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Mathematics 0580/23 October/November 2021: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_w21_qp_230580_w21_ms_230580/23/O/N/21

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/23/O/N/21
0580_w21_ms_23.pdf

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 11 mark

Question

Write 26 g as a percentage of 208 g. …… % [1]

Mark scheme

1 12.5 1

Question 22 marks

Question

x° NOT TO SCALE 132° The diagram shows two parallel lines intersecting a straight line. Find the value of x. x = …… [2]

Mark scheme

2 48 2 B1 for 132 or 48 in the correct position on the diagram or M1 for 180 – 132

Question 31 mark

Question

11 13 15 17 19 From this list, write down the number that is both a prime number and a factor of 195. …… [1]

Mark scheme

3 13 1

Question 42 marks

Question

(a) = ! 2 1 Put a ring around each of the symbols that make this statement correct. 0.5 …… 5% [1] (b) Insert one pair of brackets to make this statement correct. 7 - 3 - 1 + 2 = 7 [1]

Mark scheme

4(a) ≠ and > indicated 1 4(b) 7 – (3 – 1) + 2 = 7 cao 1

Question 51 mark

Question

Nina changes 153 euros into dollars when the exchange rate is $1 = 0.9 euros. Calculate the amount Nina receives. $ …… [1]

Mark scheme

5 170 1

Question 62 marks

Question

Marek buys a computer for $420. He sells it at a loss of 15%. Calculate the selling price of this computer. $ …… [2]

Mark scheme

6 357 2 15 M1 for 1 − × 420 oe 100 or B1 for 63

Question 72 marks

Question

Simplify. 32g 32 ' 4g 4 …… [2]

Mark scheme

7 8g 28 final answer 2 B1 for kg 28 or 8 g k as final answer or correct answer seen and spoilt

Question 83 marks

Question

Beatrice walks 1 km at a speed of 4 km/h and then 2 km at a speed of 4.5 km/h. Work out Beatrice’s average speed for the whole journey. …… km/h [3]

Mark scheme

8 4.32 3 1 2 B1 for oe or oe seen 4 4.5 1+ 2 M1 dep on B1 for oe their 4 + their 4.5 1 2

Question 91 mark

Question

o o as a fraction. Write the recurring decimal 0.27 …… [1]

Mark scheme

9 3 1 oe fraction 11

Question 103 marks

Question

These are the first four terms of a sequence. 3 -1 -5 -9 (a) Find the next term in this sequence. …… [1] (b) Find the nth term. …… [2]

Mark scheme

10(a) –13 1 10(b) –4n + 7 oe final answer 2 B1 for – 4n + k or jn + 7 (j ≠ 0) or for a correct answer spoilt

Question 115 marks

Question

P = M ( g 2 + h 2) (a) Find the value of P when M = 100, g = 3 and h = 4.5 . P = …… [2] (b) Rearrange the formula to write g in terms of P, M and h. g = …… [3] 11 3

Mark scheme

11(a) 2925 2 M1 for 100(32 + 4.52) or B1 for 29.25 seen 11(b) P 3 M1 for correct division by M [±] − h2 M1 for correct re-arrangement to isolate g M or g2 P − Mh 2 M1 for correct square root of two term or [±] final answer M expression Max 2 marks for an incorrect answer

Question 123 marks

Question

Without using a calculator, work out + . 12 4 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]

Mark scheme

12 11 9 M1 Allow any correct common denominator + oe 12k 12 12 2 A2 20 1 cao A1 for or equivalent improper fraction 3 12 or mixed number

Question 132 marks

Question

Calculate 0.04 2 + 0.03 # 0.28 . Give your answer in standard form. …… [2]

Mark scheme

13 1[.0] × 10–2 cao 2 B1 for 0.01 oe

Question 143 marks

Question

P Q b e d c f a g (a) Complete the statement. P , Q = { …… } [1] (b) Find n(Q). …… [1] (c) Find n (P l + Q) . …… [1]

Mark scheme

14(a) b, c, d, e, f, g 1 14(b) 4 1 14(c) 3 1

Question 152 marks

Question

The cost of a train journey is increased by 6% to a new cost of $153.70 . Calculate the original cost of the train journey. $ …… [2]

Mark scheme

15 145 2 6 M1 for x 1 + = 153.7 oe or better 100

Question 163 marks

Question

Jo and Mo share $26. Jo receives $5 more than Mo. Find the ratio Jo’s money : Mo’s money. Give your answer in its simplest form. …… : …… [3]

Mark scheme

16 31 : 21 3 B2 for equivalents e.g. 15.5 oe and 10.5 oe or for an equivalent ratio e.g. 3.1 : 2.1 or M1 for e.g. x + 5 + x = 26 oe or x – 5 + x = 26 oe

Question 172 marks

Question

Each interior angle of a regular polygon is 178.5°. Calculate the number of sides of this polygon. …… [2]

Mark scheme

17 240 2 M1 for 360 ÷ (180 – 178.5) oe 180(n − 2) or for = 178.5 oe n

Question 183 marks

Question

Find the equation of the straight line that passes through the points (2, -2) and (3, 10). Give your answer in the form y = mx + c . y = …… [3]

Mark scheme

18 [y =] 12x – 26 final answer 3 10 − −2 M1 for oe 3− 2 M1 for correct substitution of (2, –2) or (3, 10) into y = (their m)x + c oe

Question 194 marks

Question

12.6 cm NOT TO SCALE 80° O The diagram shows a sector of a circle, centre O, radius 12.6 cm. Calculate the perimeter of the shaded segment. …… cm [4]

Mark scheme

19 33.8 or 33.78 to 33.80 4 M2 for 2 × 12.6 × sin 40 oe or M1 for sin 40 = (...) oe 12.6 80 M1 for × 2 × π × 12.6 oe 360

Question 203 marks

Question

A lake has an area of 3 km2. On a map the area of the lake is 18.75 cm2. Find the scale of the map in the form 1 : n. 1 : …… [3]

Mark scheme

20 40 000 3 B2 for 1 cm to 0.4 km or 2.5 cm to 1 km or 1 600 000 000 3 × 10k or M2 for oe where k > 5 18.75 or M1 for 1 cm2 to 0.16 km2 or 6.25 cm2 to 1 km2 or for 3 × 1010 oe or 1.875 × 10–9 oe or 3 × 106 oe and 1.875 × 10–3 oe

Question 212 marks

Question

Simplify fully. 3 `243y 10j5 …… [2]

Mark scheme

21 27y6 final answer 2 B1 for ky6 or 27yk as final answer or correct answer seen and spoilt

Question 225 marks

Question

Solve the simultaneous equations. You must show all your working. y = x 2 - 3x - 13 y = x-1 x = …… , y = …… x = …… , y = …… [5]

Mark scheme

22 x2 – 4x – 12 [= 0] M2 M1 for x2 – 3x – 13 = x – 1 or or for y = (y + 1)2 – 3(y + 1) – 13 y2 – 2y – 15 [= 0] (x – 6)(x + 2) [= 0] M1 or for correct factors for their quadratic or equation (y – 5)(y + 3) [= 0] or for correct use of quadratic formula or completing the square for their equation [x =] 6, [y =] 5 B2 B1 for one correct pair or two correct [x =] –2, [y =] –3 x values or two correct y values If B0 scored and at least 2 method marks scored SC1 for correct substitution of both of their x values or their y values into y = x2 – 3x – 13 or y = x – 1

Question 236 marks

Question

D C 4 cm Q P 5 cm NOT TO SCALE A B 12 cm The diagram shows a triangular prism. Angle BPC = 90°. (a) Calculate AC. AC = …… cm [3] (b) Calculate the angle between AC and the base ABPQ. …… [3]

Mark scheme

23(a) 13.6 or 13.60… 3 M2 for 122 + 52 + 42 or M1 for 52 + 42 or 12 2 + 4 2 or 122 + 52 23(b) 17.1 or 17.08 to 17.10… 3 4 M2 for sin = oe or their (a) 4 their AP tan = or cos = their AP their (a) or M1 for recognising angle CAP.

Question 242 marks

Question

tan x = 3 and 0° G x G 360° . Find all the possible values of x. …… [2]

Mark scheme

24 60 2 B1 for 60 or 240 and 240 If 0 scored SC1 for two answers with a difference of 180°

Question 254 marks

Question

Simplify. 3x 2 - 18x ax - 6a + 2cx - 12c …… [4]

Mark scheme

25 3x 4 B1 for 3x(x – 6) final answer B2 for ( x − 6)(a + 2c) a + 2c or B1 for a ( x − 6) + 2c( x − 6) or x(a + 2c) − 6(a + 2c)

Question 263 marks

Question

T NOT TO t SCALE X O R r ORT is a triangle. X is a point on TR so that TX : XR = 3 : 2. O is the origin, OR = r and OT = t . Find the position vector of X. Give your answer in terms of r and t in its simplest form. …… [3]

Mark scheme

26 3 2 1 3 2 3 r + t or (3r + 2t) M2 for r + (–r + t) oe or t + (r – t) 5 5 5 5 5 oe or ρ M1 for RT = –r + t oe or TR = r − t ρ ρ ρ ρ M1 for OR + RX or OT + TX any other correct route.

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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 0580/23 October/November 2021 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/23, October/November 2021 (0580_w21_ms_23), and the question paper (0580_w21_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 October/November 2021 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/O/N/21 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.