Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 Oct/Nov Paper 1 · Variant 1

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fl uid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specifi ed in the question, and if the answer is not exact, give the answer to three signifi cant fi gures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. 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 56. MATHEMATICS 0581/11 Paper 1 (Core) October/November 2014 1 hour Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education This document consists of 12 printed pages. [Turn over IB14 11_0581_11/FP © UCLES 2014 *7397906241* PAPA CAMBRIDGE

2 0581/11/O/N/14 © UCLES 2014 1 y x 5 4 3 2 1 –1 –2 –3 –4 –5 0 –1 1 2 3 4 –2 –3 –4 –5 –6 A B Points A and B are shown on the grid. Write as a column vector. Answer f p [1] __________________________________________________________________________________________ 2 Write 15.0782 correct to (a) one decimal place, Answer(a) … [1] (b) the nearest 10. Answer(b) … [1] __________________________________________________________________________________________

3 0581/11/O/N/14 © UCLES 2014 [Turn over 3 Write down the letters in the word above that have (a) exactly one line of symmetry, Answer(a) … [1] (b) rotational symmetry of order 2. Answer(b) … [1] __________________________________________________________________________________________ 4 A B C 105° k° 98° NOT TO SCALE In the diagram, all four lines are straight. Angle A = 105°, angle B = 90° and angle C = 98°. Find the value of k. Answer k = … [2] __________________________________________________________________________________________

4 0581/11/O/N/14 © UCLES 2014 5 These are the heights, correct to the nearest centimetre, of 12 children. 132 114 151 130 132 145 163 142 153 170 132 125 Find the median height. Answer … cm [2] __________________________________________________________________________________________ 6 Write the following in order of size, smallest fi rst. π 3.14 7 22 3.142 3 Answer … < … < … < … < … [2] smallest __________________________________________________________________________________________ 7 Without using a calculator, work out 4 1 + 6 1 . Write down all the steps in your working and give your answer as a fraction in its simplest form. Answer … [2] __________________________________________________________________________________________

5 0581/11/O/N/14 © UCLES 2014 [Turn over 8 Factorise completely. 8w2x – 12wy Answer … [2] __________________________________________________________________________________________ 9 A cylinder has radius 3.6 cm and height 16 cm. Calculate the volume of the cylinder. Answer … cm3 [2] __________________________________________________________________________________________ 10 Cheryl recorded the midday temperatures in Seoul for one week in January. Day Mon Tue Wed Thu Fri Sat Sun Temperature (°C) –4 –5 –3 –11 –8 –3 –1 (a) Write down the mode. Answer(a) … °C [1] (b) On how many days was the temperature lower than the mode? Answer(b) … [1] __________________________________________________________________________________________

6 0581/11/O/N/14 © UCLES 2014 11 Simplify. 10x – 15 – 6x + 8 Answer … [2] __________________________________________________________________________________________ 12 (a) Write down a 2-digit odd number that is a factor of 182. Answer(a) … [1] (b) Find all the prime factors of 182. Answer(b) … [2] __________________________________________________________________________________________ 13 (a) Write 2.8 × 102 as an ordinary number. Answer(a) … [1] (b) Work out 2.5 × 108 × 2 × 10–2. Give your answer in standard form. Answer(b) … [2] __________________________________________________________________________________________

7 0581/11/O/N/14 © UCLES 2014 [Turn over 14 To hire a bicycle it costs $6 for each day, plus a fi xed charge of $15. (a) Maria pays $39 to hire a bicycle. How many days does she hire it for? Answer(a) … days [2] (b) Write down a formula for the cost, C dollars, to hire a bicycle for d days. Answer(b) C = … [1] __________________________________________________________________________________________ 15 140° NOT TO SCALE A B C The diagram shows two sides, AB and BC, of a regular polygon. Angle ABC = 140°. Find the number of sides of this regular polygon. Answer … [3] __________________________________________________________________________________________

8 0581/11/O/N/14 © UCLES 2014 16 O A B E C D x° y° 24° NOT TO SCALE The diagram shows a circle with centre O. ED is a tangent to the circle at C. AB is parallel to ED and angle ACO = 24°. Find the value of (a) x, Answer(a) x = … [1] (b) y. Answer(b) y = … [2] __________________________________________________________________________________________

9 0581/11/O/N/14 © UCLES 2014 [Turn over 17 Dominic invests $850 at a rate of 3.5% per year compound interest. Calculate the total amount he has after 3 years. Answer $ … [3] __________________________________________________________________________________________ 18 On a ship, the price of a gift is 24 euros (€) or $30. What is the difference in the price on a day when the exchange rate is €1 = $1.2378? Give your answer in dollars, correct to the nearest cent. Answer $ … [3] __________________________________________________________________________________________

10 0581/11/O/N/14 © UCLES 2014 19 4 cm 7 cm NOT TO SCALE The diagram shows a prism. The cross section is an equilateral triangle. On the grid, draw an accurate net of the prism. The base is drawn for you. [3] __________________________________________________________________________________________

11 0581/11/O/N/14 © UCLES 2014 [Turn over 20 Solve the simultaneous equations. 5x + 2y = 16 3x – 4y = 7 Answer x = … y = … [3] __________________________________________________________________________________________ 21 (a) Find the value of 5x2 when x = –4. Answer(a) … [2] (b) Make x the subject of the formula y = 5x2. Answer(b) x = … [2] __________________________________________________________________________________________ Question 22 is printed on the next page.

12 0581/11/O/N/14 © UCLES 2014 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the publisher will be pleased to make amends at the earliest possible opportunity. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 22 Q P 16 km 9 km North NOT TO SCALE The diagram shows the route of a ship that leaves a port, P. It travels due west for 16 km and then changes course to due south for 9 km. (a) Calculate the straight line distance PQ. Answer(a) PQ = … km [2] (b) Use trigonometry to calculate the bearing of P from Q. Answer(b) … [2]

® IGCSE is the registered trademark of Cambridge International Examinations. CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 2014 series 0581 MATHEMATICS 0581/11 Paper 1 (Core), maximum raw mark 56 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2014 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 11 © Cambridge International Examinations 2014 Abbreviations cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied Qu. Answers Mark Part Marks 1       −4 7 1 2 (a) (b) 15.1 cao 20 cao 1 1 3 (a) (b) E B A cao Z cao 1 1 4 113 2 M1 for 360 – (98 + 90 + 105) or better 5 137 2 M1 for attempt at ordering to at least 7th term or 132 and 142 indicated 6 3 3.14 π 3.142 7 22 2 B1 for 3.141[5...] to 3.1416 and 3.1428 to 3.1429 or 3.143 seen or SC1 for 4 in correct order 7 12 3 and 12 2 12 5 cao M1 A1 Equivalent denominators can be used, working must be shown. 8 ( ) y wx w 3 2 4 − Final answer 2 B1 for ( ) wy x w 3 2 4 2 − or ( ) y wx w 12 8 − or ( ) y wx w 6 4 2 − 9 651 to 652 2 M1 for π 16 6.3 2 × × or better 10 (a) (b) –3 4 1 1FT FT their numerical mode 11 4x – 7 Final answer 2 B1 for answer 4x + k or answer jx – 7 where 0 ≠ j or correct answer seen then spoilt

Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 11 © Cambridge International Examinations 2014 12 (a) (b) 91 or 13 2, 7 and 13 1 2 B1 for correct products of primes method or correct factor tree or ladder or 2 correct and 0 wrong or 3 correct and 1 extra 13 (a) (b) 280 6 10 5× 1 2 B1 for 5 000 000 oe or B1 for answer 6 10 × k or k 10 5× 14 (a) (b) 4 [days] [C=] 15 + 6d Final answer 2 1 M1 for ( ) 6 15 39 ÷ − or 6 6 6 6 15 + + + + 15 9 [sides] 3 M2 for ( ) 140 180 360 − ÷ or M1 for 140 180 − 16 (a) (b) 66 42 1 2FT FT their (a) – 24, only if their (a) > 24 or B1 for either of these, may be on diagram, angle OAC = 24 or angle BAC = their (a) 17 [$] 942.41 3 M2 for 3 035 .1 850× oe or M1 for 035 .1 035 .1 850 × × oe or SC2 for answer of interest only 18 0.29 cao 3 M2 for 2378 .1 24 30 × − or 30 2378 .1 24 − × or M1 for 2378 .1 24× 19 Correct ruled net drawn 3 B1 for rectangles, even if incorrect or not joined, drawn one on each side of the given one and two triangles opposite sides and B1 for 2 correct ruled rectangles and B1 for 2 correct ruled equilateral triangles 20 [x =] 3, [y =] 0.5 3 M1 for correct method to eliminate one variable A1 for [x =] 3 A1 for [y =] 0.5 If zero scored, SC1 for correct substitution and evaluation to find the other variable

Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE – October/November 2014 0581 11 © Cambridge International Examinations 2014 21 (a) (b) 80 [ ] 5 y ± or 5 y Final answer 2 2 M1 for ( )2 4 5 − × or 2 4 5× or better M1 for correct first step i.e. 2 5 x y = or x y 5 = or correct 2nd step after incorrect 1st step seen 22 (a) (b) 18.4 [0]60.4 to [0]60.73 2 2 M1 for [PQ2 =] 2 2 9 16 + or better M1 for [ ] 9 16 ... tan = or better or [ ] (a) their 16 ... sin = or better or [ ] (a) their 9 ... cos = or better If zero scored, SC1 for answer [0]29.3 to [0]29.4