WGSS 2024 Prelim EMath 4052(1) QP

Name Index Number Class O-LEVEL PRELIMINARY EXAMINATION 2024 LEVEL & STREAM : SECONDARY 4 EXPRESS / 5 NORMAL ACADEMIC SUBJECT (CODE) PAPER : MATHEMATICS (4052) : 01 DATE (DAY) : 27 AUGUST 2024 (TUESDAY) DURATION : 2 HOURS 15 MINUTES READ THESE INSTRUCTIONS FIRST Write your class, index number and name on the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. The number of marks in given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total number of marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer correct to three significant figures. Give answers in degrees to one decimal place. For π , use either your calculator value of 3.142. DO NOT TURN OVER THE QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Student’s Signature Parent’s Signature Date Date This document consists of 20 printed pages including this cover page. Setter : Mr Eric Bay 90

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 1 3 πr2h Volume of a sphere = 4 3 πr3 Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == 2 2 2a b c= + − 2bc cosA Statistics Mean = f fx   Standard Deviation = 22        −  f fx f fx

3 Answer all the questions. 1 (a) Calculate 2 2011 ( 11) 11 8 0.6 − + − −  . Write your answer correct to 4 significant figures. Answer …………………….. [1] (b) Write your answer to part (a) in standard form. Answer …………………….. [1] 2 Expand and simplify (2 5)(3 4 )xx++ . Answer …………………….. [2] 3 Solve (a) 3 4 21x−= . Answer …………………….. [1] (b) 2 3 1 13xx +  , Answer …………………….. [2]

4 4 (a) Express 4312 as a product of its prime factors. Answer …………………….. [1] (b) Given 22588 2 3 7=   . Find (i) The largest integer which is a factor of both 588 and 4312. Answer …………………….. [1] (ii) The smallest integer which is the multiple of both 588 and 4312. Answer …………………….. [1] (iii) The smallest integer value of m such that 4312m is a perfect square. Answer …………………….. [1]

5 5 Given that the coordinates of point A is (–2,11) and point B is (5, –11). Find (a) length AB, Answer …………………….. [2] (b) equation of the straight-line AB. Answer …………………….. [3] 6 Simplify 2 2 94 12 6 x xx − −− . Answer …………………….. [3]

6 7 Solve 21 31 2 5xx −=+− . Answer …………………….. [4]

7 8 The table below shows a multiple-choice test Sam and Roger took. Correct No attempt Incorrect Sam 14 5 1 Roger 15 0 5 (a) Represent this information in a 23 matrix, S. Answer S =    [1] (b) The marks are awarded as follow: Correct = 2 marks No attempt = 0 mark Incorrect = 1− mark Represent the information in a 31 matrix, T. Evaluate ST Answer    [2] (c) Explain what your answer to (b) represents. Answer ………………………………………………………………………….………….. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………..………………………………………………… [1]

8 9 Factorise completely. (a) 3 6 2abc c ab− − + Answer …………………….. [2] (b) 480 5x − Answer …………………….. [3] 10 Ken divides his monthly salary into daily expenses, spending and saving in the ratio 3:4:5 respectively. Later he decides to spend $1200 more daily the new ratio become 9:8:7. Calculate his monthly salary. Answer …………………….. [3]

9 11 John conducted a survey on the average time spent reading per week. This survey was carried out outside Woodlands Regional Library. The table below represents the survey results. Time spends (t) in hours 02 t 24 t 46 t 68 t 8 10t 10 12t Frequency 3 8 9 15 3 2 (a) Calculate the percentage of people spend between 6 to 8 hours per week in reading. Answer ……………..…….% [1] (b) Calculate the average time spend in reading. Answer ………..…….. hours [1] (c) John concludes that the result in part (b) is the average of time spent in reading by a Singaporean. Do you agree, give a reason. Answer ………………………………………………………………………….………….. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………..………………………………………………… [2]

10 12 The expression 2 47xx−+ can be written in the form of ( )2x a b−+ (a) Find the value of a and b. Answer a= …..…………….. [1] b= …..…………….. [1] (b) Explain why the expression gives a minimum value. Answer [2] (c) Write down the minimum value. Answer …………………….. [1]