Cambridge IGCSE Mathematics 0580 — 2006 May/June Paper 1 · Variant 1
0580/11/M/J/06 · 20 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 paper8 pages
Mark scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The temperature at noon at an Antarctic weather centre was –15 °C
1 The temperature at noon at an Antarctic weather centre was –15 °C. For At midnight it had fallen by 12 °C. Examiner's Use What was the temperature at midnight? Answer oC [1]
Mark scheme: 1 –27 1
Q2 · 9 2 0.09 90% 9% 0.9 900% 1000 100 Write down the three numbers from the list above which…
9 9 2 0.09 90% 9% 0.9 900% 1000 100 Write down the three numbers from the list above which have the same value. Answer [1]
Mark scheme: 2 9 1 0.09 9% 100 4
Q3 · Write down the number of square centimetres in one square metre
3 Write down the number of square centimetres in one square metre. Answer [1]
Mark scheme: 3 10000 or 1 x 104 oe. 1
Q4 · Write down a number, other than 1, which is a factor of both 14 and 35
4 (a) Write down a number, other than 1, which is a factor of both 14 and 35. Answer(a) [1] (b) Write down a number which is a multiple of both 14 and 35. Answer(b) [1]
Mark scheme: 4 (a) 7 1 (b) Any multiple of 70 (e.g. 490) 1
Q5 · NOT TO l m SCALE l m l m A cube of side l metres has a volume of 20 cubic metres
5 NOT TO l m SCALE l m l m A cube of side l metres has a volume of 20 cubic metres. Calculate the value of l. Answer l = [2]
Mark scheme: 5 2.71(4….) 2 M1 for attempt at cube root of 20
Q6 · Work out For 12.48 × 0.063 Examiner's
6 (a) Work out For 12.48 × 0.063 Examiner's . Use 8 + 7.52 Write down all the figures on your calculator display. Answer(a) [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer(b) [1]
Mark scheme: 6 (a) 0.075976(….) 1 (b) 0.076 1 f.t. f.t. candidates (a)
Q7 · The population of a city is 350 000 correct to the nearest ten thousand
7 The population of a city is 350 000 correct to the nearest ten thousand. Complete the statement about the limits of the population. Answer population < [2]
Mark scheme: 7 345000 355000 1, 1 2
Q8 · Factorise completely 2x2 – 6xy
8 Factorise completely 2x2 – 6xy. Answer [2]
Mark scheme: 8 2x(x – 3y) 2 M1 for 2(x2 – 3xy) or x(2x – 6y) or 2x(……)
Q9 · A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange
9 (a) A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange. Aminata chooses one piece of fruit at random. What is the probability that she chooses (i) a banana, Answer(a)(i) [1] (ii) a mango? Answer(a)(ii) [1] 5 (b) The probability that it will rain in Switzerland on 1st September is . 12 State the probability that it will not rain in Switzerland on 1st September. Answer(b) [1]
Mark scheme: 9 (a) (i) 4 1 oe. 10 (ii) 0 1 (b) 7 1 o.e. 12 5
Q10 · Simplify (a) p2 × p3, Answer(a) [1] (b) q3 ÷ q−4, Answer(b) [1] (c) (r2)3
10 Simplify (a) p2 × p3, Answer(a) [1] (b) q3 ÷ q−4, Answer(b) [1] (c) (r2)3. Answer(c) [1]
Mark scheme: 10 (a) p5 1 (b) q7 1 (c) r6 1 19 IGCSE – May/June 2006 0580 and 0581 01
Q11 · Rodriguez puts $500 into a bank account
11 Rodriguez puts $500 into a bank account. The bank pays 5% compound interest per year. For Examiner's (a) How much is the interest after one year? Use Answer(a) $ [1] (b) Work out the total amount he has in his bank account after two years. Answer(b) $ [2]
Mark scheme: 11 (a) ($) 25 1 (b) ($) 551.25 2 M1 for 500 x 1.052 or (c’s (a) + 500) x 1.05
Q12 · Draw all the lines of symmetry on the following shapes
12 (a) Draw all the lines of symmetry on the following shapes. (Shape B is a regular polygon.) Shape A Shape B [2] (b) Write down the order of rotational symmetry of shape A. Answer(b) [1]
Mark scheme: 12 (a) A-2 correct lines and B-6 correct lines 1, 1 Allow not ruled and small inaccuracies. (b) 2 1
Q13 · Solve the simultaneous equations 3x − y = 18, 2x + y = 7
13 Solve the simultaneous equations 3x − y = 18, 2x + y = 7. Answer x = y = [3]
Mark scheme: 13 (x=) 5, (y=)–3 3 M1 correct method to eliminate y or x. (add equations or correct multiply and subtract) A1, A1 ww allow SC1 for 1 correct answer. ww both correct, full marks.
Q14 · Pierre arrives at school at 08 40 and leaves at 15 30
14 (a) Pierre arrives at school at 08 40 and leaves at 15 30. How long, in hours and minutes, is he in school? Answer(a) h min [1] (b) Each day, Pierre gets up at 07 00 and goes to bed at 22 00. What percentage of each day is he in bed? Answer(b) % [2]
Mark scheme: 14 (a) 6 (h) 50 (min) 1 (b) 37.5 (%) 2 B1 for 9 (hours) seen or M1 for c’s 9 ÷ 24 x 100
Q15 · − 1 For 15 = and = 3
− 1 For 15 = and = 3 . Examiner's 4 Use (a) Write as a column vector. Answer(a) = [1] (b) Make two statements about the relationship between the lines AB and CD. Statement 1 Statement 2 [2]
Mark scheme: 15 (a) − 3 1 12 (b) Parallel oe. 1 CD is 3 times as long as AB oe. 1
Q16 · Yousef asked 24 students to choose their favourite sport
16 Yousef asked 24 students to choose their favourite sport. He recorded the information in the table below so that he could draw a pie chart. (a) Complete the table. Sport Volleyball Football Hockey Cricket Number of students 6 9 7 2 Angle on pie chart 90o 135o [2] (b) Complete the pie chart accurately to show this data. Volleyball Football [1] (c) Which is the modal sport? Answer(c) [1]
Mark scheme: 16 (a) (hockey) 105, (cricket) 30 2 1 mark each correct entry. (b) Correct line on pie chart to divide 1ft ft only if the angles in (a) total hockey and cricket. (30 ± 2) degrees 135° to left of vertical oe. (c) Football 1 19 IGCSE – May/June 2006 0580 and 0581 01
Q17 · For Examiner's Use NOT TO SCALE 90 m (a) The diagram shows the plan for a new soccer field
17 For Examiner's Use NOT TO SCALE 90 m (a) The diagram shows the plan for a new soccer field. The length of the pitch is 90 metres. The ratio length : width is 5 : 3. Calculate the width of the pitch. Answer(a) m [2] (b) The centre circle has a circumference of 57.5 metres. Calculate the radius. Answer(b) m [2]
Mark scheme: 17 (a) 54 2 M1 for 90 ÷ 5 x 3 (b) 9.15(….) 2 M1 for 57.5 ÷ (2π) or SC1 for 57.5 ÷ π. (implied by 18.3…)
Q18 · For Examiner's Use NOT TO 3 cm SCALE 2 cm 4 cm The solid shown is a cuboid with length 4…
18 For Examiner's Use NOT TO 3 cm SCALE 2 cm 4 cm The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below. [2] (b) Using your net, calculate the total surface area of the cuboid. Answer(b) cm2 [2]
Mark scheme: 18 (a) Net of the cuboid 2 M1 for a net with 6 correct size rectangles. A1 for a fully correct net. (b) 52 2ft M1 for 5 or 6 areas calculated and added or SC1 for answer of 26. ft only if 5 or 6 rectangles are shown in part (a). 8
Q19 · Joseph, Maria and Rebecca each win a prize
19 Joseph, Maria and Rebecca each win a prize. For Their total prize money is $30. Examiner's Use 7 Joseph wins of the $30. 12 Maria wins 30% of the $30. Rebecca wins the rest of the $30. Calculate the amount each receives. Answer Joseph $ [2] Maria $ [2] Rebecca $ [1]
Mark scheme: 19 (Joseph $) 17.5(0) 2 M1 for 30 ÷ 12 x 7. (Maria $) 9 2 M1 for 30 ÷ 100 x 30. (Rebecca $) 3.50 1ft 30 – c’s Joseph – c’s Maria. 6
Q20 · There are 565 sheets of paper in a book
20 There are 565 sheets of paper in a book. (a) How many sheets of paper are there in 2000 of these books? Give your answer in standard form. Answer(a) [2] (b) A pile of 565 sheets of paper is 25 millimetres high. Calculate the thickness of 1 sheet of paper. Give your answer in standard form. Answer(b) mm [3]
Mark scheme: 20 (a) 1.13 x 106 2 M1 for 2000 x 565 seen or B1 for figs 113 (b) 4.42(….) x 10–2 3 M1 for 25 ÷ 565 soi and B1 for figs 442(….) 10 Total 56
What was in this paper
The subtopics covered by these 20 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Ratio and proportion2Algebraic manipulation1Compound shapes and parts of shapes1Equations1Exponential growth and decay1Indices I1Introduction to probability1Limits of accuracy1Parallel lines1Percentages1Rates1Surface area and volume1Symmetry1The four operations1Types of number1Units of measure1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2006 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.