Cambridge IGCSE Mathematics (with coursework) 0581 — 2013 Oct/Nov Paper 3 · 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 104. MATHEMATICS 0581/32 Paper 3 (Core) October/November 2013 2 hours Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certifi cate of Secondary Education This document consists of 16 printed pages. [Turn over IB13 11_0581_32/FP © UCLES 2013 *0918791694* www.XtremePapers.com

2 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 1 B A C y x 8 7 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 –7 –8 0 –1 1 2 3 4 5 6 7 8 –2 –3 –4 –5 –6 Triangles A, B and C are shown on a 1 cm2 grid. (a) Write down the mathematical name for triangle A. Answer(a) … [1] (b) Complete the following statement. Triangles A, B and C are … triangles because they are the same shape and size. [1]

3 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use (c) Describe fully the single transformation that maps (i) triangle A onto triangle B, Answer(c)(i) … … [2] (ii) triangle A onto triangle C. Answer(c)(ii) … … [3] (d) Refl ect triangle A in the x-axis. Label the image P. [1] (e) Enlarge triangle A, scale factor 2, centre (0, 0). Label the image Q. [2] (f) Calculate the area of triangle Q. Answer(f) … cm2 [2] _____________________________________________________________________________________

4 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 2 Ravi sells cars. (a) He has a total of 144 cars for sale. (i) 64 of these cars are 3 or more years old. What fraction of the cars are less than 3 years old? Give your answer in its simplest form. Answer(a)(i) … [2] (ii) Some of the 144 cars use petrol, some use diesel and some are electric cars. The ratio of petrol to diesel to electric cars is 6 : 5 : 1 . Work out the number of these cars that use diesel. Answer(a)(ii) … [2] (b) Lola buys a car from Ravi. There are two ways she can pay for the car. Option 1: one payment of $5200 . Option 2: a payment of 5 2 of $5200 plus 24 monthly payments, each of $175 . Work out how much more Lola pays using Option 2 than Option 1. Answer(b) $ … [3] (c) For one week, Ravi reduces all his car prices by 15%. The price of a car was $3450. Show that the reduced price of the car is $2932.50 . Answer(c) [2] (d) Ravi buys a car for $2500 . He sells it for $3300 . Calculate his percentage profi t. Answer(d) … % [3] _____________________________________________________________________________________

5 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 3 (a) Sweets are sold in packets. There are n sweets in each packet. (i) Maya has 4 packets of sweets and 21 extra sweets. Write an expression, in terms of n, for the number of sweets Maya has. Answer(a)(i) … [1] (ii) Tassos has 5n + 3 sweets. Roma has 3n + 27 sweets. Tassos and Roma each have the same number of sweets. Write down an equation, in terms of n, and solve it. Answer(a)(ii) n = … [3] (iii) Work out the number of sweets Tassos and Roma have altogether. Answer(a)(iii) … [1] (b) A different packet of sweets contains 6 red sweets, 10 yellow sweets and 4 green sweets. Simon takes one sweet from the packet at random. (i) Write down the colour of sweet Simon is most likely to take. Answer(b)(i) … [1] (ii) On the probability scale, draw an arrow to show the probability that Simon’s sweet is yellow. 0 1 [1] (iii) Write down the probability that Simon’s sweet is green. Answer(b)(iii) … [1] (iv) Write down the probability that Simon’s sweet is red or yellow. Answer (b)(iv) … [1] _____________________________________________________________________________________

6 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 4 (a) North North A B Sea The scale drawing shows the position of two airfi elds, A and B. The scale is 1 cm represents 50 km. (i) Find the actual distance between A and B. Give your answer in kilometres. Answer(a)(i) … km [2] (ii) Measure the bearing of B from A. Answer(a)(ii) … [1] (iii) A third airfi eld, C, is 525 km from airfi eld A and 350 km from airfi eld B. On the scale drawing, construct the position of airfi eld C. [2] (iv) Measure the bearing of B from C. Answer(a)(iv) … [1]

7 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use (b) A plane is at airfi eld C at 10 40. It fl ies 525 km to airfi eld A at a speed of 700 km/h. Work out the time when the plane reaches airfi eld A. Answer(b) … [3] (c) This plane has a maximum take-off weight of 4173 kg. Write 4173 kg correct to the nearest hundred kilograms. Answer(c) … kg [1] (d) The plane can fl y at a maximum height of 13 107 m. Write 13 107 m in kilometres, correct to 3 signifi cant fi gures. Answer(d) … km [2] (e) In one week, the plane fl ies a total distance of 8520 km, correct to the nearest ten kilometres. Write down the lower bound of this distance. Answer(e) … km [1] _____________________________________________________________________________________

8 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 5 (a) Complete the table of values for y = x 5 . x –5 –4 –3 –2 –1 1 2 3 4 5 y –1.67 –2.5 –5 5 1.67 1.25 [2] (b) On the grid, draw the graph of y = x 5 for –5 Y x Y –1 and 1 Y x Y 5. y x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 0 –1 1 2 3 4 5 6 –2 –3 –4 –5 –6 [4] (c) Use your graph to solve the equation x 5 = 4 . Answer(c) x = … [1] (d) (i) On the grid, draw the line x = –3.5 . [1] (ii) On the grid, plot the point (5, –3) and label it P. [1] (iii) Draw the line that passes through P and is perpendicular to x = –3.5 . [1] _____________________________________________________________________________________

9 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use 6 (a) Here are three different sequences. Write the missing terms in the spaces provided. (i) 2, 8, 14, 20, … [1] (ii) 1, 4, 9, … , 25 [1] (iii) … , 12, 7, 2, … [2] (b) Here is the rule for fi nding the next term in another sequence. Double the previous term and subtract 1. The fi rst two terms in this sequence are 3 and 5. (i) Work out the next two terms in the sequence. Answer(b)(i) … , … [2] (ii) Complete the following statement. All the terms in this sequence are … numbers. [1] (c) Here is the start of a sequence of stick patterns. Pattern 1 8 sticks Pattern 2 13 sticks Pattern 3 18 sticks (i) Find the number of sticks in Pattern 4. Answer(c)(i) … [1] (ii) Write down an expression for the number of sticks in Pattern n. Answer(c)(ii) … [2] (iii) One pattern in the sequence has 98 sticks. Which pattern number is this? Answer(c)(iii) … [2] _____________________________________________________________________________________

10 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 7 12 people each solved the same puzzle. The table shows their ages and the time they each took to solve the puzzle. Age (years) 19 24 28 16 25 20 15 22 32 30 68 16 Time (seconds) 36 38 42 36 45 42 32 40 40 46 56 38 (a) Find the median age. Answer(a) … years [2] (b) For these 12 people, explain why the mean age may not be an appropriate average. Answer(b) … … [1] (c) Calculate the mean time taken. Answer(c) … seconds [2]

11 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use (d) (i) Complete the scatter diagram. The fi rst six points have been plotted for you. 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 Time (seconds) Age (years) [2] (ii) What type of correlation does the scatter diagram show? Answer(d)(ii) … [1] (iii) Draw a line of best fi t on the scatter diagram. [1] (iv) Would it be sensible to use your line of best fi t to estimate the time taken by a child aged 8 to solve the puzzle? Explain your answer. Answer(d)(iv) … because … … [1] _____________________________________________________________________________________

12 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 8 (a) Complete the table. Name of polygon Number of sides Quadrilateral 4 Heptagon 5 [2] (b) 55° 23° B C D E A NOT TO SCALE In the diagram, AB is parallel to EC and BCD is parallel to AE. Angle BAE = 55° and angle CED = 23°. (i) Complete the following statement. The mathematical name for quadrilateral ABDE is … . [1] (ii) Work out the size of angle ABC. Answer(b)(ii) Angle ABC = … [1] (iii) Work out the size of angle CDE. Answer(b)(iii) Angle CDE = … [2]

13 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use (c) 35° 52° NOT TO SCALE B C O A D Points A, B and C lie on a circle with centre O. DA is a tangent to the circle at A. Angle BAC = 35° and angle ADC = 52°. (i) Write down the size of angle ABC giving a reason for your answer. Answer(c)(i) Angle ABC = … because … … [2] (ii) Work out the size of angle BCA. Answer(c)(ii) Angle BCA = … [1] (iii) Work out the size of angle BCD. Answer(c)(iii) Angle BCD = … [3] _____________________________________________________________________________________

14 0581/32/O/N/13 © UCLES 2013 For Examiner′s Use 9 (a) The table shows some information about minimum and maximum temperatures in Moscow one January and February. Temperature January February Maximum –9°C 2°C Minimum –16°C (i) Find the difference between the maximum and minimum temperatures in January. Answer(a)(i) …°C [1] (ii) The difference between the maximum and minimum temperatures in February was 34°C. Find the minimum temperature in February. Answer(a)(ii) …°C [1] (iii) The minimum temperature in Moscow in December was 5°C higher than the minimum temperature in January. Work out the minimum temperature in December. Answer(a)(iii) …°C [1]

15 0581/32/O/N/13 © UCLES 2013 [Turn over For Examiner′s Use (b) The table shows the population of some cities in Russia. City Population Kaliningrad 4.30 × 105 Moscow Novosibirsk 1.40 × 106 Omsk 1.13 × 106 Saint Petersburg 4.58 × 106 (i) The population of Moscow is 10 500 000. Complete the table by writing the population of Moscow in standard form. [1] (ii) Write the population of Saint Petersburg as an ordinary number. Answer(b)(ii) … [1] (iii) Which city has the smallest population? Answer(b)(iii) … [1] (iv) Find the difference between the population of Novosibirsk and the population of Omsk. Give your answer in standard form. Answer(b)(iv) … [2] _____________________________________________________________________________________ Question 10 is printed on the next page.

16 0581/32/O/N/13 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. University of 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. © UCLES 2013 For Examiner′s Use 10 (a) Solve the equation. 6(x – 2) = 9 Answer(a) x = … [2] (b) Expand and simplify. 8(n – 1) – 2(3n + 5) Answer(b) … [2] (c) Factorise completely. 10p2 + 5p3 Answer(c) … [2]

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 2013 series 0581 MATHEMATICS 0581/32 Paper 3 (Core), maximum raw mark 104 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 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components. www.XtremePapers.com

Page 2 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 32 © Cambridge International Examinations 2013 Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working Question. Answers Mark Part Marks 1 (a) Scalene [triangle] (b) Congruent (c) (i) translation      − 2 6 (ii) rotation 180° [Centre] ( 0,0 ) (d) Image (1, –2), (4, –2), (2, –3) (e) Image (2, 4), (8, 4), (4, 6) (f) 6 1 1 1 1 1 1 1 1 2 2FT Accept 6 left and 2 up. SC1, 1, 1 for Enlargement, [SF=] –1,(0,0) B1 for 2 times enlargement, incorrect centre M1 for 0.5 × their base × their height

Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 32 © Cambridge International Examinations 2013 2 (a) (i) 9 5 (ii) 60 (b) 1080 (c) 0.85 × 3450 Or 3450 – 0.15 × 3450 (d) 32 2 2 3 2 3 B1 for 144 80 or better or 0.556 or 0.555… or answer 9 4 M1 for 144 ÷ (6+5+1) or 144÷12 M1 for 2 ÷ 5 × 5200 soi by 2080 And M1 for their 2080 + 24×175 – 5200 or better B1 for 0.85 or for 0.15 × 3450 M2 for 100 2500 2500 3300 × − oe or ( 2500 3300 – 1 ) × 100 oe Or B1 for 800 or 2500 2500 3300 − or 2500 3300 or 1.32 or 132 or 0.32 3 (a) (i) 4n + 21, final answer (ii) 5n + 3 = 3n + 27 [n =] 12 (iii) 126 (b) (i) yellow (ii) arrow pointing at 0.5 (iii) 20 4 o.e. or 0.2 or 20% (iv) 20 16 o.e. or 0.8 or 80% 1 1 2 1FT 1 1 1 1FT M1 for 5n – 3n = 27 – 3 or better SC1 for 4 out of 20 and 16 out of 20

Page 4 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 32 © Cambridge International Examinations 2013 4 (a) (i) 370 to 380 (ii) [0]36 to [0]40 (iii) Intersecting arcs: Arc centre A radius 10.5 cm Arc centre B radius 7 cm (iv) 300 to 310 (b) 11 25 (c) 4200 (d) 13.1 (e) 8515 2 1 2 1FT 3 1 2 1 B1 for 7.4 to 7.6 seen B1 for one correct arc or C correct with no arcs M2 for 525 ÷ 700 × 60 or better soi Or M1 for 525 ÷ 700 soi by 0.75 B1 for 13 100 or 13.107 or 13.100 Or B1FT their conversion to 4 or more sig figs seen and then correctly rounded to 3 sig figs 5 (a) –1 –1.25 2.5 1 (b) 10 correctly plotted points Two correct smooth curves through all correct points and not across y-axis (c) 1.15 to 1.35 (d) (i) Line x = –3.5 ruled (ii) (5, –3) plotted (iii) line y = –3 ruled 2 P3FT C1 1FT 1 1 1FT B1 for two correct P2FT for 8 or 9 correctly plotted P1FT for 6 or 7 correctly plotted

Page 5 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 32 © Cambridge International Examinations 2013 6 (a) (i) 26 (ii) 16 (iii) 17 –3 (b) (i) 9 17 (ii) odd (c) (i) 23 (ii) 5n + 3 oe final answer (iii) 19 1 1 2 2 1 1 2 2 B1 for each B1 for one correct in correct position or FT for fourth term B1 for 5n + k , jn + 3 j ≠ 0 Or 5n + 3 oe not as final answer M1FT for their (c)(ii) = 98 if linear soi 7 (a) 23 (b) [Affected by an] extreme value oe (c) 40.9 (d) (i) 6 points correctly plotted (ii) positive (iii) line of best fit ruled and continuous (iv) No, [estimate unreliable as] outside range [of data] 2 1 2 P2 1 1 1 M1 for clear attempt to find middle If zero scored then SC1 for 40 M1 for (36+38+42+36+45+42+32+40+40+46+56+38) ÷ 12 implied by 491 ÷ 12 If zero scored then SC1 for 26.25 or 26.3 P1 for 4 or 5 correctly plotted dep on at least 11 points on graph

Page 6 Mark Scheme Syllabus Paper IGCSE – October/November 2013 0581 32 © Cambridge International Examinations 2013 8 (a) 7 Pentagon (b) (i) trapezium (ii) 125° (iii) 32° (c) (i) 90° angle [in a] semicircle [=90°] (ii) 55° (iii) 93° 1 1 1 1 2 1 1 1 3 M1FT for 180 – 125 – 23 or better or 180 – their 125 – 23 or better M2 for 90 – 52 or 180 – 90 – 52 or 38 If M0 then B1 for angle CAD = 90° indicated 9 (a) (i) 7 (ii) –32 (iii) –11 (b) (i) 1.05 × 107 (ii) 4 580 000 (iii) Kaliningrad (iv) 2.7 × 105 1 1 1 1 1 1 2 Allow –7 B1 for figs 27 10 (a) 3.5 (b) 2n – 18 or 2 ( n – 9 ) final answer (c) 5p2(2 + p) final answer 2 2 2 M1 for 6x – 12 = 9 or better or x – 2 = 6 9 or better B1 for 8n – 8 or –6n –10 or 2n or –18 M1 for any correct incomplete factorisation or 5p2(2 + p) seen in working