Regent 4E AM Prelim Examination Paper 1 @ 2021_final

1 NAME: ________________________________ INDEX NUMBER: ________ CLASS: ________ SETTER: MDM TONG _________________________________________________________________________ ADDITIONAL MATHEMATICS 4049/01 Paper 1 13 September 2021 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. _________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this 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, 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 scientific calculator is expected, where appropriate. 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. The total of the marks for this paper is 90. TARGET PARENT’S SIGNATURE REGENT SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 SECONDARY FOUR EXPRESS 90

2 _________________________________________________________________________ This document consists of 18 printed pages. Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , Binomial expansion where n is a positive integer and 2. TRIGONOMETRY Identities

3 Formulae for

4 1 The function f , where a and b are positive constants, leaves a remainder of 1 when divided by . The function g is exactly divisible by . (a) Find the value of a and of b. [5]

5 (b) Using the values of a and b found in part (a), show that g has only one real root. [2]

6 2 The equation of a curve is for , where a, b and c are constants. The amplitude of the curve is 3 and is a minimum point of the curve. (a) Find the values of a, b and c, [3] (b) Using the values of of a, b and c found in part (a), sketch the graph of for . [3]

7 3 (a) Write down the first three terms in the expansion, in ascending powers of x, of , where a is a constant. Give the terms in their s