Cambridge IGCSE Mathematics 0580 — 2005 May/June Paper 1 · Variant 1
0580/11/M/J/05 · 23 questions · 56 marks · ≈63 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The diameter of the sun is 1 392 530 kilometres
1 The diameter of the sun is 1 392 530 kilometres. For Write this value correct to 4 significant figures. Examiner's Use Answer km [1]
Mark scheme: Question Answers Mark Notes 1 1393000 1 Allow 1393000.0 or 1.393 × 10 6 9 3
Q2 · A bag of 30 sweets contains 8 chocolates, 13 nougats and 9 toffees
2 A bag of 30 sweets contains 8 chocolates, 13 nougats and 9 toffees. A sweet is selected at random. What is the probability that it is a toffee? Answer [1]
Mark scheme: 2 9 3 1 isw only for incorrect cancelling or or 0.3 or 30% isw 30 10
Q3 · Anne took a test in chemistry
3 Anne took a test in chemistry. She scored 20 marks out of 50. Work out her percentage mark. Answer % [1]
Mark scheme: 3 40 1
Q4 · Write, in its simplest form, the ratio 3.5 kilograms : 800 grams
4 Write, in its simplest form, the ratio 3.5 kilograms : 800 grams. Answer : [2]
Mark scheme: 4 35 : 8 2 M1 for 3500 or 0.8 seen. SC1 Reversed ignore consistent units SC1 for 1: 358 or 4 38:1 ( 358 :1) or 35k : 8k (decimal form for SC1 correct to 3sf)
Q5 · Work out 4-3 as a fraction
5 Work out 4-3 as a fraction. Answer [2]
Mark scheme: 5 1 2 B1 for 1 or 4(1 ) 3 or (±) 64 seen. 64 43 decimal form only B0
Q6 · 2, 3, 5, 9, 12, 15 From the set of numbers above, write down (a) a multiple of 6, Answer…
6 2, 3, 5, 9, 12, 15 From the set of numbers above, write down (a) a multiple of 6, Answer (a) [1] (b) a prime factor of 27. Answer (b) [1]
Mark scheme: 6 (a) 12 only 1 (b) 3 only 1
Q7 · Alphonse spends $28 on food
7 Alphonse spends $28 on food. For 4 Examiner's This amount is of his allowance. Use 9 Calculate his allowance. Answer $ [2]
Mark scheme: 7 63 2 M1 for 28 ÷ 4 x 9 (can be implied by 2524 ) 63.64 or 63.63 implies M1
Q8 · When x = –3 find the value of x3+ 2x2
8 When x = –3 find the value of x3+ 2x2. Answer [2]
Mark scheme: 8 –9 www 2 B1 for – 27 or (+)18 seen
Q9 · At the market, Fernando weighs his fruit to the nearest 10 grams
9 At the market, Fernando weighs his fruit to the nearest 10 grams. He weighs a mango as 260 grams. Complete the statement in the answer space. Answer g weight of mango < g [2]
Mark scheme: 9 255 ≤ weight < 265 2 1 mark for each. Allow 255.0 and 265.0 SC1 for fully correct but reversed
Q10 · 12 m NOT TO h m SCALE 16o A ramp from a car park to a shopping centre slopes upward at an…
10 12 m NOT TO h m SCALE 16o A ramp from a car park to a shopping centre slopes upward at an angle of 16° to the horizontal. The length of the ramp is 12 metres. Calculate the difference in height, h metres, between the car park and the shopping centre. Answer m [2]
Mark scheme: 10 3.31 or 3.308 or 3.307(….) 2 M1 for 12sin16 (implied by 12 × 0.28 or better) 17 Grads 2.98…. implies M1. 3.3ww no marks
Q11 · Yasmeen is setting up a business
11 Yasmeen is setting up a business. For She borrows $5000 from a loan company. Examiner's The loan company charges 6% per year simple interest. Use How much interest will Yasmeen pay after 3 years? Answer $ [2]
Mark scheme: 11 900 2 M1 for (5000 x 3 x 6) ÷ 100 oe or B1 for 300 seen SC1 for 5900
Q12 · Make s the subject of the formula p = st – q
12 Make s the subject of the formula p = st – q. Answer s = [2]
Mark scheme: 12 (s =) (p + q)/t or p + q oe 2 B1 for p + q seen or correct ÷ by t t or p/t = s – q/t or (p –q)/t SC1 for p + q/t or p/t + q
Q13 · A B C 35o D NOT TO SCALE E In the diagram BC is parallel to DE
13 A B C 35o D NOT TO SCALE E In the diagram BC is parallel to DE. ABD and ACE are straight lines. (a) Choose one of the following words to complete the statement in the answer space. congruent equilateral isosceles similar Answer (a) Triangle ABC and triangle ADE are [1] (b) Angle BDE = 35°. Calculate the size of angle DBC. Answer (b) Angle DBC = [1]
Mark scheme: 13 (a) similar 1 (b) 145 1
Q14 · For 30 mm Examiner's Use NOT TO 2 mm SCALE An old Greek coin is a cylinder with a…
14 For 30 mm Examiner's Use NOT TO 2 mm SCALE An old Greek coin is a cylinder with a diameter of 30 millimetres and a thickness of 2 millimetres. Calculate, in cubic millimetres, the volume of the coin. [The volume of a cylinder, radius r, height h, is πr2h.] Answer mm3 [2]
Mark scheme: 14 rounds to 1410 isw 2 M1 for π × 15 2 × 2 (or π × 1.5 2 × 0.2 ) (isw only for incorrect 2 SC1 if π × 30 × 2 calculated correctly rounding eg 1413 = 141) (rounds to 5650 or 5660) (allow 3(.0)used) 1.41 cm 3 is 2 marks, 1.41 or 5.65 implies M1
Q15 · Write down a common multiple of 6 and 8
15 (a) Write down a common multiple of 6 and 8. Answer (a) [1] (b) Work out 5 3 − . 6 8 Give your answer as a fraction in its lowest terms. You must show all your working. Answer (b) [2]
Mark scheme: 15 (a) multiple of 24 1 ignore extras if lowest correct 11 2 M1 for a correct attempt at two equivalent fractions (b) 24 5×8 3×6 (e.g.. 48 and 48 seen or better) ww. and decimals alone zero
Q16 · Look at the sequence of numbers 7, 11, 15, 19, ………
16 Look at the sequence of numbers 7, 11, 15, 19, ………. (a) Write down the next number in the sequence. Answer (a) [1] (b) Find the 10th number in the sequence. Answer (b) [1] (c) Write an expression, in terms of n, for the nth number in the sequence. Answer (c) [1]
Mark scheme: 16 (a) 23 isw 1 ignore extras even if incorrect (b) 43 1ft their (a) + 20 (c) 4n + 3 oe final answer 1 allow any unsimplified form 14 e.g. 7 + (n – 1) × 4 or 7 + 4n – 4 IGCSE – JUNE 2005 0580/0581 1
Q17 · Expand the bracket and simplify the expression For Examiner's 7x + 5 – 3(x – 4)
17 (a) Expand the bracket and simplify the expression For Examiner's 7x + 5 – 3(x – 4). Use Answer (a) [2] (b) Factorise 5x2 – 7x. Answer (b) [1]
Mark scheme: 17 (a) 4x + 17 final answer 2 B1 for –3x + 12 or 4x or +17 seen (+17 strictly www) (b) x (5x – 7) 1 condone missing final bracket
Q18 · Camilla has $5 to spend in the market
18 Camilla has $5 to spend in the market. 1 She buys 12 kilograms of bananas priced at 80 cents per kilogram and 3 yams priced at 45 cents each. How much money does she have left? Answer $ [3]
Mark scheme: 18 2.45 3 B1 for 1.20 or 1.35 seen. (or 120 or 135) M1 for 5 – their (1.5 × 0.8 + 3 × 0.45) or 500 – their (1.5 × 80 + 3 × 45)
Q19 · 8.95 − 3.05 × 1.97 2.92 (a) (i) Write the above expression with each number rounded to…
19 8.95 − 3.05 × 1.97 2.92 (a) (i) Write the above expression with each number rounded to one significant figure. Answer (a)(i) [1] (ii) Use your answer to find an estimate for the value of the expression. Answer (a)(ii) [1] (b) Use your calculator to work out the value of the original expression. Give your answer correct to 2 decimal places. Answer (b) [1]
Mark scheme: 19 (a) (i) 9 – 3 × 2 1 allow slip of denominator as 3.0 or 3.00 3 (not allow zeros in other figures) (ii) (equals) 1 1ft their (a)(i) provided order of operation is as seen and both (a)(i) and (a)(ii) are to a maximum of 1dp apart from zeros (b) 1.01 1
Q20 · For Country Area (km2) Examiner's Use Brazil 8.51 x 106 Panama 7.71 x 104 Guyana 2.15 x…
20 For Country Area (km2) Examiner's Use Brazil 8.51 x 106 Panama 7.71 x 104 Guyana 2.15 x 105 Colombia 1.14 x 106 The table above gives the areas of four South American countries, correct to 3 significant figures. (a) List the countries in order of area, smallest to largest. Answer (a) < Guyana < < [1] (b) Use a whole number to complete the statement in the answer space. Answer (b) The area of Colombia is approximately times the area of Guyana. [2]
Mark scheme: 20 (a) Panama, (Guyana), 1 allow figures if correct Colombia, Brazil (b) 5 2 M1 for (1.14 × 10 6) ÷ (2.15 × 10 5) implied by figs 53(0……)
Q21 · SALE All items 35% Reduction Abdul bought a spade in this sale
21 SALE All items 35% Reduction Abdul bought a spade in this sale. Its original price was $16. (a) How much did Abdul save? Answer (a) $ [2] (b) The next day, all items were sold at half the original price. How much more would Abdul have saved if he had waited until the next day to buy the spade? Answer (b) $ [1]
Mark scheme: 21 (a) 5.6(0) oe (allow 5 35) 2 M1 for 35 ÷ 100 × 16 SC1 for $10.40 1ft $8 – their (a) if positive result from their (a) (b) 2.4(0) oe www 2 allow saving calculated from comparing costs or (allow 2 5) 15 savings
Q22 · For Examiner's DISTANCE 15 Use FROM HOME (km) 14 13 School 12 11 10 9 8 7 6 Friend's…
22 For Examiner's DISTANCE 15 Use FROM HOME (km) 14 13 School 12 11 10 9 8 7 6 Friend's House 5 4 3 2 1 Home 0 7 30 8 00 8 30 9 00 TIME (am) Ricardo rode to his friend’s house. He waited for his friend to get ready. Then they cycled together to school. Ricardo’s journey is shown on the grid. (a) Work out the speed at which Ricardo cycled to his friend’s house. Answer (a) km/h [2] (b) How long did he wait for his friend? Answer (b) min [1] (c) Ricardo’s brother left home at 8 00 am. For He cycled directly to school at a constant speed of 15 kilometres per hour. Examiner's Draw his journey on the grid opposite. Use [1] (d) How many minutes earlier than Ricardo did his brother arrive at school? Answer (d) min [1]
Mark scheme: 22 (a) 10 2 M1 for use of distance ÷ time with figures. 5/0.5, 5/30, 5/6, 5/0.30 only. Not 5/8.00, 5/0.3 (b) 20 1 (c) on the graph 1 ruled single line from 8.00 am home continued to school, 12 km line. Ignore beyond 12 km line must cross within square (d) 12 1ft ft their intended single ‘straight’ line (need not be (allow 10 < time < 15) ruled) and within a square, not on the boundary (allow 12 from unless actually on a boundary calculation)
Q23 · D C NOT TO SCALE O 25o A B E In the diagram, DE is a diameter of the circle, centre O
23 D C NOT TO SCALE O 25o A B E In the diagram, DE is a diameter of the circle, centre O. AEB is the tangent at the point E. The line DCB cuts the circle at C. Angle DEC = 25°. (a) Write down the size of angle DCE. Answer (a) Angle DCE = [1] (b) Calculate the size of angle CDE. Answer (b) Angle CDE = [2] (c) Calculate the size of angle DBE. Answer (c) Angle DBE = [2]
Mark scheme: 23 (a) 90 1 (b) 65 2ft M1 for 180 – 25 – their (a) [155 – their (a)] (c) 25 2ft ft. 90 – their (b) B1 for angle DEB = 90° used or 10 B1 for angle CEB = 65° seen
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