WGSS 2024 Prelim EMath 4052(2) QP

1 Name Index Number Class O LEVEL PRELIMINARY EXAMINATION 2024 LEVEL & STREAM : SECONDARY 4 EXPRESS / 5 NORMAL ACADEMIC SUBJECT (CODE) PAPER : MATHEMATICS (4052) : 02 DATE (DAY) : 22 AUGUST 2024 (THURSDAY) DURATION : 2 HOURS 15 MINUTES READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams, graphs, tables or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. The number of marks is 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 in 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 to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 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 22 printed pages including this cover page Setter : Mr Phillip Tan 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 = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of a 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 == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 Answer all the questions. 1 (a) 2 1=+ − ab ac (i) Find the value of b when 3=a and 4=c . Answer =b ………………….….. [1] (ii) Rearrange the formula to make a the subject. Answer ……..……………….….. [3] (b) Solve these simultaneous equations. 4 11xy− =− 5 3 1 xy+ =− Answer =x ………………….….. =y ………………….….. [3]

4 (c) Solve the equation 5 13 1 2 3−=−+ x xx . Give your solutions correct to three decimal places. Answer =x …………… or …………… [4] 2 (a) Timmy wants to invest a sum of money in one of the following investment plans. Plan A Pays 2% simple interest per year Plan B Pays 2% compound interest per year Which investment plan is the better choice for Timmy? Explain your answer. Answer : ………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… [1]

5 (b) Mary deposits $8000 in a savings account at a simple interest rate of 3.5% per year. Calculate the total value of her savings at the end of 12 years. Answer $ ……..……………….….. [2] (c) Peter invested $50 000 in an investment plan from 2010 to 2024. The value of his investment increased by r% at the end of every year. At the end of 2024, the total value of Peter’s investment is $65 320. Calculate the value of r. Answer =r ………………….….. [3]

6 (d) The current exchange rate between Singapore dollars (SGD) and Thailand baht (THB) is given as SGD 1 = THB 27.16. Susan bought a bag while shopping in Thailand. The original price of the bag was THB 56 000 and Susan bought it at a 15% discount. Susan paid for the bag using her credit card which charged her an additional 2% fee for overseas transaction. Calculate the total amount, including credit card fee, that Susan had to pay in Singapore dollars (SGD). Correct your answer to the nearest cent. Answer $ ……..……………….….. [3]

7 3 (a) The table of values for 5 7= + −yx x is given below. x 0.5 1 1.5 2 3 4 5 6 7 y 3.5 1.0− 2.2− 2.5− 2.3− 1.8− k 0.2− 0.7 Find the value of k. Answer =k ………………….….. [1] (b) On the grid below, draw the graph of 5 7= + −yx x for 0.5 7x [3]

8 (c) Use your graph to find the solutions to 5 5+=x x in the range of 0.5 7x . Answer =x …………… and …………… [3] (d) By drawing a tangent, find the gradient of the curve at ( )4, 1.8− . Answer Gradient = ………………….….. [2] (e) The solutions of 2 50+ + =Px Qx are the same as the x-coordinates of the intersections between the graph 5 7= + −yx x and the line 3=− +yx . Find the values of P and Q. Answer =P ………………….….. =Q ………………….….. [3]

9 4 (a) The diagram below shows two circles, with the same centre at O. Points A, B and C lie on the bigger circle and point D lies on the smaller circle. AC is a straight line that passes through the centre of both circles. AB and BC are both tangents to the smaller circle. (i) Show that triangles ABC and ODC are similar. Give a reason for each statement you made. Answer [2] (ii) The area of triangle ODC is given as 15cm2. Find the area of trapezium ABDO. Answer ……..……………….….. cm2 [2]

10 (b) PQRS are points on the circumference of a circle, centre O. Angle 50=OQR , angle 73=PSR and obtuse angle 156=SOQ . (i) Find angle QRS . Give a reason for each step of your working. Answer ……..……………….…..  [1] (ii) Find angle PSO . Give a reason for each step of your working. Answer ……..……………….…..  [2]