ACSI 2021 Y3EXP FYE AMath P1

INDEX NUMBER Anglo - Chinese School (Independent) FINAL EXAMINATION 2021 YEAR THREE EXPRESS ADDITIONAL MATHEMATICS PAPER 1 4049/01 Tuesday 5 October 2021 1 hour 30 minutes Candidates answer on the Question Paper. No additional materials are required. READ THESE INSTRUCTIONS FIRST Write your index number in the space 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 questions. Write your answers in the spaces provided under each question. 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 a 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 number of marks for this paper is 60. This document consists of 15 printed pages and 1 blank page. For Examiner’s Use 60

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −±−= Binomial expansion ( ) ,......21 221 nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− where n is a positive integer and ( ) ! ( 1)...( 1) !! ! n n nn n r r rnr r  − −+= = − 2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += AAec 22 cot1cos += Formulae for ∆ABC C c B b A a sinsinsin == Abccba cos2222 −+= 1 sin2 ab C∆=

3 Answer all the questions. 1 Solve the following pair of simultaneous equations 232 1xy y−+ = − 21xy−= [4] [Turn Over

4 2 Given that 8sin 17=θ and that θ is obtuse, find the exact value of (i) tan ,θ (ii) cos( ),θ− [2] [1] (iii) sec(180 ).θ°− [2]

5 3 The figure shows part of a straight line graph obtained by plotting 1 y against 2 1 x . Express y in terms of x. [4] [Turn Over

6 4 Express the following in partial fractions. (a) ( ) 2 2 3 22 22 xx xx −+ + , [5]

7 (b) 2 2 45 43 xx xx ++ ++ . [4] [Turn Over

8 5 The expression f(x) = ax3 + x2 + bx + 15 leaves a remainder of 11 and 14 when divided by (x –