Cambridge IGCSE Mathematics 0580 — 2002 Oct/Nov Paper 2 · Variant 1

This question paper consists of 11 printed pages and 1 blank page. SP (SLC/DG) S17440/2 © CIE 2002 [Turn over CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/2, 0581/2 PAPER 2 OCTOBER/NOVEMBER SESSION 2002 1 hour 30 minutes Candidates answer on the question paper. Additional materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) TIME 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown below that question. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. Candidate Centre Number Number Candidate Name FOR EXAMINER’S USE www.XtremePapers.com

2 0580/2/O/N/02 1 The table shows the maximum daily temperatures during one week in Punta Arenas. (a) By how many degrees did the maximum temperature change between Thursday and Friday? Answer (a) … [1] (b) What is the difference between the greatest and the least of these temperatures? Answer (b) … [1] 2 Nyali paid $62 for a bicycle. She sold it later for $46. What was her percentage loss? Answer …% [2] 3 Three sets A, B and K are such that A ⊂K, B ⊂K and A ∩B = Ø. Draw a Venn diagram to show this information. [2] 4 Alejandro goes to Europe for a holiday. He changes 500 pesos into euros at an exchange rate of 1 euro = 0.975 pesos. How much does he receive in euros? Give your answer correct to 2 decimal places. Answer …euros [2] 5 Write the four values in order, smallest first. , , 0.11%, 0.0108. Answer …………….. < ……….……. < …………… < …………… [2] 11 1000 1 1000 For Examiner’s Use Monday Tuesday Wednesday Thursday Friday Saturday Sunday 2°C 3°C 1°C 2.5°C –1.5°C 1°C 2°C

3 0580/2/O/N/02 [Turn over 6 Write 2x – as a single fraction. Answer … [2] 7 Find the exact value of (a) 3–2, Answer (a) … [1] (b)
1  . Answer (b) … [2] 8 The length of a road is 380m, correct to the nearest 10m. Maria runs along this road at an average speed of 3.9m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria. Answer … s [3] 1 2 7 9 10x 5 – x For Examiner’s Use

4 0580/2/O/N/02 9 (a) Draw a quadrilateral which has rotational symmetry of order 2 and whose diagonals are equal in length. [2] (b) Write down the special name of this quadrilateral. Answer (b) … [1] 10 For the numbers 8, 3, 5, 8, 7, 8 find (a) the mode, Answer (a) … [1] (b) the median, Answer (b) … [1] (c) the mean. Answer (c) … [1] 11 The radius of the Earth at the equator is approximately 6.4 × 106 metres. Calculate the circumference of the Earth at the equator. Give your answer in standard form, correct to 2 significant figures. Answer …m [3] For Examiner’s Use

5 0580/2/O/N/02 [Turn over 12 In the hexagon ABCDEF, BC is parallel to ED and DC is parallel to EF. Angle DEF = 109° and angle EFA = 95°. Angle FAB is equal to angle ABC. Find the size of (a) angle EDC, Answer (a) Angle EDC = … [1] (b) angle FAB. Answer (b) Angle FAB = … [2] NOT TO SCALE A B 95° 109° E D C F For Examiner’s Use

6 0580/2/O/N/02 13 Ameni is cycling at 4 metres per second. After 3.5 seconds she starts to decelerate and after a further 2.5 seconds she stops. The diagram shows the speed-time graph for Ameni. Calculate (a) the constant deceleration, Answer (a) …m/s2 [1] (b) the total distance travelled during the 6 seconds. Answer (b) …m [2] 1 2 3 4 6 5 t 1 2 3 4 0 v speed (m/s) time (s) For Examiner’s Use

7 0580/2/O/N/02 [Turn over 14 PQRS is a cyclic quadrilateral. The diagonals PR and QS intersect at X. Angle SPR = 21°, angle PRS = 80° and angle PXQ = 33°. Calculate (a) angle PQS, Answer (a) Angle PQS = … [1] (b) angle QPR, Answer (b) Angle QPR = … [1] (c) angle PSQ. Answer (c) Angle PSQ = … [1] 15 Solve the simultaneous equations 4x + 5y = 0, 8x – 15y = 5. Answer x = … y = … [4] NOT TO SCALE 21° P 33° 80° S R Q X For Examiner’s Use

8 0580/2/O/N/02 16 From a harbour, H, the bearing of a ship, S, is 312°. The ship is 3.5km from the harbour. (a) Draw a sketch to show this information. Label H, S, the length 3.5km and the angle 312°. [2] (b) Calculate how far north the ship is of the harbour. Answer (b) …km [2] 17 (a) On the grid, draw the lines x = 1, y = 2 and x + y = 5. [3] (b) Write R in the region where x
1, y
2 and x + y
5. [1] 1 2 3 4 6 5 x 1 2 3 4 5 6 0 y For Examiner’s Use

9 0580/2/O/N/02 [Turn over 18 Find, by using accurate constructions, the region inside the circle which contains the points more than 5 cm from G and nearer to H than to G. Shade this region. [4] 19 (a) Solve the inequality 5 – > + . Answer (a) x … [3] (b) List the positive integers which satisfy the inequality 5 – > + . Answer (b) … [1] x 4 1 2 2x 3 x 4 1 2 2x 3 H G For Examiner’s Use

10 0580/2/O/N/02 20 f: x →2x – 1 and g: x →x2 – 1. Find, in their simplest forms, (a) f–1(x), Answer (a) f–1(x) = … [2] (b) gf(x). Answer (b) gf(x) = … [2] 21 A =
 . (a) Find the 2 × 2 matrix P, such that A + P =
 , Answer (a) P =
 [2] (b) Find the 2 × 2 matrix Q, such that AQ =
. Answer (b) Q =
 [3] 1 0 0 1 0 0 0 0 2 –1 1 1 For Examiner’s Use

11 0580/2/O/N/02 22 In the circle, centre O, the chords KL and PQ are each of length 8cm. M is the mid-point of KL and R is the mid-point of PQ. OM = 3cm. (a) Calculate the length of OK. Answer (a) OK = …cm [2] (b) RM has a length of 5.5cm. Calculate angle ROM. Answer (b) Angle ROM = … [3] NOT TO SCALE P O R Q L K M 3cm 5.5cm 8cm 8cm For Examiner’s Use

CAMBRIDGE INTERNATIONAL EXAMINATIONS NOVEMBER 2002 INTERNATIONAL GCSE UNIVERSITY of CAMBRIDGE Local Examinations Syndicate

Page 1 Mark Scheme Syllabus Paper IGCSE Examinations — November 2002 0580; 0581 2 4 * indicates that it is necessary to look in the working following a wrong answer M1 for 16 = 100 or 100 — 46 x 100 62 62 B1 for A,B disjoint B1 for A,B subsets of K 512.82 cao M1 500 + 0.975 or 500 = 1.026 1_, 0.11%, 0.0108, _11 1000 1000 M1 for conversions into decimals, percentages, SIF or fractions with identical denominators = 2x 5-x (a) 1/9 (b) 1% M1 2x(5 — x) — 10x or better, brackets essential Allow 0.1recurring only M1 for 16/9 Allow 4/3 or 1.3 recurring only If no marks scored allow SC1 for 0.111 and 1.33 100 cao B1 for 385 or 3.85 seen M1 a distance + a speed oC] (b) rectangle (a) 8 (b) 7.5 (c) 6.5 B1 poor quality rectangle must be a quadrilateral M1 2x7*64x10° $C12.0 x10" 4.0 « 10*, 4.02 x10", 4 x10" score M1A1A0 B1 720 or M1 for %4(“their 720” - 313 —(a)) M1 A1 V for %4(407 — (a))

Page 2 Mark Scheme Syllabus_|_ Paper IGCSE Examinations — November 2002 0580; 0581 2 Allow - 1.6 M11 for attempting to find the area under the graph (a) 80° (b) 67° (c) 12° 147 —(a) 79 -(b) M1 multiplication M1 add or subtract A1 A1 or M1 rearrange M1 correct substitution x= 1/4 y=-1/5 -1 each item missing or wrong including the size of the angle (S and H interchanged is one error) M11 sin 42 = d/3.5 or cos 48 = d/3.5 B1 x=1 Bi y=2 B1 xty=5 B1 R correctly placed for their lines but BO if the line x + 5 = 5 is drawn with a positive gradient B1 arc radius 5cm + 1mm B1 perp. bisector, dep B1 with arcs, each correct by eye. B1 V shading for a line between G and H and the arc, with boundaries complete 19 | (a) x<4.91 M1 for 9/2 0e M1 for 11x/12 www can be implied by 4.9(1) or 54/11. or M1 multiples of 60 — 8x > 6 + 3x M1 11x < 54 (b) (0),1,2,3,4 if possible

Page 3 Mark Scheme Syllabus Paper IGCSE Examinations — November 2002 | 0580; 0581 2 (a) f= x44 2 (b) gf(x) = 4x?-4x oe M1 for (2x - 1)? -1 -1eeo or M1 for subtracting from zero matrix B1 for each diagonal of the adjoint matrix B1 for division by 3 or M1 for 2a—c=1 anda+c = 0 (or similar) A1 each column M1 for v(3? + 42) B1 for bisecting isosceles triangle M1 for sin x = 2.75/3 or M1 5.5? = 3? + 3? — 2x3x3cos A M1 cos A = - 12.(25)/18