AHS 2025 EMATH PRELIM P2 QP

NAME : _______________________________ ( ) CLASS: 4 ( ) 9o MATHEMATICS 4052/02 Paper 2 25 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use a 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 . 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. --------------------------------------------------------------------------------------------------------------------------- For Examiners’ Use Questions 1 2 3 4 5 6 7 8 Marks Questions 9 10 11 12 13 14 15 16 Marks Table of Penalties Units 90 Clarity/Logic Accuracy/Precision Parent’s Name and Signature: Date:

2 This document consists of 23 printed pages. This page is intentionally left blank Mathematical Formulae

3 Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = Anglican High School Preliminary Examination 2025 [Turn over

4 1 Rearrange the formula to make c the subject. Answer: …………………………………. [3] 2 (a) A investor deposits $18 000 with a finance company paying compound interest on a monthly basis at 6% per annum. Calculate the interest received at the end of 5 years, correct to 2 decimal places. Answer: $….……………………………….... [2] (b) The price of a washing machine is $900 before discount. After selling the machine at a 20% discount, the seller still makes a profit of 25%. Calculate the cost price of the washing machine.

5 Answer: $…………...….……………………. [3] (c) The price of a gaming laptop is $2 999. John buys this laptop on hire purchase after putting a down payment of $600. For the remaining amount of the laptop, John has to pay the seller a monthly instalment of $120 over 2 years. Calculate the interest rate charged by the seller. Answer: ….…...….………………………..% [3] 3 Write as a single fraction in its simplest form . Anglican High School Preliminary Examination 2025 [Turn over

6 Answer: ………..……….. ….…………………. [3] 4 (a) Express in the form . Answer: .….……………………………….... [2] (b) Hence, write down the coordinates of the turning point of the graph . Answer: .….……………………………….... [1] 5 In triangle ABC , angle CDE and angle CEB are right angles. cm, cm, cm and cm. (a) (i) Show that ∆ ECD and ∆ ACE are similar. Answer ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ……………………………………………………………………………………………… [1] (ii) Express y in terms of x .

7 Answer: …………………………………….. [1] (b) (i) In triangle PQR , angle , cm and cm. Express the area of triangle PQR in terms of and . Answer: Area of triangle PQR = ……………………………….cm 2 [1] (ii) The area of triangle is . Using your answer in a(ii) and b(i) , find the value of and of . Anglican High School Preliminary Examination 2025 [Turn over

8 Answer x =…………………………....….…...… y =……..……………………………. [3] 6 In the Singapore F1 Grand Prix, the drivers must complete 62 laps around a circuit that is 4.940 km long. One F1 driver completed 32 laps in 65 minutes. What must be the minimum average speed, in km/h, for the remaining laps if he wants to complete the race in at most two hours? Answer: ……..…….………………………km/h [3] 7 The position vector of point C is . The position vector of point D is . . Find the two possible values of h.

9 Answer h =….….……..…or ……..……..….. [3] 8 There are 180 oranges in a box. The table shows the distribution of the masses of these oranges. Mass ( m g) Frequency 10 28 51 45 48 (a) Calculate an estimate of the standard deviation of the masses. Answer : ……...……………………………..g [1] (b) The weighing machine was faulty and overestimated each of the oranges by 5g. Explain, with a reason, what will happen to the standard deviation. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ……………………………………………………………………………………………… [2] (c) Explain why the range of the masses of oranges may not be 50g. ………………………………………………………………………………………………….. ……………………………………………………………………………………………… [1] (d) Roy says, “The modal class is the interval but the modal mass may not be in the interval .” Is he correct? Give a reason for your answer. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ……………………………………………………………………………………………… [2] Anglican High School Preliminary Examination 2025 [Turn over

10 9 The time taken by 120 students to travel to school A was recorded. The cumulative frequency curve below shows the distribution of their commute times. (a) Calculate the percentage of students who took at least 35 minutes to reach school. Answer: ………..………………………….% [1]