Peirce Prelim 2021 S4E Add Math P1 QP

This paper consists of 19 printed pages and 1 blank page. Setter: Mdm Joscelyn Lee Class Register No. Candidate Name PEIRCE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/01 Paper 1 13 September 2021 2 hour 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

Mathematical Formulae 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

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

3 1 Solve the equation . [6]

4 2 The polynomial leaves the same remainder whether divided by x – b or x –c, where . (i) Show that . [3] (ii) Given further that 4bc = 21 and b > c, find the value of b and of c. [4]

5 3 (i) Find the first four terms in the expansion, in the ascending powers of x, of . [3] (ii) Hence obtain the coefficient of 𝑥 in the expansion of . [3]

6 4 The mass M (in grams), of a radioactive substance is given by , where k is a constant and t is measured in days after the substance is first being observed. It takes 35 days for the radioactive substance to be reduced to half of its original mass. Calculate (i) the value of k, [3] (ii) the amount of radioactive substance which indicates an observation period of one year. [2]

7 5 The equation of a curve is . (i) Find the coordinates of the points on the curve where the tangent is parallel to the line . [5] (ii) Determine whether the curve is an increasing or decreasing function for all values of x, except x = 1.5. [2]

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9 6 The diagram above shows the graph of for . (i) State the value of a and of b. [2] (ii) Hence, given that m, n, p and q are solutions to the equation , where k > a and for , express m in terms of p. [1] y x n m p q