ACSI 2023 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATION 2023 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 MONDAY 9th October 2023 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. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. ___________________________________________________________ This question paper consists of 5 printed pages. [Turn over

2 ACS(Independent)MathDept/Y3IPCoreMathPaper2/2023/FinalExamination

3 ACS(Independent)MathDept/Y3IPCoreMathPaper2/2023/FinalExamination Turn Over 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 therefore advised to show all working. Answer all the questions on the answer sheets provided. Begin each question on a new page. 1. [Maximum mark: 8] (a) Make y the subject of the formula 23 5 xy y xx + = . [2] (b) Simplify 2 12 1 111 a aa a   −−  +−   , expressing your answer as a single fraction in its simplest form. [4] (c) Evaluate 2lg[(6.82 1.55 10 )] 32.8 −÷× , leaving your answer correct to 2 significant figures. [2] 2. [Maximum mark: 8] Julian paid $168 for x tickets to a theme park. (a) Write down an expression, in terms of x, for the cost of one ticket in dollars. [1] (b) During the peak season, he could buy 7 less tickets with the same amount of money. Write down an expression, in terms of x, for the cost of one ticket during the peak season. [1] (c) Given that the increase in the cost of one ticket during the peak season is $2, form an equation in x and show that it reduces to 2 7 588 0xx−− = . [3] (d) What is the maximum number of tickets he can purchase with $200 during the peak season? [3] 3. [Maximum mark: 11] (a) Find the range of values of p for which the expression ( 6) 2 34 6x x px p+− +− is always positive for all real values of x. [4] (b) Solve the equation 2 11 12 0xx− += . [4] (c) Given that 2 77xx+=+ , find the exact values of x, leaving your answers in the simplest form. [3]

4 ACS(Independent)MathDept/Y3IPCoreMathPaper2/2023/FinalExamination 4. [Maximum mark: 6] During a workshop, water dispenser in the shape of a right circular cylinder of radius 12 cm, is provided for 250