Ratio and proportion — Paper 2 · IGCSE Mathematics 0580

7 The air resistance (R) to a car is proportional to the square of its speed (v). When R = 1800, v = 30. ForExaminer's Calculate R when v = 40. Use Answer R = [3]

3 marks

Mark scheme: 7 3200 3* M1 R = kv2 M1 k = 2 Note 2400 scores M0

This question in 0580/21 Oct/Nov 2004

13 A spray can is used to paint a wall. The thickness of the paint on the wall is t. The distance of the spray can from the wall is d. t is inversely proportional to the square of d. t = 0.2 when d = 8. Find t when d = 10. Answer t = [3]

3 marks

Mark scheme: 13 0.128 3 M1 t = k/d 2 k is any letter except t, d or α A1 k = 12.8 or M1 0.2 × 82 = 12.8 11 9

This question in 0580/21 May/June 2009

18 Two similar vases have heights which are in the ratio 3 : 2. (a) The volume of the larger vase is 1080 cm3. Calculate the volume of the smaller vase. Answer(a) cm3 [2] (b) The surface area of the smaller vase is 252 cm2. Calculate the surface area of the larger vase. Answer(b) cm2 [2]

4 marks

Mark scheme: 18 (a) 320 2 M1 1080 × 8/27 or (2/3)3 or 1080 ÷ 27/8 or (3/2)3 (b) 567 2 M1 252 × 9/4 or (3/2)2 or 252 ÷ 4/9 or (2/3)2 2

This question in 0580/21 May/June 2009

10 The braking distance, d, of a car is directly proportional to the square of its speed, v. When d = 5, v = 10. Find d when v = 70. Answer d = [3]

3 marks

Mark scheme: 10 245 3 M1 d = kv2 A1 k = 1/20 or M1 v2 = kd A1 k = 20

This question in 0580/21 Oct/Nov 2009

17 (a) In 2007, a tourist changed 4000 Chinese Yuan into pounds (£) when the exchange rate was £1 = 15.2978 Chinese Yuan. Calculate the amount he received, giving your answer correct to 2 decimal places. Answer(a) £ [2] (b) In 2006, the exchange rate was £1 = 15.9128 Chinese Yuan. Calculate the percentage decrease in the number of Chinese Yuan for each £1 from 2006 to 2007. Answer(b) % [2]

4 marks

Mark scheme: 17 (a) 261.48 cao 2 M1 4000 / 15.2978 (b) (±)3.86(48…) or 3.865 2 M1 (15.9128 – 15.2978)/15.9128 (× 100) or (“261.48 – 4000/15.9128) / “261.48”

This question in 0580/21 Oct/Nov 2009

17 (a) In 2007, a tourist changed 4000 Chinese Yuan into pounds (£) when the exchange rate was £1 = 15.2978 Chinese Yuan. Calculate the amount he received, giving your answer correct to 2 decimal places. Answer(a) £ [2] (b) In 2006, the exchange rate was £1 = 15.9128 Chinese Yuan. Calculate the percentage decrease in the number of Chinese Yuan for each £1 from 2006 to 2007. Answer(b) % [2]

4 marks

Mark scheme: 17 (a) 261.48 cao 2 M1 4000 / 15.2978 (b) (±)3.86(48…) or 3.865 2 M1 (15.9128 – 15.2978)/15.9128 (×100) oe or (“261.48” – 4000/15.9128) / “261.48”

This question in 0580/22 Oct/Nov 2009

2 Michel changed $600 into pounds (£) when the exchange rate was £1 = $2.40. He later changed all the pounds back into dollars when the exchange rate was £1 = $2.60. How many dollars did he receive? Answer $ [2]

2 marks

Mark scheme: 600 2 650 2 M1 (× 2.6) 4.2

This question in 0580/21 May/June 2010

14 y varies inversely as the square of x. Examiner's y = 1.5 when x = 8. Use Find y when x = 5. Answer y = [3]

3 marks

Mark scheme: 21 k 14 3.84 or 3 3 M1 y = 2 oe A1 k = 96 25 x IGCSE – May/June 2010 0580 21

This question in 0580/21 May/June 2010

3 Ricardo changed $600 into pounds (£) when the exchange rate was $1 = £0.60. He later changed all the pounds back into dollars when the exchange rate was $1 = £0.72. How many dollars did he receive? Answer $ [2]

2 marks

Mark scheme: 3 500 2 M1 for 600 × 0.6 ÷ 0.72 seen

This question in 0580/23 May/June 2010

19 Reina went on holiday to New Zealand. For Examiner's (a) She travelled the 65 km from Tokyo to Narita Airport by taxi. Use The taxi journey cost 300 yen (¥) per kilometre plus a fixed charge of ¥ 700. Calculate the cost of the taxi journey. Answer(a) ¥ [2] (b) At Narita Airport, Reina changed ¥ 71 190 into New Zealand dollars (NZ$). The exchange rate was NZ$1 = ¥ 56.5. How many New Zealand dollars did she receive? Answer(b) NZ$ [2]

4 marks

Mark scheme: 19 (a) 20200 2 M1 65 × 300 + 700 (b) 1260 2 M1 71190 / 56.5 8 ± k

This question in 0580/21 Oct/Nov 2010

11 The resistance, R, of an object being towed through the water varies directly as the square of the speed, v. R = 50 when v = 10. Find R when v = 16. Answer R = [3]

3 marks

Mark scheme: 11 128 3 M1 R = kv2 1 A1 k = 2 x − 7

This question in 0580/22 Oct/Nov 2010

15 The air fare from Singapore to Stockholm can be paid for in Singapore dollars (S$) or Malaysian For Ringitts (RM). Examiner's One day the fare was S$740 or RM1900 and the exchange rate was S$1= RM2.448 . Use How much less would it cost to pay in Singapore dollars? Give your answer in Singapore dollars correct to the nearest Singapore dollar. Answer S$ [3]

3 marks

Mark scheme: 15 36 cao 3 M1 1900/2.448 (= 776.14) A1 “776.(14…)” – 740 (= 36.14…) 4 8 4 8

This question in 0580/22 Oct/Nov 2010

6 NOT TO SCALE 6 cm 2 cm A company makes solid chocolate eggs and their shapes are mathematically similar. The diagram shows eggs of height 2 cm and 6 cm. The mass of the small egg is 4 g. Calculate the mass of the large egg. Answer g [2]

2 marks

Mark scheme: 3 6 108 2 M1 for 33 or 27 or  1  or 1 seen  3  27

This question in 0580/21 May/June 2011

18 27 For 7 (a) Find the value of x when = . Examiner's 24 x Use Answer(a) x = [1] 2 1 4 (b) Show that ÷ 1 = . 3 6 7 Write down all the steps in your working. Answer(b) [2]

3 marks

Mark scheme: 7 (a) 36 1 7 (b) correct working 2 M1 for 6 oe improper fraction M1 for 1221 = 74 oe or visible cancelling

This question in 0580/23 May/June 2011

11 The volume of a solid varies directly as the cube of its length. When the length is 3 cm, the volume is 108 cm3. Find the volume when the length is 5 cm. Answer cm3 [3]

3 marks

Mark scheme: 11 500 3 M1 V = kL3 any letters may be used for V, k and L A1 k = 4 IGCSE – May/June 2011 0580 23

This question in 0580/23 May/June 2011

12 Federico changed 400 euros (€) into New Zealand dollars (NZ$) at a rate of €1 = NZ$ 2.1 . For He spent x New Zealand dollars and changed the rest back into euros at a rate of €1 = NZ$ d. Examiner's Use Find an expression, in terms of x and d, for the number of euros Federico received. Answer € [3]

3 marks

Mark scheme: 12 840 − x 840 x 3 M1 400 × 2.1 − or M1 “400 × 2.1” – x d d d

This question in 0580/23 May/June 2011

17 NOT TO SCALE 20 cm 10 cm 9 cm d cm The diagrams show two mathematically similar containers. The larger container has a base with diameter 9 cm and a height 20 cm. The smaller container has a base with diameter d cm and a height 10 cm. (a) Find the value of d. Answer(a) d = [1] (b) The larger container has a capacity of 1600 ml. Calculate the capacity of the smaller container. Answer(b) ml [2]

3 marks

Mark scheme: 17 (a) 4.5(0) 1 (b) 200 2 M1 0.53 or 23 seen

This question in 0580/23 May/June 2011

19 The scale of a map is 1 : 250 000. (a) The actual distance between two cities is 80 km. Calculate this distance on the map. Give your answer in centimetres. Answer(a) cm [2] (b) On the map a large forest has an area of 6 cm2. Calculate the actual area of the forest. Give your answer in square kilometres. Answer(b) km2 [2]

4 marks

Mark scheme: 19 (a) 32 2 B1 figs 32 or 1 cm to 2.5 km or 8 000 000 seen (b) 37.5 2 B1 (figs 25)2 seen or figs 375 in answer

This question in 0580/23 May/June 2011

6 The force, F, between two magnets varies inversely as the square of the distance, d, between them. F = 150 when d = 2. Calculate F when d = 4. Answer F = [3]

3 marks

Mark scheme: 6 37.5 3 M1 F = k/d 2 A1 k = 600

This question in 0580/22 Oct/Nov 2011

1 Martha divides $240 between spending and saving in the ratio For Examiner's spending : saving = 7 : 8 . Use Calculate the amount Martha has for spending. Answer $ [2]

2 marks

Mark scheme: 1 112 2 M1 for 240 ÷ (7 + 8) × 7

This question in 0580/23 Oct/Nov 2011

12 Alberto changes 800 Argentine pesos (ARS) into dollars ($) when the rate is $1 = 3.8235 ARS. He spends $150 and changes the remaining dollars back into pesos when the rate is $1 = 3.8025 ARS. Calculate the amount Alberto now has in pesos. Answer ARS [3]

3 marks

Mark scheme: 12 225.(23112) 3 M2 for (800 ÷ 3.8235 – 150) × 3.8025 M1 for 800 ÷ 3.8235

This question in 0580/23 Oct/Nov 2011

16 The time, t, for a pendulum to swing varies directly as the square root of its length, l. For When l = 9, t = 6 . Examiner's Use (a) Find a formula for t in terms of l. Answer(a) t = [2] (b) Find t when l = 2.25 . Answer(b) t = [1]

3 marks

Mark scheme: 16 (a) t = 2 l 2 M1 for t = k l (b) 3 1ft Ft dependent on using t = k l

This question in 0580/23 Oct/Nov 2011

2 Gregor changes $700 into euros (€) when the rate is €1 = $1.4131 . Calculate the amount he receives. Answer € [2]

2 marks

Mark scheme: 2 495.36 2 M1 for 700 ÷ 1.4131

This question in 0580/21 May/June 2012

13 y is inversely proportional to x2. When x = 4, y = 3. Find y when x = 5. Answer y = [3]

3 marks

Mark scheme: k 13 1.92 3 M1 y = 2 oe B1 for k = 48 x

This question in 0580/21 May/June 2012

15 The scale of a map is 1 : 500 000 . (a) The actual distance between two towns is 172 km. Calculate the distance, in centimetres, between the towns on the map. Answer(a) cm [2] (b) The area of a lake on the map is 12 cm2. Calculate the actual area of the lake in km2. Answer(b) km2 [2]

4 marks

Mark scheme: 15 (a) 34.4 2 SC1 figs 344 seen (b) 300 2 SC1 figs 3 seen − 1 2 

This question in 0580/21 May/June 2012

7 The train fare from Bangkok to Chiang Mai is 768 baht. For The exchange rate is £1 = 48 baht. Examiner's Use Calculate the train fare in pounds (£). Answer £ [2]

2 marks

Mark scheme: 7 16 2 M1 for 768 ÷ 48 3

This question in 0580/21 Oct/Nov 2012

11 The electrical resistance, R, of a length of cylindrical wire varies inversely as the square of the diameter, d, of the wire. R = 10 when d = 2. Find R when d = 4. Answer R = [3]

3 marks

Mark scheme: 11 2.5 3 M1 R = k/d2 A1 k = 40 or M1 Rd2 = k A1 k = 40 2 2

This question in 0580/21 Oct/Nov 2012

13 The mass, m, of an object varies directly as the cube of its length, l . For Examiner's Use m = 250 when l = 5 . Find m when l = 7 . Answer m = [3]

3 marks

Mark scheme: 13 686 3 M1 m = k L3 A1 k = 2

This question in 0580/22 Oct/Nov 2012

3 Jamie needs 300 g of flour to make 20 cakes. How much flour does he need to make 12 cakes? Answer g [2]

2 marks

Mark scheme: 300× 12 3 180 2 M1 for oe 20 4 4

This question in 0580/23 Oct/Nov 2012

14 y varies inversely as the square root of x. For When x = 9, y = 6. Examiner's Use Find y when x = 36. Answer y = [3]

3 marks

Mark scheme: 14 3, –3 or ±3 3 M1 for y = k/√x oe A1 for 18 IGCSE – October/November 2012 0580 23 2 2

This question in 0580/23 Oct/Nov 2012

15 A model of a ship is made to a scale of 1 : 200. The surface area of the model is 7500 cm2. Calculate the surface area of the ship, giving your answer in square metres. Answer m2 [3]

3 marks

Mark scheme: 15 30 000 3 M2 for 7500 × 2002/1002oe or M1 for 2002 seen πx 2 − A M1 for one correct move

This question in 0580/23 Oct/Nov 2012

3 Pedro and Eva do their homework. Pedro takes 84 minutes to do his homework. The ratio Pedro’s time : Eva’s time = 7 : 6. Work out the number of minutes Eva takes to do her homework. Answer … min [2] _____________________________________________________________________________________

2 marks

Mark scheme: 3 72 2 M1 for 84 ÷ 7

This question in 0580/21 May/June 2013

13 Martina changed 200 Swiss francs (CHF) into euros (€). The exchange rate was €1 = 1.14 CHF. Calculate how much Martina received. Give your answer correct to the nearest euro. Answer € … [3] _____________________________________________________________________________________

3 marks

Mark scheme: 13 175 cao final answer 3 B2 for 175.4 ... or M1 for 200 ÷ 1.14

This question in 0580/21 May/June 2013

19 t varies inversely as the square root of u. For Examiner′s t = 3 when u = 4. Use Find t when u = 49. Answer t = … [3] _____________________________________________________________________________________

3 marks

Mark scheme: 6 k 19 or 0.857[1…] 3 M1 for t = oe 7 u A1 for k = 6

This question in 0580/21 May/June 2013

8 The mass, m, of a sphere varies directly with the cube of its radius, r. m = 160 when r = 2. Find m when r = 5. Answer m = … [3] _____________________________________________________________________________________

3 marks

Mark scheme: 8 2500 3 M1 for m = kr 3 A1 for k = 20 5 4

This question in 0580/23 May/June 2013

8 On a ship, the price of a gift is 24 euros (€) or $30. What is the difference in the price on a day when the exchange rate is €1 = $1.2378? Give your answer in dollars, correct to the nearest cent. Answer $ … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 8 0.29 cao 3 M2 for 30 − (24 × .12378) or (24 × .12378) − 30 or M1 for 24× .12378

This question in 0580/21 Oct/Nov 2014

20 The diagram shows the plan, ABCD, of a park. The scale is 1 centimetre represents 20 metres. D C A B Scale: 1 cm to 20 m (a) Find the actual distance BC. Answer(a) … m [2] (b) A fountain, F, is to be placed ● 160 m from C and ● equidistant from AB and AD. On the diagram, using a ruler and compasses only, construct and mark the position of F. Leave in all your construction lines. [5] __________________________________________________________________________________________ Question 21 is printed on the next page.

7 marks

Mark scheme: 20 (a) 102 to 106 2 B1 for 5.1 to 5.3 seen (b) Correct position of F with correct arcs for 5 B2 for Correct ruled angle bisector of A with angle bisector correct arcs or B1 for correct bisector with no/wrong arcs and B2 for Arc centre C, radius 8 cm or B1 for arc centre C with incorrect radius or correct conversion to 8cm and B1 for marking position of F on their bisector and 8cm from C or on their arc centre C x + 7

This question in 0580/22 Oct/Nov 2014

1 $1 = 8.2 rand Change $350 into rands. Answer … rand [2] __________________________________________________________________________________________

2 marks

Mark scheme: Qu. Answers Mark Part Marks 1 2870 2 M1 for 350 × 8.2

This question in 0580/23 Oct/Nov 2014

9 y varies inversely as (x + 5). y = 6 when x = 3. Find y when x = 7. Answer y = … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 9 4 3 M2 for 6(3 + 5) = y(7 + 5) oe or k M1 for y = oe x + 5 A1 for k = 48 3  5 

This question in 0580/23 Oct/Nov 2014

1 Ahmed and Babar share 240 g of sweets in the ratio 7 : 3. Calculate the amount Ahmed receives. Answer … g [2]

2 marks

Mark scheme: Question Answer Mark Part Marks 1 168 2 M1 for 240 ÷ (7 + 3) or better

This question in 0580/23 May/June 2015

7 James buys a drink for 2 euros (€). Work out the cost of the drink in pounds (£) when £1 = €1.252 . Give your answer correct to 2 decimal places. Answer £ … [3]

3 marks

Mark scheme: 7 1.60 cao 3 B2 for 1.597…. or 1.6 or M1 for 2 ÷ 1.252 15 135

This question in 0580/23 May/June 2015

4 Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1. Work out Pip’s share. Answer $ … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 785 4 628 2 M1 for [× 4 ] 1 + 4

This question in 0580/21 Oct/Nov 2015

3 Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368 . Calculate how many euros Carlos received. Answer € … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 3 694 or 694.4[4...] 2 M1 for 950 ÷ 1.368

This question in 0580/22 Oct/Nov 2015

19 y is inversely proportional to (x + 2)2. When x = 1, y = 2. Find y in terms of x. Answer y = … [2] __________________________________________________________________________________________

2 marks

Mark scheme: 18 k 19 oe 2 M1 for y = or better ( x + 22) ( x + 22) If zero scored k SC1 for final answer of y = ( x + 22) where k ≠0 or 18 877 5

This question in 0580/23 Oct/Nov 2015

10 The scale on a map is 1 : 20 000. The area of a lake on the map is 1.6 square centimetres. Calculate the actual area of the lake. Give your answer in square metres. … m2 [3]

3 marks

Mark scheme: 1.6 × 20000 10 64 000 3 M2 for 2 oe 100 or M1 for figs 64 in answer or 1 cm2 = 40 000 m2

This question in 0580/22 Feb/March 2016

5 Omar changes 2000 Saudi Arabian riyals (SAR) into euros (€) when the exchange rate is €1 = 5.087 SAR. Work out how much Omar receives, giving your answer correct to the nearest euro. € … [2]

2 marks

Mark scheme: 5 393 2 B1 for 393.1 to 393.2 or M1 for 2000 ÷ 5.087

This question in 0580/21 May/June 2016

21 y is directly proportional to the positive square root of x. When x = 9, y = 12. 1 Find y when x = 4 . y = … [3]

3 marks

Mark scheme: 21 2 3 M1 for y = k x A1 for k = 4 1 9 4 or M2 for = oe 12 y

This question in 0580/21 May/June 2016

16 y is directly proportional to (x + 2)2. When x = 8, y = 250. Find y when x = 4. y = … [3]

3 marks

Mark scheme: 16 90 3 M1 for y = k(x + 2)2 A1 for k = 2.5 (8 + 2) 2 (4 + 2) 2 or M2 for = oe 250 y

This question in 0580/23 May/June 2016

3 The price of a toy is 12 euros (€) in Germany and 14 Swiss francs in Switzerland. 1 Swiss franc = €0.905 Calculate the difference between these two prices. Give your answer in euros. € … [2]

2 marks

Mark scheme: 3 [0].67 2 M1 for 14 × 0.905 [–12] or 12.67 If zero scored, SC1 for answer [0].74[0] 8 3

This question in 0580/21 Oct/Nov 2016

12 (a) Write $0.70 as a fraction of $5.60, giving your answer in its lowest terms. … [1] (b) Write the recurring decimal .018o o as a fraction in its lowest terms. [ .018o o means 0.181818… ] … [2]

3 marks

Mark scheme: 1 12 (a) cao 1 8 2 . . . . (b) 2 M1 for 18.18 − 0.18 oe 11 2 k or B1 for (k not 0 or 1) 11k

This question in 0580/21 Oct/Nov 2016

14 y is directly proportional to the square root of (x + 2). When x = 7, y = 2. Find y when x = 98. y = … [3]

3 marks

Mark scheme: 14 6 23 oe 3 M1 for y = k x + 2 oe or better e.g. 2 = k 7 + 2 M1 for [y = ] their k × 98 + 2 or y 98 + 2 M2 for = 2 7 + 2 5

This question in 0580/21 Oct/Nov 2016

12 Ralf and Susie share $57 in the ratio 2 : 1. (a) Calculate the amount Ralf receives. $ … [2] (b) Ralf gives $2 to Susie. Calculate the new ratio Ralf’s money : Susie’s money. Give your answer in its simplest form. … : … [2]

4 marks

Mark scheme: 12 (a) 38 2 M1 for 57 ÷ (2 + 1) or better (b) 12 : 7 2 M1FT for their 38 – 2 and their 19 + 2 seen dep on sum = 57 If M0 SC1 for answer 7 : 12 2 ( )

This question in 0580/22 Oct/Nov 2016

16 d is inversely proportional to (w + 1)2. d = 3.2 when w = 4. Find d when w = 7. d = … [3]

3 marks

Mark scheme: k 16 1.25 3 M1 for d = 2 or better ( w + 1) their k M1 for [d=] ( 7 + 1) 2 or M2 for 3.2(4 + 1)2 = d(7 + 1)2 oe 1 − 3

This question in 0580/23 Oct/Nov 2016

12 y is inversely proportional to x2. When x = 5, y = 16. Find y when x = 10. y = … [3]

3 marks

Mark scheme: k 12 4 3 M1 for y = x 2 their k M1 for y = 10 2 or M2 for 52 × 16 = 10 2 × y oe 2 ( ) ( )

This question in 0580/22 Feb/March 2017

2 The thickness of one sheet of paper is 8 # 10-3 cm. Work out the thickness of 250 sheets of paper. … cm [1]

1 marks

Mark scheme: 2 2 1

This question in 0580/21 May/June 2017

9 h is directly proportional to the square root of p. h = 5.4 when p = 1.44 . Find h when p = 2.89 . h = … [3]

3 marks

Mark scheme: 9 7.65 3 M1 for h = k p oe M1 for h = their k p 5.4 h or M2 for = oe 1.44 2.89

This question in 0580/21 May/June 2017

21 y is inversely proportional to 1+ x . When x = 8 , y = 2 . Find y when x = 15 . y = … [3]

3 marks

Mark scheme: 21 3 1 3 k 1.5 or or M1 for 2 12 1 + x their k M1 for y = 1 + 15 2 y or M2 for = 1 + 15 1 + 8

This question in 0580/22 May/June 2017

7 y is inversely proportional to x2. When x = 2, y = 8. Find y in terms of x. y = … [2]

2 marks

Mark scheme: 7 32 2 k or 32x−2 final answer M1 for y = oe x 2 x 2 or [k =] 32

This question in 0580/23 May/June 2017

13 Two bottles and their labels are mathematically similar. The smaller bottle contains 0.512 litres of water and has a label with area 96 cm2. The larger bottle contains 1 litre of water. Calculate the area of the larger label. … cm2 [3]

3 marks

Mark scheme: 13 150 3 2 2  1  3  0.512  3 M2 for   oe or   oe  0.512   1  1 1  1  3  0.512  3 or M1 for scale factor   oe or   oe  0.512   [1] 

This question in 0580/23 May/June 2017

17 y is inversely proportional to (x + 1) 2 . y = 50 when x = 0.2 . (a) Write y in terms of x. y = … [2] (b) Find the value of y when x = 0.5 . y = … [1]

3 marks

Mark scheme: 17(a) 72 2 k (y =) oe M1 for y = ( x + 1) 2 ( x+ 1) 2 17(b) 32 1FT FT correct evaluation from their equation in (a) using 0.5

This question in 0580/21 Oct/Nov 2017

18 A ball falls d metres in t seconds. d is directly proportional to the square of t. The ball falls 44.1 m in 3 seconds. (a) Find a formula for d in terms of t. d = … [2] (b) Calculate the distance the ball falls in 2 seconds. … m [1]

3 marks

Mark scheme: 18(a) d = 4.9t 2 2 M1 for d = kt 2 18(b) 19.6 1 FT their 4.9 × 4

This question in 0580/22 May/June 2018

19 y is directly proportional to x - 1 2 . ^ h When x = 3, y = 24. Find y when x = 6. y = … [3]

3 marks

Mark scheme: 19 150 3 M1 for y = k ( x − 1) 2 M1 for [ y = ] their k × (6 − 1) 2 oe OR y (6 − 1) 2 M2 for = 24 (3 − 1) 2

This question in 0580/23 May/June 2018

7 y is inversely proportional to x3. When x = 2, y = 0.5 . Find y in terms of x. y = … [2]

2 marks

Mark scheme: 7 4 2 k oe final answer M1 for y = oe x 3 x 3

This question in 0580/21 Oct/Nov 2018

17 y is directly proportional to the square root of x. When x = 9, y = 6 . Find y when x = 25. y = … [3]

3 marks

Mark scheme: 17 10 3 M1 for y = k x M1 for y = their k × 25 OR y 25 M2 for = 6 9

This question in 0580/23 Oct/Nov 2018

5 A tourist changes $500 to euros (€) when the exchange rate is €1 = $1.0697 . Calculate how many euros he receives. € … [2]

2 marks

Mark scheme: 5 467.42 or 467 2 M1 for 500 ÷ 1.0697

This question in 0580/22 Feb/March 2019

9 y is directly proportional to (x - 4) . When x = 16 , y = 3 . Find y in terms of x. y = … [2]

2 marks

Mark scheme: 9 1 2 M1 for y = k ( x − 4 ) [y = ] ( x − 4) oe final answer 4

This question in 0580/22 Feb/March 2019

16 y is inversely proportional to the square root of (x + 1). When x = 8, y = 2. Find y when x = 99. y = … [3]

3 marks

Mark scheme: 16 [ ± ] 0.6 oe 3 k M1 for y = x + 1 theirk M1 for y = 99 + 1 OR 2 8 + 1 M2 for 99 + 1 or M1 for 2 8 + 1 = y 99 + 1

This question in 0580/21 May/June 2019

10 On a map with scale 1 : 25 000, the area of a lake is 33.6 square centimetres. Calculate the actual area of the lake, giving your answer in square kilometres. … km2 [2]

2 marks

Mark scheme: 10 2.1 2 33.6 × 25000 2 M1 for oe 100000 2 or answer figs 21

This question in 0580/22 May/June 2019

18 y is inversely proportional to the square of (x + 1 ) . y = 0.875 when x = 1. Find y when x = 4 . y = … [3]

3 marks

Mark scheme: 18 0.14 oe 3 k M1 for y = ( x + 1) 2 their k M1 for y = ( 4 + 1) 2 OR 0.875 (1 + 1) 2 M2 for ( 4 + 1) 2 or M1 for y(4 + 1)2 = 0.875(1 + 1)2

This question in 0580/23 May/June 2019

25 K J NOT TO E D SCALE O A C F B H G The diagram shows two regular pentagons. Pentagon FGHJK is an enlargement of pentagon ABCDE, centre O. (a) Find angle AEK. Angle AEK = … [4] (b) The area of pentagon FGHJK is 73.5 cm2. The area of pentagon ABCDE is 6 cm2. Find the ratio perimeter of pentagon FGHJK : perimeter of pentagon ABCDE in its simplest form. … : … [2]

6 marks

Mark scheme: 25(a) 126 4 360 − 180 – ( 360 ÷ 5 )  M3 for or 2 360 − 180 × ( 5 − 2 ) ÷ 5 2 180 × ( 5 − 2 ) 360 or M2 for or 180 – 5 5 360 or M1 for 180 × (5 – 2) or 5 25(b) 7 : 2 2 73.5 6 M1 for or 6 73.5

This question in 0580/23 May/June 2019

15 y is inversely proportional to x2. When x = 4, y = 2. 1 Find y when x = . 2 y = … [3]

3 marks

Mark scheme: 15 128 3 k M1 for y = x 2 their k M1 for y =  1  2    2  OR 2 × 4 2 M2 for  1  2    2  2  1  2 or M1 for 2 × 4 = y ×    2 

This question in 0580/21 Oct/Nov 2019

7 Rashid changes 30 000 rupees to dollars when the exchange rate is $1 = 68.14 rupees. How many dollars does he receive? $ … [2]

2 marks

Mark scheme: 7 440 or 440.2 to 440.3 2 M1 for 30 000 ÷ 68.14

This question in 0580/22 Oct/Nov 2019

13 Two mathematically similar containers have heights of 30 cm and 75 cm. The larger container has a capacity of 5.5 litres. Calculate the capacity of the smaller container. Give your answer in millilitres. … ml [3]

3 marks

Mark scheme: 13 352 3 B2 for figs 352  75  3  30  3 or M1 for   oe or   oe  30   75  OR  30  3 M2 for 5.5 × × 1000    75 

This question in 0580/22 Oct/Nov 2019

20 t is inversely proportional to the square of (x + 1). When x = 2, t = 5. (a) Write t in terms of x. t = … [2] (b) When t = 1.8, find the positive value of x. x = … [2]

4 marks

Mark scheme: 20(a) 45 2 k final answer M1 for t = ( x + 1) 2 ( x + 1) 2 20(b) 4 2 M1 for 1.8 × (x + 1)2 = their 45 or better

This question in 0580/23 Oct/Nov 2019

16 m is inversely proportional to the square of ( p - 1) . When p = 4, m = 5 . Find m when p = 6 . m = … [3]

3 marks

Mark scheme: 16 4 3 k 1.8 or 1 M2 for m = 2 5 ( p − 1) theirk or M1 for m = ( 6 − 1) 2 OR M2 for 5(4 − 1) 2 = m (6 − 1) 2 oe

This question in 0580/21 May/June 2020

22 p is directly proportional to ( q + 2)2 . When q = 1, p = 1. Find p when q = 10 . p = … [3]

3 marks

Mark scheme: 22 16 3 M1 for p = k ( q + 2) 2 M1 for p = (their k )(10 + 2) 2 OR p 1 M2 for = oe (10 + 2) 2 (1 + 2) 2

This question in 0580/22 May/June 2020

11 y is directly proportional to the cube root of ( x + 3 ) . When x = 5, y = 2. 3 Find y when x = 24. y = … [3]

3 marks

Mark scheme: 11 [y =] 1 3 M1 for y = k × 3 x + 3 M1 for y = their k × 3 24 + 3 OR y 2 1 M2 for = × oe 3 24 + 3 3 3 5 + 3

This question in 0580/23 May/June 2020

17 NOT TO SCALE m cm 8 cm The diagram shows two shapes that are mathematically similar. The smaller shape has area 52.5 cm2 and the larger shape has area 134.4 cm2. Calculate the value of m. m = … [3]

3 marks

Mark scheme: 17 5 3 52.5 M2 for 8 × oe 134.4 52.5 134.4 or M1 for or oe 134.4 52.5

This question in 0580/23 May/June 2020

3 Rangan buys 3.6 kg of potatoes and 2.8 kg of leeks. The total cost is $13.72 . Leeks cost $2.65 per kilogram. Find the cost of 1 kg of potatoes. $ … [3]

3 marks

Mark scheme: 3 1.75 3 M2 for (13.72 – 2.8 × 2.65) ÷ 3.6 oe or M1 for 2.8 × 2.65

This question in 0580/21 Oct/Nov 2020

8 Calculate the size of one interior angle of a regular polygon with 40 sides. … [2]

2 marks

Mark scheme: 8 171 2 M1 for 180 – (360 ÷ 40) oe or ( 40 − 2 ) × 180 oe 40

This question in 0580/22 Oct/Nov 2020

12 Alex and Chris share sweets in the ratio Alex : Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives. … [2]

2 marks

Mark scheme: 12 15 2 M1 for 4 [parts] = 20 soi or x + 20 x a correct equation e.g. = oe 7 3

This question in 0580/22 Oct/Nov 2020

23 y is inversely proportional to the square root of x. When y = 7 , x = 2.25 . Write y in terms of x. y = … [2]

2 marks

Mark scheme: 23 10.5 2 k y = oe final answer M1 for y = x x

This question in 0580/23 Oct/Nov 2020

2 Sahil and Anika share $78 in the ratio 5 : 8. Calculate the amount each receives. Sahil $ … Anika $ … [2]

2 marks

Mark scheme: 2 30 2 78 M1 for × k oe where k = 1, 5 or 8 48 5 + 8

This question in 0580/22 Feb/March 2021

56 Joseph spends of one week’s earnings to buy a jacket. 24 The cost of the jacket is $56.50 . Calculate the amount Joseph earns in a week. $ … [2]

2 marks

Mark scheme: 6 271.2[0] 2 M1 for 56.50 ÷ 5 or 56.50 × 24 oe or better

This question in 0580/22 Feb/March 2021

10 North L M NOT TO SCALE N On a map, the positions of the towns L, M and N form an equilateral triangle. The bearing of M from L is 103°. Work out the bearing of L from N. … [2]

2 marks

Mark scheme: 10 343 2 B1 for 103 in correct position and 60 or 103 17 in correct position 60 17

This question in 0580/22 Feb/March 2021

14 y is directly proportional to the square root of ( x - 3 ) . When x = 28 , y = 20 . Find y when x = 39 . y = … [3]

3 marks

Mark scheme: 14 24 3 M1 for y = k x − 3 oe M1 for y = their k 39 − 3 oe

This question in 0580/21 May/June 2021

21 The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the distance, d cm, between the magnets. When d = 1.5 , F = 48 . (a) Find an expression for F in terms of d. F = … [2] (b) When the distance between the two magnets is doubled the new force is n times the original force. Work out the value of n. n = … [1]

3 marks

Mark scheme: 21(a) 108 2 k [ F = ] 2 final answer M1 for F = 2 oe or better d d 21(b) 1 [ n = ]1 or 0.25 4

This question in 0580/22 May/June 2021

8 Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723 . Calculate the amount Alex receives. Give your answer correct to 2 decimal places. £ … [2]

2 marks

Mark scheme: 8 162.07 cao 2 M1 for 190 ÷ 1.1723

This question in 0580/23 May/June 2021

17 The interior angle of a regular polygon is 175°. Calculate the number of sides. … [2]

2 marks

Mark scheme: 17 72 2 360 180( n − 2) M1 for oe or = 175 180 − 175 n oe

This question in 0580/23 May/June 2021

2 Hank flies from Los Angeles to Shanghai. (a) The flight departs on Friday 22 July at 21 40. The flight takes 13 hours 35 minutes. The local time in Shanghai is 15 hours ahead of the local time in Los Angeles. Find the day, date and time in Shanghai when Hank’s flight arrives. Day … , Date … , Time … [3] (b) The cost of the flight is $920. The exchange rate is $1 = 6.87 Chinese yuan. Find the cost of the flight in yuan. … yuan [1]

4 marks

Mark scheme: 2(a) Sunday 24 [July] 02 15 3 B1 for Sunday 24th [July] as final answer B2 for 02 15 oe as final answer or B1 for sight of any of these 12 40 oe, 11 15 oe, 28h 35min, 50 15, 35 15 or 0215 oe spoilt or M1 for departure time + 13h35min + 15h evaluated as a time with one interval correctly added 2(b) 6320.4[0] 1

This question in 0580/21 Oct/Nov 2021

6 The scale drawing shows the positions of two towns, P and Q. The scale is 1 cm represents 4 km. North Q North P Scale: 1 cm to 4 km (a) Find the actual distance between town P and town Q. … km [2] (b) Measure the bearing of town Q from town P. … [1] (c) Town X is 28 km from town P on a bearing of 140°. On the scale drawing, mark the position of town X. [2]

5 marks

Mark scheme: 6(a) 32.8 2 M1 for 8[cm] to 8.4[cm] seen or for their measurement [in cm] multiplied by 4 6(b) 065 1 6(c) X correctly placed 7 cm from P 2 M1 for X on bearing of 140 from P on a bearing of 140° or for X 7 cm from P If 0 scored SC1 for X on bearing of 140 from Q and 7 cm from Q

This question in 0580/21 Oct/Nov 2021

10 A regular polygon has an interior angle of 174°. Find the number of sides of this polygon. … [2]

2 marks

Mark scheme: 10 60 2 M1 for 360 ÷ (180 – 174) 180 ( n − 2 ) or for = 174 oe n

This question in 0580/21 Oct/Nov 2021

14 y is inversely proportional to the square root of ( x - 2 ) . When x = 4.25, y = 12 . Find x when y = 3 . x = … [3]

3 marks

Mark scheme: 14 38 3 M2 for 12 × 4.25 − 2 = 3 × x − 2 OR k M1 for y = oe x − 2 their k M1 for 3 = oe x − 2

This question in 0580/21 Oct/Nov 2021

15 NOT TO SCALE The diagram shows three shapes that are mathematically similar. The heights of the shapes are in the ratio small : medium : large = 1 : 5 : 8. Find the ratio shaded area : total unshaded area. Give your answer in its simplest form. … : … [4]

4 marks

Mark scheme: 15 3 : 5 nfww 4 M3 for 52 – 1 oe and 82 – 52 + 1 oe or M2 for 52 – 1 oe or 82 – 52 + 1 oe or M1 for 52 oe or 82 oe seen

This question in 0580/21 Oct/Nov 2021

10 The interior angle of a regular polygon is 156°. Work out the number of sides of this polygon. … [2]

2 marks

Mark scheme: 10 15 2 M1 for 360 ÷ (180 – 156) or 180 ( n – 2 ) = 1 56 oe n

This question in 0580/22 Oct/Nov 2021

5 Nina changes 153 euros into dollars when the exchange rate is $1 = 0.9 euros. Calculate the amount Nina receives. $ … [1]

1 marks

Mark scheme: 5 170 1

This question in 0580/23 Oct/Nov 2021

16 Jo and Mo share $26. Jo receives $5 more than Mo. Find the ratio Jo’s money : Mo’s money. Give your answer in its simplest form. … : … [3]

3 marks

Mark scheme: 16 31 : 21 3 B2 for equivalents e.g. 15.5 oe and 10.5 oe or for an equivalent ratio e.g. 3.1 : 2.1 or M1 for e.g. x + 5 + x = 26 oe or x – 5 + x = 26 oe

This question in 0580/23 Oct/Nov 2021

17 Each interior angle of a regular polygon is 178.5°. Calculate the number of sides of this polygon. … [2]

2 marks

Mark scheme: 17 240 2 M1 for 360 ÷ (180 – 178.5) oe 180( n − 2) or for = 178.5 oe n

This question in 0580/23 Oct/Nov 2021

19 y is inversely proportional to the square root of (x +4). When x = 5, y = 2. Find y when x = 77. y = … [3]

3 marks

Mark scheme: 19 2 3 k oe M1 for y = 3 x + 4 theirk M1 for y = 77 + 4

This question in 0580/22 Feb/March 2022

5 Kirsty changes $380.80 into pounds (£) when £1 = $1.19 . Calculate the amount Kirsty receives. £ … [2]

2 marks

Mark scheme: 5 320 2 M1 for 380.8 ÷ 1.19 oe

This question in 0580/21 May/June 2022

12 The interior angles of a pentagon are in the ratio 4 | 5 | 5 | 7 | 9. Find the size of the largest angle. … [3]

3 marks

Mark scheme: 12 162 3  (5  2)  180  M2 for   × k where k = 1, 4, 5,  4  5  5  7  9  7, 9 or M1 for 180n ÷ (4 + 5 + 5 + 7 + 9) where n ⩾ 2 or for (5 – 2) × 180 oe

This question in 0580/21 May/June 2022

18 (a) y is directly proportional to the cube root of ( x + 1) . When x = 7 , y = 1. Find the value of y when x = 124 . y = … [3] (b) F is inversely proportional to the square of d. Explain what happens to F when d is halved. … [1]

4 marks

Mark scheme: 18(a) 2.5 3 M1 for y  k  3 x  1 M1 for y  theirk  3 124  1 18(b) multiplied by 4 oe 1

This question in 0580/22 May/June 2022

18 The bearing of B from A is x°. The bearing of A from B is y°. x : y = 2 : 7 Calculate the value of y. North North NOT TO SCALE B y° x° A y = … [3]

3 marks

Mark scheme: 18 252 3 M2 for 180 ÷ (7 – 2) oe OR M1 for 180 – x + y = 360 oe M1 for correct use of ratio

This question in 0580/23 May/June 2022

24 y is inversely proportional to the cube of ( x - 1) . y = 9.45 when x = 3 . Find y when x = 4 . y = … [3]

3 marks

Mark scheme: 24 2.8 3 k M1 for y   x  1 3 k M1 for y their  4 –1 3 OR M2 for y(4 – 1)3 = 9.45(3 – 1)3

This question in 0580/23 May/June 2022

3 Write 32 cm as a fraction of 2 m. Give your answer in its simplest form. … [2]

2 marks

Mark scheme: 3 4 2 32 cao M1 for oe 25 200

This question in 0580/21 Oct/Nov 2022

4 Divide $200 in the ratio 7 : 3. $ … , $ … [2]

2 marks

Mark scheme: 4 140, 60 2 200 M1 for  k where k = 1, 7 or 3 ( 7 + 3 )

This question in 0580/21 Oct/Nov 2022

23 y is inversely proportional to x and x is directly proportional to w2. When w = 12 , y = 12 . Find y in terms of w. y = … [3]

3 marks

Mark scheme: 23 144 3 k oe M2 for y = oe w w 2 j or M1 for x = cw or for y = oe x

This question in 0580/21 Oct/Nov 2022

5 Jenna buys 2.4 m of ribbon and 4.8 m of fabric. The total cost is $33.48 . Ribbon costs $0.85 per metre. Find the cost of 1 m of fabric. $ … [3]

3 marks

Mark scheme: 5 6.55 3 M2 for (33.48 – 2.4  0.85) oe or M1 for 2.4  0.85

This question in 0580/22 Oct/Nov 2022

17 y is proportional to the square of ( x - 7) . When x = 12, y = 2. Find y when x = 17. y = … [3]

3 marks

Mark scheme: 17 8 3

This question in 0580/23 Oct/Nov 2022

12 In a regular polygon, the interior angle and the exterior angle are in the ratio interior : exterior = 11 : 1. Find the number of sides of this regular polygon. … [3]

3 marks

Mark scheme: 12 24 3 M2 for 180 ( n − 2 ) = 11  360 oe OR 180 M1 for [× 11] oe 11 + 1 360 M1 for their 15 ( n − 2 ) 180 or for = (180 − their 15 ) n

This question in 0580/22 Feb/March 2023

16 y is inversely proportional to x2. When x = 3, y = 2 . Find y when x = 2 . y = … [3]

3 marks

Mark scheme: 16 4.5 oe 3 M2 for 2 2  y = 3 2  2 OR k M1 for y = x 2 theirk M1 for y = 2 2

This question in 0580/22 Feb/March 2023

7 The scale of a map is 1 : 125 000. On a map, the length of an island is 9.4 cm. Calculate the actual length of the island, giving your answer in kilometres.

2 marks

Mark scheme: 7 11.75 2 9.4  125000 M1 for oe 100  1000 or B1 for figs 1175 or 1 cm : 1.25 km

This question in 0580/21 May/June 2023

4 The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B. … km [2]

2 marks

Mark scheme: 4 8.75 2 3.5  250000 M1 for oe 100  1000 or B1 for figs 875 or 1 cm : 2.5 km

This question in 0580/22 May/June 2023

19 m is inversely proportional to the square of ( t + 2 ) . m = 0.64 when t = 3 . Find m when t = 8 . m = … [3]

3 marks

Mark scheme: 19 0.16 oe 3 k M1 for m  oe  t  2  2 their k M1 for substituting their k into m   8  2  2 OR M2 for 0.64 × (3 + 2)2 = m(8 + 2)2 oe

This question in 0580/22 May/June 2023

6 At the end of the day, a shopkeeper has 12 tins of cat food left. 3 This is of the number he had at the beginning of the day. 13 Calculate the number of tins he had at the beginning of the day. … [2]

2 marks

Mark scheme: 6 52 2 3 3 M1 for 12  x  oe or better e.g. 12 ÷ oe 13 13

This question in 0580/23 May/June 2023

18 y is inversely proportional to the cube root of (x + 5). When x = 3, y = 12. Find y when x = 22. y = … [3]

3 marks

Mark scheme: 18 8 3 k M1 for y  oe 3 x  5 k M1 for substituting their k into y  oe 3 22  5 OR M2 for 12 3 3  5  y 3 22  5 oe

This question in 0580/23 May/June 2023

7 The exchange rate between Singapore dollars and euros is 1 Singapore dollar = 0.62 euros. Find the value of 161.20 euros in Singapore dollars. … Singapore dollars [1]

1 marks

Mark scheme: 7 260 1

This question in 0580/21 Oct/Nov 2023

7 North NOT TO North SCALE P 39° Q East Find the bearing of Q from P. … [2]

2 marks

Mark scheme: 7 231 2 B1 for any of these angles in correct place on diagram 51 or 129 or 141 between east line drawn from P and QP or 39 between west line drawn from P and QP or indicating the correct bearing of Q from P on the diagram or M1 for 180 + (90 – 39) oe or 360 – (90 + 39) oe

This question in 0580/22 Oct/Nov 2023

22 x is inversely proportional to the square root of w. When w = 16 , x = 3 . Find x in terms of w. x = … [2]

2 marks

Mark scheme: 22 12 2 k oe final answer M1 for x = oe w w

This question in 0580/22 Oct/Nov 2023

18 F is proportional to the product of m and a. Calculate the percentage change in F when m is increased by 40% and a is decreased by 15%. … % [3]

3 marks

Mark scheme: 18 19 3  40  15  M2 for  1 +  1 −  [ma] oe  100  100  or M1 for F = kma or better or  40   15   1 +  and  1 −  oe seen  100   100 

This question in 0580/23 Oct/Nov 2023

22 y is inversely proportional to the square of ( x + 3) . When x = 5 , y = 0.375 . Find y in terms of x. y = … [2]

2 marks

Mark scheme: 22 24 2 oe final answer  y =  2 k ( x + 3) M1 for y = ( x + 3) 2

This question in 0580/22 Feb/March 2024

4 Jonah has $750. 1 He spends of this money on travel and some of this money on food. 4 He now has $437.50 . Work out the fraction of the $750 he spends on food. … [3]

3 marks

Mark scheme: 4 1 3 or equivalent fraction 6 625 B2 for oe 750 750 or M2 for 750   437.5 oe 4 750 or M1 for 750  oe 4 750 or  437.5 oe 4 437.5 or oe 750

This question in 0580/22 May/June 2024

2 19 (a) y is directly proportional to x - 1 . ` j When x = 4 , y = 3 . Find y when x = 7 . y = … [3] (b) m is inversely proportional to the square root of p. Explain what happens to the value of m when the value of p is multiplied by 9. … [1]

4 marks

Mark scheme: 19(a) 12 3 2 M1 for y  k  x  1 oe M1 for y = their k  7  1 2 oe 19(b) divided by 3 oe 1

This question in 0580/22 May/June 2024

7 The scale of a map is 1 : 40 000. On the map the distance between two villages is 37 cm. Calculate the actual distance between the two villages. Give your answer in kilometres. … km [2]

2 marks

Mark scheme: 7 14.8 2 M1 for 1 cm represents 0.4 km soi or B1 for figs 148 as answer

This question in 0580/23 May/June 2024

4 Safia has a piece of fabric of length 5.6 m. She cuts the fabric into two parts, with lengths in the ratio 3 : 4. Calculate the length of the longer part. … m [2]

2 marks

Mark scheme: 4 3.2 2 5.6 M1 for k  where k = 1, 3 or 4 3 + 4

This question in 0580/21 Oct/Nov 2024

12 y is directly proportional to the square root of x + 1. y = 10 .5 when x = 8 . Find y when x = 1.56 . y = … [3]

3 marks

Mark scheme: 12 5.6 oe 3 M1 for y = k x + 1 oe M1 for y = their k 1.56 + 1 oe

This question in 0580/22 Oct/Nov 2024

10 NOT TO Polygon A SCALE a° Polygon B b° c° Polygon C Three regular polygons A, B and C meet at a point. The interior angles of the polygons are in the ratio a : b : c = 3 : 4 : 5. Show that polygon C has twice the number of sides as polygon B. [5]

5 marks

Mark scheme: 10 Finds number of sides 6 and 12 5 B2 for 120 and 150 with appropriate supporting working for each value. or M1 for 360 ÷ (3 + 4 + 5) × k oe where k = 1, 3, 4 or 5 360 M1 for or 180 −their120 180 ( n − 2 ) = their120 oe n 360 M1 for or 180 −their150 180 ( n − 2 ) = their150 oe n

This question in 0580/22 Feb/March 2025

5 The interior angle of a regular polygon is 150°. Find the number of sides of this polygon. … [2]

2 marks

Mark scheme: 5 12 2 360 180 ( n − 2 ) M1 for or for = 150 180 − 150 n

This question in 0580/21 May/June 2025

1 Divide $90 in the ratio 2 : 3. $ … , $ … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 36, 54 2 90 M1 for k where k = 1, 2 or 3 2 + 3

This question in 0580/21 Oct/Nov 2025

13 M = 2 7 # 3 3 # 5 2 (a) Write 14M as a product of its prime factors. Give your answer in index form. … [2] (b) R is an integer. M is a cube number. R Find the smallest possible value of R. R = … [2]

4 marks

Mark scheme: 13(a) 28 × 33 × 52 × 7[1] cao 2 M1 for [14 =] 2 × 7 soi 13(b) 50 2 M1 for 23 × 33 [× 50] or 26 × 33 [× 50] oe or or 24 × 52 or 2 × 52 oe –86 400 or SC1 for answers –50, [–]400, [–]1350, [–]3200, [–]10 800, 86 400 oe

This question in 0580/22 Oct/Nov 2025

24 (a) Simplify. 125 - 20 … [2] (b) NOT TO 2 2 cm SCALE 3 8 cm The area of this rectangle is k cm 2. Work out the value of k. k = … [2] (c) Rationalise the denominator. 1 7 + 2 … [2]

6 marks

Mark scheme: 24(a) 2 3 5 B1 for 5 5 or 2 5 24(b) 24 2 M1 for 6 16 oe or 6 2  2 2 or 3 8  8 24(c) 2 7 − 2 1 2 1 7 − 2 or 7 ‒ M1 for  oe 3 3 3 7 + 2 7 − 2

This question in 0580/23 Oct/Nov 2025