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Mathematics 0580/21 October/November 2023: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_w23_qp_210580_w23_ms_210580/21/O/N/23

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/21/O/N/23
0580_w23_ms_21.pdf

0580/21 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 12 marks

Question

The diagram shows an isosceles triangle. 41° NOT TO SCALE x° Find the value of x. x = …… [2]

Mark scheme

1 98 2 M1 for x + 41 + 41 = 180 oe or better

Question 23 marks

Question

The stem‑and‑leaf diagram shows the time, in minutes, it takes each of 15 people to complete a race. 1 6 6 7 2 1 3 3 4 5 6 7 7 7 3 0 1 1 Key: 1 6 represents 16 minutes Find (a) the mode …… min [1] (b) the range …… min [1] (c) the median. …… min [1]

Mark scheme

2(a) 27 1 2(b) 15 1 2(c) 25 1

Question 32 marks

Question

Complete these statements. (a) When x = …… , x + 3 = 8 . [1] (b) When 7y = 63, 10y = …… [1]

Mark scheme

3(a) 5 1 3(b) 90 1

Question 43 marks

Question

The table shows some information about Amir’s shopping. Fruit Cost per kilogram Number of kilograms Amir buys Cost Oranges $2.35 3.2 $…… Bananas $…… 2.8 $…… Total $13.54 Complete the table. [3]

Mark scheme

4 3 B1 for 7.52 B1 for 6.02 or B1FT for 13.54 – their 7.52 correctly evaluated provided their 7.52 < 13.54 B1FT for their 6.02 ÷ 2.8 correctly evaluated

Question 53 marks

Question

Factorise completely. (a) 42mk - 35m …… [2] (b) h 2 - 144 …… [1]

Mark scheme

5(a) 7m(6k – 5) final answer 2 B1 for 7(6mk – 5m) or m(42k – 35) as final answer or 7m(6k – 5) seen and then spoiled 5(b) (h + 12)(h – 12) final answer 1

Question 63 marks

Question

For each of 10 people working in an office, the scatter diagram shows their salary and the value of their car. 10 000 9000 8000 7000 6000 Value of 5000 car ($) 4000 3000 2000 1000 0 0 10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000 Salary ($) (a) One of these people has a salary of $28 000. Find the value of their car. $ …… [1] (b) Another person starts to work in the office. Their salary is $54 000 and the value of their car is $6100. Plot this information on the scatter diagram. [1] (c) What type of correlation is shown in the scatter diagram? …… [1]

Mark scheme

6(a) 4800 1 6(b) Point plotted at (54 000, 6100) 1 6(c) Positive 1

Question 71 mark

Question

The exchange rate between Singapore dollars and euros is 1 Singapore dollar = 0.62 euros. Find the value of 161.20 euros in Singapore dollars. …… Singapore dollars [1]

Mark scheme

7 260 1

Question 81 mark

Question

Calculate. 3 3 7 #3 11 10 …… [1]

Mark scheme

8 24 cao 1

Question 92 marks

Question

Find the highest common factor (HCF) of 140 and 126. …… [2]

Mark scheme

9 14 2 B1 for answer 2 or 7 or M1 for 2 × 7 as final answer or [140 =] 2 × 2 × 5 × 7 and [126 =] 2 × 3 × 3 × 7 or 2 correct factor trees or tables

Question 105 marks

Question

Simplify. (a) n 5 # n …… [1] (b) 8x 6 ' 2x 2 …… [2] 2 (c) (243y 20) 5 …… [2]

Mark scheme

10(a) n6 final answer 1 10(b) 4x4 final answer 2 B1 for kx4 or 4xk as final answer or correct answer seen and then spoiled 10(c) 9y8 final answer 2 B1 for ky8 or 9yk final answer or correct answer seen and spoiled

Question 113 marks

Question

Solve. 4 (2x - 3) H 43 + 3x …… [3]

Mark scheme

11 x ⩾ 11 final answer 3 M1 for 8x – 12 ⩾ 43 + 3x or better M1 for e.g. 8x – 3x ⩾ 43 + 12 oe OR 43 3x M1 for 2x – 3 ⩾ + 4 4 3x 43 M1 for 2x – ⩾ +3 4 4

Question 123 marks

Question

Write 0.42o as a fraction in its simplest form. You must show all your working. …… [3]

Mark scheme

12 42.22… – 4.22… oe M1 M1 for correct working shown 19 A2 38 cao A1 for oe seen 45 90 k 19 If M0 scored SC1 for or for answer 90 45 with insufficient working.

Question 133 marks

Question

At the end of 2021 there were 27 000 rhinos living in the wild. The number of rhinos is expected to decrease exponentially by 3% each year. Work out the number of rhinos expected to be living in the wild 4 years later, at the end of 2025. Give your answer correct to the nearest whole number. …… [3]

Mark scheme

13 23 903 cao 3 B2 for answer 23900, 23902, 23902.9… or 23 903 seen then rounded OR 4 3 M1 for 27 000 × 1 − oe 100 B1 for their more accurate value seen and correctly rounded to the nearest whole number

Question 144 marks

Question

(a) A B 15 5x x+5 12 – x The Venn diagram shows information about the number of elements in sets A, B and . n() = 52. Find n( A + B ). …… [3] (b) In this Venn diagram, shade the region C + D + E . C D E [1]

Mark scheme

14(a) 9 3 B2 for x = 4 or B1 for answer 4 (without x = 4 in working) OR M1 for 5x + x + 5 + 12 – x + 15 = 52 oe or better B1FT for identifying the correct region A B 14(b) 1

Question 155 marks

Question

y 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 0 x 1 2 3 4 5 6 7 -1 -2 -3 By shading the unwanted regions of the grid, draw and label the region R which satisfies these inequalities. y21 xG2 y H x+2 [5]

Mark scheme

15 5 B1 for y = 1 dashed line B1 for x = 2 solid line B1 B1 for y = x + 2 solid line R B2 for region identified satisfying all 3 inequalities B1 or B1 for region identified satisfying only 2 of these inequalities with y = 1, x = 2 and y = x + B1 2 all drawn

Question 163 marks

Question

P = 2w + 2h w = 11 and h = 9.5, both correct to 2 significant figures. Find the lower bound and the upper bound for P. Lower bound = …… Upper bound = …… [3]

Mark scheme

16 [Lower bound =] 39.9 nfww 3 B2 for one correct [Upper bound =] 42.1 nfww or M1 for 11 + 0.5 or 9.5 + 0.05 or 11 – 0.5 or 9.5 – 0.05

Question 173 marks

Question

D C 53° NOT TO SCALE 20° E O A x° B A, B and C are points on the circumference of a circle, centre O. Tangent DE touches the circle at C. Angle BCE = 53° and angle ACO = 20°. Find the value of x. x = …… [3]

Mark scheme

17 33 3 B2 for 254 + 20 + x + 53 = 360 oe or better or 53 + 20 + x + 37 + 37 = 180 oe or better or OAB = 33 or AOB = 114 or 70 and 37 correctly identified or 53 and 20 correctly identified or B1 for any correct relevant angle identified

Question 183 marks

Question

105° 8.3 cm NOT TO SCALE y° 16.2 cm Calculate the value of y. y = …… [3]

Mark scheme

18 29.7 or 29.66[...] 3 8.3sin105 M2 for [sin y = ] 16.2 16.2 8.3 or M1 for = oe sin105 sin y

Question 194 marks

Question

(a) y 1 0 x 360° –1 Sketch the graph of y = cos x for 0° G x G 360° . [2] (b) When cos x = 0.21 , find the reflex angle x. …… [2]

Mark scheme

19(a) 2 B1 for correct cosine curve shape through (0,1) Correct sketch to go through (0, 1), close to (360, 1) and reasonably close to (180, –1) 19(b) 282.1 or 282.12… 2 B1 implied by 77.9 or 77.87 to 77.88 or 282.13 or M1 for 360 – their acute angle

Question 206 marks

Question

Write as a single fraction in its simplest form. 10x 2 - 60x (a) x 2 - x - 30 …… [3] 7 5 (b) + x + 3 8x - 1 …… [3]

Mark scheme

20(a) 10 x 3 B1 for 10x(x – 6) final answer B1 for (x – 6)(x + 5) x+5 20(b) 61x + 8 3 B1 for common denominator of (x + 3)(8x – 1) final answer ( 3)( 8 x −1) x + isw B1 for 7(8x – 1) + 5(x + 3) or better isw

Question 214 marks

Question

H G E F 9.2 cm NOT TO SCALE D C 4.5 cm A 15.1 cm B The diagram shows a cuboid ABCDEFGH. AB = 15.1 cm, BC = 4.5 cm and CG = 9.2 cm. Calculate the angle that the diagonal BH makes with the face ADHE. …… [4] Question 22 is printed on the next page.

Mark scheme

21 55.9 or 55.85… 4 15.1 M3 for tan[…] = oe 4.52 + 9.2 2 or M2 for [AH2 =] 4.52 + 9.22 or [BH2 =] 4.52 + 9.22 + 15.12 or M1 for recognising angle BHA if 0 scored SC1 for [angle BHD =] 59.7[1…] or 59.72

Question 224 marks

Question

B 41° 13.6 cm A C NOT TO SCALE D ABCD is a rhombus with side length 13.6 cm. Angle ABC = 41°. BAC is a sector of a circle with centre B. DAC is a sector of a circle with centre D. Calculate the shaded area. …… cm 2 [4]

Mark scheme

22 110 or 110.3… 4 1 41 M3 for [2 ×] (2( × 13.62 × sin 41) – ( × 2 360 π × 13.62)) oe OR 1 M1 for × 13.62 × sin 41 oe 2 41 M1 for [2×] × π × 13.62 oe 360

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How 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.

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Where can I find the 0580/21 October/November 2023 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/21, October/November 2023 (0580_w23_ms_21), and the question paper (0580_w23_qp_21), to read or download, with each question's marking points written out underneath.

How many marks is 0580/21 out of?

Mathematics 0580/21 for October/November 2023 is out of 70 marks, with 1 hour 30 minutes to answer it.

Can I get my 0580/21 answers marked?

Yes. Upload your answers to 0580/21/O/N/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.