Dunman Sec 2025 Prelims 4EXP Math Paper 1 QP

This document consists of 22 printed pages. DUNMAN SECONDARY SCHOOL CANDIDATE NAME CLASS INDEX NUMBER PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS/ 5 NORMAL ACADEMIC MATHEMATICS Paper 1 4052/01 19 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. 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, 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 π, use either your calculator 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. Calculator Model Total Marks

2 4052/01/PRELIM/4EXP5NA/2025 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== a2 = b2 + c2 − 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

3 4052/01/PRELIM/4EXP5NA/2025 [Turn Over 1 The graph below shows a company’s yearly revenue from 2020 to 2024. (a) State one misleading feature of the graph. ……………………………………………………………………………………………. ……………...…………………………………………………………………………...... [1] (b) Explain how this feature affects the reader’s interpretation of the graph. ……………………………………………………………………………………………. ……………...…………………………………………………………………………...... [1] 2 Sammi is travelling back to Singapore from Italy. She wants to change 830 euros (€) into Singapore dollars ($). The exchange rate in Italy is €1 = $1.4893. The exchange rate in Singapore is $1 = €0.6747. How many more Singapore dollars will she get by changing her money in Italy? Answer $ ….……………………… [2] Revenue ($ thousands) Year 500 0 1000 2020 2021 2022 2023 2024 Company’s Yearly Revenue Growth

4 4052/01/PRELIM/4EXP5NA/2025 3 (a) Given that 3sin 1x= , find the two possible values for angle x, where 0 180x   . Answer x = …….… or .………… [2] (b) Convert 26° into radians. Answer …………………………… [1] 4 300 ml of liquid is poured into bottles A, B and C in the ratio 2 : 8 : 5. n ml of liquid is spilled from bottle A. The ratio of the amounts of liquid in A, B and C becomes 7 : 40 : 25. Find the value of n. Answer n = ……………………… [2]

5 4052/01/PRELIM/4EXP5NA/2025 [Turn Over 5 (a) Simplify 2 12 3 3 27a b −   . Answer …………………………… [2] (b) 2413 9 4 3 3 p −  = Use the laws of indices to find the value of p. Show your working. Answer p = ……………………… [2] 6 The gravitational force F (in newtons) is inversely proportional to the square of the distance r (in metres) between two objects. John says: “If I tripled the distance between the two objects, the gravitational force they experience will be one-third as strong.” Is he correct? Explain your answer. Answer ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. [2]

6 4052/01/PRELIM/4EXP5NA/2025 7 The bullet train in Japan takes 1.55 hours to travel 341 kilometres from Tokyo to Nagoya. (a) By rounding these numbers correct to 1 significant figure, find an estimate of the speed of the bullet train. Show the numbers you use. Answer …………………….. km/h [1] (b) Without doing any further calculation, explain why the actual speed is faster than the answer to part (a). Answer ……………………………………………………………………………………….. ……………………………………………………………………………………...………… ……………………………………………………………………………………...…… [1] (c) The actual speed of a bullet train is 227 km/h. Change 227 km/h into metres per second. Answer ……………………… m/s [1] 8 Factorise completely. (a) 2216 8a b ab− Answer …………………………… [1] (b) 3 4 3 4c d cd− + − Answer …………………………… [2]

7 4052/01/PRELIM/4EXP5NA/2025 [Turn Over 9 A map of a city has a scale of 1 : n. The actual area of the city is 728.6 km2. The area of the city on the map is 29 cm2. Express the value of n in standard form, correct to 1 significant figure. Answer n = ……………………… [3] 10 Express as a single fraction in its simplest form ( )215 5 12 18 54 27 xxx −+−− . Answer …………………………… [3]

8 4052/01/PRELIM/4EXP5NA/2025 11 In the diagram, A, B, C and D are points on a circle, centre O. OE = OF. Prove that triangles OAB and OCD are congruent. Give a reason for each statement you make. Answer [2] 12 Simplify 2 4 2 7 15 16 81 xx x +− − . Answer …………………………… [3] O A B C D E F

9 4052/01/PRELIM/4EXP5NA/2025 [Turn Over 13 (a) Express 27 10 xx−+ in the form 2( ) .x a b++ Answer …………………………… [2] (b) Write down the equation of the line of symmetry of the graph of 27 10y x x= − + . Answer …………………………… [1] 14 (a)  = {integers x : 1 14}x X = {perfect square} Y = {prime numbers} (i) List the elements in '.Y Answer …………………………… [1] (ii) Explain why XY = . Answer ..……………………………………………………………………………….. …………………………………………………………………...………………..…… ……………………………………………………………………………...…….... [1] (b) On the Venn diagram, shade the region which represents ( )' '.AB [1] A B

10 4052/01/PRELIM/4EXP5NA/2025 15 Sketch the graph of ( )( )27y x x=− + − on the axes below. Indicate clearly the points where the graph crosses the x-axis. [2] 16 A sphere has radius 2r cm. A cone has a radius equal to one-third of the radius of the sphere, and a height of 10h cm. The volume of the sphere is twice the volume of the cone. Express the ratio h : r in its simplest form. Answer ………….. : ………….. [3] y x O