KSS 2021 Prelims 4E AM P2

Candidate Name: __________________________ ( ) Class: _________ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Express ADDITIONAL MATHEMATICS 4049/02 Paper 2 Friday 27 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 Question Marks 1 2 3 4 5 6 7 8 9 10 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. 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. 4E Session 1

2 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 (a) (i) Determine the set of values of m for which the equation has real roots. [4] (ii) Hence, state what can be deduced about the curve and the line Justify your statement. [2]

5 (b) Show that for the curve to lie above the line , the condition that must apply to the constants p and q is p < q < 5p. [4]

6 2 The coefficient of is 512 in the expansion of , where a < 0. (i) Find the value of a. [3]

7 (ii) Hence, using the value of a found in (i), determine whether the term in exists in the expansion . [3]

8 3 In the figure above, CA = CB and the line CZ is a tangent to the circle at the point C. AX is produced to meet the tangent at point Y. (i) Prove that AB is parallel to CY. [3] (ii) Show that and are similar. [3]

9 4 The table below shows the experimental values of two variables x and y. It is known that one value of y has been recorded incorrectly. x 0.5 1.0 1.5 2.0 2.5 3.0 y 1.20 1.00 0.86 0.62 0.66 0.59 (i) On the grid on page 9, plot against x, and draw a straight line graph. Use a scale of 2 cm to 0.2 unit on the vertical axis and 2 cm to 0.5 unit on the horizontal axis. [3] (ii) Find the gradient of your straight line and hence express in terms of x. [2] (iii) Use your graph to estimate a value of y to replace the incorrect value. [2]

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