2025 Presbyterian HS MA Prelim P2 QP + MS

Name: Register Number: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4052/02 PAPER 2 21 August 2025 Thursday 2 hours 15 minutes PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2025 SECONDARY FOUR EXPRESS/ FIVE NORMAL PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your name, index number and class on the spaces provided above. 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . Note that all the diagrams in this paper are not drawn to scale. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. For Examiner’s Use Qn 1 2 3 4 5 6 7 8 9 10 Marks Deducted Marks Setter: Ms Ong Bi Ru Vetter: Mr Tan Chee Wee This paper consists of 25 printed pages (including this cover page) and 1 blank page. Category Accuracy Notations Others Question No. TOTAL MARKS 90

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 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 triangle ABC = Cab sin2 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 TURN OVER FOR QUESTION 1

4 1 (a) Solve 3 1057 xx− + − = . Answer x = [2] (b) Simplify 23 2 10 2xy y xy  . Answer [1] (c) Simplify 2 2 18 2 15 7 4 a aa − +− . Answer [3]

5 (d) Given the equation 2 6 20 0qq+ − = . (i) Express 2 6 20 0qq+ − = in the form 2( ) 0q m n+ + = . Answer [2] (ii) Hence, solve for q, giving your answers correct to 2 decimal places. Answer q = or [2]

6 2 (a) Linus invests a sum of money at 7% per annum simple interest. At the end of n years, the amount is more than twice the initial sum of money. Find the minimum integer value of n. Answer [3] (b) Marcus wants to invest $12,000 for 4 years and is exploring two investment options with different compounding frequencies. Determine which option Marcus should choose. Justify your reasons with calculations. Answer Option [3] Option A 6.5% annual interest compounded monthly Option B 6.8% annual interest compounded half yearly

7 (c) A group of students travelled to Malaysia. They exchanged Singapore dollars (SGD) to Malaysian ringgit (MYR) at a rate of SGD 1 = MYR 3.20. They spent MYR 2525 on accommodation and food. They also bought 80 litres of fuel at MYR 2.50 per litre. They exchanged the remaining MYR at a rate of SGD 1 = MYR 3.25 and received SGD 60. Calculate the amount of SGD they exchanged at the start of their trip. Answer SGD [3]

8 3 The cumulative frequency curve below shows the distribution of masses of adults before a weight loss programme. The programme has 40 adults. (a) Using the graph, (i) find the number of adults who had a mass between 115 kg and 125 kg, Answer adults [1] (ii) estimate the 90th percentile, Answer kg [1] (iii) calculate the interquartile range. Answer kg [2] Cumulative frequency Mass (kg)

9 (b) Two adults were selected at random before the programme. Find the probability that (i) at least one of the two adults was heavier than 135 kg, Answer [2] (ii) one of the two adults was heavier than 120 kg and the other was not. Answer [2] (c) The weight of these 40 adults are taken again after the weight loss programme. The details are shown below: Median 25th percentile 75th percentile 115 kg 110 kg 119 kg Make a comparison between the before and after programme to determine if the programme is effective. Answer [1]

10 4 (a) Complete the table of values for 33 110 xyx= − + . x 3− 2− 1− 0 1 2 3 y p 0.6 1.7 1 0.3 1.4 6.1 Answer p = [1] (b) On the grid opposite, draw the graph of 33 110 xyx= − + for 33 x−   . [3] (c) The equation 33 110 xkx= − + has 2 solutions in the range 33 x−   . Write down the value(s) of k. Answer k = [1] (d) By drawing a tangent, find the gradient of the curve at 1.6.x= Answer [2] (e) By drawing a suitable straight line on the grid, solve the equation 33 30 20 0xx− − = . Answer x = [3]