AHS 2025 EMATH PRELIM P2 MS

NAME : _______________________________ ( ) CLASS: 4 ( ) 9o MATHEMATICS 4052/02 Paper 2 25 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. MARKING SCHEME 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 M L/M/M L M L M/L L/L/L L/M/H/H Questions 9 10 11 12 13 14 15 16 Marks M/H/L M/M M/H L/L/M/M/M L/L/M L/M L/L/M/M/ M/M M/L/L/M/H Table of Penalties Units 90 Clarity/Logic Accuracy/Precision Parent’s Name and Signature: Date:

2 This document consists of 24 printed pages. This page is intentionally left blank Anglican High School Preliminary Examination 2025 [Turn over

3 Mathematical Formulae 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

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5 1 Rearrange the formula to make c the subject. . M1 M1 A1 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. M1 A1 (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. M1 for selling price of washing machine M1 A1 Anglican High School Preliminary Examination 2025 [Turn over

6 (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. M1 for finding interest M1 apply formula A1 3 Write as a single fraction in its simplest form . M2 for factorising x 2 – 1 and switching operation sign. A1 Anglican High School Preliminary Examination 2025 [Turn over

7 4 (a) Express in the form . M1 for factorising A1 (b) Hence, write down the coordinates of the turning point of the graph . Coordinates of turning point = (2,1) B1 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. Angle ECD = Angle ACE (common angle) Angle EDC = Angle AEC = 90 o (given) By AA test, the 2 triangles are similar. B1 (ii) Express y in terms of x . B1 Anglican High School Preliminary Examination 2025 [Turn over

8 (b) (i) In triangle PQR , angle , cm and cm. Express the area of triangle PQR in terms of and . B1 (ii) The area of triangle is . Using your answer in a(ii) and b(i) , find the value of and of . or M1 for students to form the quadratic equation. M1 for solving the quadratic equation Anglican High School Preliminary Examination 2025 [Turn over

9 When , A1 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 for the remaining laps if he wants to complete the race in at most two hours? M1 for calculating the distance and times for the first 32 laps. M1 for setting up the inequality or equation to calculate the minimum speed in the next 30 laps. A1 7 The position vector of point C is . The position vector of point D is . . Find the two possible values of h. Anglican High School Preliminary Examination 2025 [Turn over

10 M1 for M1 to form quadratic equation A1 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. 11.9 g B1 (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. (c) Explain why the range of the masses of oranges may not be 50g. The data is grouped , the smallest data is greater than 90g and the largest data is at most 140g. therefore, the actual range could be less than 50g. B1 (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. Anglican High School Preliminary Examination 2025 [Turn over Standard deviation remains the same. Every value is an overestimate, hence, the spread will not change the standard deviation. B1 B1 for reason