TPSS 4052 EM PRE P2 2026 w AK MS

This document consists of 26 printed pages and 0 Blank Page [Turn over TAMPINES SECONDARY SCHOOL SECONDARY FOUR EXPRESS PRELIMINARY EXAMINATIONS 2026 NAME CLASS REGISTER NUMBER MATHEMATICS (EXPRESS) 4052 PAPER 2 25 August 2026 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. 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 or 3.142. 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. EXP For Examiner’s Use 90

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 1π 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 Answer all the questions. 1 (a) (i) Given the formula 45qrp qr −= + , find p when q = 5 and r = – 2. Answer p =………………………… [1] (ii) Rearrange the formula 45qrp qr −= + to make q the subject. Answer q = ………………………….. [3] (b) Factorise 2 393x x y xy−+− . Answer ………………………………... [2]

4 (c) Solve 22 5 70xx− −= . Answer: x = ……..…… or …………….. [2] 2 Triangle ABC has coordinates A (−3, 4), B (−1, −5) and C (9, −5). (a) Find the equation of AC, Answer …………………………………. [3] A (−3, 4) B (−1, −5) C (9, −5) y x O

5 (b) Calculate the length of AC. Answer …………………………… unit [1] (c) Calculate the area of triangle ABC. Answer …………………………… unit2 [1] (d) State the coordinates of D such that ACDB form a parallelogram. Answer (…………...… , ………….…..) [1] (e) The equation of a line p is 4y + 3x = 4. Determine if the line p will intersect line AC. Explain your answer with mathematical working. Answer ...…….……………………………………….……………………………………………. ...…….……………………………………….……………………………………………. ...…….……………………………………….……………………………………………. [2]

6 3 Tickets to a carnival cost $10 for adults (A), $8 for senior citizens (S) and $5 for children (C). This information can be represented by the matrix Q 10 8 5  = . (a) 68 adults, 15 senior citizens and 70 children bought tickets through ticket counter. 72 adults and x children bought tickets online. Represent this information in a 23× matrix P. Answer A S C  = P [1] (b) Find the matrix R, in terms of x such that R = PQ. Answer R = ……………………………. [2] (c) Explain what each element in matrix R represents. …………………………………………………………………………………….… ………………………………………………………………………………………. [1]

7 (d) The total amount of money collected from the ticket counter is less than that from the online sales. Find the least value of x. Answer …………………………………. [2]

8 4 The capacity of a tank is 3853 litres. (a) Tap A can fill the tank at a speed of x litres per minute. Write down an expression, in terms of x, for the duration (in minutes) taken by Tap A. Answer ………………..……… minutes [1] (b) Tap B can fill the tank at a speed of (x – 2) litres per minute. Write down an expression, in terms of x, for the duration (in minutes) taken by Tap B. Answer ………………..……… minutes [1] (c) Tap B will take 30 minutes longer than Tap A to fill the tank. Write down an equation in x and show that it reduces to 15x2 − 30x − 3853 = 0. Answer [3]

9 (d) Solve the equation 15x2 − 30x − 3853 = 0, leaving your answers to 2 decimal places. Answer x = ……………or ..…………… [3] (e) Hence, find the time taken for the tank to be filled if both taps are turned on, correct your answer to the nearest minute. Answer ………………..……...… minutes [2]

10 5 In the diagram, O is the centre of the circle ABCD. TBP and TDQ are tangents to the circle, angle BTD = 36° and AB = AD. Giving reasons for each step of your working, find (a) (i) angle BOD, Answer Angle BOD =………………..……… [2]