ACSI 2017 Y3EXP FYE AMath P1

Anglo - Chinese School (Independent) FINAL EXAMINATION 2017 YEAR THREE EXPRESS ADDITIONAL MATHEMATICS PAPER 1 Friday 6 October 2017 1 hour 30 minutes Additional Materials: Answer Paper (8 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 4 printed pages. [Turn over

ACS(Independent)MathDept/Y3Exp/AM1/2017/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/AM1/2017/Final Exam 3 Answer all the questions. 1 Given that 32() 2 2f x x ax x=+ ++ for all values of x. (a) Find the value of a if ()fx has a remainder of 1− when divided by ( )1x+ . [2] (b) Find the quotient when the expression 32 22x ax x+ ++ is divided by ( )1x+ . [2] 2 The total resistance of two resistors in an electric circuit is given by the formula 12 111 RR R= + . Given that 31R= − and ( )1 1 313R = + , find the value of R2 in the form 3ab+ where a and b are integers. [4] 3 (i) Find the coordinates of the point of intersection of 3y x= and 1 42yx= for 0x> . [2] (ii) Sketch the graph of 1 42yx= for 0x≥ and 3y x= for 0x> on the same diagram, indicating the point of intersection. [3] 4 The variables x and y are related by the equation pxxq y−= , where p and q are constants. When y is plotted against y x , a straight line graph