Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 1 · Variant 3
0580/13/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 · Write 928 correct to the nearest ten
1 Write 928 correct to the nearest ten. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 930 1
Q2 · Write down a fraction that is equivalent to 7
2 Write down a fraction that is equivalent to 7. 9 ................................................. [1]
Mark scheme: 2 7 k 1 where k is an integer >1 9 k
Question 3
3 Work out. - 4 + 6 # 3 ................................................. [1]
Mark scheme: 3 14 1
Q4 · Bobby records the number of days a shop is open during 30 days
4 Bobby records the number of days a shop is open during 30 days. Tally Frequency Days open |||| |||| |||| |||| ||| Days not open Complete the table. [2]
Mark scheme: 4 2 B1 for one correct 23, 7, |||| ||
Question 5
5 (a) Complete the statement. The diagram has rotational symmetry of order ........................ . [1] (b) On the diagram, draw all the lines of symmetry. [2]
Mark scheme: 5(a) 2 1 5(b) 2 B1 for one correct line and no extras or two correct lines and one extra
Q6 · Write down the reciprocal of 16 as a decimal
6 Write down the reciprocal of 16 as a decimal. ................................................. [1]
Mark scheme: 6 0.0625 1
Q7 · The stem-and-leaf diagram shows the ages of 21 people
7 The stem-and-leaf diagram shows the ages of 21 people. 1 6 9 2 1 4 4 5 8 3 2 6 7 9 4 0 2 4 6 8 9 5 3 4 5 7 Key : 1q6 represents 16 years (a) Find the fraction of people who are more than 30 years old. ................................................. [1] (b) Work out the range. ................................................. [1] (c) Find the median. ................................................. [1]
Mark scheme: 7(a) 2 1 oe fraction 3 7(b) 41 1 7(c) 39 1
Q8 · NOT TO 5 cm SCALE 3 cm 8 cm Find the total surface area of the cuboid
8 NOT TO 5 cm SCALE 3 cm 8 cm Find the total surface area of the cuboid. .......................................... cm2 [3]
Mark scheme: 8 158 3 M2 for 2 8 5 8 3 5 3 or M1 for 8 5 or 8 3 or 5 3
Q9 · 4 cm NOT TO 4 cm SCALE 2 cm 4 cm The diagram shows a triangular prism
9 4 cm NOT TO 4 cm SCALE 2 cm 4 cm The diagram shows a triangular prism. On the 1 cm 2 grid, draw a net of the prism. [3]
Mark scheme: 9 Correct ruled net 3 B2 for 3 rectangles of the same size and 2 triangles with at least 2 sides the same size drawn in correct places but not the correct size or B1 for one correct face drawn as part of a net
Q10 · Olga thinks that 87 is a prime number
10 Olga thinks that 87 is a prime number. Is Olga correct? Give a reason for your answer. ......................... because ..................................................................................................................... [1]
Mark scheme: 10 No 1 87 divides by 3 oe
Q11 · A film lasts for 2 hours 50 minutes
11 A film lasts for 2 hours 50 minutes. The film ends at 23 05. Find the time the film starts. ................................................. [1]
Mark scheme: 11 20 15 or [0]8.15pm 1
Q12 · A 38° NOT TO SCALE x° B C Triangle ABC is isosceles
12 A 38° NOT TO SCALE x° B C Triangle ABC is isosceles. Angle BAC = 38° and AB = AC. Find the value of x. x = ................................................ [2]
Mark scheme: 12 71 2 180 38 M1 for 2
Q13 · By writing each number in the calculation correct to 1 significant figure, find an…
13 By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 6.8 # 10.6 . 3.2 - 0. 98 You must show all your working. ................................................. [2]
Mark scheme: 13 7 10 M1 3 1 35 nfww A1 If 0 scored, SC1 for 3 correct roundings or all correct but with trailing zeros
Q14 · The scatter diagram shows information about the time spent in a shop and the number of…
14 The scatter diagram shows information about the time spent in a shop and the number of items bought. 16 14 12 10 Number of items 8 bought 6 4 2 0 0 10 20 30 40 50 60 70 80 Time (min) (a) What type of correlation is shown on the scatter diagram? ................................................. [1] (b) Describe the relationship between the time spent in the shop and the number of items bought. ..................................................................................................................................................... ..................................................................................................................................................... [1] (c) Draw a line of best fit on the scatter diagram. [1]
Mark scheme: 14(a) Positive 1 14(b) Correct description e.g. The longer 1 people spend in the shop the more items they buy 14(c) Correct ruled line 1
Q15 · Simplify d 8 ' d 2
15 Simplify d 8 ' d 2 . ................................................. [1]
Mark scheme: 15 d 6 1
Q16 · Maddie changes 4000 Swiss francs into dollars when the exchange rate is $1 = 0.913 Swiss…
16 Maddie changes 4000 Swiss francs into dollars when the exchange rate is $1 = 0.913 Swiss francs. Work out how many dollars she receives. $ ................................................ [1]
Mark scheme: 16 4380, 4381, 4381.1, 4381.2[0], 1 4381.16
Q17 · Find the highest common factor (HCF) of 32 and 120
17 Find the highest common factor (HCF) of 32 and 120. ................................................. [2]
Mark scheme: 17 8 2 B1 for final answer 2 × 2 × 2 or 23 or 2 or 4 or M1 for [32=] 2 × 2 × 2 × 2 × 2 and [120 =] 2 × 2 × 2 × 3 × 5 or 2 correct factor trees or tables
Q18 · The probability that Tom is late for school is 0.12
18 The probability that Tom is late for school is 0.12 . There are 200 school days this year. Work out the expected number of times that Tom is late for school this year. ................................................. [1]
Mark scheme: 18 24 1
Question 19
19 Expand and simplify. ( x - 5)( x + 8) ................................................. [2]
Mark scheme: 19 x2 + 3x – 40 2 B1 for x2 – 5x + 8x – 40 with at least 3 terms correct
Q20 · C x° B NOT TO SCALE O 32° A The diagram shows a circle, centre O, diameter AB
20 C x° B NOT TO SCALE O 32° A The diagram shows a circle, centre O, diameter AB. A, B and C lie on the circumference of the circle. (a) Write down the mathematical name of the line AC. ................................................. [1] (b) Find the value of x. Give a geometrical reason for your answer. x = .................... because ............................................................................................................ [2]
Mark scheme: 20(a) Chord 1 20(b) 58 1 Angle in a semicircle = 90° 1
Q21 · A spinner has five sides
21 A spinner has five sides. Each side is painted red, blue, green, yellow or orange. The table shows some of the probabilities of the spinner landing on each colour. Colour Red Blue Green Yellow Orange Probability 0.3 0.16 0.18 0.25 (a) Complete the table. [2] (b) Dan spins the spinner once. Find the probability that the spinner lands on red or blue. ................................................. [2]
Mark scheme: 21(a) 0.11 oe 2 M1 for 1 – (0.3 + 0.16 + 0.18 + 0.25) oe or B1 for 0.89 oe 21(b) 0.46 oe 2 M1 for 0.3 + 0.16
Q22 · Vanessa invests $8500 at a rate of 3.5% per year compound interest
22 Vanessa invests $8500 at a rate of 3.5% per year compound interest. Calculate the value of her investment at the end of 6 years. Give your answer correct to the nearest dollar. $ ................................................ [3]
Mark scheme: 22 10449 cao 3 B2 for 10400, 10440, 10450, 10448, 10448.7, 10448.67… 3.5 6 or M1 for 8500 [×] 1 oe 100 B1 for rounding their decimal answer correct to the nearest dollar
Q23 · The diagram shows three shapes, A, B and C, on a 1 cm 2 grid
23 The diagram shows three shapes, A, B and C, on a 1 cm 2 grid. y 7 6 5 B 4 A 3 2 C 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 x Describe fully the single transformation that maps (a) shape A onto shape B ..................................................................................................................................................... ..................................................................................................................................................... [3] (b) shape A onto shape C. ..................................................................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 23(a) Rotation 3 B1 for each [centre] (–3, 3) 90º clockwise 23(b) Translation 2 B1 for each 7 2
Q24 · 124 Without using a calculator, work out 5 + 2
11 124 Without using a calculator, work out 5 + 2 . 12 4 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 24 M1 Accept with other correct common k 27 denominators 12 12 11 3 71 f 27 f [5] + [2] e.g. 24, 36, 48 such as and or 12 12 12 f 12 f 71 c oe oe 12 12 1 A2 1 8 cao A1 for fraction equivalent to 8 6 6 49 k 1k 7 e.g. or 8 or 7 6 k 6 k 6
Q25 · In this question, both lengths are in centimetres
25 In this question, both lengths are in centimetres. B 10x - 12 NOT TO SCALE C 2x + 3 A D The diagram shows two lines, AB and CD. The length of AB is 10x - 12 . The length of CD is 2x + 3 . Line AB is 3 times as long as line CD. Work out the value of x. x = ................................................ [4]
Mark scheme: 25 5.25 oe 4 M1 for 10x – 12 = 3(2x + 3) 10 x 12 B1 for 6x + 9 or – 3 3 M1 for ax + b = cx + d leading to ax – cx = d – b
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.
3Types of number2Algebraic manipulation1Angles1Area and perimeter1Averages and range1Circle theorems1Classifying statistical data1Compound shapes and parts of shapes1Estimation1Indices I1Introduction to probability1Limits of accuracy1Money1Percentages1Ratio and proportion1Relative and expected frequencies1Scatter diagrams1Symmetry1The four operations1Time1Transformations1What you needed in this session
Cambridge’s own grade thresholds for 2023 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.