[WDL] MYE Additional Math 2020 P1

Name: _________________________( ) Class: ________ WOODLANDS SECONDARY SCHOOL WEIGHTED ASSESSMENT 2 2020 Level: Sec 4Exp Marks: 80 Subject: Additional Mathematics Day: Tuesday Paper: 4047/01 Date: 30th June 2020 Duration: 2 hours Time: 1445 – 1645 READ THESE INSTRUCTIONS FIRST Answer on the Question Paper. 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. 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. 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 number of marks for this paper is 80. DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. This document consists of 17 printed pages and 1 blank page.

2 Woodlands Secondary School Weighted Assessment 2 2020 Sec 4Exp 4047/01 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21 221 , where n is a positive integer and ( ) ( ) ( ) ! 1...1 !! ! 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 sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Cab sin2 1=

3 Woodlands Secondary School Weighted Assessment 2 2020 Sec 4Exp 4047/01 1 Find the values of x and y which satisfy the equations 2 16 32 4 x y= logx (y + 3) = 1 + logx 4. [5]

4 Woodlands Secondary School Weighted Assessment 2 2020 Sec 4Exp 4047/01 2 (a) Find the range of values of p for which the quadratic equation 2 2 5 0x px p− + + = has (i) real roots, [3] (ii) one positive and one negative root. [2] (b) Consider the function f such that its derivative ( ) ( ) 22' 2 5 3 2f x x kx k= + + + , where x and k are real numbers. Given that f is an i ncreasing function, find the range of values of k. [4]

5 Woodlands Secondary School Weighted Assessment 2 2020 Sec 4Exp 4047/01 3 The diagram shows a trapezium ABCD such that AD is perpendicular to DC and AB is parallel to DC. It is given that ( )4 3 5AB=