Cambridge IGCSE Mathematics (with coursework) 0581 — 2014 May/June Paper 2 · Variant 2

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 70. MATHEMATICS 0581/22 Paper 2 (Extended) May/June 2014 1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) This document consists of 12 printed pages. [Turn over IB14 06_0581_22/RP © UCLES 2014 *5382204847* Cambridge International Examinations Cambridge International General Certifi cate of Secondary Education PAPA CAMBRIDGE

2 0581/22/M/J/14 © UCLES 2014 1 Calculate 2 16 1.3 3 . Answer … [1] __________________________________________________________________________________________ 2 (a) Write 569 000 correct to 2 signifi cant fi gures. Answer(a) … [1] (b) Write 569 000 in standard form. Answer(b) … [1] __________________________________________________________________________________________ 3 Solve the simultaneous equations. 2x – y = 7 3x + y = 3 Answer x = … y = … [2] __________________________________________________________________________________________

3 0581/22/M/J/14 © UCLES 2014 [Turn over 4 C B A 8 cm 28° NOT TO SCALE Calculate the length of AB. Answer AB = … cm [2] __________________________________________________________________________________________ 5 l P NOT TO SCALE y x 0 The equation of the line l in the diagram is y = 5 – x . (a) The line cuts the y-axis at P. Write down the co-ordinates of P. Answer(a) (… , …) [1] (b) Write down the gradient of the line l. Answer(b) … [1] __________________________________________________________________________________________

4 0581/22/M/J/14 © UCLES 2014 6 The mass of 1 cm3 of copper is 8.5 grams, correct to 1 decimal place. Complete the statement about the total mass, T grams, of 12 cm3 of copper. Answer … Y T < … [2] __________________________________________________________________________________________ 7 Write the following in order, smallest fi rst. 0.1 201 43 2 2 1 % 0.2 Answer … < … < … < … [2] __________________________________________________________________________________________ 8 Without using your calculator, work out 6 5 – 2 2 1 1 1 # ` j. Write down all the steps of your working. Answer … [3] __________________________________________________________________________________________

5 0581/22/M/J/14 © UCLES 2014 [Turn over 9 At the beginning of July, Kim had a mass of 63 kg. At the end of July, his mass was 61 kg. Calculate the percentage loss in Kim’s mass. Answer … % [3] __________________________________________________________________________________________ 10 V = 3 1 Ah (a) Find V when A = 15 and h = 7 . Answer(a) V = … [1] (b) Make h the subject of the formula. Answer(b) h = … [2] __________________________________________________________________________________________

6 0581/22/M/J/14 © UCLES 2014 11 Anita buys a computer for $391 in a sale. The sale price is 15% less than the original price. Calculate the original price of the computer. Answer $ … [3] __________________________________________________________________________________________ 12 Solve the equation. 2 3 1 1 x x + + = 0 Answer x = … [3] __________________________________________________________________________________________

7 0581/22/M/J/14 © UCLES 2014 [Turn over 13 w varies inversely as the square root of x. When x = 4, w = 4. Find w when x = 25. Answer w = … [3] __________________________________________________________________________________________ 14 R O P Q M r p NOT TO SCALE OPQR is a trapezium with RQ parallel to OP and RQ = 2OP. O is the origin, = p and = r. M is the midpoint of PQ. Find, in terms of p and r, in its simplest form (a) , Answer(a) = … [1] (b) , the position vector of M. Answer(b) = … [2] __________________________________________________________________________________________

8 0581/22/M/J/14 © UCLES 2014 15 M = 4 3 2 5 e o Find (a) M2, Answer(a) [2] (b) the determinant of M. Answer(b) … [1] __________________________________________________________________________________________ 16 Factorise completely. (a) 4p2q – 6pq2 Answer(a) … [2] (b) u + 4t + ux + 4tx Answer(b) … [2] __________________________________________________________________________________________

9 0581/22/M/J/14 © UCLES 2014 [Turn over 17 (a) Simplify (3125t 125) 1 5. Answer(a) … [2] (b) Find the value of p when 3 p = 9 1 . Answer(b) p = … [1] (c) Find the value of w when x72 ÷ xw = x8. Answer(c) w = … [1] __________________________________________________________________________________________ 18 NOT TO SCALE The two containers are mathematically similar in shape. The larger container has a volume of 3456 cm3 and a surface area of 1024 cm2. The smaller container has a volume of 1458 cm3. Calculate the surface area of the smaller container. Answer … cm2 [4] __________________________________________________________________________________________

10 0581/22/M/J/14 © UCLES 2014 19 Simplify. 2 3 21 6 7 x x x + + - Answer … [4] __________________________________________________________________________________________ 20 32 25 18 11 4 These are the fi rst 5 terms of a sequence. Find (a) the 6th term, Answer(a) … [1] (b) the n th term, Answer(b) … [2] (c) which term is equal to –332. Answer(c) … [2] __________________________________________________________________________________________

11 0581/22/M/J/14 © UCLES 2014 [Turn over 21 P D C B A M 6 cm 4 cm 4 cm NOT TO SCALE The diagram shows a pyramid on a square base ABCD with diagonals, AC and BD, of length 8 cm. AC and BD meet at M and the vertex, P, of the pyramid is vertically above M. The sloping edges of the pyramid are of length 6 cm. Calculate (a) the perpendicular height, PM, of the pyramid, Answer(a) PM = … cm [3] (b) the angle between a sloping edge and the base of the pyramid. Answer(b) … [3] __________________________________________________________________________________________ Question 22 is printed on the next page.

12 0581/22/M/J/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 P Q k m n i j f g h (a) Use the information in the Venn diagram to complete the following. (i) P ∩ Q = {…} [1] (ii) P' ∪ Q = {…} [1] (iii) n(P ∪ Q)' = … [1] (b) A letter is chosen at random from the set Q. Find the probability that it is also in the set P. Answer(b) … [1] (c) On the Venn diagram shade the region P' ∩ Q. [1] (d) Use a set notation symbol to complete the statement. {f, g, h} … P [1]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2014 series 0581 MATHEMATICS 0581/22 Paper 2 (Extended), maximum raw mark 70 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 May/June 2014 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. PAPA CAMBRIDGE

Page 2 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 22 © 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 1.49 or 1.491… 1 2 (a) 570 000 1 (b) 5 10 69 .5 × 1 3 [x =] 2, [y =] – 3 2 B1 B1 or SC1 for reversed answers 4 7.06 or 7.063 to 7.064 2 M1 for [ ] 28 cos 8 = or better 5 (a) (0, 5) 1 (b) – 1 1 6 101.4, 102.6 2 M1 for 8.45 and 8.55 seen If 0 scored, SC1 for one correct value in correct position on answer line or for two correct reversed answers 7 2 2 1 %, 0.2, 201 43 , 1.0 2 B1 for 0.3… , 0.21… and 0.025 s een or for three in correct order 8 [ ]4 3 2 1 1 2 1 = × oe 2 6 2 5 × × and 3 4 3 3 × × oe or better 12 1 oe working must be shown B1 M1FT A1

Page 3 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 22 © Cambridge International Examinations 2014 9 3.17 or 3.174 to 3.175 3 M2 for 100 63 61 63 × − oe or 100 63 61 100 × − oe or M1 for 63 61 63− oe or 100 63 61× 10 (a) 35 1 (b) A V 3 or 1 3 − VA 2 M1 for multiplying by 3 or for dividing by 3 1 or M1 for dividing by A 11 460 3 M2 for ) 15 100 ( 100 391 − × oe or M1 for recognising 391 as (100 – 15)% soi 12 5 3 − oe 3 B2 for 5x + 3 = 0 oe or B1 for a numerator of ( ) [ ] 0 2 1 3 = + + x x seen 13 1.6 oe 3 M1 for x k w = A1 for k = 8 Alternative method: M2 for 4 4 25 = w oe 14 (a) p + r 1 (b) 2 3 p + 2 1 r 2 M1 for correct route from O to M or M1 for p + ½their(a) 15 (a)       31 27 18 22 2 B1 for any correct column or row (b) 14 1

Page 4 Mark Scheme Syllabus Paper IGCSE – May/June 2014 0581 22 © Cambridge International Examinations 2014 16 (a) ( ) q p pq 3 2 2 − 2 B1 for ( ) q p pq 6 4 − or ( ) pq p q 3 2 2 2 − or ( ) 2 3 2 2 q pq p − (b) ) 1 )( 4 ( x t u + + 2 B1 for ) 4 ( ) 4 (1 t u x t u + + + or ) 1( 4 ) 1( x t x u + + + 17 (a) 5t25 2 B1 for 5tk or mt25 (m ≠ 0) (b) –2 1 (c) 64 1 18 576 4 M1 for 3456 1458 or 1458 3456 M1 dep for 3 fraction their M1 for (their cube root )2 19 3 1 − x final answer 4 B2 for ) 7 )( 1 ( + − x x or SC1 for ) )( ( b x a x + + where ab = – 7 or a + b = 6 B1 for ) 7 ( 3 + x 20 (a) –3 1 (b) 39 – 7n oe 2 M1 for – 7n [+ k] (c) 53 2 M1 for their (b) = –332 shown provided their(b) is linear and their answer for (c) is a positive integer 21 (a) 4.47 or 4.472[…] 3 M2 for 2 2 4 6 − or M1 for [ ] 2 2 2 6 4 = + PM or 2 2 4 6 − (b) 48.2 or 48.18 to 48.19 3 M2 for cos[correct angle] 6 4 = oe or M1 for recognising a correct angle

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