Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 2 · Variant 1
0580/21/M/J/23 · 21 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 scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · B A 104° 71° NOT TO SCALE 56° C E D CDE is a straight line
1 B A 104° 71° NOT TO SCALE 56° C E D CDE is a straight line. Find angle ADE. ................................................. [2]
Mark scheme: Question Answer Marks Partial Marks 1 51 2 M1 for 360 – (56 + 104 + 71)
Q2 · A train journey starts at 21 43
2 A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes. ................................................. [1]
Mark scheme: 2 06 15 or 6:15 am 1
Q3 · 58° a° NOT TO SCALE b° The diagram shows a straight line intersecting two parallel lines
3 58° a° NOT TO SCALE b° The diagram shows a straight line intersecting two parallel lines. Find the value of a and the value of b, giving a geometrical reason for each answer. a = ................... because .................................................................................................................... b = ................... because .................................................................................................................... [4]
Mark scheme: 3 58, vertically opposite 2 B1 for each 122, interior 2 B1 for each
Q4 · By writing each number in the calculation correct to 1 significant figure, work out an…
4 By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 6.7 # 2.1 . 18 - 5.9 You must show all your working. ................................................. [2]
Mark scheme: 4 7 2 M1 20 6 1 nfww A1 If 0 scored SC1 for 3 correct roundings or for all correct but with any trailing zeros
Q5 · Eric has four colours of paint
5 Eric has four colours of paint. The table shows the probability that he uses each colour. Colour Red Blue Green Yellow Probability 0.3 0.35 0.13 x Find the value of x. x = ................................................ [2]
Mark scheme: 5 0.22 oe 2 M1 for 1 – (0.3 + 0.35 + 0.13) oe or B1 for 0.78 oe
Q6 · Calculate the volume of a sphere with diameter 4.8 cm
6 Calculate the volume of a sphere with diameter 4.8 cm. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 ......................................... cm3 [2]
Mark scheme: 6 57.9 or 57.90 to 57.91... 2 3 4 4.8 M1 for 3 2
Q7 · The scale of a map is 1 : 125 000
7 The scale of a map is 1 : 125 000. On a map, the length of an island is 9.4 cm. Calculate the actual length of the island, giving your answer in kilometres.
Mark scheme: 7 11.75 2 9.4 125000 M1 for oe 100 1000 or B1 for figs 1175 or 1 cm : 1.25 km
Q8 · The nth term of a sequence is 10 - n 2
8 (a) The nth term of a sequence is 10 - n 2 . Write down the first three terms of this sequence. ............... , ............... , ............... [2] (b) These are the first four terms of another sequence. 7 10 13 16 Find an expression for the nth term of this sequence. ................................................. [2]
Mark scheme: 8(a) 9 6 1 2 B1 for 2 correct 8(b) 3n + 4 oe final answer 2 B1 for 3n j or kn 4 k 0 , or 3n 4 seen then spoilt
Q9 · D A NOT TO h cm 5.6 cm SCALE B C E F 7.2 cm 8.1 cm Triangle ABC is similar to triangle DEF
9 D A NOT TO h cm 5.6 cm SCALE B C E F 7.2 cm 8.1 cm Triangle ABC is similar to triangle DEF. Calculate the value of h. h = ................................................ [2]
Mark scheme: 9 6.3 2 5.6 7.2 M1 for oe or better h 8.1
Q10 · 510 Without using a calculator, work out 2 '
1 510 Without using a calculator, work out 2 ' . 7 9 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 10 15 9 M2 15 oe B1 for oe 7 5 7 135 35 their 15 9 or oe with common or M1 for oe 63 63 7 5 denominator
Q11 · Y 8 7 6 A 5 B 4 3 2 C 1 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 Describe the single…
11 y 8 7 6 A 5 B 4 3 2 C 1 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 x – 1 Describe the single transformation that maps (a) triangle A onto triangle B ..................................................................................................................................................... ..................................................................................................................................................... [3] (b) triangle A onto triangle C. ..................................................................................................................................................... ..................................................................................................................................................... [3]
Mark scheme: 11(a) Enlargement 3 B1 for each [sf] 2 (0, 7) 11(b) Rotation 3 B1 for each (3, 1) 90° clockwise oe
Q12 · A NOT TO SCALE O C B AO, OB and OC are all radii of the circle
12 (a) A NOT TO SCALE O C B AO, OB and OC are all radii of the circle. AB = BC. Therefore triangle AOB is congruent to triangle COB. Draw a ring around the correct criterion for this statement. SAS RHS SSS ASA [1] (b) S P O NOT TO SCALE R 42°42° T Q U P, Q, R and S are points on the circle and TQU is a tangent to the circle at Q. PR and SQ intersect at the centre of the circle, O, and PQ is parallel to SR. Angle RQU = 42°. Calculate (i) angle QSR Angle QSR = ................................................ [1] (ii) angle PQS Angle PQS = ................................................ [1] (iii) angle POS. Angle POS = ................................................ [1]
Mark scheme: 12(a) SSS 1 12(b)(i) 42 1 12(b)(ii) 42 1 FT their part (i) 12(b)(iii) 84 1 FT 2 their part (ii)
Q13 · Anya invests $6000 in an account that pays compound interest at a rate of r % per year
13 Anya invests $6000 in an account that pays compound interest at a rate of r % per year. At the end of 8 years, the account has earned $621.70 in interest. Calculate the value of r. r = ................................................ [3]
Mark scheme: 13 1.24[0…] 3 6000 621.70 M2 8 oe 6000 or M1 for 6000 621.70 6000 k 8 oe
Q14 · Y is directly proportional to the square of (x + 3)
14 y is directly proportional to the square of (x + 3). When x = 2, y = 5. Find y when x = 1. y = ................................................ [3]
Mark scheme: 14 3.2 oe 3 2 M1 for y k x 3 oe or better M1 for substituting their k into y k 1 3 2
Q15 · A bag contains 5 green buttons, 2 blue buttons and 6 white buttons
15 A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Calculate the probability that one button is green and the other button is not green. ................................................. [3]
Mark scheme: 15 20 3 5 8 oe M2 for 2 oe 39 13 12 5 8 5 8 or M1 for or or or 13 12 12 13 80 If 0 scored SC1 for answer oe 169
Q16 · - 4 16 (a) Find the magnitude of the vector e 5o
- 4 16 (a) Find the magnitude of the vector e 5o. ................................................. [2] (b) C y NOT TO SCALE O x A B The diagram shows a triangle OAC. A is the midpoint of the straight line OB. OA = x and OC = y . Find CB in terms of x and y. CB = ................................................ [1]
Mark scheme: 16(a) 6.4[0] or 6.403... 2 2 2 M1 for 4 5 oe 16(b) 2x − y 1
Q17 · 17 Simplify 81 x 12 4
3 17 Simplify 81 x 12 4 . ` j ................................................. [2]
Mark scheme: 17 27 x 9 final answer 2 B1 for answer 27 x n or nx 9 , or for correct answer seen and spoilt
Q18 · North W NOT TO SCALE 62.4 km U 27.3 km V The diagram shows the position of three towns…
18 North W NOT TO SCALE 62.4 km U 27.3 km V The diagram shows the position of three towns, U, V and W. U is due west of V and angle UVW = 125°. Calculate the bearing of U from W. ................................................. [4]
Mark scheme: 18 236[.0…] 4 27.3 sin125 M2 for 62.4 27.3 62.4 or M1 for sin UWV sin125 M1 for 180 + (125 – 90 ) + their 21 oe or 180 90 their 34 oe If 0 scored SC1 for the correct bearing marked at W
Q19 · On the diagram, sketch the graph of y = cos x for 0° G x G 360°
19 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . y 1 0 180° 360° x – 1 [2] (b) Solve the equation 5 cosx + 3 = 0 for 0° G x G 360° . x = .................... or x = .................... [3]
Mark scheme: 19(a) correct sketch 2 B1 for correct cosine curve shape through (0, 1) Correct sketch to go through (0, 1), (360, 1) and (180, –1) 19(b) 126.9 or 126.86 to 126.87 3 B2 for 1 correct angle 233.1 or 233.13 to 233.14 3 or M1 for cos x = oe 5 If M1 or 0 scored SC1 for two angles with a sum of 360
Q20 · The table shows some values for y = 3x 2 - 2x - 1
20 The table shows some values for y = 3x 2 - 2x - 1. x -1 -0.5 0 0.5 1 1.5 y 4 -1 0 2.75 (a) Complete the table. [1] (b) On the grid, draw the graph of y = 3x 2 - 2x - 1 for - 1 G x G 1.5 . y 4 3 2 1 – 1 – 0.5 0 0.5 1 1.5 x – 1 – 2 [3] (c) By drawing a suitable straight line, solve the equation 3x 2 - 4x - 2 = 0 for - 1 G x G 1.5 . x = ................................................ [3] Question 21 is printed on the next page.
Mark scheme: 20(a) 0.75 and –1.25 1 20(b) Correct curve 3 B2 FT for 6 or 5 correct plots or B1 FT for 4 or 3 correct plots 20(c) ruled line y 2 x 1 B2 B1 for correct equation y 2 x 1 soi or y 2 x k or y kx 1 drawn −0.35 to −0.45 B1
Q21 · A curve has equation y = x 3 - 12x
21 A curve has equation y = x 3 - 12x . (a) Find the gradient of the curve at the point (1,−11). ................................................. [3] (b) Find the coordinates of the turning points of the curve. (................ , ...............) and (................ , ...............) [3]
Mark scheme: 21(a) − 9 3 B2 for 3 x 2 12 isw or B1 for 3 x 2 k or kx 2 12 21(b) (− 2, 16) (2, − 16) 3 2 dy M1 for their (3 x 12 ) = 0 or stating 0 dx A1 for x = 2 or (− 2, 16) or (2, − 16)
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.
2Circle theorems I1Differentiation1Equations1Estimation1Fractions, decimals and percentages1Graphs of functions1Introduction to probability1Non-right-angled triangles1Percentages1Powers and roots1Probability of combined events1Proportion1Ratio and proportion1Sequences1Similarity1Surface area and volume1Time1Transformations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2023 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.