c) Ruled line from (07 25, 0) to 1 (08 45, 8) 8(d) 08 00 1 8(e) Caroline 1 FT from William’s straight line, provided it William reaches at 8 km Rob

This question in 0580/31 May/June 2018

3 A car company has three sales people, Anna, Mustapha and Joshua. (a) During March, Anna sold 21 cars, Mustapha sold 12 cars and Joshua sold 15 cars. Write down and simplify the ratio of the number of cars they sold during March. Anna : Mustapha : Joshua = … : … : … [2] (b) Each month, they receive a bonus which is proportional to the number of cars they sell. The total bonus in March is $1248. (i) Show that Anna receives a bonus of $546. [1] (ii) Calculate the bonuses received by Mustapha and Joshua. Mustapha $ … Joshua $ … [2] 3 (c) The total bonus of $1248 is of the total profit in March. 7 Calculate the total profit in March. $ … [2] (d) Ella wants to buy a car with a price of $13 500. The company reduces this price by 16%. Ella then pays a deposit of $500. Show that the amount left for her to pay is $10 840. [2] (e) Ella borrows $10 840 from a bank. She pays this back over 3 years at a rate of $340 per month. (i) Show that the total amount she pays back during the 3 years is $12 240. [1] (ii) Calculate the percentage increase from $10 840 to $12 240. … % [3]

13 marks

Mark scheme: 3(a) 7 : 4 : 5 2 B1 for any correct ratio other than 21 : 12 : 15, not in simplest form 3(b)(i) 7 B1 oe × 1248 16 3(b)(ii) [Mustapha] 312 2 B1 for each [Joshua] 390 or 1248 M1 for × k where k = 12 or 15 21 + 12 + 15 1248 or × k oe where their 7 + their 4 + their 5 k = their 4 or their 5 3(c) 2912 2 M1 for 1248 ÷ 3 [× 7] 3(d) 13 500 – 0.16 × 13 500 − 500 M2 M1 for 0.16 × 13 500 or 0.84 × 13 500 seen or 0.84 × 13 500 − 500 3(e)(i) 3 × 12 × 340 B1 3(e)(ii) 12.9 or 12.91 to 12.92 3 12240 − 10840 M2 for [× 100 ] 10840 12240 or × 100 [ − 100 ] or 10840  12240   − 1  [× 100 ]  10840  12240 or M1 for 12240 – 10840 or oe 10840

This question in 0580/32 May/June 2018

5 The scale drawing represents three sides, AB, BC and CD, of a wildlife park. The scale is 1 centimetre represents 50 metres. A B C D Scale: 1 cm to 50 m (a) Find the actual distance AB in metres. … m [2] (b) Point E is 550 metres from A and 600 metres from D. Use a ruler and compasses only to find the point E and draw the lines AE and DE. [3] (c) Two straight paths cross the wildlife park, ABCDE. Using a straight edge and compasses only, construct (i) the path that bisects angle ABC, [2] (ii) the path that is equidistant from point C and point D. [2] (d) The path from B crosses over a circular lake with radius 150 m. The centre of the lake is on this path and is 350 m from B. (i) On the scale drawing, construct the lake. [3] (ii) Calculate the actual circumference of the lake in metres. … m [2]

14 marks

Mark scheme: 5(a) 250 2 B1 for 5 [ cm] oe 5(b) Correct point E joined to A and D 3 B2 for correct point E with arcs without with ruled lines and with arcs lines or correct ruled shape without arcs or B1 for drawing AE = 11 cm or drawing DE = 12 cm or correct point E without arcs and lines 5(c)(i) Correct ruled bisector of angle ABC B2 B1 for a correct ruled angle bisector with which reaches DE with two correct no/wrong arcs or two correct pairs of arcs pairs of arcs 5(c)(ii) Correct ruled perpendicular bisector B2 B1 for a correct ruled perpendicular of side CD which reaches AE with bisector with no/wrong arcs or two correct two correct pairs of arcs pairs of arcs 5(d)(i) Constructed circle, centre 7 cm from 3 3FT along their (c)(i) B along bisector of ABC, with radius B1 for a circle, centre 7 cm from B, any 3 cm radius M1 for a circle, radius 3 cm seen anywhere 5(d)(ii) 942 or 943 or 942.4 to 942.6 2 M1 for (2 × 150)π or 300π soi

This question in 0580/32 May/June 2018

7 Louise leaves home at 09 55 and cycles the 5.6 km to the supermarket at a constant speed. She takes 15 minutes to complete the journey. (a) Write down the time she arrives at the supermarket. … [1] (b) Calculate Louise’s average speed from her home to the supermarket (i) in kilometres per hour, … km/h [1] (ii) in metres per second, giving your answer correct to 1 decimal place. … m/s [2] (c) Louise stays at the supermarket for 23 minutes. On the grid opposite, draw the travel graph of her journey from home and her stay at the supermarket. [2] (d) Louise’s mother leaves home at 10 07 to meet Louise at the supermarket. She cycles at a constant speed of 28 km/h. (i) Work out how long she takes for the 5.6 km journey. Give your answer in minutes. … min [2] (ii) On the grid, show her mother’s journey. [1] (e) They cycle home together at a constant speed and arrive at 10 54. (i) On the grid, show their journey home. [1] (ii) Calculate, in km/h, their constant speed on the journey home. … km/h [2] 7 6 Supermarket 5 4 Distance from home (km) 3 2 1 Home 0 09 50 10 00 10 10 10 20 10 30 10 40 10 50 11 00 Time

12 marks

Mark scheme: 7(a) 10 10 1 7(b)(i) 22.4 1 7(b)(ii) 6.2 2 2FT their (b)(i) × 1000 ÷ (60 × 60) oe rounded to 1dp or M1 for their (b)(i) × 1000 ÷ (60 × 60) oe or 5600 ÷ (15 × 60) oe 7(c) Two correct ruled lines 2 B1FT for a line (09 55, 0) to (their 7(a), 5.6) B1FT for horizontal line (their 7(a), 5.6) to (their 7(a) + 23, 5.6) 7(d)(i) 12 2 M1 for 5.6 ÷ 28 [× 60] 7(d)(ii) Correct line 1 FT line from (10 07, 0) to (10 07 + their (d)(i), their 5.6) 7(e)(i) Correct line 1 FT line from (their 7(a) + 23, 5.6) to (10 54, 0) 7(e)(ii) 16 2 2FT 5.6 ÷ (their time in minutes) × 60 M1 for 5.6 ÷ 21 [× 60] soi or for 5.6 ÷ (their time in minutes)[× 60]

This question in 0580/32 May/June 2018

1 (a) The table shows the temperature at Lexford Station at 10 00 each day for a week. Day Mon Tue Wed Thu Fri Sat Sun Temperature - 3 4 - 1 0 - 5 2 1 (°C) (i) Write down the day which had the coldest temperature. … [1] (ii) Work out the difference in the temperature between Monday and Tuesday. … °C [1] (iii) The temperature falls 6°C from 10 00 to midnight on Sunday. Work out the temperature at midnight. … °C [1] (b) The distance between Lexford Station and Crowton Station is 6.5 km. (i) A train travels between these stations at an average speed of 39 km/h. Work out how long, in minutes, it takes the train to travel between these stations. … min [3] (ii) Each wheel on the train has a diameter of 1.8 m. Work out the number of complete turns each wheel makes in travelling the 6.5 km. … [4] (c) A northbound train leaves Lexford Station every 30 minutes. A bus leaves Lexford Station every 45 minutes. At 11 40 a northbound train and a bus leave the station together. Find the next time when this happens. … [3] (d) Here is part of a timetable for trains going east to west from Lexford Station. Lexford 09 14 09 47 10 21 11 15 11 48 Crowton 09 26 09 59 10 33 11 27 12 00 Doniton Halt 09 42 10 15 10 49 11 43 12 16 Mosshead 10 01 10 34 11 08 12 02 12 35 (i) Work out the number of minutes the 09 14 train takes to travel from Lexford to Mosshead. … min [1] (ii) Freda must arrive at Mosshead by 11 30. Write down the latest time she can catch a train from Lexford. … [1] (e) 437 people go on a coach trip. Each coach seats 62 people. How many coaches are needed? … [2]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Fri[day] 1 1(a)(ii) 7 1 1(a)(iii) –5 1 1(b)(i) 10 cao 3 6.5 × 60 M2 for oe 39 or M1 for distance ÷ speed 1(b)(ii) 1149 4 M2 for (6.5 × 1000) ÷ (π × 1.8) oe or M1 for π × 1.8 oe A1 for 1149.3 to 1149.5 B1 for their answer to at least 1dp truncated to the integer 1(c) 13 10 3 M2 for [LCM=] 2 × 3 × 3 × 5 or 90 or M1 for [30=] 2 × 3 × 5 or [45=] 3 × 3 × 5 OR M2 for listing times or multiples to at least 13 10 or 90 or M1 for adding times i.e. one correct addition e.g. 12 10 1(d)(i) 47 1 1(d)(ii) 10 21 1 1(e) 8 2 M1 for 437 ÷ 62 oe implied by 7.04… or 7.05

This question in 0580/33 May/June 2018

6 Mr Patel is travelling by train to the city. He is going to the library. 36 32 Library City station 28 24 Distance 20(km) 16 Lanay 12 station 8 4 Keela 0 station 09 00 09 30 10 00 10 30 11 00 11 30 12 00 Time The travel graph shows his journey from Keela station to the library. (a) Write down the total time it takes Mr Patel to travel from Keela station to the library. … min [1] (b) Work out the speed of the train between Lanay station and City station in km/h. … km/h [2] (c) Use the following information to complete the travel graph for Mr Patel. • He spends 35 minutes at the library. • He walks back to City station at the same constant speed he walked to the library. • The train takes 20 minutes to travel from City station to Lanay station. • The train stops for 10 minutes at Lanay station. • The train travels at a constant speed of 48 km/h from Lanay station to Keela station. [4]

7 marks

Mark scheme: 6(a) 55 1 6(b) 108 2 18 M1 for × [ 60 ] oe 10 6(c) Correct graph 4 Ruled lines B1 for ruled lines (09 55, 31.5) to (10 30, 31.5) (09 55, 31.5) to (10 30, 31.5) and (10 30, 31.5) to (10 50, 30) (10 30, 31.5) to (10 50, 30) (10 50, 30) to (11 10, 12) B1 for ruled line from (their10 50, 30) to (their 10 50+20, 12) (11 10, 12) to (11 20, 12) B1 for ruled line from (their 11 10, 12) to (their 11 10+10, 12) (11 20, 12) to (11 35, 0) B1 for ruled line (their11 20, 12) to (their11 20+15, 0) or for 15 mins soi

This question in 0580/32 Feb/March 2019

1 Here is part of the menu for Jamie’s café. Menu Price ($) Tea 2.35 Coffee 3.40 Lemonade 1.80 Cake 4.45 Biscuit 0.85 (a) Sue has one tea and one cake. Calculate how much she pays. $ … [1] (b) Derrick has one coffee and two biscuits. How much change does he receive from a $10 note? $ … [2] (c) Harriet works at the café for 34 hours each week. She is paid $8.25 for each hour. (i) Work out the amount she is paid each week. $ … [1] (ii) One week she works 8 hours extra. The extra hours are paid at 1.5 times her usual rate of $8.25 for each hour. Work out the total amount she is paid for that week. $ … [2] (d) Peter works these hours each week at the café. Day Time Monday 08 30 to 16 00 Tuesday 10 00 to 17 00 Thursday 08 30 to 16 30 Saturday 08 00 to 18 30 Work out the number of hours he works in one week. … hours [2] (e) Jamie buys a clock for the café from Japan for 9395 yen. The exchange rate is $1 = 110.27 yen. Work out the cost of the clock in dollars, correct to the nearest cent. $ … [3] (f) Jamie invests $12 000 at a rate of 5% per year compound interest. Calculate the value of his investment at the end of 3 years. $ … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6.8[0] 1 1(b) 4.9[0] 2 M1 for 3.4[0] + 2 × [0].85 soi 1(c)(i) 280.5[0] 1 1(c)(ii) 379.5[0] 2 FT their (c)(i) + 99 M1 for 8 × 1.5 × 8.25 soi or (8 × 1.5 + 34) × 8.25 soi 1(d) 33 2 M1 for 7.5, 7, 8, 10.5 1(e) 85.20 cao 3 B2 for 85.1999… OR M1 for 9395 ÷ 110.27 B1 for their answer to at least 3 dp correctly rounded to 2 dp 1(f) 13 891.5[0] 3 M2 for 12 000 × (1 + 1005 )3 oe or M1 for 12 000 × (1 + 1005 )2 oe

This question in 0580/31 May/June 2019

1 (a) Write this number in figures. One million three hundred and two thousand five hundred and ninety-six. … [1] (b) (i) Two numbers are added together to give the number in the box immediately above. 2 5 – 3 – 4 Complete the diagram. [2] (ii) Two numbers are multiplied together to give the number in the box immediately above. 5 – 3 – 4 Complete the diagram. [3] (c) Write these in order of size, starting with the smallest. 5 -1 18.4% .183 # 10 5-1 27 … 1 … 1 … 1 … [2] smallest (d) Work out 142 as a percentage of 304. … % [1] (e) (i) Find the highest common factor (HCF) of 28 and 98. … [2] (ii) Find the lowest common multiple (LCM) of 28 and 98. … [2] (f) The average distance from Earth to Mars is .225 # 108 km. A space ship travels from Earth to Mars at an average speed of .58 # 104 km/h. Find how long, in hours, the journey takes. … hours [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 302 596 1 1(b)(i) −5 2 B1 for −7 −7 B1FT for 2 + their −7 1(b)(ii) −180 3 B1 for −15 −15 12 B1 for 12 and B1FT for their −15 × their 12 1(c) 5 2 M1 for 3 in correct order or for 1.83 × 10−1 18.4% 5−1 27 5 three of [ =]0.185 … , [18.4% =] 0.184, 27 [1.83 × 10−1 =] 0.183, [5−1=] 0.2 1(d) 46.7 or 46.71... 1 1(e)(i) 14 2 B1 for answer of 2 or 7 or 2 × 7 or 2 × 2 × 7 and 2 × 7 × 7 or list (28 =) 2, 2, 7 and (98 =)2, 7, 7 1(e)(ii) 196 2 B1 for 28, 56, 84, 112,… and 98, 196 or [1 ×]2 × 2 × 7 × 7 or 196k 1(f) 3880 or 3879[⋅…] 2 M1 for 2.25 × 108 ÷ 5.8 × 104 oe or 3.88(0...) × 103 or 3.879… × 103 or figs (388 or 3879…) as the answer

This question in 0580/33 May/June 2019

7 The travel graph shows part of a train journey between station A and station C. 160 Station C 140 120 Distance (km) 100 Station B 80 60 40 20 Station A 0 12 30 13 00 13 30 14 00 14 30 15 00 15 30 Time (a) (i) Calculate, in km/h, the speed of the train between station A and station B. … km/h [2] (ii) The train leaves station B at 14 40. For how many minutes did the train stop at station B? … min [1] (iii) The train travels at a constant speed between station B and station C, arriving at 15 20. Complete the travel graph for the journey between station B and station C. [1] (iv) On which part of the journey was the train travelling faster? Between station … and station … [1] (b) Another train leaves station C at 12 45. It travels to station A at a constant speed of 62 km/h without stopping at station B. (i) Work out how long, in hours and minutes, this journey takes. … h … min [2] (ii) Write down the time this train arrives at station A. … [1] (iii) On the grid, show the journey of this train. [1] (iv) Find the distance from station A when the two trains pass each other. … km [1]

10 marks

Mark scheme: 7(a)(i) 120 2 M1 for 90 ÷ their time for A to B [× 60] or B1 for 2[km/min] 7(a)(ii) 10 1 7(a)(iii) Ruled line from (14 40, 90) 1 to (15 20, 155) 7(a)(iv) A [and] B 1 7(b)(i) 2 [hours] 30 [minutes] 2 M1 for 155 ÷ 62 7(b)(ii) 15 15 1 FT their (b)(i) + 12 45 7(b)(iii) Ruled line from (12 45, 155) to 1 (their7(b)(ii), 0) 7(b)(iv) 58 to 63 1 FT their crossing point

This question in 0580/33 May/June 2019

2 Henry decorates a room. (a) Complete Henry’s shopping bill. Item Cost ($) 3 tins of paint at $15.95 each 2 brushes at $7.50 each 1 roll of tape at $2.90 2.90 Total [2] (b) 5.3 m 1.8 m NOT TO 3.2 m SCALE 2.4 m The diagram shows the floor of the room. (i) Calculate the area of the floor. … m2 [2] (ii) Henry buys varnish for the floor of the room. 500 ml of varnish covers 8 m2 of floor. Calculate the amount of varnish Henry needs. … ml [2] (c) This scale drawing shows the window in the room. The scale is 1 centimetre represents 40 centimetres. Scale: 1 cm to 40 cm Work out the actual length and height of the window. Length = … cm Height = … cm [2] (d) NOT TO SCALE 2.6 m 1.9 m 1.8 m The diagram shows one wall of the room. Calculate the area of the wall. … m2 [2] (e) Henry buys a circular mirror for the room. The diameter of the mirror is 80 cm. Calculate the circumference of the mirror. … cm [2]

12 marks

Mark scheme: 2(a) 47.85 2 B1 for one of first two values correct 15[.00] 65.75 2(b)(i) 12.9 2 M1 for 1.8 × 5.3 + 2.4 × (3.2 – 1.8) oe or 3.2 × 2.4 + 1.8 × (5.3 – 2.4) oe or 5.3 × 3.2 − (5.3 – 2.4) × (3.2 – 1.8) oe 2(b)(ii) 806.25 2 FT their (b)(i) × 62.5 M1 for their (b)(i) ÷ 8 × 500 oe 2(c) 160 2 B1 for each 100 or for 4 and 2.5 seen 2(d) 4.05 2 1 M1 for × (9.1 + 6.2 ) × 8.1 oe 2 2(e) 251 or 251.3 to 251.4 2 M1 for π × 80 oe

This question in 0580/32 Oct/Nov 2019

5 (a) c 40 30 Cost ($) 20 10 0 0 1 2 3 4 5 6 7 8 9 10 d Distance travelled (km) (i) The graph shows the cost, $c, of travelling a distance, d km, with Saanvi’s Taxis. (a) Write down the cost of a 4 km journey. $ … [1] (b) Complete this statement. Saanvi’s Taxis cost $ … for each kilometre travelled. [1] (c) Find the equation of the line. c = … [1] (ii) Krishna’s Taxis cost $5 to hire plus $2 for each kilometre travelled. (a) Show that the cost of a 4 km journey with Krishna’s Taxis is $13. [1] (b) Find an equation for the cost, $c, of travelling d kilometres with Krishna’s Taxis. c = … [2] (c) On the grid, draw a line to show the cost of travelling with Krishna’s Taxis. [2] (d) Mrs Singh wants to hire a taxi. She says that Saanvi’s Taxis are always cheaper than Krishna’s Taxis. Is Mrs Singh correct? Give a reason for your answer. Use your graph to help you. … because … … [1] (b) A minibus can be hired from Dhruv’s Minibuses. The cost is $h per hour plus $p per passenger. (i) When the minibus is hired for 3 hours with 10 passengers the cost is $61. Complete the equation. 3h + 10p = … [1] (ii) When the minibus is hired for 5 hours with 8 passengers the cost is $80. Write this information as an equation. … = … [2] (iii) Solve your two simultaneous equations to find h and p. You must show all your working. h = … p = … [4]

16 marks

Mark scheme: 5(a)(i)(a) 14 1 5(a)(i)(b) 3.5[0] 1 5(a)(i)(c) [c=] 3.5d 1 FT their (a)(i)(b) 5(a)(ii)(a) 2 × 4 + 5 1 5(a)(ii)(b) [c=] 2d + 5 2 M1 for 2 d + k or md + 5, m ≠ 0 5(a)(ii)(c) Correct ruled line 2 M1 for ruled line with intercept (0, 5) or for ruled line with gradient 2 or for 2 correct points plotted or for their c= 2d + 5 correctly drawn 5(a)(ii)(d) No, with correct reason 1 FT if two intersecting linear graphs 5(b)(i) 61 1 5(b)(ii) 5h + 8p = 80 2 M1 for 5h + 8p 5(b)(iii) For correctly equating one set of M1 coefficients For correct method to eliminate M1 one variable [h =] 12 A1 [p =] 2.5 A1 If 0 scored, SC1 for 2 values satisfying one of the original equations or SC1 for both correct but no working

This question in 0580/32 Feb/March 2020

7 (a) The diagram shows a regular polygon. (i) Write down the mathematical name for this shape. … [1] (ii) Write down the order of rotational symmetry of this shape. … [1] (b) The diagram shows part of a different regular polygon. NOT TO SCALE i e i e e is an exterior angle. i is an interior angle. The ratio e : i = 2 : 13 . (i) Work out angle e. … [3] (ii) Work out the number of sides of this regular polygon. … [1] (c) Using a straight edge and compasses only, construct the equilateral triangle ABC. Side AB has been drawn for you. A B [2] (d) In this part, all angles are in degrees. 2x NOT TO SCALE x + 23 2x - 13 (i) Use the information in the triangle to write down an equation in terms of x. … [1] (ii) Solve this equation to find the value of x. x = … [3] (iii) Work out the size of the smallest angle in the triangle. … [2]

14 marks

Mark scheme: 7(a)(i) Hexagon 1 7(a)(ii) 6 1 7(b)(i) 24 3 180 M2 for × k where k = 1, 2 or 13 2 + 13 or B1 for e + i = 180 soi 7(b)(ii) 15 1 360 FT if is an integer their (b)(i) 7(c) Correct ruled triangle with arcs 2 M1 for correct triangle without arcs or for correct arcs and no lines 7(d)(i) 2x + x + 23 + 2x – 13 = 180 oe 1 7(d)(ii) 34 3 M1 for correctly collecting their like terms in form ax + b = k M1 for correctly isolating their x k − b x = a 7(d)(iii) 55 2 M1 for evaluating 2x – 13 and x + 23 with their x

This question in 0580/33 May/June 2020

9 (a) A speedboat travels at 84 kilometres per hour. Change this speed into metres per minute. … m/min [2] (b) North X 39 km North NOT TO 21 km SCALE Y Z The speedboat starts at X and travels to Y, then to Z and then back to X. Z is due south of X and Y is due west of Z. XY = 39 km and XZ = 21 km. (i) Calculate YZ. YZ = … km [3] (ii) Calculate angle YXZ. Angle YXZ = … [2] (iii) Find the bearing of Y from X. … [1]

8 marks

Mark scheme: 9(a) 1400 2 84 × 1000 M1 for 60 or B1 for final answer figs 14 9(b)(i) 32.9 or 32.86… 3 M2 for 39 2 − 212 or better or M1 for x 2 + 212 = 39 2 9(b)(ii) 57.4 or 57.42 2 FT their (b)(i) if used in tan or sin for angle at X 21 M1 for cos = oe 39 If 0 scored, SC1 for finding other angle in triangle, possibly with their 32.9 9(b)(iii) 237.4 1 FT their (b)(ii) + 180

This question in 0580/33 May/June 2020

2 A family go on a skiing holiday to America. (a) The hotel has 840 rooms. 735 rooms are occupied. Calculate the percentage of rooms that are occupied. … % [1] (b) The temperature in the hotel is 21 °C. The temperature in the hotel is 26.7 °C warmer than at the top of the mountain. The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain. Work out the temperature at the bottom of the mountain. … °C [2] (c) Hire cost ($) Equipment 3 days 4 days 7 days Ski equipment 80.80 94.60 128.00 Adult Snowboard equipment 96.80 112.60 151.20 Helmet 12.80 15.20 20.70 Ski equipment 47.60 55.40 75.80 Child Snowboard equipment 59.00 70.20 94.60 Helmet 10.40 12.00 16.70 There are two adults and one child in the family. They hire all their equipment. The child skis for 3 days and snowboards for 4 days. Both adults ski for 7 days. All three of them hire a helmet for 7 days. Work out the total cost of the equipment hire for the family. $ … [2] (d) A ski lift, when full, takes 4000 passengers per hour. This lift works for 10 hours a day. One day, this lift is 90% full for 3 hours and 75% full for 7 hours. Work out the number of passengers who take the lift that day. … [3] (e) The family buy their lift passes before the holiday for a total of 51 400 rupees. In America, the passes cost a total of $684. The exchange rate is 1 rupee = $0.0129 . Show that the family save 1620 rupees, correct to the nearest 10 rupees, by buying the passes before their holiday. [3] (f) The height, h metres, of the mountain is 2642 m, correct to the nearest metre. Complete this statement about the value of h. … G h 1 … [2]

13 marks

Mark scheme: 2(a) 87.5 1 2(b) −2.5 2 M1 for 21 − 26.7 or 26.7 − 3.2 2(c) 431.9[0] 2 M1 for 47.6 + 70.2 + 16.7 oe or 2 × 128 + 2 × 20.7 oe or B1 for 134.5, 148.7, 297.4, 58.1 or 373.8 or 283.2 2(d) 31 800 3 90 M2 for 3 × × 4000 oe 100 75 or 7 × × 4000 oe 100 90 or M1 for × 4000 oe 100 75 or × 4000 oe 100 2(e) 684 M1 or 684 − 51400 × 0.0129 0.0129 53023 − 51400 M1 20.94 or 0.0129 1623 A1 2(f) 2641.5 2642.5 2 B1 for each If 0 scored, SC1 for answers correct but reversed

This question in 0580/32 Feb/March 2021

3 The scale drawing shows the position of town R on a map. The scale is 1 centimetre represents 5 kilometres. North R Scale : 1 cm to 5 km (a) Town M is 36 km from R on a bearing of 163°. Mark the position of M on the map. [2] (b) A railway track, 36 km long, is to be built in a straight line from R to M. (i) The track costs $1070 per metre to build. Work out the cost of building the track. $ … [2] (ii) 15 people can build 60 metres of track per day. Work out how many days it will take 45 people to build the whole track. … days [3] (c) Trains will travel the 36 km at an average speed of 75 km/h. Work out the journey time. Give your answer in minutes. … min [2] (d) Town K is on a bearing of 312° from R. Work out the bearing of R from K. … [2]

11 marks

Mark scheme: 3(a) M marked correctly 2 B1 for correct bearing B1 for correct distance 3(b)(i) 38 520 000 2 M1 for [1070 ×] 36 × 1000 or 1070 × 36 or figs 3852 oe 3(b)(ii) 200 3 36 × 1000 × 15 M2 for oe 60 × 45 or figs 2 nfww 36 × 1000 60 × 45 M1 for oe or oe 60 15 3(c) 28.8 2 36 M1 for [× 60 ] 75 3(d) 132 2 M1 for 312 −180 or 180 − 48

This question in 0580/31 May/June 2021

3 Pierre travels from his home in Lyon to Singapore. (a) He travels by train from Lyon to Paris. The train leaves Lyon at 9.05 am and arrives in Paris at 1.30 pm. (i) Write 1.30 pm in the 24-hour clock system. … [1] (ii) Work out, in hours and minutes, the time the train journey takes. … h … min [1] (b) He then travels by plane from Paris to Singapore. The plane leaves Paris at 16 35 on Thursday and arrives in Singapore 13 hours and 45 minutes later. The local time in Singapore is 6 hours ahead of the local time in Paris. Work out the day and time in Singapore when the plane arrives. Day … Time … [3] (c) The distance from Paris to Singapore is 10 736 kilometres. Work out the average speed of the plane. … km/h [2] (d) Pierre buys a watch for 400 Singapore dollars. The exchange rate is 1 Singapore dollar = 0.658 euros. Work out the cost of the watch in euros. … euros [1] (e) Pierre stays at a hotel in Singapore for 5 nights. The cost per night of the room is $170. His total hotel bill is $975.40 . Calculate how much Pierre spends on other hotel items. $ … [2]

10 marks

Mark scheme: 3(a)(i) 13 30 1 3(a)(ii) 4 [h] 25 [min] 1 3(b) Friday 3 B1 for Friday, as final answer 12 20 B2 for 12 20, as final answer or B1 for [0]6 20 or 22 35 or 19h 45 min or 12 20 seen then spoilt or M1 for their arrival time of flight + 6 hours 3(c) 780.8 2 M1 for 10 736 ÷ time of flight 3(d) 263.2[0] cao 1 3(e) 125.4[0] cao 2 M1 for 975.4 – 5 × 170 or better

This question in 0580/32 May/June 2021

1 Ray owns an electrical shop. (a) The table shows the opening times of the shop. Sunday Closed Monday Closed Tuesday 08 00 to 12 30 and 13 30 to 17 00 Wednesday 08 00 to 12 30 and 13 30 to 17 00 Thursday 08 00 to 12 30 and 13 30 to 17 00 Friday 08 00 to 12 30 and 13 30 to 17 00 Saturday 08 00 to 13 00 and 14 00 to 19 00 Work out how many hours the shop is open in one week. … hours [3] (b) Saeed buys 2 ovens costing $440 each, 4 grills costing $184 each and 3 fridges costing $1280 each. Calculate the total cost. $ … [3] (c) Alice buys 3 batteries costing $2.85 each. Work out how much change she receives from $10. $ … [2] (d) Cherie works 32 hours one week and she is paid $8.48 per hour. In another week she works 37 hours. For each hour over 32 hours she works, she is paid 1.25 times her hourly rate. Calculate her pay for the week she works 37 hours. $ … [4] (e) Ray buys a toaster for $36. When he sells it he makes a profit of 40%. Calculate the selling price of this toaster. $ … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 42 3 M1 for 4.5 + 3.5 or 9 – 1 M1 for 5 + 5 or 11 – 1 or M1 for 4.5 × 4 + 5 or 18 + 5 oe M1 for 3.5 × 4 + 5 or 14 + 5 oe 1(b) 5456 3 B2 for 880, 736 and 3840 or B1 for one of these or M1 for 2 × 440 or 4 × 184 or 3 × 1280 1(c) 1.45 2 M1 for 10 – 3 × 2.85 1(d) 324.36 cao 4 M1 for 32 × 8.48 M1 for 8.48 × 1.25 oe M1 for (37 – 32) × their 10.6[0] Accept alternative methods 1(e) 50.4[0] 2 M1 for 36 × 1.4 oe or B1 for 14.4[0]

This question in 0580/33 May/June 2021

3 360 people go on a school trip to one of four places. Some of the information is shown in the table. Adventure Botanic Wildlife Red castle Total park gardens centre Boys 65 12 36 Girls 9 62 163 Staff 15 3 37 Total 144 24 121 71 360 (a) Complete the table. [3] (b) Find the probability that (i) a girl, picked at random, visits the Wildlife centre, … [1] (ii) a person, picked at random from those visiting the Botanic gardens, is a girl, … [1] (iii) a person, picked at random, visits the Adventure park or the Botanic gardens. … [1] (c) The people who visit the Adventure park travel by coach. Each coach has 52 seats for passengers. Complete this statement. The least number of coaches needed for the trip to the Adventure park is … and there will be a total of … empty seats. [2] (d) The school hires one coach from each of two different companies for the trip to Red castle. A coach from Fast Track coaches costs $600 plus $0.72 per kilometre travelled. The total cost, in dollars, for travelling x kilometres is 600 + 0.72x . (i) A coach from Rapid coaches costs $550 plus $1.12 per kilometre travelled. Write an expression for the total cost, in dollars, for travelling x kilometres. … [1] (ii) Both companies charge the same amount for the trip. Write down an equation and solve it to find the distance travelled. … km [3] (e) The length, l km, of the journey to the Wildlife centre is 53 km, correct to the nearest kilometre. Complete this statement about the value of l. … G l 1 … [2] (f) Samira takes $31.50 to spend in the Botanic gardens. 2 (i) She spends of this money on food. 7 Work out how much Samira spends on food. $ … [1] (ii) At the end of the visit to the Botanic gardens, Samira has $4.50 left. What fraction of her money does Samira spend? Give your answer in its simplest form. … [2]

17 marks

Mark scheme: 3(a) 3 B2 for 4 or 5 correct A B W R Tot or B1 for 2 or 3 correct B 47 160 G 64 28 S 12 7 Tot 3(b)(i) 62 1 oe 163 3(b)(ii) 3 1 oe 8 3(b)(iii) 7 1 oe 15 3(c) 3, 12 2 B1 for 3 (coaches) nfww or M1 for 144 ÷ 52 3(d)(i) 550 + 1.12x 1 3(d)(ii) 600 + 0.72x = 550 + 1.12x 1 FT 600 + 0.72x = their (d)(i) 125 2 M1FT for isolating x terms and constant terms or better for their linear equation DEP on their (d)(i) of the form ax + b (a ≠ 0) 3(e) 52.5, 53.5 2 B1 for each If zero scored, SC1 for both values correct but reversed 3f(i) 9 1 3(f)(ii) 6 2 31.5 [ 0 ] − 4.5 [ 0 ] cao M1 for oe 7 31.5 [ 0 ]

This question in 0580/31 Oct/Nov 2021

6 (a) The diagram shows the travel graph of a train journey from Wengen to Kleine Scheidegg. 7 Kleine Scheidegg 6 5 Wengernalp 4 Distance from Wengen (km) 3 2 Allmend 1 Wengen 0 13 50 14 00 14 10 14 20 14 30 Time (i) Explain what happens between 14 09 and 14 10. … [1] (ii) Find the journey time from Allmend to Wengernalp in minutes. … min [1] (iii) Calculate the average speed for the train journey from Wengen to Kleine Scheidegg. Give your answer in km/h. … km/h [3] (iv) Another train travels from Kleine Scheidegg to Wengen. The table gives information about its journey. Station Arrival time Departure time Kleine Scheidegg 14 01 Wengernalp Train does not stop Allmend 14 18 14 20 Wengen 14 30 On the travel graph, draw the journey for this train. [3] (v) Write down the time when the two trains pass each other. … [1] (b) The temperature in Wengen at 5 am was -3 °C. At 4 pm the temperature has increased by 10 °C. Work out the temperature at 4 pm. … °C [1] (c) A formula to work out the temperature at different heights above Wengen is h T = 2 - 130 where T is the temperature in °C and h is the height, in metres, above Wengen. Kleine Scheidegg is 780 m above Wengen. Work out the temperature at Kleine Scheidegg. … °C [1]

11 marks

Mark scheme: 6(a)(i) [Train] stopped oe 1 6(a)(ii) 10 1 6(a)(iii) 15.36 3 B1 for 25 [mins] or 6.4 [km] or 0.416[6…][h] or 0.417[h] soi M1 for 6.4 ÷ their time 6(a)(iv) Three correct ruled lines 3 B1 for a line from (14 01, 6.4) to (14 18, 1.9) B1FT for a line from their (14 18, 1.9) to (their 14 18 + 2, their 1.9) B1FT for a line from (their (14 18 + 2), (their 1.9) to (14 30, 0) 6(a)(v) 14 09 1 FT their (a)(iv) 6(b) 7 1 6(c) –4 1

This question in 0580/31 Oct/Nov 2021

3 (a) Simone completes one lap of a 400 metre running track in 79 seconds. Work out how long it will take her to run 6 km at the same rate. Give your answer in minutes and seconds. … minutes … seconds [4] (b) The probability that she does not win a race is 0.94 . Find the probability that she wins a race. … [1] (c) Each day she records the number of laps she runs. Here is her record for one week. 15 42 28 16 24 15 32 (i) Write down the mode. … [1] (ii) Find the median. … [2] (iii) Find the range. … [1] (d) Wilfred records his times, in seconds, for each of 5 laps. 59 74 69 63 65 After running a 6th lap his mean time is 67 seconds. Find his time for the 6th lap. … seconds [3]

12 marks

Mark scheme: 3(a) 19 [min] 45 [secs] 4 6000 79 M3 for × oe 400 60 or B2 for figs 1975 6000 or M2 for 79 × oe 400 or B1 for figs 1185 6000 400 79 79 or M1 for or or or 400 79 400 0.4 oe 3(b) 0.06 oe 1 3(c)(i) 15 1 3(c)(ii) 24 2 M1 for full list or 15 15 16 24 or 42 32 28 24 3(c)(iii) 27 1 3(d) 72 3 M2 for 6 × 67 – (59 + 74 + 69 + 63 + 65) oe or M1 for (59 + 74 + 69 + 63 + 65 + x) ÷ 6 = 67 or 6 × 67 oe

This question in 0580/32 Oct/Nov 2021

1 Roberto and his family fly from London to Los Angeles on a holiday. (a) The flight takes 11 hours 15 minutes. (i) The flight leaves London at 15 40 local time. The local time in Los Angeles is 8 hours behind the local time in London. Work out the local time in Los Angeles that the plane arrives. … [2] (ii) The plane flies a total of 8760 km. Calculate the average speed of the plane. … km/h [3] (b) Roberto hires a car. (i) The cost of hiring a car is $56 per day, plus a fixed cost of $436. Write down a formula for the cost, C dollars, of hiring a car for d days. … [2] (ii) Roberto is given a car at random. There are four colours of car. Colour Red Silver Black White Probability 0.17 0.24 0.3 Complete the table. [2] (c) The family visit a national park which has an area of 4986 km2. (i) Write 4986 correct to the nearest hundred. … [1] (ii) Write 4986 in standard form. … [1] (d) A ticket for the park costs $17.50 plus 8% tax. Calculate the amount of tax paid. $ … [1] (e) The scale drawing shows the positions of two viewing points, A and B, in the park. The scale is 1 centimetre represents 5 kilometres. North North B A Scale : 1 cm to 5 km (i) Work out the actual distance between point A and point B. … km [2] (ii) Point C is 20 km from point A on a bearing of 072°. On the scale drawing mark the position of point C. [2]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 18 55 2 B1 for 07 40 or 02 55 or 3[h] 15 [min] or M1 for departure time + 11h 15 min −8h evaluated as a time with one interval correctly added 1(a)(ii) 779 or 778.6 to 778.7 3 8760 M2 for 8760 ÷ 11.25 oe × 60 675 or B1 for 11.25 or M1 for 8760 ÷ their time 1(b)((i) C = 56d + 436 cao 2 B1 for C = 56d + 436 seen and spoilt or 56d + 436 as final answer 1(b)(ii) 0.29 2 M1 for 1 – (0.17 + 0.24 + 0.3) oe or better 1(c)(i) 5000 1 1(c)(ii) 4.986 × 103 1 1(d) 1.4[0] 1 1(e)(i) 35 2 B1 for 7 1(e)(ii) Correct length and bearing 2 B1 for length 4 cm from A B1 for bearing 072° from A

This question in 0580/33 Oct/Nov 2021

7 (a) 1 mile = 1.609344 kilometres Change 6 miles into metres. Give your answer correct to the nearest metre. … m [3] (b) (i) The bearing of a boat from a harbour is 322°. Work out the bearing of the harbour from the boat. … [2] (ii) The boat is 12 km from the harbour. At 2.30 pm the boat starts to sail to the harbour. The speed of the boat is 5 km/h. Work out the time the boat arrives at the harbour. … [3] (c) The scale drawing shows the positions of Shakti’s house, S, and Mairi’s house, M, on a map. The scale is 1 cm represents 4 km. North S North M Scale: 1 cm to 4 km (i) Measure the bearing of M from S. … [1] (ii) North S Scale: 1 cm to 5 km This scale drawing shows another map with Shakti’s house, S, marked on it. The scale of this map is 1 cm represents 5 km. Mark the position of Mairi’s house, M, on this map. [4]

13 marks

Mark scheme: 7(a) 9656 cao 3 M2 for 6 × 1.609344 × 1000 or M1 for 6 × 1.609344 or B1 for final answer figs 9654 to 9660 If 0 scored, SC1 for their decimal answer correctly rounded to nearest integer 7(b)(i) 142 2 M1 for 322 −180 oe or a clear diagram with both 322 or 38 marked and the reverse bearing to be found 7(b)(ii) 4.54 pm or 16 54 3 12 M1 for soi 5 A1 for 2 h 24 [mins] 7(c)(i) 107 1 7(c)(ii) The position of M correctly marked 4 B1 for SM = 9[cm] soi on the diagram  1  M1 for their SM × 4 ×    5  B1 for 7.2[cm] soi or for bearing of M drawn at 107°

This question in 0580/32 Feb/March 2022

3 Sachin, his wife and three children go on a coach holiday. (a) Each adult ticket costs $375 and each child ticket costs $194. Work out the total cost of the tickets. $ … [2] (b) A meal costs $110 plus a service charge of 18%. Calculate the total cost of the meal. $ … [2] (c) One day, the temperature at midday is 16 °C. At midnight the temperature has fallen by 23 °C. Work out the temperature at midnight. … °C [1] (d) Sachin spends $768 on holiday. 3 He spends of this amount on presents. 8 Find how much he spends on presents. $ … [1] (e) There are 604 passengers on the holiday. (i) The coach company uses coaches which can carry 46 passengers. Work out the number of coaches needed. … [2] (ii) 268 of the 604 passengers are women. Find the percentage of the passengers that are women. … % [1] (f) A coach travels at an average speed of 54 km/h. Find how long, in hours and minutes, this coach takes to travel 126 km. … h … min [3]

12 marks

Mark scheme: 3(a) 1332 2 M1 for 2  375 + 3  194 oe 3(b) 129.8[0] 2 M1 for 110  (1  10018 ) oe or B1 for 19.8[0] 3(c) −7 1 3(d) 288 1 3(e)(i) 14 2 M1 for 604 ÷ 46 or 13.1[3…] 3(e)(ii) 44.4 or 44.37… 1 3(f) 2 (h) 20 (min) 3 M1 for 126 ÷ 54 A1 for 2.33… or 140 mins If A0 scored, SC1 for their (decimal time) correctly changed to hours and minutes

This question in 0580/31 May/June 2022

6 Mr Vay works in a bank. (a) The travel graph shows Mr Vay’s journey from his home to the bank. 7 Bank 6 5 4 Distance (km) 3 2 1 Home 0 07 00 07 04 07 08 07 12 07 16 07 20 07 24 Time (i) Write down the distance Mr Vay travels in the first 8 minutes. … km [1] (ii) Explain what is happening between 07 08 and 07 12. … [1] (iii) Between which times is Mr Vay’s journey the fastest? Give a reason for your answer. Between … and … Reason … [2] (iv) Work out Mr Vay’s average speed for the whole journey. Give your answer in kilometres per hour. … km/h [3] (b) Katya takes some coins to the bank. The table shows the number of each type of coin. Number of Type of coin coins 1 cent 12 5 cent 23 10 cent 17 25 cent 9 50 cent 7 1 dollar 24 Work out the total amount of money Katya takes to the bank. Give your answer in dollars. $ … [2] (c) Adam changes $700 into euros at the bank. The exchange rate is $1 = 0.904 euros. Work out the amount Adam receives. … euros [1] (d) Clara invests $8500 for 4 years at a rate of 1.7% per year simple interest. Calculate the total interest earned during the 4 years. $ … [2]

12 marks

Mark scheme: 6(a)(i) 0.8 1 6(a)(ii) He is stationary oe 1 6(a)(iii) 07 12 07 24 2 B1 for each gradient is steepest 6(a)(iv) 16 3 6.4 M2 for  60  oe 24 their distance or M1 for their time 6(b) 32.72 cao 2 M1 for 1  12 5 23  10  17  25  9  50  7  100  24   100  oe or B1 for 12,115,170,225,350,2400 6(c) 632.8 cao 1 6(d) 578 cao 2 1.7 M1 for 8500   4  100 or B1 for final answer of 9078

This question in 0580/32 May/June 2022

3 Miguel works in an office. (a) It takes Miguel 40 minutes to drive to work. (i) He leaves home at 07 45. What time does he arrive at work? … [1] (ii) Miguel drives to work at an average speed of 57 km/h. Show that he drives 38 km. [2] (b) White paper costs w cents per sheet and pink paper costs p cents per sheet. Miguel uses 56 sheets of white paper and 21 sheets of pink paper. Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses. … cents [2] (c) Miguel has a closed box of pens. The box is in the shape of a cuboid measuring 20 cm by 12 cm by 7 cm. Calculate the surface area of the box. … cm2 [3] (d) Miguel records the length of time of each telephone call he receives, correct to the nearest minute. 7 15 6 28 8 21 17 19 20 12 11 19 12 3 20 23 14 9 4 18 (i) Complete the frequency table. You may use the tally column to help you. Time (minutes) Tally Frequency 0 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 [2] (ii) Draw a bar chart to show this information. Complete the scale on the frequency axis. Frequency 0 0 – 5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 Time (minutes) [3] (iii) Use the bar chart to write down the modal group. … — … [1]

14 marks

Mark scheme: 3(a)(i) 08 25 1 3(a)(ii) 40 2 40 57  [= 38] M1 for or 57  40 60 60 3(b) 56w + 21p final answer 2 B1 for 56w or 21p in final answer or for 56w + 21p seen then spoilt 3(c) 928 3 M2 for [2 ](20  12 + 20  7 + 12  7) oe or M1 for (20  12) or (20  7) or (12  7) 3(d)(i) 2 4 5 6 2 1 2 B1 for 4 or 5 correct frequencies If 0 scored SC1 for correct tallies if frequency column blank or all frequencies correct but not in the frequency column 3(d)(ii) Suitable scales on y-axis 1 Bars at correct height 1 FT their frequency Bars equal width 1 3(d)(iii) 16 – 20 1 FT their bar chart

This question in 0580/31 Oct/Nov 2022

3 (a) The population of Alaska is 735 720. (i) Write this number in words. … … [1] (ii) The land area of Alaska is 1 477 300 square kilometres. Work out the average number of people per square kilometre. … [1] (iii) In Alaska, the city with the highest population is Anchorage with 291 830 people. What percentage of the population of Alaska live in Anchorage? … % [1] (b) The length, L km, of a race is 1569 km, correct to the nearest kilometre. Complete this statement about the value of L. … G L 1 … [2] (c) The table gives some information about two mountains. The temperatures are taken at the top of each mountain on the same day. Maximum Minimum Height in metres temperature temperature Highest mountain Denali 6190 -9 °C -20 °C in Alaska Highest mountain Everest 8849 … °C -38 °C in the world (i) Find the difference between the height of Denali and the height of Everest. … m [1] (ii) Find the difference between the maximum temperature and the minimum temperature at the top of Denali. … °C [1] (iii) The maximum temperature at the top of Everest was 27 °C colder than the maximum temperature at the top of Denali. Complete the table. [1]

8 marks

Mark scheme: 3(a)(i) Seven hundred [and] thirty-five thousand, 1 seven hundred [and] twenty 3(a)(ii) 0.498 or 0.4980… 1 3(a)(iii) 39.7 or 39.66 to 39.67 1 3(b) 1568.5, 1569.5 2 B1 for each If 0 scored, SC1 for both values correct but reversed 3(c)(i) 2659 1 3(c)(ii) 11 1 3(c)(iii) –36 1

This question in 0580/33 Oct/Nov 2022

4 A path from Bay Park to Ocean Park passes through Sandy Cove. (a) Tia cycles along the path. The diagram shows the travel graph of Tia’s journey. 20 Ocean Park 16 Sandy Cove 12 Distance from Bay Park (km) 8 4 Bay Park 0 10 00 10 20 10 40 11 00 11 20 11 40 12 00 Time (i) Between which two times is Tia cycling the fastest? … and … [1] (ii) Andy leaves Bay Park at 10 20 and runs to Sandy Cove at a constant speed of 8 km/h. He then stops to rest until 12 00. On the travel graph, draw Andy’s journey. [2] (iii) Write down the time and the distance from Bay Park when Tia and Andy pass each other. Time … Distance … km [2] (b) In June, the number of cyclists using the path is 3546. In July, the number of cyclists using the path is 4067. Work out the percentage increase in the number of cyclists from June to July. … % [2] (c) In one week, 432 walkers and 528 runners use the path. (i) Write the ratio walkers : runners in its simplest form. … : … [1] (ii) In the same week, the ratio of cyclists and walkers using the path is cyclists : walkers = 14 : 3. Find the total of the number of cyclists, walkers and runners using the path in this week. … [3]

11 marks

Mark scheme: 4(a)(i) 10 20 10 40 1 4(a)(ii) Line from (10 20, 0) to (11 50, 12) 2 B1 for line from (10 20, 0) to (11 50, 12) and from (11 50, 12) to (12, 12) or B1FT for line from (their 11 50, 12) to (12, 12) 4(a)(iii) 11 30 2 Strict FT their graph 9.2 to 9.6 B1 for each 4(b) 14.7 or 14.69… 2 4067 − 3546 M1 for [ 100] 3546  4067  or  − 1  [ 100]  3546  4067 or  100 [– 100] 3546 4(c)(i) 9 : 11 1 4(c)(ii) 2976 3 B2 for 2016 or 2448 or M1 for 432[k ] oe, k is 1, 14 or 17 3

This question in 0580/33 Oct/Nov 2022

7 The scale drawing shows the positions of three towns, R, S and T, on a map. RS and ST are straight roads between the towns. The scale is 1 centimetre represents 8 kilometres. North North T R North S Scale: 1 cm to 8 km (a) Work out the actual distance between R and S. … km [2] (b) Another town, V, is on a bearing of 163° from R and on a bearing of 215° from T. Mark the position of V on the map. [2] (c) A man cycles at a constant speed of 24 km/h along the straight road from S to T. After 1 hour and 50 minutes he stops at a café, C. Mark the position of C on the map. You must show all your working. [3] (d) A hotel, H, is on a bearing of 321° from R. Work out the bearing of R from H. … [2] (e) Write the scale 1 cm to 8 km in the form 1 : n. 1 : … [1]

10 marks

Mark scheme: 7(a) 48 2 B1 for 6 cm or M1 for their 6  8 7(b) The position of V correctly marked on the 2 B1 for V on bearing 163° from R diagram B1 for V on bearing 215° from T 7(c) The position of C correctly marked on the 3 B2 for 5.5 seen diagram with correct working seen 24 their time or M2 for oe 8 or M1 for 24 their time oe If 0 scored, SC1 for C correctly marked on diagram with no working 7(d) 141 2 M1 for 321 −180 or a clear diagram with both 321 marked and the reverse bearing to be found shown 7(e) 800 000 1

This question in 0580/32 Feb/March 2023

8 Two friends, Diego and Javier, meet at a swimming pool. The travel graph shows Diego’s journey by bicycle from his home to the swimming pool. Javier’s 10 home 9 8 7 Swimming pool 6 5 Distance from Diego’s home (km) 4 3 2 1 Diego’s 0 10 00 10 30 11 00 11 30 12 00 12 30 13 00home Time (a) Calculate Diego’s speed for his journey from his home to the swimming pool. Give your answer in kilometres per hour. … km/h [2] (b) Diego stays at the swimming pool until 12 20. (i) On the grid, draw the line representing the time he stays at the swimming pool. [1] (ii) Work out how long, in hours and minutes, he is at the swimming pool. … h … min [1] (c) Javier leaves his home 15 minutes later than Diego. He walks to the swimming pool at a constant speed of 6 km/h. On the grid, show Javier’s journey from his home to the swimming pool. [3] (d) They both leave the swimming pool at 12 20 and return to their own homes, each at a constant speed. Diego arrives home at 12 45. Javier arrives home 5 minutes later than Diego. Complete the travel graph. [2]

9 marks

Mark scheme: 8(a) 9 2 M1 for 6 ÷ 40 [× 60] oe 8(b)(i) Ruled straight line from 1 (10 40, 6) to (12 20, 6) 8(b)(ii) 1 [h] 40 [min] 1 8(c) Ruled straight line from (10 15, 10) 3 B1 for (10 15, 10) marked to (10 55, 6) M1 for 4 ÷ 6 [× 60] If 0 scored, then SC1 for straight line from (10 15, 0) to (11 15, 6) 8(d) Ruled straight line from 2 FT (their12 20, 6) to (12 45, 0) B1 for each Ruled straight line from (their 12 20, 6) to (12 50, 10)

This question in 0580/31 May/June 2023

2 A shop sells food and drink. (a) Bananas cost $1.20 per kilogram and apples cost $2.25 per bag. Work out the total cost of 3.5 kg of bananas and 2 bags of apples. $ … [3] (b) Students receive a 10% discount on their shopping. Before the discount, the cost of a student’s shopping is $16.80 . Work out the amount of the discount. $ … [1] (c) The cost of a cabbage increases by 15%. Calculate the new price if the original price is $1.80 . $ … [2] (d) Some customers have their shopping delivered to their home. The cost is $5 plus $1.50 for each kilometre travelled from the shop to their home. (i) Show that the cost for a customer living 10 km from the shop is $20. [1] (ii) 25 20 15 Cost ($) 10 5 0 0 1 2 3 4 5 6 7 8 9 10 Distance travelled (km) On the grid, draw a line to show the cost of having shopping delivered. [2] (e) A bottle of water costs $1.55 . Suki has $20. Work out the maximum number of bottles Suki can buy and the change she receives. Maximum number of bottles … Change $ … [3] (f) A farmer delivers eggs to the shop in trays of 50. The eggs are then put into boxes of 12. There are no eggs left in the trays and all of the egg boxes are full. Work out the smallest possible number of eggs that the farmer delivers. … [2] (g) The shop sells bottles of orange juice in three different sizes. Bottle A Bottle B Bottle C 0.5 litres 1.2 litres 2 litres $1.30 $3.20 $5.25 Work out which bottle is the best value. Show how you decide. Bottle … [3]

17 marks

Mark scheme: 2(a) 8.7[0] 3 M2 for 3.5  1.2  2  2.25 oe or B2 for 4.2[0] and 4.5[0] or M1 for 3.5  1.2 oe or 2  2.25 oe 2(b) 1.68 cao 1 2(c) 2.07 cao 2  15  M1 for  1    1.8 oe  100  or B1 for 0.27 2(d)(i) 5  10  1.5 [=20] 1 2(d)(ii) Ruled line from (0, 5) to (10, 20) 2 B1 for one correct point plotted 2(e) 12 3 M2 for 20  12  1.55 oe 1.4[0] or B2 for 18.6 20 or M1 for soi by 12.9… 1.55 or 12 in the answer space 2(f) 300 2 B1 for 300k as final answer or M1 for [12 =] 2 × 2 × 3 and [50 =] 2 × 5 × 5 or 2 correct factor trees/lists/tables or a list of multiples of both 12 and 50 with at least 3 of each or 2 × 2 × 3 × 5 × 5 or 2,2,3,5,5 12 or 50  oe 50  (12  4) 2(g) A 3 M2 for 3 correct comparable With correct comparisons made of the 3 values, or for a correct method to bottles with suitable accuracy shown compare 3 bottles shown but not evaluated to enough accuracy or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but not evaluated

This question in 0580/33 May/June 2023

8 (a) The length, l m, of a piece of wire is 18.7 metres, correct to the nearest 10 centimetres. Complete the statement about the value of l. … G l 1 … [2] (b) 850 metres of wire has a mass of 130.5 kilograms. Work out the length of wire, in metres, that has a mass of 900 grams. … m [3] (c) Aluminium is used to make the wire. The mass of 1 cm 3 of aluminium is 2.7 grams. Work out the mass, in grams, of 6000 cm 3 of aluminium. Give your answer in standard form. … g [2] (d) A 12 metre length of wire increases in length to 12.017 metres when its temperature rises. Calculate the percentage increase in the length of the wire. … % [2]

9 marks

Mark scheme: 8(a) 18.65 18.75 2 B1 for each If 0 scored, SC1 for both correct but reversed or 1865  l  1875 8(b) 5.86 or 5.862… 3 900 M2 for  850 oe 130500 OR B1 for a correct conversion 130.5 kg=130500 [g] or 900 g =0.9 [kg] figs 9 or M1 for  850 figs130.5 8(c) 1.62  10 4 cao 2 M1 for 2.7  6000 or their number correctly converted to standard form 8(d) 0.142 or 0.1416 to 0.1417 2 12.017  12 M1 for  100  12  12.017  100  or   1    12  12.017 or  100   100  12

This question in 0580/33 May/June 2023

5 A railway line has three stations, Town, Port and Cove. Train A leaves Town for Cove and train B leaves Cove for Town. Both trains stop at Port. 25 Cove B 20 Distance from Town (km) 15 Port 10 5 A Town 0 14 00 14 10 14 20 14 30 14 40 14 50 Time (a) Write down the time that train B leaves Cove. … [1] (b) Write down how long train A stops at Port. … min [1] (c) How many more minutes does train A take to complete the whole journey than train B? … min [2] (d) Write down the time that the two trains pass each other. … [1] (e) Work out the average speed of train A between Town and Cove in kilometres per hour. … km/h [3]

8 marks

Mark scheme: 5(a) 14 10 1 5(b) 4 1 5(c) 2 2 B1 for 40 or 38 5(d) 14 25 1 5(e) 34.5 3 23 M2 for  60 oe 40 23 or M1 for their time

This question in 0580/31 Oct/Nov 2023

6 (a) Town S is 44 km from town R on a bearing of 117°. (i) Using a scale of 1 cm represents 8 km, mark the position of town S. North R Scale: 1 cm to 8 km [2] (ii) Anvi cycles the 44 km from R to S. She leaves R at 13 15 and cycles at a speed of 12 km/h. Work out the time she arrives at S. … [3] (b) A tower has a height of 16 metres. When Jai makes a scale drawing of the tower it has a height of 20 cm. Work out the scale Jai uses, giving your answer in the form 1 : n. 1 : … [2] (c) X, Y and Z are three towns. Z North NOT TO 9.7 km SCALE X 6 km Y X is on a bearing of 288° from Y. Z is on a bearing of 018° from Y. (i) Show that angle XYZ is 90°. [2] (ii) XY = 6 km and YZ = 9.7 km . Calculate XZ. XZ = … km [2]

11 marks

Mark scheme: 6(a)(i) The position of S correctly marked on the 2 B1 for S on bearing 117° from R diagram B1 for S 5.5 cm from R 6(a)(ii) 16 55 3 B2 for 3 [h] 40 [min] 44 or M1 for 12 6(b) [1:]80 2 M1 for 20:1600 or 0.2:16 or better 1600 16 or or 20 0.2 or B1 for answer figs 8 6(c)(i) 360 − 288 + 18 oe M2 M1 for 360 − 288 or 288 − 18 If 0 scored SC1 for 72 and 18 correctly marked on the diagram 6(c)(ii) 11.4 or 11.40 to 11.41 2 M1 for 6 2 + 9.7 2 or better

This question in 0580/32 Feb/March 2024

7 (a) P = 3a + 5 Find the value of P when a = 2 . P = … [1] (b) Solve these equations. (i) 7x =-42 x = … [1] (ii) 9 ( 8x - 7) = 72 x = … [3] (c) 5 8 # 5 k = 5 -24 Find the value of k. k = … [1] (d) Solve the simultaneous equations. -6x - y = 13 8x + y =- 51 x = … y = … [2] (e) n is an integer where n 2- 3 and n G 1. Write down all the possible values of n. … [2] (f) A boy walks for 35 minutes at x metres per minute. He then runs for t minutes at 160 metres per minute. Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels. … m [2] (g) NOT TO SCALE x – 2 x + 5 Find an expression for the area of this rectangle. Give your answer in the form x 2 + ax + b . … [3] Question 8 is printed on the next page.

15 marks

Mark scheme: 7(a) 11 1 7(b)(i) −6 1 7(b)(ii) 1.875 oe 3 M1 for a correct first step e.g. 8 x − 7 = 8 or 72 x− 63 = 72 M1FT for a correct second step e.g. 8 x = 15 or 72 x = 135 7(c) −32 1 7(d)  x =  − 19  y = 101 2 B1 for  x =  − 19 B1 for  y = 101 7(e) −2, −1, 0, 1 2 B1 for 3 correct and no extras or 4 correct and one extra 7(f) 35x + 160t final answer 2 B1 for 35x or 160t seen in final answer or 35 x + 160t seen and spoilt 7(g) x 2 + 3 x − 10 final answer 3 B2 for x 2 + 5 x − 2 x − 10 with at least 3 terms correct or B1 for ( x + 5 )( x − 2 ) oe

This question in 0580/32 Feb/March 2024

7 The area of some land is in the ratio park : gardens : playground = 11 : 2 : 3. The park has an area of 4620 m 2. (a) Work out the area of the gardens and the area of the playground. Gardens … m2 Playground … m2 [3] (b) The park area of 4620 m 2 is made up of paths and grassland. 18% of the park area is paths. (i) Show that the grassland area is 3788.4 m 2. [1] (ii) Seed for the grassland is sold in bags. The seed in one bag covers an area of 280 m 2. The bags cost $72 each for the first 5 bags and then $58 each for any extra bags. Calculate the cost of the seed needed to cover the grassland. $ … [4] (c) The owners of the land buy new equipment for the playground. They borrow $8500 for 4 years at a rate of 6.5% per year compound interest. Calculate the amount they repay at the end of the 4 years. Give your answer correct to the nearest dollar. $ … [3] (d) The café in the park sells water in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 330 ml 500 ml 750 ml $1.98 $3.20 $5.10 Work out which bottle is the best value. You must show all your working. Bottle … [3]

14 marks

Mark scheme: 7(a) 840 3 B2 for 1 correct answer in correct place 1260 or answers reversed or M1 for 4620 ÷ 11 × k (k = 1, 2, or 3) 7(b)(i) (100  18) M1 18  4620 accept 4620 –  4620 100 100 18 or 4620 ( 1 – ) 100 7(b)(ii) [$]882 4 B3 for 854.74, 853, 824 OR M3 for 5 × 72 + (their 14 – 5) × 58 oe or B2 for 14 [bags] or M1 for 3788.4 ÷ 280 OR M3 for 5 × 72 + (their 9 ) × 58 oe or B2 for 9 [bags] or M1 for (3788.4 – 5  280) ÷ 280 oe OR if 0 scored SC2 for 1056 or SC1 for 1027 or 998 7(c) [$]10935 cao 3 4  6.5  M1 for 8500 × 1  oe    100  A1 for 10934.96…… If A0 scored SC1 for their answer correct to at least 1 decimal place correctly rounded to nearest whole number. 7(d) A 3 With correct comparisons made of the 3 M2 for 3 correct comparable values bottles with suitable accuracy shown or for a correct method to compare 3 bottles shown but not evaluated to enough accuracy. or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but incorrect or not evaluated.

This question in 0580/32 May/June 2024

9 (a) Sara rides her bicycle at a speed of 420 metres per minute. Work out her speed in kilometres per hour. … km/h [2] (b) Jan cycles a distance of 51 km. She starts at 11 55. She has a rest stop for 25 minutes. She finishes at 14 41. Calculate her average speed, in km/h, for the time she is cycling. … km/h [4]

6 marks

Mark scheme: 9(a) 25.2 2 M1 for 420 ÷ 1000 × 60 or B1 for figs 252 final answer 9(b) 21.7 or 21.70….. 4 B2 for 2 h 21 [min] or 2°21° or 2.35 [h] or 141 [min] or B1 for 2 h 46 [min] or 2°46° or 2.76… [h] or 2.77[h] or 166 [min] or 1416 or 1220 M1 for 51 ÷ their time period

This question in 0580/32 May/June 2024

2 (a) Here is part of the timetable for buses from the station to the city centre. All buses take the same time to travel from the station to the city centre. Station 09 24 11 06 City centre 10 03 … (i) Complete the timetable. [2] (ii) Beth walks 4 km from her home to the station at a speed of 6 km/h. She wants to travel on the 09 24 bus. Work out the latest time she can leave her home. … [3] (iii) 45 seats on the bus are occupied. 3 This is of the total number of seats on the bus. 5 Work out the total number of seats on the bus. … [2] (b) Beth buys 2.4 kg of onions costing $1.25 per kilogram and 4.5 kg of potatoes. The total cost is $11.64 . Find the cost of 1 kg of potatoes. $ … [3] (c) (i) One day 140 people enter a shop. The ratio adults : children = 3 : 2. Find the number of adults who enter the shop. … [2] (ii) The price of a television in this shop is $624. 37.5% of this price is profit. Calculate the profit on this television. $ … [1] (iii) The price of a phone in this shop is $420. This price increases by 12%. Calculate the new price. $ … [2]

15 marks

Mark scheme: 2(a)(i) 11 45 2 B1 for 39 [m] or 1 [h] 42 [m] or 102 [m] 2(a)(ii) 08 44 3 B2 for 40 [m] or M1 for 4 ÷ 6 [×60] oe 2(a)(iii) 75 2 45 M1 for [×5] oe 3 2(b) 1.92 3 M2 for (11.64 – 2.4 × 1.25) ÷ 4.5 oe or M1 for 2.4 × 1.25 oe 2(c)(i) 84 2 140 M1 for [× k] oe where k = 1, 2 or 3 2  3 2(c)(ii) 234 1 2(c)(iii) 470.40 cao 2  12  M1 for 420   1   oe  100  or B1 for 50.40

This question in 0580/33 May/June 2024

9 Samir leaves home at 2 pm. He jogs 6 km to a café at a constant speed of 8 km per hour. He stops to rest for 1 hour. He then walks back home at a constant speed and arrives at 4.36 pm. (a) On the grid, draw a travel graph to show Samir’s whole journey. 8 7 Café 6 Distance 5 from home (km) 4 3 2 1 0 2 pm 2.30 pm 3 pm 3.30 pm 4 pm 4.30 pm 5 pm Time [3] (b) Calculate Samir’s average speed for the whole journey. … km/h [3]

6 marks

Mark scheme: 9(a) Three correct ruled lines 3 B1 for a line from (2pm, 0) to (2 45, 6) B1FT for a line from (their 2 45, their 6) to (their 2 45 + 1, their 6) B1FT for a line from (their 2 45 + 1, their 6) to (4 36, 0) 9(b) 4.62 or 4.615… 3 12 M2 for  60 oe 156 or M1 for 12 ÷ their time

This question in 0580/31 Oct/Nov 2024

6 (a) 8 m NOT TO SCALE 11 m 6 m 15 m The diagram shows a plan of Zak’s garden. Find the perimeter of the garden. … m [2] (b) Zak records the temperature in his garden each night for one week. Sunday Monday Tuesday Wednesday Thursday Friday Saturday 4 °C 1 °C -2 °C 2 °C -5 °C 3 °C -4 °C (i) Which night was coldest? … [1] (ii) Find the difference in temperature between Friday night and Saturday night. … °C [1] (c) Zak buys pea plants, bean plants and sunflower plants in the ratio peas : beans : sunflowers = 7 : 5 : 2. He buys 45 bean plants. Show that the total number of plants he buys is 126. [2] (d) Zak has a water barrel. On Monday the barrel contains 120 litres of water. On Friday the barrel contains 43.2 litres of water. Calculate the percentage decrease of the water in the barrel. … % [2] (e) Zak drives to a shop. 1 The journey takes 1 hours. 4 He drives at an average speed of 57 km/h. Calculate the distance he drives. … km [2] (f) Machine hire charges 1st day $22.60 Each additional day $11.80 Zak pays $69.80 to hire a machine. Calculate the number of days he hires it for. … days [3]

13 marks

Mark scheme: 6(a) 52 2 M1 for 15 – 8 and 11 – 6 or 2 × 11 + 2 × 15 oe or 11 + 8 + (11 − 6 ) + (15 − 8 ) + 6 + 15 oe 6(b)(i) Thursday 1 6(b)(ii) 7 1 6(c) 45 ÷ 5 × (7 + 5 + 2) [=126] M2 M1 for 45 ÷ 5 6(d) 64 2 120 − 43.2 M1 for [×100] 120 43.2 or [100−] ×100 120  43.2  or  1 −  [×100]  120  6(e) 71.25 2 M1 for their time × 57 oe 6(f) 5 nfww 3 69.80 – 22.60 M2 for oe 11.80 or M1 for 69.80 – 22.60 or 22.60 + 11.80 + 11.80 +. or better

This question in 0580/33 Oct/Nov 2024

15 (a) A car travels 95 km in 2 hours and 15 minutes. Calculate the average speed of the car in km/h. … km/h [1] (b) Convert 8 m/s into km/h. … km/h [2]

3 marks

Mark scheme: 15(a) 42.2 or 42.22… 1 15(b) 28.8 2 8  60  60 M1 for oe 1000 or B1 for answer figs 288

This question in 0580/32 Feb/March 2025

7 A train leaves station A at 13 44. The train arrives at station B after 3 hours and 30 minutes. (a) Work out the time the train arrives at station B. … [1] (b) The distance between station A and station B is 210 km. Calculate the average speed of the train in km/h. … km/h [1]

2 marks

Mark scheme: 7(a) 17 14 1 7(b) 60 1

This question in 0580/32 May/June 2025

4 Tim drives home from work. The travel graph shows his journey. Work 36 30 Distance 24 from home (km) 18 12 6 Home 0 14 00 14 30 15 00 15 30 Time (a) Write down the time Tim leaves work. … [1] (b) Tim stops on the way home. (i) Find how far Tim travels before he stops. … km [1] (ii) Find how long Tim stops for. … min [1]

3 marks

Mark scheme: 4(a) 14 10 1 4(b)(i) 24 1 4(b)(ii) 20 1

This question in 0580/33 May/June 2025

15 The table gives information about the costs of hiring bikes. Type of bike Cost for first day Cost for each extra day Road $25 $20 Mountain $40 $35 Electric $70 $50 (a) Work out the cost of hiring 2 road bikes for 3 days. $ … [2] (b) The cost, M, of hiring a mountain bike for d days can be written as M = 35d + 5 . (i) Write a formula for the cost, E, of hiring an electric bike for d days. E = … [2] (ii) The cost of hiring an electric bike for 6 days is the same as the cost of hiring a mountain bike for d days. Find the value of d. d = … [3]

7 marks

Mark scheme: 15(a) 130 2 B1 for 65 or M1 for 2 × (25 + 2 × 20) oe 15(b)(i) 50d + 20 oe final answer 2 B1 for 50d + j or kd + 20 k ≠ 0, or 50d + 20 seen then spoilt 15(b)(ii) 9 nfww 3 320 − 5 M2 for 35d = 320 – 5 oe or for 35 oe or M2FT for 35d = correct evaluation of 6 in their(b)(i) – 5 oe or B1 for 320 soi or M1 for 70 + 50 × 5 = 35d + 5 oe or 50 × 6 + 20 = 35d + 5 oe or M1FT for substitution of 6 into their (b)(i) = 35d + 5 If 0 scored, SC1 for correct evaluation of 6 substituted into their (b)(i)

This question in 0580/33 May/June 2025

21 (a) These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A B C D E 35 800 .78 # 102 .15 # 106 535 2 # 104 (i) Write these distances in order, starting with the shortest. … , … , … , … , … [2] shortest (ii) The radius of Earth is 6370 km. Satellite A is k times further from the centre of Earth than satellite D. Show that k = 6.11 correct to 2 decimal places. [2] (b) A satellite travels at a speed of 27 000 km/h. Find the distance the satellite travels in 95 minutes. … km [2] (c) A different satellite travels at a speed of 25 200 km/h. Convert this speed into m / s. … m / s [2]

8 marks

Mark scheme: 21(a)(i) 535, 7.8×102, 2×104, 35 800, 1.5×106 2 B1 for 4 in correct order or M1 for (B)780, (C)1 500 000 and (E)20 000 seen or for 3.58 × 104 and 5.35 × 102 seen 21(a)(ii) (35800 + 6370) ÷ (535 + 6370) M1 6.107…. A1 21(b) 42750 2 M1 for 27000 × their time 21(c) 7000 2 25200  1000 M1 for oe 60  60 or B1 for final answer figs 7

This question in 0580/33 May/June 2025

22 The diagram shows a solid cylinder with height 10 cm. NOT TO SCALE 10 cm The volume of the cylinder is 478 cm3. (a) Find the radius of the cylinder. … cm [3] (b) The cylinder is made from gold. The density of the gold is 19.3 g/cm3. Calculate the mass of the cylinder. mass :Density = D volume … g [1]

4 marks

Mark scheme: 22(a) 3.9[0] or 3.900 to 3.901 3 2 478 M2 for  r =  oe   10π or M1 for π × r2 × 10 = 478 22(b) 9225.4 1

This question in 0580/33 May/June 2025

3 Total cost of a journey = number of litres of fuel used # cost of fuel per litre. A journey uses 128 litres of fuel. The cost of fuel is $1.52 per litre. Calculate the total cost of this journey. $ … [1]

1 marks

Mark scheme: 3 194.56 cao 1

This question in 0580/31 Oct/Nov 2025

16 Bob travels from town A to town B. The travel graph shows his journey. 600 500 400 Distance from town A (km) 300 200 100 0 08 00 09 00 10 00 11 00 12 00 13 00 14 00 15 00 Time (a) Between which two times did Bob stop for a rest? Explain how you know. … and … because … … [2] (b) Calculate Bob’s average speed, in km/h, for the whole journey. … km/h [3]

5 marks

Mark scheme: 16(a) 10 30 and 11 15 1 line is horizontal oe 1 distance remains the same oe 16(b) 100 nfww 3 M2 for 625 ÷ 6.25 or M1 for 625 ÷ their time

This question in 0580/31 Oct/Nov 2025

28 The travel graph shows Chi’s journey from home to the station. 6 Station 5 4 Distance 3 (km) 2 1 Home 0 08 00 08 05 08 10 08 15 08 20 08 25 08 30 08 35 08 40 Time Calculate Chi’s average speed for the whole journey. Give your answer in kilometres per hour. … km/h [3] Question 29 is printed on the next page.

3 marks

Mark scheme: 28 9 3 5.4 M2 for × 60 oe 36 their distance or M1 for their time

This question in 0580/33 Oct/Nov 2025