ANDSS 4E2021AM Prelim P1 Question Paper

O ANDERSON SECONDARY SCHOOL Preliminary Examination 2021 Secondary Four Express CANDIDATE NAME: CLASS: / INDEX NUMBER: ADDITIONAL MATHEMATICS Paper 1 4049/01 23 August 2021 2 hours 15 minutes 1100 – 1315h Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid/tape. Answer all the questions. Omission of essential working will result in loss of marks. 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 number of marks for this paper is 90. This document consists of 19 printed pages. Setter: Mr Low Kok Ming

2 PRELIM 4E Add Math 2021 4049/1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ΔABC

3 PRELIM 4E Add Math 2021 4049/1 1 A curve is such that . The equation of the normal to the curve at the point is . Find the equation of the curve. [6]

4 PRELIM 4E Add Math 2021 4049/1 2 (i) Show that is a factor of the expression . [2] (ii) Factorise completely. [2] (iii) Hence solve the equation . [2]

5 PRELIM 4E Add Math 2021 4049/1 3 (a) Solve , for . [5] (b) Prove that . [3]

6 PRELIM 4E Add Math 2021 4049/1 4 (i) Write down and simplify, in descending powers of x, the first three terms in the expansion of , where n > 0. [2] (ii) When the third term of the expansion is divided by the second term, is obtained. Show that . [2]

7 PRELIM 4E Add Math 2021 4049/1 (iii) Using the value of n found in (ii), without expanding , show that there is no constant term in the expansion. [3]

8 PRELIM 4E Add Math 2021 4049/1 5 (a) Solve the equation . [5]

9 PRELIM 4E Add Math 2021 4049/1 (b) Show that can be expressed in the form where m and n are constants to be determined. [4]

10 PRELIM 4E Add Math 2021 4049/1 6 (i) Express in partial fractions. [6]