Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 1 · Variant 2
0580/12/M/J/23 · 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 scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write down all the factors of 18
1 (a) Write down all the factors of 18. ..................................................................... [2] (b) Write down the reciprocal of 8. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 1, 2, 3, 6, 9, 18 2 B1 for 6 correct and one extra or for at least four correct and no extras or for all the correct factor pairs 1(b) 1 1 or [0].125 8
Q2 · B A (a) Draw a line perpendicular to the line AB
2 B A (a) Draw a line perpendicular to the line AB. [1] (b) Measure the line AB in centimetres. .............................................cm [1]
Mark scheme: 2(a) Accurate ruled perpendicular line 1 2(b) 7.4 1
Q3 · Shade two squares so that the diagram has rotational symmetry of order 4
3 Shade two squares so that the diagram has rotational symmetry of order 4. [2]
Mark scheme: 3 2 B1 for one correct square and a maximum of one incorrect square
Q4 · Kai and Ava each have a piece of wood 57 cm long
4 Kai and Ava each have a piece of wood 57 cm long. (a) Kai cuts his piece into 4 equal length parts. Find the length of one part. .............................................cm [1] (b) Ava cuts her piece into two parts and the lengths are in the ratio 5 | 1. Find the length of the longer part. .............................................cm [2]
Mark scheme: 4(a) 14.25 1 4(b) 47.5 2 57 M1 for [×5] 1 5
Q5 · B NOT TO 59° SCALE 73° x° y° A C D In the diagram, ABC is a triangle and ACD is a…
5 B NOT TO 59° SCALE 73° x° y° A C D In the diagram, ABC is a triangle and ACD is a straight line. Find the value of x and the value of y. x = ................................................ y = ................................................ [2]
Mark scheme: 5 [x= ] 48 2 B1 for each [y = ]132 If 0 scored, SC1 for two answers that add up to 180
Q6 · Find the temperature that is 8 °C colder than - 5 °C
6 Find the temperature that is 8 °C colder than - 5 °C. ............................................. °C [1]
Mark scheme: 6 –13 1
Q7 · There are two prime numbers in this list
7 There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers. ................................................. [2]
Mark scheme: 7 108 2 B1 for 47 or 61 identified
Q8 · On ten days, Stefan records the number of minutes he has to wait for a train
8 On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8 (a) Complete the stem-and-leaf diagram to show this information. 0 1 3 1 2 Key: 0 q1 represents 1 minute [2] (b) Find the median. .......................................... min [1]
Mark scheme: 8(a) 2 B1 for a correct diagram with one 0 (1 3) 4 5 5 8 error or omission or for a fully 1 1 2 correct unordered stem-and-leaf diagram 2 3 4 8(b) 6.5 1
Q9 · The scale drawing shows the positions of town A and town B
9 The scale drawing shows the positions of town A and town B. North A B Measure the bearing of town B from town A. ................................................. [1]
Mark scheme: 9 135 1
Q10 · 5 cm NOT TO SCALE 4 cm 6 cm 3 cm The diagram shows a right-angled triangular prism
10 5 cm NOT TO SCALE 4 cm 6 cm 3 cm The diagram shows a right-angled triangular prism. On the 1 cm2 grid, complete the net of this prism. One face has been drawn for you. [3]
Mark scheme: 10 Fully correct net 3 B2 for 2 correct rectangles in the correct places but in either order or B1 for 1 correct rectangle in the correct place If B0 or B1 scored, SC1 for two 3 4 5 triangles on opposite sides of a rectangle
Q11 · The distance from town A to town B on a map is 3.5 cm
11 The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B. ........................................... km [2]
Mark scheme: 11 8.75 2 3.5 250000 M1 for oe 100 1000 or B1 for figs 875 or 1 cm : 2.5 km
Q12 · A spinner is spun
12 A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Letter on A B C D spinner Probability 0.2 0.05 0.35 Complete the table. [2]
Mark scheme: 12 0.4 oe 2 M1 for 1 – (0.2 + 0.05 + 0.35) oe or B1 for 0.6 oe
Q13 · = { x| 1 G x G 20 } E = {even numbers} M = {multiples of 5} (a) Find n ( M )
13 = { x| 1 G x G 20 } E = {even numbers} M = {multiples of 5} (a) Find n ( M ) . ................................................. [1] (b) Find the elements in the set E + M . ................................................. [1]
Mark scheme: 13(a) 4 cao 1 13(b) 10, 20 1
Q14 · 514 Without using a calculator, work out ' 1
4 514 Without using a calculator, work out ' 1 . 7 21 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 14 4 21 M2 26 21 oe B1 for or oe 7 26 21 26 12 26 4 21 or oe with common denominator or M1 for oe 21 21 7 their 26 6 A1 cao 13
Q15 · - 12 15 F is the point ( 1, - 4 ) , FG = and GH = e- 3o e 35o
8 - 12 15 F is the point ( 1, - 4 ) , FG = and GH = e- 3o e 35o. Find (a) 3FG [1] f p (b) FG + GH [1] f p (c) the coordinates of the point G. (...................... , ......................) [1]
Mark scheme: 15(a) 24 1 9 15(b) 4 1 32 15(c) (9, –7) 1
Q16 · X is an integer where x H- 3 and x 1 3
16 x is an integer where x H- 3 and x 1 3 . Write down all the possible values of x. ..................................................................... [2]
Mark scheme: 16 −3, −2, −1, 0, 1, 2 2 B1 for 6 correct and one extra or for 5 correct and none incorrect
Q17 · Find the size of an interior angle of a regular 15-sided polygon
17 Find the size of an interior angle of a regular 15-sided polygon. ................................................. [2]
Mark scheme: 17 156 2 M1 for 180 − (360 ÷ 15) oe or{(15 − 2)×180}÷ 15 oe
Q18 · Write 45 000 in standard form
18 (a) Write 45 000 in standard form. ................................................. [1] (b) Calculate 6.75 # 10 -3 # 4.2 # 10 5 . Give your answer in standard form. ................................................. [1]
Mark scheme: 18(a) 4.5 × 104 1 18(b) 2.835 × 103 1
Question 19
19 Simplify. 18x 12 ' 3x 3 ................................................. [2]
Mark scheme: 19 6x9 final answer 2 B1 for kx9 or 6xk, k ≠ 0 as final answer or for correct answer seen and spoilt
Q20 · Buses at a station go to the port or to the town
20 Buses at a station go to the port or to the town. Buses leave every 28 minutes for the port. Buses leave every 48 minutes for the town. At 10 18 a bus for the port and a bus for the town leave the station together. Find the next time when a bus for the port and a bus for the town leave the station together. ................................................. [3]
Mark scheme: 20 15 54 or 3 54 pm 3 B2 for 336 or 5 hr 36 mins or M1 for 336k or 2×2×2×2×3×7 or [28=] 2×2×7 and [48=] 2×2×2×2×3 or correct factor trees/tables of both 28 and 48 OR M2 for listing times/multiples of both 28 and 48 to at least 1554 or 336 or M1 for listing at least next 3 of each or one full list
Q21 · NOT TO SCALE R C 9 cm A B P Q 15 cm 18 cm Triangle ABC is similar to triangle PQR
21 NOT TO SCALE R C 9 cm A B P Q 15 cm 18 cm Triangle ABC is similar to triangle PQR. Calculate QR. QR = ........................................... cm [2]
Mark scheme: 21 10.8 2 QR 18 M1 for oe or better 9 15
Q22 · A 8.6 cm NOT TO SCALE 42° B C The diagram shows a right-angled triangle ABC
22 (a) A 8.6 cm NOT TO SCALE 42° B C The diagram shows a right-angled triangle ABC. Calculate AB. AB = ........................................... cm [2] (b) P NOT TO SCALE 23.8 cm Q R 11.2 cm S 20 cm The diagram shows right-angled triangles PQS and PRS. PQ = 23. 8 cm , QS = 11.2 cm and SR = 20 cm . Calculate PR. PR = ........................................... cm [4] Question 23 is printed on the next page.
Mark scheme: 22(a) 5.75 or 5.754 to 5.755 2 AB M1 for sin 42 = or better 8.6 22(b) 29 4 M2 for 23.82 – 11.22 or M1 for […]2 + 11.22 = 23.82 and M1dep for (their 21)2 + 202
Q23 · The mass, m kilograms, of object A is 350 kg, correct to the nearest 10 kg
23 (a) The mass, m kilograms, of object A is 350 kg, correct to the nearest 10 kg. Complete this statement about the value of m. ......................... G m 1 ..................... [2] (b) The mass of object B is 348 kg, correct to the nearest kilogram. Show that the mass of object B may be more than the mass of object A. ..................................................................................................................................................... [1]
Mark scheme: 23(a) 345 355 2 B1 for one correct and in the correct position If 0 scored, SC1 for both correct but reversed 23(b) Any correct response e.g. A could be 345 1 Dependent on 345 given as a limit in part (a)
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.
3Scale drawings2Algebraic manipulation1Angles1Area and perimeter1Classifying statistical data1Compound shapes and parts of shapes1Fractions, decimals and percentages1Introduction to probability1Limits of accuracy1Perpendicular lines1Ratio and proportion1Right-angled triangles1Sets1Similarity1Standard form1Symmetry1The four operations1Time1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2023 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.