Cambridge IGCSE Mathematics 0580 — 2022 May/June Paper 1 · Variant 3
0580/13/M/J/22 · 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 the number one hundred and three thousand eight hundred and six in figures
1 Write the number one hundred and three thousand eight hundred and six in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 103 806 1
Q2 · B A (a) Measure the length of the line AB in millimetres
2 B A (a) Measure the length of the line AB in millimetres. .......................................... mm [1] (b) Mark the midpoint, M, of the line AB. [1] (c) Draw a line through M that is perpendicular to the line AB. [1]
Mark scheme: 2(a) 86 1 2(b) Point marked at 4.3 cm from A 1 2(c) Ruled line through M perpendicular to 1 AB
Question 3
3 Simplify. 3x - 4x + 7x ................................................. [1]
Mark scheme: 3 6x 1
Q4 · Work out the area of a rectangle that is 9.5 m long and 6.8 m wide
4 Work out the area of a rectangle that is 9.5 m long and 6.8 m wide. ............................................ m2 [2]
Mark scheme: 4 64.6 2 M1 for 9.5 × 6.8
Q5 · The probability of picking a red sweet from a bag is 0.05
5 The probability of picking a red sweet from a bag is 0.05 . Find the probability of not picking a red sweet. ................................................. [1]
Mark scheme: 5 0.95 oe 1
Q6 · North A North B Measure the bearing of point B from point A
6 North A North B Measure the bearing of point B from point A. ................................................. [1]
Mark scheme: 6 142° 1
Q7 · Mk 37 Work out the value of when m = 4 and k = 7
mk 37 Work out the value of when m = 4 and k = 7 . 3 ................................................. [2]
Mark scheme: 7 792 or 792.1… 2 4 7 3 M1 for oe 3 or B1 for 1372
Q8 · A box, in the shape of a cuboid, has volume 357 cm3
8 A box, in the shape of a cuboid, has volume 357 cm3. It has a length of 8.5 cm and a width of 6 cm. Calculate the height of the box. ............................................ cm [2]
Mark scheme: 8 7 2 M1 for 357 ÷ (8.5 × 6)
Q9 · T NOT TO S SCALE R 73° 75° P 129° Q PQRS is a quadrilateral
9 T NOT TO S SCALE R 73° 75° P 129° Q PQRS is a quadrilateral. RST is a straight line. Find angle PST. Angle PST = ................................................ [2]
Mark scheme: 9 97 2 M1 for 360 – (73 + 129 + 75)
Q10 · These are the masses, in kg, of 12 parcels
10 These are the masses, in kg, of 12 parcels. 0.3 0.4 1.2 0.8 1.1 2.1 1.7 1.8 1.2 2.3 0.7 1.1 (a) Complete the stem-and-leaf diagram for the 12 parcels. 0 3 4 1 2 Key: 0 q3 represents 0.3 kg [2] (b) Find the median. ............................................ kg [1]
Mark scheme: 10(a) 2 B1 for two rows correct or for fully 0 (3 4) 7 8 correct unordered stem-and-leaf diagram 1 1 1 2 2 7 8 or for a correct diagram with one error or omission 2 1 3 10(b) 1.15 1
Q11 · The grid shows point P and point R
11 The grid shows point P and point R. y 5 P 4 3 2 1 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x – 1 – 2 – 3 R – 4 – 5 (a) Write down the coordinates of point P. ( .................... , .................... ) [1] 3 (b) PQ = e- 2o Mark point Q on the grid. [1] (c) Find QR. QR = [1] f p (d) Complete this statement. [1] PQ + QR = ...........
Mark scheme: 11(a) (−1, 4) 1 11(b) Q marked at (2, 2) 1 11(c) 6 1 FT their point Q 5 11(d) PR 1
Question 12
12 Simplify. (a) y 3 ' y 5 ................................................. [1] (b) 7x 0 ................................................. [1]
Mark scheme: 12(a) 1 1 y−2 or final answer y 2 12(b) 7 1
Q13 · The scatter diagram shows the number of visitors and the total amount spent, in thousands…
13 The scatter diagram shows the number of visitors and the total amount spent, in thousands of dollars, at a zoo on each of eight days. 45 40 35 30 Total 25 amount spent 20 ($1000) 15 10 5 0150 200 250 300 350 400 450 500 550 600 Number of visitors (a) On one of the eight days there are 410 visitors. Find the total amount spent by visitors during this day. $ ................................................ [1] (b) Information for the ninth day is shown in the table. Number of visitors 175 Total amount spent ($1000) 9 Plot this information on the scatter diagram. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) On the tenth day the total amount spent is $22 000. Estimate the number of visitors on this day. ................................................. [1]
Mark scheme: 13(a) 27 000 1 13(b) Point plotted at (175, 9) 1 13(c) Correct single ruled line of best fit 1 13(d) 300 to 350 1 FT their straight line of best fit provided positive gradient
Q14 · NOT TO SCALE 5 cm 5 cm h 4 cm (a) Calculate the height, h, of the triangle
14 NOT TO SCALE 5 cm 5 cm h 4 cm (a) Calculate the height, h, of the triangle. h = ........................................... cm [3] (b) The triangle is one face of a square-based pyramid. On the 1 cm2 grid, draw a net of this pyramid. [3]
Mark scheme: 14(a) 4.58 or 4.582 to 4.583 3 M2 for 52 − 22 or better or M1 for 52 = 22 + h2 or better 14(b) Correct ruled net of the pyramid 3 B2 for a 4 by 4 square and 4 isosceles triangles on the sides of the square or B1 for a 4 by 4 square or at least one isosceles triangle drawn on a side of a square
Question 15
15 Factorise completely. 18px - 27p ................................................. [2]
Mark scheme: 15 9p(2x – 3) final answer 2 B1 for 9(2px – 3p) or p(18x – 27) or 3p(6x – 9) or 9p(2x – 3) seen and spoilt
Q16 · The nth term of a sequence is n 2 - 1
16 The nth term of a sequence is n 2 - 1. Find the first three terms of this sequence. ....................... , ....................... , ....................... [2]
Mark scheme: 16 0 3 8 2 B1 for 2 correct terms in correct position or SC1 for −1 0 3
Q17 · Q C NOT TO SCALE 9.2 cm 9.2 cm 7.3 cm A 7.3 cm B R P The diagram shows two right-angled…
17 Q C NOT TO SCALE 9.2 cm 9.2 cm 7.3 cm A 7.3 cm B R P The diagram shows two right-angled triangles, ABC and PQR. (a) Complete this statement with a geometrical term. Triangle ABC is ............................................... to triangle PQR. [1] (b) Calculate angle ABC. Angle ABC = ................................................. [2]
Mark scheme: 17(a) Congruent 1 17(b) 37.5 or 37.48 to 37.49 2 7.3 M1 for cos[ABC =] 9.2
Q18 · Find the lowest common multiple (LCM) of 32 and 40
18 Find the lowest common multiple (LCM) of 32 and 40. ................................................. [2]
Mark scheme: 18 160 2 B1 for 160k as final answer or M1 for [32=] 2 × 2 × 2 × 2 × 2 and [40=] 2 × 2 × 2 × 5 or two correct factor trees or correct tables or a list of multiples of both 32 and 40 with at least 3 of each or 2 × 2 × 2 × 2 × 2 × 5
Q19 · Joe thinks of a number, n, trebles it, and subtracts 5
19 Joe thinks of a number, n, trebles it, and subtracts 5. The result is 22. Write this as an equation in terms of n, and solve the equation. n = ................................................ [3]
Mark scheme: 19 3n – 5 = 22 1 9 final answer 2 B2FT their equation providing their equation is in the form an+b=22 where a≠0 or 1 and b≠0 5 22 or M1FT for 3n = 22 + 5 or n − = 3 3
Q20 · Y 4 3 L 2 1 – 3 – 2 – 1 0 1 2 x – 1 – 2 – 3 – 4 – 5 – 6 Find the gradient of line L
20 y 4 3 L 2 1 – 3 – 2 – 1 0 1 2 x – 1 – 2 – 3 – 4 – 5 – 6 Find the gradient of line L. ................................................. [2]
Mark scheme: 20 −2 2 k2 M1 for 1k y 2 y1 or for for 2 points on the line x2 x1
Q21 · Dominic asks 30 students in his class if they are right-handed or left-handed
21 Dominic asks 30 students in his class if they are right-handed or left-handed. 7 students are left-handed. Work out the expected number of left-handed students in the whole school of 960 students. ................................................. [2]
Mark scheme: 21 224 2 7 M1 for 960 oe 30
Q22 · 722 Without using a calculator, work out 4 - 1
1 722 Without using a calculator, work out 4 - 1 . 6 8 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 22 B1 Correct step for dealing with mixed 25 15 1 7 or numbers 6 8 36 8 25k 15 k Allow or 6 k 8 k M1 Correct method to find common 100 45 4 21 and oe [3] and denominator 24 24 24 24 4 21 e.g. 4 and 1 24 24 7 A1 2 final answer 24
Q23 · Solve the simultaneous equations
23 Solve the simultaneous equations. You must show all your working. 4x - 3y = 26 5x + 6y = 13 x = ................................................. y = ................................................ [3]
Mark scheme: 23 For correct method to eliminate one M1 variable [x =] 5 A1 [y =] −2 A1 If zero scored, SC1 for 2 values satisfying one of the original equations or SC1 if no working shown, but 2 correct answers
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.
2Angles2Equations2Types of number2Area and perimeter1Fractions, decimals and percentages1Gradient of linear graphs1Indices I1Interpreting statistical data1Introduction to probability1Powers and roots1Pythagoras’ theorem1Ratio and proportion1Right-angled triangles1Sequences1Statistical charts and diagrams1Surface area and volume1Units of measure1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2022 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.