ACSI 2022 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATION 2022 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 Thursday 6th October 2022 1 hour 30 minutes ADDITIONAL MATERIALS: Answer Paper (6 sheets) Graph Paper ( 1 sheet) INSTRUCTIONS TO STUDENTS Do not open this examination paper until instructed to do so. A calculator is required for this paper. Answer all the questions on the answer sheets provided. At the end of the examination, fasten the answer sheets together. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. Answers in degrees are to be given to one decimal place. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. ______________________________________________________________ This question paper consists of 4 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2022/FinalExamination 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 correct method, provided this is shown by written working. You are t herefore advised to show all working. Answer all the questions on the answer sheets provided. Begin each question on a new page. 1. [Maximum mark: 6] (a) Simplify 22 22 2a ab b b a ab − + +− − . [3] (b) Subtract 2 4 4x − from 11 22 xx−−+ , expressing your answer as a single fraction in its simplest form. [3] 2. [Maximum mark: 8] Joe bought x number of books, each at the same price, for a total cost of $336. (a) Write down an expression for the cost of each book in terms of x . [1] Joe sold 20 of them for $480, and the rest at a loss of $4 per book. (b) Write down an expression for the total amount, in dollars, he received for all the books. [2] (c) Given that Joe made a profit of $184 altogether, form an equation in x and show that it reduces to 2 94 1680 0xx−+ = . [2] (d) Hence, solve the equation 2 94 1680 0xx−+ = and state the cost price of each book. [3] 3. [Maximum mark: 13] (a) Evaluate 2 3 2 2.15log 0.25 e −  +  , leaving your answer correct to 2 significant figures. [3] (b) Given that ( ) ( ) 31 43 23144 216 2 3 xy zpp p −−÷= , evaluate x , y and z . [4] (c) Simplify 22 1 6 2(3 ) 48 ww w+ + + . [3] (d) Find the range of values of x if 22 5277xx−− < . [3]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2022/FinalExamination 3 4. [Maximum mark: 8] (a) Solve the equation 134yy+ = . [4] (b) Solve the equation ( ) 2 33 9log log ( 3) log (9 )xx x+ −= . [4] 5. [Maximum mark: 12] In the figure, A, B and C are three points on a horizontal field. A is due west of B, the bearing of B from C is 125o, AB = 4