SAJC 9758 2023 Prelim P1

Question 1 2 3 4 5 6 7 8 9 10 11 TOTAL Marks 5 7 7 10 5 12 7 8 12 13 14 100 This document consists of 30 printed pages and 2 blank page including this page. ST ANDREW’S JUNIOR COLLEGE PRELIMINARY EXAMINATION MATHEMATICS HIGHER 2 9758/01 Tuesday 29 August 2023 3 hr Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) NAME:_________________________________________( _____ ) C.G.: __________ TUTOR’S NAME: _________________________________________ SCIENTIFIC / GRAPHIC CALCULATOR MODEL: _______________________ NUMBER OF ADDITIONAL PIECES OF WRITING PAPER :________________ READ THESE INSTRUCTIONS FIRST Write your name, civics group, index number and calculator models on the cover page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Total marks : 100 Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 signi ficant 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 allowed in a question, you are required to present the mathematical steps using mathem atical 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.

2 [Turn Over 1 A function f is defined by 32f ( )x ax bx cx d   . The graph of f ( )yx passes through the points ( 1, 15) and (2, 3). The graph has a turning point at 1x  , and 2 0 f ( ) d = 5.xx∫ Find the values of a, b, c and d. [5] 2 (a) The sum, ,nS of the first n terms of a sequence is given by 2 nSnn= + Show that the sequence follows an arithmetic progression and state the value of the common difference. [3] (b) An arithmetic series has first term b and common difference d, where b and d are non-zero. A geometric series has first term a and common ratio r, where a is non- zero and r is positive. It is given that the 3rd, 5th and 7th terms of a geometric series are equal to the 7th, 13th and 25th terms of an arithmetic series respectively. Find the value of r and determine if the geometric series is convergent. [4] 3 Figure 1 shows the net of a square-based pyramid. The net consists of a square of side length x cm and four isosceles triangles, each with base x cm and fixed sides k cm. The net is folded to form a right pyramid which has