2026 CCH MAIN P1 QP

2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2026 SECONDARY 4 MATHEMATICS 4052/01 Paper 1 Thursday 20 August 2026 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. 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. 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 of the 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 , use either your calculator value or 3.142. For Examiner’s Use Total / 90 This document consists of 21 printed pages and 1 blank page.

2 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 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 = 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    f xf 22           f xf f xf

3 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Answer all the questions. 1 (a) Factorise 24 2 8p q pq p   . Answer ……………………… [2] (b) Simplify   22 3 3 2 xyx y z z  . Answer ……………………… [3] SPACE

4 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 SPACE 2 (a) Solve the inequalities 7 4 2 3 8.x x x     Answer ……………………… [2] (b) Illustrate your answer to part (a) on the number line below. [1] 3 Solve the equation 2 1 4 363 x x   . Answer x ………………… [3] x 0 1 2 3 4 5 6 7 8 9 10

5 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over SPACE 4 Expand   4 3 1x x  . Answer …… ………………… [2] SPACE 5 Light takes approximately 8 minutes to travel 150 million kilometres. (a) Find the average speed of light, in metres per second. Give your answer in standard form. Answer ………………… m/s [2] (b) The star Proxima Centauri is 4×1013 km from Earth. Find the time, in years, it takes for light to travel from Proxima Centauri to Earth. [Assume 1 year = 365 days] Answer ………… …… .. years [2] SPACE

6 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 6 (a) Sketch the graph of   2 2 4y x   on the axes below. Indicate clearly the turning point and the points where the graph crosses the axes. [2] (b) On the same graph in (a), draw and label the line of symmetry of the graph. [1] 7 In a regular n-sided polygon, the interior angle is 3 times that of the exterior angle. Find the value of n. Answer n = ………………… [2] y x O

7 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over SPACE SP 8 Solve the following equations. (a) 4 3 3 4 x x    , Answer x = ……… or ……… [2] (b) 3 1 37 2 x x   . Answer x = ……………… …. [3]

8 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 9 Solve these simultaneous equations. 2 5 2 0 x y x y     Answer x = …………………. y = …………………. [3] SP

9 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over SPACE 10 (a) { : is an integer, 0 10}x x x    { : is a prime number}P x x { : is a perfect square}S x x { : is an even number}E x x (i) Write down the relationship between set P and set S using set notation. Answer ……………………… [1] (ii) Complete the Venn Diagram below to represent set P, set S and set E.  [2] (b) On the Venn diagram, shade the region which represents 'A B .   [1] A B

10 2026 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 SPACE 11 The drink stall at a hawker centre sells tea, coffee and Milo. In one week, the drink stall sells 500 cups of tea (T), 1200 cups of coffee (C) and 800 cups of Milo (M). The next week, the drink stall sells 400, 900 and 700 cups of tea, coffee and Milo respectively. (a) Represent this information in a 2×3 matrix, P. T C M Answer P            Week 1 Week 2 [1] (b) The cost of a cup of tea, coffee and Milo are $1.00, $1.10 and $1.70 respectively. Represent this information in a 3×1 matrix R.  Answer R = ……………………………… [1] (c) Evaluate the matrix PR. Answer PR = ……………………………… [2] (d) Explain what each of the elements in the matrix PR represent. ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [1] SPACE