Cambridge IGCSE Mathematics 0580 — 2016 May/June Paper 1 · Variant 2
0580/12/M/J/16 · 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write these numbers in order of size, starting with the smallest
1 Write these numbers in order of size, starting with the smallest. 0.304 0.2 0.008 0.57 ..................... < ..................... < ..................... < ..................... [1] smallest
Mark scheme: Question Answer Mark Part marks 1 0.008 < 0.2 < 0.304 < 0.57 1
Question 2
2 Calculate. 4 3.07 + 2 5.03 - 1.79 .................................................. [1]
Mark scheme: 2 5.89 or 5.885 to 5.886 1
Q3 · Write 3.5897 correct to 4 significant figures
3 Write 3.5897 correct to 4 significant figures. .................................................. [1]
Mark scheme: 3 3.590 cao 1
Q4 · A quadrilateral has rotational symmetry of order 2 and no lines of symmetry
4 A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the mathematical name of this quadrilateral. .................................................. [1]
Mark scheme: 4 Parallelogram 1
Q5 · Sonia earns $8.12 for each hour she works
5 Sonia earns $8.12 for each hour she works. She works for 35 hours each week. Work out how much she earns each week. $ .................................................. [1]
Mark scheme: 5 284.2[0] cao 1
Q6 · Work out $216 as a percentage of $600
6 Work out $216 as a percentage of $600. ...............................................% [1]
Mark scheme: 6 36 1
Question 7
7 Simplify. (a) 3f + 4f – 2f .................................................. [1] (b) g3 × g5 .................................................. [1]
Mark scheme: 7 (a) 5f final answer 1 (b) g8 final answer 1
Q8 · David goes to college by bus
8 David goes to college by bus. On 6 mornings out of 45, the bus is late. In one year David goes to college by bus 180 times. Estimate how many mornings the bus is late in one year. .................................................. [2]
Mark scheme: 8 24 2 M1 for 6 ÷ 45 or 180 ÷ 45
Q9 · Here are the first five terms in a sequence
9 Here are the first five terms in a sequence. 4 11 18 25 32 Find an expression for the nth term of this sequence. .................................................. [2]
Mark scheme: 9 7n – 3 oe 2 M1 for 7n + a or bn – 3 (b ≠ 0)
Q10 · NOT TO x cm SCALE B 9 cm A 20 cm 12 cm Triangle A and triangle B are similar
10 NOT TO x cm SCALE B 9 cm A 20 cm 12 cm Triangle A and triangle B are similar. Find the value of x. x = ................................................. [2]
Mark scheme: 10 15 2 M1 for 20 ÷ 12 or 12 ÷ 9 or 9 ÷ 12 or 12 ÷ 20
Q11 · Write 2 600 000 in standard form
11 (a) Write 2 600 000 in standard form. .................................................. [1] (b) Write 5.8 × 10–3 as an ordinary number. .................................................. [1]
Mark scheme: 11 (a) 2.6 × 106 1 (b) [0].0058 1 1
Question 12
12 Complete the table. Fraction Decimal 1 = 0.5 2 = 0.25 3 = 10 2 = 25 [3]
Mark scheme: 112 1 4 [0].3 1 1 0.08
Q13 · A bag contains 16 counters
13 (a) A bag contains 16 counters. 4 of the counters are blue. A counter is taken from the bag at random. On the probability scale, draw an arrow (↓) to show the probability that this counter is blue. 0 0.5 1 [1] (b) Another bag contains 5 black counters, 8 white counters, 6 green counters and 1 yellow counter. A counter is taken from this bag at random. Find the probability that this counter is (i) white, .................................................. [1] (ii) not white. .................................................. [1]
Mark scheme: 13 (a) Arrow 2 cm from 0 1 8 (b) (i) 1 oe 20 12 (ii) 1FT FT 1 – their (b)(i) provided their (b)(i) < 1 oe 20
Q14 · This is a graph for converting between dollars ($) and pounds (£)
14 This is a graph for converting between dollars ($) and pounds (£). 60 50 40 Pounds (£) 30 20 10 0 20 40 60 80 100 Dollars ($) (a) Use the graph to convert $80 to pounds. £ .................................................. [1] (b) Daniyar changes £100 to dollars. Work out how many dollars he receives. $ .................................................. [2]
Mark scheme: 14 (a) 44 1 (b) 180 to 184 2 M1 for £50 = $90 to $92 oe soi 12
Q15 · - 3 15 (a) p = q = 2 e - o e 0 o Work out (i) 3p, [1] f p (ii) p – q
4 - 3 15 (a) p = q = 2 e - o e 0 o Work out (i) 3p, [1] f p (ii) p – q. [1] f p (b) B 3 Point B is marked on the grid and AB = e - 2 o. On the grid, mark point A. [1]
Mark scheme: 12 15 (a) (i) 1 −6 7 (ii) 1 −2 (b) A in correct position 1
Q16 · The equation of line L is y = 4x – 3
16 The equation of line L is y = 4x – 3. Write down (a) the co-ordinates of the point where the line L crosses the y-axis, (................ , ................) [1] (b) the gradient of the line L, .................................................. [1] (c) the equation of the line parallel to line L that passes through the origin. .................................................. [1]
Mark scheme: 16 (a) (0, –3) 1 (b) 4 1 (c) y = 4x [+0] 1FT FT y = their (b)x for numerical gradient only
Q17 · A regular polygon has an interior angle of 172°
17 A regular polygon has an interior angle of 172°. Find the number of sides of this polygon. .................................................. [3]
Mark scheme: 17 45 3 M2 for 360 ÷ (180 – 172) 180 ( n – 2 ) or M1 for 180 – 172 or = 172 oe n 21 3
Q18 · 3 # 7 .18 Without using a calculator, work out 2 8 Show all your working and give your…
5 3 # 7 .18 Without using a calculator, work out 2 8 Show all your working and give your answer as a mixed number in its lowest terms. .................................................. [3]
Mark scheme: 21 3 18 × oe M1 Must be shown 8 7 1 9 63 for oe e.g. 18 cao final answer A2 A1 8 56
Q19 · Solve the simultaneous equations
19 Solve the simultaneous equations. Show all your working. 3x + 4y = 14 5x + 2y = 21 x = ................................................. y = ................................................. [3]
Mark scheme: 19 Correctly eliminating one variable M1 If zero scored SC1 for x = 4 A1 2 values satisfying one of the original equations y = 0.5 oe A1 or if no working shown, but 2 correct answers given
Q20 · The diagram shows triangle ABC
20 The diagram shows triangle ABC. A C B (a) Using a straight edge and compasses only, construct the bisector of angle ABC. [2] (b) Draw the locus of points inside the triangle that are 3 cm from AC. [1]
Mark scheme: 20 (a) Bisector of angle B accurate with 2 B1 for accurate line with no/wrong arcs two pairs of correct arcs or for correct arcs with no/wrong line (b) Ruled line parallel to AC at a 1 distance of 3 cm to AC only inside the triangle
Q21 · The table shows the temperature each night for a week
21 The table shows the temperature each night for a week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday –3 °C 1 °C – 4 °C –2 °C 5 °C 3 °C –1 °C (a) Which night was the coldest? .................................................. [1] (b) Find the difference between the temperature on Monday night and the temperature on Tuesday night. ..............................................°C [1] (c) Find the range. ..............................................°C [1] (d) Find the median. ..............................................°C [1]
Mark scheme: 21 (a) Wed[nesday] 1 (b) 4 1 (c) 9 1 (d) –1 nfww 1 1
Q22 · 7 cm NOT TO SCALE 6 cm 10 cm (a) Calculate the area of the trapezium
22 7 cm NOT TO SCALE 6 cm 10 cm (a) Calculate the area of the trapezium. ........................................... cm2 [2] (b) The trapezium is the cross section of a prism. The length of the prism is 12 cm. Calculate the volume of the prism. Give the units of your answer. ................................. ............... [2] Question 23 is printed on the next page.
Mark scheme: 1 22 (a) 51 2 M1 for × (10 + 7) × 6 oe 2 (b) 612 1FT FT 12 × their (a) cm3 1
Q23 · 10 Sports 8 centre 6 Distance (km) 4 2 Home 0 15 30 15 45 16 00 16 15 16 30 16 45 17 00…
23 10 Sports 8 centre 6 Distance (km) 4 2 Home 0 15 30 15 45 16 00 16 15 16 30 16 45 17 00 17 15 17 30 17 45 Time Sonali cycles from home to the sports centre. The travel graph shows her journey. (a) At what time does she arrive at the sports centre? .................................................. [1] (b) Work out Sonali’s cycling speed in kilometres per hour. ......................................... km/h [2] (c) Sonali stays at the sports centre for 45 minutes. She then takes 30 minutes to cycle home. Complete the travel graph. [2]
Mark scheme: 23 (a) 16 10 or 4 10 pm 1 (b) 12 2 M1 for 8 ÷ 40 or better (c) Line from (16 10, 8) to (16 55, 8) 1 Line from (16 55, 8) to (17 25, 0) 1FT FT line from their (16 55, 8) to ((their 16 55 + 30 mins), 0)
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Percentages2Algebraic manipulation1Angles1Area and perimeter1Averages and range1Equations1Equations of linear graphs1Geometrical constructions1Introduction to probability1Limits of accuracy1Money1Ordering1Ratio and proportion1Sequences1Similarity1Standard form1Symmetry1The four operations1Time1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2016 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.