KSS 2021 Prelims 4E AM P1

Candidate Name: __________________________ ( ) Class: _________ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Express ADDITIONAL MATHEMATICS 4049/01 Paper 1 Wednesday 25 August 2021 2 hr 15 min KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI Questio n Mark s 1 2 3 4 5 6 7 8 9 10 11 12 Total READ THESE INSTRUCTIONS FIRST: Do not open this question paper until you are told to do so. Write your name, class and register 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. 4E Session 2

2 Answer all questions. Give non-exact numerical answers correct to three 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. Set by: Ms Priscilla Lee This Question Booklet consists of 20 printed pages including the cover page. [Turn over

3 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation Binomial expansion where n is a positive integer and 2. TRIGONOMETRY Identities cosec2 A = 1 + cot2 A Formulae for

4 1 Express in partial fractions. [5] 2 Represent the solution set of on a number line and determine if x = 5 satisfies the inequality. [6]

5 3 The term containing the highest power of x in the polynomial is . It is given that is a quadratic factor of and one of the roots of the equation = 0 is – 1. (i) Find an expression for in descending powers of x. [2]

6 (ii) Find the number of real roots of the equation = 0, justifying your answer. [2] (iii) Find the remainder when is divided by . [2] 4 (a) A circle, C, has the equation (i) Find the radius and the coordinates of the centre of C. [2]

7 (ii) The coverage of a Wi -Fi signal is represented by the equation of the circle C. Show, with working, why a person standing at the point A(10, 7) is not able to make use of the free Wi-Fi. [2] (b)A rhombus ABCD has vertices A(1, 5), B(b, 0), where b is a constant, and C(–6, 2). (i) Find the equation of the line BD. [3]

8 (ii) Hence, or otherwise, find the coordinates of B and D. [3] (iii) Explain why ABCD is a square. [2] 5 (i) Show that has no turning point for all values of x. [4]

9 (ii) Find the range of values of x in which the graph of is decreasing. [3] 6 Find, in exact values, the coordinates of the stationary points of the curve for and determine the nature of each stationary point. [7]

10 7 y = 2x 9 A B C O D y x