BVSS 2024 Prelim EM Paper 2

BUKIT VIEW SECONDARY SCHOOL Secondary Four Express/Five Normal (Academic) Preliminary Examination 2024 CANDIDATE NAME CLASS REGISTER NUMBER Mathematics 4052/02 Paper 2 20 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class in the spaces provided on top of this cover 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, 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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . At the end of the examination, fasten all your work securely together. 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. Marks 90 Setter: Mrs Irni Prasad Parents’ Signature: This question paper consists of 20 printed pages and 2 blank pages BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL BUKIT VIEW SECONDARY SCHOOL

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 = 2 2 1r , 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 =   f fx Standard deviation = 22       −     f fx f fx

3 Answer all the questions. 1. (a) Factorise completely 2 44x x xy y− − + . Answer ………………………… [2] (b) Given that 11 1244 8 2 x− += , find the exact value of x. Answer x = …………………… [3] (c) Given that 13 12 − += h hk , express h in terms of k. Answer h = …………………… [2] (d) Solve 4 73 2 12 3 2 ++ xxx . Answer ………………………… [3]

4 2. The diagram shows three points, A, B and C on the ground. AB = 174 m and BC = 195 m. The bearing of A from B is 238°. The bearing of C from A is 108°. A point D lies on the path AC such that it is equidistant to A and to B (a) Show that angle BAC = 50. Answer : [3] (b) Find the angle BCA. Answer ………….………….. [2] North A B C 174 195 D

5 (c) Find the area of triangle ABC. Answer ………….………… m2 [3] (d) Find distance from C to D. Answer ………….………… m [4] ----------------------------------------------------------------------------------------------------------------

6 3. The variables x and y are connected by the equation 3 432 xyx= − + . Some corresponding values of x and y are given in the table below. . x . . 3.5− . . 3− . . 2− . . 1− . . 0 . . 1 . . 2 . . 2 .5. . 3 . . y . 4.4− . . 1.5 . . p . . 6.5 . . 3 . . 0.5− . . 1− . 0.8 . 4.5 . (a) Find the value of p . Answer p = ………………… [1] (b) On the graph paper found in the next page, draw the graph of 3 432 xyx= − + for 33.5 x−  . [3] (c) By drawing a tangent, find the gradient of the curve at x = 2.5. Answer …………………… [2] (d) (i) On the same axes, draw the line 1yx=− − for 33.5 x−  . Answer [on graph] [1] (ii) Write down the x-coordinate of the point where this line intersects the curve. Answer x = ………………… [1] (e) State the minimum value of 3 432 xyx= − + for 03 x . Answer ………….………… [1]

7 (f) The equation 3 4 5 02 x x− + = has only one solution. Explain how this can be seen from your graph. Answer : [2] –6 –5 –4 –3 –2 –1 0 1 2 8 6 –4 –3 –2 –1 0 1 2 3 1 2 3 4 5 6 x y –2 4 –4 2

8 4. The diagram shows a circle with centre O. ABCDE is a straight line. AC = CD and line OD meets the circle at F. It is given that OB = 7.5 cm, CD = 12 cm and OBD = 90. (a) Find the length of OD. Answer ………….………… cm [1] (b) Without the use of a calculator, find the value of cos ODE in its simplest form. Answer ………….…………… [1] (c) Show that angle COD is approximately 0.501 rad. Answer : [3] A B C D E O 7.5 cm 12 cm F

9 (d) Find the perimeter of shaded region. Answer ………………………. cm [3] ----------------------------------------------------------------------------------------------------------------

10 5. A lead technician working with his trainee, can repair a machine in 4.2 hours together. If each of them worked alone, the lead technician would take x hours, while the trainee will need 3.5 hours more. (a) If each of them worked alone, find in terms of x, (i) the fraction of work done by the lead technician in one hour, Answer ………….………… [1] (ii) the fraction of work done by the trainee in one hour. Answer ………….………… [1] (b) Form an equation and show that it reduces to 210 49 147 0xx− − = . [3]