Cambridge IGCSE Mathematics 0580 — 2014 May/June Paper 1 · Variant 2
0580/12/M/J/14 · 21 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Question 1
1 Simplify the expression. p + p + p + p Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Qu. Part Answers Mark Part Marks 1 4p 1
Q2 · 16 2 Calculate 2
3 16 2 Calculate 2 . 1.3 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 1.49 or 1.491... 1
Q3 · Write down in fi gures (a) three hundred and forty thousand, Answer(a)…
3 Write down in fi gures (a) three hundred and forty thousand, Answer(a) ................................................ [1] (b) the number that is one less than one million. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 (a) 340 000 1 (b) 999 999 1 9 5 0 2 45 4%
Q4 · Write the following numbers in order, starting with the smallest
4 Write the following numbers in order, starting with the smallest. 5 9 0.2 45.4% 11 20 Answer ...................... < ...................... < ...................... < ...................... [2] __________________________________________________________________________________________
Mark scheme: 9 5 4 0.2 45.4% 2 B1 for 3 from 0.4545[…], 0.447[2….], 0.454, 20 11 0.45 or equivalent percentages seen or three in the correct order. If zero SC1 for correct but in reverse order.
Q5 · The temperature on Monday was –6°C
5 (a) The temperature on Monday was –6°C. On Tuesday the temperature was 3 degrees lower. Write down the temperature on Tuesday. Answer(a) ........................................... °C [1] (b) The temperature on Saturday was –2°C. The temperature on Sunday was 8°C. Write down the difference in these two temperatures. Answer(b) ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: 5 (a) –9 1 (b) 10 or −10 1
Q6 · Write 569 000 correct to 2 signifi cant fi gures
6 (a) Write 569 000 correct to 2 signifi cant fi gures. Answer(a) ................................................ [1] (b) Write 569 000 in standard form. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 6 (a) 570 000 1 (b) 5.69 × 105 1
Q7 · Find three numbers which have a mode of 4 and a mean of 6
7 Find three numbers which have a mode of 4 and a mean of 6. Answer ...................... , ...................... , ...................... [2] __________________________________________________________________________________________
Mark scheme: 7 4 4 10 2 B1 for answer of 4 4 k or 4 p q where p + q = 14
Q8 · Y NOT TO P SCALE l x 0 The equation of the line l in the diagram is y = 5 – x
8 y NOT TO P SCALE l x 0 The equation of the line l in the diagram is y = 5 – x . (a) The line cuts the y-axis at P. Write down the co-ordinates of P. Answer(a) (...................... , ......................) [1] (b) Write down the gradient of the line l. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 8 (a) (0, 5) 1 (b) – 1 1
Q9 · Solve the simultaneous equations
9 Solve the simultaneous equations. 2x – y = 7 3x + y = 3 Answer x = ................................................ y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 9 [x =] 2, [y =] – 3 2 B1 B1 or SC1 for reversed answers [ ] 1 f 28 b
Q10 · C 8 cm NOT TO SCALE 28° B A Calculate the length of AB
10 C 8 cm NOT TO SCALE 28° B A Calculate the length of AB. Answer AB = .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: [ ] 10 7.06 or 7.063 to 7.064 2 M1 for = cos28 or better 8
Q11 · The height of Mount Everest is 8800 m, correct to the nearest hundred metres
11 The height of Mount Everest is 8800 m, correct to the nearest hundred metres. Complete the statement about the height, h metres, of Mount Everest. Answer ......................... Ğ h < ......................... [2] __________________________________________________________________________________________
Mark scheme: 11 8750 8850 1, 1 If zero, SC1 for both correct but reversed
Q12 · Colin is travelling from Sydney, Australia, to Auckland, New Zealand
12 Colin is travelling from Sydney, Australia, to Auckland, New Zealand. (a) Colin’s bus leaves for Sydney airport at 12 38. The bus arrives at the airport at 13 24. How many minutes does the bus journey take? Answer(a) ......................................... min [1] (b) Colin’s fl ight from Sydney to Auckland leaves at 14 45 local time and takes 3 hours 20 minutes. The time in Auckland is 2 hours ahead of the time in Sydney. What is the local time in Auckland when his fl ight arrives? Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 12 (a) 46 1 (b) 20 05 or 8 05 pm 2 M1 for adding 3 h 20 min and 2 hours to 14 45 or B1 for 18 05 or 6 05 pm or 16 45 or 4 45 pm or 20 h [0]5 or 20 05 pm or 20 05 am IGCSE – May/June 2014 0580 12
Q13 · The scale drawing shows the positions of two villages, A and B
13 (a) The scale drawing shows the positions of two villages, A and B. The scale is 1 centimetre represents 200 metres. North B North A Scale: 1 cm to 200 m (i) Measure the bearing of B from A. Answer(a)(i) ................................................ [1] (ii) Work out the actual distance from A to B. Answer(a)(ii) ............................................ m [1] (b) The post box in Village A has a volume of 84 000 cm3. The post box in Village B has a volume of 0.1 m3. Which post box has the greater volume? Show how you decide. Answer(b) Post box in Village ............... [1] __________________________________________________________________________________________
Mark scheme: 13 (a) (i) 326 – 330 1 (a) (ii) 1100 – 1140 1 (b) B 1 dep on 100 000 or [0].084 seen www scores 0
Q14 · 14 V = Ah 3 (a) Find V when A = 15 and h = 7
1 14 V = Ah 3 (a) Find V when A = 15 and h = 7 . Answer(a) V = ................................................ [1] (b) Make h the subject of the formula. Answer(b) h = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 14 (a) 35 1 1 3V (b) or 3VA–1 2 M1 for multiplying by 3 or for dividing by A 3 or M1 for dividing by A 63− 61 61 M2 for × 100 oe or 100 ×100 oe
Q15 · At the beginning of July, Kim had a mass of 63 kg
15 At the beginning of July, Kim had a mass of 63 kg. At the end of July, his mass was 61 kg. Calculate the percentage loss in Kim’s mass. Answer ............................................ % [3] __________________________________________________________________________________________
Mark scheme: M2 for × 100 oe or 100 – ×100 oe 15 3.17 or 3.174 to 3.175 3 63 63 63− 61 61 or M1 for oe or × 100 63 63 1 1 3 1
Q16 · 1 1 16 Without using your calculator, work out – # 1 6 2 2 ` j
5 1 1 16 Without using your calculator, work out – # 1 6 2 2 ` j. Write down all the steps of your working. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 1 1 3 = × 1 oe B1 16 2 4 2 5 × 2 3 × 3 and oe or better M1FT 6 × 2 4 × 3 1 oe A1 12 working must be shown
Q17 · A plane is travelling at 180 metres per second
17 A plane is travelling at 180 metres per second. How many minutes will it take the plane to travel 800 km? Give your answer correct to the nearest minute. Answer ......................................... min [4] __________________________________________________________________________________________
Mark scheme: 17 74 4 M1 for 800 × 1000 or 180 ÷ 1000 soi and M1 for figs 8 ÷ figs 18 and M1 for converting (secs) to mins 74.1 or 74.07… implies M3
Q18 · The probability that FC Victoria wins the cup is 0.18
18 (a) The probability that FC Victoria wins the cup is 0.18 . Work out the probability that they do not win the cup. Answer(a) ................................................ [1] (b) After training, the shirts are washed. There are 5 red, 3 blue and 6 green shirts. One shirt is taken from the washing machine at random. Find the probability that it is (i) red, Answer(b)(i) ................................................ [1] (ii) blue or green, Answer(b)(ii) ................................................ [1] (iii) white. Answer(b)(iii) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 18 (a) (0).82 oe 1 5 (b) (i) oe 1 in (b) penalise consistent incorrect 14 denominator once 9 (ii) oe 1 14 (iii) 0 1 IGCSE – May/June 2014 0580 12
Q19 · Similar acute line perpendicular radius refl ex obtuse parallel congruent isosceles Choose…
19 similar acute line perpendicular radius refl ex obtuse parallel congruent isosceles Choose the correct word from this box to complete each of these statements. (a) A Angle A is ..................................... [1] (b) B Angle B is ..................................... [1] (c) These lines are ..................................... [1] (d) These lines are ..................................... [1] __________________________________________________________________________________________
Mark scheme: 19 (a) acute 1 (b) reflex 1 (c) parallel 1 (d) perpendicular 1 3
Q20 · NOT TO SCALE 6.7 cm Each edge of this cube is 6.7 cm long
20 NOT TO SCALE 6.7 cm Each edge of this cube is 6.7 cm long. Work out (a) the volume, Answer(a) ......................................... cm3 [2] (b) the surface area. Answer(b) ......................................... cm2 [2] __________________________________________________________________________________________
Mark scheme: 20 (a) 300.763 cao 2 M1 for 6.73 oe (b) 269.34 cao 2 M1 for 6.72 × 6 oe 2
Q21 · B NOT TO SCALE O 63° A C The diagram shows a circle, centre O with diameter AB = 15 cm
21 B NOT TO SCALE O 63° A C The diagram shows a circle, centre O with diameter AB = 15 cm. AC is a tangent to the circle at A and angle AOC = 63°. (a) Calculate the area of the circle. Answer(a) ......................................... cm2 [2] (b) (i) Work out the size of angle ACO. Answer(b)(i) Angle ACO = ................................................ [2] (ii) Give one geometrical reason for your answer to part (b)(i). Answer(b)(ii) ............................................................................................................................... ..................................................................................................................................................... [1] __________________________________________________________________________________________
Mark scheme: 21 (a) 177 or 176.7 to 176.74 2 M1 for π × 7.52 oe (b) (i) 27 2 B1 for angle CAO marked, or clearly used, as a right-angle (or 90°) or M1 for 180 – 90 – 63 oe (ii) one correct geometrical reason 1 [angle between a] radius [and a] tangent [is a] right-angle or [angles in a] triangle [add up to] 180° or [the] angles [have to] add to 180°
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Algebraic manipulation1Angles1Averages and range1Circle theorems1Coordinates1Equations1Fractions, decimals and percentages1Introduction to algebra1Introduction to probability1Ordering1Percentages1Rates1Right-angled triangles1Scale drawings1Surface area and volume1The four operations1Time1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2014 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.