ACSI 2023 Y3 Core Mathematics Paper 2 Solution

Anglo - Chinese School (Independent) FINAL EXAMINATION 2023 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 Thursday 6th 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. 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 5 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2023/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) 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] 𝑥𝑥𝑥𝑥 + 2𝑥𝑥 𝑥𝑥 = 3𝑥𝑥 5 5𝑥𝑥𝑥𝑥 + 10𝑥𝑥 = 3𝑥𝑥2 𝑥𝑥(5𝑥𝑥 + 10) = 3𝑥𝑥2 𝑥𝑥 = 3𝑥𝑥2 5𝑥𝑥 + 10 � 1 𝑎𝑎 + 1 − 2𝑎𝑎 (𝑎𝑎 − 1)(𝑎𝑎 + 1)� �1 − 𝑎𝑎 𝑎𝑎 � = � 𝑎𝑎 − 1 − 2𝑎𝑎 (𝑎𝑎 − 1)(𝑎𝑎 + 1)� �1 − 𝑎𝑎 𝑎𝑎 � = � −1 − 𝑎𝑎 (𝑎𝑎 − 1)(𝑎𝑎 + 1)� �−(𝑎𝑎 − 1) 𝑎𝑎 � = 1 + 𝑎𝑎 𝑎𝑎(𝑎𝑎 + 1) = 1 𝑎𝑎 Do not leave answers in fraction over a fraction for example 𝑥𝑥 = 3 5𝑥𝑥2 (𝑥𝑥+2)

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2023/FinalExamination 3 (c) Evaluate 2lg[(6.82 1.55 10 )] 32.8 −÷× , leaving your answer correct to 2 significant figures. [1] 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 a 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 session. [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] 168 𝑥𝑥 168 𝑥𝑥 − 7 168 𝑥𝑥 − 7 − 168 𝑥𝑥 = 2 168𝑥𝑥 − 168(𝑥𝑥 − 7) 𝑥