Question 12 marks
Question
Simplify. 3a + 7b - 4a + b …… [2]
Mark scheme
1 –a + 8b final answer 2 B1 for –a or [+]8b in final answer or for –a + 8b spoilt
Mathematics 0580/21 October/November 2020: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w20_qp_210580_w20_ms_210580/21/O/N/20
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/21/O/N/20
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 23 marks
Question
A field, ABC, is in the shape of a triangle. AC = 500 m and BC = 650 m. Using a ruler and compasses only, complete the scale drawing of the field ABC. Leave in your construction arcs. Use a scale of 1 cm to represent 100 m. The side AB has been drawn for you. A B Scale: 1 cm to 100 m [3]
Mark scheme
2 Correct triangle constructed with 3 B2 for correct triangle with no/incorrect AC = 5 cm and BC = 6.5 cm and arcs intersecting arcs or SC2 for accurate triangle with arcs but sides interchanged or B1 for 6.5 [cm] or 5 [cm] soi
Question 33 marks
Question
Rangan buys 3.6 kg of potatoes and 2.8 kg of leeks. The total cost is $13.72 . Leeks cost $2.65 per kilogram. Find the cost of 1 kg of potatoes. $ …… [3]
Mark scheme
3 1.75 3 M2 for (13.72 – 2.8 × 2.65) ÷ 3.6 oe or M1 for 2.8 × 2.65
Question 45 marks
Question
Aisha records the distance she runs and her average speed. The results are shown in the scatter diagram. 16 15 14 13 12 Average speed 11 (km/h) 10 9 8 7 6 5 0 1 2 3 4 5 6 7 8 9 10 Distance (km) (a) The table shows the results of four more runs. Distance (km) 4.2 5.7 7.1 8.8 Average speed (km/h) 13.4 11.8 9.8 8.3 On the scatter diagram, plot these points. [2] (b) What type of correlation is shown in the scatter diagram? …… [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) Use your line of best fit to estimate her average speed when she runs a distance of 6 km. …… km/h [1] 49.2 - 9.59
Mark scheme
4(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted 4(b) Negative 1 4(c) Correct ruled line of best fit 1 4(d) 10 to 12 1 FT their straight line of best fit
Question 52 marks
Question
T= 4.085 # 2.35 By writing each number correct to 1 significant figure, work out an estimate for T. You must show all your working. …… [2] 2 3
Mark scheme
5 50 –10 M1 Allow M1 for 3 out of 4 values correctly 4× 2 rounded or for all correct but with any trailing zeros 5 A1 50 –10 dep on 4× 2
Question 63 marks
Question
Without using a calculator, work out 2 # 2 . 3 4 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
6 8 11 M1 and oe improper fractions 3 4 88 A1 oe improper fraction 12 1 A1 dep on 1st A1 7 cao final answer 8 11 3 If M0 scored SC1 for or oe 3 4 improper fraction
Question 72 marks
Question
Make x the subject of this formula. 2y = 5x - 7 x = …… [2]
Mark scheme
7 2y +7 2y 7 2 2y 7 [ x =] oe or [ x =] + oe M1 for 2 y + 7 = 5 x oe or = x – oe 5 5 5 5 5 final answer
Question 83 marks
Question
(a) 1, 2, 3, 5 and 7 are all common factors of two numbers. Write down the digit that the two numbers must end in. …… [1] (b) Write 84 as a product of its prime factors. …… [2]
Mark scheme
8(a) 0 1 8(b) 22 × 3 × 7 or 2 × 2 × 3 × 7 2 B1 for 2, 2, 3, 7
Question 92 marks
Question
(a) Ahmed increases 40 by 300%. From this list, put a ring around the correct calculation. 40 # 1.300 40 # 3 40 # 400 40 # 4 40 # 300 [1] 2 (b) Ahmed finds the magnitude of the vector e o. -3 From this list, put a ring around the correct calculation. 2 2 +- 3 2 22 - 32 22 - 32 2 2 + (- 3) 2 2 2 + (- 3) 2 [1]
Mark scheme
9(a) 40 × 4 1 9(b) 1 2 2 + ( − 3) 2
Question 103 marks
Question
A town has a population of 45 000. This population increases exponentially at a rate of 1.6% per year. Find the population of the town at the end of 5 years. Give your answer correct to the nearest hundred. …… [3]
Mark scheme
10 48 700 cao 3 1.6 5 M1 for 45 000 × 1 + oe 100 A1 for 48 710 to 48 720 If A0 scored B1 for their more accurate value correctly rounded to the nearest 100
Question 112 marks
Question
y x=2 (-1, 4) NOT TO SCALE (-1, 1) 0 x The diagram shows a rectangle with a line of symmetry at x = 2 . Two vertices of the rectangle are at (-1, 1) and (-1, 4). The shaded region is defined by the inequalities a G x G b and c G y G d . Find the values of a, b, c and d. a = …… b = …… c = …… d = …… [2]
Mark scheme
11 [a =] –1 2 B1 for two or three correct [b =] 5 [c =] 1 or SC1 for [d =] 4 [a =] x ⩾ –1 [b =] x ⩽ 5 [c =] y ⩾ 1 [d =] y ⩽ 4
Question 122 marks
Question
The interior angle of a regular polygon with n sides is 156°. Work out the value of n. n = …… [2]
Mark scheme
12 15 2 360 180 ( n − 2 ) M1 for or =156 oe 180 − 156 n
Question 133 marks
Question
Write the recurring decimal 0.17o as a fraction in its simplest form. You must show all your working. …… [3]
Mark scheme
13 17.77… – 1.77… oe M1 M1 for correct working shown 8 A2 16 cao B1 for oe seen 45 90
Question 142 marks
Question
Find the gradient of a line that is perpendicular to 8y + 4x = 5. …… [2]
Mark scheme
14 2 2 5 –4x M1 for y = oe or better 8
Question 154 marks
Question
20 Car 18 16 14 Motorbike 12 Speed 10 (m/s) 8 6 4 2 0 0 10 20 30 40 50 60 70 80 90 100 Time (s) The diagram shows the speed–time graph for 100 seconds of the journey of a car and of a motorbike. (a) Find the deceleration of the car between 60 and 100 seconds. …… m/s2 [1] (b) Calculate how much further the car travelled than the motorbike during the 100 seconds. …… m [3]
Mark scheme
15(a) 0.3 1 15(b) 360 3 M2 for correct complete area statement e.g. 1 18 × 60 + × 40 × (18 + 6) – 12 × 100 2 1 1 or × 6 × (60 + 80) – × 6 × 20 2 2 or for answer 420 or M1 for one area calculation
Question 162 marks
Question
Factorise 6x 2 + 7x - 20 . …… [2]
Mark scheme
16 (3x – 4)(2x + 5) final answer 2 B1 for (ax + b)(cx + d) where ac = 6 and ad + bc = 7 or bd = – 20
Question 176 marks
Question
(a) f (x) = 3x 2 + a where a is an integer. f (- 2) = 19 Find the value of a. a = …… [2] (b) g (x) = 2x + 7 h (x) = 3x - 8 (i) Find gh(x) in its simplest form. …… [2] (ii) Find g -1 (x) . g -1 (x) = …… [2]
Mark scheme
17(a) [a =] 7 2 M1 for 3(–2)2 + a = 19 or better 17(b)(i) 6x – 9 or 3(2x – 3) final answer 2 M1 for 2(3x – 8) + 7 or better 17(b)(ii) x−7 2 M1 for a correct first step final answer x = 2 y + 7 or y − 7 = 2 x 2 y 7 or = x + 2 2
Question 184 marks
Question
7 cm NOT TO SCALE 12 cm The diagram shows a solid made from a cylinder and a hemisphere, both of radius 7 cm. The cylinder has length 12 cm. Work out the total surface area of the solid. [The surface area, A, of a sphere with radius r is A = 4rr 2 .] …… cm2 [4]
Mark scheme
18 990 or 989.58 to 989.73 4 M1 for 4 × π × 72 [÷2] M1 for π × 72 M1 for π × 7 × 2 × 12
Question 191 mark
Question
In this Venn diagram, shade the region M l , N , P . M N P [1]
Mark scheme
19 1 ξ M N P
Question 204 marks
Question
(4x - 87) ° NOT TO SCALE (x + 60) ° 2x° y° The diagram shows a cyclic quadrilateral. Find the value of y. y = …… [4]
Mark scheme
20 107 4 B2 for x = 40 or M1 for 2x + x + 60 = 180 oe M1 for correctly substituting their x into 4x – 87 + y = 180 oe or 4x – 87 + x + 60 + y + 2x = 360 oe
Question 213 marks
Question
P Q S R NOT TO SCALE U T W V The diagram shows a cuboid PQRSTUVW. PV = 17.2 cm The angle between the line PV and the base TUVW of the cuboid is 43°. Calculate PT. PT = …… cm [3]
Mark scheme
21 11.7 or 11.73… 3 PT M2 for sin 43 = oe 17.2 or M1 for identifying angle PVT
Question 224 marks
Question
Simplify. x 2 - 5x 2x 2 - 50 …… [4] Question 23 is printed on the next page.
Mark scheme
22 x x 4 B1 for x(x – 5) or final answer B2 for 2(x – 5)(x + 5) or (x – 5)(2x + 10) 2 ( x + 5) 2 x + 10 or (2x – 10)(x + 5) or B1 for 2(x2 – 25) or (x – 5)(x + 5)
Question 235 marks
Question
(a) C B D A n NOT TO SCALE F m E The diagram shows a parallelogram CDEF. FE = m and CE = n . B is the midpoint of CD. FA = 2AC Find an expression, in terms of m and n, for AB. Give your answer in its simplest form. AB = …… [3] (b) GH = 56 (2p + q) 5 JK = 18 (2p + q) Write down two facts about vectors GH and JK . …… [2]
Mark scheme
23(a) 5 1 3 B2 for correct unsimplified answer in m– n 1 1 6 3 terms of m and n e.g. (m – n) + m 3 2 or M1 for a correct route or for ρ ρ FC = m – n or CF = n – m or better e.g. ρ 1 AC = (m – n) 3 ρ ρ ρ 23(b) GH = 3 JK oe or GH has a greater 2 B1 for each magnitude ρ ρ GH and JK are parallel
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Where can I find the 0580/21 October/November 2020 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/21, October/November 2020 (0580_w20_ms_21), and the question paper (0580_w20_qp_21), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/21 for October/November 2020 is out of 70 marks, with 1 hour 30 minutes to answer it.
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