CEDAR 2025 EMATH PRELIM P1 QP

CEDAR GIRLS’ SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 SECONDARY FOUR CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/01 Paper 1 21 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, 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. Gives answers in degrees to one decimal place. For  , use either your calculator value or 3.142. For Examiner’s Use 990 This document consists of 20 printed pages. [Turn over]

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 2 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  − 

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 3 Answer all the questions. 1 (a) Given 22 2 vta s −= , express v in terms of a, t and s. Answer v = ………………… [2] (b) Simplify 22 2 4 4 4 2 xy y x xy y y x −− + − . Answer ………………………… [3] 2 The diameter of a solid sphere is 7.12 cm, measured correct to 3 significant figures. Its density is 2.2 g/cm3. Find the smallest possible mass of the sphere. Answer …...………………….. g [2]

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 4 3 An area of 512 km2 is represented by 50 cm2 on a map. Find the scale of the map in the form 1 : n. Answer ..………. : .………… [2] 4 (a) Factorise completely 32 30 5 6m m m+ + + . Answer …………….………… [2] (b) Given that m is a positive integer, explain why 32 30 5 6m m m+ + + is not a prime number. Answer ……………………..…..……………………..…..……………………..……… ……………………..…..……………………..…..……………………..……… [1] 5 Mary cycles 2.8 km at an average speed of 12 km/h and takes a break. She then continues to cycle a further 1.4 km in 5 minutes. Given that her average speed for the whole journey is 19 3 km/h, find the duration of her break. Answer ..………..….…….. h [2]

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 5 6 (i) The diagram below shows 3 lighthouses A, B and C at sea. AC = 12 km. BC = 18 km. AB = 17 km. The bearing of B from C is 136o. Find the bearing of A from C. Answer ..………..….…….. o [2] (ii) Find the area of the region enclosed by triangle ABC. Answer ..………..….……km2 [2] A C North B 17 12 18

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 6 7 On the axes given, sketch the graphs 3xy= and 3y x= , indicating the x- and y- intercepts where relevant. The point (1, 1) is marked in the diagram. Answer [2] 8 (a)  = {all real numbers} A = {all perfect cubes} B = {all rational numbers} C = {all recurring decimals} D = {1, 2, 3, 4, 5, 6, 7, 8, 9} (i) List all the elements contained in the set AD . Answer …………….……………………….………… [1] (ii) Explain why ' CB = . Answer ……………………..…..……………………..…..……………………..…. ……………………..…..……………………..…..……………………..…. ……………………..…..……………………..…..……………………..…. [1] x y O

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 7 (b) On the Venn diagram, shade the region(s) which represent ( ) ( )''A B A B   . Answer [1] 9 A quadratic curve 2 3.5y x mx=− + + has a turning point at ( )1.5, p− , where both m and p are constants. Find the value of m and of p. Answer m = …………….. p = …………….. [4] A B 

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 8 10 A pet dish bowl is in the shape of a frustum, as shown in the diagram. It is formed by removing a smaller cone from the top of a larger cone. The smaller cone is similar to the original cone, and its volume is 3 8 of the volume of the original cone. The original cone has a height of 40 cm. (a) Find h, the height of the frustum. Answer h = …………….......... [2] (b) Given that the curved surface area of the frustum is 966 cm2, find the curved surface area of the smaller cone. Answer …………………. cm2 [2] h 40

Cedar Girls’ Secondary School 4052/01/S4/Prelim Exam/2025 [Turn over 9 11 The table shows the income tax rates for different tax brackets. Chargeable income Income tax rate (%) First $20 000 0 Next $10 000 2 Next $10 000 3.5 Next $40 000 7 Next $40 000 11.5 In 2022, given that David’s chargeable income is $60,500, find his income tax payable for YA 2022. Answer $ …………………... [2] 12 (a) Express 630 as a product of its prime factors. Answer ….…………………… [1] (b) Find the smallest integer value of m such that 630m is a perfect square.