2023 CGS Prelim P2

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION 2023 MATHEMATICS 4052/02 Paper 2 22 Aug 2023 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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. 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 𝜋𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋𝜋. 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. Question 1 2 3 4 5 6 7 8 9 Marks Table of Penalties Question No. Presentation –1 Accuracy/ Units –1 Parent’s / Guardian’s Signature This document consists of 22 printed pages For Examiner’s Use 90

2 Crescent Girls’ School 2023 Prelim S4 Math P2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP + Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = 21 3 rhπ Volume of a sphere = 34 3 rπ Area of triangle ABC = 1 sin2 ab C Arc length = rθ , where 𝜃𝜃 is in radians Sector area = 21 2 r θ , where 𝜃𝜃 is in radians Trigonometry sin sin sin abc ABC= = 2 22 2 cosa b c bc A=+− Statistics Mean = fx f ∑ ∑ Standard deviation = 22fx fx ff ∑∑ − ∑∑ 

3 Crescent Girls’ School 2023 Prelim S4 Math P2 [Turn Over 1 (a) (i) Factorise 224 20 25x xy y−+ . Answer …………………… [1] (ii) Hence, factorise 224 20 25 12 30 xyx xy y −− ++ completely. Answer ………………………………… [1] (b) 1 24 x ky xy + = −− (i) Evaluate k when x = −2 and y = 1. Answer k = ………………… [1] (ii) Express y in terms of x and k. Answer y = ………………… [3]

4 Crescent Girls’ School 2023 Prelim S4 Math P2 (c) Solve the equation 2 41 036x xx −=− +− . Answer x = ………………… [3]

5 Crescent Girls’ School 2023 Prelim S4 Math P2 [Turn Over [3] (b) Find the speed of the current, giving your answers correct to 3 decimal places. Answer speed = ………………… km/h [3] (c) Find the time taken by the boat to complete a journey of 300 km against the current. Leave your answer in hours and minutes, to the nearest minute. Answer ……… hours ……… minutes [2] (d) State one assumption that you made to solve this problem. [1] 2 A ship sails from Sunny Island to Windy Island and back to Sunny Island on a particular day. The distance between Sunny Island and Windy Island is 60 km and there is a constant current of speed x km/h flowing from Sunny Island to Windy Island. It is given that the speed of the ship in still water is 80 km/h and it takes the ship 30 minutes longer to travel from Windy Island back to Sunny Island. (a) Show that 2 240 6400 0xx +−= .

6 Crescent Girls’ School 2023 Prelim S4 Math P2 3 TA is a tangent to the circle ABCD at the point A. It is given that angle 88BAD = ° , angle 46ABD = ° and BC = CD. (a) Prove that AC is the diameter of the circle. [3] (b) Find (i) angle ,DAT Answer ……………………° [2] T B C D A E 88° 46°

7 Crescent Girls’ School 2023 Prelim S4 Math P2 [Turn Over (ii) angle ,DEC Answer ……………………° [2] (iii) angle .ATD Answer ……………………° [2] (c) Name the quadrilateral ABCD. Answer …………………… [1]

8 Crescent Girls’ School 2023 Prelim S4 Math P2 4 The following is the table of values for 2 10 25yx x=+− . x 1 1.5 2 2.5 3 4 5 6 y 7 2.4 1.5 1.6 2.1 3.6 p 7.3 (a) Calculate the value of p, correct to one decimal place. Answer p = …………………… [1] (b) On the grid, draw the graph of 2 10 25yx x=+− for 16 x≤≤ . [2]

9 Crescent Girls’ School 2023 Prelim S4 Math P2 [Turn Over (c) By drawing a tangent, find the gradient at the point where 1.5x = . Answer gradient = …………………… [2] (d) Draw the graph of 7 0.5yx= − on the grid in part (b) for 06 x≤≤ . [1] (e) (i) Write down the x coordinates of the points at which the two graphs intersect. Answer x = ……………… or ………………… [1] (ii) Given that a, b, c and d are integers, find the equation, in the form 32 0a bx cxx d+ + += , which is satisfied by the values of x found in (e)(i). Answer …………………… [2]

10 Crescent Girls’ School 2023 Prelim S4 Math P2 5 A container is formed by joining a cone of base radius 4 cm and a hemisphere of radius 4 cm as shown in Diagram 1. It is given that the volume of the cone is 3 5 the volume of the hemisphere. Diagram 1 Diagram 2 (a) Show that the height of the cone is 4.8 cm. [2] 4 cm 3 cm