Cambridge IGCSE Mathematics (US) 0444 — 2020 May/June Paper 3 · Variant 1

This document has 20 pages. Blank pages are indicated. DC (RW/FC) 190966/2 © UCLES 2020 [Turn over * 2 5 0 0 7 2 1 5 7 7 * Cambridge IGCSE™ MATHEMATICS (US) 0444/31 Paper 3 (Core) May/June 2020 2 hours You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, center number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a calculator where appropriate. ● You may use tracing paper. ● You must show all necessary work clearly. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ● For r, use either your calculator value or 3.142. INFORMATION ● The total mark for this paper is 104. ● The number of marks for each question or part question is shown in parentheses [ ].

2 0444/31/M/J/20 © UCLES 2020 Formula List Area, A, of triangle, base b, height h. A = 2 1 bh Area, A, of circle, radius r. A = rr2 Circumference, C, of circle, radius r. C = 2rr Lateral surface area, A, of cylinder of radius r, height h. A = 2rrh Surface area, A, of sphere of radius r. A = 4rr2 Volume, V, of prism, cross-sectional area A, length l. V = Al Volume, V, of cylinder of radius r, height h. V = rr2h Volume, V, of sphere of radius r. V = 3 4 rr3

3 0444/31/M/J/20 © UCLES 2020 [Turn over 1 The diagram shows a triangle with each side of length 5 cm. (a) Write down the mathematical name for this type of triangle. … [1] (b) (i) Measure the perpendicular height of the triangle. … cm [1] (ii) Calculate the area of the triangle. … cm2 [2] (iii) The triangle is the cross-section of a prism with length 6 cm. Calculate the volume of the prism. … cm3 [2]

4 0444/31/M/J/20 © UCLES 2020 2 Gabriela designs the seating layout for a new theater. There are three sections of seats, A, B, and C. (a) Section A has 152 seats. Section B has 12.5% more seats than Section A. Section C has 8 3 of the number of seats in Section A. (i) Show that the number of seats in Section B is 171. [1] (ii) Show that the total number of seats is 380. [2] (b) Write down and simplify the ratio of the number of seats in each section A : B : C. A : B : C = … : … : … [2] (c) In Section A: • There are 12 seats in the front row. • Each row has 2 more seats than the row in front of it. Work out the number of rows for the 152 seats in Section A. … rows [2]

5 0444/31/M/J/20 © UCLES 2020 [Turn over (d) For a concert in the theater, the ticket prices are in the ratio A : B : C = 9 : 7 : 4. A ticket for Section C costs $6. (i) Show that a ticket for Section B costs $10.50 . [1] (ii) Find the cost of a ticket for Section A. $ … [1] (iii) The table shows the number of tickets sold in each section. Section Number of tickets sold A 120 B 136 C 30 Calculate the total amount received from the ticket sales. $ … [3] (iv) The concert costs $4500 to organize. Calculate the amount received from the ticket sales as a percentage of the $4500. … % [1]

6 0444/31/M/J/20 © UCLES 2020 3 The grid shows a point E and four quadrilaterals, A, B, C, and D. y x 0 1 1 2 3 4 5 6 7 8 – 1 – 1 – 2 – 2 – 3 – 3 – 4 – 4 – 5 – 5 – 6 – 6 – 7 – 7 2 3 4 5 6 7 A E C B D (a) Write down the mathematical name of shape A. … [1]

7 0444/31/M/J/20 © UCLES 2020 [Turn over (b) Describe fully the single transformation that maps (i) shape A onto shape B, … … [2] (ii) shape A onto shape C, … … [2] (iii) shape A onto shape D. … … [3] (c) (i) Write down the coordinates of the point E. ( … , … ) [1] (ii) On the grid, draw the image of shape A after an enlargement by scale factor 3, center E. [2]

8 0444/31/M/J/20 © UCLES 2020 4 (a) Complete the table of values for y x x 7 2 2 = + - . x -2 -1 0 1 2 3 4 y -1 8 7 -1 [2] (b) On the grid, draw the graph of y x x 7 2 2 = + - for x 2 4 G G - . – 1 – 2 0 1 2 3 4 – 2 – 1 1 2 3 4 5 6 7 8 9 y x [4]

9 0444/31/M/J/20 © UCLES 2020 [Turn over (c) Write down the equation of the line of symmetry of the graph. … [1] (d) Use your graph to solve the equation x x 7 2 0 2 + - = . x = … or x = … [2]

10 0444/31/M/J/20 © UCLES 2020 5 (a) Using the integers from 60 to 75 only, find (i) a multiple of 17, … [1] (ii) the prime numbers. … [2] (b) Find (i) the square root of 4489, … [1] (ii) 43, … [1] (iii) 274 625 3 , … [1] (iv) 2 24 3 2 # - . … [1] (c) Write 0.0379 correct to 2 significant figures. … [1] (d) Find the least common multiple (LCM) of 8 and 14. … [2]

11 0444/31/M/J/20 © UCLES 2020 [Turn over (e) Write 479 000 000 in scientific notation. … [1] (f) George invests $8000 at a rate of 3.6% per year compound interest. Calculate the value of his investment at the end of 9 years. $ … [2]

12 0444/31/M/J/20 © UCLES 2020 6 11 cm 140° NOT TO SCALE C B H O F E A G D The diagram shows a circle, center O, radius 11 cm. C, F, G, and H are points on the circumference of the circle. The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle ABO = 140°. (a) Write down the mathematical name of the straight line AD. … [1] (b) (i) Calculate the circumference of the circle. … cm [2] (ii) Work out angle FOH. Angle FOH = … [2] (iii) Calculate the length of the minor arc FH. … cm [2]

13 0444/31/M/J/20 © UCLES 2020 [Turn over (c) (i) Give a reason why angle BCO is 90°. … [1] (ii) Show that BC = 13.11 cm, correct to 2 decimal places. [3] (iii) Calculate BH. BH = … cm [3]

14 0444/31/M/J/20 © UCLES 2020 7 (a) 20 students from College A each run 5 km. The times, correct to the nearest minute, are recorded. 32 51 25 40 47 21 37 32 48 36 46 39 30 29 44 39 53 35 40 31 (i) Find the median of the times. … min [1] (ii) Explain why mode is not a suitable measure of average in this case. … [1] (iii) Find the probability that a student, chosen at random, took less than 33 minutes. … [1] (iv) Complete the frequency table. Time (minutes) Frequency 20 to 29 3 30 to 39 40 to 49 50 to 59 [1] (v) Complete the bar chart for the times of the students. 0 20 to 29 30 to 39 40 to 49 Time (minutes) Number of students 50 to 59 1 2 3 4 5 6 7 8 9 10 [2]

15 0444/31/M/J/20 © UCLES 2020 [Turn over (b) 20 students from College B each run 5 km. Their times, correct to the nearest minute, are recorded and the results are shown in the table. Time (minutes) Number of students Pie chart sector angle 30 to 39 5 90° 40 to 49 8 50 to 59 7 (i) Complete the table. [2] (ii) Complete the pie chart. [2] (c) Write down two comments comparing the times of students from College A with the times of students from College B. 1 … … 2 … … [2]

16 0444/31/M/J/20 © UCLES 2020 8 (a) Simplify c d c d 3 5 2 - - + . … [2] (b) Solve the equation x 12 7 23 - = . x = … [2] (c) Expand. 9(3 - x) … [1] (d) ( ) A a b h 2 = + Work out the value of h when . A 38 64 = , . , a 5 5 = and . b 3 7 = . h = … [3]

17 0444/31/M/J/20 © UCLES 2020 [Turn over (e) Alphonse is x years old and Beatrice is y years old. Three times Alphonse’s age is equal to 5 times Beatrice’s age. Twice Beatrice’s age is 4 years more than Alphonse’s age. (i) Use this information to write down two equations in x and y. … … [2] (ii) Find the age of Alphonse and the age of Beatrice. Alphonse … years old Beatrice … years old [3]

18 0444/31/M/J/20 © UCLES 2020 9 (a) (i) Complete the mapping diagram for the function :f x x 4 1 " - . … x 0 0.5 1 -5 -1 … 3 x 4 1 - [2] (ii) Write down the domain of the function f. … [1] (b) 0 1 4 8 12 16 20 2 3 4 y x The diagram shows the graph of the function ( ) g y x = where ( ) g x x 2 2 = + for x 0 4 G G . Complete the range of ( ) g x . … g G G … [2]

19 0444/31/M/J/20 © UCLES 2020 [Turn over (c) -2 -1 -2 -1 1 2 3 4 5 1 0 2 3 4 5 6 x y The graph of ( ) h y x = is shown on the grid. On this grid, draw the graph of ( ) h y x 1 = - . [2] Question 10 is printed on the next page.

20 0444/31/M/J/20 © UCLES 2020 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 Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. 10 Point B is 36 km from point A on a bearing of 140°. (a) Using a scale of 1 centimeter to represent 4 kilometers, mark the position of B. North A Scale: 1 cm to 4 km [2] (b) (i) Point C is 28 km from A and 20 km from B. The bearing of C from A is less than 140°. Using a ruler and compasses only, construct triangle ABC. Show all your construction arcs. [3] (ii) Measure angle ACB. Angle ACB = … [1]

This document consists of 7 printed pages. © UCLES 2020 [Turn over Cambridge IGCSE™ MATHEMATICS (US) 0444/31 Paper 3 (Core) May/June 2020 MARK SCHEME Maximum Mark: 104 Published Students did not sit exam papers in the June 2020 series due to the Covid-19 global pandemic. This mark scheme is published to support teachers and students and should be read together with the question paper. It shows the requirements of the exam. The answer column of the mark scheme shows the proposed basis on which Examiners would award marks for this exam. Where appropriate, this column also provides the most likely acceptable alternative responses expected from students. Examiners usually review the mark scheme after they have seen student responses and update the mark scheme if appropriate. In the June series, Examiners were unable to consider the acceptability of alternative responses, as there were no student responses to consider. Mark schemes should usually be read together with the Principal Examiner Report for Teachers. However, because students did not sit exam papers, there is no Principal Examiner Report for Teachers for the June 2020 series. Cambridge International will not enter into discussions about these mark schemes. Cambridge International is publishing the mark schemes for the June 2020 series for most Cambridge IGCSE™ and Cambridge International A & AS Level components, and some Cambridge O Level components.

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 2 of 7 Generic Marking Principles These general marking principles must be applied by all examiners when marking candidate answers. They should be applied alongside the specific content of the mark scheme or generic level descriptors for a question. Each question paper and mark scheme will also comply with these marking principles. GENERIC MARKING PRINCIPLE 1: Marks must be awarded in line with: • the specific content of the mark scheme or the generic level descriptors for the question • the specific skills defined in the mark scheme or in the generic level descriptors for the question • the standard of response required by a candidate as exemplified by the standardisation scripts. GENERIC MARKING PRINCIPLE 2: Marks awarded are always whole marks (not half marks, or other fractions). GENERIC MARKING PRINCIPLE 3: Marks must be awarded positively: • marks are awarded for correct/valid answers, as defined in the mark scheme. However, credit is given for valid answers which go beyond the scope of the syllabus and mark scheme, referring to your Team Leader as appropriate • marks are awarded when candidates clearly demonstrate what they know and can do • marks are not deducted for errors • marks are not deducted for omissions • answers should only be judged on the quality of spelling, punctuation and grammar when these features are specifically assessed by the question as indicated by the mark scheme. The meaning, however, should be unambiguous. GENERIC MARKING PRINCIPLE 4: Rules must be applied consistently e.g. in situations where candidates have not followed instructions or in the application of generic level descriptors. GENERIC MARKING PRINCIPLE 5: Marks should be awarded using the full range of marks defined in the mark scheme for the question (however; the use of the full mark range may be limited according to the quality of the candidate responses seen). GENERIC MARKING PRINCIPLE 6: Marks awarded are based solely on the requirements as defined in the mark scheme. Marks should not be awarded with grade thresholds or grade descriptors in mind. Maths-Specific Marking Principles 1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required then no marks will be awarded for a scale drawing.

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 3 of 7 2 Unless specified in the question, answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the degree of accuracy is not affected. 3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points. 4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw). 5 Where a candidate has misread a number in the question and used that value consistently throughout, provided that number does not alter the difficulty or the method required, award all marks earned and deduct just 1 mark for the misread. 6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear.

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 4 of 7 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 Question Answer Marks Partial Marks 1(a) Equilateral 1 1(b)(i) 4.1 to 4.5 1 1(b)(ii) 10.25 to 11.25 2 FT their (b)(i) M1 for 0.5 × 5 × their (b)(i) 1(b)(iii) 61.5 to 67.5 2 FT their (b)(ii) M1 for their (b)(ii) × 6 2(a)(i) 112.5 ÷ 100 × 152 oe 1 2(a)(ii) 3 ÷ 8 × 152 + 152 + 171 2 B1 for 3 ÷ 8 × 152 2(b) 8 : 9 : 3 2 B1 for 152 : 171 : 57 2(c) 8 2 M1 for correct attempt e.g. 12 + 14 + 16 … 2(d)(i) 6 ÷ 4 × 7 1 2(d)(ii) 13.5[0] 1 2(d)(iii) 3228 3 FT their(d)(ii) M2 for 120 × their(d)(ii) + 136 × 10.5 + 30 × 6 or B1 for their 1620 or 1428 or 180 2(d)(iv) 71.7 or 71.7[3…] 1 FT their (d)(iii) 3(a) Kite 1 3(b)(i) Translation 4 9    2 B1 for each 3(b)(ii) Reflection x = 0.5 oe 2 B1 for each 3(b)(iii) Rotation 90˚ clockwise oe [centre] (0, 0) oe 3 B1 for each 3(c)(i) (−5, −6) 1

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 5 of 7 Question Answer Marks Partial Marks 3(c)(ii) Image at (−5, 0), (−2, 3), (7, 0),(−2, −3) 2 B1 for correct size, wrong position or correct shape and orientation with incorrect scale factor 4(a) 4 7 4 2 B1 for one correct 4(b) Correct curve 4 B3FT for 6 or 7 points correct or B2FT for 4 or 5 points correct or B1FT for 2 or 3 points correct 4(c) x = 1 oe 1 4(d) −1.9 to −1.7 and 3.7 to 3.9 2 B1 for each 5(a)(i) 68 1 5(a)(ii) 61, 67, 71, 73 2 B1 for 3 correct and none incorrect or 4 correct and one incorrect 5(b)(i) 67 1 5(b)(ii) 64 1 5(b)(iii) 65 1 5(b)(iv) 72 1 5(c) 0.038 cao 1 5(d) 56 2 B1 for 56k or lists of multiples of 8 and 14 (at least 3 of each) 5(e) 4.79 × 108 1 5(f) 11 000 or 10 998 or 10 998.35 to 10 998.36 2 M1 for 9 3.6 8000 1 100   +     6(a) Tangent 1 6(b)(i) 69.1 or 69.11 to 69.12... 2 M1 for 2 × 11 × π 6(b)(ii) 40 2 B1 for angle OBC = 40˚ or angle BOG = 140˚ 6(b)(iii) 7.68 or 7.679 to 7.680… 2 FT their (b)(ii) and (b)(i) M1 for 360 × their their (b)(ii) (b)(i) 6(c)(i) Angle [between] tangent [and] radius oe 1

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 6 of 7 Question Answer Marks Partial Marks 6(c)(ii) 180 – 140 or 90 – their(b)(ii) B1 tan (180 – 140) = 11 BC oe M1 [BC =] 13.109[…] [ = 13.11 correct to 2 dp] A1 6(c)(iii) 6.11 or 6.112 to 6.114 3 M1 for [OB2 =] 13.112 + 112 A1 for 17.1 or 17.11 or 17.112 to 17.114 OR M1 for 11 sin 40 or 11 cos50 or 13.11 sin50 or 13.11 cos40 oe A1 for 17.1 or 17.11… or 17.112 to 17.113 7(a)(i) 38 1 7(a)(ii) Correct explanation e.g. there is more than one mode 1 7(a)(iii) 7 20 1 7(a)(iv) 9 6 2 1 7(a)(v) Correct bar chart 2 FT their (a)(iv) B1 FT for two heights correct 7(b)(i) 144 126 2 B1 for each If 0 scored, M1 for 90 ÷ 5 or 360 ÷ 20 or 18 7(b)(ii) Correct pie chart 2 FT their (b)(i) angles if they total 270 B1 for one correct sector 7(c) 2 correct comments 2 B1 for one statistical comparison B1 for another comparison 8(a) 2c – 3d 2 B1 for 2c or −3d 8(b) [x =] 2.5 2 M1 for 12x = 23 + 7 or 7 23 12 12 − = x 8(c) 27 – 9x 1

0444/31 Cambridge IGCSE – Mark Scheme PUBLISHED May/June 2020 © UCLES 2020 Page 7 of 7 Question Answer Marks Partial Marks 8(d) [h =] 8.4 3 B2 for 38.64 = 4.6h or 77.28 = 9.2h or 2 38.64 5.5 3.7 × + oe or B1 for (5.5 3.7) 38.64 2 + = h oe or M1 for [h=] 2 + A a b 8(e)(i) 3x = 5y oe 2y = x + 4 oe 2 B1 for each 8(e)(ii) [x =] 20 [y =] 12 3 M1 for correctly eliminating one variable B1 for one correct 9(a)(i) −1 1 2 B1 for each 9(a)(ii) −1, 0, 0.5, 1 1 FT their(a)(i) 9(b) 2 18 2 B1 for each If zero scored, SC1 for 18 2 9(c) Correct graph 2 B1 for a horizontal translation through 0    k , k ≠ 1 10(a) Correct position of town B 2 B1 for correct bearing B1 for correct distance 10(b)(i) Correct triangle drawn 3 B2 for correct triangle with no or wrong arcs or correct position of C with arcs (no triangle) or C indicated as the point with bearing greater than 140° from A (with triangle) or B1 for one line correct length drawn or 7 and 5 seen or C indicated as the point with bearing greater than 140° from A (no triangle) 10(b)(ii) 94 to 98 1 FT their measured angle at C 1 2 3 4 5 1 2 3 4 0 x y