Cambridge IGCSE Mathematics 0580 — 2016 May/June Paper 1 · Variant 3
0580/13/M/J/16 · 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
Q1 · Write in figures the number nine million eighty two thousand five hundred and seven
1 Write in figures the number nine million eighty two thousand five hundred and seven. .................................................. [1]
Mark scheme: Question Answer Mark Part marks 1 9 082 507 1
Q2 · Write 71 496 correct to 2 significant figures
2 Write 71 496 correct to 2 significant figures. .................................................. [1]
Mark scheme: 2 71 000 cao 1
Q3 · Find the cube root of 4913
3 Find the cube root of 4913. .................................................. [1]
Mark scheme: 3 17 1
Q4 · What type of correlation is shown by the scatter diagram?
4 What type of correlation is shown by the scatter diagram? .................................................. [1]
Mark scheme: 4 Negative 1
Question 5
5 Calculate. 17.85 - 7.96 18 - 3.5 2 .................................................. [1]
Mark scheme: 5 1.72 1
Q6 · 2 3 –4 –6 –8 From the list of numbers, write down (a) three numbers whose sum is –12…
6 2 3 –4 –6 –8 From the list of numbers, write down (a) three numbers whose sum is –12, ................. , ................. , ................. [1] (b) two numbers whose product is –24. ........................... , ........................... [1]
Mark scheme: 6 (a) 2 −6 −8 1 (b) 3 −8 1 1
Question 7
7 Solve the equation. 6(y + 1) = 9 y = ................................................. [2]
Mark scheme: 1 7 0.5 or 2 M1 for correct first step e.g. 6y + 6 = 9 2 9 or y + 1 = 6 −6
Q8 · -2 8 (a) Write 3 as a single vector
-2 8 (a) Write 3 as a single vector. e 1 o [1] f p (b) y 4 2 x –4 –2 0 2 4 –2 A –4 -7 Point A is marked on the grid and AB = . e 4 o On the grid, mark the point B. [1]
Mark scheme: 6 8 (a) 1 3 (b) Point B at (−3, 2) 1
Q9 · NOT TO SCALE 6 cm 5 cm x cm The area of this parallelogram is 51.5 cm2
9 NOT TO SCALE 6 cm 5 cm x cm The area of this parallelogram is 51.5 cm2. Work out the value of x. x = ................................................. [2]
Mark scheme: 9 10.3 oe 2 M1 for 5x = 51.5 oe
Q10 · Lanying sells potatoes in bags
10 Lanying sells potatoes in bags. Each bag contains 5 kg of potatoes, correct to the nearest 0.1 kg. Complete the statement about the mass, m kilograms, of potatoes in each bag. ............................. G m 1 ............................. [2]
Mark scheme: 10 4.95 5.05 1, 1 SC1 for both correct but reversed 1 6
Q11 · 1 # 1 5 .11 Without using a calculator, work out 12 Show all your working and give your…
1 1 # 1 5 .11 Without using a calculator, work out 12 Show all your working and give your answer as a fraction in its lowest terms. .................................................. [2]
Mark scheme: 1 6 11 × oe M1 Must be shown 12 5 1 A1 final answer cao 10 AC
Q12 · B 23 m NOT TO SCALE 16° A C A ramp, AB, with length 23 m, slopes up at an angle of 16° to…
12 B 23 m NOT TO SCALE 16° A C A ramp, AB, with length 23 m, slopes up at an angle of 16° to the horizontal, AC. Use trigonometry to calculate AC. AC = ..............................................m [2]
Mark scheme: AC 12 22.1 2 M1 for cos 16 = soi 23
Q13 · Jamal changes 800 Chinese Yuan into dollars
13 Jamal changes 800 Chinese Yuan into dollars. The exchange rate is $1 = 6.24 Chinese Yuan. Calculate the number of dollars he receives. Give your answer correct to the nearest dollar. $ .................................................. [3]
Mark scheme: 13 128 3 M1 for 800 ÷ 6.24 A1 for 128.2 .........
Q14 · Cheng invested $4500 at a rate of 3.5% per year compound interest
14 Cheng invested $4500 at a rate of 3.5% per year compound interest. Calculate the total amount he has after 3 years. $ .................................................. [3]
Mark scheme: 3.5 1 +14 4 990 or 4 989 or 4 989.2 or 4 989.23 3 M2 for 4 500 oe 100 2 3.5 or M1 for 4 500 1 + oe 100
Q15 · NOT TO SCALE x° y° 42° The diagram is made from 5 congruent kites
15 NOT TO SCALE x° y° 42° The diagram is made from 5 congruent kites. Work out the value of (a) x, x = ................................................. [1] (b) y. y = ................................................. [2]
Mark scheme: 15 (a) 72 1 (b) 123 2FT FT dep. on answer being obtuse M1 for (360 – their ( a ) – 42) [÷2]
Q16 · Solve the simultaneous equations
16 Solve the simultaneous equations. You must show all your working. 3x + 7y = –21 6x + 4y = 3 x = ................................................. y = ................................................. [3]
Mark scheme: 16 For correctly eliminating one M1 Or correctly rearranging one equation and variable substituting into the other [x =] 3.5 A1 [y =] −4.5 A1 If zero scored SC1 for 2 values satisfying one of the original equations or if no working shown but 2 correct answers given 24
Q17 · The table shows the number of screws of different lengths in a box of 100 screws
17 The table shows the number of screws of different lengths in a box of 100 screws. Length (mm) 20 40 50 60 Number of screws 18 36 24 22 A screw is chosen at random from the box. Find the probability that the screw has length (a) 50 mm, .................................................. [1] (b) less than 60 mm, .................................................. [2] (c) 70 mm. .................................................. [1]
Mark scheme: 24 17 (a) oe 1 100 78 18 + 36 + 24 22 (b) oe 2 M1 for or 1 − 100 100 100 (c) 0 1
Q18 · Y 7 6 L 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 (a) Work out the gradient of the line…
18 y 7 6 L 5 4 3 2 1 x –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 (a) Work out the gradient of the line L. .................................................. [2] (b) Write down the equation of the line parallel to the line L that passes through the point (0, 6). .................................................. [2]
Mark scheme: 18 (a) 2 cao 2 M1 for rise/run attempted e.g. 4/2 or other correct method for finding gradient or SC1 for y = 2x – 1 as answer (b) y = 2x + 6 oe 2FT FT for y = their(a)x + 6 B1 for y = mx + 6 (m ≠ 0 or 2) or y = 2x [+ k] or y = their(a)x [+ k] (k ≠ 6) or for answer 2x + 6 or answer their(a)x + 6
Q19 · A D 93.5 m NOT TO SCALE B C 82.5 m The diagram shows a rectangular field, ABCD, with a…
19 A D 93.5 m NOT TO SCALE B C 82.5 m The diagram shows a rectangular field, ABCD, with a straight path, BD. (a) Calculate the distance from C to D. ...............................................m [3] (b) Yan walks along the edge of the field from B to C and then from C to D. Lee walks along the straight path BD. Work out how much further Yan walks than Lee. ...............................................m [1]
Mark scheme: 19 (a) 44 3 M2 for 93.52 − 82.5 2 or M1 for CD2 + 82.52 = 93.52 (b) 33 1FT FT 93.5 – (82.5 + their (a))
Q20 · Alice leaves home at 08 15 and walks at 80 metres per minute, arriving at her friend’s…
20 (a) Alice leaves home at 08 15 and walks at 80 metres per minute, arriving at her friend’s house half an hour later. (i) Work out the distance she walks, in metres, from her home to her friend’s house. ...............................................m [1] (ii) On the grid, show her journey from her home to her friend’s house. [1] 3000 2400 1800 Distance (m) 1200 600 Home 0 08 00 08 30 09 00 09 30 10 00 10 30 11 00 Time 1 (b) Alice stays at her friend’s house for 1 2 hours. She then jogs home, arriving 15 minutes later. (i) On the grid, complete the travel graph for her journey. [2] (ii) Calculate her average speed, in metres per minute, on her journey home. ....................................... m/min [2]
Mark scheme: 20 (a) (i) 2400 1 (ii) Ruled line (08 15, 0) to 1FT Follow through their 2400 and 30 minute (08 45, their 2400) time period
Q21 · 45 members of an athletics club were asked to choose a colour for their club vests
21 45 members of an athletics club were asked to choose a colour for their club vests. The choices were red, blue and green. The pie chart shows the sector for the number of members who chose red. Red (a) (i) Measure the sector angle for red. .................................................. [1] (ii) Calculate the number of members who chose red. .................................................. [2] (b) 24 members chose blue. Calculate the sector angle for blue. .................................................. [2] (c) Complete the pie chart. [1] (d) What colour should the athletics club choose for their club vests? Give a reason for your answer. ......................... because ..................................................................................................................... [1]
Mark scheme: 21 (a) (i) 120 1 (ii) 15 2 M1 for their 120 ÷ 360 [ × 45] or 45 ÷ 360 [ × their 120] (b) 192 2 M1 for 24 ÷ 45 [ × 360] (c) Line giving angles of 192° and 1FT FT their 192 48° from given lines (d) Blue and an acceptable reason 1
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.
2Limits of accuracy2The four operations2Angles1Area and perimeter1Fractions, decimals and percentages1Gradient of linear graphs1Graphs in practical situations1Introduction to probability1Percentages1Powers and roots1Pythagoras’ theorem1Ratio and proportion1Right-angled triangles1Scatter diagrams1Statistical charts and diagrams1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2016 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.