Cambridge IGCSE Mathematics 0580 — 2018 May/June Paper 2 · Variant 1
0580/21/M/J/18 · 24 questions · 70 marks · ≈79 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 scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write down a prime number between 20 and 30
1 Write down a prime number between 20 and 30. .............................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 23 or 29 1
Q2 · Write 0.000 038 7 in standard form
2 Write 0.000 038 7 in standard form. .............................................. [1]
Mark scheme: 2 3.87 × 10−5 1
Q3 · Write the recurring decimal .063o o as a fraction
3 Write the recurring decimal .063o o as a fraction. .............................................. [1]
Mark scheme: 3 7 1 oe 11
Q4 · Find the value of 7x + 3y when x = 12 and y = -6
4 Find the value of 7x + 3y when x = 12 and y = -6. .............................................. [2]
Mark scheme: 4 66 2 B1 for 84 or −18 seen
Q5 · Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT
5 Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT. AB = AC and angle QAC = 43°. Find the value of x. x = ....................................... [2]
Mark scheme: 5 94 2 B1 for ACB or PAB or ABC = 43 or M1 for 180 −×2 43 or 12 x = 90 − 43
Q6 · Calculate the area of a circle with radius 5.1 cm
6 Calculate the area of a circle with radius 5.1 cm. .......................................cm2 [2]
Mark scheme: 6 81.7 or 81.71 to 81.72… 2 M1 for π × 5.12
Q7 · A NOT TO 2.5 cm SCALE C B 4.1 cm Calculate the length of AC
7 A NOT TO 2.5 cm SCALE C B 4.1 cm Calculate the length of AC. AC = ........................................ cm [2]
Mark scheme: 7 4.8[0] or 4.802… 2 M1 for [ AC 2 = ] 2.5 2 + 4.12
Question 8
8 Expand and simplify. 6(2y - 3) - 5(y + 1) .............................................. [2]
Mark scheme: 8 7y − 23 final answer 2 M1 for 12 y − 18 or −5 y − 5 or B1 for answer 7y − k or cy − 23 c ≠ 0
Q9 · -q 19 3 # = 81 27 Find the value of q
-q 19 3 # = 81 27 Find the value of q. q = .............................................. [2]
Mark scheme: 9 −7 2 B1 for 3−3 or 34 or 73 or 3–7 seen or SC1 for final answer 7
Q10 · Calculate 2.38 + 6.42 , writing down your full calculator display
10 (a) Calculate 2.38 + 6.42 , writing down your full calculator display. .............................................. [1] (b) Write your answer to part (a) correct to 4 decimal places. .............................................. [1]
Mark scheme: 10(a) 6.58331… 1 10(b) 6.5833 1 FT their (a) correctly rounded to 4 dp
Q11 · 1 Find the exact value of 8 2 3 # 49 - 1
211 Find the exact value of 8 2 3 # 49 - 1 . .............................................. [2]
Mark scheme: 11 4 2 1 oe exact answer B1 for 4 or 7 7
Question 12
12 Solve the inequality. 3n - 5 2 17 + 8n .............................................. [2]
Mark scheme: 12 2 2 M1 for 8n − 3n < −−5 17 or better n < − 4.4 or n < − 4 5 or 3n – 8n > 17 + 5 or better final answer
Q13 · 613 Without using your calculator, work out 1 #
3 613 Without using your calculator, work out 1 # . 4 35 You must show all your working and give your answer as a fraction in its simplest form. .............................................. [3]
Mark scheme: 13 7 M1 k 6 or × where k > 4 4 4 35 3 A2 42 21 6 cao A1 for or or 10 140 70 20
Q14 · C 84.6° NOT TO 5.9 cm SCALE B 17.8 cm A Use the sine rule to find angle ABC
14 C 84.6° NOT TO 5.9 cm SCALE B 17.8 cm A Use the sine rule to find angle ABC. Angle ABC = .............................................. [3]
Mark scheme: 14 19.3 or 19.26 to 19.27 nfww 3 sin84.6 M2 for [sin = ]5.9 × 17.8 5.9 17.8 or M1 for = oe sin B sin84.6
Q15 · Y is directly proportional to (x - 1 ) 2
15 y is directly proportional to (x - 1 ) 2 . When x = 5, y = 4. Find y when x = 7. y = .............................................. [3]
Mark scheme: 15 9 3 2 M1 for y = k ( x − 1) M1 for [ y = ]their k ( 7 − 1) 2 OR 4 y M2 for = oe ( 5 − 1) 2 ( 7 − 1) 2
Q16 · Y 7 6 5 4 3 2 1 R x 0 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 0 - 1 On the grid, draw the image…
16 y 7 6 5 4 3 2 1 R x 0 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 0 - 1 On the grid, draw the image of shape R after the transformation represented by the matrix [3] c1 0m.
Mark scheme: 16 Shape with vertices at 3 M2 for 3 correct vertices on grid or in (1, 1), (1, 4), (−1, 2), (−1, 4) working or M1 for correct set-up 0 − 1 2 1 4 4 1 0 1 − 1 − 1 1 or for rotation, 90° [anti-clockwise], centre O
Q17 · 20 NOT TO Speed SCALE (m/s) 0 0 10 100 130 Time (seconds) The speed-time graph shows…
17 20 NOT TO Speed SCALE (m/s) 0 0 10 100 130 Time (seconds) The speed-time graph shows information about the journey of a tram between two stations. (a) Calculate the distance between the two stations. ..........................................m [3] (b) Calculate the average speed of the tram for the whole journey. ....................................... m/s [1]
Mark scheme: 17(a) 2200 3 M2 for 12 ( 90 + 130 ) × 20 or 1 2 (10 × 20) + (90 × 20) + 12 (30 × 20) or M1 for one area 17(b) 16.9 or 16.92… 1 FT their (a) ÷ 130
Q18 · The cumulative frequency diagram shows information about the time, m minutes, taken by…
18 The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework. 120 100 80 Cumulative 60 frequency 40 20 0 m 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the interquartile range, .......................................min [2] (b) the number of students who took more than 50 minutes to complete the homework. .............................................. [2]
Mark scheme: 18(a) 10 nfww 2 B1 for UQ = 30 or LQ = 20 clearly identified 18(b) 4 2 B1 for 116 indicated
Q19 · N 16 cm 14 cm NOT TO SCALE L M 19 cm Calculate angle LMN
19 N 16 cm 14 cm NOT TO SCALE L M 19 cm Calculate angle LMN. Angle LMN = ............................................... [4]
Mark scheme: 19 46.2 or 46.17 to 46.18 4 16 2 + 19 2 − 14 2 M2 for [cos =] 2 × 16 × 19 or M1 for 142 = 192 + 162 – 2 × 19 × 16cosM 421 A1 for 0.692… or 608
Q20 · A box contains 3 blue pens, 4 red pens and 8 green pens only
20 (a) A box contains 3 blue pens, 4 red pens and 8 green pens only. A pen is chosen at random from the box. Find the probability that this pen is green. .............................................. [1] (b) Another box contains 7 black pens and 8 orange pens only. Two pens are chosen at random from this box without replacement. Calculate the probability that at least one orange pen is chosen. .............................................. [3]
Mark scheme: 20(a) 8 1 oe 15 20(b) 168 3 M2 for oe 210 7 6 7 × 8 1 − × oe or 3( ) oe 15 14 15 × 14 or M1 for 7 6 7 8 8 7 × or × or × oe 15 14 15 14 15 14
Q21 · Y 3 2 R 1 x 0 1 2 3 4 5 6 There are four inequalities that define the region R
21 y 3 2 R 1 x 0 1 2 3 4 5 6 There are four inequalities that define the region R. One of these is y G x + 1. Find the other three inequalities. .............................................. .............................................. .............................................. [4]
Mark scheme: 21 y ⩾ 1.5 oe 4 3 SC3 for y >1.5 oe and y > x oe and 4 y ⩾3 x oe 4 1 y ⩽ − x + 3 oe 1 2 y < − x + 3 oe 2 or B3 for any two correct inequalities or B1 for y ⩾ 1.5 oe and 3 1 B2 for y ⩾ x oe or y < − x + 3 oe 4 2 3 1 or y = x oe and y = − x + 3 oe or 4 2 with incorrect inequality signs 3 or B1 for y = x oe OR 4 1 y = − x + 3 oe or with incorrect 2 inequality signs
Q22 · F(x) = 5 - 2x g(x) = x2 + 8 (a) Calculate ff(-3)
22 f(x) = 5 - 2x g(x) = x2 + 8 (a) Calculate ff(-3). .............................................. [2] (b) Find (i) g(2x), .............................................. [1] (ii) f -1(x). f -1(x) = .............................................. [2]
Mark scheme: 22(a) −17 2 M1 for f (11) seen or 5 − 2(5 − 2x) or better 22(b)(i) 4 x 2 + 8 oe 1 22(b)(ii) 5 − x 2 M1 for x = 5 − 2 y or 2 x = 5 − y or oe final answer 2 y 5 y – 5 = –2x or = − x 2 2
Q23 · 40 people were asked how many times they visited the cinema in one month
23 40 people were asked how many times they visited the cinema in one month. The table shows the results. Number of cinema visits 0 1 2 3 4 5 6 7 Frequency 5 5 6 6 7 3 6 2 (a) (i) Find the mode. .............................................. [1] (ii) Calculate the mean. .............................................. [3] (b) Omar wants to show the information from the table in a pie chart. Calculate the sector angle for the people who visited the cinema 5 times. .............................................. [2] Question 24 is printed on the next page.
Mark scheme: 23(a)(i) 4 1 23(a)(ii) 3.2 3 M1 for Σ fx , allow one error or omission their 128 and M1dep for 40 23(b) 27 2 3 360 M1 for or 40 40
Q24 · Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5)
24 (a) Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5). Calculate the angle between the line AB and the x-axis. .............................................. [3] (b) The line PQ has equation y = 3x - 8 and point P has co-ordinates (6, 10). Find the equation of the line that passes through P and is perpendicular to PQ. Give your answer in the form y = mx + c. y = .............................................. [3]
Mark scheme: 24(a) 78.7 or 78.69… 3 5 M2 for tan = oe 2 − 1 or M1 for use of tangent oe 24(b) 1 3 1 [ y = ] − x + 12 final answer M1 for gradient = − 3 3 M1 for substituting (6, 10) into y = their mx + c
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.
2Fractions, decimals and percentages2Inequalities2Non-right-angled triangles2Algebraic manipulation1Angles1Area and perimeter1Circles, arcs and sectors1Functions1Gradient of linear graphs1Indices I1Introduction to algebra1Powers and roots1Probability of combined events1Proportion1Pythagoras’ theorem1Standard form1Transformations1Types of number1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2018 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.