Cambridge IGCSE Mathematics 0580 — 2024 May/June Paper 1 · Variant 3
0580/13/M/J/24 · 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 scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write the number two million two thousand and two in figures
1 Write the number two million two thousand and two in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 2 002 002 1
Q2 · Put one pair of brackets into this calculation to make it correct
2 Put one pair of brackets into this calculation to make it correct. 5 + 4 # 3 + 9 = 53 [1]
Mark scheme: 2 5 + 4 × (3 + 9) = 53 1
Question 3
3 Simplify. 7x - 8y - x - y ................................................. [2]
Mark scheme: 3 6x – 9y or 3(2x – 3y) final answer 2 B1 for 6x or – 9y in final answer or 6x – 9y seen then spoilt
Q4 · Write 164 703 correct to the nearest thousand
4 (a) Write 164 703 correct to the nearest thousand. ................................................. [1] (b) Write 16.983 correct to 1 decimal place. ................................................. [1] (c) Write 0.037 665 correct to 2 significant figures. ................................................. [1]
Mark scheme: 4(a) 165 000 cao 1 4(b) 17.0 cao 1 4(c) 0.038 cao 1
Q5 · On the diagram, draw any lines of symmetry
5 (a) On the diagram, draw any lines of symmetry. [1] (b) Write down the order of rotational symmetry of this shape. ................................................. [1]
Mark scheme: 5(a) Correct line of symmetry 1 5(b) 3 1
Q6 · Write these numbers in order, starting with the smallest
6 Write these numbers in order, starting with the smallest. 4 2 0.45 42% 11 5 ....................... 1 ....................... 1 ....................... 1 ....................... [2] smallest
Mark scheme: 6 4 2 2 B1 for 3 in correct order 42% 0.45 or M1 for 3 equivalent decimals ..., 0.42, 11 5 0.36, 0.4,
Q7 · The base of a cuboid measures 10 cm by 7 cm
7 The base of a cuboid measures 10 cm by 7 cm. The volume of the cuboid is 280 cm3. Calculate the height of the cuboid. ............................................ cm [2]
Mark scheme: 7 4 2 M1 for 10 × 7 × [...] = 280 oe
Q8 · In a city, the probability that it will rain today is 0.15
8 In a city, the probability that it will rain today is 0.15 . Find the probability that it will not rain today in this city. ................................................. [1]
Mark scheme: 8 0.85 oe 1
Q9 · One day the temperature in Tokyo is - 5 °C and the temperature in Manila is 18 °C
9 One day the temperature in Tokyo is - 5 °C and the temperature in Manila is 18 °C. (a) Work out the difference between these two temperatures. ............................................ °C [1] (b) The temperature in Tokyo rises by 4 °C. Find the new temperature in Tokyo. ............................................. °C [1]
Mark scheme: 9(a) 23 1 9(b) –1 1
Q10 · These are the first four terms of a sequence
10 (a) These are the first four terms of a sequence. 3 10 17 24 (i) Write down the next term. ................................................. [1] (ii) Write down the term to term rule for continuing the sequence. ................................................. [1] (b) These are the first four terms of another sequence. 16 14 11 7 Write down the next two terms of this sequence. ....................... , ....................... [2]
Mark scheme: 10(a)(i) 31 1 10(a)(ii) add 7 oe 1 10(b) 2 –4 2 B1 for each or 0 scored SC1 for two terms with a difference of −6
Q11 · X° NOT TO SCALE 36° The diagram shows an isosceles triangle
11 x° NOT TO SCALE 36° The diagram shows an isosceles triangle. Find the value of x. x = ................................................ [2]
Mark scheme: 11 108 2 M1 for 180 – 36 – 36 oe
Q12 · The diagram shows a cuboid
12 The diagram shows a cuboid. NOT TO 3 cm SCALE 2 cm 6 cm On the 1 cm2 grid, complete a net of this cuboid. One face has been drawn for you. [3]
Mark scheme: 12 Fully correct net 3 B2 for 3 or 4 extra correct faces in the correct places B1 for 1 or 2 extra correct faces in the correct places
Question 13
13 Factorise completely. 4x 2 y - 5xy 2 ................................................. [2]
Mark scheme: 13 xy(4x – 5y) final answer 2 B1 for y(4x2 – 5xy) or x(4xy – 5y2) or xy(4x – 5y) seen then spoilt
Q14 · The scale of a map is 1 : 40 000
14 The scale of a map is 1 : 40 000. On the map the distance between two villages is 37 cm. Calculate the actual distance between the two villages. Give your answer in kilometres. ............................................ km [2]
Mark scheme: 14 14.8 2 M1 for 1 cm represents 0.4 km soi or B1 for figs 148 as answer
Q15 · 1 15 Without using a calculator, work out -
3 1 15 Without using a calculator, work out - . 7 14 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]
Mark scheme: 15 6 1 M1 Allow any correct denominator 14k and oe 14 14 5 A1 cao 14
Q16 · The price of a game increases from $48 to $56.40
16 The price of a game increases from $48 to $56.40 . Calculate the percentage increase in the price. .............................................. % [2]
Mark scheme: 16 17.5 2 56.40 M1 for ( − 1) [× 100] oe or 48 56.40 48 [×100] 48 56.40 or 100 [− 100] 48
Q17 · C NOT TO SCALE 8 cm 37° A B The diagram shows a right-angled triangle
17 C NOT TO SCALE 8 cm 37° A B The diagram shows a right-angled triangle. Calculate AB. AB = ........................................... cm [2]
Mark scheme: 17 6.39 or 6.389... 2 M1 for cos37 AB oe 8
Q18 · The length, s metres, of a ship is 83 m, correct to the nearest metre
18 The length, s metres, of a ship is 83 m, correct to the nearest metre. Complete this statement about the value of s. ......................... G s 1 ......................... [2]
Mark scheme: 18 82.5 83.5 2 B1 for one correct or both correct but reversed
Q19 · Solve the simultaneous equations
19 Solve the simultaneous equations. 5t - 2w = 19 3t + 2w = 5 t = ................................................ w = ................................................ [2]
Mark scheme: 19 [t = ] 3 2 B1 for each [w = ] –2
Q20 · The diagram shows the positions of three towns A, B and C
20 The diagram shows the positions of three towns A, B and C. North B North North 103° NOT TO SCALE A C Angle ABC = 103° . The bearing of town B from town A is 048°. Town C is due east of town A. Find the bearing of town C from town B. ................................................. [4]
Mark scheme: 20 125 4 B1 for 48 between the North line and AB at A. M1 for 180 ─ their 48 M1 dep for 360 ─ (103 + their 132) OR M1 for [angle ACB =] 180 ─ 103 ─ (90 ─ their 48) M1 dep for 90 + their ACB or for 180 ─ (90 ─ their ACB)
Q21 · % = {1, 4, 5, 8, 9, 12, 16, 64} C = {cube numbers} S = {square numbers} C S (i) Complete…
21 (a) % = {1, 4, 5, 8, 9, 12, 16, 64} C = {cube numbers} S = {square numbers} C S (i) Complete the Venn diagram. [2] (ii) Find n ( C , S ) . ................................................. [1] (b) A B On this Venn diagram, shade the region A + B . [1]
Mark scheme: 21(a)(i) 2 B1 for 4 or more numbers in the correct place 1 4 8 9 64 16 21(a)(ii) 6 1FT Strict ft their diagram 21(b) 1
Q22 · Write these numbers in standard form
22 (a) Write these numbers in standard form. (i) 0.007 ................................................. [1] (ii) 700 000 000 ................................................. [1] 3200 # 5 .4 # 10 -3 (b) Calculate . 4.8 # 10 -4 Give your answer in standard form. ................................................. [2]
Mark scheme: 22(a)(i) 7 × 10–3 1 22(a)(ii) 7 × 108 1 22(b) 3.6 × 104 2 B1 for 36 000 or for writing their ordinary number correctly in standard form or for 36 000 written in incorrect standard form
Q23 · 0.5 m NOT TO 32 cm SCALE 24 cm The diagram shows a spherical tank with radius 0.5 m and a…
23 0.5 m NOT TO 32 cm SCALE 24 cm The diagram shows a spherical tank with radius 0.5 m and a cylindrical jug with diameter 24 cm and height 32 cm. The tank is full of water. Calculate how many times the jug can be completely filled with water from the tank. 4 3 [The volume, V, of a sphere with radius r is rr .] 3 ................................................. [5]
Mark scheme: 23 36 5 B4 for 36.16 to 36.17 or 36.2 or B1 for 50 or 0.12 and 0.32 M1 for 43 ×π×(their50)3 or 43 ×π× 0.53 M1 for π ×122×32 or π × their 0.122× their 0.32 M1 for their 523 598 ÷ their 14 476 or their 0.523 598 ÷ their 0.014 476 dep on M1 M1and correct formulae used If 1,2or 3 scored award SC1 for their decimal answer correctly rounded down to the nearest integer
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.
2Area and perimeter2Limits of accuracy2The four operations2Angles1Coordinates1Equations1Fractions, decimals and percentages1Introduction to probability1Ordering1Percentages1Right-angled triangles1Scale drawings1Sequences1Sets1Standard form1Surface area and volume1Symmetry1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2024 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.