2026 CCH MAIN P2 MS

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 1 Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2026 SECONDARY 4 (MARKING SCHEME) MATHEMATICS 4052/02 Paper 2 Tuesday 18 August 2026 Candidates answer on the Question Paper 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 number of 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. This document consists of 21 printed pages and 1 blank page. For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 Total Marks

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 2 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = V olume of a cone = V olume of a sphere = Area of triangle ABC = Arc length = , where is in radian Sector area = , where is in radian Trigonometry Statistics Mean = f fx   Standard deviation = 22          f fx f fx nrP       1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin  Acbcba cos 2 222 

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 3 TURN OVER FOR QUESTION 1

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 4 1 (a) It is given that 6 ay a x  . (i) Express x in terms of a and y . Answer x ……………… …. [2] (ii) Given that : : 1: 2 :3x y a  , find the value of y . Answer y.……………… …. [3] 2y x and 3a x 6 32 3 xx x x  -------------- M1 (Apply ratio to simplify eq. in one unknown) 22 3x x  22 2 3x x  22 3 2 0x x   ---------- M1 (Simplify into a quadratic equation)   2 1 2 0x x   1 or 2 (rej.)2x x  12 12y      ----------------- A1 6 ay a x  6a yx a  ------------ B1 6a ay x a  2 6 ax ay  -------------- B1

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 5 (b) Solve the equation 2 10 7 0x x   by completing the square. Give your solutions correct to 1 decimal place. Answer x……… or ……….. [4] 2 10 7 0x x     2 5 25 7 0x    ---------------- B1 for   2 5x   2 5 32x  5 32x  ----------------------- M1 (applying square root) 32 5 or 32 5x   10.7 (1 d.p) or 0.7 (1 d.p) A1, A1

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 6 2 (a) Mei invests a sum of money at a compound interest of r % per annum. At the end of 4 years, the value of her investment has increased by 25%. Find the value of r . Answer r .………………… [3] (b) John borrows $15 000 from a Singapore bank for 3 years to pay for an overseas course in France that costs €9,800. The exchange rate between Singapore dollars and euros is $1 = €0.625. The bank charges simple interest at a rate of 5% per annum. (i) Show with clear workings whether the amount borrowed is sufficient to pay for the course fee. Answer [1] (ii) Calculate the total amount John has to repay the Singapore bank after 3 years. Answer $ …………………… . [2] 1 100 n rA P      1.25 and 4A nP   ---------------- B1 (recognise that 1.25A P  ) 4 1.25 1 100 r     41 1.25100 r  ------------------- M1 (applying 4th root) 5.74 (3 s.f)r  ----------------- A1 Amount borrowed € 15000 0.625 €9375 Since the amount borrowed is less than €9800, it is insufficient to pay for the course fee. Total interest 5$ 15000 3 100       M1 (allow for ‘copy’ error in 15000) $2250 Total amount  $ 2250 15000  $17250 A1

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 7 (c) In a number sequence, the sum of the first n terms is given by 2 3nS n n  . (i) Find the sum of the 15th to the 30th term. Answer ……………… ……… [1] (ii) By finding 1nS  , show that all the terms in the number sequence are always even. Answer [3] (iii) 3T , 6T , 9T , … . is a new sequence formed by taking every 3rd term of the original sequence. Find an expression, in terms of m to represent the mth term of the new sequence. Answer ……………… ……… [2] Sum 30 14S S      2 230 3 30 14 3 14          752     2 1 1 3 1nS n n     ----------- M1 (Simplifying) 2 2 1 3 3n n n     2 2n n   1n n nT S S       2 2 3 2n n n n     ------- M1 (Recognise nT ) 2 2n   2 1n  Since 1n is an integer and nT is a multiple of 2, therefore all the terms in the number sequence are always even. [A1] From (ii), 2 2nT n  The mth term of the new sequence is the (3m)th term of the original sequence. mth term  2 3 2m  6 2m  [B1, B1] B1 (has a factor 2)

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 8 3 A weather station recorded the temperature of a city , T in degrees Celsius , at various times between 8.30 p.m. on 15 July and 3.30 a.m. on 16 July. Let t be the time, in hours, measured relative to midnight at the start of 16 July. Some of the recorded temperatures are shown in the table below. t –3.5 –3 –2 –1 0 1 2 2.5 3.5 T –3.9 0 3.75 3.6 1.35 –1.2 –2.25 –1.65 2.93 For example: 3t correspond to 9 p.m. on 15 July. The temperature can be modelled by the equation    3T k t t p t q    where ,k p and q are constants. (a) On the grid opposite, plot the points given in the table and join them with a smooth curve. [3] (b) Using your graph, estimate the values of p and q . Answer p  …………………… ... q  ……………………… [2] (c) By drawing a tangent, find the gradient of the curve at 2t and state the units in your answer. Answer ……………… ……… . [3] (d) A warning is issued whenever 1.5T  . Using your graph, estimate the duration in which the warning would have been active. Answer ……………… .. hours [1] 0.5 3 Gradient 5 2 1.3 3    1.76 C/h (3 s.f)  ------ A1, B1 (for units) Duration = 1.4 + 0.25 = 1.65 hours B1 B1 B1 (±0.1) (±0.1) (1.45 to 1.85) (±0.1 dependent on working lines)

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 9 t T –4 –3 –2 –1 O 1 2 3 4 –1 –2 –3 –4 1 2 3 4            (–3, 2) (–1.3, 5) P2: all points plotted accurately P1: less than 6 points plotted accurately C1: Smooth curve    3T k t t p t q    M1: Drawing of tange