Ratio and proportion — Paper 4 · IGCSE Mathematics 0580

1 A Spanish family went to Scotland for a holiday. (a) The family bought 800 pounds (£) at a rate of £1 = 1.52 euros (€). How much did this cost in euros? [1] (b) The family returned home with £118 and changed this back into euros. They received €173.46. Calculate how many euros they received for each pound. [1] (c) A toy which costs €11.50 in Spain costs only €9.75 in Scotland. Calculate, as a percentage of the cost in Spain, how much less it costs in Scotland. [2] (d) The total cost of the holiday was €4347.00. In the family there were 2 adults and 3 children. The cost for one adult was double the cost for one child. Calculate the cost for one child. [2] (e) The original cost of the holiday was reduced by 10% to €4347.00. Calculate the original cost. [2] (f) The plane took 3 hours 15 minutes to return to Spain. The length of this journey was 2350 km. Calculate the average speed of the plane in (i) kilometres per hour, [2] (ii) metres per second. [1]

11 marks

Mark scheme: 1 (a) 1216 B1 (b) 1.47 B1 (c) 11 . 5 − 9 . 75 M1 × 100 11 . 5 15.2 A1 ww2 SC1 for 17.9 (d) 4347 ÷ 7 o.e. M1 621 A1 ww2 (e) 4347 ÷ 0 . 9 o.e. M1 4830 A1 ww2 (f)(i) 2350 M1 Must deal with the minutes correctly o.e. 3 . 25 723 to 723.1 A1 ww2 (ii) 200.9 to 201 A1ft their (i) ÷ 3.6 r.o.t. to 3sf or better [11]

This question in 0580/41 Oct/Nov 2005

7 35 m 1.1 m NOT TO 24 m SCALE D C 2.5 m B A The diagram shows a swimming pool of length 35 m and width 24 m. A cross-section of the pool, ABCD, is a trapezium with AD = 2.5 m and BC = 1.1 m. (a) Calculate (i) the area of the trapezium ABCD, [2] (ii) the volume of the pool, [2] (iii) the number of litres of water in the pool, when it is full. [1] (b) AB = 35.03 m correct to 2 decimal places. The sloping rectangular floor of the pool is painted. It costs $2.25 to paint one square metre. (i) Calculate the cost of painting the floor of the pool. [2] (ii) Write your answer to part (b)(i) correct to the nearest hundred dollars. [1] (c) (i) Calculate the volume of a cylinder, radius 12.5 cm and height 14 cm. [2] (ii) When the pool is emptied, the water flows through a cylindrical pipe of radius 12.5 cm. The water flows along this pipe at a rate of 14 centimetres per second. Calculate the time taken to empty the pool. Give your answer in days and hours, correct to the nearest hour. [4]

14 marks

Mark scheme: 7 (a) (i) 1 (2 . 5 + 1 . 1) × 35 o.e. M1 2 63 A1 (ii) their (a) x 24 M1 1512 A1ft (iii) 1512000 B1ft their (a)(ii) x 1000 (b) (i) 35.03 x 24 x 2.25 M1 1891.62… A1 www2 (ii) 1900 B1ft their b(i) rounded to nearest 100 (c) (i) 2 M1 π × 12 . 5 × 14 6870 or better A1 (6872.2339 or 6873.125 (π = 3.142)) (ii) [their (a)(ii) ÷ their (c)(i)] M1 x 1 000 000 A1 o.e. e.g. using litres ÷ (60 x 60 x 24) M1 Implied by 2.54 2 days 13 hours A1 www4 [14]

This question in 0580/41 Oct/Nov 2005

8 (a) (i) The cost of a book is $x. Write down an expression in terms of x for the number of these books which are bought for $40. [1] (ii) The cost of each book is increased by $2. The number of books which are bought for $40 is now one less than before. Write down an equation in x and show that it simplifies to x 2 + 2 x − 80 = 0 . [4] (iii) Solve the equation x 2 + 2 x − 80 = 0 . [2] (iv) Find the original cost of one book. [1] (b) Magazines cost $m each and newspapers cost $n each. One magazine costs $2.55 more than one newspaper. The cost of two magazines is the same as the cost of five newspapers. (i) Write down two equations in m and n to show this information. [2] (ii) Find the values of m and n. [3] QUESTION 9 is on page 8.

13 marks

Mark scheme: 8 (a) (i) 40 B1 x (ii) 40 40 M2 40 = − 1 o.e. SC1 for seen x + 2 x x + 2 40x = 40(x + 2) – x(x + 2) o.e. M1 Correctly removes the fraction 40x = 40x + 80 – x2 – 2x x2 + 2x – 80 = 0 E1 Correct conclusion – no errors (iii) –10 B1 8 B1 (iv) 8 B1ft their positive x dep on one of each sign (b) (i) m = n + 2.55 o.e. B1 2m = 5n o.e. B1 (ii) 2(n + 2.55) = 5n M1 f.t. their linear equations in n and m any correct method to an equation in one variable m = 4.25 A1 n = 1.7 A1 [13] IGCSE – NOVEMBER 2005 0580/0581 4

This question in 0580/41 Oct/Nov 2005

5 The length, y, of a solid is inversely proportional to the square of its height, x. (a) Write down a general equation for x and y. Show that when x = 5 and y = 4.8 the equation becomes x 2 y = 120 . [2] (b) Find y when x = 2. [1] (c) Find x when y = 10. [2] (d) Find x when y = x. [2] (e) Describe exactly what happens to y when x is doubled. [2] (f) Describe exactly what happens to x when y is decreased by 36%. [2] (g) Make x the subject of the formula x 2 y = 120 . [2]

13 marks

Mark scheme: 5 (a) 1 k M1 y ∝ or y = o.e x 2 x 2 k = 4.8 x 52 A1 (b) 30 B1 (c) 10x2 = 120 o.e. M1 3.46 (3.464101…..) A1 (d) x2 x x = 120 o.e. M1 4.93 (4.932424…..) A1 (e) Divided by 4 o.e. B2 SC1 for (2x)2y = 120 o.e. seen or a correct calculation using a value of x. e.g. x = 4, y = 7.5 x = 8, y = 1.875 (f) Increases by 25% o.e. B2 SC1 for 1.5625 seen (g) Division by y M1 Square root M1 13 √ 2 2

This question in 0580/41 May/June 2006

1 (a) The scale of a map is 1:20 000 000. On the map, the distance between Cairo and Addis Ababa is 12 cm. (i) Calculate the distance, in kilometres, between Cairo and Addis Ababa. [2] (ii) On the map the area of a desert region is 13 square centimetres. Calculate the actual area of this desert region, in square kilometres. [2] (b) (i) The actual distance between Cairo and Khartoum is 1580 km. On a different map this distance is represented by 31.6 cm. Calculate, in the form 1 : n, the scale of this map. [2] (ii) A plane flies the 1580 km from Cairo to Khartoum. It departs from Cairo at 11 55 and arrives in Khartoum at 14 03. Calculate the average speed of the plane, in kilometres per hour. [4]

10 marks

Mark scheme: 1 (a) (i) 2 400 B2 SC1 for figures 24 (ii) 520 000 B2 SC1 for figures 52 (b) (i) 1 : 5 000 000 or n = 5 000 000 B2 SC1 for 5 000 000 seen in final answer or n = figs 5 oe in final answer (ii) Time = 2hrs 8 mins or 128 (mins) B1 = 2.13(33..) (hours) oe soi B1 Implies previous B1 Accept 128 60 1580 ÷ their time M1 soi is by correct answer 738 – 742 cso A1 www 4 (12.3 seen earns B1M1) [10]

This question in 0580/41 May/June 2007

3 (a) A B 55° 40.3 cm NOT TO 26.826.826.8cmcmcm SCALE 92° X 20.120.120.1 cmcmcm C D A, B, C and D lie on a circle. AC and BD intersect at X. Angle ABX = 55° and angle AXB = 92°. BX = 26.8 cm, AX = 40.3 cm and XC = 20.1 cm. (i) Calculate the area of triangle AXB. You must show your working. [2] (ii) Calculate the length of AB. You must show your working. [3] (iii) Write down the size of angle ACD. Give a reason for your answer. [2] (iv) Find the size of angle BDC. [1] (v) Write down the geometrical word which completes the statement “Triangle AXB is to triangle DXC.” [1] (vi) Calculate the length of XD. You must show your working. [2] (b) P Q y cm cm +2) (y X NOT TO SCALE cm (y 1) + – (2y 1) cm R S In the diagram PQ is parallel to RS. PS and QR intersect at X. PX = y cm, QX = (y + 2) cm, RX = (2y – 1) cm and SX = (y + 1) cm. (i) Show that y2 – 4y – 2 = 0. [3] (ii) Solve the equation y2 – 4y – 2 = 0. Show all your working and give your answers correct to two decimal places. [4] (iii) Write down the length of RX. [1]

19 marks

Mark scheme: 3 (a) (i) 0.5×40.3×26.8sin92 oe M1 Any other method must be complete (s = 58.13 – 58.15) 539.6 – 540 A1 ww scores zero 2 2 + 26 8. 2 (ii) AB 403. M1 ( AB ) = 403. = oe M1 sin 92 sin 55 − 2 × 40 3. × 26 8. cos 92 403. × sin 92 ( AB = ) M1 (AB = ) square root of above and a sin 55 correct combination M1 (dep) Accept if found in (i) ww scores zero 49.2 or 49.16 – 49.18 A1 (iii) 55 B1 Angles in the same segment oe B1dep (iv) 33 correct or ft B1 ft 88 – their 55, if answer is positive (v) Similar or enlarged B1 (vi) XD 201. M1 XD 201. = oe = 403. 26 8. sin their (iii ) sin their (iv ) A1 30.2(25) 30.2(309…) cao Any other method must be complete ww scores zero (b) (i) y y + 1 M1 May be implied by next line = oe Accept correct ratio statement y + 2 2 y − 1 y(2y – 1) = (y + 1)(y + 2) M1 May be implied by next line 2y2 – y = y2 + y + 2y + 2 Implies previous M2 y2 – 4y – 2 = 0 E1 Dep (no errors in any line) If M0, SC1 for y(2y – 1) – (y + 1)(y + 2) = 2y2 – y – y2 – y – 2y – 2 = y2 – 4y – 2 (ii) 4 ± 16 + 8 B1,B1 p + ( or − ) q If of form 2 r B1for 4 and 2, B1 for 42-4(1)(-2) q If of form p + ( or − ) r B1 for 42-4(1)(-2) but may recover the other B1 from answers -0.45, 4.45 cao B1,B1 SC1 for rounding or truncating to 1 dp or more – 0.44948…, 4.44948… ww scores max of 2 (iii) 7.9(0) or better 7.8989.. ft B1ft ft 2 × a positive root -1 [19] IGCSE – May/June 2007 0580 and 0581 04

This question in 0580/41 May/June 2007

1 Each year a school organises a concert. (a) (i) In 2004 the cost of organising the concert was $ 385. In 2005 the cost was 10% less than in 2004. Calculate the cost in 2005. [2] (ii) The cost of $ 385 in 2004 was 10% more than the cost in 2003. Calculate the cost in 2003. [2] (b) (i) In 2006 the number of tickets sold was 210. The ratio Number of adult tickets : Number of student tickets was 23 : 19. How many adult tickets were sold? [2] (ii) Adult tickets were $ 2.50 each and student tickets were $ 1.50 each. Calculate the total amount received from selling the tickets. [2] (iii) In 2006 the cost of organising the concert was $ 410. Calculate the percentage profit in 2006. [2] (c) In 2007, the number of tickets sold was again 210. Adult tickets were $ 2.60 each and student tickets were $ 1.40 each. The total amount received from selling the 210 tickets was $ 480. How many student tickets were sold? [4]

14 marks

Mark scheme: 1 (a) (i) 385 × 0.9 oe M1 Implied by ans 346 or 347 ($) 346.5(0) cao A1 www2 (ii) 385 ÷ 1.1(0) oe M1 ($) 350 cao A1 www2 (b) (i) 23 M1 × 210 oe 23 +19 115 cao A1 www2 (ii) their (i) × .250 + (210 – their (i)) × 1.50 M1 (287.5 + 142.5) A1 www2 ($) 430 cao (iii) {their (ii) – 410} / 410 ( ×100 )oe M1 Dep on (ii) being greater than 410 A1 www2 (4.878 …) 4.88 After M0, SC1 for 104.9 or better or 4.9 ww (c) 2.6(210 – x) or 1.4(210 – x) seen M1 2.6(210 – x) + 1.4x = 480 M1 Allow 2.6x + 1.4 (210 – x ) = 480 546 – 480 = 2.6x – 1.4x or 2.6x – 1.4x = 480 – 294 M1 Dep on M2 55 cao A1 if trial and error, B4 or B0 if using simultaneous equations x + y = 210 M1 4.1 x + 6.2 y = 480 M1 variable eliminated by correct method M1d After 0 scored, SC2 for ans 155 [14]

This question in 0580/41 Oct/Nov 2007

4 [The surface area of a sphere of radius r is 4πr2 and the volume is 4 πr 3 .] 3 (a) A solid metal sphere has a radius of 3.5 cm. One cubic centimetre of the metal has a mass of 5.6 grams. Calculate (i) the surface area of the sphere, [2] (ii) the volume of the sphere, [2] (iii) the mass of the sphere. [2] (b) NOT TO SCALE h 8 cm 16 cm 16 cm Diagram 1 Diagram 2 Diagram 1 shows a cylinder with a diameter of 16 cm. It contains water to a depth of 8 cm. Two spheres identical to the sphere in part (a) are placed in the water. This is shown in Diagram 2. Calculate h, the new depth of water in the cylinder. [4] (c) A different metal sphere has a mass of 1 kilogram. One cubic centimetre of this metal has a mass of 4.8 grams. Calculate the radius of this sphere. [3]

13 marks

Mark scheme: 4 (a) (i) 4 π 5.3 2 = 153.86 to 153.96 or 154 M1A1 www2 (ii) 4 3 π 5.3 3 = 179.5 to 179. 62 or 180 M1A1 www2 (iii) their (ii)× 5.6 M1 1005 to 1006 or 1008or 1010 (g) A1ft their (ii)× 5.6 correct to 3sf or better (allow in kg) (b) π 82 × 8 (1608-1609) M1 Alt π 8 2 d = 2 × their (ii) M1 2 M1dep 2 π 8 h = 2×their (ii) + π 82 × 8 (2×their (a)(ii)) ÷ (π 8 ) M1dep (2×their (ii) + π 82 × 8 ) ÷( π 8 2 ) M1dep add 8 M1dep 9.78 to 9.79 (cm) A1 www4 (c) 1000 (or 1) ÷4.8 ÷ 43 π M1 49.7….. (or 0.0497) 3 3 M1dep Dep on previous M1 ans (or 10 × ans ) 3.67 to 3.68 (cm) A1 www3 figs 368 or ans 3.7 gets M2 [13] IGCSE – October/November 2007 0580/0581 04

This question in 0580/41 Oct/Nov 2007

1 Marcus receives $800 from his grandmother. For Examiner's (a) He decides to spend $150 and to divide the remaining $650 in the ratio Use savings : holiday = 9 : 4. Calculate the amount of his savings. Answer(a) $ [2] (b) (i) He uses 80% of the $150 to buy some clothes. Calculate the cost of the clothes. Answer(b)(i) $ [2] (ii) The money remaining from the $150 is 37 1 % of the cost of a day trip to Cairo. 2 Calculate the cost of the trip. Answer(b)(ii) $ [2] (c) (i) Marcus invests $400 of his savings for 2 years at 5 % per year compound interest. Calculate the amount he has at the end of the 2 years. Answer(c)(i) $ [2] (ii) Marcus’s sister also invests $400, at r % per year simple interest. At the end of 2 years she has exactly the same amount as Marcus. Calculate the value of r. Answer(c)(ii) r = [3]

11 marks

Mark scheme: 1 (a) ($) 450 B2 M1 for 650 ÷ (9 + 4) × 9 (÷ 14 does not imply 9 + 4) (b) (i) ($) 120 B2 M1 for 0.8 × 150 o.e. (ii) ($) 80 ft B2 ft M1 for (150 – their(b)(i)) ÷ 0.375 o.e. only if +ve. After M0, SC1 for answer 320 (c) (i) ($) 441 B2 M1 for 400 × 1.052 o.e. or for answer 41 (ii) If use Simple Int in (i), M0, M0 in this part 1 their ( (i) − 400 ) ÷ 400 × 100 o.e. M2 i.e. a full explicit method for r 2 If M0, 400 × r × 2 5.125 or 5.13 or 5.12 c.a.o. www3 A1 M1 for = their (i) − 400 100 or their (i) ÷ 400 × 100 then – 100 their (i) - 400 or × 100 (s.o.i. by 10.25) 400 If still M0, SC1 for answers 55.125 or 55.12 or 55.13 or 55.1 or 0.05125 or 0.0512 or 0.0513 [11]

This question in 0580/41 May/June 2009

1 A school has 220 boys and 280 girls. Examiner's Use (a) Find the ratio of boys to girls, in its simplest form. Answer(a) : [1] (b) The ratio of students to teachers is 10 : 1. Find the number of teachers. Answer(b) [2] (c) There are 21 students on the school’s committee. The ratio of boys to girls is 3 : 4. Find the number of girls on the committee. Answer(c) [2] (d) The committee organises a disco and sells tickets. 35% of the school’s students each buy a ticket. Each ticket costs $1.60. Calculate the total amount received from selling the tickets. Answer(d) $ [3] (e) The cost of running the disco is $264. This is an increase of 10% on the cost of running last year’s disco. Calculate the cost of running last year’s disco. Answer(e) $ [2]

10 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 11:14 1 (b) 50 2 M1 for (220 + 280) ÷ 10 o.e. (c) 12 2 M1 for 21 ÷ (4 + 3) × 4 (or 3) o.e. (d) 280 3 M1 for 0.35 × their 500 (175) M1 dependent × 1.60 (e) 240 2 M1 for dividing 264 by 1.1 oe

This question in 0580/41 May/June 2010

5 Examiner's North Use A NOT TO SCALE 180 km 115 km 90 km T H 30° 70° R The diagram shows some straight line distances between Auckland (A), Hamilton (H), Tauranga (T) and Rotorua (R). AT = 180 km, AH = 115 km and HT = 90 km. (a) Calculate angle HAT. Show that this rounds to 25.0°, correct to 3 significant figures. Answer(a) [4] (b) The bearing of H from A is 150°. Find the bearing of (i) T from A, Answer(b)(i) [1] (ii) A from T. Answer(b)(ii) [1] For (c) Calculate how far T is east of A. Examiner's Use Answer(c) km [3] (d) Angle THR = 30° and angle HRT = 70°. Calculate the distance TR. Answer(d) km [3] (e) On a map the distance representing HT is 4.5cm. The scale of the map is 1 : n. Calculate the value of n. Answer(e) n = [2]

14 marks

Mark scheme: 180 + 115 90 5 (a) (cos) M2 M1 for correct implicit expression 902 = …… 2 × 180 × 115 24.98 – 24.99 A2 A1 for (cos) = 0.9064… (b) (i) 125(.0….) ft 1ft ft 150 – their (a) (ii) 305(.0….) ft 1ft ft 180 + their (b)(i) (c) 180sin (54.98 to 55) M2 B1 for 54.98 to 55 or 35 to 35.02 soi in correct or 180cos (35 to 35.02) oe position. or 180sin (360 – their (b)(ii)) Provided either angle is acute or 180cos(their (b)(i) – 90) oe 147(.4….) cao www 3 A1 90 sin 30 TR 90 (d) M2 M1 for = or other correct sin 70 sin 30 sin 70 implicit equation 47.9 (47.88 – 47.89) cao www 3 A1 (e) 2 000 000 oe 2 Allow 1 : 2 000 000 as answer. SC1 figs 2 in answer which could be a ratio. 4 3

This question in 0580/42 May/June 2010

10 Examiner's Use The diagrams show some polygons and their diagonals. (a) Complete the table. Number of sides Name of polygon Total number of diagonals 3 triangle 0 4 quadrilateral 2 5 5 6 hexagon 9 7 heptagon 14 8 [3] (b) Write down the total number of diagonals in (i) a decagon (a 10-sided polygon), Answer(b)(i) [1] (ii) a 12-sided polygon. Answer(b)(ii) [1] For 1 Examiner's (c) A polygon with n sides has a total of n ( n − q ) diagonals, where p and q are integers. Use p (i) Find the values of p and q. Answer(c)(i) p = q = [3] (ii) Find the total number of diagonals in a polygon with 100 sides. Answer(c)(ii) [1] (iii) Find the number of sides of a polygon which has a total of 170 diagonals. Answer(c)(iii) [2] (d) A polygon with n + 1 sides has 30 more diagonals than a polygon with n sides. Find n. Answer(d) n = [1]

12 marks

Mark scheme: 10 (a) Pentagon 1 Octagon 20 1, 1 (b)(i) 35 1 (ii) 54 1 (c)(i) p = 2, q = 3 3 M1 for substituting a value of n e.g. 1 4( 4 −q ) = 2 n ≥ 3 p or M1 for number of diagonals from one vertex is n – 3 (allow in words) and B1 for one correct value. If 0, SC1 for n ( n − 3) seen. 2 (ii) 4850 ft 1ft ft their (c)(i) allow only if ft calculates to a positive integer. (iii) 20 cao 2 SC1 for answer of 17 or M1 for their formula = 170 (d) 31 cao 1

This question in 0580/42 May/June 2010

1 Daniella is 8 years old and Edward is 12 years old. Examiner's Use (a) Their parents give them some money in the ratio of their ages. (i) Write the ratio Daniella’s age : Edward’s age in its simplest form. Answer(a)(i) : [1] (ii) Daniella receives $30. Show that Edward receives $45. Answer(a)(ii) [1] (iii) What percentage of the total amount of money given by their parents does Edward receive? Answer(a)(iii) % [2] (b) Daniella invests her $30 at 3% per year, compound interest. Calculate the amount Daniella has after 2 years. Give your answer correct to 2 decimal places. Answer(b) $ [3] (c) Edward also invests $30. He invests this money at a rate of r % per year, simple interest. After 5 years he has a total amount of $32.25. Calculate the value of r. Answer(c) r = [2]

9 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 2 : 3 1 (ii) 30 ÷ 2 × 3 o.e. E1 Allow 2 : 3 (oe) = 30 : 45 (iii) 60 2 M1 for 3 ÷ 5 × 100 oe (b) 31.83 3 SC2 for 31.827 as final answer or not spoiled. or M1 for × 1.03 twice oe 30 × r × 5 (c) 1.5 2 M1 for = .225 oe 100 or for 2.25 ÷ 5 then ÷ 30 × 100 2 2

This question in 0580/43 May/June 2010

1 (a) Hansi and Megan go on holiday. For The costs of their holidays are in the ratio Hansi : Megan = 7 : 4. Examiner's Hansi’s holiday costs $756. Use Find the cost of Megan’s holiday. Answer(a) $ [2] (b) In 2008, Hansi earned $7800. (i) He earned 15% more in 2009. Calculate how much he earned in 2009. Answer(b)(i) $ [2] (ii) In 2010, he earns 10% more than in 2009. Calculate the percentage increase in his earnings from 2008 to 2010. Answer(b)(ii) % [3] (c) Megan earned $9720 in 2009. This was 20% more than she earned in 2008. How much did she earn in 2008? Answer(c) $ [3] (d) Hansi invested $500 at a rate of 4% per year compound interest. Calculate the final amount he had after three years. Answer(d) $ [3]

13 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 432 2 M1 for 756 ÷ 7 × 4 oe (b) (i) 8970 2 M1 for 7800 × 1.15 oe After 0 scored, SC1 for 1170 as answer their 9867 ( −7800) (ii) (× 100) M2 Their 9867 is their (b)(i) × 1.1 7800 Implied by 1.265 or 0.265 or 126.5 or 1.15 × 1.10 or M1 for their (b)(i) × 1.10 (9867 seen or 2067 seen) 26.5 % cao A1 www3 (c) 8100 3 M2 for 9720 ÷ 1.2 oe or M1 for 120% = 9720 oe (d) 562.43 or 562 or 562.4(0) or 562.432 3 M2 for 500 × 1.04³ or alt complete method or M1 for 1.04² or 1.04³ oe soi e.g. $540.80 or 562.(43..) seen in working

This question in 0580/42 Oct/Nov 2010

4 (a) For Examiner's 4 cm Use NOT TO SCALE 13 cm The diagram shows a cone of radius 4 cm and height 13 cm. It is filled with soil to grow small plants. Each cubic centimetre of soil has a mass of 2.3g. (i) Calculate the volume of the soil inside the cone. 1 2 [The volume, V, of a cone with radius r and height h is V = π r h .] 3 Answer(a)(i) cm3 [2] (ii) Calculate the mass of the soil. Answer(a)(ii) g [1] (iii) Calculate the greatest number of these cones which can be filled completely using 50 kg of soil. Answer(a)(iii) [2] (b) A similar cone of height 32.5 cm is used for growing larger plants. Calculate the volume of soil used to fill this cone. Answer(b) cm3 [3] (c) For Examiner's Use NOT TO SCALE 12 cm Some plants are put into a cylindrical container with height 12 cm and volume 550 cm3. Calculate the radius of the cylinder. Answer(c) cm [3]

11 marks

Mark scheme: 4 (a) (i) 218 (217.7 to 218) 2 M1 for 1/3π × 42 × 13 (ii) 501 (500.7 to 501.4) 1ft ft their (a) × 2.3 (iii) 99 2ft ft 50 000 ÷ their (a)(ii) and truncated to whole number M1 for 50 000 ÷ their (a)(ii) oe or answers 99.8 or 100 3  325.  (b) their (a)(i) ×   oe M2 or 1/3π × 102 × 32.5  13  or M1 for (32.5 ÷ 13)³ (=15.625) seen or (13 ÷ 32.5)³ (= 0.064) seen 3400 or 3410 (3401 to 3407) A1 www3 (c) (r² =) 550 ÷ 12π M2 (14.58 to 14.6) or M1 for 12π r² = 550 or better 3.82 (3.818 to 3.821) A1 www3 IGCSE – October/November 2010 0580 42

This question in 0580/42 Oct/Nov 2010

1 Thomas, Ursula and Vanessa share $200 in the ratio For Examiner's Thomas : Ursula : Vanessa = 3 : 2 : 5. Use (a) Show that Thomas receives $60 and Ursula receives $40. Answer(a) [2] (b) Thomas buys a book for $21. What percentage of his $60 does Thomas have left? Answer(b) % [2] (c) Ursula buys a computer game for $36.80 in a sale. The sale price is 20% less than the original price. Calculate the original price of the computer game. Answer(c) $ [3] (d) Vanessa buys some books and some pencils. Each book costs $12 more than each pencil. The total cost of 5 books and 2 pencils is $64.20. Find the cost of one pencil. Answer(d) $ [3]

10 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 200 ÷ 10 × 3 oe M1 200 ÷ 10 × 2 oe M1 39 (b) 65 2 M1 for × 100 oe 35 is M0 60 (c) 46 3 M2 for 36.80 ÷ 0.8 oe or M1 for 80% = 36.80 oe (d) 0.6(0) 3 M2 for 5(x + 12) + 2x = 64.2 oe or (64.2 – 5 × 12) ÷ 7 or 5x + 2(x – 12) = 64.2 oe or (64.2 + 2 × 12) ÷ 7 or M1 for y = x + 12 and 5y + 2x = 64.2 or y = x – 12 and 5x + 2y = 64.2 After M0, SC1 for k(x ± 12) seen 4 2 + 4 5 2 7 2

This question in 0580/43 Oct/Nov 2010

1 (a) Abdullah and Jasmine bought a car for $9000. For Abdullah paid 45% of the $9000 and Jasmine paid the rest. Examiner's Use (i) How much did Jasmine pay towards the cost of the car? Answer(a)(i) $ [2] (ii) Write down the ratio of the payments Abdullah : Jasmine in its simplest form. Answer(a)(ii) : [1] (b) Last year it cost $2256 to run the car. Abdullah, Jasmine and their son Henri share this cost in the ratio 8 : 3 : 1. Calculate the amount each paid to run the car. Answer(b) Abdullah $ Jasmine $ Henri $ [3] (c) (i) A new truck costs $15 000 and loses 23% of its value each year. Calculate the value of the truck after three years. Answer(c)(i) $ [3] (ii) Calculate the overall percentage loss of the truck’s value after three years. Answer(c)(ii) %[3]

12 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 4950 2 M1 for 9000 × 0.55 oe (ii) 9 : 11 1 Accept 1 : 1.22 or 0.818 : 1 After 4050 in (a)(i) allow SC1 for 11 : 9 etc (b) 1504 1 564 1 188 1 After 0 scored M1 for 2256 ÷ (8 + 3 + 1) soi (c) (i) 6847.99 or 6848 or 6850 3 M2 for 15000 × 0.77³ oe (6847. (..)ww imp M2) or M1 for 15000 × 0.77² oe soi (8893.5) After 0 scored SC1 for art 27913 or 27910 or 27900 (ii) 54.3 (54.33 to 54.35) 3ft ft their (15000 – their (c)(i))/15000 × 100 to 3sf or better but not for negative answer or from 4650 in (c)(i) leading to 69% M2 for 1 – 0.77³ (0.543..) or their (15000 – their (c)(i))/15000 (× 100) or SC2ft their (c)(i)/15000 × 100 correctly evaluated (45.65 to 45.67 or 45.7) or M1 for 0.77³ (0.4565..) or their (c)(i)/15000 IGCSE – October/November 2011 0580 41

This question in 0580/41 Oct/Nov 2011

8 Mr Chang hires x large coaches and y small coaches to take 300 students on a school trip. For Large coaches can carry 50 students and small coaches 30 students. Examiner's There is a maximum of 5 large coaches. Use (a) Explain clearly how the following two inequalities satisfy these conditions. (i) x Y 5 Answer(a)(i) [1] (ii) 5x + 3y [ 30 Answer(a)(ii) [2] Mr Chang also knows that x + y Y 10. (b) On the grid, show the information above by drawing three straight lines and shading the unwanted regions. y 10 8 6 4 2 x 0 2 4 6 8 10 [5] (c) A large coach costs $450 to hire and a small coach costs $350. For Examiner's (i) Find the number of large coaches and the number of small coaches that would give the Use minimum hire cost for this school trip. Answer(c)(i) Large coaches Small coaches [2] (ii) Calculate this minimum cost. Answer(c)(ii) $ [1]

11 marks

Mark scheme: 8 (a) (i) There are up to 5 large coaches 1 E.g. can’t hire more than 5 large coaches oe The maximum is 5 large coaches The large coaches are less than or equal to 5 (ii) 50x + 30y ≥ 300 oe E2 No errors Allow in words provided clear e.g. 50 in large coaches and 30 in small coaches must equal 300 seats or more M1 for associating 50 with x or large coaches and 30 with y or small coaches (b) Freehand lines –1 pen once. All lines must be long enough to make full boundary of their region accept dashed or solid lines x = 5 ruled L1 x + y = 10 ruled L1 5x + 3y = 30 ruled L2 L1 for ruled line with intercepts at (0, 10) or (6, 0) within 2mm by eye at intercepts (extend if line is short) Correct region indicated cao R1 Allow if slight inaccuracy(s) in diagonal lines Allow any clear indication of region (c) (i) 5 1 After 5 and 2 in working ignore attempts to 2 1 calculate costs (ii) 2950 1ft ft their 5 × 450 + their 2 × 350 provided positive integers

This question in 0580/41 Oct/Nov 2011

10 Hassan stores books in large boxes and small boxes. For Each large box holds 20 books and each small box holds 10 books. Examiner's He has x large boxes and y small boxes. Use (a) Hassan must store at least 200 books. Show that 2x + y [ 20. Answer(a) [1] (b) Hassan must not use more than 15 boxes. He must use at least 3 small boxes. The number of small boxes must be less than or equal to the number of large boxes. Write down three inequalities to show this information. Answer(b) [3] (c) On the grid, show the information in part (a) and part (b) by drawing four straight lines and shading the unwanted regions. y 20 18 16 14 12 10 8 6 4 2 x 0 2 4 6 8 10 12 14 16 18 20 [6] (d) A large box costs $5 and a small box costs $2. For Examiner's (i) Find the least possible total cost of the boxes. Use Answer(d)(i) $ [1] (ii) Find the number of large boxes and the number of small boxes which give this least possible cost. Answer(d)(ii) Number of large boxes = Number of small boxes = [2] Question 11 is printed on the next page.

13 marks

Mark scheme: 10 (a) 20x + 10y ≥ 200 1 In (a), (b) −1 once for wrong symbol (b) x + y ≤ 15, y ≥ 3, y ≤ x 3 B1 for each (c) All lines long enough to make full boundary of region, accept dashed or solid lines, 2 mm acc at intercepts 2x + y = 20 ruled B2 B1 for ruled line through (10, 0) or (0, 20) x + y = 15 ruled B1 y = x ruled B1 y = 3 ruled B1 −1 once, freehand Quadrilateral identified R1 Allow if slight inaccuracy(s) in diagonal lines Allow any clear indication of region (d) (i) 47 cao 1 (ii) 7, 6 cao 2 M1 for any 5x + 2y in their region evaluated to equal their 47 IGCSE – October/November 2011 0580 43 8 

This question in 0580/43 Oct/Nov 2011

5 (a) In Portugal, Miguel buys a book about planets. For The book costs €34.95. Examiner's In England the same book costs £27.50. Use The exchange rate is £1 = €1.17. Calculate the difference in pounds (£) between the cost of the book in Portugal and England. Answer(a) £ [2] (b) In the book, the distance between two planets is given as 4.07 × 1012 kilometres. The speed of light is 1.1 × 109 kilometres per hour. Calculate the time taken for light to travel from one of these planets to the other. Give your answer in days and hours. Answer(b) days hours [3] (c) In one of the pictures in the book, a rectangle is drawn. The rectangle has length 9.3 cm and width 5.6 cm, both correct to one decimal place. (i) What is the lower bound for the length? Answer(c)(i) cm [1] (ii) Work out the lower and upper bounds for the area of the rectangle. Answer(c)(ii) Lower bound = cm2 Upper bound = cm2 [2]

8 marks

Mark scheme: 5 (a) (£) 2.37 or 2.371 to 2.372 www 2 2 M1 for 34.95 ÷ 1.17 implied by 29.87…or 29.9 or SC1 for 2.77 or 2.78 or 2.775 (b) 154 days 4 hours cao 3 M1 for 4.07 × 1012 ÷ (1.1 × 109) implied by figs 37 or 154. (….) A1 for 3700 seen or 3.7 × 103 seen or 154 16 oe or 154 rem 4 (c) (i) 9.25 1 (ii) Lower = 51.3375 final answer 1 After 0 scored Upper = 52.8275 final answer 1 SC1 for answers reversed or 9.35 and 5.65 seen or 51.3375 and 52.8275 seen

This question in 0580/42 May/June 2012

10 (a) Rice costs $x per kilogram. For Potatoes cost $(x + 1) per kilogram. Examiner's The total cost of 12 kg of rice and 7 kg of potatoes is $31.70 . Use Find the cost of 1 kg of rice. Answer(a) $ [3] (b) The cost of a small bottle of juice is $y. The cost of a large bottle of juice is $(y + 1). When Catriona spends $36 on small bottles only, she receives 25 more bottles than when she spends $36 on large bottles only. (i) Show that 25y2 + 25y O 36 = 0 . Answer(b)(i) [3] (ii) Factorise 25y2 + 25y O 36 . Answer(b)(ii) [2] (iii) Solve the equation 25y2 + 25y O 36 = 0 . Answer(b)(iii) y = or y = [1] (iv) Find the total cost of 1 small bottle of juice and 1 large bottle of juice. Answer(b)(iv) $ [1]

10 marks

Mark scheme: 10 (a) 1.3[0] 3 M2 for (31.7[0] – 7) ÷ (12 + 7) or better Or M1 for 12x + 7(x + 1) = 31.7[0] or better or 31.7[0] – 7 or better) (b) (i) 36 36 36 36 = 25 oe M2 SC1 for oe or oe seen y −y + 1 y y + 1 36 ( y + )1 − 36 y = 25 y ( y + )1 oe Accept both all over y(y + 1) 2 Must see at least one of these lines before E mark 36 y + 36 − 36 y = 25 y + 25 y oe 25 y 2 + 25 y − 36 = 0 E1 Final line reached without any errors or omissions (ii) (5 y + 9 )(5 y − 4 ) 2 Accept (25y – 20)(y + 1.8) oe SC1 for (5 y + m )(5 y + n ) where mn = − 36 or m + n = 5 (iii) –1.8 oe, 0.8 oe 1ft ft only SC1 from (b)(ii) (iv) 2.6[0] 1ft ft 2 × positive root from (b)(iii) +1 Dep on pos and neg root in (b)(iii) IGCSE – May/June 2012 0580 43

This question in 0580/43 May/June 2012

5 (a) For NOT TO Examiner's Use SCALE 20 cm 24 cm 46 cm Jose has a fish tank in the shape of a cuboid measuring 46 cm by 24 cm by 20 cm. Calculate the length of the diagonal shown in the diagram. Answer(a) cm [3] (b) Maria has a fish tank with a volume of 20 000 cm3. Write the volume of Maria’s fish tank as a percentage of the volume of Jose’s fish tank. Answer(b) % [3] (c) Lorenzo’s fish tank is mathematically similar to Jose’s and double the volume. Calculate the dimensions of Lorenzo’s fish tank. Answer(c) cm by cm by cm [3] (d) A sphere has a volume of 20 000 cm3. Calculate its radius. 4 [The volume, V, of a sphere with radius r is V = πr3.] 3 Answer(d) cm [3]

12 marks

Mark scheme: 5 (a) 55.6 to 55.61 www 3 M2 for 46 2 + 24 2 + 20 2 oe [ 3092 ] or M1 for 46² + 24² oe [soi by 2692 or art 51.9] or 46² + 20² oe [soi by 2516 or art 50.2] or 24² + 20² oe [soi by 976 or art 31.2] (b) 90.6 or 90.57 to 90.58 3 20000 M2 for × 100 oe (20 × 24 × 46 ) or M1 for 20 × 24 × 46 [22080] (c) 25.19 to 25.21, 30.23 to 30.246 or 3 M2 for 20 × 3 2 or 24 × 3 2 or 46 × 3 2 30.2, 57.95 to 57.97 or 58[.0] 3 2 oe seen [1.259 to 1.261] M1 for 3 20000 (d) 16.8 to 16.842 3 M2 for oe or answer figs 168 to 4 3π 16842 3 20000 or M1 for [4770 – 4780] seen 4 3π IGCSE – October/November 2012 0580 41

This question in 0580/41 Oct/Nov 2012

9 Distances from the Sun can be measured in astronomical units, AU. For Earth is a distance of 1 AU from the Sun. Examiner's Use One AU is approximately 1.496 × 108 km. The table shows distances from the Sun. Name Distance from the Sun in AU Distance from the Sun in kilometres Earth 1 1.496 × 108 Mercury 0.387 Jupiter 7.79 × 108 Pluto 5.91 × 109 (a) Complete the table. [3] (b) Light travels at approximately 300 000 kilometres per second. (i) How long does it take light to travel from the Sun to Earth? Give your answer in seconds. Answer(b)(i) s [2] (ii) How long does it take light to travel from the Sun to Pluto? Give your answer in minutes. Answer(b)(ii) min [2] (c) One light year is the distance that light travels in one year (365 days). How far is one light year in kilometres? Give your answer in standard form. Answer(c) km [3] (d) How many astronomical units (AU) are equal to one light year? Answer(d) AU [2]

12 marks

Mark scheme: 9 (a) 5.79 × 107 oe 1 Accept ans in range 57890000 to 57900000 5.21 1 5.207 39.5 1 39.50…. or 39.51 Accept answers to greater than 3sf (b) (i) 498.6... to 499 2 M1 for 1.496 × 10 8 ÷ 300 000 (ii) 328 or 328.3... 2 M1 for figs 197 or figs 328[3.. ] seen Or their 39.5 × their (b)(i) (c) 9.46[0] to 9.461 × 1012 3 B2 for any correct equivalent or M1 for 300 000 × 3600 × 24 × 365 oe or for answer figs 946 to 9461 (d) 63200 or 63235 to 63242 oe 2 M1 for figs (their (c) ÷ 1496). Implied by first 3 figs correct

This question in 0580/41 Oct/Nov 2012

1 (a) Ali and Ben receive a sum of money. For Examiner′s They share it in the ratio 5 : 1. Use Ali receives $2345. Calculate the total amount. Answer(a) $ … [2] (b) Ali uses 11% of his $2345 to buy a television. Calculate the cost of the television. Answer(b) $ … [2] (c) A different television costs $330. (i) Ben buys one in a sale when this cost is reduced by 15%. How much does Ben pay? Answer(c)(i) $ … [2] (ii) $330 is 12% less than the cost last year. Calculate the cost last year. Answer(c)(ii) $ … [3] (d) Ali invests $1500 of his share in a bank account. For Examiner′s The account pays compound interest at a rate of 2.3% per year. Use Calculate the total amount in the account at the end of 3 years. Answer(d) $ … [3] (e) Ali also buys a computer for $325. He later sells this computer for $250. Calculate Ali’s percentage loss. Answer(e) … % [3] _____________________________________________________________________________________

15 marks

Mark scheme: 1 (a) 2814 final answer 2 M1 for 2345 ÷ 5 soi by 469 or ans = 2810 (b) 257.95 final answer 2 M1 for 2345 × 0.11 oe or ans = 258 (c) (i) 280.5[0] final answer 2 M1 for 330 × (1 – 0.15) oe or ans = 281 (ii) 375 3 M2 for 330 ÷ (1 – 0.12) oe Or M1 for 330 = (100 – 12)% oe (d) 1605.89 or 1605.9[0] 3 M2 for 1500 × (1 + 0.023)3 oe soi by 1605.898751 or 1500 × 1.07(05…) 2 Or M1 for 1500 × (1 + 0.023) oe 325 − 250 (e) 23.1 or 23.07 to 23.08 3 M2 for × 100 oe 325 325 − 250 Or M1 for soi by 0.2307… 3sf or 325 better 250 or × 100 soi by 76.9… 325 IGCSE – May/June 2013 0580 43

This question in 0580/43 May/June 2013

1 David sells fruit at the market. For Examiner′s Use (a) In one week, David sells 120 kg of tomatoes and 80 kg of grapes. (i) Write 80 kg as a fraction of the total mass of tomatoes and grapes. Give your answer in its lowest terms. Answer(a)(i) … [1] (ii) Write down the ratio mass of tomatoes : mass of grapes. Give your answer in its simplest form. Answer(a)(ii) … : … [1] (b) (i) One day he sells 28 kg of oranges at $1.56 per kilogram. He also sells 35 kg of apples. The total he receives from selling the oranges and the apples is $86.38 . Calculate the price of 1 kilogram of apples. Answer(b)(i) $ … [2] (ii) The price of 1 kilogram of oranges is $1.56 . This is 20% more than the price two weeks ago. Calculate the price two weeks ago. Answer(b)(ii) $ … [3] (c) On another day, David received a total of $667 from all the fruit he sold. The cost of the fruit was $314.20 . 1 David worked for 10 2 hours on this day. Calculate David’s rate of profi t in dollars per hour. Answer(c) … dollars/h [2] _____________________________________________________________________________________

9 marks

Mark scheme: Qu Answers Mark Part Marks 1 2 (a) (i) cao 1 5 (ii) 3 : 2 cao 1 (b) (i) 1.22 2 M1 for 86.38 – 28 × 1.56 (ii) 1.3 [0] nfww 3 M2 for 1.56 ÷ 1.2 oe or M1 for 1.56 = 120% soi (c) 33.6[0] 2 M1 for (667 – 314.2) ÷ 10.5 oe

This question in 0580/41 Oct/Nov 2013

8 (a) Solve the equation 8x2 – 11x – 11 = 0. For Examiner′s Show all your working and give your answers correct to 2 decimal places. Use Answer(a) x = … or x = … [4] (b) y varies directly as the square root of x. y = 18 when x = 9. Find y when x = 484. Answer(b) y = … [3] (c) Sara spends $x on pens which cost $2.50 each. For Examiner′s She also spends $(x – 14.50) on pencils which cost $0.50 each. Use The total of the number of pens and the number of pencils is 19. Write down and solve an equation in x. Answer(c) x = … [6] _____________________________________________________________________________________

13 marks

Mark scheme: 2  8 (a) (− 11) − 4(8 )(− 11) or better B1 Seen anywhere or for  x − 11  16  + − p q p q p = –(– 11), r = 2(8) or better B1 Must be in the form or r r 11  11  2 11 or B1 for +   + 8  16  16 – 0.67, 2.05 final answers B1B1 SC1 for – 0.7 or – 0.672 to – 0.671 and 2.0 or 2.046 to 2.047 or answers 0.67 and – 2.05 (b) 132 3 M1 for y = k x oe or x = ky oe A1 for k = 6 oe or better or for k = 0.1666 to 0.167 [k = 6 implies M1A1] oe x x − 14 5. (c) 20 with supporting algebraic working 6 B2 for + = 19 oe 5.2 5.0 x x − 14 5. or B1 for or 5.2 5. M1dep on B2 for first completed correct move to clear both fractions M1 for second completed correct move to collect terms in x to a single term M1 for third completed correct move to collect numeric term[s] leading to ax = b SC1 for 20 with no algebraic working

This question in 0580/41 Oct/Nov 2013

9 For Examiner′s y Use L2 5 4 3 R 2 L1 1 x 0 1 2 3 4 5 6 7 8 9 10 L3 (a) Find the equations of the lines L1, L2 and L3. Answer(a) L1 … L2 … L3 … [5] (b) Write down the three inequalities that defi ne the shaded region, R. Answer(b) … … … [3] (c) A gardener buys x bushes and y trees. For Examiner′s The cost of a bush is $30 and the cost of a tree is $200. Use The shaded region R shows the only possible numbers of bushes and trees the gardener can buy. (i) Find the number of bushes and the number of trees when the total cost is $720. Answer(c)(i) … bushes … trees [2] (ii) Find the number of bushes and the number of trees which give the greatest possible total cost. Write down this greatest possible total cost. Answer(c)(ii) … bushes … trees Greatest possible total cost = $ … [3] _____________________________________________________________________________________

13 marks

Mark scheme: 9 (a) y = 2 oe 1 y = 2x oe 2 M1 for y = kx, k ≠ 0 or gradient 2 soi 1 M1 for gradient – ½ soi or y = kx + 5oe y = – x + 5 oe 2 2 or x + 2y = k k ≠ 0 oe If L2 and L3 both correct but interchanged then SC3 (b) y ≥ 2 oe y ≤ 2x oe 1 y ≤ – x + 5 oe 3 B1 for each correct inequality, allow in any 2 order After 0 scored, SC1 for all inequalities reversed (c) (i) 4 [bushes], 3 [trees] 2 M1 for any correct trial using integer coordinates in region or 30x + 200y = 720 seen (ii) 2 [bushes], 4 [trees] 2 M1 for any correct trial using integer coordinates in region 860 1 IGCSE – October/November 2013 0580 41

This question in 0580/41 Oct/Nov 2013

7 Noma fl ies from Johannesburg to Hong Kong. For Examiner′s Her plane leaves Johannesburg at 18 45 and arrives in Hong Kong 13 hours and 25 minutes later. Use The local time in Hong Kong is 6 hours ahead of the time in Johannesburg. (a) At what time does Noma arrive in Hong Kong? Answer(a) … [2] (b) Noma sleeps for part of the journey. The time that she spends sleeping is given by the ratio sleeping : awake = 3 : 4 . Calculate how long Noma sleeps during the journey. Give your answer in hours and minutes. Answer(b) … h … min [2] (c) (i) The distance from Hong Kong to Johannesburg is 10 712 km. For Examiner′s The time taken for the journey is 13 hours and 25 minutes. Use Calculate the average speed of the plane for this journey. Answer(c)(i) … km/h [2] (ii) The plane uses fuel at the rate of 1 litre for every 59 metres travelled. Calculate the number of litres of fuel used for the journey from Johannesburg to Hong Kong. Give your answer in standard form. Answer(c)(ii) … litres [4] (d) The cost of Noma’s journey is 10 148 South African Rand (R). This is an increase of 18% on the cost of the journey one year ago. Calculate the cost of the same journey one year ago. Answer(d) R … [3] _____________________________________________________________________________________

13 marks

Mark scheme: 7 (a) 14 10 or 2 10 pm final answer 2 M1 for (0)8 10 oe or answer 14 hours and 10 minutes or answer 2 10 [am] (b) 5 hours 45 minutes cao 2 M1 for 345 [mins] seen or for 805 /7 × 3 oe or 5.75 seen 25 (c) (i) 798 or 798.2 to 798.4…. 2 M1 for 10712 / 13 or 10712 ÷ 13.4… 60 (ii) 1.82 × 105 4 B3 for 182000 or 181500 to 181600 seen or 1.815 × 105 to 1.816 × 105 or M2 for 10712000/59 oe or M1 for figs 10712/figs 59 soi by figs 182 or figs 1815 to 1816 and B1 FT for their number of litres correctly converted to standard form rounded to 3sf or better (d) 8600 3 M2 for 10148 ÷ 1.18 oe or M1 for 10148 associated with 118[%]

This question in 0580/42 Oct/Nov 2013

1 (a) (i) In a camera magazine, 63 pages are used for adverts. For Examiner′s The ratio number of pages of adverts : number of pages of reviews = 7 : 5 . Use Calculate the number of pages used for reviews. Answer(a)(i) … [2] (ii) In another copy of the magazine, 56 pages are used for reviews and for photographs. The ratio number of pages of reviews : number of pages of photographs = 9 : 5 . Calculate the number of pages used for photographs. Answer(a)(ii) … [2] (iii) One copy of the magazine costs $4.90 . An annual subscription costs $48.80 for 13 copies. Calculate the percentage discount by having an annual subscription. Answer(a)(iii) … % [3] (b) In a car magazine, 25% of the pages are used for selling second-hand cars, For 1 Examiner′s 62 2 % of the remaining pages are used for features, Use and the other 36 pages are used for reviews. Work out the total number of pages in the magazine. Answer(b) … [4] _____________________________________________________________________________________

11 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 45 2 M1 for 5 × 63 ÷ 7 (ii) 20 2 M1 for 5 × 56 ÷ 14 13 × 9.4 – 48 8. (iii) 23.4 or 23.38 to 23.41 3 M2 for × 100 13 × 9.4 9.4 – 488. ÷ 13 or × 100 9.4 Or 13 × 9.4 – 48 8. 48 8. M1 for or × 100 or 76.6[…] 13 × 9.4 13 × 9.4 (b) 128 4 Using fractions (percentages / decimals): 3 3 9  75 M1 for × = or × 37 5. [= 28.125%] 4 8  32  100 9 A1 for or 28.125[%] 32 9 M1 for 36 ÷ oe 32 100 or 36 × oe 28 . 125 Partial percentages 100 × 36 M1 for (Remaining) [= 96] 375. A1 for 96 75 M1 for 96 ÷ oe 100 SC1 for 288 IGCSE – October/November 2013 0580 43 62 × sin 122

This question in 0580/43 Oct/Nov 2013

3 (a) The running costs for a papermill are $75 246. This amount is divided in the ratio labour costs : materials = 5 : 1. Calculate the labour costs. Answer(a) $ … [2] (b) In 2012 the company made a profi t of $135 890. In 2013 the profi t was $150 675. Calculate the percentage increase in the profi t from 2012 to 2013. Answer(b) … % [3] (c) The profi t of $135 890 in 2012 was an increase of 7% on the profi t in 2011. Calculate the profi t in 2011. Answer(c) $ … [3] (d) 2 cm NOT TO SCALE 21 cm 30 cm Paper is sold in cylindrical rolls. There is a wooden cylinder of radius 2 cm and height 21 cm in the centre of each roll. The outer radius of a roll of paper is 30 cm. (i) Calculate the volume of paper in a roll. Answer(d)(i) … cm3 [3] (ii) The paper is cut into sheets which measure 21 cm by 29.7 cm. The thickness of each sheet is 0.125 mm. (a) Change 0.125 millimetres into centimetres. Answer(d)(ii)(a) … cm [1] (b) Work out how many whole sheets of paper can be cut from a roll. Answer(d)(ii)(b) … [4] __________________________________________________________________________________________

16 marks

Mark scheme: 3 (a) 62 705 2 M1 for 75 246 ÷ 6 soi by 12 541 or 75 246 × 5 (b) 10.9 or 10.88… 3 (150 675 − 135 890) M2 for × 100 oe 135 890 or M1 for correct fraction soi by 0.1088… 150 675 or × 100 soi by 110.88… 135 890 IGCSE – May/June 2014 0580 41 Qu Answers Mark Part Marks (c) 127 000 3 M2 for 135 890 ÷ 1.07 oe or M1 for 135 890 associated with 107% (d) (i) 59 112 to 59 113 or 59 100 or 59 110 3 M2 for π × 21 × (302 – 22) oe or 59 119 to 59 120 or 59 100 Or nfww M1 for π × 21 × 302 or π × 21 × 22 (ii) (a) 0.0125 1 (b) 7580 or 7582 or 7581 or 7583 nfww 4 M1 for 21 × 29.7 × their 0.0125 [=7.796 or 7.8[0]] and M1 for their (d)(i) ÷ (21 × 29.7 × their 0.0125) A1 for 7580 to 7583.2 (non integer) If 0 then SC1 for their (d)(i) ÷ (21 × 29.7 × 0.125)

This question in 0580/41 May/June 2014

11 The total area of each of the following shapes is X. The area of the shaded part of each shape is kX. For each shape, fi nd the value of k and write your answer below each diagram. E NOT TO NOT TO SCALE J SCALE NOT TO F SCALE I O 72° K G A B C D H AB = BC = CD Angle JOK = 72° EF = FG and EI = IH k = … k = … k = … A NOT TO NOT TO SCALE SCALE O B The shape is a regular hexagon. The diagram shows a sector of a circle centre O. Angle AOB = 90° k = … k = … [10]

10 marks

Mark scheme: 1 11 1 Allow equivalent decimal throughout 3 (3sf or better where necessary) 72 oe 1 360 2 1  1  2 M1 for   or (2)2 or 12 : 22 or 22 : 12 oe seen 4  2  1 2 M1 for [X = 6 × ] 0.5 × l2 × sin60 6 or [X = 6 × ] 0.5 × l2 × sin120 Or recognition that the area of the obtuse- angled triangle shaded is equal to the area of one of the 6 equilateral triangles from the centre π − 2 2 or 1− or 0.363 or 0.3630 to 4 If fraction given as answer, check if it falls π π into range 0.3635 1 2 B1 for [sector=] π r oe 4 1 2 B1 for [triangle =] r oe 2 their sector − their triangle M1dep for dep their sector on B1B1 earned

This question in 0580/42 May/June 2014

10 The school cook buys potatoes in small sacks, each of mass 4 kg, and large sacks, each of mass 10 kg. He buys x small sacks and y large sacks. Today, he buys less than 80 kg of potatoes. (a) Show that 2x + 5y < 40. Answer(a) [1] (b) He buys more large sacks than small sacks. He buys no more than 6 large sacks. Write down two inequalities to show this information. Answer(b) … … [2] (c) On the grid, show the information in part (a) and part (b) by drawing three straight lines and shading the unwanted regions. y 9 8 7 6 5 4 3 2 1 x 0 5 10 15 20 25 [5] (d) Find the greatest mass of potatoes the cook can buy today. Answer(d) … kg [2] __________________________________________________________________________________________ Question 11 is printed on the next page.

10 marks

Mark scheme: 10 (a) 4 x + 10 y < 80 1 With no errors seen (b) y > x 1 y ≤ 6 or y < 7 1 Accept 0 ≤ y ≤ 6 or 0 < y ≤ 6 or 0 ≤ y < 7 or 0 < y < 7 (c) ruled broken line through (5, 6) to B2 SC1 for correct only at (5, 6) or (10, 4) (10,4) ruled broken line y = x B1 ruled solid line y = 6 or broken y = 7 B1 Must be consistent with their (b) correct region indicated B1 (d) 76 2 SC1 for ( 4, 6 ) indicated or 4 x + 10 y evaluated for ( x, y ) in their region, x, y integers

This question in 0580/42 Feb/March 2015

1 12 000 vehicles drive through a road toll on one day. The ratio cars : trucks : motorcycles = 13 : 8 : 3. (a) (i) Show that 6500 cars drive through the road toll on that day. Answer(a)(i) [1] (ii) Calculate the number of trucks that drive through the road toll on that day. Answer(a)(ii) … [1] (b) The toll charges in 2014 are shown in the table. Vehicle Charge Cars $2 Trucks $5 Motorcycles $1 Show that the total amount paid in tolls on that day is $34 500. Answer(b) [2] (c) This total amount is a decrease of 8% on the total amount paid on the same day in 2013. Calculate the total amount paid on that day in 2013. Answer(c) $ … [3] (d) 2750 of the 6500 car drivers pay their toll using a credit card. Write down, in its simplest terms, the fraction of car drivers who pay using a credit card. Answer(d) … [2] (e) To the nearest thousand, 90 000 cars drive through the road toll in one week. Write down the lower bound for this number of cars. Answer(e) … [1]

10 marks

Mark scheme: Question Answers Mark Part Marks 1313 1 (a) (i) × 12000 with no 1 13 + 8 + 3 subsequent errors (ii) 4000 1 (b) 2 × 6500 + 5 × their (a)(ii) + 2 B1 for any two of (12000 − 6500 − their (a)(ii) ) 2 × 6500, 5 × their (a)(ii) , (12000 – 6500 – their(a)(ii)) seen or or (13 × 2 + 8 × 5 + 3 × 1) × 500 13 × 2 + 8 × 5 + 3 × 1 34500 (c) 37 500 3 M2 for × 100 oe 100 − 8 or M1 for 34500 associated with (100 – 8)% 11 (d) cao 2 M1 for any correct simplified version of 26 2750 6500 (e) 89 500 1

This question in 0580/41 May/June 2015

1 (a) Last year a golf club charged $1650 for a family membership. This year the cost increased by 12%. Calculate the cost of a family membership this year. Answer(a) $ … [2] (b) The golf club runs a competition. The total prize money is shared in the ratio 1st prize : 2nd prize = 9 : 5. The 1st prize is $500 more than the 2nd prize. (i) Calculate the total prize money for the competition. Answer(b)(i) $ … [2] (ii) What percentage of the total prize money is given as the 1st prize? Answer(b)(ii) … % [1] (c) For the members of the golf club the ratio men : children = 11 : 2. The ratio women : children = 10 : 3. (i) Find the ratio men : women. Answer(c)(i) … : … [2] (ii) The golf club has 24 members who are children. Find the total number of members. Answer(c)(ii) … [3] (d) The club shop sold a box of golf balls for $20.40 . The shop made a profit of 20% on the cost price. Calculate the cost price of the golf balls. Answer(d) $ … [3] __________________________________________________________________________________________

13 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 1848 final answer 2 M1 for 1650 × + 1 1212  oe  100  (b) (i) 1750 2 500 M1 for [×5] or [×9] or any equation which 9 − 5 would lead to 4x = 500 or 4x = 2500 or 4x = 4500 or 4x = 7000 when simplified 2 (ii) 64 or 64.3 or 64.28 to 64.29 1 7 (c) (i) 33 : 20 oe 2 B1 for 33 : 6 or 20 : 6 or 5.5 oe seen or 3.33…oe seen or M1 for two ratios with a common number of children implied by 20k and 33k seen, k > 0 24 24 (ii) 236 3 M2 for × 11 + × 10 oe 2 3 or ((3 × 11) + (2 × 10)) × 24 ÷ 6 6 or × x = 24 6 + 20 + 33 24 24 or M1 for × 11 or × 13 soi 2 2 24 24 or × 10 or × 13 soi oe or 24 ÷ 6 soi 3 3 (d) 17[.00] 3 M2 for 20.40 ÷ + 1 20  oe  100  or M1 for (100 + 20)% oe associated with 20.40 seen

This question in 0580/42 May/June 2015

1 (a) Luc is painting the doors in his house. He uses 34 of a tin of paint for each door. Work out the least number of tins of paint Luc needs to paint 7 doors. Answer(a) … [3] (b) Jan buys tins of paint for $17.16 each. He sells the paint at a profit of 25%. For how much does Jan sell each tin of paint? Answer(b) $ … [2] (c) The cost of $17.16 for each tin of paint is 4% more than the cost in the previous year. Work out the cost of each tin of paint in the previous year. Answer(c) $ … [3] (d) In America a tin of paint costs $17.16 . In Italy the same tin of paint costs €13.32 . The exchange rate is $1 = €0.72 . Calculate, in dollars, the difference in the cost of the tin of paint. Answer(d) $ … [2] (e) Paint is sold in cylindrical tins of height 11 cm. Each tin holds 750 ml of paint. (i) Write 750 ml in cm3. Answer(e)(i) … cm3 [1] (ii) Calculate the radius of the tin. Give your answer correct to 1 decimal place. Answer(e)(ii) … cm [3] (iii) A mathematically similar tin has a height of 22 cm. How many litres of paint does this tin hold? Answer(e)(iii) … litres [2] (f) The mass of a tin of paint is 890 grams, correct to the nearest 10 grams. Work out the upper bound of the total mass of 10 tins of paint. Answer(f) … g [1] (g) The probability that a tin of paint is dented is 0.07 . Out of 3000 tins of paint, how many would you expect to be dented? Answer(g) … [2] (h) Tins of paint are filled at the rate of 2 m3 per minute. How many 750 ml tins of paint can be filled in 1 hour? Answer(h) … [3] __________________________________________________________________________________________

22 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 6 3 1 B2 for 5 or 5.25 shown in working isw 4 3 or M1 for × 7 soi by answer 5 4 (b) 21.45 cao final answer 2 M1 for 17.16 × 0.25 or 17.16 × 1.25 (c) 16.5[0] nfww 3 M2 for 17.16 ÷ 1.04 oe or M1 for 17.16 associated with 104[%] oe isw (d) 1.34 cao final answer 2 M1 for 13.32 ÷ 0.72 soi by 18.5[0] or for any correct complete longer method If zero scored, SC1 for 0.96 [euros] seen (e) (i) 750 1 (ii) 4.7 cao 3 B2 for 4.658 to 4.66 or M2 for their (e)(i) ÷ 11π or M1 for 11πr2 = their (e)(i) 1 (iii) 6 2 M1 for 23 or 3 oe seen 2 or for π × (2 × their (e)(ii))2 × 22 If zero scored, SC1 for answer 6 000 (f) 8 950 1 (g) 210 2 M1 for 0.07 × 3 000 (h) 160 000 3 M2 for 2 × 60 × 1003 ÷ 750 oe or M1 for figs 16 as answer or 1003 seen

This question in 0580/41 Oct/Nov 2015

7 The scale drawing shows the positions of three towns A, B and C on a map. The scale of the map is 1 centimetre represents 10 kilometres. C North A North Scale: 1 cm to 10 km B (a) Find the actual distance AB. Answer(a) … km [1] (b) Measure the bearing of A from B. Answer(b) … [1] (c) Write the scale 1 cm to 10 km in the form 1 : n. Answer(c) 1 : … [1] (d) A national park lies inside the triangle ABC. The four boundaries of the national park are • equidistant from C and B • equidistant from AC and CB • 15 km from CB • along AB. On the scale drawing, shade the region which represents the national park. Leave in your construction arcs. [7] (e) On the scale drawing, a lake inside the national park has area 0.4 cm2. Calculate the actual area of the lake. Answer(e) … km2 [2] __________________________________________________________________________________________

12 marks

Mark scheme: 7 (a) 123 to 127 1 (b) 288 to 292 1 (c) [1:] 1 000 000 1

This question in 0580/41 Oct/Nov 2015

1 A film company uses 512 actors in a film. The actors are in the ratio men : women : children = 7 : 11 : 14. (a) (i) Show that there are 224 children in the film. Answer(a)(i) [2] (ii) Find the number of men in the film. Answer(a)(ii) … [1] (b) Every working day, each child is given $1 to spend. Each child works for 45 days. Calculate the total amount that the film company gives the children to spend. Give your answer correct to the nearest $100. Answer(b) $ … [2] (c) The children have lessons every day in groups of no more than 12. Calculate the smallest possible number of groups. Answer(c) … [2] (d) The film costs four million and ninety three thousand dollars to make. (i) Write this number in figures. Answer(d)(i) … [1] (ii) Write your answer to part (d)(i) in standard form. Answer(d)(ii) … [1] (e) A DVD copy of the film costs $2.75 to make. The selling price is $8.20 . Calculate the percentage profit. Answer(e) … % [3]

12 marks

Mark scheme: Question Answer Mark Part marks 512512 5125121 (a) (i) × 14 M2 or M1 for 7 + 11 + 14 7 + 11 + 14 (ii) 112 1 (b) 10 100 2 M1 for 224 × 45 soi by 10080 (c) 19 2 M1 for 224 ÷ 12 soi by 18.66 to 18.67 or 18.7 or 2 18 3 (d) (i) 4 093 000 1 (ii) 4.093 × 106 1FT FT their (d)(i) 2.8 − .275 (e) 198 or 198.1 to 198.2 3 M2 for × 100 oe .275 2.8 2.8 − .275 or M1 for × 100 or .275 .275

This question in 0580/42 Oct/Nov 2015

1 (a) Kolyan buys water for $2.60 . He also buys biscuits. (i) The ratio cost of biscuits : cost of water = 3 : 2. Find the cost of the biscuits. Answer(a)(i) $ … [2] (ii) Kolyan has $9 to spend. Work out the total amount Kolyan spends on water and biscuits as a fraction of the $9. Give your answer in its lowest terms. Answer(a)(ii) … [2] (iii) The $9 is 62.5% less than the amount Kolyan had to spend last week. Calculate the amount Kolyan had to spend last week. Answer(a)(iii) $ … [3] (b) Priya buys a bicycle for $250. Each year the value of the bicycle decreases by 8% of its value at the beginning of that year. Calculate the value of Priya’s bicycle after 10 years. Give your answer correct to the nearest dollar. Answer(b) $ … [3] __________________________________________________________________________________________

10 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 3.9[0] 2 M1 for 2.6 ÷ 2 13 (ii) cao 2 B1 for any correct unsimplified fraction 18 (iii) 24 3 M2 for 9 ÷ 0.375 oe or M1 for associating 9 with (100 – 62.5)% (b) 109 cao 3 B2 for 108.5 to 108.6 or 10 8  M1 for 250 × − 1  oe  100  −4  k 

This question in 0580/43 Oct/Nov 2015

7 (a) The cost of a loaf of bread is x cents. The cost of a cake is (x – 5) cents. The total cost of 6 loaves of bread and 11 cakes is $13.56 . Find the value of x. Answer(a) x = … [4] (b) NOT TO y + 1 SCALE y y + 3 2y + 1 The area of the rectangle and the area of the triangle are equal. Find the value of y. Answer(b) y = … [4] (c) The cost of a bottle of water is (w – 1) cents. The cost of a bottle of milk is (2w – 11) cents. A certain number of bottles of water costs $4.80 . The same number of bottles of milk costs $7.80 . Find the value of w. Answer(c) w = … [4] (d) NOT TO u cm SCALE t (3u – 2) cm The area of the triangle is 2.5 cm2. (i) Show that 3u2 – 2u – 5 = 0. Answer(d)(i) [2] (ii) Factorise 3u2 – 2u – 5. Answer(d)(ii) … [2] (iii) Find the size of angle t. Answer(d)(iii) t = … [3] __________________________________________________________________________________________

19 marks

Mark scheme: 7 (a) 83 nfww 4 B3 for 17x = 1411 or 17x = 14.11 oe in form ax = b or final answer of 0.83 or B2 for 6x + 11x – 55 = 1356 oe or 6x + 11x –[0.] 55 = 13[.]56 or M1 for 6x + 11(x – [0.0]5) = 13[.]56 1 1 (b) oe nfww 4 M1 for y ( y + )3 oe or ( 2 y + 1)( y + )1 oe 3 2 and B2 for 2 y 2 + 6 y = 2 y 2 + 2 y + y + 1 oe or better or B1 for ( 2 y + 1)( y + )1 = 2 y 2 + 2 y + y + 1 soi 4[.]80 7[.]80 (c) 25 nfww 4 M1 for or w − 1 2 w − 11 4[.]80 7[.]80 M1 for = oe w − 1 2 w − 11 M1 for 480 ( 2 w − 11) = 780 ( w − )1 oe or ALT M1 for n ( w − )1 = 4[.]80 or n ( 2 w − 11) = 7[.]80 M1 for 2 wn − 11n = 7[.]80 2 wn −n2 = 9[.]60 oe M1 for 9 n = 180 oe or better or ALT M1 for n ( w − )1 = 4[.]80 or n ( 2 w − 11) = 7[.]80 4[.]80 + n 7[.]80 + 11n M1 for = n 2 n M1 for 9 n = 180 oe or better 1 1 (d) (i) u (3u − 2) = 2.5 M1 First step must involve u (3u − 2) 2 2 One further correct step leading to 3u 2 −u2 − 5 = 0 with no errors A1 (ii) (3u − 5)(u + )1 2 SC1 for (3u + a )(u + b ) where ab = − 5 or a + 3b = − 2 [a, b integers] their 53 (iii) 29.1 or 29.05… 3 M2 for tan = 3 × their 53 − 2 or M1 for substituting their positive value of u into [u and] 3u – 2

This question in 0580/43 Oct/Nov 2015

1 Aasha, Biren and Cemal share $640 in the ratio 8 : 15 : 9. (a) Show that Aasha receives $160. [1] (b) Calculate the amount that Biren and Cemal receive. Biren $ … Cemal $ … [2] (c) Aasha uses her $160 to buy some books. Each book costs $15.25 . Find the greatest number of books that she can buy. … [2] 3 1 (d) Biren spends of his share on clothes and of his share on a computer. 8 3 Find the fraction of his share that he has left. Write your fraction in its lowest terms. … [3]

8 marks

Mark scheme: 8 1 (a) × 640 oe 1 With no errors seen 8 + 15 + 9 (b) 300 and 180 2 B1 for each or SC1 for answers reversed (c) 10 nfww 2 M1 for 160 ÷ 15.25 implied by 10.5 or 10.49... nfww 7 3 1 (d) 3 M1 for + oe 24 8 3 3 1 M1dep on previous M1 for 1 − their ( + ) oe 8 3

This question in 0580/42 Feb/March 2016

5 (a) Meena sells her car for $6000. This is a loss of 4% on the price she paid. Calculate the price Meena paid for the car. $ … [3] (b) Eisha changes some euros (€) into dollars ($) when the exchange rate is €1 = $1.351 . She receives $6000. Calculate how many euros Eisha changes. Give your answer correct to the nearest euro. € … [3] (c) Meena and Eisha both invest their $6000. Meena invests her $6000 at a rate of 1.5% per year compound interest. Eisha invests her $6000 in a bank that pays simple interest. After 8 years, their investments are worth the same amount. Calculate the rate of simple interest per year that Eisha received. … % [5]

11 marks

Mark scheme: 6000 5 (a) 6250 3 M2 for × 100 oe 100 − 4 or M1 for 6000 associated with 96 [%] (b) 4441 3 B2 for 4441.1 to 4441.2 or 4440 6000 or M1 for 1.351 Qu. Answers Mark Part Marks 8  1.5  (c) 1.58 or 1.581… 5 M1 for 6000 ×  1 +  oe  100  A1 for 6758.95… … or 6758.96 to 3 sf or better or 758.95 or 758.96 rounded or truncated to 3 sf and M2 for 8 100 {their (6000 × 1.015 ) − 6000} × oe 6000 × 8 6000 × r × 8 or M1 for oe 100

This question in 0580/42 Feb/March 2016

8 (a) y is directly proportional to the positive square root of ^ x + 2h. When x = 7, y = 9. Find y when x = 23. y = … [3] (b) Simplify. x 2 + 12x + 36 x 2 + 4x - 12 … [5] X - a(c) W = a Make a the subject of the formula. a = … [5] (d) Write as a single fraction in its simplest form. x - 2 x + 3 - x + 1 x - 1 … [5]

18 marks

Mark scheme: 8 (a) 15 nfww 3 M1 for y = k ( x + 2 ) oe A1 for k = 3 x + 6 2 (b) nfww final answer 5 B2 for ( x + 6 ) oe x − 2 or SC1 for ( x + a )( x + b ) where ab = 36 or a + b = 12 or x(x + 6) + 6( x + 6) B2 for ( x − 2 )( x + 6 ) or SC1 for ( x + a )( x + b ) where ab = − 12 or a + b = 4 or x(x + 6) – 2( x + 6) or x(x – 2) + 6(x – 2) X 2 X − a (c) 2 nfww final answer 5 M1 for W = or W a = X − a W + 1 a M1 for next productive step M1 for 2nd productive step M1 for 3rd productive step M1 for final step leading to a = −7 x − 1 −7 x − 1 (d) 2 or 5 M1 for common denominator ( x − 1)( x + 1) isw x − 1 ( x − 1)( x + 1) final answer M1 for ( x − 2 )( x − 1) − ( x + 3 )( x + 1) B2 for x 2 − 2 x − x + 2 − ( x 2 + 3 x + x + 3) oe or B1 for either expansion Qu. Answers Mark Part Marks

This question in 0580/42 Feb/March 2016

1 (a) Kristian and Stephanie share some money in the ratio 3 : 2. Kristian receives $72. (i) Work out how much Stephanie receives. $ … [2] (ii) Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game. $ … [1] (iii) Kristian also buys a meal for $8.40 . Calculate the fraction of the $72 Kristian has left after buying the computer game and the meal. Give your answer in its lowest terms. … [2] (iv) Stephanie buys a book in a sale for $19.20 . This sale price is after a reduction of 20%. Calculate the original price of the book. $ … [3] (b) Boris invests $550 at a rate of 2% per year simple interest. Calculate the amount Boris has after 10 years. $ … [3] (c) Marlene invests $550 at a rate of 1.9% per year compound interest. Calculate the amount Marlene has after 10 years. $ … [2] (d) Hans invests $550 at a rate of x% per year compound interest. At the end of 10 years he has a total amount of $638.30, correct to the nearest cent. Find the value of x. x = … [3]

16 marks

Mark scheme: Question Answer Mark Part marks 72721 (a) (i) 48 2 M1 for 3 (ii) 32.4[0] 1 13 72 − their ( ii ) − 8.4 (iii) 2 M1 for oe 30 72 19.2 (iv) 24 3 M2 for oe 0.8 or M1 for recognising 19.2 is 80% 550 × 2 × 10 (b) 660 3 M2 for + 550 oe 100 550 × 2 × 10 or M1 for oe 100 (c) 663.9[0] 2 M1 for 550 × 1.01910 oe 638.3[0] 10 oe (d) 1.5[0] 3 M2 for 550 or M1 for 550 × m10 = 638.3[0] 5  k 

This question in 0580/41 May/June 2016

1 Mr Chan flies from London to Los Angeles, a distance of 8800 km. The flight takes 11 hours and 10 minutes. (a) (i) His plane leaves London at 09 35 local time. The local time in Los Angeles is 8 hours behind the time in London. Calculate the local time when the plane arrives in Los Angeles. … [2] (ii) Work out the average speed of the plane in km/h. … km/h [2] (b) There are three types of tickets, economy, business and first class. The price of these tickets is in the ratio economy : business : first class = 2 : 5 : 9. (i) The price of a business ticket is $2350. Calculate the price of a first class ticket. $ … [2] (ii) Work out the price of an economy ticket as a percentage of the price of a first class ticket. … % [1] (c) The price of a business ticket for the same journey with another airline is $2240. (i) The price of a first class ticket is 70% more than a business ticket. Calculate the price of this first class ticket. $ … [2] (ii) The price of a business ticket is 180% more than an economy ticket. Calculate the price of this economy ticket. $ … [3] (d) Mr Chan hires a car in Los Angeles. The charges are shown below. Car Hire $28.00 per day plus $6.50 per day insurance. $1.25 for every kilometre travelled after the first 800 km. The first 800 km are included in the price. Mr Chan hired the car for 12 days and paid $826.50 . (i) Find the number of kilometres Mr Chan travelled in this car. … km [4] (ii) The car used fuel at an average rate of 1 litre for every 10 km travelled. Fuel costs $1.30 per litre. Calculate the cost of the fuel used by the car during the 12 days. $ … [2]

18 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 12 45 [pm] 2 B1 for 20 45 seen or 8 45 pm seen or [0]1 35 seen (ii) 788 or 787.8 to 788.1 2 M1 for 8800 ÷ 11h 10 mins oe (b) (i) 4230[.00] 2 M1 for 2350 ÷ 5 oe (ii) 22.2 or 22.2… 1 100 + 70 (c) (i) 3808 final answer 2 M1 for 2240 × oe 100 100 + 180 (ii) 800 3 M2 for 2240 ÷ oe 100 or M1 for 2240 associated with 280% (d) (i) 1130 4 M3 for (826.5[0] – 12 × (28 + 6.5[0])) ÷ 1.25 seen or M2 for 826.5[0] – 12 × (28 + 6.5[0]) seen or M1 for 12 × (28 + 6.5[0]) seen (ii) $146.9[0] final answer 2FT FT their(d)(i) × 0.13 correctly evaluated If answer not exact to at least 3 sf or better M1 for their (d)(i) ÷ 10 × 1.3

This question in 0580/42 May/June 2016

1 A football club sells tickets at different prices dependent on age group. (a) (i) At one game, the club sold tickets in the ratio under 18 : 18 to 60 : over 60 = 2 : 7 : 3. There were 6100 tickets sold for people aged under 18. Calculate the total number of tickets sold for the game. … [3] (ii) Calculate the percentage of tickets sold for people aged under 18. … % [1] (b) The table shows the football ticket prices for the different age groups. Age Price Under 18 $15 18 to 60 $35 Over 60 $18 At a different game there were 42 600 tickets sold. • 14% were sold to people aged under 18 2 • 3 of the tickets were sold to people aged 18 to 60 • The remainder were sold to people aged over 60 Calculate the total amount the football club receives from ticket sales for this game. $ … [5] (c) In a sale, the football club shop reduced the price of the football shirts to $23.80 . An error was made when working out this sale price. The price was reduced by 30% instead of 20%. Calculate the correct sale price for the football shirt. $ … [5]

14 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 3 M2 for 6100 ÷ 2 × (2 + 7 + 3) oe 36 600 or M1 for 6100 ÷ 2 soi 2 (ii) 16 or 16.7 [16.66 to 16.67] 1 3 (b) 1 231 708 final answer nfww 5 M4 for 5964 × 15 + 28400 × 35 + 8236 × 18 or M3 for 5964 × 15 and 28 400 × 35 2 or for 5964 × 15 + 42 600 × their decimal 3 × 35 + (42 600 – 5964 – 42 600 × their 2 decimal ) × 18 3 or M2 for 5964 × 15 or 28 400 × 35 2 or for 42 600 × their decimal × 35 3 or M1 for 0.14 × 42 600 or 42 600 ÷ 3 × 2 (c) 27.2[0] nfww 5 M2 for 23.80 ÷ 0.7 oe or M1 for 23.80 associated with 70% oe and M2 for their (23.80 ÷ 0.7) × 0.8 or M1 for their (23.80 ÷ 0.7) × 0.2

This question in 0580/43 May/June 2016

1 (a) (i) Divide $105 in the ratio 4 : 3. $ … and $ … [2] (ii) Increase $105 by 12%. $ … [2] (iii) In a sale the original price of a jacket is reduced by 16% to $105. Calculate the original price of the jacket. $ … [3] (b) Jakob invests $500 at a rate of 2% per year compound interest. Claudia invests $500 at a rate of 2.5% per year simple interest. Calculate the difference between these two investments after 30 years. Give your answer in dollars correct to the nearest cent. $ … [6] (c) Michel invests $P at a rate of 3.8% per year compound interest. After 30 years the value of this investment is $1469. Calculate the value of P. P = … [3] (d) The population of a city increases exponentially at a rate of x% every 5 years. In 1960 the population was 60 100. In 2015 the population was 120 150. Calculate the value of x. x = … [3]

19 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 60 and 45 2 M1 for 105 ÷ ( 4 + 3) (ii) 117.6[0] final answer 2 M1 for 105 × 1.12 oe 16 (iii) 125 3 M2 for 105 ÷ (1 – ) oe 100 or M1 for 105 seen associated with 84% (b) 30.68 final answer 6 B5 for 30.7[0] or 30.68… or B4 for 905 to 906 and 875 or 405 to 406… and 375 OR  2  30 M1 for 500 × 1 + [ – 500] oe    100  500 × 2.5 × 30 M1 for [500 +] 100 B1 for 905 to 906 or 875 or 405 to 406 or 375  3.8  30 (c) 480 or 479.8 to 479.9… 3 M2 for 1469 ÷ 1 + oe    100   3.8  30 or M1 for P × 1 + = 1469 oe    100  120150 (d) 6.5[0] or 6.500… 3 M2 for 11 [× 100 − 100] oe 60100 or M1 for 60100 ×( )n = 120150 oe where n = 5 or 11 or 55

This question in 0580/41 Oct/Nov 2016

7 (a) $1= 3.67 dirhams Calculate the value, in dollars, of 200 dirhams. Give your answer correct to 2 decimal places. $ … [2] (b) (i) Write as a single fraction, in its simplest form. 1000 1000 - x x + 1 … [3] (ii) One day in 2014, 1 euro was worth x rand. One year later, 1 euro was worth (x + 1) rand. Winston changed 1000 rand into euros in both years. In 2014 he received 4.50 euros more than in 2015. Write an equation in terms of x and show that it simplifies to 9x 2 + 9x - 2000 = 0 . [3] (iii) Use the quadratic formula to solve the equation 9x 2 + 9x - 2000 = 0 . Show all your working and give your answers correct to 2 decimal places. x = … or x = … [4] (iv) Calculate the number of euros Winston received in 2014. Give your answer correct to 2 decimal places. … euros [2]

14 marks

Mark scheme: 7 (a) 54.50 final answer 2 B1 for 54.495 to 54.496 or 54.5 or M1 for 200 ÷ 3.67 1000 (b) (i) final answer 3 M1 for 1000 (x + 1) – 1000x x ( x + 1) M1 for denominator x(x + 1) 1000 1000 (ii) − = 4.5[0] oe M1 Allow their (b)(i) for first M1 only for a single x x + 1 fraction 1000 or = 4.5 x ( x + 1) Correctly multiplying by algebraic 1000 = 4.5x (x + 1) M1dep denominator 4.5x2 + 4.5x – 1000 = 0 9x2 + 9x – 2000 = 0 A1 Equation reached without any errors or omissions and at least one step after clearing the denominators of the fractions still with brackets included −±9 9 2 − 4(9)( − 2000) 2 (iii) 2 B1 for 9 − 4(9)( − 2000) 2(9) p + q p − q If in form or then r r B1 for p = – 9 and r = 2(9) – 15.42 B1 SC1 for answers 14.42 B1 – 15.4 or – 15.42 to – 15.41 and 14.4 or 14.41 to 14.42 or for – 14.42 and 15.42 or – 15.42 and 14.42 seen but not final answer Answers without working only score B1, B1 or SC1 (iv) 69.34 to 69.37 final answer 2FT FT 1000 ÷ their positive x with final answer must be 2 dp rounded up or down to 2 dp or M1 for 1000 ÷ their positive x

This question in 0580/42 Oct/Nov 2016

1 (a) A jigsaw puzzle has edge pieces and inside pieces. The ratio edge pieces : inside pieces = 3 : 22. (i) There are 924 inside pieces. Calculate the total number of pieces in the puzzle. … [2] (ii) Find the percentage of the total number of pieces that are edge pieces. … % [1] (iii) Anjum and Betty spent a total of 9 hours completing the puzzle. The ratio Anjum’s time : Betty’s time = 7 : 5. Work out how much time Anjum spent on the puzzle. … hours [2] (b) The price of the puzzle was $15.99 in a sale. This was 35% less than the original price. Calculate the original price of the puzzle. $ … [3] (c) Betty takes a photograph of the completed puzzle. The photograph and the completed puzzle are mathematically similar. The area of the photograph is 875 cm2 and the area of the puzzle is 2835 cm2. The length of the photograph is 35 cm. Work out the length of the puzzle. … cm [3] (d) (i) The area of another puzzle is 6610 cm2. Change 6610 cm2 into m2. … m2 [1] (ii) The cost price of this puzzle is $12.50 . The selling price is $18.50 . Calculate the percentage profit. … % [3]

15 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 1050 2 M1 for 924 ÷ 22 oe or 924 ÷ 0.88 oe If zero scored, SC1 for 126 seen (ii) 12 1 (iii) 5 ¼ hrs or 5.25 hrs 2 M1 for 9 ÷ (7 + 5) or 540 ÷ (7 + 5) If zero scored, SC1 for answer 3.75h or 3h 45 mins  35  (b) 24.6[0] 3 M2 for 15.99 ÷  1 −  oe  100  or M1 for 65% associated with 15.99 2835 (c) 63 3 M2 for 35 × oe 875 2835 875 or M1 for or or better or 875 2835 2835 875 = oe ? 35 OR 35 M2 for 2835 × oe their (875 ÷ 35) or 35 their (875 ÷ 35) M1 for or their (875 ÷ 35) 35 (d) (i) 0.661[0] 1 18.50 − 12.50 (ii) 48 3 M2 for × 100 12.50 18.50 − 12.50 18.50 or M1 for or × 100 12.50 12.50

This question in 0580/43 Oct/Nov 2016

6 D C NOT TO SCALE 40 km B L 61.1 km North 92.1 km A The diagram shows the position of a port, A, and a lighthouse, L. The circle, centre L and radius 40 km, shows the region where the light from the lighthouse can be seen. The straight line, ABCD, represents the course taken by a ship after leaving the port. When the ship reaches position B it is due west of the lighthouse. AL = 92.1 km, AB = 61.1 km and BL = 40 km. (a) Use the cosine rule to show that angle ABL = 130.1°, correct to 1 decimal place. [4] (b) Calculate the bearing of the lighthouse, L, from the port, A. … [4] (c) The ship sails at a speed of 28 km/h. Calculate the length of time for which the light from the lighthouse can be seen from the ship. Give your answer correct to the nearest minute. … h … min [5]

13 marks

Mark scheme: 6 (a) 40 2 + 61.12 − 92.12 [cosABL =] 2 × 40 × 61.1 M2 M1 for correct implicit version 130.11… 7873 A2 A1 for [cosABL =] –0.644… or – or 12220 3149.2 – 4888 40sin130.1 61.1sin130.1 (b) [0]59.5 or 59.50 to 59.511 4 M2 for or 92.1 92.1 or sin A sin130.1 sin L sin130.1 M1 for = or = 40 92.1 61.1 92.1 and A1 for 19.39 to 19.4… or 30.48 to 30.49…

This question in 0580/43 Oct/Nov 2016

1 The Smith family paid $5635 for a holiday in India. The total cost was divided in the ratio travel : accommodation : entertainment = 10 : 17 : 8. (a) Calculate the percentage of the total cost spent on entertainment. … % [2] (b) Show that the amount spent on accommodation was $2737. [2] (c) The $5635 was the total amount Mr Smith received from an investment he made 5 years ago. Compound interest at a rate of 2.42% per year was paid on this investment. Calculate the amount he invested 5 years ago. $ … [3] (d) Mr Smith, his wife and their three children visit a theme park. The tickets cost 2500 Rupees for an adult and 1650 Rupees for a child. Calculate the total cost of the tickets. … Rupees [2] (e) One day the youngest child spent 130 Rupees on sweets. On this day the exchange rate was 1 Rupee = $0.0152 . Calculate the value of the sweets in dollars, correct to the nearest cent. $ … [2]

11 marks

Mark scheme: Question Answer Marks Part Marks 1 (a) 22.9 or 22.85 to 22.86 2 8 M1 for [× 100] oe 10 + 17 + 8 17 5635 (b) 5635 × or better [= 2737] 2 M1 for 10 + 17 + 8 (10 + 17 + 8)  2.42  5 (c) 5000 3 M2 for 5635 = k 1 + oe    100   2.42  or B1 for  1 +   100  (d) 9950 2 M1 for 2 × 2500 or 3 × 1650 (e) 1.98 final answer 2 B1 for 1.976 or 1.98 not final answer or M1 for 130 × 0.0152

This question in 0580/42 Feb/March 2017

1 (a) Annie and Dermot share $600 in the ratio 11 : 9. (i) Show that Annie receives $330. [1] (ii) Find the amount that Dermot receives. $ … [1] (b) (i) Annie invests $330 at a rate of 1.5% per year compound interest. Calculate the amount that Annie has after 8 years. Give your answer correct to the nearest dollar. $ … [3] (ii) Find the amount of interest that Annie has, after the 8 years, as a percentage of the $330. … % [2] (c) Dermot has $70 to spend. He spends $24.75 on a shirt. (i) Find $24.75 as a fraction of $70. Give your answer in its lowest terms. … [1] (ii) The $24.75 is the sale price after reducing the original price by 10%. Calculate the original price. $ … [3] (d) After one year, the value of Annie’s car had reduced by 20%. At the end of the second year, the value of Annie’s car had reduced by a further 15% of its value at the end of the first year. (i) Calculate the overall percentage reduction after the two years. … % [2] (ii) After three years the overall percentage reduction in the value of Annie’s car is 40.84%. Calculate the percentage reduction in the third year. … % [2]

15 marks

Mark scheme: Question Answer Marks Part marks 1(a)(i) 600 ÷ (11+ 9) × 11 [ =330] M1 Could be in separate steps with no errors seen 1(a)(ii) 270 1 1(b)(i) 372 cao nfww 3 B2 for answer 371.7…  1.5  8 or M1 for 330 × 1 + oe not spoiled    100  After zero scored, SC1 for answer 42 or 41.7… 1(b)(ii) 12.6 or 12.7 or 12.63 to 12.73 2 their (b)(i) − 330 their (b)(i) M1 for or × 100 soi by 112.7 330 330 or 113 After zero scored, SC1 for answer 12% 1(c)(i) 99 1 cao final answer 280 1(c)(ii) 27.5[0] 3 100 − 10 M2 for 24.75 ÷ oe 100 or M1 for recognising 24.75 as 90[%] oe 1(d)(i) 32 cao 2  20  15  M1 for  1 −  1 −  [x]oe  100  100  or for 0.15 × 0.8 [x] oe 1(d)(ii) 13 cao 2  20  15  M1 for  1 −  1 −  × x = 40.84 – 32 oe seen  100  100    their (d)(i)   or for their (d)(i) +  1 −    x = 40.84 oe   100  

This question in 0580/42 May/June 2017

1 (a) A library has a total of 10 494 fiction and non-fiction books. The ratio fiction books : non-fiction books = 13 : 5. Find the number of non-fiction books the library has. … [2] (b) The library has DVDs on crime, adventure and science fiction. The ratio crime : adventure : science fiction = 11 : 6 : 10. The library has 384 more science fiction DVDs than adventure DVDs. Calculate the number of crime DVDs the library has. … [2] (c) Every Monday, Sima travels by car to the library. The distance is 20 km and the journey takes 23 minutes. (i) Calculate the average speed for the journey in kilometres per hour. … km/h [2] (ii) One Monday, she is delayed and her average speed is reduced to 32 km/h. Calculate the percentage increase in the journey time. … % [5] (d) In Spain, the price of a book is 11.99 euros. In the USA, the price of the same book is $12.99 . The exchange rate is $1 = 0.9276 euros. Calculate the difference between these prices. Give your answer in dollars, correct to the nearest cent. $ … [3] (e) 7605 books were borrowed from the library in 2016. This was 22% less than in 2015. Calculate the number of books borrowed in 2015. … [3]

17 marks

Mark scheme: Question Answer Marks Partial marks 1(a) 2915 2 M1 for 10 494 ÷ (13 + 5) oe 1(b) 1056 2 M1 for 384 ÷ (10 – 6) oe 1(c)(i) 2 M1 for 20 ÷ 23 or 20 × 60 or 23 ÷ 60 isw 52.2 or 52.17… If zero scored, SC1 for answer 52.6 (from use of 0.38) 1(c)(ii) 63[.0] or 63.03 to 63.05… 5 their 52.17... − 32 M4 for × 100 oe 32 their 52.17... − 32 or M3 for oe or 32 their 52.17... × 100 oe 32 OR 5 B2 for [hours] oe or 37.5 [minutes] 8 or M1 for 20 ÷ 32 or better and their 37.5 − 23 M2 for × 100 oe 23 their 37.5 − 23 their 37.5 or M1 for or ×100 23 23 1(d) 0.06 final answer nfww 3 M1 for 11.99 ÷ 0.9276 or 12.99 × 0.9276 A1 for 12.93 or 12.925 to 12.926 1(e) 9750 3  22  M2 for 7605 ÷  1 −  oe  100  or M1 for (100 – 22)[%] correctly associated with 7605 seen

This question in 0580/41 Oct/Nov 2017

1 Adele, Barbara and Collette share $680 in the ratio 9 : 7 : 4. (a) Show that Adele receives $306. [1] (b) Calculate the amount that Barbara and Collette each receives. Barbara $ … Collette $ … [3] (c) Adele changes her $306 into euros (€) when the exchange rate is €1 = $1.125 . Calculate the number of euros she receives. € … [2] (d) Barbara spends a total of $17.56 on 5 kg of apples and 3 kg of bananas. Apples cost $2.69 per kilogram. Calculate the cost per kilogram of bananas. $ … [3] 1 (e) Collette spends half of her share on clothes and of her share on books. 5 Calculate the amount she has left. $ … [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9 1 × 680 9 + 7 + 4 1(b) 238 136 3 B2 for 238 or 136 7 or M1 for × 680 oe or 9 + 7 + 4 4 × 680 oe seen 9 + 7 + 4 1(c) 272 2 M1 for 306 ÷ 1.125 1(d) 1.37 3 M2 for (17.56 −×5 2.69 ) ÷ 3 or M1 for 17.56 − 5 × 2.69 or B1 for 13.45 [cost of apples] 1(e) 40.8[0] 3 3FT for 0.3 × their 136 from part (b) 1 1 or M2 for their 136( + ) or better 2 5 1 1 or M1 for their 136 × or their 136 × 2 5 3 or B1 for 68 or 27.2 or or 0.3 seen 10

This question in 0580/41 May/June 2018

1 (a) Here is a list of ingredients to make 20 biscuits. 260 g of butter 500 g of sugar 650 g of flour 425 g of rice (i) Find the mass of rice as a percentage of the mass of sugar. … % [1] (ii) Find the mass of butter needed to make 35 of these biscuits. … g [2] (iii) Michel has 2 kg of each ingredient. Work out the greatest number of these biscuits that he can make. … [3] (b) A company makes these biscuits at a cost of $1.35 per packet. These biscuits are sold for $1.89 per packet. (i) Calculate the percentage profit the company makes on each packet. … % [3] (ii) The selling price of $1.89 has increased by 8% from last year. Calculate the selling price last year. $ … [3] (c) Over a period of 3 years, the company’s sales of biscuits increased from 15.6 million packets to 20.8 million packets. The sales increased exponentially by the same percentage each year. Calculate the percentage increase each year. … % [3] (d) The people who work for the company are in the following age groups. Group A Group B Group C Under 30 years 30 to 50 years Over 50 years The ratio of the number in group A to the number in group B is 7 : 10. The ratio of the number in group B to the number in group C is 4 : 3. (i) Find the ratio of the number in group A to the number in group C. Give your answer in its simplest form. … : … [3] (ii) There are 45 people in group C. Find the total number of people who work for the company. … [3]

21 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 85 1 1(a)(ii) 455 2 M1 for 260 ÷ 20 × 35 oe 1(a)(iii) 61 3 B2 for 61.5… seen or M1 for 2000 ÷ 650 soi x 20 or for = oe or other attempt at 2000 650 scaling up with 650 or for 650 ÷ 20 oe 1(b)(i) 40 3 1.89 − 1.35 M2 for [× 100] oe 1.35 1.89 or × 100 oe 1.35 or M1 for oe 1.89[× 100] soi 1.35 1(b)(ii) 1.75 nfww 3  100 + 8  M2 for 1.89 ÷   or better  100  or M1 for 1.89 associated with 108 [%] 1(c) 10.1 or 10.06… 3 20.8 M2 for 3 oe 15.6 or M1 for 15.6 × k 3 = 20.8 oe 1(d)(i) 14:15 3 B2 for correct unsimplified 3 term ratio A: B: C or correct unsimplified two term ratio A : C or M1 for attempt to find common multiple of 4 and 10 or other common value for B 4 10 or for 7 × oe or 3 × oe 10 4 1(d)(ii) 147 3 45 M2 for (14 + 20 [ +15] ) oe or 15 45 ÷ 3 × 4 + (45 ÷ 3 × 4) ÷ 10 × 7 [+ 45] or M1 for 45 ÷ 3 oe or 45 ÷ their (d)(i) value for C shown

This question in 0580/42 May/June 2018

1 Marianne sells photos. (a) The selling price of each photo is $6. (i) The selling price for each photo is made up of two parts, printing cost and profit. For each photo, the ratio printing cost : profit = 5 : 3. Calculate the profit she makes on each photo. $ … [2] (ii) Calculate her profit as a percentage of the selling price. … % [1] (iii) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 = $1.091 . € … [2] (b) Marianne sells two sizes of photo. These photos are mathematically similar rectangles. The smaller photo has length 15 cm and width 12 cm. The larger photo has area 352.8 cm2. Calculate the length of the larger photo. … cm [3] (c) In a sale, Marianne buys a new camera for $483. This is a reduction of 8% on the original price. Calculate the original price of the camera. $ … [3]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 2.25 final answer 2 3 6 M1 for or oe 5 + 3 5 + 3 1(a)(ii) 37.5 1 (a)(i) FT their × 100 6 1(a)(iii) 5.5[0] or 5.499 to 5.500 2 M1 for 6 ÷ .1091 1(b) 21 3 3528. M2 for 15 × oe 15 × 12 or SC2 for answer 16.8 352 8. 15× 12 or M1 for or seen 15 × 12 352 8. or M1 for a correct implicit statement for the length 1(c) 525 3 483 M2 for [× 100] oe 100 − 8 or M1 for 483 associated with 92 [%]

This question in 0580/41 Oct/Nov 2018

1 (a) The Muller family are on holiday in New Zealand. (i) They change some euros (€) and receive $1962 (New Zealand dollars). The exchange rate is €1 = $1.635 . Calculate the number of euros they change. € … [2] (ii) The family spend 15% of their New Zealand dollars on a tour. Calculate the number of dollars they have left. $ … [2] (iii) The family visit two waterfalls, the Humboldt Falls and the Bridal Veil Falls. The ratio of the heights Humboldt Falls : Bridal Veil Falls = 5 : 1. The Humboldt Falls are 220 m higher than the Bridal Veil Falls. Calculate the height of the Humboldt Falls. … m [2] (b) (i) Water flows over the Browne Falls at a rate of 3680 litres per second. After rain, this rate increases to 9752 litres per second. Calculate the percentage increase in this rate. … % [3] (ii) After rain, water flows over the Sutherland Falls at a rate of 74 240 litres per second. This is an increase of 45% on the rate before the rain. Calculate the rate before the rain. … litres/second [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 1200 2 M1 for 1962 ÷ 1.635 1(a)(ii) 1667.7[0] final answer 2 15 M1 for 1962 × (1 – ) oe 100 or B1 for 294.3[0] If 0 scored, SC1 for answer 1020 1(a)(iii) 275 2 M1 for 220 ÷ their (5 – 1) soi 1b(i) 165 3 9752 − 3680 M2 for [× 100 ] oe or 3680 9752 × 100 oe 3680 9752 or M1 for or 9752 – 3680 3680 1b(ii) 51 200 3 74240 M2 for [× 100 ] oe 100 + 45 or M1 for 74 240 associated with 145[%] oe

This question in 0580/42 Oct/Nov 2018

2 (a) Solve 30 + 2x = 3(3 – 4x). x = … [3] (b) Factorise 12ab3 + 18a3b2. … [2] (c) Simplify. (i) 5a3c2 × 2a2c7 … [2] 3 16a 8 4 (ii) 12 e c o … [2] (d) y is inversely proportional to the square of (x + 2). When x = 3, y = 2. Find y when x = 8. y = … [3] (e) Write as a single fraction in its simplest form. 5 x - 5 - x - 2 2 … [3]

15 marks

Mark scheme: 2(a) –1.5 3 M1 for 30 + 2x = 9 – 12x or 2 10 + x = 3 – 4x 3 M1 for collecting their terms correctly to reach ax = b 2(b) 6ab2(2b + 3a2) final answer 2 M1 for any correct partial factorisation seen or for correct answer seen 2(c)(i) 10a5c9 final answer 2 B1 for final answer with 10akc9 or 10a5ck or ka5c9 2(c)(ii) 6 2 6 k 8a 8a 8a 9 or 8a6 c–9 final answer B1 for final answer with k or 9 or c c c ka 6 9 [k ≠ 0] c or for correct answer seen 2(d) 1 3 k 0.5 or M1 for y = 2 oe 2 ( x + 2 ) B1 for k = 50 or M2 for 2(3 + 2)2 = y(8 + 2)2 oe 2(e) 7 x − x 2 7 x − x 2 3 M1 for 5 × 2 – (x – 5)(x – 2) oe seen or oe final answer 2 ( x − 2 ) 2 x − 4 M1 for common denominator 2(x – 2) oe isw

This question in 0580/42 Oct/Nov 2018

2 (a) A school has 240 students. The ratio girls : boys = 25 : 23. (i) Show that the number of boys is 115. [1] (ii) One day, there are 15 girls absent and 15 boys absent. Find the ratio girls : boys in school on this day. Give your answer in its simplest form. … : … [2] (iii) Next year, the number of students will increase by 15%. Calculate the number of students next year. … [2] (iv) Since the school was opened, the number of students has increased by 60%. There are now 240 students. Calculate the number of students when the school was opened. … [3] (b) The population of a city is increasing exponentially at a rate of 2% each year. The population now is 256 000. Calculate the population after 30 years. Give your answer correct to the nearest thousand. … [3] (c) A bacteria population increases exponentially at a rate of r% each day. After 32 days, the population has increased by 309%. Find the value of r. r = … [3]

14 marks

Mark scheme: 2(a)(i) 240 M1 × 23 (23 + 25) 2(a)(ii) 11 : 10 2 M1 for 110 : 100 or better or SC1 for 10 : 11, following boys 100, girls 110 2(a)(iii) 276 2  15  M1 for 240 ×  1 +  oe  100  or B1 for 36 seen 2(a)(iv) 150 3 240 M2 for [× 100] oe 100 + 60 or M1 for evidence of 160[%] associated 240 2(b) 464 000 3 30  2  M1 for 256 000 ×  1 +  oe  100  A1 for 463 700 to 463 710 B1 for their more accurate answer seen and rounded to nearest 1000 2(c) 4.5[0] 3 M2 for [x =] 32 .409 oe 32 = .409 oe or M1 for ( x ) If 0 scored, SC2 for answer 3.6 or 3.59 or 3.588… or SC1 for 32 3.09 or 1.0358 to 1.036 seen

This question in 0580/43 Oct/Nov 2018

1 Amol and Priya deliver 645 parcels in the ratio Amol : Priya = 11 : 4. (a) Calculate the number of parcels Amol delivers. … [2] (b) Amol drives his truck at an average speed of 50 km/h. He leaves at 07 00 and arrives at 11 15. Calculate the distance he drives. … km [2] (c) Priya drives her van a distance of 54 km. She leaves at 10 55 and arrives at 12 38. Calculate her average speed. … km/h [3] (d) Priya has 50 identical parcels. Each parcel has a mass of 17 kg, correct to the nearest kilogram. Find the upper bound for the total mass of the 50 parcels. … kg [1] (e) 67 of the 645 parcels are damaged on the journey. Calculate the percentage of parcels that are damaged. … % [1] (f) (i) 29 parcels each have a value of $68. By writing each of these numbers correct to 1 significant figure, find an estimate for the total value of these 29 parcels. $ … [1] (ii) Without doing any calculation, complete this statement. The actual total value of these 29 parcels is less than the answer to part (f)(i) because … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 473 2 M1 for 645 ÷ (11 + 4) 1(b) 212.5 2 M1 for 50 × 4.25 1(c) 31.5 or 31.45 to 31.46 3 43 M2 for 54 ÷ 160 oe or M1 for time =1h 43min or 103 [mins] or 54 ÷ their time 1(d) 875 1 1(e) 10.4 or 10.38 to 10.39 1 1(f)(i) 30 [×] 70 and 2100 1 1(f)(ii) both numbers rounded up oe 1

This question in 0580/42 Feb/March 2019

4 The diagram shows an incomplete scale drawing of a market place, ABCD, where D is on CX. The scale is 1 centimetre represents 5 metres. X C A B Scale : 1 cm to 5 m D lies on CX such that angle DAB = 75°. (a) On the diagram, draw the line AD and mark the position of D. [2] (b) Find the actual length of the side BC of the market place. … m [2] (c) In this part, use a ruler and compasses only. Street sellers are allowed in the part of the market place that is • more than 35 metres from A and • nearer to C than to B and • nearer to CD than to BC. On the diagram, construct and shade the region where street sellers are allowed. [7] (d) Write the scale of the drawing in the form 1 : n. 1 : … [1]

12 marks

Mark scheme: 4(a) Correct ruled line with D marked 2 B1 for correct ruled line or short line 4(b) 47.5 2 B1 for 9.5 or 95 mm seen or for answer figs 465 to figs 485 4(c) Correct arc radius 7 cm 2 B1 for complete arc other radius, centre A or correct but short arc Correct ruled perpendicular bisector of 2 B1 for correct perpendicular bisector BC with correct pairs of arcs without correct arcs or for correct arcs, no/incorrect line Correct ruled bisector of angle BCD with 2 B1 for correct angle bisector without correct pairs of arcs correct arcs or for correct arcs, no/incorrect line correct region shaded 1 Dep on at least B1B1B1 and five boundaries one of which is an arc 4(d) [1 :] 500 1

This question in 0580/42 Feb/March 2019

1 (a) The price of a newspaper increased from $0.97 to $1.13 . Calculate the percentage increase. … % [3] (b) One day, the newspaper had 60 pages of news and advertisements. The ratio number of pages of news : number of pages of advertisements = 5 : 7. (i) Calculate the number of pages of advertisements. … [2] (ii) Write the number of pages of advertisements as a percentage of the number of pages of news. … % [1] (c) On holiday Maria paid 2.25 euros for the newspaper when the exchange rate was $1 = 0.9416 euros. At home Maria paid $1.13 for the newspaper. Calculate the difference in price. Give your answer in dollars, correct to the nearest cent. $ … [3] (d) The number of newspapers sold decreases exponentially by x% each year. Over a period of 21 years the number of newspapers sold decreases from 1 763 000 to 58 000. Calculate the value of x. x = … [3] (e) Every page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre. Calculate the upper bound of the area of a page. … cm2 [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 16.5 or 16.49... 3 .1 13 − .0 97 .1 13 M2 for [× 100 ] oe or × 100 oe .0 97 .0 97 .1 13 or M1 for oe .0 97 1(b)(i) 35 2 M1 for 60 ÷ (5 + 7 ) 1(b)(ii) 140 1 1(c) $1.26 final answer 3 B2 for 1.259... or 1.26 but not as final answer or M1 for .225 ÷ .09416 If 0 scored, SC1 for 1.13 × 0.9416 1(d) 15[.0…] 3 58000 M2 for 21 oe 1763000 21 or M1 for 58000 = 1763000 (k ) 1(e) 1239.75 2 B1 for 43 + 0.5 or 28 + 0.5 oe seen

This question in 0580/42 May/June 2019

2 (a) Ali and Mo share a sum of money in the ratio Ali : Mo = 9 : 7. Ali receives $600 more than Mo. Calculate how much each receives. Ali $ … Mo $ … [3] (b) In a sale, Ali buys a television for $195.80 . The original price was $220. Calculate the percentage reduction on the original price. … % [3] (c) In the sale, Mo buys a jacket for $63. The original price was reduced by 25%. Calculate the original price of the jacket. $ … [3]

9 marks

Mark scheme: 2(a) [Ali] 2700 3 B2 for one correct or for correct values [Mo] 2100 reversed or M1 for 600 ÷ (9 – 7) or for any equation that would lead to an answer of 300, 2700 or 2100, or 4800 (for the total) 2(b) 11 3 220 − 1958. M2 for [× 100] or for 220 1958. [100 − ] × 100 220 195 8. or M1 for 220 – 195.8 or for or a 220 correct implicit equation for percentage 195.8 − 220 reduction or for 220 2(c) 84 3 63 M2 for oe 25 1 − 100 or M1 for associating 63 with (100 – 25)% or a correct implicit equation for the original price.

This question in 0580/41 Oct/Nov 2019

1 (a) Mohsin has 600 pear trees and 720 apple trees on his farm. (i) Write the ratio pear trees : apple trees in its simplest form. … : … [1] (ii) Each apple tree produces 16 boxes of apples each year. One box contains 18 kg of apples. Calculate the total mass of apples produced by the 720 trees in one year. Give your answer in standard form. … kg [3] (b) (i) One week, the total mass of pears picked was 18 540 kg. For this week, the ratio mass of apples : mass of pears = 13 : 9. Find the mass of apples picked that week. … kg [2] (ii) The apples cost Mohsin $0.85 per kilogram to produce. He sells them at a profit of 60%. Work out the selling price per kilogram of the apples. $ … [2] (c) Mohsin exports some of his pears to a shop in Belgium. The shop buys the pears at $1.50 per kilogram. The shop sells the pears for 2.30 euros per kilogram. The exchange rate is $1 = 0.92 euros. Calculate the percentage profit per kilogram made by the shop. … % [5] (d) Mohsin’s earnings increase exponentially at a rate of 8.7% each year. During 2018 he earned $195 600. During 2027, how much more does he earn than during 2018? $ … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 5 : 6 1 1(a)(ii) 2.0736[0] × 105 final answer 3 B2 for 207360 oe or M1 for 16 × 18 × 720 1(b)(i) 26780 2 M1 for 18540 ÷ 9 soi 1(b)(ii) 1.36 2 M1 for 0.85 × 1.6 oe or B1 for 0.51 or 51 1(c) 66.7 or 66.66 to 66.67 5 (2.3 − 1.5 × M4 for 0.92)[× 100] oe or 1.5 × 0.92 2.3 × 100 oe 1.5 × 0.92 OR Working in euros B2 for [€]1.38 or M1 for 1.5[0] × 0.92 M2dep on B2 or M1 for 2.3 − their 1.38[× 100] oe their 1.38 2.3 − their 1.38 or × 100 oe their 1.38 2.3 or M1 for 2.3 – their 1.38 or their 1.38 OR Working in dollars B2 for [$]2.50 or M1 for or 2.3[0] ÷ 0.92 M2dep on B2 or M1 for their 5.2 − 5.1 their 2.5 [×100] oe or × 100 5.1 1.5 their 2.5 or M1 for their 2.5 – 1.5 or 1.5 1(d) 219 000 3 B2 for 414000 or 414414[.3.…] rounded to 4 or 218814[.3.…] rounded to 4 sf or sf or more more 9  8.7  or M2 for 195600 ×  1 +  [– 195600]  100   8.7  k or M1 for 195600 ×  1 +  or better  100  (k >1 and an integer)

This question in 0580/42 Oct/Nov 2019

1 (a) In a cycling club, the number of members are in the ratio males : females = 8 : 3. The club has 342 females. (i) Find the total number of members. … [2] (ii) Find the percentage of the total number of members that are female. … % [1] (b) The price of a bicycle is $1020. Club members receive a 15% discount on this price. Find how much a club member pays for this bicycle. $ … [2] (c) In 2019, the membership fee of the cycling club is $79.50 . This is 6% more than last year. Find the increase in the cost of the membership. $ … [3] (d) Asif cycles a distance of 105 km. On the first part of his journey he cycles 60 km in 2 hours 24 minutes. On the second part of his journey he cycles 45 km at 20 km/h. Find his average speed for the whole journey. … km/h [4] (e) Bryan invested $480 in an account 4 years ago. The account pays compound interest at a rate of 2.1% per year. Today, he uses some of the money in this account to buy a bicycle costing $430. Calculate how much money remains in his account. $ … [3] 1 2(f) The formula s = at is used to calculate the distance, s, travelled by a bicycle. 2 When a = 3 and t = 10 , each correct to the nearest integer, calculate the lower bound of the distance, s. … [2]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 1254 2 M1 for 342 ÷ 3 1(a)(ii) 27.3 or 27.27… 1 1(b) 867 2 15 M1 for 1020 × oe 100  15  or 1020 ×  1 −  oe  100  1(c) 4.5[0] 3 79.5 [ 0 M2 for ][× 6 ] oe 100 + 6 79.5 [ 0 ] or × 100 oe 100 + 6 or M1 for 79.5[0] associated with 106[%] 1(d) 22.6 or 22.58… nfww 4 45 M1 for or better 20 and 60 + 45 M2 for 45 their 2h 24min + their 20 45 or M1 for their + their 2h 24min 20 1(e) 91.6[0] to 91.61 3 4  2.1  M2 for 480 × 1 + − 430 oe    100   2.1  4 OR M1 for 480 × 1 + oe    100  A1 for 522, 521.6[0] to 521.61 1(f) 112.8125 2 B1 for 2.5 or 9.5 seen

This question in 0580/43 Oct/Nov 2019

1 (a) In 2018, Gretal earned $32 000. (i) She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018. $ … [2] (ii) In 2019, Gretal’s earnings increased by 7%. Work out her earnings in 2019. $ … [2] (b) Gretal invests $5000 at a rate of 2% per year compound interest. Calculate the value of her investment at the end of 3 years. $ … [2] (c) One month, Gretal spent a total of $360 on presents. She spent 15 of this total on presents for her parents. She spent 23 of the remaining money on presents for her friends. She spent the rest of the money on presents for her sisters. Calculate the percentage of the $360 that she spent on presents for her sisters. … % [4] (d) Arjun earned $36 515 in 2019. This was an increase of 9% on his earnings in 2018. Work out his earnings in 2018. $ … [2] (e) Arjun and Gretal each pay rent. In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7. In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13. Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019. $ … [4]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 7680 2 M1 for 0.24 × 32 000 oe 1(a)(ii) 34 240 2 100 + 7 M1 for 32 000 × oe 100 1(b) 5306.04 2 3  2  M1 for 5000 ×  1 +  oe  100  1(c) 26.7 or 26.66... to 26.67 4 96 B3 for 96 or oe 360 OR 1 M3 for (1 − ) × (1 −2 ) × 100 oe 5 3 1 or M2 for (1 − ) and (1 −2 ) oe 5 3 OR M1 for 360 ÷ 5 [× 4] oe M1 for their 288 ÷ 3 [× 2] 1(d) 33 500 2 100 + 9 M1 for 36 515 ÷ oe 100 1(e) 6525 4  65 63  M3 for  −  [ A ] = 290 oe  45 45   13 7  or M2 for  −  [ A ] = 290 oe  9 5  or M1 for correct attempt to convert to a common ratio value for Arjun 13 7 or for − oe 9 5

This question in 0580/41 May/June 2020

1 (a) (i) Divide $24 in the ratio 7 : 5. $ … , $ … [2] (ii) Write $24.60 as a fraction of $2870. Give your answer in its lowest terms. … [2] (iii) Write $1.92 as a percentage of $1.60 . … % [1] (b) In a sale the original prices are reduced by 15%. (i) Calculate the sale price of a book that has an original price of $12. $ … [2] (ii) Calculate the original price of a jacket that has a sale price of $38.25 . $ … [2] (c) (i) Dean invests $500 for 10 years at a rate of 1.7% per year simple interest. Calculate the total interest earned during the 10 years. $ … [2] (ii) Ollie invests $200 at a rate of 0.0035% per day compound interest. Calculate the value of Ollie’s investment at the end of 1 year. [1 year = 365 days.] $ … [2] (iii) Edna invests $500 at a rate of r % per year compound interest. At the end of 6 years, the value of Edna’s investment is $559.78 . Find the value of r. r = … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 14, 10 2 M1 for 24 ÷ (7 + 5) 1(a)(ii) 3 2 B1 for correct fraction not in lowest terms 350 1(a)(iii) 120 1 1(b)(i) 10.2[0] 2 15 M1 for × 12 oe or better 100 1(b)(ii) 45 2 38.25 M1 for oe 15 1 − 100 1(c)(i) 85 2 500 × 1.7 × 10 M1 for oe 100 1(c)(ii) 203 or 202.5 to 202.6 2 365  0.0035  M1 for 200 ×  1 +   100  1(c)(iii) 1.9 3 559.78 M2 for 6 500  r 6 or M1 for 500  1 +  = 559.78  100 

This question in 0580/42 May/June 2020

1 (a) Campsite fees (per day) Tent … $15.00 Caravan … $25.00 The sign shows the fees charged at a campsite. Today there are 54 tents and 18 caravans on the site. Calculate the fees charged today. $ … [2] (b) In September the total income at the campsite was $37 054. This was a decrease of 4.5% on the total income in August. Calculate the total income in August. $ … [2] (c) The visitors to the campsite today are in the ratio men : women = 5 : 4 and women : children = 3 : 7. (i) Calculate the ratio men : women : children in its simplest form. … : … : … [2] (ii) Today there are 224 children at the campsite. Calculate the total number of men and women. … [3] (d) The space allowed for each tent is a rectangle measuring 8 m by 6 m, each correct to the nearest metre. Calculate the upper bound for the area of the space allowed for each tent. … m2 [2] (e) The value of the campsite has increased exponentially by 1.5% every year since it opened 30 years ago. Calculate the value of the campsite now as a percentage of its value 30 years ago. … % [2]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1260 2 M1 for 15 × 54 + 25 × 18 1(b) 38 800 2  4.5  M1 for 37054 ÷  1 −  oe  100  1(c)(i) 15 : 12 : 28 2 M1 for correct attempt to find a common multiple for the women oe 1(c)(ii) 216 3 M2 for 224 ÷ their 28 × their (15 + 12) or M1 for 224 ÷ their 28 1(d) 55.25 2 M1 for 8 + 0.5 or 6 + 0.5 seen 1(e) 156 or 156.3… 2 30  1.5  M1 for  1 +   100 

This question in 0580/43 May/June 2020

2 (a) A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats. Find the ratio First Class seats : Premium seats : Economy seats. Give your answer in its simplest form. … : … : … [2] (b) (i) For a morning flight, the costs of tickets are in the ratio First Class : Premium : Economy = 14 : 6 : 5. The cost of a Premium ticket is $114. Calculate the cost of a First Class ticket and the cost of an Economy ticket. First Class $ … Economy $ … [3] (ii) For an afternoon flight, the cost of a Premium ticket is reduced from $114 to $96.90 . Calculate the percentage reduction in the cost of a ticket. … % [2] (c) When the local time in Athens is 09 00, the local time in Berlin is 08 00. A plane leaves Athens at 13 15. It arrives in Berlin at 15 05 local time. (i) Find the flight time from Athens to Berlin. … h … min [1] (ii) The distance the plane flies from Athens to Berlin is 1802 km. Calculate the average speed of the plane. Give your answer in kilometres per hour. … km/h [2]

10 marks

Mark scheme: 2(a) 1 : 5 : 12 2 1 5 12 M1 for 2 : 10 : 24 or 7 : 35 : 84 or : : 18 18 18 2(b)(i) 266 and 95 3 B2 for 266 or 95 or 266 and 95 reversed 114 or M1 for 6 2(b)(ii) 15 2 114 − 96.9 M1 for [× 100] oe 114 96.9 or × 100 114 2(c)(i) 2h 50min 1 2(c)(ii) 636 2 M1 for 1802 ÷ their 2h 50min

This question in 0580/41 Oct/Nov 2020

1 Karel travelled from London to Johannesburg and then from Johannesburg to Windhoek. (a) The flight from London to Johannesburg took 11 hours 10 minutes. The average speed was 813 km/h. Calculate the distance travelled from London to Johannesburg. Give your answer correct to the nearest 10 km. … km [3] (b) The total time for Karel’s journey from London to Windhoek was 15 hours 42 minutes. The total distance travelled from London to Windhoek was 10 260 km. (i) Calculate the average speed for this journey. … km/h [2] (ii) The cost of Karel’s journey from London to Windhoek was $470. (a) Calculate the distance travelled per dollar. … km per dollar [1] (b) Calculate the cost per 100 km of this journey. Give your answer correct to the nearest cent. $ … per 100 km [2] (c) Karel changed $300 into 3891 Namibian dollars. Complete the statement. $1 = … Namibian dollars [1]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 9080 cao 3 B2 for 9078 to 9081… or M1 for 813 × their 11h 10min 1(b)(i) 654 or 653.5… 2 M1 for 10260 ÷ 15 h 42 min oe 1(b)(ii)(a) 21.8 or 21.82 to 21.83 1 1(b)(ii)(b) 4.58 or 4.59 cao 2 M1 for 470 ÷ (10260 ÷ 100) oe or 100 ÷ their (b)(ii)(a) 1(c) 12.97 1

This question in 0580/42 Oct/Nov 2020

10 (a) A box is a cuboid with length 45 cm, width 30 cm and height 42 cm. The box is completely filled with 90.72 kg of sand. Calculate the density of this sand in kg/m3. [Density = mass ÷ volume] … kg/m3 [3] (b) A bag contains 15000 cm 3 of sand. Some of this sand is used to completely fill a hole in the shape of a cylinder. The hole is 30 cm deep and has radius 10 cm. Calculate the percentage of the sand from the bag that is used. … % [3] (c) Sand costs $98.90 per tonne. This cost includes a tax of 15%. Calculate the amount of tax paid per tonne of sand. $ … [3] (d) Raj buys some sand for 3540 rupees. Calculate the cost in dollars when the exchange rate is $1 = 70.8 rupees. $ … [2]

11 marks

Mark scheme: 10(a) 1600 3 B2 for answer figs 16 or M2 for 90.72 ÷ (figs45 × figs3 × figs42) or M1 for volume = figs 45 × figs 3 × figs 42 isw 10(b) 62.8 or 62.83 to 62.84 3 π× 10 2 × 30 M2 for × 100 15000 or M1 for π × 10 2 × 30 10(c) 12.9[0] 3 B2 for 86 OR 98.9 98.9 M2 for × 0.15 oe or 98.9 − oe 15 15 1 + 1 + 100 100  15  or M1 for  1 +  a = 98.9 oe isw  100  10(d) 50 2 M1 for 3540 ÷ 70.8

This question in 0580/42 Feb/March 2021

4 (a) The exchange rate is 1 euro = $1.142 . (i) Johann changes $500 into euros. Calculate the number of euros Johann receives. Give your answer correct to the nearest euro. … euros [2] (ii) Johann buys a computer for $329. The same computer costs 275 euros. Calculate the difference in cost in dollars. $ … [2] 3 (b) Lucy spends of the money she has saved this month on a book that costs $5.25 . 8 Calculate how much money Lucy has saved this month. $ … [2] (c) Kamal invests $6130 at a rate of r% per year compound interest. The value of his investment at the end of 5 years is $6669. Calculate the value of r. r = … [3]

9 marks

Mark scheme: 4(a)(i) 438 cao 2 500 M1 for 1.142 4(a)(ii) 14.95 2 M1 for [329 –] 275 × 1.142 oe 4(b) 14 2 8 M1 for 5.25 × oe 3 4(c) 1.7[0] or 1.699… 3 6669 M2 for 5 6130 or M1 for 6669 = 6130 ( k ) 5

This question in 0580/41 May/June 2021

1 (a) A 2.5-litre tin of paint costs $13.50 . In a sale, the cost is reduced by 14%. (i) Work out the sale price of this tin of paint. $ … [2] (ii) Work out the cost of buying 42.5 litres of paint at this sale price. $ … [2] (b) Henri buys some paint in the ratio red paint : white paint : green paint = 2 : 8 : 5. (i) Find the percentage of this paint that is white. … % [1] (ii) Henri buys a total of 22.5 litres of paint. Find the number of litres of green paint he buys. … litres [2] (c) Maria paints a rectangular wall. The length of the wall is 20.5 m and the height is 2.4 m, both correct to 1 decimal place. One litre of paint covers an area of exactly 10 m2. Calculate the smallest number of 2.5-litre tins of paint she will need to be sure all the wall is painted. Show all your working. … [4]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 11.61 final answer 2  14  M1 for 13.5[0] ×  1 −  oe  100  or B1 for 1.89 1(a)(ii) 197.37 final answer 2 FT 17 × their (a)(i) exact or correct to nearest cent M1 for 42.5 ÷ 2.5 1(b)(i) 53.3 or 53.33… 1 1(b)(ii) 7.5 2 M1 for 22.5 ÷ (2 + 8 + 5) oe soi 1(c) 20.55 × 2.45 oe M2 M1 for 20.5 + 0.05 oe seen or 2.4 + 0.05 oe seen If 0 scored, SC1 here for 20.45 × 2.35 oe 3 nfww A2 M1 for their area ÷ 10 ÷ 2.5 oe

This question in 0580/42 May/June 2021

8 (a) A cuboid has length L cm, width W cm and height H cm. L cm H cm NOT TO SCALE 20.1 cm W cm 37.8 cm The diagram shows the net of this cuboid. The ratio W : L = 1 : 2. Find the value of L, the value of W and the value of H. L = … W = … H = … [5] (b) E NOT TO SCALE 24 cm D C 15 cm A 18 cm B The diagram shows a solid pyramid with a rectangular base ABCD. E is vertically above D. Angle EDC = angle EDA = 90°. AB = 18 cm, BC = 15 cm and EC = 24 cm. (i) The pyramid is made of wood and has a mass of 800 g. Calculate the density of the wood. Give the units of your answer. 1 [The volume, V, of a pyramid is V = # area of base # height.] 3 [Density = mass ' volume] … … [5] (ii) Calculate the angle between BE and the base of the pyramid.

14 marks

Mark scheme: 8(a) [L =] 11.8 5 M1 for L = 2W oe soi [W =] 5.9 M1 for W + 2H = 20.1 oe [H =] 7.1 M1 for 2L + 2H = 37.8 oe B1 for at least one correct answer 8(b)(i) 0.559 to 0.56[0…] B4 1 2 2 M2 for × 18 × 15 × 24 − 18 isw 3 conversion or M1 for h2 + 182 = 242 oe or better M1 for figs 800 ÷ figs their volume isw g/cm3 or g cm–3 final answer B1 8(b)(ii) 34.1 or 34.11 to 34.12 4 2 2 24 − 18 M3 for tan [ ] = oe 18 2 + 15 2 or M2 for 18 2 + 15 2 isw or 24 2 + 15 2 isw or M1 for 182 + 152 isw or 242 + 152 isw or M1 for indicating required angle is EBD

This question in 0580/42 May/June 2021

1 (a) (i) Yasmin and Zak share an amount of money in the ratio 21 : 19. Yasmin receives $6 more than Zak. Calculate the total amount of money shared by Yasmin and Zak. $ … [2] (ii) In a sale, all prices are reduced by 15%. (a) Yasmin buys a blouse with an original price of $40. Calculate the sale price of the blouse. $ … [2] (b) Zak buys a shirt with a sale price of $29.75 . Calculate the original price of the shirt. $ … [2] (b) Xavier’s salary increases by 2% each year. In 2010, his salary was $40 100. (i) Calculate his salary in 2015. Give your answer correct to the nearest dollar. $ … [3] (ii) In which year is Xavier’s salary first greater than $47 500? … [3] (c) In January 2020, the population of a town was 5% more than its population in January 2018. In January 2021, the population of this town was 2% less than its population in January 2020. Calculate the overall percentage increase in the population from January 2018 to January 2021. … % [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 120 2 M1 for 6 ÷ (21 – 19) oe soi 2 x or for = 6 40 1(a)(ii)(a) 34 2 15 M1 for 40 – × 40 oe or better 100 or B1 for 6 1(a)(ii)(b) 35 2  15  M1 for  1 −  × p = 29.75 or better  100  1(b)(i) 44 274 cao 3 B2 for 44273 to 44274 or 44270  2  5 or M1 for 40100 ×  1 +  oe  100  1(b)(ii) 2019 nfww 3 M2 for one correct trial of n = 8 or n = 9 either to find a salary or, if working with 1.02n and 47 500÷ 40 100 [= 1.1845], to find a value of 1.02n or B2 for final answer 9 or 4 nfww or M1 for  2  n their 44 274 ×  1 +  = 47 500 oe  100   2  n or 40 100 ×  1 +  = 47 500 oe  100  or for at least one trial giving a value greater than their 44 274 1(c) 2.9 [increase] 2  5  2  M1 for  1 + × 1 −  oe  100  100  implied by 1.029 or 102.9[%]

This question in 0580/43 May/June 2021

2 Bob, Chao and Mei take part in a run for charity. (a) Their times to complete the run are in the ratio Bob : Chao : Mei = 4 : 5 : 7. (i) Find Chao’s time as a percentage of Mei’s time. … % [1] (ii) Bob’s time for the run is 55 minutes 40 seconds. Find Mei’s time for the run. Give your answer in minutes and seconds. … min … s [3] (b) Chao collects $47.50 for charity. (i) Bob collects 28% more than Chao. Find the amount Bob collects. $ … [2] (ii) Chao collects 60% less than Mei. Find how much more money Mei collects than Chao. $ … [3] (c) When running, Chao has a stride length of 70 cm, correct to the nearest 5 cm. Chao runs a distance of 11.2 km, correct to the nearest 0.1 km. Work out the minimum number of strides that Chao could take to complete this distance. … [4] (d) In 2015, a charity raised a total of $1.6 million. After 2015, this amount increased exponentially by 2.4% each year for the next 5 years. Work out the amount raised by the charity in 2020. $ … million [2]

15 marks

Mark scheme: 2(a)(i) 71.4 or 71.42 to 71.43 1 2(a)(ii) 97 [min] 25 [s] 3 B2 for 13 min 55 sec seen or 97.4 or 97.41 to 97.42 seen or 5845 seen OR M2 for 55.66… ÷ 4 × 7 oe or 3340 ÷ 4 × 7 oe or for 7/4 × 55 + 7/4 × 40 oe or M1 for 55 min 40 sec ÷ 4 oe or M1 for total time ÷ 16 soi 2(b)(i) 60.8[0] 2  28  M1 for 47.5 ×  1 +  oe  100  or B1 for 13.3[0] 2(b)(ii) 71.25 3 B2 for 118.75  60  Or M2 for 47.50 ÷  1 −  – 47.50  100   60  or M1 for x ×  1 −  = 47.50 oe or  100  better 2(c) 15 380 4 M3 for (1 120 000 – 5000) ÷ (70 + 2.5) oe or B2 for answer figs 15 379 to figs 15 380 or M2 for (1 120 000 ± 5000) ÷ (70 ± 2.5) oe or M1 for one of figs 675, 725, 1115, 1125 seen 2(d) 1.8[0] or 1.801 to 1.802 [million] nfww 2 5  2.4  M1 for figs 16 ×  1 +  oe  100 

This question in 0580/41 Oct/Nov 2021

1 (a) Malena has 450 fruit trees. The fruit trees are in the ratio apple : pear : plum = 8 : 7 : 3. (i) Show that Malena has 200 apple trees. [2] (ii) Find the number of plum trees. … [1] (iii) Malena wants to increase the number of pear trees by 32%. Calculate the number of extra pear trees she needs. … [2] (iv) Each apple tree produces 48.5 kg of apples. The apples have an average mass of 165 g each. Calculate the total number of apples produced by the 200 trees. Give your answer correct to the nearest 1000 apples. … [3] (b) Malena’s land is valued at three million and seventy-five thousand dollars. (i) Write this number in figures. … [1] (ii) Write your answer to part (b)(i) in standard form. … [1] (c) In 2020, each plum tree produced 37.7 kg of plums. This was 16% more than in 2019. Calculate the mass of plums produced by each plum tree in 2019. … kg [2] (d) Malena invests $1800 at a rate of 2.1% per year compound interest. Calculate the value of her investment at the end of 15 years. $ … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 450 2 450 × 8 oe M1 for 8 + 7 + 3 8 + 7 + 3 1(a)(ii) 75 1 1(a)(iii) 56 2 32 M1 for × (450 – 200 – their 75) oe 100 32 450 or × × 7 oe 100 8 + 7 + 3 If 0 scored, SC1 for answer 231 1(a)(iv) 59 000 nfww 3 B2 for 58 600 to 58 800 or B1 for 293 to 294 figs485 × 200 or M1 for oe 165 If 0 scored, SC1 for their more accurate answer seen and rounded to the nearest 1000 1(b)(i) 3 075 000 1 1(b)(ii) 3.075 × 106 1 FT their (b)(i) 1(c) 32.5 2  16  M1 for x ×  1 +  = 37.7 or better  100  1(d) 2460 or 2458. … 2 15  2.1  M1 for 1800 1 +  oe  100 

This question in 0580/42 Oct/Nov 2021

1 A company employed 300 workers when it started and now employs 852 workers. (a) Calculate the percentage increase in the number of workers. … % [2] (b) Of the 852 workers, the ratio part-time workers : full-time workers = 5 : 7. Calculate the number of full-time workers. … [2] (c) The company makes 40 600 headphones in one year. Write this number (i) in words, … [1] (ii) in standard form. … [1] (d) In one month, the company sells 3 000 headphones. 3 Of these, 48% are exported, are sold to shops and the rest are sold online. 8 Calculate the number of headphones that are sold online. … [3] (e) One year, sales increased by 15%. The following year sales increased by 18%. Calculate the overall percentage increase in sales. … % [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 184 2 852 − 300 M1 for [× 100 ] oe 300 852 or for × 100 [ −100 ] oe 300 1(b) 497 2 852 M1 for × k oe where k = 1, 5 or 7 5 + 7 1(c)(i) Forty thousand six hundred 1 1(c)(ii) 4.06 × 10 4 1 1(d) 435 3  48 3  M2 for 3000 ×  1 − −  oe  100 8  or B2 for 2565, or 1440 and 1125 or 1875 and 1440 or 1560 and 1125 48 3  48 3  or M1 for 1 − − or 3000 ×  +  oe 100 8  100 8  or B1 for 1440 or 1125 or 1560 or 1875 If 0 scored SC1 for answer 975 1(e) 35.7 3 100 + 15 100 + 18 M2 for × [–1] oe or better 100 100 100 + 15 100 + 18 or M1 for k × × oe 100 100

This question in 0580/42 Feb/March 2022

2 (a) Alex, Bobbie and Chris share strawberries in the ratio Alex : Bobbie : Chris = 3 : 2 : 2. Chris receives 12 strawberries. Calculate the total number of strawberries shared. … [2] (b) In a sale, a shop reduces all prices by 12%. (i) Dina buys a book which has an original price of $6.50 . Calculate how much Dina pays for the book. $ … [2] (ii) Elu pays $11 for a toy. Calculate the original price of the toy. $ … [2] (c) Feri invests some money. The rate of interest for the first year is 2.5%. At the end of the second year the overall percentage increase of Feri’s investment is 6.6%. Find the rate of interest for the second year. … % [2] (d) A radioactive substance decays at an exponential rate of 2% per day. The initial mass is 80 g. (i) Find the mass at the end of 5 days. … g [2] (ii) Find how many more whole days, after day 5, it takes for the mass to reduce to less than 67 g. … [3]

13 marks

Mark scheme: 2(a) 42 2 M1 for 12 ÷ 2 or better 2(b)(i) 5.72 2 M1 for 100 12 6.50 100   oe or B1 for 0.88 oe 2(b)(ii) 12.5[0] 2 M1 for 100 12 11 100    x or better oe Question Answer Marks Partial Marks 2(c) 4 2 M1 for 100 2.5 100 6.6 [...] 100 100     oe 2(d)(i) 72.3 or 72.31... 2 M1 for 5 100 2 80 100        oe 2(d)(ii) 4 nfww 3 B2 for answer 9 nfww or M2 for correct trials with values giving either side of 67 or M1 for 100 2 80 100        n = 67 or  100 2 67 100          k their i or an evaluated trial with n ⩾ 6 or k ⩾ 1

This question in 0580/41 May/June 2022

1 (a) Find the lowest common multiple (LCM) of 30 and 75. … [2] (b) Share $608 in the ratio 4 : 5 : 7. $ … $ … $ … [3] 6 .39 # 10 4 (c) Work out 6 . 2 .45 # 10 Give your answer in standard form. … [2] (d) Write .027o o as a fraction. … [1] (e) A stone has volume 45 cm 3 and mass 126 g. Find the density of the stone, giving the units of your answer. [Density = mass ' volume] … … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 150 2 B1 for answer 150k or M1 for prime factors of 30 or 75 seen or a list of multiples of both 30 and 75 with at least 3 of each 30  75 or for oe 15 or for answer 2  3  52 1(b) 152 3 Accept in any order B2 for two correct answers 190 608 or M1 for  k oe where k =1, 4, 5, 7 4  5  7 266 1(c) 2.61  10–2 2.61  10 2 or 2 B1 for figs 2608 or 261 seen 2.608…  10–2 If 0 scored, SC1 for answer 2.6[0]  10–2 without more accurate value in standard form seen 1(d) 27 1 oe fraction 99 1(e) 2.8 1 g/cm3 or g cm–3 1

This question in 0580/42 May/June 2022

6 (a) At a festival, 380 people out of 500 people questioned say that they are camping. There are 55 300 people at the festival. Calculate an estimate of the total number of people camping at the festival. … [2] (b) 12 friends travel to the festival. 5 travel by car, 4 travel by bus and 3 travel by train. Two people are chosen at random from the 12 friends. Calculate the probability that they travel by different types of transport. … [4] (c) Arno buys a student ticket for $43.68 . This is a saving of 16% on the full price of a ticket. Calculate the full price of a ticket. $ … [2] (d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave. … min [3] (ii) At a cricket match there are 27 500 people, correct to the nearest 100. Calculate the upper bound for the difference between the number of people at the football match and at the cricket match. … [2]

13 marks

Mark scheme: 6(a) 42 028 2 380 M1 for oe soi isw 500 6(b) 47 4 0.712[1…] oe 66  5 4   4 3   5 3  M3 for 2   2   2         12 11   12 11   12 11  oe  5 4 4 3 3 2  or 1 –      oe    12 11 12 11 12 11  or M2 for sum of 3 or more correct product pairs and no incorrect pairs 5 4 4 3 3 2 or for      and no other 12 11 12 11 12 11 pairs k j or M1 for  seen 12 11 94 If 0 scored SC1 for answer oe 144 6(c) 52 2 100  16 M1 for x   43.68 oe or better 100 6(d)(i) 70 or 70.16[5…] or 70.17 or 70.2 3 29750 to 29800 29750 to 29800 M2 for or or 400  25 400  24 29800  50 400to425 or B1 for 29 750 or 29 850 or 29 849 or 375 or 425 or 424 seen 6(d)(ii) 2399 2 B1 for 27 450 or 27 550 or 27 549 or 29 850 or or 2400 nfww 29 849 seen

This question in 0580/42 May/June 2022

1 (a) (i) At a football club, season tickets are sold for seated areas and for standing areas. The cost of season tickets are in the ratio seated : standing = 5 : 3. The cost of a season ticket for the standing area is $45. Find the cost of a season ticket for the seated area. $ … [2] (ii) In 2021, the value of the team’s players was $2.65 million. In 2022 this value has decreased by 12%. Find the value in 2022. $ … million [2] (iii) The number of people at a football match is 1455. This is 6.25% of the total number of people allowed in the stadium. Find the total number of people allowed in the stadium. … [2] (iv) The average attendance increased exponentially by 4% each year for the three years from 2016 to 2019. In 2019 the average attendance was 1631. Find the average attendance for 2016. … [3] (b) Another club sells season tickets for individuals and for families. In 2018, the number of season tickets sold is in the ratio family : individual = 2 : 7. (i) The number of family season tickets sold is x. Write an expression, in terms of x, for the number of individual season tickets sold. … [1] (ii) In 2019, the number of family season tickets sold increases by 12 and the number of individual season tickets sold decreases by 26. Complete the table by writing expressions, in terms of x, for the number of tickets sold each year. Year Family tickets Individual tickets 2018 x 2019 [2] (iii) In 2019, the number of individual season tickets sold is 3 times the number of family season tickets sold. Write an equation in x and solve it to find the number of family tickets sold in 2018. x = … [4]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 75 2 45 M1 for [× k] where k is 1, 5 or 8 3 1(a)(ii) 2.332 oe 2  12  M1 for 2.65 [million]   1 −  oe  100  or B1 for 0.318[million] seen 1(a)(iii) 23 280 cao 2 6.25 M1 for  x = 1455 or better 100 1(a)(iv) 1450 or 1449 to 1450 3 3  4  M2 for 1631 = k 1 + oe or better    100   4 3 or B1 for 1 + oe seen    100   4  n or M1 for 1631 = k 1 + , n > 0 oe    100  1(b)(i) 7 x 1 oe 2 1(b)(ii) 7 x 2 FT their (b)(i) x + 12 – 26 oe B1 for x + 12 2 final answer 7 x B1 for their – 26 2 1(b)(iii) 7 x 4  7 x  − 26 = 3(x + 12) oe M1dep for their  − 26  = 3  their (x + 12) oe 2  2  leading to 124 M2dep for isolating x terms, dep on eqn with term in x and constant on each side and with a bracket or fraction. or M1dep for correctly removing brackets or dealing with fractions, dep on eqn with term in x and constant on each side and with a bracket or fraction.

This question in 0580/42 Oct/Nov 2022

1 (a) Here are the ingredients needed to make a pasta bake to serve 12 people. 250 g butter 600 g pasta 460 g mushrooms 280 g cheese 800 ml milk (i) Find the mass of the cheese as a percentage of the mass of the mushrooms. … % [1] (ii) Find the mass of butter needed to make a pasta bake to serve 18 people. … g [2] (iii) Monica has 2.2 litres of milk and 1.5 kg of each other ingredient. Calculate the greatest number of people she can serve with pasta bake. … [3] (b) In 2019, a packet of pasta cost $2.40 . This was an increase of 25% of the cost of a packet in 2018. (i) Work out the cost in 2018. $ … [2] (ii) In 2020, the cost of a packet increased by 15% from the cost in 2019. Work out the total percentage increase in the cost of a packet from 2018 to 2020. … % [3] (c) width NOT TO SCALE Pasta is sold in packets with width 11.5 cm, correct to the nearest 0.5 cm. A shop places these packets in a single line on a shelf of length 2 m, correct to the nearest 0.1 m. Find the maximum number of these packets that will fit along this shelf. You must show all your working. … [3]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 60.9 or 60.86 to 60.87 1 1(a)(ii) 375 2 250 M1 for [ 18] oe 12 1(a)(iii) 30 nfww 3 M1 for figs2200 ÷ 800 [× 12]oe M1 for 1500 ÷ 600 [× 12] oe 1(b)(i) 1.92 2  25  M1 for k   1 +  = 2.4[0] oe or better  100  1(b)(ii) 3 3 43.75 or 43 4   25  15   100 oe M2 for   1 +  1 +  [ −1]     100  100    25  15  or  1 +  1 +   100 [–100]  100  100   15  2.40   1 +  or for  100  100 [– 100] oe their(b)(i)  15   25   15  or M1 for 2.40 ×  1 +  or  1 +    1 +  oe  100   100   100  1(c) 18 nfww 3 200 to 210 200 + 5 M2 for or oe 11.5 − 0.25 11 to 11.5 or M1 for 200 + 5, 200 – 5, 11.5 + 0.25 or 11.5 – 0.25

This question in 0580/43 Oct/Nov 2022

1 (a) (i) Alain and Beatrice share $750 in the ratio Alain : Beatrice = 8 : 7. Show that Alain receives $400. [1] (ii) (a) Alain spends $150. Write $150 as a percentage of $400. … % [1] (b) He invests the remaining $250 at a rate of 2% per year simple interest. Calculate the amount Alain has at the end of 5 years. $ … [3] (iii) Beatrice invests her $350 at a rate of 0.25% per month compound interest. Calculate the amount Beatrice has at the end of 5 years. Give your answer correct to the nearest dollar. $ … [3] (b) Carl, Dina and Eva share 100 oranges. The ratio Carl’s oranges : Dina’s oranges = 3 : 5. The ratio Carl’s oranges : Eva’s oranges = 2 : 3. Find the number of oranges Carl receives. … [2] (c) Fred buys a house. At the end of the first year, the value of the house increases by 5%. At the end of the second year, the value of the house increases by 3% of its value at the end of the first year. The value of Fred’s house at the end of the second year is $60 564. Calculate how much Fred paid for the house. $ … [3] (d) Gabrielle invests $500 at a rate of r % per year compound interest. At the end of 8 years the value of Gabrielle’s investment is $609.20 . Find the value of r. r = … [3]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 750 M1  8 [= 400] 8 + 7 1(a)(ii)(a) 37.5 1 1(a)(ii)(b) 275 3 250 2 5 M2 for 250 + oe 100 250 2 5 or M1 for oe 100 1(a)(iii) 407[.00] cao nfww 3 B2 for 406.5 to 406.7  0.25  60 or M1 for 350  1 + oe isw    100  If 0 scored SC1 for answer 354 or answer 406 1(b) 24 2 M1 for [C : D =] 6 : 10 oe and [C : E =] 6 : 9 oe 6 or for [ 100] oe 6 + 10 + 9 1(c) 56 000 nfww 3  3   5  M2 for 60564  1 +  1 + oe      100   100   3  5  or M1 for [ x ] 1 +  1 +     100  100   3   5  or for 60564  1 + oe or 60564  1 +      100   100  If 0 scored, SC1 for answer 65499 to 65500 1(d) 2.5[0] or 2.499... 3 609.20 M2 for 8 oe 500 or M1 for 500  (...)8 = 609.2[0] oe

This question in 0580/42 Feb/March 2023

1 (a) An orchard has 1250 trees. The trees are in the ratio apple : pear : cherry = 12 : 9 : 4. (i) Calculate the number of apple trees. … [2] (ii) Last year in the orchard, the mean mass of fruit produced was 64 kg per tree. Calculate the total mass of fruit produced last year. Give your answer in tonnes. [1 tonne = 1000 kg] … tonnes [2] (iii) Last year, the mean mass of pears produced was 54 kg per tree. This was a decrease of 10% on the mean mass of pears produced per tree from the year before. Calculate the mean mass of pears produced by each pear tree the year before. … kg [2] 1 (iv) The orchard loses of its total number of trees in a storm. 5 Calculate the number of trees that remain. … [2] (b) Paulo buys some pears from a market. Pears cost $0.54 each or 0.51 euros each. (i) Paulo pays in dollars for 12 pears. Calculate the change he receives from $10. $ … [2] (ii) The exchange rate is $1 = 0.826 euros. Calculate how much more Paulo pays for each pear when he pays in euros. Give your answer in dollars, correct to the nearest cent. $ … [3]

13 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 600 2 1250 M1 for  k where k = 1, 4, 9, 12 oe 12  9  4 1(a)(ii) 80 2 M1 for 1250 × 64 [÷ 1000] 1(a)(iii) 60 2  10  M1 for x  1   54 oe    100  1(a)(iv) 1000 2 M1 for 1250 – (1250 ÷ 5) oe or B1 for 250 1(b)(i) 3.52 2 M1 for [10 –] 12 × 0.54 or B1 for 6.48 1(b)(ii) 0.08 3 B2 for 0.077[4...] or M1 for 0.51 ÷ 0.826 If 0 or 1 scored award instead SC2 for 0.93 final answer OR If 0 scored SC1 for 0.06 as answer

This question in 0580/41 May/June 2023

1 (a) 42° NOT TO SCALE x° The diagram shows an isosceles triangle with the base extended. Find the value of x. x = … [3] (b) The diagram shows three lines meeting at a point. The ratio a : b : c = 3 : 4 : 5. Find the value of c. a° NOT TO c° b° SCALE c = … [3] (c) A regular pentagon has an exterior angle, d. A regular hexagon has an interior angle, h. d Find the fraction . h Give your answer in its simplest form. … [4] (d) S R x° ( x + 20)° NOT TO SCALE ( 3x – 40)° Q ( 2x – 5)° P Show that PQRS is a cyclic quadrilateral. [5] (e) B A 50° 9 cm NOT TO O SCALE The diagram shows a circle of radius 9 cm, centre O. The minor sector AOB, with sector angle 50°, is removed from the circle. Calculate the length of the major arc AB. … cm [3]

18 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 111 3  42 M2 for 180 –180 oe or 42 + 2 180  42 oe 2 180  42 or M1 for oe 2 1(b) 150 3 M1 for k ÷ (3 + 4 + 5) [×p] where p = 1, 3, 4 or 5 5 or oe 12 B1 for 360 used 1(c) 3 4 72 cao nfww B3 for 5 120 or B2 for [d = ] 72 or [h = ] 120 or M1 for 360 ÷ 5 oe isw or 180 – (360 ÷ 6) isw or for (6 – 2) × 180 [÷ 6] 1(d) x + 2x – 5 + x + 20 + 3x – 40 = 360 M1 Accept equivalent equation e.g. 7x – 25 = 360 7x = 360 + 5 – 20 + 40 or better M1 FT their equation, accept e.g. 7x = 385 x = 55 B1 55 and 125 B1dep Dep on M1M1B1 or 105 and 75 Accept 55 + 3 × 55 – 40 = 180 or 2 × 55 – 5 + 55 + 20 = 180 If B0 scored, SC1 for 55, 75, 105 and 125 Opposite angles sum to 180 oe A1 Dep on M1M1B1B1 [so PQRS is a cyclic quadrilateral ] 1(e) 48.7 or 48.69 to 48.70… 3 360  50 M2 for 2 π oe9 360 50 or M1 for  2  π oe9 360

This question in 0580/42 May/June 2023

1 (a) Tomas sells a computer, a bike and a phone. The amounts he receives are in the ratio computer : bike : phone = 14 : 17 : 9. (i) Calculate the amount he receives for the phone as a percentage of the total. … % [2] (ii) The total amount he receives is $560. Calculate how much he receives for the bike. $ … [2] (iii) Tomas originally bought the bike for $195. He wanted to make a profit of at least 25% when he sold it. Does Tomas make a profit of at least 25%? You must show all your working to support your decision. [3] (b) Ulla invests $725 for 6 years in an account paying simple interest at a rate of 1.3% per year. Calculate the total interest earned at the end of 6 years. $ … [2] (c) In a sale, all prices are reduced by 24%. Victor pays $36.86 for a pair of shoes in the sale. Calculate the original price of the shoes. $ … [2]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 22.5 2 9 M1 for [ 100] 14  17  9 1(a)(ii) 238 2 FT their 14 + 17 + 9 = N seen in (a)(i) 560 M1 for  k, their 14  17  9  where k = 1, 9, 14 or 17 1(a)(iii) METHOD 1 M2 25 M1 for  195 100 1.25  195 oe 243[.75] and No oe A1 Strict FT yes if their (a)(ii) > 243.75 If M0 scored, then SC1 for 243.75 and a correct conclusion. METHOD 2 (M2) their 238 M1 for = 1.22... oe 195 their 238 – 1 = 0.22… oe 195 22[%] (or better) and No oe (A1) Strict FT yes if their (a)(ii) gives answer > 25 If M0 scored, then SC1 for 22.05 and a correct conclusion. METHOD 3 (M2) M1 for 0.25  195 195  0.25 = 48.75 oe and their 238 – 195 = 43 43 and 48.75 and NO (A1) Strict FT yes if their (a)(ii) gives profit > 48.75 If M0 scored, then SC1 for 43 and 48.75 and a correct conclusion. METHOD 4 (M2)  25  M1 for x   1   = their 238  100  their 238  100 125 190.4 and NO (A1) Strict FT yes if their (a)(ii) gives answer > 195 If M0 scored then SC1 for 190.4 and a correct conclusion. 1(b) 56.55 2 725  1.3[ 6] M1 for oe 100 1(c) 48.5[0] 2  24  M1 for x   1   = 36.86 oe  100 

This question in 0580/43 May/June 2023

1 The table shows the amount received when exchanging $100 in some countries. Country Amount received for $100 Wales 77.05 pounds India 7437.05 rupees China 671.20 yuan Spain 85.35 euros (a) Brad changes $250 to Indian rupees. Calculate the amount he receives correct to the nearest rupee. … rupees [2] (b) Wang changes 5400 Chinese yuan into dollars. Calculate how much he receives in dollars, correct to the nearest cent. $ … [2] (c) Gretal lives in Spain and goes on holiday to Wales. She spends 3500 euros in total on travel and hotels in the ratio travel: hotels = 4 : 3 . (i) Work out how much Gretal spends, in euros, on travel. … euros [2] (ii) Work out how much she spends, in pounds, on hotels. … pounds [3] (iii) Gretal flies home to Spain. The plane flies a distance of 2200 km, correct to the nearest 100 km. The average speed of the plane is 740 km/h, correct to the nearest 20 km/h. Calculate the lower bound of the time taken, in hours and minutes, for this flight. … h … min [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 18593 cao 2 M1 for 7437.05  250 ÷ 100 oe 1(b) 804.53 cao 2 M1 for 5400 ÷ 671.20 [ 100] oe 1(c)(i) 2000 2 M1 for 3500 ÷ (4 + 3) [× k] oe 1(c)(ii) 1354.13 … 3 77.05 M2 for (3500 – their (c)(i))  oe 85.35 or M1 for (3500 – their (c)(i)) ÷ figs 85.35 oe 77.05 or for oe 85.35 or for (3500 – their (c)(i))  figs 77.05 1(c)(iii) 2 [h] 52 [min] nfww 3 2100 to 2200 2200 − 50 M2 for or 740 + 10 740 to 760 or M1 for 2200 + 50 or 2200 – 50 or 740 + 10 or 740 – 10

This question in 0580/43 Oct/Nov 2023

1 A grocer sells potatoes, mushrooms and carrots. (a) A customer buys 3 kg of mushrooms at $1.04 per kg and 4 kg of carrots at $1.28 per kg. Calculate the total cost. $ … [2] (b) In one week, the ratio of the masses of vegetables sold by the grocer is potatoes : mushrooms : carrots = 11 : 8 : 6. (i) Work out the mass of mushrooms sold as a percentage of the total mass. … % [2] (ii) The total mass of potatoes, mushrooms and carrots sold is 1500 kg. Find the mass of carrots the grocer sells this week. … kg [2] (iii) The profit the grocer makes selling 1 kg of carrots is $0.75 . Find the total profit the grocer makes selling carrots this week. $ … [1] (iv) On the last day of the week, the grocer reduces the price of 1 kg of potatoes by 8% to $1.15 . Calculate the original price of 1 kg of potatoes. $ … [2] (c) The grocer buys 620 kg of onions, correct to the nearest 20 kg. He packs them into bags each containing 5 kg of onions, correct to the nearest 1 kg. Calculate the upper bound for the number of bags of onions that he packs. … [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 8.24 cao 2 M1 for 3 1.04 + 4 1.28 1(b)(i) 32 2 8 M1 for  100  oe 11 + 8 + 6 1(b)(ii) 360 2 1500 M1 for  k where k = 1 , 11, 8 or 6 11 + 8 + 6 1(b)(iii) 270 1 FT 0.75 × their 360 1(b)(iv) 1.25 cao 2  8  M1 for x   1 −  = 1.15 oe or better  100  1(c) 140 nfww 3 620 to 640 620 + 10 M2 for or oe 5 − 0.5 4 to 5 or M1 for 620 +10 oe or 620 – 10 oe or 5 + 0.5 oe or 5 – 0.5 oe seen

This question in 0580/42 Feb/March 2024

1 (a) The table shows the areas, in km2, of the four largest rainforests in the world. Rainforest Area (km2) Amazon 5 500 000 Congo 2 000 000 Atlantic 1 315 000 Valdivian 250 000 (i) Find the area of the Valdivian rainforest as a percentage of the area of the Amazon rainforest. … % [1] (ii) Write, in its simplest form, the ratio of the areas of the rainforests Valdivian : Atlantic : Congo. … : … : … [2] (iii) The Amazon rainforest has 60% of its area in Brazil and 10% of its area in Colombia. 43 1% of the remaining area of the rainforest is in Peru. 3 Find the percentage of the Amazon rainforest that is in Brazil, Colombia and Peru. … % [3] 27 (iv) The area of the Amazon rainforest represents of the total area of rainforest in the world. 50 Calculate the total area of rainforest in the world. Give your answer correct to the nearest 100 000 km2. … km 2 [3] (v) In the world, 60.7 hectares of rainforest are lost every minute. Calculate the total area, in hectares, of rainforest that is lost in 365 days. Give your answer in standard form. … hectares [3] (b) The Amazon river has a length of 6440 km, correct to the nearest 10 km. The Congo river has a length of 4400 km, correct to the nearest 100 km. Calculate the upper bound of the difference between the lengths of the Amazon river and the Congo river. … km [3]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 4.55 or 4.545… 1 1(a)(ii) 50 : 263 : 400 cao 2 M1for a correct simplification from 250 000 : 1 315 000 : 2 000 000 1(a)(iii) 83 cao 3 1 433 M2 for  100  60  10  oe 100 or M1 for 100 – 60 – 10 seen 1(a)(iv) 10 200 000 cao 3 B2 for 10 185 185 to 10 185 200 or M1 for 5 500 000 ÷ 27 [× 50] 1(a)(v) 3.19 × 107 or 3.190… × 107 3 B2 for 31903920 or M1 for 60.7 × 60 × 24 × 365 If B0 scored SC1 for correctly converting their number seen to standard form to 3sf or better 1(b) 2095 nfww 3 M2 for 6445 – C where 4300 ⩽ C < 4400 oe or A – 4350 where 6440 < A ⩽ 6450 oe or M1 for 6440 +5 or 6440 –5 or 4400 + 50 or 4400 – 50 seen oe

This question in 0580/41 May/June 2024

1 (a) A fruit drink is made using 1.5 litres of apple juice and 450 millilitres of mango juice. Write the ratio apple juice : mango juice in its simplest form. … : … [2] (b) One litre of fruit drink is shared between three cups. The amount in the cups is in the ratio 9 : 6 : 10. Calculate the number of millilitres in each cup. … ml , … ml , … ml [3] (c) A shop buys bottles of the fruit drink for $3.20 each. It sells them at a profit of 15%. Calculate the selling price of each bottle of fruit drink. $ … [2] (d) The number of bottles of fruit drink sold has grown exponentially at a constant rate of 2.5% per year. 5 years ago, the shop sold 16 620 bottles. Calculate the number of bottles sold this year. … [2] (e) d cm NOT TO 23 cm SCALE 18.5 cm The bottles of juice are 18.5 cm tall, correct to the nearest millimetre. They are stored on shelves. The distance between the shelves is 23 cm, correct to the nearest centimetre. Calculate the lower bound for the distance, d cm, between the top of a bottle and the shelf above it. … cm [3]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 10 : 3 final answer 2 M1 for 1500 : 450 oe in ratio form If 0 scored SC1 for answer 3 : 10 1(b) 360 240 400 3 B2 for answer 0.36 0.24 0.4 or for answer two of 360 240 400 1000 or M1 for [ k ] where k = 1, 9, 9  6  10 6 or 10 If 0 scored, SC1 for answer with 3 values in ratio 9 : 6 : 10 in that order 1(c) 3.68 cao 2  15  M1 for  1    3.2 oe  100  or B1 for answer 0.48 1(d) 18 804[.0...] 2  2.5  5 1 for 16620   1   oe  100  1(e) 3.95 3 M2 for 22.5 – (18.5 to 18.6) or (22 to 23) −18.55 or M1 for 23 – 0.5 oe seen or 23 + 0.5 oe seen or 18.5– 0.05 oe seen or 18.5 + 0.05 oe seen

This question in 0580/42 May/June 2024

4 (a) Enzo, Rashid and Blessy each swim as many lengths of a swimming pool as they can in 15 minutes. The results are shown in the table. Name Number of lengths Enzo 11.25 Rashid 18.75 Blessy 20 (i) Find the number of lengths Enzo swims as a percentage of the total number of lengths all three people swim. … % [2] (ii) Write the ratio of the number of lengths each person swims in the form Enzo : Rashid : Blessy. Give your answer in its simplest form. … : … : … [2] (iii) Each length of the pool is 25 m. (a) Work out Blessy’s average swimming speed for the 15 minutes. Give your answer in metres per second. … m/s [3] (b) Rashid continues to swim at the same rate. Calculate the time it takes Rashid to swim a total distance of 5 km. Give your answer in hours and minutes. … h … min [4] (iv) Blessy swims for one hour. The number of lengths she swims decreases by 5% every 15 minutes. Calculate the number of lengths she swims in the final 15 minutes. … [3] (b) Another swimmer, Adam, swims 450 m, correct to the nearest 25 metres. This takes 10 minutes, correct to the nearest minute. Calculate the minimum distance Adam swims in one hour at this rate. … m [3]

17 marks

Mark scheme: 4(a)(i) 22.5 2 11.25 M1 for 100  oe 11.25 + 18.75 + 20 4(a)(ii) 9 : 15 : 16 2 M1 for 1125 : 1850 : 2000 or better 4(a)(iii)(a) 5 3 or 0.556 or 0.5555 to 0.5556 9 20  25 M2 for oe 15[ 60] or M1 for 20 × 25 or for their distance ÷ (15 [× 60]) oe 4(a)(iii)(b) 2 h 40 mins 4 Approach 1 8 B3 for [h]oe or 160 [mins] or 9600[s] 3 Or M3 for 5000 ÷ (18.75 × 25 × 4)[h] oe or 5000 ÷ (18.75 × 25 ÷ 15)[mins] oe or 5000 ÷ ((18.75 × 25 × 4) ÷ (60 × 60))[secs] oe Or M2 for (18.75 × 25 × 4)[m/h] oe or (18.75 × 25 ÷ 15)[m/min] oe or (18.75 × 25 × 4) ÷ (60 × 60))[m/sec] oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time Figs 267 or figs 2666 to 2667 or figs 16 or figs 96 Approach 2 B3 for 160 [mins] Or M3 for 15 × 5000 ÷ (18.75 × 25) [mins] oe Or M2 for 5000 ÷ (18.75 × 25) oe Or B1 for 200 or 1 km =1000m soi After 0 scored SC1 for time figs 16 4(a)(iv) 17.1 or 17.14 to 17.15 3 3  100 − 5  M2 for 20 ×   oe  100   100 − 5  k or M1 for 20 ×   where k is 2, or  100  4  100 − 5  3 or for 20 ×   oe seen and spoiled  100  4(b) 2500 3 425to450 450 − 12.5 M2 for or or 10 + 0.5 10 to 11 425 to 450 450 − 12.5 or 630 600 to 660 or M1 for 10.5 or 9.5 or 437.5 or 462.5 or 630[s] or 570[s]

This question in 0580/41 Oct/Nov 2024

4 (a) The angles of a quadrilateral are w°, x°, y° and z°. The ratio w : ( x + y + z) = 3 : 5. Find the value of w. w = … [2] (b) B M 105° P C NOT TO SCALE N 49° 45° A D Q A, B, C and D are points on a circle. PQ is the tangent to the circle at A. BMND is a straight line. Angle ACD = 49°, angle AMB = 105° and angle PAB = 45°. (i) Find angle BAM. Angle BAM = … [2] (ii) (a) Find angle BAD. Angle BAD = … [2] (b) Give a geometrical reason why BD is not the diameter of the circle. … … [1] (c) A B O NOT TO T D SCALE C A, B, C and D are points on a circle, centre O. TA and TC are tangents to the circle. OA = 6.75 cm and OT = 11.5 cm. (i) Show that angle AOC = 108.12°, correct to 2 decimal places. [3] (ii) Calculate the length of the minor arc ABC. … cm [2] (iii) Calculate the area of the major sector OCDA. … cm2 [3]

15 marks

Mark scheme: 4(a) 135 2 360 M1 for × k, where k = 1, 3 or 5 oe 5 + 3 4(b)(i) 26 2 B1 for ABD = 49 4(b)(ii)(a) 86 2 B1 for QAD = 49 or for BDA = 45 or for BCA = 45 4(b)(ii)(b) Angle in a semicircle = 90 1 4(c)(i) −1 6.75  M2 6.75 [2  ] cos   oe M1 for cos(…) = oe  11.5  11.5 108.117… A1 4(c)(ii) 12.7 or 12.73 to 12.74 2 108.12 M1 for  2  π  6.75 360 4(c)(iii) 100 or 100.1 to 100.2 3 360 − 108.12 M2 for  π  6.752 oe 360 108.12 or M1 for  π  6.752 360 360 − 108.12 If 0 scored, SC1 for  π  k 360

This question in 0580/42 Oct/Nov 2024

1 Dinari sells fruit and vegetables. (a) One day the mass of fruit and vegetables he sells is in the ratio fruit : vegetables = 9 : 8. He sells 48 kg of vegetables. Find the mass of the fruit he sells. … kg [2] (b) On another day he receives $280 for the fruit and vegetables he sells. The $280 is in the ratio fruit : vegetables = ( c + 3) : ( c - 1) . Find the amount he receives from selling the fruit. $ … [3] (c) In one week Dinari buys fruit and vegetables for $1620. He sells the fruit and vegetables for $1750. Calculate his percentage profit. … % [2] (d) In another week Dinari sells fruit and vegetables for $1738. He makes a profit of 10%. Calculate the amount he paid for the fruit and vegetables in that week. $ … [2]

9 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 54 2 48 M1 for 8 1(b) 142 3 B2 for 2c = 278 or better or M1 for c + 3 + c – 1 = 280 OR B2 for 2x = 276 or better or M1 for c + 3 – (c – 1) = 4 1(c) 8.02 or 8.024 to 8.025 2 1750 − 1620 M1 for [100] 1620 1750 or for 100[ −100] 1620 1(d) 1580 2 + 10 M1 for 100...  =1738 oe or better 100

This question in 0580/43 Oct/Nov 2024

3 Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B. box A … kg box B … kg [3]

3 marks

Mark scheme: 3 [A =] 3.2 3 B2 for one correct or for both correct but [B =] 5.6 reversed 2.4 or M1 for  k where k = 1, 4, 7 or 11 oe 7 − 4 x 4 or for = oe x + 2.4 7

This question in 0580/42 May/June 2025

15 m is inversely proportional to the square root of ( t + 2 ) . m = 0.5 when t = 23 . Find m when t = 98 . m = … [3]

3 marks

Mark scheme: 15 1 3 M2 for m 98 + 2 = 0.5 23 + 2 0.25 or 4 OR k M1 for m = t + 2 their k M1 for m = 98 + 2

This question in 0580/43 May/June 2025