2026 CCH MAIN P2 QP

1 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2026 SECONDARY 4 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 22 printed pages and 2 blank pages. For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 Total Marks

2 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone rl Surface area of a sphere 24 r V olume of a cone 21 3 r h Volume of a sphere 34 3 r Area of 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 f f          nrP       1001

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

4 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 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]

5 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over (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]

6 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 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 €9800. 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 working 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. Answer $ .………………… … [2]

7 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over (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 terms. 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 is 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]

8 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 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  corresponds 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 for which the warning would have been active. Answer ……………… .. hours [1]

9 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over t –4 –3 –2 –1 O 1 2 3 4 –1 –2 –3 –4 1 2 3 4 T

10 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/02 [Turn over 4 A fruit wholesaler collects information about the masses of pears supplied by Farm A and Farm B. The stem-and-leaf diagram shows the masses of a sample of 20 pears from Farm A. 15 5 8 16 0 2 3 5 7 9 17 0 1 2 4 4 5 6 8 18 0 2 3 5 Key: 15  8 means 158 grams Find (a) the median, Answer …………… …. grams [1] (b) the interquartile range. Answer …………… ….. grams [2] The box-and-whisker diagram shows the masses of 20 pears sampled from Farm B. (c) The fruit wholesaler examines the box-and-whisker diagram and comments: “A higher proportion of Farm B's pears are heavier, since its right whisker is longer than its left whisker”. Comment on whether the wholesaler’s comment is correct. Answer …………………………………………………………………………………… … . …………………………………………………………………………………… … . …………………………………………………………………………………… ….. [2] 160 165 170 175 180 185 190 195