SJI_HL_Math_EOY_papers_2018-2022_COMBINE

STUDENT NAME: TEACHER NAME: ____________________________ ST. JOSEPH’S INSTITUTION YEAR 5 END OF YEAR EXAMINATION 2018 MATHEMATICS HIGHER LEVEL PAPER 1 Wednesday 26th September 2018 1 hr 30 mins 0800 – 0930 hrs INSTRUCTIONS TO CANDIDATES  Write your session number in the boxes above.  Write your name and teacher’s name in the spaces provided.  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 [80 marks].  This question paper consists of 10 printed pages including the Cover Sheet.  Sections A and B are to be submitted separately. _______________________________________________________________________ FOR MARKER USE ONLY: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 TOTAL /80

Year 5 HL Maths End of Year Exam 2018/P1 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 advised to show all working. SECTION A (40 marks) Answer all questions in the spaces provided. 1 [Maximum mark: 4] The complex numbers 23ui and 32vi satisfy the equation 1 1 10 u v w , w . Express w in the form a ib where ,ab  and 2 1i  . ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. TURN OVER

Year 5 HL Maths End of Year Exam 2018/P1 3 2 [Maximum: 5 marks] Let 𝑔: ℕ ⟶ ℤ+ be a piecewise function defined as 𝑔(𝑛) = { 1, if 𝑛 = 0 𝑔 (1 2𝑛) , if 𝑛 is even 1 + 𝑔(𝑛 − 1), if 𝑛 is odd (a) Find g(3). [3] (b) Does g have an inverse? Justify your answer. [2] ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. ……………………………………………………………………………………………………. …………………………………………………………