Cambridge IGCSE Mathematics 0580 — 2024 May/June Paper 1 · Variant 2
0580/12/M/J/24 · 25 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 paper8 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write the number 31 072 000 in words
1 Write the number 31 072 000 in words. ............................................................................................................................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 Thirty-one million[s] [and] 1 seventy-two thousand[s]
Q2 · C B x A (a) Measure the size of angle x
2 C B x A (a) Measure the size of angle x. ................................................. [1] (b) Measure the length of line AB in millimetres. .......................................... mm [1] (c) Mark the midpoint, M, of line AB. [1] (d) Draw a line through the point M that is perpendicular to line AB. [1]
Mark scheme: 2(a) 46° 1 2(b) 84 1 2(c) Mid-point marked 42 mm along AB from A. 1 2(d) Line at 90° to AB at M. 1 FT their mid-point
Q3 · Find the value of the reciprocal of 0.4
3 Find the value of the reciprocal of 0.4 . ................................................. [1]
Mark scheme: 3 2.5 oe 1
Q4 · Write these numbers in order, starting with the smallest
4 Write these numbers in order, starting with the smallest. 6 -1 11 8.6 # 10 86. 5% 7 13 ................. 1 ................. 1 ................. 1 ................. [2] smallest
Mark scheme: 4 11 6 1 2 B1 for 3 in correct order 8.6 10 86.5% or M1 for 0.857[…], 0.86, 0.846[…], 13 7 0.865 or 85.7%, 86%, 84.6%
Q5 · Draw all the lines of symmetry on this quadrilateral
5 (a) Draw all the lines of symmetry on this quadrilateral. [2] (b) Write down the mathematical name of a quadrilateral that has rotational symmetry of order 2. ................................................. [1]
Mark scheme: 5(a) 4 correct lines of symmetry 2 B1 for two or three correct lines drawn and none incorrect or 4 correct and one additional line. 5(b) Rectangle or rhombus or parallelogram 1
Q6 · The temperature at midnight is -4 °C
6 The temperature at midnight is -4 °C. The temperature at noon is 25 °C. Work out the difference between these two temperatures. ............................................ °C [1]
Mark scheme: 6 29 1
Q7 · A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50
7 A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50 . Calculate the total amount he charges when he works for 4 hours. $ ................................................ [2]
Mark scheme: 7 41.7[0] 2 M1 for 6.55 × 4 + 15.50
Question 8
8 Jonah has $750. 1 He spends of this money on travel, and some of this money on food. 4 He now has $437.50 . Work out the fraction of the $750 he spends on food. ................................................. [3]
Mark scheme: 8 1 3 or equivalent fraction 625 6 B2 for oe 750 750 or M2 for 750 437.5 oe 4 750 or M1 for 750 oe 4 750 or 437.5 oe 4 or 437.5oe 750
Q9 · A delivery driver records the number of pizzas she delivers each month for one year
9 A delivery driver records the number of pizzas she delivers each month for one year. 48 44 39 28 57 22 36 41 54 57 49 52 (a) Complete the stem-and-leaf diagram. 2 3 4 5 Key: 4 q8 represents 48 pizzas [2] (b) Find the median. ................................................. [1]
Mark scheme: 9(a) Correct table 2 B1 for two rows correct or for fully correct unordered stem-and-leaf diagram. 2 2 8 3 6 9 4 1 4 8 9 5 2 4 7 7 9(b) 46 1
Q10 · 6 10 a = b = e- 7o e- 7o Work out a - b
5 6 10 a = b = e- 7o e- 7o Work out a - b . [1] f p
Mark scheme: 10 1 1 0
Q11 · These are the first four terms of a sequence
11 These are the first four terms of a sequence. 23 17 11 5 (a) Write down the next two terms. ....................... , ....................... [2] (b) Find the nth term. ................................................. [2]
Mark scheme: 11(a) −1 −7 2 B1 for each If 0 scored, SC1 for two terms with a difference of −6 11(b) – 6n + 29 oe final answer 2 B1 for −6n + j or kn + 29 k ≠ 0 or – 6n + 29 oe seen but spoilt.
Q12 · Write 0.04628 correct to 2 significant figures
12 Write 0.04628 correct to 2 significant figures. ................................................. [1]
Mark scheme: 12 0.046 cao 1
Q13 · A B On the Venn diagram, shade the region A , B
13 A B On the Venn diagram, shade the region A , B . [1]
Mark scheme: 13 1 A B
Question 14
14 Factorise completely. 20x - 90 x 2 ................................................. [2]
Mark scheme: 14 10x(2 – 9x) final answer 2 B1 for answer of 10(2x – 9x2) or x(20 – 90x) or 2x(10 –45x) or 5x(4 – 18x) or 10x(2 – 9x) seen and spoilt.
Q15 · Describe the type of correlation between the speed of runners and the time taken to…
15 Describe the type of correlation between the speed of runners and the time taken to complete a race. ................................................. [1]
Mark scheme: 15 Negative 1
Q16 · A circle has an area of 36r cm 2
16 A circle has an area of 36r cm 2 . (a) Find the circumference of the circle. Give your answer in terms of r. ............................................ cm [3] (b) The circle forms the base of a cylinder with height h cm. The volume of the cylinder is 540r cm 3 . Work out the value of h. h = ................................................ [2]
Mark scheme: 16(a) 12π cao 3 B2 for r = 6 or M1 for πr2 = 36π oe 16(b) 15 cao 2 M1 for [h =] 540π ÷ 36π or better
Q17 · Write 174 000 in standard form
17 Write 174 000 in standard form. ................................................. [1]
Mark scheme: 17 1.74 × 105 1
Q18 · NOT TO SCALE 14 cm x° 8.5 cm The diagram shows a right-angled triangle
18 NOT TO SCALE 14 cm x° 8.5 cm The diagram shows a right-angled triangle. Calculate the value of x. x = ................................................ [2]
Mark scheme: 18 52.6 or 52.61 to 52.62 2 8.5 M1 for cos[... ] oe 14
Q19 · 719 Without using a calculator, work out 2 ' 1
1 719 Without using a calculator, work out 2 ' 1 . 4 8 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 19 9 8 M2 oe 4 15 18 15 or oe with common denominator 8 8 9 15 B1 for or oe 4 8 their 9 8 or M1 for oe 4 their 15 1 A1 Dep on M2 15 cao
Question 20
20 Expand and simplify. ( x - 4)( x - 7) ................................................. [2]
Mark scheme: 20 x2 – 11x + 28 final answer 2 B1 for x2 – 4x – 7x + 28 with at least 3 terms correct
Q21 · 5 7 ' 5 x = 5 3 Find the value of x
21 5 7 ' 5 x = 5 3 Find the value of x. x = ................................................ [1]
Mark scheme: 21 4 cao 1
Q22 · The length, l metres, of a piece of material is 4.5 m, correct to the nearest 10 cm
22 The length, l metres, of a piece of material is 4.5 m, correct to the nearest 10 cm. Complete this statement about the value of l. ..................... G l 1 ................. [2]
Mark scheme: 22 4.45 4.55 2 B1 for each If 0 scored, SC1 for both correct but reversed or for 445 ⩽ l < 455
Q23 · % = {x: x is a natural number less than 12} S = {1, 4, 7, 10} T = {1, 3, 5, 7, 9, 11} S T…
23 % = {x: x is a natural number less than 12} S = {1, 4, 7, 10} T = {1, 3, 5, 7, 9, 11} S T 10 2 8 Complete the Venn diagram. [2]
Mark scheme: 23 2 B1 for at least 5 numbers in the S T correct places and not repeated elsewhere. [10] 3 5 1 4 9 11 7 [2] 6 [8]
Q24 · In a class of 30 students, 13 travel to school by bus
24 In a class of 30 students, 13 travel to school by bus. There are 570 students in the school. Find the expected number of students in the school who travel by bus. ................................................. [2] Question 25 is printed on the next page.
Mark scheme: 24 247 2 13 M1 for [570] 30
Q25 · D NOT TO SCALE 21.2 m 48° A B C 16.5 m The diagram shows a flagpole, BD, held by two…
25 D NOT TO SCALE 21.2 m 48° A B C 16.5 m The diagram shows a flagpole, BD, held by two ropes, AD and CD. ABC is a straight line and angle ABD = 90°. AD = 21.2 m, AB = 16.5 m and angle BCD = 48°. (a) Show that the height of the flagpole BD is 13.3 m, correct to 1 decimal place. [3] (b) Calculate the length of the rope CD. CD = ............................................ m [3]
Mark scheme: 25(a) 2 2 M2 M1 for BD2 + 16.52 = 21.22 or better [BD =] 21.2 16.5 13.31….. A1 25(b) 17.9 or 17.89 to 17.91….. 3 13.3 M2 for [CD =] or [CD =] sin 48 13.3 cos42 13.3 or M1 for sin 48 [=] or better CD 13.3 or for cos 42 [=] or better CD
What was in this paper
The subtopics covered by these 25 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Limits of accuracy2Ratio and proportion2Right-angled triangles2Sets2Types of number2Angles1Circles, arcs and sectors1Fractions, decimals and percentages1Indices I1Money1Ordering1Scatter diagrams1Sequences1Standard form1Statistical charts and diagrams1Symmetry1The four operations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2024 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.