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Mathematics 0580/21 October/November 2019: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_w19_qp_210580_w19_ms_210580/21/O/N/19

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/21/O/N/19
0580_w19_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 11 mark

Question

Work out 5% of $25. $ …… [1]

Mark scheme

1 1.25 1

Question 21 mark

Question

Factorise 5p + pt. …… [1]

Mark scheme

2 p(5 + t) final answer 1

Question 32 marks

Question

Calculate. 16.379 - 0.879 # 1.241 4.2 Give your answer correct to 2 significant figures. …… [2]

Mark scheme

3 4.6 cao nfww 2 B1 for 4.57 or 4.58 or 4.579 to 4.580 If 0 scored, SC1 for their calculation rounded to 2 sf if more than 2sf seen

Question 42 marks

Question

Write 15 060 (a) in words, …… [1] (b) in standard form. …… [1]

Mark scheme

4(a) Fifteen thousand [and] sixty 1 4(b) 1.506[0] × 104 1

Question 52 marks

Question

Simplify 5c - d - 3d - 2c . …… [2]

Mark scheme

5 3c – 4d final answer 2 B1 for 3c + kd or kc – 4d

Question 62 marks

Question

Solve. x-2 =3 3 x = …… [2]

Mark scheme

6 11 2 x 2 M1 for x − 2 = 3 × 3 oe or = 3 + oe or 3 3 better

Question 72 marks

Question

Simplify 2x 3 # 3x 2 . …… [2] 5 1

Mark scheme

7 6x5 final answer 2 B1 for kx5 or 6 x k

Question 82 marks

Question

Without using a calculator, work out #1 . 16 7 You must show all your working and give your answer as a fraction in its simplest form. …… [2]

Mark scheme

8 5 8 M1 × 16 7 5 A1 cao 14

Question 92 marks

Question

Paula invests $600 at a rate of r % per year simple interest. At the end of 10 years, the total interest earned is $90. Find the value of r. r = …… [2]

Mark scheme

9 1.5 2 600 × r × 10 M1 for = 90 oe or better 100

Question 102 marks

Question

Simplify. 4 - ex o 3 3 8 …… [2]

Mark scheme

10 16 2 4 – 1 or 16x −4  x −4  8 3  x12  3 x4 M1 for   or  3  or   or 2 x   4096  better 16 k or B1 for k or 16xk or 4 or kx–4 final x x answer

Question 112 marks

Question

P = 2r + rr Rearrange the formula to write r in terms of P and r. r = …… [2]

Mark scheme

11 P 2 M1 for P = r (2 + π) 2+ π

Question 122 marks

Question

The sides of a square are 15.1 cm, correct to 1 decimal place. Find the upper bound of the area of the square. …… cm2 [2]

Mark scheme

12 229.5225 final answer cao 2 M1 for (15.1 + 0.05)2 or B1 for 15.15 seen

Question 132 marks

Question

11 cm NOT TO 39° SCALE 13 cm Calculate the area of the triangle. …… cm2 [2]

Mark scheme

13 45[.0] or 44.99 to 45.00 2 1 M1 for × 13 × 11 × sin 39 oe 2

Question 143 marks

Question

The scale of a map is 1 : 10 000 000. On the map, the area of Slovakia is 4.9 cm2. Calculate the actual area of Slovakia. Give your answer in square kilometres. …… km2 [3]

Mark scheme

14 49 000 3 M1 for 4.9 × (10 000 000)2 M1 for ÷ (100 000)2 OR M1 for 1 cm : 100 km M1 for 4.9 × (their 100)2 OR M2 for ( 4.9 × 10 000 000 ÷ 100 000)2 or M1 for 4.9 × 10 000 000 ÷ 100 000

Question 153 marks

Question

y is inversely proportional to x2. When x = 4, y = 2. 1 Find y when x = . 2 y = …… [3]

Mark scheme

15 128 3 k M1 for y = x2 their k M1 for y = 2 1   2 OR 2 × 42 M2 for 2 1   2 2 1 2 or M1 for 2 × 4 = y ×   2

Question 163 marks

Question

12 cm NOT TO 8 cm SCALE x 39° Calculate the obtuse angle x in this triangle. x = …… [3]

Mark scheme

16 109.3 or 109.26 to 109.27 3 12 sin 39 M2 for 8 8 12 or M1 for = oe sin 39 sin(...)

Question 173 marks

Question

5 cm NOT TO SCALE 45° 3 cm The diagram shows two sectors of circles with the same centre. Calculate the shaded area. …… cm2 [3] x 2x + 4

Mark scheme

17 6.28 or 6.283 to 6.284 3 45 45 M2 for × π × 52 oe and × π × 32 360 360 oe 45 or M1 for × π × 52 oe 360 45 or × π × 32 oe 360 or π × 52 − π × 32 oe

Question 183 marks

Question

Write - as a single fraction, in its simplest form. 2 x+1 …… [3] 1 2 5 6

Mark scheme

18 x 2 − 3x − 8 x 2 − 3x − 8 3 B1 for common denominator 2( x + 1) or or final answer 2( x + 1) 2x + 2 2x + 2 M1 for x( x + 1) − 2(2 x + 4) or better

Question 193 marks

Question

M=e o P =e o 3 4 7 8 (a) Find MP. f p [2] (b) Find M . …… [1] 9

Mark scheme

19(a)  19 22  2 B1 for 2 or 3 elements correct    43 50  19(b) –2 final answer 1

Question 203 marks

Question

The probability that the school bus is late is . 10 15 If the school bus is late, the probability that Seb travels on the bus is . 16 3 If the school bus is on time, the probability that Seb travels on the bus is . 4 Find the probability that Seb travels on the bus. …… [3]

Mark scheme

20 147 3 1 3 9 15 oe M2 for × + × 160 10 4 10 16 1 3 9 15 or M1 for × or × 10 4 10 16

Question 214 marks

Question

y 8 7 T 6 5 4 3 2 A 1 0 x 1 2 3 4 5 6 7 8 (a) Describe fully the single transformation that maps shape T onto shape A. …… [2] (b) On the grid, reflect shape T in the line y = x. [2]

Mark scheme

21(a) Translation 2 B1 for each  − 1    − 5 21(b) Correct reflection at 2 B1 for three correct vertices (6, 2), (6, 6), (7, 6), (7, 3)

Question 224 marks

Question

A pipe is completely full of water. Water flows through the pipe at a speed of 1.2 m/s into a tank. The cross-section of the pipe has an area of 6 cm2. Calculate the number of litres of water flowing into the tank in 1 hour. …… litres [4]

Mark scheme

22 2592 4 M3 for 1.2 × 100 × 60 × 60 × 6 ÷ 1000 oe or M2 for 1.2 × 60 × 60 × 6 oe or M1 for figs 12 × figs 6 or 60 × 60 or correct conversion e.g. their value in cm3 ÷ 1000 their value in m3 × 1000 1.2 × 100 6 ÷ 10 000

Question 234 marks

Question

 = {0, 1, 2, 3, 4, 5, 6} A = {0, 2, 4, 5, 6} B = {1, 2, 5} Complete each of the following statements. A + B = {……} n(B) = …… {0, 4, 6} = …… + …… {2, 4} …… A [4]

Mark scheme

23 2, 5 4 B1 for each 3 A.....B ′ ⊂

Question 244 marks

Question

f (x) = 3x - 5 g (x) = 2 x (a) Find fg(3). …… [2] (b) Find f -1 (x) . f -1 (x) = …… [2]

Mark scheme

24(a) 19 ( ) 2 M1 for 3 2 x − 5 soi or for f(8) 24(b) x+5 2 M1 for correct first step oe final answer y 3 5 y + 5 = 3x or = x − or x = 3y – 5 3 3

Question 254 marks

Question

Q NOT TO M SCALE B O P A O is the origin, OP = 2 OA, OQ = 3 OB and PM = MQ . OP = p and OQ = q . Find, in terms of p and q, in its simplest form (a) BA, BA = …… [2] (b) the position vector of M. …… [2]

Mark scheme

25(a) 1 1 2 M1 for correct unsimplified answer or – q + p oe correct route 3 2 25(b) 1 1 2 M1 for correct unsimplified answer or p + q oe correct route 2 2

Question 265 marks

Question

20 Speed NOT TO (m/s) SCALE 0 0 15 Time (seconds) A car travels at 20 m/s for 15 seconds before it comes to rest by decelerating at 2.5 m/s2. Find the total distance travelled. …… m [5]

Mark scheme

26 380 5 B2 for time = 8, implied by 23 on t-axis 20 20 or M1 for = 2.5 or = 2.5 or t t − 15 0 − 20 = −2.5 oe t − 15 1 M2 for (their 23 + 15) × 20 or 2 1 20 × 15 + × their 8 × 20 oe 2 or M1 for any relevant area found

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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 2019 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/21, October/November 2019 (0580_w19_ms_21), and the question paper (0580_w19_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 2019 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/19 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.