ACSI 2016 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 1 Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2016 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 WEDNESDAY 5th OCTOBER 2016 1 h 30 min Additional Material Graph Paper (1 sheet) INSTRUCTIONS TO CANDIDATES  Write your index number in the boxes above.  Do not open this examination paper until instructed to do so.  You are not permitted access to any calculator for this paper.  Answer all questions in the spaces provided.  Unless otherwise stated in the question, all nu merical answers must be given exactly or correct to three significant figures.  The maximum mark for this paper is 80. For Examiner’s Use _______________________________________________________________ This paper consists of 14 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by writte n working. You are therefore advised to show all working. Answer all the questions in the spaces provided. 1 [Maximum mark: 8] (a) Simplify ac ac bc bc ab ba  . [2 marks] (b) Simplify 42 333 yx xyx  , giving your answer in the form mn yx , where n and m are rational numbers. [3 marks] (c) Factorise completely 6)()( 2  yxyx . [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 3 ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 4 2 [Maximum mark: 8] Mrs. Lim imported some olive oil for $500. She paid x$ for each liter of the olive oil. (a) Find, in terms of x , an expression for the amount of olive oil she bought. [1 mark] During transportation, 30 liters of olive oil was spilled. She sold the remaining olive oil for $1 more per liter than what she paid initially. (b) If she sold all the oil, write down an expression, in terms of x , for the sum of money she received from the sale. [2 marks] Mrs. Lim made a loss of $25. (c) Write down an equation in x to represent this information, and show that it can be reduced to 01006 2  xx . [2 marks] (d) Solve the equation 01006 2  xx , and hence, find the amount of olive oil she bought. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 5 3 [Maximum mark: 8] (a) Given that baln is a solution to 9225  xe , find the value of a and of b , where a and b are integers. [4 marks] (b) Solve )213(log)1(log 42 xx  . [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 6 4 [Maximum mark: 5] The quadratic graph below represents the motion of a cannonball which was fired from a height of 3 meter. The trajectory of the cannonball reached a maximum height of 8 m after 2 seconds. S (a) Given that 𝑦 is the vertical distance in meters and 𝑥 is the time in seconds, express the equation of the trajectory in the form   khxay  2 , where a , h and k are constants. [3 marks] (b) Hence, find the range of values of x for which   3 2  khxa . [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… 3 𝑦 (meter) 𝑥 (seconds) 8 2

ACS(Independent)/Y3IPCoreMathsP1/2016/Final Year 7 5 [Maximum mark: 5] Given that 105  a and 16  b , where a and b are integers. Find (a) the largest possible value of ba , [1 mark] (b) the smallest possible value of ab 2 , [1 mark] (c) the smallest possible value of b aa 31122  . [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ……………