TPSS 4052 EM PRE P1 2026 w AK MS

This document consists of 23 printed pages and 1 Blank Page [Turn over TAMPINES SECONDARY SCHOOL SECONDARY FOUR EXPRESS PRELIMINARY EXAMINATIONS 2026 NAME CLASS REGISTER NUMBER MATHEMATICS (EXPRESS) 4052 PAPER 1 24 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) Calculate 2( 12) ( 12) 4 11 ( 3) 2 11 −− + − − × ×− × . Write your answer correct to 3 significant figures. Answer: ……………………………….. [1] (b) The number of people in a carnival is given to be 500, corrected to the nearest hundred. Write down the minimum number of people that could be at the carnival. Answer ……………………………….. [1] 2 (a) Express 360 as the product of its prime factors. Answer ……………………………….. [1] (b) The number 360h is a perfect square. Find the smallest positive integer value of h. Answer ……………………………….. [1] (c) The integer k is such that 200 < k < 420. The highest common factor of 360 and k is 40. Find the smallest possible value of k. Answer k =……..……………………… [2]

4 3 Simplify the following. (a) (i) 1 15 3 128 a b −  Answer …………………………………. [2] (ii) 2 3 4 20xx yy÷ Answer …………………………………. [2] (b) Given that 45 125 1xx− ×= , find the value of x. Answer x = ……………………………. [2]

5 4 (a) Singapore consumes 440 million gallons of water daily. Given that 1 gallon = 3.785 litres, express 440 million gallons in litres. Leave your answer in standard form. Answer …………………...……… litres [1] (b) On a particular day in Singapore, it was estimated that the average water consumption is 142 litres per person. Using the daily water consumption from part (a), calculate the number of people in Singapore on that particular day. Give your answer in standard form correct to 3 significant figures. Answer ………………..………………... [2] 5 Write as a single fraction in its simplest form 45 32 3aa−−+ . Answer ……………………....………….. [2]

6 6 In the diagram, PRS is a straight line. P is due north of Q. PQ = 12 cm, QR = 35 cm and angle PQR is 90°. (a) Find the value of cos QRS∠ , leaving your answer as a fraction in its simplest form. Answer ……………………....………….. [2] (b) Find the bearing of R from P. Answer ……………………....………….. [2] P R S Q 12 cm 35 cm North

7 7 The area of a plot of land on a map is 575 cm2. The actual area of the plot of land is 23 km2. If the map is drawn to a scale of 1 : n, find the value of n. Answer n = ………………..……………. [2] 8 The stem-and-leaf diagram shows the amount of time in minutes that 23 people spent on an online shopping platform. 7 5 6 8 9 9 9 8 0 0 1 1 2 3 4 7 9 3 4 4 5 6 8 10 0 1 2 Key 7 | 5 represents 75 minutes (a) Write down the median time. Answer ……………………… minutes [1] (b) An additional person’s time spent on the online shopping platform was added to the above stem-and-leaf diagram, and the range increased to 34 minutes. Find the two possible times that this person spent on the online shopping platform. Answer ……….. or ………… minutes [2]

8 9 (a) The high-speed train travelling from Xi’an to Chengdu is 95 m/s. Convert this speed into km/h. Answer ……………….……….…km/h [1] (b) The distance from Xi’an to Chengdu is 658 km. By rounding the distance and the speed in part (a) to 1 significant figure, estimate the time taken for the high-speed train to travel from Xi’an to Chengdu. Answer ……………….……...……..… h [1] (c) Without doing any further calculation, explain why the actual time is shorter than the answer to part (b). …………………………………………………………………………………….… …………………………………………………………………………………….… ………………………………………………………………………………………. [1]

9 10 The expression x2 – 8x + 11 is equivalent to (x + a)2 + b. (a) Find the value of a and of b. Answer a = …………, b = …………… [2] (b) Sketch the graph of y = x2 – 8x + 11, indicating clearly the y-intercept and the turning point of the curve. [3]

10 11 The table below shows the time taken by 100 students to complete a hiking trail. Time (t minutes) 30 < t ≤ 40 40 < t ≤ 50 50 < t ≤ 60 60 < t ≤ 70 70 < t ≤ 80 Frequency 15 32 30 16 7 Calculate an estimate of the (a) mean time, Answer ……………………… minutes [1] (b) standard deviation of the above times. Answer ……………………… minutes [2] 12 P is directly proportional to the square of Q. Aaron says: “If the value of Q is halved, the value of P will also be halved.” Determine if Aaron is correct. Explain your answer, with mathematical calculations. Answer …………………………………………………………………………………….……… …………………………………………………………………………………….……… ……………………………………………………………………………………….…… [3]