Cambridge IGCSE Mathematics 0580 — 2015 Feb/March Paper 2 · Variant 2
0580/22/F/M/15 · 6 questions · 70 marks · ≈79 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q17 · S R NOT TO b SCALE P Q 2a PQRS is a trapezium with PQ = 2SR
17 (a) S R NOT TO b SCALE P Q 2a PQRS is a trapezium with PQ = 2SR. = 2a and = b. Find in terms of a and b in its simplest form. Answer(a) = ................................................ [2] (b) X M x NOT TO SCALE O Y y = x and = y. M is a point on XY such that XM : MY = 3 : 5. Find in terms of x and y in its simplest form. Answer(b) = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 17 (a) b − a 2 M1 if unsimplified or correct route in terms of P,Q,R, S 5 3 (b) x + y 2 M1 for a correct route e.g. OX + XM 8 8 or 3 5 for XY or YX 8 8 6
Q18 · F 6 m NOT TO SCALE D C 15 m A B 18 m The diagram shows a rectangular playground ABCD on…
18 F 6 m NOT TO SCALE D C 15 m A B 18 m The diagram shows a rectangular playground ABCD on horizontal ground. A vertical flagpole CF, 6 metres high, stands in corner C. AB = 18 m and BC = 15 m. Calculate the angle of elevation of F from A. Answer ................................................ [4] __________________________________________________________________________________________
Mark scheme: 6 18 14.4 or 14.36... 4 M3 for tan = 2 2 oe or better their 15 + 18 or M1 for AC = 15 2 + 18 2 and M1 for identifying required angle 18
Q19 · Fritz drives a distance of 381 km in 2 hours and 18 minutes
19 Fritz drives a distance of 381 km in 2 hours and 18 minutes. He then drives 75 km at a constant speed of 30 km/h. Calculate his average speed for the whole journey. Answer ....................................... km/h [4] __________________________________________________________________________________________
Mark scheme: 18 19 95 4 B1 for 2.3 or 2 60 M1 for 75 ÷ 30 (= 2.5) 381 + 75 M1 for their 3.2 + their 5.2
Q20 · W V NOT TO 88° SCALE X Z 57° Y Two straight lines VZ and YW intersect at X
20 (a) W V NOT TO 88° SCALE X Z 57° Y Two straight lines VZ and YW intersect at X. VW is parallel to YZ, angle XYZ = 57° and angle VXW = 88°. Find angle WVX. Answer(a) Angle WVX = ................................................ [2] (b) A NOT TO 7.2 cm SCALE P Q 8.4 cm B C 12.6 cm ABC is a triangle and PQ is parallel to BC. BC = 12.6 cm, PQ = 8.4 cm and AQ = 7.2 cm. Find AC. Answer(b) AC = .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: 20 (a) 35 2 M1 for [Z =] 180 − 88 − 57 or VWX = 57 or YZX = 35 AC 126. (b) 10.8 2 M1 for = oe 2.7 4.8
Q21 · Simplify (i) x0, Answer(a)(i) ...............................................
21 (a) Simplify (i) x0, Answer(a)(i) ................................................ [1] (ii) m4 × m3, Answer(a)(ii) ................................................ [1] 1 (iii) ( 8p6) 3 . Answer(a)(iii) ................................................ [2] (b) 243 x = 3 2 Find the value of x. Answer(b) x = ................................................ [2] __________________________________________________________________________________________ Question 22 is printed on the next page.
Mark scheme: 21 (a) (i) 1 1 (ii) 7 1 m (iii) 2p 2 2 SC1 for 2 p k or kp 2 k ≠ 0 2 1 2 5 or 243 5 seen (b) or 0.4 2 B1 for 53 or 3 5 x or 243 5
Q22 · F(x) = 5x – 3 g(x) = x2 (a) Find fg(–2)
22 f(x) = 5x – 3 g(x) = x2 (a) Find fg(–2). Answer(a) ................................................ [2] (b) Find gf(x), in terms of x, in its simplest form. Answer(b) ................................................ [2] (c) Find f –1(x). Answer(c) f –1(x) = ................................................ [2]
Mark scheme: 22 (a) 17 2 M1 for [g(−2) =] 4 seen or for 5x2 – 3 (b) 2 M1 for g(5 x − 3) 25 x 2 − 30 x + 9 or (5x – 3)2 as final answer x + 3 (c) 2 M1 for 5 x = y + 3 or x = 5 y − 3 or 5 y 3 = x − 5 5
What was in this paper
The subtopics covered by these 6 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2015 Feb/March, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.