Cambridge IGCSE Mathematics 0580 — 2018 May/June Paper 1 · Variant 2
0580/12/M/J/18 · 24 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · One morning, Marcia works from 08 20 to 11 15
1 One morning, Marcia works from 08 20 to 11 15. Find how long she works for. Give your answer in hours and minutes. .................... h .................... min [1]
Mark scheme: Question Answer Marks Partial Marks 1 2[h] 55[min] 1
Question 2
2 Simplify. 7g – g + 2g ................................................. [1]
Mark scheme: 2 8g 1
Question 3
3 Expand. 7(x – 8) ................................................. [1]
Mark scheme: 3 7x – 56 final answer 1
Q4 · Find the value of p when 5 p ' 5 8 = 5 13
4 Find the value of p when 5 p ' 5 8 = 5 13 . p = ................................................. [1]
Mark scheme: 4 21 1
Q5 · 22 17 25 41 39 4 Work out the difference between the two prime numbers in the list above
5 22 17 25 41 39 4 Work out the difference between the two prime numbers in the list above. ................................................. [2]
Mark scheme: 5 24 2 B1 for 17 or 41 identified
Q6 · Here is a sequence
6 Here is a sequence. a, 13, 9, 3, –5, –15, b, … Find the value of a and the value of b. a = ................................................ b = ................................................ [2]
Mark scheme: 6 [a =]15 2 B1 for each [b =] −27 or SC1 for reversed answers
Q7 · The bearing of a lighthouse from a coastguard station is 113°
7 The bearing of a lighthouse from a coastguard station is 113°. Work out the bearing of the coastguard station from the lighthouse. ................................................. [2]
Mark scheme: 7 293° 2 M1 for 113 + 180 oe or a sketch with the correct angle identified
Q8 · For this diagram, write down (a) the number of lines of symmetry…
8 For this diagram, write down (a) the number of lines of symmetry, ................................................. [1] (b) the order of rotational symmetry. ................................................. [1]
Mark scheme: 8(a) 4 1 8(b) 4 1
Q9 · Write these numbers in order, starting with the smallest
9 Write these numbers in order, starting with the smallest. -2 1 2 5 0.038 27 55 ........................ 1 ........................ 1 ........................ 1 ........................ [2] smallest
Mark scheme: 9 2 1 2 M1 for decimals to accuracy minimum 0.038 5–2 0.04, 0.037, 0.036 55 27 or B1 for 3 in the correct order
Question 10
10 Factorise completely. 4xy 2 - 6y 3 ................................................. [2]
Mark scheme: 10 2y2( 2x – 3y) final answer 2 B1 for 2y( 2xy – 3y2) or 2(2xy2 – 3y3) or y(4xy – 6y2) or y2(4x – 6y)
Q11 · Here are some numbers written in standard form
11 Here are some numbers written in standard form. .34 # 10 -1 .136 # 106 .79 # 100 .24 # 105 .521 # 10 -3 .43 # 10 -2 From these numbers, write down (a) the largest number, ................................................. [1] (b) the smallest number. ................................................. [1]
Mark scheme: 11(a) 1.36 × 106 oe 1 11(b) 5.21 × 10–3 oe 1
Q12 · 5 - 7 a = b = c- 2m c- 3m Work out a + 3b
12 5 - 7 a = b = c- 2m c- 3m Work out a + 3b. [2] f p
Mark scheme: 12 − 16 2 −21 − 16 k B1 for [3b =] or or − 11 −9 k −11
Q13 · Make y the subject of the equation 5x - 2y + 7 = 0
13 Make y the subject of the equation 5x - 2y + 7 = 0 . y = ................................................ [2]
Mark scheme: 13 5 x + 7 2 M1 for 2y = 5x + 7 or −2y = −5x – 7 [y =] oe 5 7 2 or x – y + = 0 2 2
Q14 · Change 600 euros into dinars when the exchange rate is 1 euro = 0.429 dinars
14 Change 600 euros into dinars when the exchange rate is 1 euro = 0.429 dinars. Give your answer correct to the nearest dinar. ..................................... dinars [2]
Mark scheme: 14 257 2 B1 for 257.4
Question 15
15 Complete these statements. (a) When w = ........................ , 10w = 70. [1] (b) When 5x = 15, 12x = ........................ [1]
Mark scheme: 15(a) [w =] 7 1 15(b) [12x =] 36 1
Q16 · NOT TO SCALE 8 cm x° 5 cm Use trigonometry to calculate the value of x
16 NOT TO SCALE 8 cm x° 5 cm Use trigonometry to calculate the value of x. x = ................................................ [2]
Mark scheme: 16 51.3 or 51.31 to 51.32 2 5 M1 for cos [x =] 8
Q17 · NOT TO SCALE 1 cm 7 cm The diagram shows a solid cuboid with base area 7 cm2
17 NOT TO SCALE 1 cm 7 cm The diagram shows a solid cuboid with base area 7 cm2. The volume of this cuboid is 21 cm3. Work out the total surface area. ......................................... cm2 [3]
Mark scheme: 17 62 3 M1 for [height = ] 21 ÷ 7 M1 for 2(1 × their3 + their3 × 7 + 1 × 7) oe
Q18 · D C NOT TO 35.1 m SCALE A B 23.4 m The diagram shows a rectangular playground ABCD
18 D C NOT TO 35.1 m SCALE A B 23.4 m The diagram shows a rectangular playground ABCD. AB = 23.4 m and AC = 35.1 m. Calculate BC. BC = ........................................... m [3]
Mark scheme: 18 26.2 or 26.16(.....) 3 2 2 M2 for 35.1 − 23.4 or better or M1 for 35.12 = 23.42 + BC2 or better
Q19 · Friedrich borrows $1200 for 3 years at a rate of 5.6% per year compound interest
19 Friedrich borrows $1200 for 3 years at a rate of 5.6% per year compound interest. Work out the total amount he pays back at the end of the 3 years. $ ................................................ [3]
Mark scheme: 19 1410 or 1413 or 1413.1[0 ............] 3 3 5.6 M2 for 1200 1 + oe 100 5.6 2 or M1 for 1200 1 + oe 100
Q20 · A cylindrical glass has radius 3.6 cm and height 11 cm
20 A cylindrical glass has radius 3.6 cm and height 11 cm. It is filled with water. (a) Calculate, in cubic centimetres, the volume of water it contains. ......................................... cm3 [2] (b) Write your answer to part (a) in litres. ....................................... litres [1]
Mark scheme: 20(a) 448 or 447.85 to 447.95 2 M1 for π × 3.62 × 11 20(b) [0].448 or [ 0].44785 to [0].44795 1 FT their (a) ÷ 1000
Q21 · The cost of hiring a car for 12 days is $167.90
21 The cost of hiring a car for 12 days is $167.90 . The cost of hiring this car for the first day is $20.50 . Work out the cost per day for the remaining 11 days. $ ................................................ [3]
Mark scheme: 21 13.4[0] 3 M2 for (167.9 – 20.5) ÷ 11 or M1 for 167.9[0] – 20.5[0]
Q22 · Monday Tuesday Wednesday Thursday Friday Saturday 67 75 53 68 94 87 The table shows the…
22 Monday Tuesday Wednesday Thursday Friday Saturday 67 75 53 68 94 87 The table shows the number of customers in a restaurant on each day it is open during one week. (a) Write down the day most customers came into the restaurant. ................................................. [1] (b) Calculate the mean number of customers per day. ................................................. [2] (c) Find the range of the number of customers. ................................................. [1]
Mark scheme: 22(a) Friday 1 22(b) 74 2 M1 for (67 + 75 + 53 + 68 + 94 + 87) ÷ 6 22(c) 41 1
Q23 · The scatter diagram shows the value, in thousands of dollars, of eight houses in 1996 and…
23 The scatter diagram shows the value, in thousands of dollars, of eight houses in 1996 and the value of the same houses in 2016. 200 180 160 140 120 Value in 2016 ($ thousands) 100 80 60 40 20 0 10 20 30 40 50 60 70 80 90 100 Value in 1996 ($ thousands) (a) One of these eight houses had a value of $70 000 in 1996. Write down the value of this house in 2016. $ ................................................ [1] (b) The values of two more houses are shown in the table. Value in 1996 ($ thousands) 40 80 Value in 2016 ($ thousands) 80 150 On the scatter diagram, plot these values. [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) Another house had a value of $50 000 in 1996. Find an estimate of the value of this house in 2016. $ ................................................ [1] Question 24 is printed on the next page.
Mark scheme: 23(a) 140 000 1 23(b) Points correctly plotted at 1 (40, 80) and (80, 150) 23(c) Correct ruled line of best fit 1 23(d) 80 000 to 110 000 1 FT their straight line provided it has positive gradient
Q24 · Without using your calculator, work out the following
24 Without using your calculator, work out the following. You must show all your working and give each answer as a fraction in its simplest form. 2 1 (a) - 3 12 ................................................. [2] 3 5 (b) 3 ' 4 7 14 ................................................. [3]
Mark scheme: 24(a) 8 1 M1 For correct fractions with a common and oe denominator 12k 12 12 7 A1 cao 12 24(b) 24 61 B1 or equivalent improper fractions or 7 14 their 24 14 M1 their 48 their 61 × oe or ÷ 7 their 61 14 14 oe common denominator 48 A1 cao 61
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Surface area and volume2Time2Averages and range1Equations1Fractions, decimals and percentages1Indices I1Money1Ordering1Percentages1Pythagoras’ theorem1Ratio and proportion1Right-angled triangles1Scatter diagrams1Sequences1Standard form1Symmetry1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2018 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.