Cambridge IGCSE Mathematics 0580 — 2010 Oct/Nov Paper 2 · Variant 1
0580/21/O/N/10 · 10 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 scheme3 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q13 · X − 1 For 13 Solve the inequality
x − 1 For 13 Solve the inequality. 2x + 5 I Examiner's 4 Use Answer [3]
Mark scheme: 13 x < –3 3 M1 correct move M1 correct move M1 correct move
Q14 · Find the value of n in the following equations
14 Find the value of n in the following equations. (a) 2n = 1024 Answer(a) n = [1] (b) 42n – 3 = 16 Answer(b) n = [2]
Mark scheme: 14 (a) 10(.0) 1 1 (b) 2 , 2.5(0) 2 M1 2n – 3 = 2 2 1
Q15 · 8 cm NOT TO SCALE 6 cm 6 cm A semicircle of diameter 6 cm is cut from a rectangle with…
15 8 cm NOT TO SCALE 6 cm 6 cm A semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm. Calculate the perimeter of the shaded shape, correct to 1 decimal place. Answer cm [3]
Mark scheme: 1 15 31.4 cao 3 M1 × 2 × π × 3 oe 2 M1 6 + 8 + 6 + 1 + 1 + k π 3
Question 16
16 Simplify this fraction. For Examiner's 2 Use x − 5 x + 6 x 2 − 4 Answer [4]
Mark scheme: 16 x − 3 4 B2 (x – 3)(x – 2) or B1 (x + a)(x + b) x + 2 where ab = 6 or a + b = –5 B1 (x – 2)(x + 2) 8 0
Q17 · 2 2 A = 2 −2 Work out (a) A2, Answer(a) [2] (b)…
17 2 2 A = 2 −2 Work out (a) A2, Answer(a) [2] (b) A–1, the inverse of A. Answer(b) [2]
Mark scheme: 17 (a) 8 0 oe 2 B1 for one column (or row) correct 0 8 1 1 a c 4 4 (b) oe 2 B1 for –1/8 seen 1 1 d b or B1 for −− 22 − 22 4 −4
Q18 · For 60 Examiner's Use 50 40 Speed 30 (m / s) 20 10 t 0 5 10 15 20 25 30 35 Time (seconds)…
18 For 60 Examiner's Use 50 40 Speed 30 (m / s) 20 10 t 0 5 10 15 20 25 30 35 Time (seconds) The graph shows the speed of a sports car after t seconds. It starts from rest and accelerates to its maximum speed in 12 seconds. (a) (i) Draw a tangent to the graph at t = 7. [1] (ii) Find the acceleration of the car at t = 7. Answer(a)(ii) m/s2 [2] (b) The car travels at its maximum speed for 13 seconds. Find the distance travelled by the car at its maximum speed. Answer(b) m [2]
Mark scheme: 18 (a) (i) Tangent 1 Correct tangent drawn (ii) 4.4 to 6 2 dep M1 attempting to find gradient of their tangent (b) 780 2 M1 evidence of finding the area under the graph ONLY from t = 12 to t = 25
Q19 · Reina went on holiday to New Zealand
19 Reina went on holiday to New Zealand. For Examiner's (a) She travelled the 65 km from Tokyo to Narita Airport by taxi. Use The taxi journey cost 300 yen (¥) per kilometre plus a fixed charge of ¥ 700. Calculate the cost of the taxi journey. Answer(a) ¥ [2] (b) At Narita Airport, Reina changed ¥ 71 190 into New Zealand dollars (NZ$). The exchange rate was NZ$1 = ¥ 56.5. How many New Zealand dollars did she receive? Answer(b) NZ$ [2]
Mark scheme: 19 (a) 20200 2 M1 65 × 300 + 700 (b) 1260 2 M1 71190 / 56.5 8 ± k
Question 20
20 Solve the equation. x2 – 8x + 6 = 0 Show all your working and give your answers correct to 2 decimal places. Answer x = or x = [4]
Mark scheme: 8 ± k 20 x = 0.84 or 7.16 4 B1 B1 √(82 – 4 × 1 × 6) or better 2 A1 A1
Q21 · For y Examiner's A Use 8 7 6 5 4 3 2 1 0 x 1 2 3 4 5 6 7 –1 –2 –3 –4 B (a) Using a…
21 For y Examiner's A Use 8 7 6 5 4 3 2 1 0 x 1 2 3 4 5 6 7 –1 –2 –3 –4 B (a) Using a straight edge and compasses only, construct the perpendicular bisector of AB on the diagram above. [2] (b) Write down the co-ordinates of the midpoint of the line segment joining A(1, 8) to B(7, –4). Answer(b) ( , ) [1] (c) Find the equation of the line AB. Answer(c) [3] Question 22 is printed on the next page.
Mark scheme: 21 (a) Bisector 2 B1 accurate line B1 two sets of correct arcs (b) (4, 2) 1 (c) y = –2x + 10 oe 3 B1 correct m B1 correct c M1 correct use of y = mx + c oe on answer line
Q22 · In a survey of 60 cars, 25 use diesel, 20 use liquid hydrogen and 22 use electricity
22 In a survey of 60 cars, 25 use diesel, 20 use liquid hydrogen and 22 use electricity. For Examiner's No cars use all three fuels and 14 cars use both diesel and electricity. Use There are 8 cars which use diesel only, 15 cars which use liquid hydrogen only and 6 cars which use electricity only. In the Venn diagram below = {cars in the survey}, D = {cars which use diesel}, L = {cars which use liquid hydrogen}, E = {cars which use electricity}. D E 8 6 ........ ........ ........ ........ 15 ........ L (a) Use the information above to fill in the five missing numbers in the Venn diagram. [4] (b) Find the number of cars which use diesel but not electricity. Answer(b) [1] (c) Find n(D'∩ (E ∪ L)). Answer(c) [1]
Mark scheme: 22 (a) 4 B1 0 and 14 in correct place B1 2 in correct place D E 14 B1 3 in correct place 0 B1 12 in correct place 3 2 12 L (b) 11 1ft B1ft 8 + their 3 (c) 23 1ft B1ft 21 + their 2
What was in this paper
The subtopics covered by these 10 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 2010 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.