Geylang Methodist Sec 2024 AM P2 PRELIM Student

[Turn Over Candidate Name Class Index Number ADDITIONAL MATHEMATICS Paper 2 4049 / 02 4 Express/5 Normal(A) Candidates answer on the Question Paper. No Additional Materials are required. 2 hours 15 minutes Setters: Mr Johney Joseph Ms Ng Siew Lee 19 August 2024 READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total score for this paper is 90. For Examiner’s Use This document consists of 19 printed pages and 1 blank page. Geylang Methodist School (Secondary) Preliminary Examination 2024

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− 221 21 , where n is a positive integer and ( ) ( ) ( ) ! 11 !! ! r rnnn rnr n r n +−−=−=       2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += AA 22 cot1cosec += ( ) BABABA sincoscossinsin = ( ) BABABA sinsincoscoscos = ( ) BA BABA tantan1 tantantan  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= Formulae for ABC C c B b A a sinsinsin == Abccba cos2222 −+= Cabsin2 1=

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) [Turn Over 3 1 Solve the equation 422sin 7cos 4xx+= for 0 360x . [6]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) 4 2 At a certain time, the mass of a radioactive substance was recorded as 150 g. This mass decreased with time due to decay and after t hours, the recorded mass was M g. It is known that M can be modelled by the formula 150 ktMe −= , where k is a positive constant. After 50 hours, its mass has decreased to 120g. (a) Estimate the mass of the substance after 120 hours. [4] (b) Estimate after how many hours one third of the substance is decayed. [3]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) [Turn Over 5 3 A curve has the equation 2 , where 22 xeyx x= − . (a) Find d d y x . [2] (b) Find the exact value of the coordinates of the stationary point. [3] (c) Determine the nature of the stationary point. [2]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) 6 4 The line 1xy ab+= , where a and b are positive constants, intersects the x-axis at A and the y-axis at B. The perpendicular bisector of the line joining A and B passes through the point P ( )3, 7−− . (a) Show that 22 6 14a a b b+ = + . [6]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) [Turn Over 7 (b) Given that the gradient of the perpendicular bisector of AB is 2, find the values of a and b. [4]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) 8 5 A circle, with centre C, has equation 22 10 4 25 0x y x y+ − − + = . (a) Find the coordinates of C and the radius of the circle. [4] (b) Explain why the x-axis is a tangent to the circle. [2]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) [Turn Over 9 (c) The tangent to the circle at the point where x = 3 meets the x-axis at the point P. Find the coordinates of P. [3]

GMS(S)/AMath/P2/Prelim2024/4E/5N(A) 10 6 The diagram shows two rods PQ and QR, of lengths 12m and 5m respectively. The rods are fixed at Q such that angle PQR = 90 and hinged at P so as to rotate in a vertical plane. The rod PQ makes an angle  with horizontal ground. (a) Obtain an expression, in terms of  , for d, where d is the horizontal distance of R from P. [3] 12m 5m P Q R d m