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EM-2018-AHS-SA2-P1 Name ____________ _______________________ ( ) Class 4 _______ MATHEMATICS 4048/01 Paper 1 Monday 10 September 2018 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name and index numbe r on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil fo r any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any questi on it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not s pecified in the question, and if the answer is not exa ct, give the answer to three significant figures. Gi ve answers in degrees to one d ecimal place. For  , use either your calculator value or 3.142, unless the questio n requires the answer in terms of  . At the end of the examination, fa sten all your work securely to gether. The number of marks is given in brackets [ ] at the end of eac h question or part question. The total of the marks for this paper is 80 . This question paper consis ts of 17 printed pages. Table of Penalties Qn. No. Presentation – 1 Units –1 Significant Figures –1 Parent’s/ Guardian’s Name/ Signature/ Date Question 1 2 3 4 5 6 7 8 9 10 Marks Question 11 12 13 14 15 16 17 18 19 20 Marks For Examiner’s Use S4 ANGLICAN HIGH SCHOOL PRELIMINARY EXAMINATION 2018 SECONDARY FOUR 80 [Turn over

EM-2018-AHS-SA2-P1 Mathematical Formulae Compound Interest Total amount = n r P        100 1 Mensuration Curved surface area of a cone = rl  Surface area of a sphere = 2 4 r  Volume of a cone = h r 2 3 1  Volume of a sphere = 3 3 4 r  Area of triangle ABC = ab 2 1 C sin Arc length =  r , where  is in radians Sector area =  2 2 1 r , where  is in radians Trigonometry C c B b A a sin sin sin   bc c b a 2 2 2 2    A cos Statistics Mean = f fx   Standard deviation = 2 2              f fx f fx

EM-2018-AHS-SA2-P1 Answer all the questions. 1 One solution of 221 2 0xk x is 4x . Find (a) the value of k, Answer k = ……….….………….. [1] (b) the other solution of the equation. Answer ….………….…………… [1] 2 Adapted from https://www.youtube.com/watch?v=ETbc8GIhfHo. State one aspect of the above graph that may be misleading and explain how this may lead to a m i s i n t e r p r e t a t i o n o f t h e g r a p h . Answer ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………….. [2] Average Ticket Prices (Sports Events) Ticket Price ($) Sports [Turn over

EM-2018-AHS-SA2-P1 3 (a) Express 5 121 in index form with base 11. Answer …...…….…..…………… [1] (b) Evaluate 21 33 32 4  without using a calculator. Answer …......…….…..……… [2] (c) Simplify 2 2 ab a      Answer ….…….………………… [1] 4 (a) Solve the inequality 17 8 4 3 1 25 42 3 xx      . Answer ….…….………………… [2] (b) Hence , state the smallest prime number that satisfies the inequality . Answer ….…….………………… [1]

EM-2018-AHS-SA2-P1 5 It is given that 3 2bca cb   . (a) Express b in terms of a and c. Answer ….…….………………… [2] (b) Find the value of b when a = 2 and c = 5 . Answer b = …………....………… [1] 6 (a) Simplify   253 5 35 3x x . Answer ….…….………………… [2] (b) Factorise completely 225 5 1y xy x   . Answer ….…….………………… [2] [Turn over

EM-2018-AHS-SA2-P1 7 (a) It is given that  = { x : x is an integer between 0 and 9 inclusive} A   and B      0, 2 ' A B  , 7 A B  ,       1, 4, 5, 8 ' A BB   and  3, 6, 9 A B  Draw a Venn diagram to represe nt the information given. [3] Answer (b) List down all the proper subsets of the set   ,, abc . Answer ………………………………………………………………….… [1]

EM-2018-AHS-SA2-P1 8 In the diagram below, not drawn to scale, A is the point (1, 2), B is the point (p, 2) and C is the point (0, 12). (a) Find the length of the line AC. Answer …….……………….units [2] (b) Write down the value of cos BAC . Answer …………..……………… [1] (c) Given that the length of the line BC is 55 units, find the value of p. Answer p = …………..…..……… [2] A(1, 2) C(0, 12) 0  x  y  B(p, 2) [Turn over

EM-2018-AHS-SA2-P1 9 (a) Mr Tan wants to change $4 000 Si ngapore dollars to US dollars for a holiday trip to the USA. The exchange rate in Singa pore is 1 SGD = 0.736 USD. The exchange rate in USA is 1 USD = 1.352 SGD. In which country should he change his money and how much more U SD can he get? Answer ………………………………………………………………………… [2] (b) In 2017, Matthew earned an annual income of $80 000. He is req uired to pay tax based on net income. His net income is obtained after deducting CPF contribution of $16 000 and personal expenses relief of $3000 from the annua l income. The tax rate is $200 for the first $30 000 of net income and 5% for the remaining net income. Calculate Matthew’s (i) net income, Answer $ ………………...……… [1] (ii) income tax. Answer $ ………………...……… [2]

EM-2018-AHS-SA2-P1 10 Amanda wrote down four numbers. The mean of these numbers is 15, the median is 12 and the mode is 8. F i n d t h e f o u r n u m b e r s . Answer ………., ………., ………., ………. [2] 11 Write down a possible equation for each of the graphs shown below. (a) Answer …...………….…..……… [1] (b) Answer …...………….…..……… [1] 0 y x [Turn over 0 y x

EM-2018-AHS-SA2-P1 12 (a) Find the greatest integer tha t will divide both 126 and 2100. Answer ………..………………… [2] (b) A rectangular field is measured as 49.9 and 24.5 correct to th e nearest 0.1 metre. Find, (i) the least possible perimeter in metres. Answer ……...…..….………… m [1] (ii) the greatest possible area in square metres. Express your answ er in standard form correct t o 4 significant figures. Answer ………..…..………… m 2 [2] 13 The surface area of a sphere is directly proportional to the s quare of its radius. If the radius increases by 15%, find th e percentage increase in the s urface area. Answer …....…...………..……. % [2]