Question 11 mark
Question
The probability of picking a red sweet from a bag is 0.05 . Find the probability of not picking a red sweet. …… [1] m k3
Mark scheme
1 0.95 oe 1
Mathematics 0580/23 May/June 2022: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2022. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s22_qp_230580_s22_ms_230580/23/M/J/22
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/23/M/J/22
0580/23 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
Work out the value of when m = 4 and k = 7 . 3 …… [2]
Mark scheme
2 792 or 792.1… 2 4 × 73 M1 for oe 3 or B1 for 1372
Question 32 marks
Question
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
3 97 2 M1 for 360 – (73 + 129 + 75)
Question 43 marks
Question
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
4(a) 2 B1 for two rows correct or for fully correct 0 (3 4) 7 8 unordered stem-and-leaf diagram or for a 1 1 1 2 2 7 8 correct diagram with one error or omission 2 1 3 4(b) 1.15 1
Question 52 marks
Question
The nth term of a sequence is n 2 - 1. Find the first three terms of this sequence. …… , …… , …… [2]
Mark scheme
5 0, 3, 8 2 B1 for 2 correct terms in correct position or SC1 for −1, 0, 3
Question 62 marks
Question
Simplify. (a) y 3 ' y 5 …… [1] (b) 7x 0 …… [1]
Mark scheme
6(a) 1 1 y –2 or final answer y2 6(b) 7 1
Question 74 marks
Question
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 amount 25 spent ($1000) 20 15 10 5 0 150 200 250 300 350 400 450 500 550 600 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] 2 5
Mark scheme
7(a) 27 000 1 7(b) Point plotted at (175, 9) 1 7(c) Correct single ruled line of best fit 1 7(d) 300 to 350 1 FT their straight line of best fit provided positive gradient
Question 82 marks
Question
Without using a calculator, work out ' . 9 6 You must show all your working and give your answer as a fraction in its simplest form. …… [2]
Mark scheme
8 2 6 4 15 M1 × or ÷ oe 9 5 18 18 4 A1 cao 15
Question 92 marks
Question
Change 300 m / min to km / h. …… km / h [2]
Mark scheme
9 18 2 300 × 60 M1 for oe 1000 or B1 for figs 18 in their answer
Question 101 mark
Question
A B 25 33 12 3 Find n `A + Bjl . …… [1]
Mark scheme
10 40 1
Question 115 marks
Question
ABC, DEF and GHK are triangles with all vertices on the circumference of a circle. D A K 8° 85° NOT TO 6° SCALE 85° H G 94° B 82° F E C From the list, draw a ring around the line that is a diameter of the circle. AB AC DE DF GH GK [1] 12 f is a common factor of 14 and 28. m is a common multiple of 10 and 25. p is a prime number. f Work out the largest possible value of . mp …… [4]
Mark scheme
11 DE 1
Question 12
Question
In the question paper above.
Mark scheme
12 0.14 oe nfww 4 14 M3 for with at least 2 out of 3 50 × 2 values correct and for the one incorrect value: f must be 1, 2 or 7 m must be a multiple of 50 p must be prime OR B1 for f = 14 B1 for m = 50 B1 for p = 2 If 0 scored SC1 for a correct multiple for m, factor for f or prime for p
Question 134 marks
Question
Factorise completely. (a) 18px - 27p …… [2] (b) mt - n - m + nt …… [2]
Mark scheme
13(a) 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 13(b) (m + n)(t – 1) final answer 2 B1 for m(t – 1) + n(t – 1) or t(m + n) – [1](m + n) or correct answer seen and spoilt
Question 142 marks
Question
Find the nth term of this sequence. 8, 17, 32, 53, 80, … …… [2]
Mark scheme
14 3n2 + 5 oe final answer 2 M1 for correctly finding second differences or an answer that is a quadratic sequence
Question 152 marks
Question
Solve. 12x - 3 H 4x + 13 …… [2]
Mark scheme
15 x ⩾ 2 final answer 2 M1 for 12x – 4x ≥ 13 + 3 oe
Question 164 marks
Question
Abdul draws this speed–time graph for a journey. The graph has four sections A, B, C and D. 12 B 10 C 8 Speed A 6 (m/s) 4 D 2 0 0 10 20 30 40 50 60 70 80 90 100 110 Time (s) Complete these statements about the speed–time graph. Section …… cannot be correct. Section …… shows constant speed. Section …… shows deceleration. Section A shows acceleration of …… m / s2. The distance travelled in the first 30 seconds of the journey is …… m. [4]
Mark scheme
16 D B1 B C 1 B1 or 0.333… 3 150 B2 1 or M1 for × 30 × 10 2
Question 173 marks
Question
A NOT TO SCALE B D C In triangle ABC, AC = AB. D is the point on BC such that AD is perpendicular to BC. Complete the following statements to show that triangle ACD and triangle ABD are congruent. AD is perpendicular to BC so that Angle …… = Angle …… = …… ° AC = AB is given information. Side …… is common to both triangles. Triangle ACD is congruent to triangle ABD because of the congruency criterion …… [3]
Mark scheme
17 ADC and ADB and 90 3 B1 for each correct line AD RHS
Question 183 marks
Question
The bearing of B from A is x°. The bearing of A from B is y°. x: y = 2:7 Calculate the value of y. North North NOT TO SCALE B y° x° A y = …… [3] 1 7x - 2 3 - 10x
Mark scheme
18 252 3 M2 for 180 ÷ (7 – 2) oe OR M1 for 180 – x + y = 360 oe M1 for correct use of ratio
Question 197 marks
Question
f (x) = kx 2 g (x) = h (x) = j (x) = x 5 14 (a) f (- 5k) = 675 Find the value of k. k = …… [2] (b) Find gh (x) . …… [1] (c) Find h -1 (x) + j (x) . Give your answer in its simplest form. …… [4]
Mark scheme
19(a) 3 2 M1 for k(–5k)2 = 675 or better 19(b) 5 1 final answer 7x − 2 19(c) 1 4 7 or 0.5 B3 for answer 2 14 OR 5x + 2 B2 for 7 or M1 for correct first step for h –1(x) 7y − 2 e.g. x = 5y = 7x − 2 5 2 7x y+ = 5 5 2 ( 5 x + 2 ) 3 − 10 x M1FT for + oe with 14 14 common denominator
Question 204 marks
Question
k cm B C NOT TO E SCALE A M D The diagram shows a square ABCD with side length k cm. MDE is a sector of a circle, centre D. E lies on the diagonal, BD, of the square. M is the midpoint of AD. Find the percentage of the square that is shaded. …… % [4]
Mark scheme
20 90.2 or 90.18… 4 B3 for 9.82[%] OR 2 45 k 2 2 M3 for [100 ×] k − ×π × ÷ k 360 2 oe 2 45 k or M2 for [100 ×] × π × ÷ k 2 oe 360 2 2 45 k or k 2 − ×π × 360 2 or 100× (k – mπk2 ) ÷ k2 2 2 c k or M1 for × π × oe 360 2 or for (k – mπk ) ÷ k2 2 2 or for 100× (k2 – mk2 ) ÷ k2
Question 213 marks
Question
Neha has a piece of ribbon of length 23 cm, correct to the nearest cm. From this ribbon she cuts off a piece with length 87 mm, correct to the nearest mm. Work out the lower bound and the upper bound for the length of the remaining ribbon. Give your answer in centimetres. Lower bound = …… cm Upper bound = ……cm [3]
Mark scheme
21 13.75 3 B2 for one correct answer or both correct 14.85 answers seen in working then rounded to 3sf or both correct but reversed or M1 for 2 correct seen from 23 + 0.5, 23 – 0.5, 8.7 + 0.05 or 8.7 – 0.05 or better
Question 223 marks
Question
Simplify. 5x - x 2 25 - x 2 …… [3]
Mark scheme
22 x 3 B1 for x(5 – x) final answer nfww B1 for (5 – x)(5 + x) or 5+ x
Question 236 marks
Question
Solve the equation 3 sin x + 3 = 1 for 0° G x G 360° . x = …… or x = …… [3] 24 y is inversely proportional to the cube of (x - 1) . y = 9.45 when x = 3. Find y when x = 4 . y = …… [3] 1
Mark scheme
23 221.8 or 221.81... 3 B2 for one correct and 2 318.2 or 318.18 to 318.19 or M1 for sin x = – oe 3 If 0 scored, SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180
Question 24
Question
In the question paper above.
Mark scheme
24 2.8 3 k M1 for y = ( x − 1) 3 their k M1 for y = ( 4 – 1) 3 OR M2 for y(4 – 1)3 = 9.45(3 – 1)3
Question 253 marks
Question
m - 4 = 27m -1 Find the value of m. m = …… [3]
Mark scheme
25 81 3 3 M2 for m 4 = 27 or better 1 27 or M1 for 1 = or better m m4 1 − −−1 or m 4 = 27 1 If 0 scored SC1 for answer 81
Checked your answers against these? Let AI mark the whole paper, on your own working.
Mark my 0580/23How this paper is marked
Examiners 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.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Other variants, May/June 2022
Find another Mathematics paper
Every IGCSE Mathematics mark schemeQuestion papers and mark schemes © Cambridge University Press & Assessment. CIE Buddy is independent and not connected to Cambridge.
0580/23 questions
Where can I find the 0580/23 May/June 2022 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/23, May/June 2022 (0580_s22_ms_23), and the question paper (0580_s22_qp_23), to read or download, with each question's marking points written out underneath.
How many marks is 0580/23 out of?
Mathematics 0580/23 for May/June 2022 is out of 70 marks, with 1 hour 30 minutes to answer it.
Can I get my 0580/23 answers marked?
Yes. Upload your answers to 0580/23/M/J/22 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.