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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s23_qp_230580_s23_ms_230580/23/M/J/23
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question
(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
1(a) 2 1 1(b) 2 B1 for one correct line and no extras or two correct lines and one extra
Question
A film lasts for 2 hours 50 minutes. The film ends at 23 05. Find the time the film starts. …… [1]
Mark scheme
2 20 15 or [0]8.15pm 1
Question
NOT TO 5 cm SCALE 3 cm 8 cm Find the total surface area of the cuboid. …… cm 2 [3]
Mark scheme
3 158 3 M2 for [ 2] ( 8 × 5 + 8 × 3 + 5 × 3) or M1 for 8 × 5 or 8 × 3 or 5 × 3
Question
v = u - 9.8t Find the value of v when u = 4 and t =- 7 . v = …… [2]
Mark scheme
4 72.6 2 M1 for 4 − 9.8 × −7 or better
Question
Simplify d 8 ' d 2 . …… [1]
Mark scheme
5 d6 1
Question
At the end of the day, a shopkeeper has 12 tins of cat food left. 3 This is of the number he had at the beginning of the day. 13 Calculate the number of tins he had at the beginning of the day. …… [2]
Mark scheme
6 52 2 3 3 M1 for 12 = x × oe or better e.g. 12 ÷ oe 13 13
Question
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
7(a) 0.11 oe 2 M1 for 1 – (0.3 + 0.16 + 0.18 + 0.25) oe or B1 for 0.89 oe 7(b) 0.46 oe 2 M1 for 0.3 + 0.16
Question
y 5 A 4 3 2 1 –1 0 1 2 3 4 5 6 7 x –1 B –2 –3 –4 Describe fully the single transformation that maps triangle A onto triangle B. …… [3]
Mark scheme
8 Rotation 3 B1 for each (0,0) oe 90° clockwise oe
Question
The distance–time graph shows information about Kai’s journey from home to the office. 70 Office 60 50 40 Distance (km) 30 20 10 Home 0 10 00 11 00 12 00 13 00 14 00 Time (a) Calculate the average speed, in km/h, for Kai’s journey from home to the office. …… km/h [2] (b) When Kai arrives at the office, he finds his meeting is cancelled. He immediately returns home at a constant speed of 50 km/h. Complete the distance–time graph to show his journey home. [1] 11 1
Mark scheme
9(a) 32.5 2 65 their distance M1 for or their time 2 9(b) correct ruled line 1 from (12 00, 65) to (13 18, 0)
Question
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
10 M1 Accept with other correct common k 27 11 + [5] and denominators 12 12 12 3 71 f 27 f or [2] oe e.g. 24, 36, 48 such as and 12 12 f 12 f 71 c + oe 12 12 1 A2 1 8 cao A1 for fraction equivalent to 8 6 6 49k 1k 7 e.g. or 8 or 7 6k 6k 6
Question
(a) = { a, b, e, g, l, m, o, r, t, y } P = { a, b, e, g, l, r } Q = { e, g, m, o, r, t, y } P Q Complete the Venn diagram. [2] (b) A B Shade the region Al + B . [1] 5 4
Mark scheme
11(a) 2 B1 for 1 region correct a b e m o g t y l r 11(b) 1
Question
The position vector of A is e o and BA = e o. 3 8 Show that OB = 5.1 , correct to 1 decimal place. [3]
Mark scheme
12 M2 1 12 + ( −5 ) 2 M1 for −5 or (5 – 4)2 + (3 − 8)2 ρ e or e2 + f 2 from their OB = f or their B = (e, f) or only 1 + 25 Correct working leading to A1 Dep. on M2 or M1 for only 1 + 25 5.09[9..]
Question
Calculate 42 + 3 0.4 . …… [1] o o as a fraction.
Mark scheme
13 8.03 or 8.032 to 8.033 1
Question
Write 0.581 You must show all your working and give your answer in its simplest form. …… [3]
Mark scheme
14 581.81...− 5.81...oe M1 32 A2 576 cao A1 for oe 55 990 k 32 If M0 scored SC1 for or for answer 990 55 with insufficient working.
Question
The number of trees in a forest is decreasing exponentially at a rate of 1.75% per year. Eleven years ago there were 980 trees. Calculate the number of trees in the forest now. Give your answer correct to the nearest integer. …… [2]
Mark scheme
15 807 2 1.75 11 M1 for 980 × 1 − oe or better 100
Question
The volume of a cylinder is 1970 cm 3 . The height of the cylinder is 12.8 cm . Calculate the radius of the cylinder. …… cm [3]
Mark scheme
16 7.00 or 6.998 to 7.002 3 1970 M2 for [r2 ]= oe or better 12.8 × π or M1 for 1970 = π × r 2 × 12.8 or better
Question
Rearrange the formula to make m the subject. 2 (m - k) R= m m = …… [4] 18 y is inversely proportional to the cube root of (x + 5). When x = 3, y = 12. Find y when x = 22. y = …… [3]
Mark scheme
17 2k −2k 4 m= or m = ( 2 − R) ( R − 2) M1 for clearing fractions final answer M1 for expanding brackets (or ÷ 2) M1 for collecting terms in m on one side and terms not in m on the other M1 for dividing by a bracket maximum of 3 if final answer incorrect
Question
In the question paper above.
Mark scheme
18 8 3 k M1 for y = 3 oe x+5 k M1 for substituting their k into y = 3 oe 22 + 5 OR M2 for 12 3 3 + 5 = y 3 22 + 5 oe
Question
Solve the equation x 2 + 5x - 7 = 0 . You must show all your working and give your answers correct to 2 decimal places. x = …… or x = …… [4]
Mark scheme
19 −5 ± 52 − 4 × 1× −7 B2 B1 for 5 2 − 4 × 1 × −7 2 ×1 p+ q p− q and if in form or r r B1 for p = −5 and r = 2×1 −6.14 and 1.14 cao B2 B1 for 1 correct answer for −6.1 and 1.1 or −6.140... and 1.140... or 6.14 and −1.14 or correct answers seen in working
Question
f (x) = 6x - 7 g (x) = x -3 (a) Find f (x + 2) . Give your answer in its simplest form. …… [2] (b) Find f -1 (x) . f -1 (x) = …… [2] (c) Find x when g(x) = f(22) . x = …… [2]
Mark scheme
20(a) 6 x + 5 cao final answer 2 M1 for 6 ( x + 2 ) − 7 oe 20(b) x+7 x 7 2 y 7 or + final answer M1 for x = 6 y − 7 or y + 7 = 6 x or = x− 6 6 6 6 6 20(c) 1 2 M1 for x −3 = 6 ×22 − 7 or better or 0.2 5
Question
Simplify. 2x 2 + 5x - 12 4x 2 - 9 …… [4]
Mark scheme
21 x+4 4 B1 for ( 2 x − 3)( 2 x + 3) final answer 2x + 3 B2 for ( 2 x − 3)( x + 4 ) or B1 for (2x + a)(x + b) where ab = −12 or a + 2b = 5 or x ( 2 x − 3) + 4 ( 2 x − 3 ) or 2 x ( x + 4 ) − 3 ( x + 4 )
Question
These are the first four terms of a sequence. 2.75 6 11.25 20 1 3 The nth term of this sequence is n + an 2 + bn . 4 Calculate the value of a and the value of b. a = …… b = …… [5]
Mark scheme
22 −1 5 1 3 1 2 [a =] oe B4 for n − n + 3n seen 2 4 2 OR [b =] 3 1 M2 for any two of + a + b = 2.75 4 1 8× + 4a + 2b = 6 4 1 27 × + 9a + 3b = 11.25 4 1 64 × + 16a + 4b = 20 4 or M1 for one correct equation M1 for correct method to eliminate 1 variable B1 for 1 correct answer
Question
A train travels between two stations. The distance between the stations is 220 km, correct to the nearest kilometre. The speed of the train is 125 km/h, correct to the nearest 5 km/h. Calculate the upper bound for the time the journey takes. Give your answer in hours and minutes. …… h …… min [4]
Mark scheme
23 1h 48 min nfww 4 4 9 B3 for 1.8 [hrs], 1 [hrs], [hrs] or 108 5 5 [mins] nfww 220 to 221 220 + 0.5 or M2 for or 125 − 2.5 120 to125 or M1 for 220 + 0.5 or 220 – 0.5 or 125 + 2.5 or 125 – 2.5
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Mark my 0580/23Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
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On this page, free: the mark scheme for IGCSE Mathematics 0580/23, May/June 2023 (0580_s23_ms_23), and the question paper (0580_s23_qp_23), to read or download, with each question's marking points written out underneath.
Mathematics 0580/23 for May/June 2023 is out of 70 marks, with 1 hour 30 minutes to answer it.
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