Question 11 mark
Question
Find the temperature that is 8 °C colder than - 5 °C. …… °C [1]
Mark scheme
1 –13 1
Mathematics 0580/22 May/June 2023: question paper and mark scheme
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_220580_s23_ms_220580/22/M/J/23
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/M/J/23
0580/22 mark scheme, question by question
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 22 marks
Question
There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers. …… [2]
Mark scheme
2 108 2 B1 for 47 or 61 identified
Question 33 marks
Question
On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8 (a) Complete the stem-and-leaf diagram to show this information. 0 1 3 1 2 Key: 0 q1 represents 1 minute [2] (b) Find the median. …… min [1]
Mark scheme
3(a) 2 B1 for a correct diagram with one error or omission or for a fully correct unordered stem-and-leaf 0 (1 3) 4 5 5 8 diagram 1 1 2 2 3 4 3(b) 6.5 1
Question 42 marks
Question
The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B. …… km [2]
Mark scheme
4 8.75 2 3.5 × 250000 M1 for oe 100 × 1000 or B1 for figs 875 or 1 cm : 2.5 km
Question 52 marks
Question
A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Letter on A B C D spinner Probability 0.2 0.05 0.35 Complete the table. [2]
Mark scheme
5 0.4 oe 2 M1 for 1 – (0.2 + 0.05 + 0.35) oe or B1 for 0.6 oe
Question 6
Question
= {x| 1 G x G 20} E = {even numbers} M = {multiples of 5} (a) Find n (M) . (b) Find the elements in the set E + M . (c) y g E. Write down a possible value of y. 4 5
Mark scheme
6(a) 4 cao 1 6(b) 10, 20 1 6(c) An odd number or decimal in 1 the range 1 ⩽ x ⩽ 20
Question 73 marks
Question
Without using a calculator, work out ' 1 . 7 21 You must show all your working and give your answer as a fraction in its simplest form. …… [3]
Mark scheme
7 4 21 M2 26 21 × oe B1 for or oe 7 26 21 26 or 4 21 or M1 for × oe 12 26 7 their 26 ÷ oe with common 21 21 denominator 6 A1 cao 13
Question 84 marks
Question
Solve. 30 (a) =6 x x = …… [1] (b) 11x - 3 H 2 (2x + 9) …… [3] 8 - 12
Mark scheme
8(a) 5 1 8(b) x ⩾ 3 final answer 3 M1 for correct first step 11x – 3 ≥ 4x + 18 or 5.5x – 1.5 ⩾ 2x + 9 or better M1 for correctly collecting their x terms on one side and their number terms on the other side e.g. 11x – 4x ⩾ 18 + 3 or better
Question 95 marks
Question
F is the point (1, - 4) , FG = e o and GH = e o. -3 35 Find (a) 3FG f p [1] (b) FG + GH f p [1] (c) the coordinates of the point G (…… , ……) [1] (d) the magnitude of vector GH . …… [2]
Mark scheme
9(a) 24 1 −9 9(b) –4 1 32 9(c) (9, –7) 1 9(d) 37 2 M1 for (–12)2 + 352 oe
Question 106 marks
Question
y 10 9 8 7 6 B 5 4 3 2 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 A –2 –3 –4 –5 –6 (a) Describe fully the single transformation that maps shape A onto shape B. …… [2] (b) Rotate shape A 90° clockwise about the point (- 1, 2) . [2] (c) Enlarge shape A by scale factor - 2 , centre (2, 0). [2]
Mark scheme
10(a) Reflection 2 B1 for each y=2 10(b) Shape at 2 (–2, –2), (–6, –5), (–6, –3), B1 for correct size and orientation but wrong (–4, –2) position or for rotation of 90° anticlockwise about (–1, 2) or for three correct vertices 10(c) Shape at 2 (0, –2), (0, 2), (–2, 6), (–6, 6) B1 for correct size and orientation but wrong position or for three correct vertices
Question 113 marks
Question
B 2.6 cm C 3.2 cm NOT TO SCALE O D A The diagram shows a shape, ABCD, formed by the sectors of two circles with the same centre O. Both sector angles are 140°, OC = 3.2 cm and CB = 2.6 cm . The area of the shape is k r cm2 . Find the value of k. k = …… [3]
Mark scheme
11 9.1 3 M2 for 140 140 × [ π ] × ( 3.2 + 2.6 ) – × [ π ] × 3.22 oe 2 360 360 140 or M1 for × [ π ] × 3.22 oe 360 140 × [ π ] × ( 3.2 + 2.6 ) oe 2 or 360 or [ π ] × ( 3.2 + 2.6 ) – [ π ] × 3.2 2 2
Question 123 marks
Question
One solution of the equation ax 2 + b = 181 is x = 8 . a and b are both positive integers greater than 1. (a) Find the value of b. b = …… [2] (b) Write down the other solution of the equation ax 2 + b = 181. x = …… [1]
Mark scheme
12(a) 53 2 M1 for a × 82 + b = 181 oe seen 12(b) –8 1
Question 132 marks
Question
D NOT TO E 32° SCALE A C x° B A, B, C and D are points on a circle. AB is parallel to DC and angle ACD = 32° . Chords AC and DB intersect at E. Find the value of x� x = …… [2]
Mark scheme
13 116 2 B1 for ABD = 32, CAB = 32, BDC = 32 or CED = 116 or M1 for 180 – 32 – 32
Question 142 marks
Question
f (x) = 5x + 2 Find f -1 (x) . f -1 (x) = …… [2]
Mark scheme
14 x−2 2 M1 for a correct first step oe final answer 5 y 2 x = 5 y + 2 or y − 2 = 5 x or = x+ 5 5
Question 157 marks
Question
C is the point (5, - 1) and D is the point (13, 15). (a) Find the midpoint of CD. (…… , ……) [2] (b) Find the gradient of CD. …… [2] (c) Find the equation of the perpendicular bisector of CD� Give your answer in the form y = mx + c . y = …… [3] o o as a fraction in its simplest form.
Mark scheme
15(a) (9, 7) 2 B1 for each 15(b) 2 2 15 – – 1 M1 for oe 13 – 5 15(c) 1 23 3 [y =] – x+ oe 2 2 final answer 1 M1 for gradient = − oe their (b) M1 for correct substitution of their (a) into y = (their m)x + c oe
Question 163 marks
Question
Write 0.621 You must show all your working. …… [3]
Mark scheme
16 621.21… – 6.21… oe M1 41 A2 615 cao A1 for oe 66 990 k 41 If M0 scored SC1 for or for answer with 990 66 insufficient working
Question 172 marks
Question
NOT TO 92.5 cm SCALE x° 71 cm The diagram shows a triangle with an acute angle marked x°. The area of the triangle is 2143 cm 2 . Work out the value of x. x = …… [2]
Mark scheme
17 40.7 or 40.73 to 40.74 2 1 M1 for × 92.5 × 71 sinx = 2143 oe 2
Question 187 marks
Question
Make x the subject of the formula. 3x c= 2x - 5 x = …… [4] 19 m is inversely proportional to the square of (t + 2) . m = 0.64 when t = 3 . Find m when t = 8 . m = …… [3]
Mark scheme
18 5c 4 M1 for correctly clearing the denominator and oe final answer expanding bracket 2c − 3 or correctly clearing the denominator and dividing by c M1 for correctly collecting terms in x on one side and terms not in x on the other M1 for correct factorising M1 for correct division dependent on x appearing only once in a factorised expression Maximum 3 marks for an incorrect answer
Question 19
Question
In the question paper above.
Mark scheme
19 0.16 oe 3 k M1 for m = oe ( t + 2 )2 their k M1 for substituting their k into m = ( 8 + 2 )2 OR M2 for 0.64 × (3 + 2)2 = m(8 + 2)2 oe
Question 201 mark
Question
In the Venn diagram, shade the region A + Bl + C . A B C [1]
Mark scheme
20 E A 1 B C
Question 21
Question
Solve the equation 5 sin x = - 3 for 0° G x G 360° . Questions 22 and 23 are printed on the next page.
Mark scheme
21 216.9 or 216.86 to 216.87 3 323.1 or 323.13… B2 for one correct angle 3 or M1 for sinx = − or better 5 If M1 or 0 scored SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180
Question 22
Question
Write as a single fraction in its simplest form. 5 4 + 3x + 2 2x - 1
Mark scheme
22 22 x + 3 3 B1 for a common denominator (3x + 2)(2x – 1) oe final answer ( 2 )( 2 x −1) 3 x + isw B1 for 5(2x – 1) + 4(3x + 2) oe isw
Question 233 marks
Question
Bag A and bag B each contain red sweets and yellow sweets. Anna picks a sweet at random from bag A. Ben picks a sweet at random from bag B. 2 The probability that Anna picks a red sweet is . 5 1 The probability Anna and Ben both pick a yellow sweet is . 10 Find the probability that Anna and Ben both pick a red sweet. …… [3]
Mark scheme
23 1 3 2 1 oe M1 for 1 − × p = oe 3 5 10 2 M1 for × (1 − their p ) where 0 < their p < 1 5
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0580/22 questions
Where can I find the 0580/22 May/June 2023 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, May/June 2023 (0580_s23_ms_22), and the question paper (0580_s23_qp_22), to read or download, with each question's marking points written out underneath.
How many marks is 0580/22 out of?
Mathematics 0580/22 for May/June 2023 is out of 70 marks, with 1 hour 30 minutes to answer it.
Can I get my 0580/22 answers marked?
Yes. Upload your answers to 0580/22/M/J/23 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.