GESS 2025 EM PRELIM P2

This document consists of 26 printed pages including the cover page. GAN ENG SENG SCHOOL Preliminary Examination 2025 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Sec 4 Express / 5 Normal (Academic) 4052/02 29 August 2025 2 hour 15 minutes READ THESE INSTRUCTIONS FIRST Candidates are to answer on the Question Paper. No Additional Materials are required. Write your class, index number and name 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, highlighters, glue or correction fluid. Answer all 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 of the marks for this paper is 90. For Examiner‘s Use Total 90

2 GESS 4E5N EM P2 PRELIM 2025 SZK Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh 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 ff  −  

3 GESS 4E5N EM P2 PRELIM 2025 SZK 1. (a) Solve the inequality 2 1 3 1 35 xx+−− − . Answer [2] (b) Express as a single fraction in its simplest form 2 7 1 3 (3 1) x xx−+−− . Answer [3]

4 GESS 4E5N EM P2 PRELIM 2025 SZK (c) Solve the simultaneous equations. 5 49 4 4 5 10 xy xy =− − =− Answer x = y = [3] (d) Simplify 2 15 3 1264 h f −   . Answer [2]

5 GESS 4E5N EM P2 PRELIM 2025 SZK 2. The organiser of the SG60 events held SG60 concerts on two specific weekends in June 2025. The seats in the concert hall were divided into three sections. The table below summarises the number of tickets sold on Saturday and Sunday in week 1. Section A Section B Section C (obstructed view) Saturday 164 144 50 Sunday 128 90 40 (a) Write down a 2 × 3 matrix A to represent the information shown in the above table. Answer [1] The price per ticket for each section is as shown in the table below. Section A Section B Section C Price per ticket $30 $25 $20 (b) Represent the price of the tickets in a 31 column matrix P. Answer [1]

6 GESS 4E5N EM P2 PRELIM 2025 SZK (c) Evaluate the matrix (1 1)AP and interpret the element(s) in the matrix. Answer [2] _________________________________________________________________ _________________________________________________________________ [1] (d) In week 2, the number of tickets sold changes for the various sections on Saturday and Sunday. The number tickets sold for section A increased by 25%. The number of tickets sold for section B increased by 50%. The number to tickets sold for section C decreased to 80%. (i) Write down a matrix M such that the elements of matrix F, where F = AM, represents the number of tickets sold for sections A, B and C respectively on Saturday and Sunday in week 2. Answer [1] (ii) State what each element of matrix FP represents. Answer _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ [1]

7 GESS 4E5N EM P2 PRELIM 2025 SZK 3. The diagram below shows the points A, B, C and D on the level ground where D is due north of B. CD = 9 m, AB = 14.5 m, AD = 6 m, = 30DBC and = 85DCB . (a) Calculate the length of BD. Answer m [2] (b) Calculate the bearing of A from D. Answer [3] 14.5 m 6 m 9 m 30 85 A N C B D

8 GESS 4E5N EM P2 PRELIM 2025 SZK (c) CT is a vertical pole of height 12 m standing at C. X is a point along the path BD such that the angle of elevation of the top of the pole, T, from X is the greatest. Find the angle of elevation of T from X. Answer [3]

9 GESS 4E5N EM P2 PRELIM 2025 SZK 4. A container is in the shape of a cylinder of height 10 cm with a conical top of height 2 cm. The base of the container has a diameter of 3 cm. (a) Calculate the volume of the container correct to 3 significant figures. Answer cm3 [3] 2 cm 3 cm 10 cm

10 GESS 4E5N EM P2 PRELIM 2025 SZK (b) 75% of the container is filled with water as shown in the diagram below. Calculate the depth, d cm, of the empty space in the container. Answer cm [3] d cm 3 cm 10 cm 2 cm