Cambridge IGCSE Mathematics 0580 — 2021 May/June Paper 2 · Variant 3
0580/23/M/J/21 · 26 questions · 70 marks · ≈79 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 down the number that is 23 less than - .16
1 Write down the number that is 23 less than - .16 . ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 –24.6 1
Q2 · Write as a fraction in its simplest form
2 Write as a fraction in its simplest form. (a) 72% ................................................. [1] (b) 0.004 ................................................. [1]
Mark scheme: 2(a) 18 1 cao 25 2(b) 1 1 cao 250
Q3 · X NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line
3 x NOT TO SCALE 40° The diagram shows a pair of parallel lines and a straight line. Complete the statement with the correct geometrical reason. x = 40° because the angles are ............................................ [1]
Mark scheme: 3 Corresponding 1
Q4 · NOT TO SCALE 100° y° y° Find the value of y
4 NOT TO SCALE 100° y° y° Find the value of y. y = ..................................................... [2]
Mark scheme: 4 130 2 M1 for 360 – 100 or better
Q5 · Jo invests $600 for 7 years at a rate of 1.5% per year simple interest
5 Jo invests $600 for 7 years at a rate of 1.5% per year simple interest. Calculate the total interest earned during the 7 years. $ ..................................................... [2]
Mark scheme: 5 63 2 1.5 M1 for 600 × oe or better 100 If 0 scored SC1 for answer 663
Q6 · Maria buys n pencils that cost p cents each
6 Maria buys n pencils that cost p cents each. She pays with a $y note. Find, in terms of n, p and y, the amount of change Maria receives. Give your answer in cents. ......................................... cents [2]
Mark scheme: 6 100y – np 2 B1 for 100y seen or for answer [10k] y – np
Q7 · 12 18 29 49 91 125 From the list of numbers, write down (a) a cube number…
7 12 18 29 49 91 125 From the list of numbers, write down (a) a cube number, ................................................. [1] (b) a prime number. ................................................. [1]
Mark scheme: 7(a) 125 1 7(b) 29 1
Q8 · Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723
8 Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723 . Calculate the amount Alex receives. Give your answer correct to 2 decimal places. £ ..................................................... [2]
Mark scheme: 8 162.07 cao 2 M1 for 190 ÷ 1.1723
Q9 · 19 Without using a calculator, work out 1 ' 7
2 19 Without using a calculator, work out 1 ' 7 . 3 2 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 9 5 2 M2 5 15 × oe or B1 for oe or oe 3 15 3 2 5 2 or M1 for their × their 10 45 3 15 ÷ oe with common denominator 6 6 2 A1 cao 9
Q10 · Y 8 6 4 T 2 – 8 – 6 – 4 – 2 0 2 4 6 8 x – 2 – 4 A – 6 – 8 (a) Describe fully the single…
10 y 8 6 4 T 2 – 8 – 6 – 4 – 2 0 2 4 6 8 x – 2 – 4 A – 6 – 8 (a) Describe fully the single transformation that maps triangle T onto triangle A. ..................................................................................................................................................... ..................................................................................................................................................... [2] 1 (b) Draw the image of triangle T after an enlargement, scale factor - , centre (0, 0). [2] 2
Mark scheme: 10(a) Translation 2 B1 for each − 1 − 8 10(b) Image at (–1, –1), (–4, –1), (–1, –2) 2 B1 for image correct scale factor and orientation but wrong position 1 or for enlargement scale factor centre 2 (0, 0)
Q11 · Simplify 3x 3 # 4x 4
11 Simplify 3x 3 # 4x 4 . ................................................. [2]
Mark scheme: 11 12x 7 final answer 2 B1 for 12xj or kx7 (j,k ≠ 0) as final answer
Q12 · X is an integer and - 3 G 2 x - 1 1 3
12 x is an integer and - 3 G 2 x - 1 1 3 . Find the values of x. ................................................. [2]
Mark scheme: 12 –1, 0, 1 final answer 2 B1 for –1 ⩽ x < 2 or two correct answers and no extras or three correct answers and one extra/wrong
Question 13
13 Expand and simplify. 6 ( t - q ) - 2 ( t - 3q) ................................................. [2]
Mark scheme: 13 4t final answer 2 B1 for 6t – 6q or – 2t + 6q or 2t – 6q or for 4t or 0q in the final answer
Q14 · 14 The magnitude of the vector is 29
20 14 The magnitude of the vector is 29. e k o Find the value of k. k = ..................................................... [3]
Mark scheme: 14 [±] 21 3 M2 for 292 – 202 oe or better or M1 for 202 + k2 = 292 oe
Q15 · 6 cm A B NOT TO SCALE X 8 cm 7 cm C D 12 cm In the diagram, AB is parallel to CD
15 6 cm A B NOT TO SCALE X 8 cm 7 cm C D 12 cm In the diagram, AB is parallel to CD. AD and BC intersect at X. AB = 6 cm , CD = 12 cm , CX = 8 cm and DX = 7 cm . (a) Complete the statement. Triangle ABX is ................................................ to triangle DCX. [1] (b) Work out the length of BX. BX = ................................................ cm [2] (c) The area of triangle DCX is 26. 906 cm 2. Use this value to find the area of (i) triangle ABX, .......................................... cm2 [2] (ii) triangle ACX. .......................................... cm2 [1]
Mark scheme: 15(a) Similar 1 15(b) 4 2 12 8 M1 for = oe or better 6 BX If 0 scored SC1 for answer 3.5 15(c)(i) 6.7265 or 6.73 or 6.726 to 6.727 2 2 1 M1 for scale factor 22 or oe soi 2 15(c)(ii) 13.453 or 13.5 or 13.45 to 13.46 1 FT their (c)(i) × 2
Q16 · The sides of a regular hexagon are 80 mm, correct to the nearest millimetre
16 The sides of a regular hexagon are 80 mm, correct to the nearest millimetre. Calculate the lower bound of the perimeter of the hexagon. ........................................... mm [2]
Mark scheme: 16 477 2 M1 for 80 – 0.5 oe or better seen
Q17 · The interior angle of a regular polygon is 175°
17 The interior angle of a regular polygon is 175°. Calculate the number of sides. ................................................. [2]
Mark scheme: 17 72 2 360 180( n − 2) M1 for oe or = 175 180 − 175 n oe
Q18 · A car starts from rest and accelerates at a rate of 3 m/s 2 for 4 seconds
18 A car starts from rest and accelerates at a rate of 3 m/s 2 for 4 seconds. The car then travels at a constant speed for 10 seconds. V Speed NOT TO (m/s) SCALE 00 4 14 Time (seconds) The diagram shows the speed–time graph for this journey. (a) Find the value of V. V = ..................................................... [1] (b) Calculate the total distance travelled by the car during the 14 seconds. .............................................. m [2]
Mark scheme: 18(a) 12 1 18(b) 144 2 FT 12 × their V M1 for any relevant area FT their V
Q19 · A T 50° P NOT TO B SCALE Q P, Q and T are points on a circle
19 (a) A T 50° P NOT TO B SCALE Q P, Q and T are points on a circle. ATB is a tangent to the circle at T and PT = PQ. Find angle TPQ. Angle TPQ = ..................................................... [2] (b) 68° 3x° NOT TO SCALE 2x° w° The diagram shows a cyclic quadrilateral with an exterior angle of 68°. Find the value of w and the value of x. w = ..................................................... x = ..................................................... [3]
Mark scheme: 19(a) 80 2 B1 for angle PQT = 50 19(b) [w =] 68 3 B1 for 68 [x =] 36 B2 for 36 or M1 for 3x + 2x + 68 + 112 = 360 or better
Q20 · Simplify 2.1 # 10 p + 2.1 # 10 p - 1
20 Simplify 2.1 # 10 p + 2.1 # 10 p - 1 . Give your answer in standard form. ................................................. [2]
Mark scheme: 20 2.31 × 10 p 2 B1 for 21 × 10 p −1 or 0.21 × 10 p or answer with figs 231
Q21 · A NOT TO SCALE 65° B C The shortest distance from B to AC is 12.8 cm
21 A NOT TO SCALE 65° B C The shortest distance from B to AC is 12.8 cm. Calculate BC. BC = ................................................. cm [3]
Mark scheme: 21 14.1 or 14.12... 3 12.8 M2 for sin 65 = oe or better BC or M1 for recognition that the line from B is perpendicular to AC
Q22 · Z is inversely proportional to the square of ( y - 2)
22 z is inversely proportional to the square of ( y - 2) . When y = 5, z = 9 . Find z in terms of y. z = ..................................................... [2]
Mark scheme: 22 81 2 k final answer M1 for z = oe or better ( y − 2 ) 2 ( y − 2 ) 2
Q23 · A triangle has sides of length 11 cm, 10 cm and 9 cm
23 A triangle has sides of length 11 cm, 10 cm and 9 cm. Calculate the largest angle in the triangle. ................................................. [4]
Mark scheme: 23 70.5 or 70.52 to 70.53 4 B3 for 59(.0) or 58.99… or 50.5 or 50.47 to 50.48 OR 10 2 + 9 2 − 112 M2 for oe or equivalent 2 × 10 × 9 expression for smaller angle or M1 for 112 = 10 2 + 9 2 − 2 × 10 × 9cos(...) oe or equivalent expression for smaller angle 1 A1 for oe 3
Q24 · On the axes, sketch the graph of each of these functions
24 On the axes, sketch the graph of each of these functions. 2 (a) y = x y O x [2] (b) y = 2 -x y O x [2] Questions 25 and 26 are printed on the next page.
Mark scheme: 24(a) Correct sketch 2 B1 for one correct branch or attempt at 4444 correct shape 2222 -10-10-10-10 -5-5-5-5 0000 0000 5555 10101010 -2-2-2-2 -4-4-4-4 24(b) Correct sketch 2 B1 for correct shape but crossing x-axis or for correct shape but just drawn in one quadrant
Q25 · Find the x-coordinates of the points on the graph of y = x 5 - 5x 4 where the gradient is…
25 Find the x-coordinates of the points on the graph of y = x 5 - 5x 4 where the gradient is 0. ................................................. [4]
Mark scheme: 25 0 and 4 final answer 4 B3 for 5x3(x – 4) or better or B2 for 5 x 4 − 20 x 3 or B1 for 5x 4 or − 20 x 3
Q26 · Malik goes to a shop every day to buy bread
26 Malik goes to a shop every day to buy bread. On any day, the probability that Malik goes to the shop in the morning is 0.7 . If he goes in the morning, the probability that there is bread for Malik to buy is 0.95 . If he goes later, the probability that there is bread for Malik to buy is 0.6 . Calculate the probability that, on any day, there is bread for Malik to buy. ................................................. [3]
Mark scheme: 26 0.845 oe 3 M2 for 0.7 × 0.95 + (1 – 0.7) × 0.6 oe or M1 for one of these products
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Fractions, decimals and percentages2Graphs of functions2Ratio and proportion2Algebraic manipulation1Area and perimeter1Circle theorems I1Indices II1Inequalities1Limits of accuracy1Magnitude of a vector1Money1Non-right-angled triangles1Probability of combined events1Proportion1Rates1Right-angled triangles1Similarity1Standard form1The four operations1Transformations1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2021 May/June, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.