2019 J2 EJC H2 Math Prelim (with ans)

EUNOIA JUNIOR COLLEGE JC2 Preliminary Examination 2019 General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CLASS INDEX NO. MATHEMATICS Paper 1 [100 marks] 9758/01 04 September2019 3 hours Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civic s group and question number on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all 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. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not al lowed 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. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 27 printed pages (including this cover page) and1 blank page. For markers’ use: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Total www.KiasuExamPaper.com 247

2019 JC2 H2 Mathematics Preliminary Examination 1 Electricity cost per household is calculated by multiplying th e electricity consumption (in kWh), by the tariff (in cents/kWh). The tariff is set by the government and reviewed every 4 months. The amount of electricity used by each household for each 4-mon th period, together with the total electricity cost for each household in the year, are given in the following table. Jan – April (in kWh) May – Aug (in kWh) Sept – Dec (in kWh) Total electricity cost in the year ($) Household 1 677 586 699 529.53 Household 2 1011 871 1048 790.63 Household 3 1349 1174 1417 1063.28 Write down and solve equations to find the tariff, in cents/kWh, to 2 decimal places, for each 4- month period. [4] 2 A string of fixed length l is cut into two pieces. The first piece is used to form a square of side s and the second piece is used to form a circle of radius r. Find the ratio of the length of the first piece to the second piece that gives the smallest possible combined area of the square and circle. [6] 3 A geometric progression has first term a and common ratio r, and an arithmetic progression has first term a and common difference d, where a and d are non-zero. The sums of the first 2 and 4 terms of the arithmetic progression are equal to the respective sums of the first 2 and 4 terms of the geometric progression. (i) By showing 32 53 0rr r , or otherwise, find the value of the common ratio. [5] (ii) Given that 0a and t