* 5 9 3 6 5 8 7 8 5 0 * Cambridge International Examinations Cambridge Ordinary Level MATHEMATICS (SYLLABUS D) 4024/12 Paper 1 May/June 2016 Candidates answer on the Question Paper. Additional Materials: Geometrical instruments 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, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 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 80. 2 hours This document consists of 20 printed pages. DC (RW/AR) 115690/2 [Turn over
2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1 (a) Evaluate ^2. 05 + 1. 4h # 0. 2. (b) Evaluate 1 4 1 -. 3 5 2 (a) Complete this description. A rectangle has rotational symmetry of order Answer... [1] Answer [1] and lines of symmetry. [1] (b) Shade 4 more small squares in the shape below to make a pattern with rotational symmetry of order 4. [1]
3 3 It is given that 100 dollars ($) is equivalent to 56 pounds ( ). (a) Use this information to draw a conversion graph between pounds and dollars on the grid below. Pounds ( ) 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 180 200 (b) Use your graph to convert $64 to pounds. Dollars ($) [1] Answer... [1] [Turn over
4 4 Complete the table. Fraction Decimal Percentage 1 2 3 20... = 0.5 = 50% = =...... 5 The table shows some information about the temperatures in a city. =... = 62.5% Date Maximum temperature Minimum temperature 1 February 10 C T C 1 March 4 C 5 C (a) Find the difference between the maximum and minimum temperatures on 1 March. [2] Answer... C [1] (b) The minimum temperature, T C, on 1 February was 13 degrees lower than the minimum temperature on 1 March. Find T. Answer T =... [1]
5 6 (a) Express 96 as a product of its prime factors. (b) 24 is a common factor of 96 and the integer n. Given that n is less than 96, find the largest possible value of n. 7 The table shows information about some flights from Dubai to Mumbai. Answer... [1] Answer... [1] Departs Dubai (local time) 03 30 16 10 21 55 Arrives Mumbai (local time) 08 10 02 30 Flight duration 3 hours 10 minutes 2 hours 55 minutes 3 hours 5 minutes (a) Work out the time difference between Dubai and Mumbai. (b) Work out the local time in Mumbai when the 16 10 flight arrives. Answer... [1] Answer... [1] [Turn over
6 8 y is directly proportional to the square of x. When x = 10, y = 20. Find the value of y when x = 6. 9 50 students are asked what type of movie they like to watch. Of these students, 26 like comedy, 15 like both action and comedy and 8 like neither action nor comedy. Answer y =... [2] Using a Venn diagram, or otherwise, find the number of students who like action but not comedy. Answer... [2]
7 10 Solve the simultaneous equations. 11 Simplify (a) (b) 7 5x y 3 4 15x y 1 2-2, 4t c 4 m. v 6x + y = 1 4x - y = 4 Answer x =... y =... [2] Answer... [1] Answer... [1] [Turn over
8 12 The diagram below shows triangle ABC. B (a) On the diagram construct the locus of points inside the triangle that are (i) 3.5 cm from A, [1] (ii) equidistant from AC and BC. [1] (b) On the diagram, shade the region inside the triangle containing the points that are more than 3.5 cm from A and closer to AC than to BC. [1] A C
9 13 (a) Write these values in order of size, starting with the smallest. 2 5 5 2 1000 (b) Write down one possible value of x that satisfies each inequality. (i) (ii) 2 1 x 1 3 3-1 1 x 1 0 14 The coordinates of the midpoint of the line AB are (1, 2). The length of the line AB is 10 units. (a) If the gradient of AB is 0, find the coordinates of A and B. 3 27 0 (b) If the gradient of AB is 4 3, find the coordinates of A and B. Answer...,...,...,... [1] smallest Answer x =... [1] Answer x =... [1] Answer A = (...,...) B = (...,...) [1] Answer A = (...,...) B = (...,...) [2] [Turn over
10 15 The diagram shows the lines x + y = 8 and 2y = x + 4. y 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 x (a) The shaded region on the diagram is defined by three inequalities. Write down these three inequalities. Answer......... [2] (b) Another region, R, is defined by the inequalities x + y G 8, 2y G x + 4 and y H a, where a is an integer. This region contains 5 points with integer coordinates. Write down the value of a. Answer a =... [1]
11 16 Anil has some sweets with a mass of 600 g, correct to the nearest 10 grams. (a) Write down the lower bound of the mass of sweets. (b) Anil sells the sweets in small portions. Each portion has a mass of 25 g, correct to the nearest gram. He sells 10 portions of the sweets. Calculate the lower bound of the mass of sweets remaining. 17 In the diagram, the bearing of B from A is 170. The bearing of A from C is 060. The bearing of C from B is x. Answer... g [1] Answer... g [2] North C 060 Given that triangle ABC is isosceles, find the three possible values of x. North A 170 North Answer x =... or... or... [3] B x [Turn over
12 18 The diagram is the speed-time graph for part of a car s journey. Speed (m/s) 0 0 8 12 Time (t seconds) The retardation of the car between t = 8 and t = 12 is 4 m/s 2. (a) Find v. v (b) Find the total distance travelled by the car in the 12 seconds. Answer v =... [1] Answer... m [2]
13 19 P AB is a diameter of the circle, centre O. PA and QB are tangents to the circle at A and B respectively. Prove that triangle PAO is congruent to triangle QBO. Give a reason for each statement you make. A O............ [3] B Q [Turn over
14 20 A bag contains 10 counters of which 8 are blue and 2 are white. Two counters are taken from the bag at random without replacement. (a) Complete the tree diagram to show the possible outcomes and their probabilities. First counter 8 10... Blue White (b) Find, as a fraction, the probability that (i) both counters are blue, Second counter......... (ii) one counter is blue and the other is white. 7 9 White Blue Blue White [1] Answer... [1] Answer... [2]
15 21 (a) The table shows the values of the function f^xh for some values of x. (b) x 1 2 3 4 5 f^xh 5 7 9 11 13 Express the function f^xh in terms of x. (i) Evaluate g^-2h. (ii) Find - ^ x h. g 1 8 3x g ^xh = - 2 Answer f^xh =... [1] Answer... [1] Answer - ^ x h =... [2] g 1 [Turn over
16 22 The table shows the populations, correct to 2 significant figures, of some African countries in 2014. Country Nigeria Population Sudan 3.6 10 7 Chad 1.1 10 7 Namibia 2.2 10 6 (a) In 2014, the population of Nigeria was 177 156 000. Complete the table with the population of Nigeria using standard form, correct to 2 significant figures. [2] (b) Complete the following. The population of Chad was... times the population of Namibia. [1] (c) The population density of a country is measured as the number of people per square kilometre. It can be found by dividing the population of the country by its area in km 2. The area of Sudan is 1.86 10 6 square kilometres. Estimate the population density of Sudan. Give your answer correct to 1 significant figure. Answer...people / km 2 [2]
17 23 The table and histogram show some information about the times taken by a group of students to travel to school one day. Time (t minutes) 0 1 t G 10 10 1 t G 20 20 1 t G 30 30 1 t G 60 60 1 t G 120 Frequency 28 40 52 18 m Frequency density 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 110 120 Time (t minutes) (a) Complete the histogram. [2] (b) Find the value of m. Answer m =... [1] (c) Work out the fraction of students who took more than half an hour to travel to school. Answer... [2] [Turn over
18 24 3r a r The diagram shows a sector of a circle with radius 3r cm and angle a and a circle with radius r cm. The ratio of the area of the sector to the area of the circle with radius r cm is 8 : 1. (a) Find the value of a. (b) Find an expression, in terms of r and r, for the perimeter of the sector. Answer a =... [3] Answer... cm [2]
19 25 (a) The nth term of a sequence is given by n 2-5n. (i) Find the 2nd term in the sequence. (ii) The pth term in the sequence is 150. Find the value of p. (b) The nth term of another sequence is given by 3n 2 - kn. The 5th term in this sequence is 55. Find the value of k. Question 26 is printed on the next page Answer... [1] Answer p =... [2] Answer k =... [2] [Turn over
20 p + 3 26 (a) Make p the subject of the formula t =. p - 4 (b) Simplify fully 2 4x - 1 2. 2x - 9x - 5 Answer p =... [3] Answer... [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 www.cie.org.uk 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.
IGCSE is the registered trademark of Cambridge International Examinations. Cambridge International Examinations Cambridge Ordinary Level MATHEMATICS (SYLLABUS D) 4024/12 Paper 1 May/June 2016 MARK SCHEME Maximum Mark: 80 Published 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 2016 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. This document consists of 5 printed pages. [Turn over
Page 2 Mark Scheme Syllabus Paper Cambridge O Level May/June 2016 4024 12 Question Answers Mark Part marks 1 (a) 0.69 1 (b) 8 15 oe 1 2 (a) 2... 2 1 (b) 1 3 (a) Ruled straight line through (0, 0) and (100, 56) (b) 35 to 37 1 4 = 0.15 = 15[%] 5 8 = 0.625 = 5 (a) 9 1 (b) 18 1 6 (a) 2 5 3 1* (b) 72 1 7 (a) 1.5 [hours] or 90 [minutes] oe 1 (b) 20 35 1 1 2 C1 for two or three correct 8 7.2 or 36 5 oe 2* M1 for 20 = 20 102 k oe or = y oe 2 2 10 6 9 16 2* B1 for 15, 8 and 11 correctly placed and 26 not placed in Venn diagram or for x + 26 + 8 = 50 oe or for 50 26 8 oe leading to answer 10 x = 0.5 oe y = 2 11 (a) (b) 4 x 3y 2 v 2t 3 2* C1 for either x or y correct or for two values that fit one equation 1 1 Cambridge International Examinations 2016
Page 3 Mark Scheme Syllabus Paper Cambridge O Level May/June 2016 4024 12 Question Answers Mark Part marks 12 (a) (i) arc radius 3.5 cm, centre A 1 (ii) bisector of angle ACB 1 (b) Correct region shaded 1 13 (a) 27 0, 3 1000, 5 2, 2 5 1 (b) (i) any value in range 4 < x < 9 1 (ii) any value in range 1 < x < 0 1 14 (a) ( 4, 2) (6, 2) 1 Both correct (b) ( 3, 1) (5, 5) 2 C1 for one correct or for two x-values or two y-values correct or for both (4, 6) and ( 2, 2) 15 (a) x + y 8 oe 2y x + 4 oe x 0 (b) 3 1 16 (a) 595 1 2 C1 for two correct (b) 340 2* M1 for 10 25.5 soi 17 280, 295, 310 3* C2 for two correct values OR B2 for two from 70, 40 and 55 seen OR B1 for 70 seen or for 10 or 120 correctly positioned on diagram 18 (a) 16 1 (b) 160 or 10 their (a) 2ft* M1 for 0.5 their v (8 + 12) oe or 0.5 their v 4 + their v 8 oe Cambridge International Examinations 2016
Page 4 Mark Scheme Syllabus Paper Cambridge O Level May/June 2016 4024 12 Question Answers Mark Part marks 19 POA = QOB vertically opposite AO = OB equal radii PAO = QBO = 90 tangent perpendicular to radius 20 (a) (b) (i) (ii) 2 10, 2 9, 8 9, 1 correctly positioned 1 9 56 oe 1* 90 3* B1 for two pairs of equal angles: POA = QOB and PAO = QBO or for one pair of angles and pair of sides: POA = QOB or PAO = QBO and AO = OB AND B1 for a correct reason linked with a correct pair of angles / sides 32 90 oe 2ft* M1 for 8 2 + 2 8 10 9 10 9 ft their tree diagram with fractions < 1 21 (a) 2x + 3 oe 1 (b) (i) 7 1 (ii) 8 2x oe final answer 2* B1 for 3x = 8 2y or 3y = 8 2x 3 or 2x = 8 3y or 2y = 8 3x or 1.5x = 4 y or 1.5y = 4 x or 8 2 x 8 2y oe seen or oe 3 3 seen 22 (a) 1.8 10 8 cao 2 C1 for 1.7[ ] 10 8 or answer figs 18 (b) 5 1 (c) 20 cao 2* C1 for answer figs 2 or answer 18 OR B1 for 4 10 7 oe and 2 10 6 oe seen 23 (a) Two correct bars drawn 2 C1 for rectangle base 0 to 10 height 2.8 or for rectangle base 30 to 60 height 0.6 (b) 12 1 (c) 30 18 + m oe or oe evaluated 2ft* B1 FT for fraction with numerator or 150 138 + m denominator correct or for answer 20% or 0.2 Cambridge International Examinations 2016
Page 5 Mark Scheme Syllabus Paper Cambridge O Level May/June 2016 4024 12 Question Answers Mark Part marks 24 (a) 320 3* a 2 2 M2 for (3 ) 8 360 π r = π r oe OR a 2 M1 for (3 ) 360 π r oe seen or for 8π r 2 seen (b) 6r + 16 π r 16π r final answer 2* C1 for kr +, where k 0 3 3 OR their320 M1 FT for 2 π 3 r oe 360 their320 or for 6r+ nπ r oe 360 where n is a positive integer 25 (a) (i) 6 1 26 (a) (ii) 15 2* C1 for 15 2 5 15 or for 15, 10 OR M1 for (p + 10)(p 15) [= 0] (b) 4 2* B1 for 3 5 2 5k = 55 oe (b) 3+ 4t t 1 oe 3* 7 C2 for or 3 4 t t 1 t 1 OR M1 for t(p 4) = p + 3 or pt 4t = p + 3 AND M1 for isolating p terms after fraction eliminated e.g. pt p = 3 + 4t or p(t 1) = 3 + 4t 2x 1 final answer 3* B1 for (2x + 1)(2x 1) seen x 5 AND B1 for (2x + 1)(x 5) seen Cambridge International Examinations 2016