Sembawang 2021 4E AMaths Prelims P1 V3

[Turn over CANDIDATE NAME CLASS INDEX NUMBER SEMBAWANG SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 SECONDARY FOUR EXPRESS ADDITIONAL MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4049/01 26 Aug 2021 1050 – 1305 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. 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 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. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of the marks for this paper is 90. FOR EXAMINER’S USE TOTAL 90 PARENT’S SIGNATURE Setter: Ms Siew Yan Yee This document consists of 19 printed pages and 1 blank page.

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation x = Binomial Theorem where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for

3 [Turn over 1 The equation of a curve is where k is a constant. In the case where find the set of values of k for which the curve lies completely above the x-axis. [3] 2 Given that find the value of [4]

4 3 Given that for , find the range of values of x for which y is a decreasing function of x. [4]

5 [Turn over 4 A rectangular block has a square base of side cm and a height of h cm. The volume of the rectangular block is Without using a calculator, show that h can be expressed as where a and b are integers. [5]

6 5 The term containing the highest power of x in the polynomial f(x) is Given that f(x) has two roots –2 and 3, and that is a quadratic factor of f(x), (i) express f(x) as a polynomial in x with integer coefficients, [3] (ii) explain why f(x) has exactly two real roots. [2]

7 [Turn over 6 It is given that and (a) Show that there are no real values of a and b for which f(x) and g(x) leave the same remainder when divided by [4] (b) Given that is a factor of g(x), express a in terms of b. [2]

8 7 Winston believes that the depth of water, d metres, at the end of a jetty, t hours after low tide, can be modelled by the equation where a, b and k are constants. (i) Assuming that low tides occur every 12 hours, show that [2] (ii) Winston measures the depth of water at low tide and high tide to be 2 metres and 6 metres respectively. Calculate the value of a and of b. [2] (iii) Winston requires the depth of water at the end of the jetty to be at least 3 metres to sail his boat. Given that the low tide on a particular day was at 0830, find the earliest time that Winston could sail his boat. [3]

9 [Turn over 8 A curve is such that (i) Find the coordinates of the stationary points of the curve. [4] (ii) Obtain an expression for and hence, or otherwise, determine the nature of each stationary point. [3]

10 9 In a factory, a machine part P, which is connected to a food cutter, moves in a straight line from a fixed point O so that t seconds after passing O, its velocity, v m s–1, is given by where (i) Find the value of t when P first comes to an instantaneous rest, giving your answer in terms of [3]