Dunman Sec 2025 Prelims 4EXP Math Paper 2 QP

This document consists of 21 printed pages and 1 blank page. DUNMAN SECONDARY SCHOOL CANDIDATE NAME CLASS INDEX NUMBER PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS / 5 NORMAL ACADEMIC MATHEMATICS 4052/02 Paper 2 26 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all 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 total of the 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 to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. Calculator Model Total Marks

2 4052/02/PRELIM/4E5NA/2025 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 = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

3 4052/02/PRELIM/4E5NA/2025 [Turn over BLANK PAGE

4 4052/02/PRELIM/4E5NA/2025 Answer all the questions. 1 (a) Solve the inequality 5921 2 xx +− . Answer ……………………… [2] (b) It is given that ( ) 2 2 25np b np − = − . (i) Find b when n = 1 and p = −2. Answer ……………………… [1] (ii) Express p in terms of b and n. Answer p = …………………..[3[3]

5 4052/02/PRELIM/4E5NA/2025 [Turn over (c) Solve the equation 32 72 1 5 x xx −=−− . Answer ……….. or ………… [5]

6 4052/02/PRELIM/4E5NA/2025 2 (a) In 2023, the amount of waste recycled in Singapore was 3.553 million tonnes. The amount of waste disposed in Singapore was 3.3064 million tonnes. (i) How much more waste (in tonnes) was recycled than disposed in Singapore in 2023? Write the difference (in tonnes) in standard form, correct to three significant figures. Answer ……………… tonnes [2] (ii) The amount of waste recycled in Singapore in 2020 was 3.040 million tonnes. Calculate the percentage increase in the amount of waste recycled from 2020 to 2023. Answer …………………… % [2] (iii) From 2022 to 2023, the amount of waste recycled in Singapore decreased by 15.2%. Calculate the amount of waste recycled (in tonnes) in 2022. Answer ……………… tonnes [2]

7 4052/02/PRELIM/4E5NA/2025 [Turn over (b) The cash price of a new car is $120 000. (i) Jason buys the car on hire purchase. He pays a deposit of 20% of the cash price. He then makes 84 monthly payments of $1400. What is the total amount that Jason pays for the car? Answer $ ……………………… [2] (ii) The original value of the car is its cash price of $120 000. Each year, the value of the car decreases by 15% of its value at the start of the year. Calculate the overall percentage decrease in the value of the car compared with its original value after 5 years. Answer …………………… % [2]

8 4052/02/PRELIM/4E5NA/2025 3 The daily growth rate, h millimeters per day, of Plant A is related to the number of hours of sunlight it receives each day, t, by the formula ( ) 21 46h t t=− . (a) Complete the table of values for ( ) 21 46h t t=− . Values are given to 2 decimal places where appropriate. t 0.5 1 1.5 2 2.5 3 3.5 4 h 0.5 0.94 1.33 1.56 1.5 1.02 0 [1] (b) On the grid opposite, draw the graph of ( ) 21 46h t t=− for 04 t . [3] (c) Use your graph to find the maximum number of hours of sunlight Plant A can receive to achieve a daily growth rate of 1 millimetre per day. Answer ……….……….. hours [1] (d) (i) By drawing a tangent, find the gradient of the curve at (3, 1.5). Answer ……………………… [2] (ii) What does the gradient in part (i) tell us about the effect of additional sunlight on the daily growth rate of plant A at this point? Explain your answer. Answer …………………………………………………………………………... ………………………………………………………………………………….... ………………………………………………………………………………….. [1]

9 4052/02/PRELIM/4E5NA/2025 [Turn over The daily growth rate, h millimeters per day, of another Plant B is related to the t hours of sunlight it receives each day by the formula 2ht= . (e) (i) On the grid above, draw the graph of 2ht= for 04 t . [1] (ii) Find an equation in the form 32 0t pt qt r+ + + = , where p, q and r are constants to be found, such that the solutions represent the number of hours of sunlight when both Plant A and Plant B have the same daily growth rate. Answer [2] 2 0 1 1.5 0.5 −0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 t (hours) h (millimetres per day)

10 4052/02/PRELIM/4E5NA/2025 4 OACB is a trapezium. 2OA= a , 3OB= b and 2 3OA BC= . X is the point on AB such that AX : XB = 1 : 3. (a) Express, as simply as possible, in terms of a and/or b, (i) AX , Answer ……………………… [2] (ii) OX . Answer ……………………… [1] (b) Y is the point on BC produced such that 3BY OA= . Find, in terms of a and/or b, XY . Answer ……………………… [2] O A B X C 2a 3b