2025 GDLSS P2 QP

Name:____________________________ ( ) Class:________ TG : _______ This document consists of 23 printed pages, including this cover page and 1 blank page. Greendale Secondary School 2025 GREENDALE SECONDARY SCHOOL Preliminary Examination 2025 MATHEMATICS 4052/02 Paper 2 19 August 2025 Secondary 4 EXP / 5 N(A) 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name 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 staples, paper clips, 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 π . 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. No of additional booklets/ writing paper used No of additional graph paper used Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 a,b c a,b,d c a b a b Strand Marks 90

Greendale Secondary School 2 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curve surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22 −  ffxffx

Greendale Secondary School 3 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 Blank Page

Greendale Secondary School 4 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 Answer all questions. 1 (a) The table shows the visitor arrivals to Singapore in the past three years. Year 2022 2023 2024 Visitor Arrivals 6 305 744 13 610 404 16 526 312 (i) Write the 2023 visitor arrivals in standard form, correct to three significant figures. Answer …………………………… [1] (ii) Calculate the percentage increase in the visitor arrivals from 2022 to 2024. Answer …………………………% [2] (b) During the sale, a pair of running shoes originally priced at $175 was marked down by 15%. Customers with a membership card get an additional 12% discount off the marked down price. How much would a member save in total during the sale? Answer $………………………… [2]

Greendale Secondary School 5 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 (c) A forest with an area of 13.02 km2 is represented on a map with an area of 52.08 cm2. (i) Find the scale, in the form 1 : n, used for the map. Answer 1 : ……………………… [2] (ii) Two locations are 65 cm apart on the map. Calculate the actual distance between the two locations in kilometres. Answer ……………………… km [1] (iii) The government plans to plant new trees in 25% of the forested area. If each tree requires 5 m2 of space, calculate the number of trees that can be planted. Answer …………………………… [2]

Greendale Secondary School 6 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 2 (a) Solve ( ) ( )4 3 6 7 2 3xx− − = − − . Answer x =………………………… [2] (b) Solve the inequality 9 3 5xx−  − . Answer …………………………… [1] (c) Given the formula 23 nRm t= , (i) express t in terms of m, n and R, Answer t =………………………… [3] (ii) find the value of t when 1 ,2m=− 5n = and 2R= . Answer t =………………………… [1]

Greendale Secondary School 7 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 (d) Solve the equation 2 13 1 5xxx −=−− , giving your answers correct to 2 decimal places. Answer x =……………… or ……………… [5]

Greendale Secondary School 8 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 3 Diagram A below shows a solid toy in the shape of a hemisphere of radius 26 cm, surmounted by a frustum of height 18 cm. The toy is packed in a cylindrical box with a lid as shown in Diagram B. (a) The frustum is obtained by removing the smaller cone from the bigger cone. Show that the height of the smaller cone that was removed is 11.25 cm. Answer [2] (b) Find the volume of the empty space inside the container. 26 10 18 Diagram A Diagram B 26 10 18 [Please turn over.]

Greendale Secondary School 9 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 Answer ………………………… cm3 [4] (c) Find the total surface area of the solid toy. Answer ………………………… cm2 [4]

Greendale Secondary School 10 Secondary 4 Express / 5N(A) Preliminary Examination 2025 Mathematics Paper 2 4 The variables x and y are connected by the equation 3 342xyx= + − . Some corresponding values of x and y are given in the table below. x 4− 3− 2− 1− 0 1 2 3 4 y 48− 26.5− 14− 7.5− 4− 0.5− 6 18.5 p (a) Find the value of p. Answer p =………………………… [1] (b) On the grid opposite, draw the graph of 3 342xyx= + − for 44 x−   . [3] (c) Use the graph to write down an inequality in x to describe the range of values of where 10y . Answer …………………………… [1] (d) (i) On the same grid, draw the graph of 10 6yx=− for 44 x−   . [2] (ii) Show that the points of intersection of the line and the curve give the solution of the equation 3 14 4 0xx− + = . Answer [2] (iii) Use your graph to solve the equation 3 14 4 0xx− + = . Answer x =……………… or ……………… or ……………… [2]