SCSS 2024 EM Prelim P2 QP

SWISS COTTAGE SECONDARY SCHOOL SECONDARY FOUR AND FIVE PRELIMINARY EXAMINATION O Name: ( ) Class: MATHEMATICS Paper 2 Candidates answer on the Question Paper. 4052/02 Tuesday 27 August 2024 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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  , 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 number of marks for this paper is 90. This document consists of 21 printed pages and 1 blank page. Setter: Mdm Tan Poh Kim Vetter: Mdm Zoe Pow [Turn over Home of Thoughtful Leaders: Serve with Honour, Lead with Humility For Examiner’s Use Section A 31 Section B 59 Total 90

2 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n rP      +1001 lr 24 r hr 2 3 1 3 3 4 r Cba sin2 1 r  2 2 1 r  C c B b A a sinsinsin == Acbcba cos2222 −+=   f fx 22       −     f fx f fx

3 TURN OVER FOR QUESTION 1

4 Section A (31 marks) 1 (a) Solve the inequality 3 1 2 5 34 xx+− . Answer …………………………. [2] (b) It is given that 23 2 bca bc −= + . (i) Find a when 0.2b= and 1.5c=− . Answer a = …………………….. [1] (ii) Express b in terms of a and c. Answer b = ……………………... [3] Questions 1 2 3 Marks 11 10 10

5 (c) Solve the equation 52 13 2 3 x xx −=−− . Give your solutions correct to 3 decimal places. Answer x = ……………...……. or …………….………. [5]

6 2 (a) Complete the table of values for 2 21y x x= + − x 4− 3− 2− 1− 0 1 2 y 2 1− 2− 1− 2 7 (b) On the grid opposite, draw the graph of 2 21y x x= + − for 42 x−   . [3] (c) Use your graph (i) to write down an inequality in x to describe the range of values where 3y , Answer …...……………………... [1] (ii) to solve the equation 2 120 2xx+ + = . Answer x = .….…..… or ….…....... [3] (d) Based on the graph, Eileen stated that ‘the coordinates of the minimum point of the graph is ( )1, 2−− ’. Show, with working, how you can verify this by expressing 2 21xx+− in the form ( )2x p q++ . Answer [2] [1]

7 y 1 x 2− 0 2 3 4 2 4 6 8 10

8 3 The diagram shows a solid formed from a cone, a cylinder and a hemisphere. The cone has base radius 1.5x cm and height y cm. The cylinder has radius 1.5x cm and height 3x cm. The hemisphere has radius 3x cm. (a) The volume of the hemisphere is thrice the volume of the cone. Show that y = 8x. Answer [3] 3x y 1.5x 3x h

9 (b) The total surface area of the solid is 450 cm2. Calculate the total height, h cm, of the solid. Answer h = ………………..….... cm [7]

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