2024 TPSS EMATH P2 PRELIM QP

This document consists of 22 printed pages and 2 blank pages. TAMPINES SECONDARY SCHOOL Secondary Four Express / Five Normal Academic PRELIMINARY EXAMINATION 2024 NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 23 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. 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 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 π , use either your calculator value of 3.142, unless the question requires the answer in terms of π . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. [Turn over Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Total

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = h r2 3 1 π Volume of a sphere = 3 3 4 rπ Area of a triangle ABC = C absin2 1 Arc length = rθ , where θ is in radians Sector area = 21 2 r θ , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = f fx Σ Σ Standard deviation = 22       Σ Σ−Σ Σ f fx f fx

3 1 (a) Simplify 36( 1) 9( 1) 7 28 aa bb ++ ÷ . Answer ……………………………… [2] (b) 2bvxa k= + (i) Find x when a = 2, b = 3, v = – 4 and k = 5. Answer x = ………………………… [1] (ii) Rearrange the formula to make v the subject. Answer v = ………………………… [3]

4 (c) Solve the simultaneous equations. 4 7 23 62 3 xy xy += − −= You must show your working. Answer x = ………………………… y = ………………………… [3] (d) Write as a single fraction in its simplest form 2 ( )( 3 ) 3 x xy x y xyxy −−+− − . Answer ……………………………… [2]

5 2 (a) Faiz invested $25 000 in an account which paid simple interest. At the end of 9 months, the value of the investment was $26 500. Calculate the interest rate per annum of the investment. Answer ………………………… % [2] (b) Jane exchanged 500 Singapore dollars ($) into Thai baht (THB) when the exchange rate was $1 = 26.77 THB. She travelled to Thailand and spent 10 600 THD. On her return to Singapore, she exchanged the remaining Thai baht into dollars with the exchange rate $1 = 26.88 THB. Calculate the amount she received in dollars. Correct your answer to the nearest cent. Answer $…………………………… [2]

6 (c) The cash price of a furniture set was $2700. Kim bought the set under a hire purchase scheme: 15% deposit and monthly instalments of $68 for 36 months. Calculate the amount of interest paid as a percentage of the cash price. Answer ………………………… % [3] (d) By selling an item at 25% discount off the marked price, a shopkeeper still makes 10% profit on his cost. If the cost price is $180, calculate the marked price of the item. Answer $ …………………………… [3]

7 3 The diagram shows a rectangular cardboard ABCD with AB = (3 1)x + cm and AD = ( 13)x + cm. A square of side 3 cm is cut from each corner. The remaining cardboard is then folded along the dotted lines to form an open rectangular box with base PQRS and height 3 cm. The volume of the tray is 930 cm3. (a) Form an equation, in terms of x, to represent this information and show that it simplifies to 23 16 345 0xx +−= . [4] 3x + 1 x + 13

8 (b) Solve the equation 23 16 345 0xx +−= . Give your solutions correct to two decimal places. Answer x = ……………… or x = ……………… [3] (c) Find the length of the diagonal SQ. Answer ………………………………………… cm [3]

9 4 (a) A is the point (3, 7) and B is the point (13, – 8). (i) Find AB   . Answer ………………………………… [2] (ii) Given that 2BA AP=     , find the coordinates of P. Answer ( …………… , …………… ) [2]

10 (b) In triangle OCB , A is the midpoint of OC and P is the point on CB such that 3 4CP CB= . The line OB produced to D such that OB = 2 BD. 2OA =    a and 2OB =   b. (i) Express CP    in terms of a and b, as simply as possible. Answer ………………………………… (ii) Express AP   in terms of a and b, as simply as possible. Answer ………………………………… [2] [1]