ACSI 2019 Y3EXP FYE AMath P2

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 1 Anglo - Chinese School (Independent) FINAL EXAMINATION 2019 YEAR THREE EXPRESS ADDITIONAL MATHEMATICS PAPER 2 Wednesday 09 Oct 2019 1½ hours Candidates answer on the Question Paper. No additional materials are required. _______________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your index number on the space provided above. Do not open this examination paper until instructed to do so. 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 spaces 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. 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 12 printed pages. [Turn Over For Examiner’s Use Candidate Index Number 60

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 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 Abccba cos2222 −+= 1 sin2 ab C∆=

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 3 Answer all the questions. 1. The graphs 22 1x pxy y− += and 20x py− −= intersect at ( )0, 1− . Find, (i) the value of p, [1] (ii) and the other point of intersection. [3] 2. The polynomial 32 7bx cx x c+ −+ leaves a remainder of 7 when it is divided by )1( +x and a remainder of 43 when it is divided by ( 3)x− . Find the value of b and of c. [4] [Turn Over

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 4 3. Find the point of intersection of 1y x= and 2 2yx= . Hence, sketch the graphs of 1y x= and 2 2yx= on the same diagram, indicating the point of intersection clearly. [4] 4. A cuboid has a volume of ( ) 314 12 3 cm+ and a square base of side ( )1 3 cm+ . Find the height of the cuboid in the form a bc+ where a, b and c are integers. [4]

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 5 5. Express ( ) 2 2 54 4 xx xx ++ + in partial fractions. [5] [Turn Over

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 6 6 (i) Show that ( 1)y+ is a factor of the polynomial 322 ( 2) ( 7) 3y my my+− +− − for all values of m. [2] (ii) If (2 1)y− is also a factor of the polynomial, find the value of m. [3] (iii) Hence, solve 322 ( 2) ( 7) 3 0y my my+− +− − = [2]

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 7 7 (a) Find the range of values of m for which 2 68mx m x+ − >− for all real values of x. [4] (b) Explain why ( ) 22 21 2x kx k++= − has real and distinct roots for all real values of k. [4] [Turn Over

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 8 8 (a) Solve 32 16 4 8 x x x − − = [4] (b) Solve ( ) 23 53 6 0xx+ −= [4]

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 9 (c) Given that 237 28xx−+ = , find the value of 142x. Hence, solve for x. [5] [Turn Over

ACS(Independent)MathDept/Y3AddMathP2/2019/FinalExam 10 9 The following table shows some corresponding values of x and y which are related by the equation y = x + axb. (a) Using a scale of 1 cm to 0.1 unit on each axis, draw the graph of )lg( xy− against lg x on a piece of graph paper. [3] (b) Use the graph to i) find the value of a and of b, [3] ii) find the value of y when x = 15, and [3] iii) identify the abnormal reading of y, and estimate its correct value. [2] x 2 3 4 5 6 10 y 5.80 9.33 11.00 12.59 14.12 19.90