Cambridge IGCSE Mathematics 0580 — 2010 May/June Paper 4 · Variant 3

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]

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

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8 Examiner's Use NOT TO SCALE 3 cm 6 cm 10 cm A solid metal cuboid measures 10 cm by 6 cm by 3 cm. (a) Show that 16 of these solid metal cuboids will fit exactly into a box which has internal measurements 40 cm by 12 cm by 6 cm. Answer(a) [2] (b) Calculate the volume of one metal cuboid. Answer(b) cm3 [1] (c) One cubic centimetre of the metal has a mass of 8 grams. The box has a mass of 600 grams. Calculate the total mass of the 16 cuboids and the box in (i) grams, Answer(c)(i) g [2] (ii) kilograms. Answer(c)(ii) kg [1] For (d) (i) Calculate the surface area of one of the solid metal cuboids. Examiner's Use Answer(d)(i) cm2 [2] (ii) The surface of each cuboid is painted. The cost of the paint is $25 per square metre. Calculate the cost of painting all 16 cuboids. Answer(d)(ii) $ [3] (e) One of the solid metal cuboids is melted down. Some of the metal is used to make 200 identical solid spheres of radius 0.5 cm. Calculate the volume of metal from this cuboid which is not used. 4 [The volume, V, of a sphere of radius r is V = π r 3.] 3 Answer(e) cm3 [3] (f) 50 cm3 of metal is used to make 20 identical solid spheres of radius r. Calculate the radius r. Answer(f) r = cm [3]

Mark scheme: (iv) 8 ft 1ft ft a positive root –4 if positive answer − ( −)1 ± ( −)1 2 − 41()( −4) 2 (c) 2 B1 for ( −)1 − 41()( −4) or better 2 )1( p + q p − q If in form or r r then B1 for –(–1) and 2(1) or better Brackets and full line may be implied later –1.56, 2.56 2 B1 B1 If B0, SC1 for –1.6 or –1.562 to –1.561 and 2.6 or 2.561 to 2.562 10 (a) Dots all correctly placed in Diagram 4 1 (b) Column 4 16, 25, 16, 41 7 B2 or B1 for three correct Column 5 25, 41, 20, 61 B2 or B1 for three correct Column n: n2, 4n, n2 + (n + 1)2 oe B1 B1 B1 oe likely to be (n –1)2 + n2 + 4n or 2n2 + 2n + 1 After any correct answer for column n, apply isw (c)(i) 79 601 cao 1 (ii) 800 ft 1ft ft their 4n linear expression only

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