Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 1 · Variant 1
0580/11/M/J/23 · 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 paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Work out the number of months in 5 years
1 Work out the number of months in 5 years. ..................................... months [1]
Mark scheme: Question Answer Marks Partial Marks 1 60 1
Q2 · Write 3752 correct to the (a) nearest 10 ................................................
2 Write 3752 correct to the (a) nearest 10 ................................................. [1] (b) nearest 100. ................................................. [1]
Mark scheme: 2(a) 3750 cao 1 2(b) 3800 cao 1
Q3 · Magazines cost $3.40 each
3 Magazines cost $3.40 each. Rosina has $15 to buy as many magazines as possible. Complete the statement. Rosina can buy ................. magazines and will have $ ................. left. [3]
Mark scheme: 3 4 1.4[0] 3 B2 for 4 or M1 for 15 ÷ 3.4 A1 for 1.4[0]
Q4 · Write down the mathematical name of a 4-sided shape that has rotational symmetry of order…
4 Write down the mathematical name of a 4-sided shape that has rotational symmetry of order 2 and no lines of symmetry. ................................................. [1]
Mark scheme: 4 Parallelogram 1
Q5 · 21 8 15 32 3 29 19 45 8 Calculate the mean of these numbers
5 21 8 15 32 3 29 19 45 8 Calculate the mean of these numbers. ................................................. [2]
Mark scheme: 5 20 2 M1 for sum of the nine numbers ÷ 9
Q6 · A train journey starts at 21 43
6 A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes. ................................................. [1]
Mark scheme: 6 06 15 or 6:15am 1
Q7 · Write these numbers in order, starting with the smallest
7 Write these numbers in order, starting with the smallest. 15 0.071 0.7 7% 213 ......................... 1 ......................... 1 ....................... 1 ......................... [2] smallest
Mark scheme: 7 15 2 B1 for 3 in correct order 7% 0.071 0.7 213 15 or M1 for 0.0704… (for ) 213 and 0.07 (for 7%)
Q8 · 8 Write the fraction in its simplest form
248 Write the fraction in its simplest form. 84 ................................................. [1]
Mark scheme: 8 2 1 cao 7
Question 9
9 Simplify. 3a - 5b - a - 6b ................................................. [2]
Mark scheme: 9 2a – 11b final answer 2 B1 for 2a or −11b in final answer or for 2a – 11b seen then spoilt
Q10 · The cost of hiring a bicycle, $C, for y hours is given by the formula C = 12 + 3.5y
10 The cost of hiring a bicycle, $C, for y hours is given by the formula C = 12 + 3.5y . Maria pays $36.50 to hire this bicycle. Work out the number of hours she hires the bicycle for. ........................................ hours [2]
Mark scheme: 10 7 2 M1 for 36.5[0] – 12 = 3.5y or better
Q11 · 3 - 2 a = b = e 7 o e 5o Work out a - 2 b
11 3 - 2 a = b = e 7 o e 5o Work out a - 2 b . [2] f p
Mark scheme: 11 7 2 7 b B1 for or as answer 3 a 3 4 4 or or in working 10 10
Q12 · NOT TO SCALE 52° x° The diagram shows a pair of parallel lines and a straight line
12 (a) NOT TO SCALE 52° x° The diagram shows a pair of parallel lines and a straight line. Write down the geometrical reason why the value of x is 52. ............................................................................... [1] (b) NOT TO 126° SCALE 38° y° Find the value of y and write down the geometrical reason for your answer. y = .................. because .............................................................................................................. [2]
Mark scheme: 12(a) Alternate angles 1 12(b) 196 2 B1 for each Angles at a point sum to 360
Q13 · Calculate the volume of a sphere with diameter 4.8 cm
13 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: 13 57.9 or 57.90 to 57.91…. 2 3 4 4.8 M1 for π 3 2
Q14 · By writing each number in the calculation correct to 1 significant figure, work out an…
14 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: 14 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
Q15 · Eric has four colours of paint
15 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: 15 0.22 oe 2 M1 for 1 – (0.3 + 0.35 + 0.13) oe or B1 for 0.78 oe
Question 16
16 Factorise completely. 8x 2 - 20x ................................................. [2]
Mark scheme: 16 4x(2x – 5) final answer 2 B1 for x(8x – 20) or 4(2x2 – 5x) or 2x(4x – 10) or 4x(2x – 5) seen and then spoilt
Q17 · The nth term of a sequence is 10 - n 2
17 (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: 17(a) 9 6 1 2 B1 for 2 correct 17(b) 3n + 4 oe final answer 2 B1 for 3n + j or kn + 4 (k ≠ 0) or 3n + 4 seen and spoilt
Q18 · The length, l metres, of a piece of wood is 3.6 metres, correct to the nearest 10…
18 The length, l metres, of a piece of wood is 3.6 metres, correct to the nearest 10 centimetres. Complete this statement about the value of l. ................... G l 1 ................... [2]
Mark scheme: 18 3.55 3.65 2 B1 for each If 0 scored, SC1 for correct but reversed or for 355 ⩽ l < 365
Q19 · Calculate 1 ' ( 6.4 # 10 -5 )
19 Calculate 1 ' ( 6.4 # 10 -5 ) . Give your answer in standard form. ................................................. [2]
Mark scheme: 19 1.5625 × 104 2 B1 for 1.56 × 104 or 1.562 × 104 or 1.563 × 104 or figs 15625
Q20 · 520 Without using a calculator, work out 2 '
1 520 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: 20 15 9 M2 15 oe B1 for oe 7 5 7 135 35 their 1 5 9 or oe or M1 for oe 63 63 7 5 with common denominator 6 A1 37 cao
Q21 · 4x° NOT TO SCALE (3x - 1)° The diagram shows a right-angled triangle
21 4x° NOT TO SCALE (3x - 1)° The diagram shows a right-angled triangle. Use the information in the diagram to write down and solve an equation to find the value of x. x = ................................................ [3]
Mark scheme: 21 4x + 3x – 1 + 90 = 180 oe B1 13 2 M1 for 4x + 3x = 90 + 1 or better
Q22 · NOT TO 7.5 cm SCALE y° 12.8 cm The diagram shows a right-angled triangle
22 NOT TO 7.5 cm SCALE y° 12.8 cm The diagram shows a right-angled triangle. Calculate the value of y. y = ................................................. [2]
Mark scheme: 22 30.4 or 30.36 to 30.37 2 7.5 M1 for tan [y =] or better 12.8
Q23 · 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
23 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: 23 6.3 2 5.6 7.2 M1 for oe or better h 8.1
Q24 · = {a, b, c, d, e, f, g, h, i, j, k} F = {f, a, c, e} B = {b, a, c, k} (a) Complete the…
24 = {a, b, c, d, e, f, g, h, i, j, k} F = {f, a, c, e} B = {b, a, c, k} (a) Complete the Venn diagram. F B f d h [2] (b) Find n ( F , B ) . ................................................. [1]
Mark scheme: 24(a) 2 B1 for 4 letters in correct regions 24(b) 6 1 FT their Venn diagram
Q25 · At a cinema, an adult ticket costs $a and a child ticket costs $c
25 At a cinema, an adult ticket costs $a and a child ticket costs $c. (a) Farah buys 3 adult tickets and 4 child tickets for $38.50 . Complete the equation. 3a + 4c = ................................ [1] (b) Hana buys 6 adult tickets and 5 child tickets for $65.00 . Write down another equation in terms of a and c. ................................................. [1] (c) Solve the two simultaneous equations to find the value of a and the value of c. You must show all your working. a = ................................................ c = ................................................. [3]
Mark scheme: 25(a) 38.5 1 25(b) 6a + 5c = 65 1 If 0 scored in part(a) and part(b), SC1 for 3850 in part(a) and 6a + 5c = 6500 in part(b) 25(c) Correctly eliminating one variable M1 Follow through their linear equations [a =] 7.5 A1 [c =] 4 A1 If M0 or M0 FT scored, SC1 for 2 values which satisfy one correct equation or one of their equations
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.
2Angles2Fractions, decimals and percentages2Limits of accuracy2Time2Averages and range1Equations1Estimation1Introduction to probability1Money1Ordering1Rates1Right-angled triangles1Sequences1Sets1Similarity1Standard form1Surface area and volume1Symmetry1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2023 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.