Cambridge International Examinations Cambridge International General Certificate of Secondary Education

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1 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/11 Paper 1 (Core) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 11 printed pages and 1 blank page. DC (ST/FD) /2 [Turn over

2 1 Write, in figures, the number seventy thousand and twenty [1] 2 Write, as a decimal, the value of [1] 3 The thickness of one sheet of paper is 8 # 10-3 cm. Work out the thickness of 250 sheets of paper.... cm [1] 4 Simplify. (x 2 ) 5... [1] 5 A B opposite congruent reflected translated Choose the mathematical word from the list to complete this statement. Pentagon A is... to pentagon B. [1] 0580/11/M/J/17

3 From the list, write down a prime number.... [1] 7 Write correct to (a) 4 significant figures, (b) the nearest [1]... [1] 8 Factorise completely. 12n 2-4mn... [2] 9 Find the highest common factor (HCF) of 126 and [2] 0580/11/M/J/17 [Turn over

4 10 The table shows the temperatures in five places at 10 am one day in January. 4 Place Temperature ( C) Helsinki -7 Chicago -10 London 3 Moscow -4 Bangkok 26 (a) Which place was the coldest?... [1] (b) At 2 pm the temperature in Helsinki had increased by 4 C. Write down the temperature in Helsinki at 2 pm.... C [1] 11 Expand the brackets and simplify. 72 ( x+ 3y) -x( 14 - y)... [2] 12 The mass, m kilograms, of an elephant is 3570 kg, correct to the nearest 5 kg. Complete this statement about the value of m.... G m 1... [2] 0580/11/M/J/17

5 5 13 a 5 = c m b -1 3 = c - -4 m Write a + 2b as a single vector. f p [2] 14 Manuel changes 5000 Mexican Pesos to dollars. He receives $336. Complete this statement about the exchange rate. Give your answer correct to 2 decimal places. $1 =... Mexican Pesos [2] 15 Maria asks 50 students in her school when their birthday is. She records the information in the table. Jan to Mar Apr to Jun Jul to Sep Oct to Dec Number of birthdays (a) Find the relative frequency of a student having a birthday in April, May or June. (b) There are 750 students in the school. Estimate the number of students who have a birthday in April, May or June.... [1]... [1] 0580/11/M/J/17 [Turn over

6 16 Work out Write your answer as a fraction in its lowest terms [2] 17 A = 4rr 2 Make r the subject of this formula. r =... [2] 18 (a) Work out. 3+ 2# -4 (b) In each of these, insert one pair of brackets to make the statement correct.... [1] (i) 3 # = 23 [1] (ii) = 2 [1] 0580/11/M/J/17

7 7 19 Without using a calculator, work out Write down all the steps of your working and give your answer as a mixed number in its simplest form.... [3] 20 Solve the simultaneous equations. You must show all your working. 5x- 2y = 24 7x+ 4y = -14 x =... y =... [3] 0580/11/M/J/17 [Turn over

8 21 A cuboid has length 6 cm, width 5 cm and height 3 cm. On the 1 cm 2 grid, complete the net of the cuboid. The base is drawn for you. 8 [3] 0580/11/M/J/17

9 22 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test Mark Time (hours) (a) The data for two more students is shown in the table. Time (hours) Mark Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram?... [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student.... [1] 0580/11/M/J/17 [Turn over

10 10 23 B C A The diagram shows the positions of three points, A, B and C. (a) Using a ruler and compasses only, construct (i) the perpendicular bisector of the line AB, [2] (ii) the locus of all points that are 3 cm from C. [2] (b) Shade the region that is closer to A than to B and less than 3 cm from C. [1] 0580/11/M/J/17

11 11 24 The diagram shows a notice board. NOT TO SCALE 74 cm The board is in the shape of a semicircle joined to a square with side 74 cm. (a) Calculate (i) the perimeter of the board,... cm [3] (ii) the area of the board....cm 2 [3] (b) The board is a prism that is 5 cm thick. Calculate the volume of the board....cm 3 [1] 0580/11/M/J/17

12 12 BLANK PAGE 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/11/M/J/17

13 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/12 Paper 1 (Core) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 12 printed pages. DC (RW/JG) /2 [Turn over

14 2 1 Write correct to 2 significant figures.... [1] 2 The probability that Stephanie wins her next tennis match is Find the probability that Stephanie does not win her next tennis match.... [1] 3 Calculate [1] 4 Work out 85 cents as a percentage of $ % [1] 5 Change 6200 cm 2 into m m 2 [1] 6 Factorise. 14x- 21y... [1] 0580/12/M/J/17

15 3 7 The daily temperature, in C, at 3 pm in a town is shown below. Monday Tuesday Wednesday Thursday Friday Saturday Sunday (a) Which day had the coldest temperature? (b) Work out the difference in the temperatures on Friday and Saturday.... [1]... C [1] 8 Write these numbers in order of size, smallest first % [2] smallest 9 The shape above is a rhombus. Draw all the lines of symmetry on the shape. [2] 0580/12/M/J/17 [Turn over

16 4 10 (a) Write 0.03 as a percentage.... % [1] (b) Write 37% as a fraction.... [1] 11 Find the value of 5a- 3b when a = 7 and b = [2] 12 q p 70 NOT TO SCALE The diagram shows a straight line intersecting two parallel lines. Find the value of p and the value of q. p =... q =... [2] 13 Solve. 2- x = 5x+ 1 x =... [2] 0580/12/M/J/17

17 5 14 (a) Write in standard form.... [1] (b) Calculate 01. # 51. # 10 4, giving your answer in standard form.... [1] 15 The mass, m kilograms, of a cat is 2.7 kg, correct to 1 decimal place. Complete the statement about the value of m.... G m 1... [2] 16 4 cm 7 cm NOT TO SCALE x Calculate the value of x. x =... [2] 0580/12/M/J/17 [Turn over

18 y B A x Find the gradient of the line AB.... [2] 0580/12/M/J/17

19 cm A D NOT TO SCALE 5 cm B C E F 16.5 cm Triangles ABC and DEF are similar. Find the length of EF. EF =... cm [2] 19 The exchange rate between dollars and euros( ) is 1 = $ (a) Felicity changes 4900 into dollars. Work out how many dollars she receives. (b) Ricky changes $2895 into euros. Work out how many euros he receives. $... [1]... [2] 0580/12/M/J/17 [Turn over

20 8 20 B NOT TO SCALE C A 42 A, B and C are points on the circumference of a circle with diameter AB. A tangent is drawn at A. Find (a) angle BAC, (b) angle ABC. Angle BAC =... [1] Angle ABC =... [2] 0580/12/M/J/17

21 21 (a) Without using a calculator, work out Show all the steps of your working and give your answer as a fraction in its simplest form (b) Show that 4 # 1 = 7. Do not use a calculator and show all the steps of your working.... [2] [2] 0580/12/M/J/17 [Turn over

22 10 22 (a) Each diagram shows the net of a solid. Write down the mathematical name of each solid. (i)... [1] (ii)... [1] (b) The cross section of this prism is a trapezium. NOT TO SCALE 8 cm 5 cm 18 cm 14 cm Calculate the volume of the prism. 0580/12/M/J/17... cm 3 [3]

23 11 23 Pablo has $ to invest in one of these savings plans. Plan A pays compound interest at a rate of 4% per year. Plan B pays simple interest at a rate of 4% per year. Pablo invests the $ for 3 years. Calculate how much more he will receive from Plan A than from Plan B. Give your answer correct to 2 decimal places. $... [5] Question 24 is printed on the next page. 0580/12/M/J/17 [Turn over

24 24 (a) Work out the area of a circle with radius 6 cm cm 2 [2] (b) A solid cylinder has length 15 cm and radius 6 cm. 6 cm NOT TO SCALE 15 cm Calculate the total surface area of the cylinder.... cm 2 [4] 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/12/M/J/17

25 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/13 Paper 1 (Core) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 11 printed pages and 1 blank page. DC (ST/SW) /2 [Turn over

26 1 Change $400 into euros ( ) using the exchange rate $1 = [1] 2 B O C A A, B and C are points on the circumference of a circle, centre O. Write down the mathematical name for (a) the line OA,... [1] (b) the line BC.... [1] 3 Write 16% as (a) a decimal,... [1] (b) a fraction.... [1] 0580/13/M/J/17

27 3 4 Green Lane School ends each day at 3.45 pm. (a) Show this time on the clock [1] (b) Write 3.45 pm using the 24-hour clock.... [1] 5 (a) Write 5367 correct to the nearest hundred.... [1] (b) Write correct to 3 decimal places.... [1] 6 25 students chose their favourite drink. The results are listed below. Tea Hot chocolate Coffee Milkshake Tea Hot chocolate Coffee Hot chocolate Hot chocolate Milkshake Lemonade Tea Milkshake Milkshake Lemonade Coffee Hot chocolate Lemonade Tea Tea Hot chocolate Lemonade Hot chocolate Lemonade Lemonade Complete the frequency table for the results. You may use the tally column to help you. Favourite drink Tally Frequency Tea Coffee Lemonade Milkshake Hot chocolate [2] 0580/13/M/J/17 [Turn over

28 4 7 (a) Write down the next term in this sequence. 24, 22, 18, 12, 4, (b) The nth term of another sequence is 3n + 5. Write down the first three terms in this sequence.... [1]...,...,... [1] 8 Find the value of (a) 17 3, 3 (b) [1]... [1] 9 Factorise completely. 4x 2-8xy... [2] 10 Line l has the equation y = 4x - 6. (a) Write down the co-ordinates of the point where line l crosses the y-axis. (...,...) [1] (b) Write down the gradient of line l.... [1] 0580/13/M/J/17

29 11 Complete these calculations to make them correct. 5 (a) =... 4 [1] (b) = 2 [1] (c) # = [1] 12 The three angles in a triangle are 5x, 6x and 7x. 7x NOT TO SCALE 6x 5x (a) Find the value of x. x =... [2] (b) Work out the size of the largest angle in the triangle.... [1] 0580/13/M/J/17 [Turn over

30 (a) GH = c m -4 Find (i) 5 GH, f p [1] (ii) HG. f p [1] (b) c m+ c m= c m 7 y 3 Find the value of y. y =... [1] 14 These are the weights, in kilograms, of 10 babies (a) Find the range. (b) Calculate the mean.... kg [1]... kg [2] 0580/13/M/J/17

31 15 (a) Write down a prime number between 80 and [1] (b) Find the lowest common multiple (LCM) of 21 and [2] 16 (a) 5 x 25 = 5 6 Find the value of x. x =... [1] (b) Solve the simultaneous equations. You must show all your working. 2x+ 3y = 16-2x+ 5y = 24 x =... y =... [2] 0580/13/M/J/17 [Turn over

32 17 $600 is invested for 3 years at a rate of 2.5% per year compound interest. Calculate the total value of the investment at the end of the 3 years. 8 $... [3] Without using your calculator, work out c - m. 4 3 You must show all your working and give your answer as a fraction in its simplest form.... [4] 0580/13/M/J/17

33 19 A café owner records the number of hours of sunshine and the number of ice-creams sold for 10 days. The results are shown in the table. 9 Day Hours of sunshine Number of ice-creams sold Number of ice-creams sold Hours of sunshine (a) Complete the scatter diagram. The first 8 points have been plotted for you. [1] (b) What type of correlation is shown on the scatter diagram?... [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) The weather forecast predicts 7 hours of sunshine for tomorrow. Use your line of best fit to estimate the number of ice-creams that will be sold tomorrow.... [1] 0580/13/M/J/17 [Turn over

34 10 20 (a) A 6.3 m 6.3 m NOT TO SCALE B C Calculate the length BC. (b) D 52 cm 223 cm BC =... m [2] NOT TO SCALE E F Calculate angle DFE. Angle DFE =... [2] 0580/13/M/J/17

35 11 21 Simplify. (a) 6w 0... [1] (b) 5x 3 3x 3... [1] (c) 3y 6 # 5y [2] 0580/13/M/J/17

36 12 BLANK PAGE 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/13/M/J/17

37 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/21 Paper 2 (Extended) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 30 minutes 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 15 printed pages and 1 blank page. DC (ST/FC) /3 [Turn over

38 2 1 Simplify. (x 2 ) 5... [1] 2 The thickness of one sheet of paper is 8 # 10-3 cm. Work out the thickness of 250 sheets of paper.... cm [1] 3 Write correct to (a) 4 significant figures,... [1] (b) the nearest [1] 4 The table shows the temperatures in five places at 10 am one day in January. Place Temperature ( C) Helsinki -7 Chicago -10 London 3 Moscow -4 Bangkok 26 (a) Which place was the coldest?... [1] (b) At 2 pm the temperature in Helsinki had increased by 4 C. Write down the temperature in Helsinki at 2 pm.... C [1] 0580/21/M/J/17

39 3 5 Factorise completely. 12n 2-4mn... [2] 6 (a) 2 r 1 = 16 Find the value of r. r =... [1] t 5 (b) 3 = 3 Find the value of t. t =... [1] Without using a calculator, work out Write down all the steps of your working and give your answer as a mixed number in its simplest form.... [3] 0580/21/M/J/17 [Turn over

40 8 Simon has two boxes of cards. In one box, each card has one shape drawn on it that is either a triangle or a square. In the other box, each card is coloured either red or blue. Simon picks a card from each box at random. The probability of picking a triangle card is t. The probability of picking a red card is r. Complete the table for the cards that Simon picks, writing each probability in terms of r and t. 4 Event Probability Triangle and red Square and red (1 - t) r Triangle and blue Square and blue [3] 9 h is directly proportional to the square root of p. h = 5.4 when p = Find h when p = h =... [3] 0580/21/M/J/17

41 5 10 y x 1 By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities. y G 2 y H 1 y G 2x - 1 y G 5 - x [3] 11 The two barrels in the diagram are mathematically similar. h cm 90 cm NOT TO SCALE The smaller barrel has a height of h cm and a capacity of 100 litres. The larger barrel has a height of 90 cm and a capacity of 160 litres. Work out the value of h. h =... [3] 0580/21/M/J/17 [Turn over

42 6 12 A line has gradient 5. M and N are two points on this line. M is the point (x, 8) and N is the point (k, 23). Find an expression for x in terms of k. x =... [3] 13 A 5 cm E D 13 cm B F C NOT TO SCALE 4 cm H G The diagram shows a cuboid ABCDEFGH. AE = 5 cm, EH = 4 cm and AG = 13 cm. Calculate the angle between the line AG and the base EFGH of the cuboid.... [3] 0580/21/M/J/17

43 14 The diagram shows a regular octagon joined to an equilateral triangle. 7 NOT TO SCALE x Work out the value of x. x =... [3] 0580/21/M/J/17 [Turn over

44 15 The diagram shows information about the first 100 seconds of a car journey Speed (m/s) Time (s) (a) Calculate the acceleration during the first 20 seconds of the journey....m/s 2 [1] (b) Work out the total distance travelled by the car in the 100 seconds.... m [3] 0580/21/M/J/17

45 16 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test Mark Time (hours) (a) The data for two more students is shown in the table. Time (hours) Mark Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram?... [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student.... [1] 0580/21/M/J/17 [Turn over

46 17 (a) In this Venn diagram, shade the region F, Gl. 10 F G [1] (b) = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x: x is an odd number} B = {x: x is a square number} C = {x: x is a multiple of 3} (i) Write all the elements of in the Venn diagram below. A B C [2] (ii) Another number is included in the set. This number is in the region Al + B+ C. Write down a possible value for this number.... [1] 0580/21/M/J/17

47 11 18 The diagram shows a parallelogram OCEG. b B C D E H F NOT TO SCALE O a A G O is the origin, OA = a and OB = b. BHF and AHD are straight lines parallel to the sides of the parallelogram. OG = 3OA and OC = 2OB. (a) Write the vector HE in terms of a and b. HE =... [1] (b) Complete this statement. a + 2b is the position vector of point... [1] (c) Write down two vectors that can be written as 3a - b.... and... [2] 0580/21/M/J/17 [Turn over

48 12 19 ABCD is a rhombus with side length 10 cm. A 10 cm NOT TO SCALE D 40 B C Angle ADC = 40. DAC is a sector of a circle with centre D. BAC is a sector of a circle with centre B. Calculate the shaded area.... cm 2 [4] 0580/21/M/J/17

49 13 20 The diagram shows a fair spinner Anna spins it twice and adds the scores. (a) Complete the table for the total scores. Score on first spin Score on second spin [1] (b) Write down the most likely total score.... [1] (c) Find the probability that Anna scores (i) a total less than 6,... [2] (ii) a total of [1] 0580/21/M/J/17 [Turn over

50 21 (a) 14 D NOT TO SCALE A 35 v X C u B A, B, C and D are points on the circle. AD is parallel to BC. The chords AC and BD intersect at X. Find the value of u and the value of v. u =... v =... [3] (b) NOT TO SCALE 210 O p H F G F, G and H are points on the circle, centre O. Find the value of p. p =... [2] 0580/21/M/J/17

51 15 22 Write as a single fraction in its simplest form. (a) 2 x - 3x 2 x [3] (b) 3 2 x x [3] 0580/21/M/J/17

52 16 BLANK PAGE 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/21/M/J/17

53 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/22 Paper 2 (Extended) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 30 minutes 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 12 printed pages. DC (RW/JG) /2 [Turn over

54 2 1 Write correct to 2 significant figures.... [1] 2 The probability that Stephanie wins her next tennis match is Find the probability that Stephanie does not win her next tennis match.... [1] 3 Change 6200 cm 2 into m m 2 [1] 4 Calculate [1] 5 Work out 85 cents as a percentage of $ % [1] 6 Factorise. 14x- 21y... [1] 0580/22/M/J/17

55 7 Find the value of 5a- 3b when a = 7 and b = [2] 8 q p 70 NOT TO SCALE The diagram shows a straight line intersecting two parallel lines. Find the value of p and the value of q. p =... q =... [2] 9 Without using a calculator, work out Show all the steps of your working and give your answer as a fraction in its simplest form.... [2] 0580/22/M/J/17 [Turn over

56 4 10 Solve. 2- x = 5x+ 1 x =... [2] 11 (a) Write in standard form.... [1] (b) Calculate 01. # 51. # 10 4, giving your answer in standard form.... [1] 12 4 cm 7 cm NOT TO SCALE x Calculate the value of x. x =... [2] 0580/22/M/J/17

57 5 13 Solve the inequality. 3n n [2] 14 Work out. (a) (b) J N K O L 3 P [1]... [1] 15 Make q the subject of the formula p = 2q 2. q =... [2] 0580/22/M/J/17 [Turn over

58 6 16 B A C (a) Using a straight edge and compasses only, construct the bisector of angle BAC. [2] (b) Shade the region inside the triangle that is nearer to AC than to AB. [1] 17 C 8.15 m 30 B 110 NOT TO SCALE A Calculate AC. AC =... m [3] 0580/22/M/J/17

59 18 A rectangle has length 62 mm and width 47 mm, both correct to the nearest millimetre. The area of this rectangle is A mm 2. Complete the statement about the value of A G A 1... [3] 19 In a triangle PQR, PQ = 8 cm and QR = 7 cm. The area of this triangle is 17 cm 2. Calculate the two possible values of angle PQR. Angle PQR =... or... [3] 20 Write as a single fraction in its simplest form. 2x x [3] 0580/22/M/J/17 [Turn over

60 8 21 y is inversely proportional to 1 + x. When x = 8, y = 2. Find y when x = 15. y =... [3] 22 Factorise completely. (a) 9t 2 - u 2... [2] (b) 2c-4d- pc + 2pd... [2] 0580/22/M/J/17

61 9 23 (a) = {students in a class} P = {students who study physics} C = {students who study chemistry} The Venn diagram shows numbers of students. P C (i) Find the number of students who study physics or chemistry.... [1] (ii) Find n^pk Clh.... [1] (iii) A student who does not study chemistry is chosen at random. Find the probability that this student does not study physics.... [1] (b) On the Venn diagram below, shade the region Dj El. D E [1] 0580/22/M/J/17 [Turn over

62 10 24 C 4 cm D 2 cm 2.8 cm X NOT TO SCALE A 8 cm B In the diagram, AB and CD are parallel. AD and BC intersect at X. AB = 8 cm, CD = 4 cm, CX = 2 cm and DX = 2.8 cm. (a) Complete this mathematical statement. (b) Calculate AX. Triangle ABX is... to triangle DCX. [1] (c) The area of triangle ABX is y cm 2. Find the area of triangle DCX in terms of y. AX =... cm [2]... cm 2 [1] 0580/22/M/J/17

63 11 25 (a) Simplify. 3 ^16x 16 h4... [2] (b) 3 = 2p 2 54 Find the value of p. p =... [2] 26 D x C E 140 y w 95 A B F NOT TO SCALE A, B, C, D and E lie on the circle. AB is extended to F. Angle AED = 140 and angle CBF = 95. Find the values of w, x and y. w =... x =... y =... [5] Question 27 is printed on the next page. 0580/22/M/J/17 [Turn over

64 12 27 y B NOT TO SCALE A O x A is the point (-2, 0) and B is the point (0, 4). (a) Find the equation of the straight line joining A and B.... [3] (b) Find the equation of the perpendicular bisector of AB.... [4] 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/22/M/J/17

65 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/23 Paper 2 (Extended) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 1 hour 30 minutes 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 11 printed pages and 1 blank page. DC (ST/SW) /2 [Turn over

66 2 1 Calculate 1 ( 1 - cos 48 ) [1] 2 Factorise completely. 4x 2-8xy... [2] 3 Find the lowest common multiple (LCM) of 20 and [2] 4 Make a the subject of the formula. x = y+ a a =... [2] 5 Calculate the volume of a hemisphere with radius 3.2 cm. 4 [The volume, V, of a sphere with radius r is V = rr 3.] 3...cm 3 [2] 0580/23/M/J/17

67 3 6 The probability that Pedro scores a goal in any match is 5 2. Calculate the probability that Pedro scores a goal in each of the next two matches.... [2] 7 y is inversely proportional to x 2. When x = 2, y = 8. Find y in terms of x. y =... [2] 8 Simplify c 12m a... [2] 0580/23/M/J/17 [Turn over

68 4 6 9 (a) GH = c m -4 Find (i) 5 GH, f p [1] (ii) HG. f p [1] (b) c m+ c m= c m 7 y 3 Find the value of y. y =... [1] 10 The three angles in a triangle are 5x, 6x and 7x. 7x NOT TO SCALE 6x 5x (a) Find the value of x. x =... [2] (b) Work out the size of the largest angle in the triangle.... [1] 0580/23/M/J/17

69 5 11 y x By shading the unwanted regions of the grid above, find and label the region R that satisfies the following four inequalities. x H 0 x + y H 7 y H x x + 2y G 20 [3] 12 f(x) = 3 + 4x g(x) = 6x + 7 Find, in its simplest form, (a) f(3x),... [1] (b) fg(x).... [2] 0580/23/M/J/17 [Turn over

70 13 Two bottles and their labels are mathematically similar. The smaller bottle contains litres of water and has a label with area 96 cm 2. The larger bottle contains 1 litre of water. Calculate the area of the larger label. 6...cm 2 [3] 14 Write the recurring decimal 063. oo as a fraction in its lowest terms. You must show all your working.... [3] cm 39 cm NOT TO SCALE x 71.8 Find the value of x. x =... [3] 0580/23/M/J/17

71 7 16 (a) Solve the inequality. x+ 13 H 3x [2] (b) List the positive integers that satisfy the inequality in part (a).... [1] 17 p P Z NOT TO SCALE O q Q O is the origin, OP = p and OQ = q. Z is a point on PQ such that PZ : ZQ = 5 : 2. Work out, in terms of p and q, the position vector of Z. Give your answer in its simplest form.... [3] 0580/23/M/J/17 [Turn over

72 18 The diagram shows a speed-time graph for the journey of a car. 8 Speed (m/s) 12.5 NOT TO SCALE Time (s) Calculate the total distance travelled.... m [3] Without using your calculator, work out c - m. 4 3 You must show all your working and give your answer as a fraction in its simplest form.... [4] 0580/23/M/J/17

73 9 20 Simplify. (a) 6w 0... [1] (b) 5x 3 3x 3... [1] (c) 3y 6 # 5y [2] 21 Solve the equation 5x x+ 2 = 0. You must show all your working and give your answers correct to 2 decimal places. x =... or x =... [4] 0580/23/M/J/17 [Turn over

74 10 22 The diagram shows a cube ABCDEFGH of side length 26 cm. H G E F NOT TO SCALE D C A B Calculate the angle between AG and the base of the cube.... [4] 23 (a) Simplify. 4( x - 6) 2 ( x - 6)... [1] (b) Expand the brackets and simplify. 2 ( x+ 4) + 5( 3x+ 2)... [3] 0580/23/M/J/17

75 24 Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest. Jacques invests $2000 for 3 years at a rate of x% per year compound interest. At the end of the 3 years Marcel and Jacques receive the same amount of interest. 11 Calculate the value of x correct to 3 significant figures. x =... [5] 0580/23/M/J/17

76 12 BLANK PAGE 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/23/M/J/17

77 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/31 Paper 3 (Core) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 2 hours 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 16 printed pages. DC (LK/FD) /3 [Turn over

78 1 Camilla joins a soccer club. The total cost of joining is made up of membership, kit and travel. (a) The ratio membership : kit : travel = 3 : 5 : 6. The cost of membership is $78. (i) Show that the total cost of joining is $ [1] (ii) Calculate the cost of the kit and the cost of the travel. Kit = $... Travel = $... [3] 10 (b) Camilla s father pays of the $ Camilla pays the rest. Calculate how much she pays. $... [2] (c) Camilla s brother joins the soccer club. He receives a 12% discount on the $364 because he is younger than Camilla. Calculate the total cost of joining for him. $... [2] 0580/31/M/J/17

79 (d) During the year, Camilla s team played 24 matches. The table gives some information about the results of these matches. 3 Played Won Drawn Lost 24 W 6 L (i) Write down an equation, in terms of W and L, for the number of matches played.... [1] (ii) Points are given when a team wins or draws a match. The points are Match won 3 points Match drawn 1 point Match lost 0 points. The team has a total of 54 points. Write down an equation, in terms of W, for the total points given. (iii) Work out the value of W and the value of L.... [1] W =... L =... [3] 0580/31/M/J/17 [Turn over

80 4 2 y A x B 8 10 (a) Write down the mathematical name of the shaded polygon.... [1] 0580/31/M/J/17

81 5 (b) Describe fully the single transformation that maps the shaded polygon onto polygon A [3] (c) Describe fully the single transformation that maps the shaded polygon onto polygon B [2] (d) On the grid, draw the reflection of the shaded polygon in the line x = 2. [2] (e) On the grid, draw the rotation of the shaded polygon through 90 anti-clockwise about the origin. [2] 0580/31/M/J/17 [Turn over

82 3 Francis asks 30 families how many children they have. The table shows the results. 6 Number of children in each family Number of families (a) (i) Write down the mode.... [1] (ii) Find the median.... [1] (iii) Calculate the mean.... [3] (iv) Complete the bar chart, including the vertical scale. Number of families Number of children in each family 0580/31/M/J/17 [3]

83 (b) Francis also recorded the age group and gender of the children aged 12 or less. The information is shown in the table. 7 Age 4 and younger Age 5 to 8 Age 9 to 12 Total Male 9 Female Total Complete the table. [2] (c) Francis displays the results for the totals of each age group on a pie chart. The sector angle for the group Age 4 and younger is 120. Calculate the sector angle for (i) age 5 to 8, (ii) age 9 to [2]... [1] (d) Complete the pie chart. Age 4 and younger [1] 0580/31/M/J/17 [Turn over

84 8 4 (a) NOT TO SCALE D O A cm B C The diagram shows a circle, centre O, with points B and D on the circumference. The line AC touches the circle at B. OB is parallel to DC and angle OAB = 49. (i) Write down the mathematical name of the line OB.... [1] (ii) Write down the reason why angle ABO is [1] (iii) Find angle AOB. Angle AOB =... [1] (iv) Write down the reason why angle ADC = angle AOB.... [1] (v) Complete the statement using a mathematical word. Triangle AOB is... to triangle ADC. [1] 0580/31/M/J/17

85 9 (vi) AB = 5.4 cm Calculate (a) OB, OB =... cm [2] (b) OA, OA =... cm [2] (c) the area of triangle AOB....cm 2 [2] (b) Here is a polygon with 7 sides. Show that the sum of the interior angles of this polygon is /31/M/J/17 [1] [Turn over

86 10 5 (a) Complete the table of values for y = x + 2x x y [3] (b) On the grid, draw the graph of y = x + 2x - 1for - 5 G x G 3. 2 y x /31/M/J/17 4 [4]

87 11 (c) (i) On the grid, draw the line of symmetry. [1] (ii) Write down the equation of the line of symmetry.... [1] (d) (i) On the grid, plot the points (- 5, 7) and ( 0, - 3) and join them with a straight line, L. [2] (ii) Write down the x co-ordinate of each point where the line L crosses the graph of y = x + 2x (iii) Work out the gradient of the line L. x =... and x =... [2]... [2] 0580/31/M/J/17 [Turn over

88 6 Eduardo goes to the Theatre. He leaves his house at twenty-five minutes to six in the evening. (a) Write down this time using the 24-hour clock [1] (b) He travels to the Theatre by bus. Part of the timetable is shown below. Belmont Road Railway Station Leisure Centre Theatre Bus Station It takes Eduardo 16 minutes to walk to the Railway Station from his house. (i) Find the time he arrives at the Railway Station.... [1] (ii) He gets on the next bus to the Theatre. Find the time he arrives at the Theatre.... [1] (iii) The bus from Belmont Road takes the least time to travel to the Bus Station. Work out how many minutes quicker this journey is than the journey on the bus....min [2] (iv) The distance from Belmont Road to the Bus Station is 8.5 km. Calculate the average speed for the bus leaving Belmont Road at Give your answer in kilometres per hour, correct to 1 decimal place....km/h [4] 0580/31/M/J/17

89 7 Here is a sequence of diagrams made using identical rectangles. A dot is shown at the junction of three lines. A cross is shown at the junction of two lines. 13 x x x x x x x x x x x x x x x x x x x x x x x Diagram 1 Diagram 2 Diagram 3 Diagram 4 x (a) Write down the order of rotational symmetry of Diagram [1] (b) Complete Diagram 4 using dots and crosses. [1] (c) Complete the table for Diagram 4 and Diagram 5. Diagram Number of dots Number of crosses [3] (d) (i) Describe, in words, the rule for continuing the sequence for the number of dots.... [1] (ii) The expression for the number of dots in Diagram n is n 2 + n- 2. Find the number of dots in Diagram [2] (e) (i) Write down an expression for the number of crosses in Diagram n.... [2] (ii) Diagram n has 100 crosses. Find the value of n. 0580/31/M/J/17 n =... [2] [Turn over

90 8 The scale drawing shows the positions of Bogota (B) and Quito (Q). The scale is 1 centimetre represents 150 kilometres. North 14 North B Scale: 1 cm to 150 km Q (a) (i) Measure the length of the line BQ.... cm [1] (ii) Work out the actual distance from Bogota to Quito.... km [1] (iii) Measure the bearing of Quito from Bogota.... [1] (b) A plane leaves Quito and flies straight to Manaus. Manaus is 2100 km on a bearing of 100 from Quito. On the scale drawing, mark the position of Manaus (M). [3] 0580/31/M/J/17

91 (c) The plane flies the 2100 km from Quito to Manaus at an average speed of 550 km/h. Calculate the time taken for this flight 15 (i) in hours, correct to 3 significant figures,... h [2] (ii) in hours and minutes, correct to the nearest minute.... h... min [1] Question 9 is printed on the next page. 0580/31/M/J/17 [Turn over

92 9 Francesca owns a business. One year she has a total of $6000 to spend on rent, furniture and office equipment. 16 (a) (i) The rent is $400 per month. Work out how much Francesca spends on rent in this year. $... [1] (ii) Desks cost $58.50 each and chairs cost $15 each. Francesca buys 2 desks and 5 chairs. Work out how much Francesca spends on furniture. $... [2] (iii) Francesca also spends $800 on office equipment. Work out how much remains of the $6000. $... [2] (iv) She spends this remaining amount on boxes of paper. Paper costs $4.95 per box. Work out how many boxes she buys.... boxes [2] (b) Francesca needs to buy computer equipment. She borrows $2000 from a bank for 3 years at a rate of 5% per year compound interest. Calculate the total amount she pays back at the end of the 3 years. $... [3] 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. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at after the live examination series. 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. 0580/31/M/J/17

93 Cambridge International Examinations Cambridge International General Certificate of Secondary Education * * MATHEMATICS 0580/32 Paper 3 (Core) May/June 2017 Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional) 2 hours 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 fluid. 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 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 r, use either your calculator value or 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. This document consists of 15 printed pages and 1 blank page. DC (RW/SW) /2 [Turn over

94 2 1 Here is part of the menu in a café. Item Price Tea... $2.40 Coffee... $2.80 Fruit juice... $1.85 Pizza... $4.15 Vegetable pasty... $3.60 Chicken curry... $5.20 Ice cream... $2.80 Cake... $3.25 Yoghurt... $1.40 (a) Jenna buys 3 coffees and 2 cakes. Work out how much she spends altogether. $... [3] (b) Find the maximum number of pizzas Harry can buy for $20. Work out the change he receives from a $20 note. (c) Priti s meal costs $7.60. She gives the waitress 15% extra for service. Work out the total amount she pays. Number of pizzas =... Change = $... [3] (d) Elena and Maria are waitresses in the café. One day they receive $96 for service. They share the $96 in the ratio Elena : Maria = 3 : 1. Work out how much Elena receives. $... [2] $... [2] 0580/32/M/J/17

95 3 (e) The café s opening hours are shown below. Day Opening hours Monday CLOSED Tuesday to 1500 and 1700 to 2200 Wednesday to 1500 and 1700 to 2200 Thursday to 1500 and 1700 to 2200 Friday to 1500 and 1700 to 2200 Saturday 1030 to 2300 Sunday 0930 to 2100 (i) Find the number of hours the café is open during one week.... hours [2] (ii) During opening hours the café needs 3 people on duty. Each person works 36 hours in a week. Find the number of people the café needs in a week.... [3] (f) The café owner pays rent. The monthly rent is $6.40 for each square metre of floor area. The floor area is 72.5 m 2. Calculate the total rent the café owner pays in one year. $... [3] 0580/32/M/J/17 [Turn over

96 4 2 (a) Simplify. 5a+ 6a-a... [1] (b) 5f + 2g 3f 4g NOT TO SCALE Write an expression for the perimeter of the rectangle. Give your answer in its simplest form.... [3] (c) (i) Work out the value of 5x+ 10y when x = 7 and y = [2] (ii) Work out the value of 4r 2 - pr when p = 3 and r = [2] (d) Solve. 53 ^ x - 6h = 75 x =... [3] 0580/32/M/J/17