Question 11 mark
Question
Work out $1.20 as a percentage of $16. ……% [1]
Mark scheme
1 7.5 oe 1
Mathematics 0580/21 May/June 2019: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s19_qp_210580_s19_ms_210580/21/M/J/19
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/21/M/J/19
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 21 mark
Question
Factorise 5y - 6py. …… [1] 3
Mark scheme
2 y (5 − 6 p) final answer 1
Question 31 mark
Question
Calculate 8.1 2 - 1.3 0.8 . …… [1]
Mark scheme
3 4.01 or 4.007 to 4.008 1
Question 41 mark
Question
An equilateral triangle has sides of length 15 cm, correct to the nearest centimetre. Calculate the upper bound of the perimeter of this triangle. …… cm [1]
Mark scheme
4 46.5 1
Question 52 marks
Question
The volume of a cuboid is 180 cm3. The base is a square of side length 6 cm. Calculate the height of this cuboid. …… cm [2]
Mark scheme
5 5 2 M1 for 180 ÷ 62 oe
Question 62 marks
Question
Simplify. (a) t 21 ÷ t 7 …… [1] 5 (b) (u5) …… [1]
Mark scheme
6(a) t14 final answer 1 6(b) u 25 final answer 1
Question 72 marks
Question
NOT TO SCALE 12 cm x cm 35° The diagram shows a right-angled triangle. Calculate the value of x. x = …… [2]
Mark scheme
7 6.88 or 6.882 to 6.883 2 x M1 for sin 35 [=] oe or better 12
Question 82 marks
Question
NOT TO O SCALE C A 130° B A, B and C are points on the circle, centre O. Find the obtuse angle AOC. Angle AOC = …… [2]
Mark scheme
8 100 2 M1 for reflex angle = 2 × 130 or opposite angle of a cyclic quadrilateral shown = 50
Question 92 marks
Question
Write the recurring decimal 0.47o as a fraction. Show all your working. …… [2]
Mark scheme
9 47.77…– 4.77… oe M1 43 A1 Allow equivalent fractions 90 43 If M0 then SC1 for or equivalent 90 fraction with no/insufficient working
Question 102 marks
Question
f(x) = 2x + 3 Find f(1 - x) in its simplest form. …… [2]
Mark scheme
10 5 – 2x final answer 2 M1 for 2(1 – x) + 3 oe
Question 112 marks
Question
1 2 3 4 5 The diagram shows five cards. Two of the cards are taken at random, without replacement. Find the probability that both cards show an even number. …… [2]
Mark scheme
11 2 2 2 1 oe M1 for × oe 20 5 4
Question 123 marks
Question
27 28 29 30 31 32 33 From the list of numbers, write down (a) a multiple of 7, …… [1] (b) a cube number, …… [1] (c) a prime number. …… [1]
Mark scheme
12(a) 28 1 12(b) 27 1 12(c) 29 or 31 1
Question 133 marks
Question
x 2 + 4x - 9 = (x + a) 2 + b Find the value of a and the value of b. a = …… b = …… [3] 5 2
Mark scheme
13 [a = ] 2 3 B2 for either correct or (x + 2)2 – 13 [b = ] – 13 OR M1 for 2a = 4 soi M1 for a2+ b = – 9 soi OR M1 for x2 + ax + ax + a2 [+b] or better
Question 143 marks
Question
Without using a calculator, work out + . 6 3 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
14 5 4 M1 2 correct fractions with a suitable common + oe denominator 6k 6 6 1 A2 9 1 cao A1 for oe 2 6
Question 153 marks
Question
Expand and simplify. (x + 1) (x + 2) + 2x (x - 3) …… [3]
Mark scheme
15 3x 2 − 3x + 2 final answer 3 B2 for x 2 + 2 x + x + 2 + 2 x 2 − 6 x oe or B1 for 3 correct terms of x 2 + 2 x + x + 2 oe
Question 163 marks
Question
y is inversely proportional to the square root of (x + 1). When x = 8, y = 2. Find y when x = 99. y = …… [3]
Mark scheme
16 [ ± ] 0.6 oe 3 k M1 for y = x +1 theirk M1 for y = 99 + 1 OR 2 8 +1 M2 for 99 + 1 or M1 for 2 8 + 1 = y 99 + 1
Question 173 marks
Question
(a) Factorise p 2 - q 2 . …… [1] (b) p 2 - q 2 = 7 and p - q = 2 . Find the value of p + q. …… [2] (a) Simplify `81y 16j . 3
Mark scheme
17(a) ( p − q )( p + q ) final answer 1 17(b) 7 2 M1 for 2 × (p + q) = 7 oe or for ( 2 + q ) − q 2 = 7 or p 2 − ( p − 2 ) = 7 2 2 2
Question 183 marks
Question
4 …… [2] (b) 2 3 = 4 p Find the value of p. p = …… [1]
Mark scheme
18(a) 27 y12 final answer 2 B1 for ky12 or 27 y k in final answer 18(b) 3 1 oe 2
Question 193 marks
Question
A model of a car has a scale 1 : 20. The volume of the actual car is 12 m3. Find the volume of the model. Give your answer in cubic centimetres. ……cm3 [3]
Mark scheme
19 1500 3 20 3 M2 for 12 ÷ oe 100 3 3 20 100 or M1 for or oe 100 20 OR M1 for ÷ 203 oe M1 for × 1003 oe
Question 203 marks
Question
Write as a single fraction in its simplest form. 1 2 - x + 2 3x - 1 …… [3]
Mark scheme
20 x−5 3 B1 for common denominator isw expansion final answer ( x + 2)(3 x − 1) M1 for 3 x − 1 − 2( x + 2) or better
Question 214 marks
Question
V NOT TO SCALE 10 cm D C M A 8 cm B The diagram shows a pyramid with a square base ABCD of side length 8 cm. The diagonals of the square, AC and BD, intersect at M. V is vertically above M and VM = 10 cm. Calculate the angle between VA and the base. …… [4]
Mark scheme
21 60.5 or 60.50… 4 10 M3 for tan = oe 1 2 2 8 +8 2 1 or M2 for [ ×] 8 2 + 82 2 or M1 for 82 + 82 or 42 + 42 or B1 for recognising the angle required
Question 224 marks
Question
(a) These are the first four terms of a sequence. 5 8 11 14 (i) Write down the next term. …… [1] (ii) Find an expression, in terms of n, for the nth term. …… [2] (b) These are the first five terms of another sequence. 1 3 7 13 21 2 4 6 8 10 Find the next term. …… [1] 3 1
Mark scheme
22(a)(i) 17 1 22(a)(ii) 3n + 2 oe final answer 2 B1 for 3n + k or cn + 2, c ≠ 0 22(b) 31 1 oe 12
Question 234 marks
Question
P =e o 2 4 (a) Find P2. f p [2] (b) Find P –1. f p [2]
Mark scheme
23(a) 11 7 2 B1 for 2 or 3 correct elements 14 18 23(b) 1 4 −1 2 4 −1 oe isw B1 for k or for det = 10 soi 10 −2 3 −2 3
Question 244 marks
Question
20 NOT TO Speed SCALE (m/s) 0 0 60 70 Time (seconds) The diagram shows information about the final 70 seconds of a car journey. (a) Find the deceleration of the car between 60 and 70 seconds. ……m/s2 [1] (b) Find the distance travelled by the car during the 70 seconds. …… m [3]
Mark scheme
24(a) 2 1 24(b) 1300 3 20 M2 for × (60 + 70) oe 2 or M1 for any relevant area
Question 254 marks
Question
C K B M NOT TO q SCALE L O p A OABC is a parallelogram and O is the origin. CK = 2KB and AL = LB. M is the midpoint of KL. OA = p and OC = q. Find, in terms of p and q, giving your answer in its simplest form (a) KL, KL = …… [2] (b) the position vector of M. …… [2] Question 26 is printed on the next page.
Mark scheme
25(a) 1 1 2 M1 for a correct unsimplified answer or a p − q oe simplified correct route 3 2 25(b) 5 3 2 M1 for a correct unsimplified answer or a p + q oe simplified correct route 6 4
Question 265 marks
Question
Line L passes through the points (0, -3) and (6, 9). (a) Find the equation of line L. …… [3] (b) Find the equation of the line that is perpendicular to line L and passes through the point (0, 2). …… [2]
Mark scheme
26(a) y = 2 x − 3 oe 3 B2 for 2 x − 3 or y = theirm x – 3 or y = 2x + c 9 − ( −3) or M1 for oe or 9 = 6m – 3 oe 6−0 or B1 for 2x seen or [y =]mx – 3 m ≠ 0 26(b) 1 2 1 y = − x + 2 oe FT their (a) y = – x+2 2 their m 1 B1 for gradient – , gradient FT their (a) 2 or for y = mx + 2 m ≠ 0
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0580/21 questions
Where can I find the 0580/21 May/June 2019 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/21, May/June 2019 (0580_s19_ms_21), and the question paper (0580_s19_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 May/June 2019 is out of 70 marks, with 1 hour 30 minutes to answer it.
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