ACSI 2013 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 1 Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2013 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 FRIDAY 4th OCTOBER 2013 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 numeric al 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 13 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2013/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 written working. You are therefore advised to show all working. Answer all the questions in the spaces provided. 1 [Maximum mark: 3] Ann buys y erasers at $0.50 each and 4y pens at $1.20 each. She wishes to spend less than $40. (a) Form an inequality in y . [1 mark] (b) Solve the inequality and hence, find the largest possible value of y . [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 3 2 [Maximum mark: 6] (a) (i) Given that ym m   5 3 , express m in terms of y . (ii) Hence, find the value of m when 3y . [4 marks] (b) Simplify and express xx x 62 31 2   as a single fraction. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 4 3 [Maximum mark: 6] In the diagram, BC = 12 cm, CD = 4 cm , DA = 5 cm, oACB 90 and ADC is a straight line. (a) Calculate AB. [2 marks] (b) Write down, as a fraction, the value of (i) CBDsin . (ii) ADBcos . [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… A B C D 4 cm 5 cm 12 cm

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 5 4 [Maximum mark: 7] In the diagram, A, B, C and D are points on level ground. A is north of B. The bearing of D from A is o115 and the bearing of D from B is o25 . oBDC 132 , 7BD m, 5CD m and 11BC m. (a) Find the value of ADB . [2 marks] (b) Find the bearing of C from D. [2 marks] (c) Calculate the value of o132cos , leaving your answer in fraction. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… A N B C D 5 7 132𝑜 11

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 6 5 [Maximum mark: 7] Jacob bought x calculators, each at the same price, for a total cost of $258. (a) Write down an expression for the cost of each calculator in terms of x . [1 mark] (b) He kept 3 calculators for himself and sold the rest at a profit of $3 per calculator. Write down an expression, in terms of x , the total amount, in dollars, he received for all the calculators sold. [1 mark] (c) Given that Jacob made a profit of $102 altogether, form an equation in x and show that it reduces to 0258372  xx . [2 marks] (d) Solve the equation in part (c) and hence find the selling price of each calculator. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 7 6 [Maximum mark: 7] A metal wire, of length 128 cm is to be bent to form the frame of a rectangular box as shown below. Given that the dimensions of the box are x2 cm  16 cm  h cm, (a) express h in terms of x . [2 marks] (b) express the volume V cm3 of the box in term of x . [2 marks] (c) hence, by completing the square, find the maximum volume of the box. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… x2 cm h cm 16 cm

ACS(Independent)/Y3IPCoreMathsP1/2013/Final Year 8 7 [Maximum mark: 3] The diagram below shows the straight line obtained by plotting ylg against xlg . Given that 2 3 2 10 xy  , calculate the value of k . [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………