Cambridge IGCSE Mathematics 0580 — 2013 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/13 · 10 questions · 45 marks · ≈51 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
Q12 · A circle has a radius of 8.5 cm correct to the nearest 0.1 cm
12 A circle has a radius of 8.5 cm correct to the nearest 0.1 cm. The lower bound for the area of the circle is pπ cm2. The upper bound for the area of the circle is qπ cm2. Find the value of p and the value of q. Answer p = ............................................... q = ............................................... [3] _____________________________________________________________________________________
Mark scheme: 12 p = 71.4025 cao 3 B1 for 8.45 and 8.55 seen q = 73.1025 cao M1 for their LB2 [π] or their UB2 [π] If 0 scored, SC1 for one correct.
Q13 · Pam wins the student of the year award in New Zealand
13 Pam wins the student of the year award in New Zealand. For Examiner′s She sends three photographs of the award ceremony by post to her relatives. Use ● one of size 13 cm by 23 cm to her uncle in Australia ● one of size 15 cm by 23 cm to her sister in China ● one of size 23 cm by 35 cm to her mother in the UK Maximum lengths Australia Rest of the world 13 cm by 23.5 cm $1.90 $2.50 15.5 cm by 23.5 cm $2.40 $2.90 23 cm by 32.5 cm $2.80 $3.40 26 cm by 38.5 cm $3.60 $5.20 The cost of postage is shown in the table above. Use this information to calculate the total cost. Answer $ ................................................ [3] _____________________________________________________________________________________
Mark scheme: 13 10[.00] 3 M2 for 1.90 and 2.90 and 5.20 only or M1 for two of 1.90, 2.90, 5.20 in a list of three or two values from the table .3 40 + .5 20 or SC1 FOR 1.90, 2.90, 4.30 from 2
Q14 · C NOT TO SCALE O A B 142° D A, B and C are points on the circumference of a circle centre…
14 C NOT TO SCALE O A B 142° D A, B and C are points on the circumference of a circle centre O. OAD is a straight line and angle DAB = 142°. Calculate the size of angle ACB. Answer Angle ACB = ............................................... [3] _____________________________________________________________________________________
Mark scheme: 14 52 3 B2 for AOB = 104 or B1 for OAB or OBA = 38
Q15 · Find the co-ordinates of the point of intersection of the two lines
15 Find the co-ordinates of the point of intersection of the two lines. For Examiner′s Use 2x – 7y = 2 4x + 5y = 42 Answer (.............. , ..............) [3] _____________________________________________________________________________________
Mark scheme: 15 (8, 2) 3 M1 for correctly eliminating one variable A1 for x = 8 A1 for y = 2 If 0 scored, SC2 for correct substitution and correct evaluation to find the other value.
Question 16
16 Solve the inequality. x x - 2 + < 5 2 3 Answer ............................................... [4] _____________________________________________________________________________________
Mark scheme: 16 x <6.8 4 B3 for 6.8 with wrong inequality or equal as answer. Or M1 for first move completed correctly and M1 for second move completed correctly and M1 for third move completed correctly 11 5
Q17 · For Examiner′s 2 1 5 0 Use M = N = 4 6 1 5 f p f p (a) Work out MN
17 For Examiner′s 2 1 5 0 Use M = N = 4 6 1 5 f p f p (a) Work out MN. Answer(a) MN = [2] (b) Find M–1. Answer(b) M–1 = [2] _____________________________________________________________________________________
Mark scheme: 17 (a) 2 SC1 for one correct row or column 26 30 1 6 − 1 6 − 1 (b) oe 2 B1 for k 8 − 4 2 − 4 2 1 a b or B1 for 8 c d
Q18 · A (5, 23) and B (–2, 2) are two points
18 A (5, 23) and B (–2, 2) are two points. For Examiner′s Use (a) Find the co-ordinates of the midpoint of the line AB. Answer(a) (............ , ............) [2] (b) Find the equation of the line AB. Answer(b) ............................................... [3] (c) Show that the point (3, 17) lies on the line AB. Answer(c) [1] _____________________________________________________________________________________
Mark scheme: 18 (a) (1.5, 12.5) oe 2 B1 for either coordinate (b) y = 3x + 8 oe 3 B2 for y = mx + 8 or y = 3x + c or 3x + 8 or B1 for gradient (or m) = 3 and B1 for c = 8 If 0 scored, SC1 for 23 = their m × 5 + c or for 2 = their m × –2 + c or for 12.5 = their m × 1.5 + c (c) Most common methods: 1 Correctly substituting P (3, 17) into y = 3x + 8 Showing the gradient of AP or BP = 3 Other methods possible. IGCSE – October/November 2013 0580 22
Q19 · For Examiner′s C Use D B c O a E A F O is the origin
19 For Examiner′s C Use D B c O a E A F O is the origin. ABCDEF is a regular hexagon and O is the midpoint of AD. = a and = c. Find, in terms of a and c, in their simplest form (a) , Answer(a) = ............................................... [2] (b) , Answer(b) = ............................................... [2] (c) the position vector of E. Answer(c) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 19 (a) –2a – 2c oe 2 M1 for BO = –a – c or for any correct route or correct unsimplified expression (b) 2a + c 2 M1 for any correct route or correct unsimplified expression (c) –a – c oe 2FT FT their (a) or correct answer Or M1 for a correct non direct route from O to E or for correct unsimplified expression or for correct FT unsimplified
Q20 · During one day 48 people visited a museum
20 During one day 48 people visited a museum. For Examiner′s The length of time each person spent in the museum was recorded. Use The results are shown on the cumulative frequency diagram. 50 40 30 Cumulative frequency 20 10 0 1 2 3 4 5 6 Time (hours) Work out (a) the median, Answer(a) ............................................ h [1] (b) the 20th percentile, Answer(b) ............................................ h [2] (c) the inter-quartile range, Answer(c) ............................................ h [2] (d) the probability that a person chosen at random spends 2 hours or less in the museum. Answer(d) ............................................... [2] _____________________________________________________________________________________ Question 21 is printed on the next page.
Mark scheme: 20 (a) 4.05 to 4.2 1 (b) 2.6 to 2.75 2 B1 for 9.6 seen (c) 2.05 to 2.25 2 B1 for [UQ] 5.0 to 5.1 and [LQ] 2.85 to 2.95 seen 5 (d) 2 M1 for 5 48 4× sin 65
Q21 · For Examiner′s B Use NOT TO 6 cm 4 cm SCALE 65° C A In triangle ABC, AB = 6 cm, BC = 4 cm…
21 For Examiner′s B Use NOT TO 6 cm 4 cm SCALE 65° C A In triangle ABC, AB = 6 cm, BC = 4 cm and angle BCA = 65°. Calculate (a) angle CAB, Answer(a) Angle CAB = ............................................... [3] (b) the area of triangle ABC. Answer(b) ........................................ cm2 [3]
Mark scheme: 4× sin 65 21 (a) 37.2 or 37.17 to 37.19 3 M2 for sin[ ] = 6 4 6 or M1 for = oe sin[] sin 65 (b) 11.7 or 11.72 to 11.74 3 M1 for [B =] 160 – 65 – their (a) 1 M1 for × 4 × 6 × sin their 77.8 2
What was in this paper
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