CJC_H2_MATH_P1_QP

9740/01/Prelim/2015 [Turn over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/01 Paper 1 26 Aug 2015 3 hours Additional Materials: List of Formulae (MF15) Graph Paper Name: ___________________________ Class: ________________ READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. At the end of the examination, arrange your answers in NUMERICAL ORDER. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 5 printed pages, including the cover page.

2 9740/01/Prelim/2015 [Turn over 1 A calculator is not to be used in answering this question. By considering 2wz z or otherwise, solve 432 223 1 0 0zzzz   where z , leaving the roots in exact form. [4] 2 With reference to the origin O , two points A and B have position vectors a and b respectively. The points O , A and B are not collinear. The point P divides AB in the ratio :3 : 2AP PB  . It is given that a is a unit vector, 4OB , angle π 3AOB and the foot of the perpendicular from P to the line passing through points O and A is F . Show that OF  a   , where  is a constant to be determined. [5] 3 John decided to embark on a 100-day skipping exer cise challenge. The duration of his skipping exercise each day, in seconds, follows an arithmetic progression for the odd days, and another arithmetic progression for the even days. Day Duration (s) Day 1 20 Day 2 20 Day 3 29 Day 4 30 Day 5 38 Day 6 40 Day 7 47 Day 8 50 Day 9 56 Day 10 60   (i) Find the duration of the skippi ng exercise that he does on the 75th day. [2] (ii) Find the total duration of the skipping exer cise that he does for the first 75 days. [3] (iii) After the 75 th day, John thinks that the workout is too strenuous so he decides to modify the workout such that he does 80% of the pr