SJI 2016-2022 Math Prelims

STUDENT NAME: TEACHER INITIALS: _________ ST JOSEPH’S INSTITUTION JC2 PRELIMINARY EXAMINATION 2016 MATHEMATICS HIGHER LEVEL PAPER 1 Tuesday 5th July 2016 2 hours 1400 – 1600 hrs INSTRUCTIONS TO CANDIDATES • Do not open this examination paper until instructed to do so. • Section A: Answer all questions showing working and answers in the spaces provided in the exam paper. • Section B: Answer all questions using the foolscap paper provided. • The use of calculators is not permitted in this paper. • A clean copy of the Mathematics HL Formulae Booklet is required for this paper. • Unless otherwise stated in the question all numerical answers are to be given exactly. • The maximum mark for this examination paper is [120 marks]. • This question paper consists of 14 printed pages including the Cover Sheet. _______________________________________________________________________ FOR MARKER USE ONLY: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 TOTAL /120

-2- JC2 HL Maths Prelim Exam 2016/P1 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 advised to show all working. SECTION A (60 marks) 1 [Maximum mark: 4] The mean and standard deviation of a data set ! is given by ! and !. Denote by (!"+!) the set derived by adding ! after multiplying by ! each element in !. (a) Express in terms of ! the mean of the data set (2!−1). [1] (b) Express in terms of ! the standard deviation of (2!+1). [1] (c) Find ! if the variance of (2!+1) is 3. [2] ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. TURN OVER

-3- JC2 HL Maths Prelim Exam 2016/P1 2 [Maximum mark: 7] (a) Given that log!!2+2log!!!−!=log!!!+log!!!, find the value of !!. [4] (b) Solve the equation: 3!!2!!−4−2!!+4=0. [3]