ACSI 2018 Y3EXP FYE AMath P1

Anglo - Chinese School (Independent) FINAL EXAMINATION 2018 YEAR THREE EXPRESS ADDITIONAL MATHEMATICS PAPER 1 Friday 5 October 2018 1 hour 30 minutes Additional Materials: Answer Paper (6 Sheets) READ THESE INSTRUCTIONS FIRST Write your index number on all the work you hand in. 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 on the separate Answer Paper provided. 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. 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 60. _____________________________________________________________________ This question paper consists of 5 printed pages. [Turn over

ACS(Independent)MathDept/Y3EXP/AMP1/2018/FINAL EXAM 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∆=

ACS(Independent)MathDept/Y3EXP/AMP1/2018/FINAL EXAM 3 Answer all the questions. 1 Solutions to this question by accurate drawing will not be accepted. In the diagram below, A(0, 2), B(6, 0) and C(h, k) are the midpoints of the sides of the triangle PQR, and Q is the point )1 ,2( −− . Find the coordinates of C. [4] 2 (a) Simplify 2 180 245 3 125+− , leaving your answer in surd form [2] (b) Solve the equation 1 213 x x = − . [3] 3 When the graph of xy x+ against y is drawn, a straight line is obtained. Given that the line passes through the points ( )5, 2− and ( )1, 4 , find (i) y in terms of x, and [4] (ii) the value of x when y = 2. [2] 4 A rectangle has a length of 2α cm and