Peirce Prelim 2021 S4E Add Math P2 QP

This paper consists of 19 printed pages and 1 blank page. Setter: Mr Cheng SK Class Register No. Candidate Name PEIRCE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 SECONDARY 4 EXPRESS/ 5 NORMAL ACADEMIC ADDITIONAL MATHEMATICS 4049/02 Paper 2 14 Sep 2021 2 hours 15 minutes Additional Materials: Plain Paper (for rough work) INSTRUCTIONS TO CANDIDATES Candidates answer on the Question Paper. Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a 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 a 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. For Examiner’s Use PARENT’S SIGNATURE Total

2 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = Binomial expansion (a + b)n = an + an − 1b + an − 2b2 + ......... + an − r br + … + bn , where n is a positive integer and = = 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin(A ± B) = sin A cos B ± cos A sin B cos(A ± B) = cos A cos B sin A sin B tan(A ± B) = sin 2A = 2 sinA cosA cos 2A = cos2 A − sin2 A = 2 cos2 A − 1 = 1 − 2 sin2 A tan 2A = Formulae for ΔABC = =

3 a2 = b2 + c2 − 2bc cos A Δ = bc sin A

4 1 (i) Factorise completely. [2] (ii) Hence solve the equation . [3]

5 2 (i) Express in partial fractions. [5]

6 (ii) Hence, evaluate . [4]

7 3 (i) State the range of values of x for to be defined. [1] (ii) Solve the equation . [5]

8 (iii) Given , express z in terms of k. [4]

9 4 (a) Without using a calculator, given that , find the exact value of tan A. [4]

10 (b) (i) Find cos 105° in the form , where p and q are integers. [3] (ii) Hence, calculate the exact value of sec 105°. [3]