AM4 4049 BSSS 2023 P1 QP

BEDOK SOUTH SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 4E5N CANDIDATE NAME CLASS REGISTER NUMBER ADDITIONAL MATHEMATICS Paper 1 4049 / 01 21 August 2023 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST 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 HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees. For π, use your calculator value or 3.142. 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. If working is needed for any question it must be shown in the space below the question. Omission of essential working will result in loss of marks. The total number of marks for this paper is 90. Setter : Mr Loh Jia Perng For Examiner’s Use Student Check & Sign Marks before deduction Parent’s Signature TOTAL 90 This paper consists of 25 printed pages.

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ += , Binomial Expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ABC

3 Answer all questions. 1. Find the coordinates of the intersection(s) for the following graphs. 2𝑥𝑥 + 3𝑦𝑦 + 4 = 0, 3 𝑥𝑥 + 2 𝑦𝑦 = 1 4. [5]

4 2. (a) Express 30 18 2 22 + + in the form 2rs+ , where r and s are integers [2]

5 (b) The diagram shows a triangle XYZ. XY is 4 22+ cm and YZ is ( )2ab+ cm, where a and b are integers. The included angle XYZ is 135°. Given that the area of the triangle is ( )15 9 2+ cm2, find the value of a and of b. [3] 4 22+ ( )2 cmab+

6 3. The function 𝑓𝑓 is defined by 𝑓𝑓(𝑥𝑥) = 5−𝑥𝑥2 𝑥𝑥2+3, 𝑥𝑥 > 0. A point 𝑃𝑃 moves along the curve 𝑦𝑦 = 𝑓𝑓(𝑥𝑥) in such a way that the 𝑦𝑦-coordinate of 𝑃𝑃 is increasing at a constant rate of 0.2 units per second. (a) Explain, with working, whether 𝑓𝑓 is an increasing or decreasing function. [3]

7 (b) Find the rate of change of the 𝑥𝑥-coordinate of 𝑃𝑃 when 𝑥𝑥 = 4. [3]

8 4. (a) Find the range of values of h for which the line 24y hx+= .and the curve 25 20yx+= do not intersect. [3] (b) By expressing in the form of ( ) 2 xh k−+ , where h and k are constants, explain why 2 47xx−+ is always greater than or equal to 3. [2]

9 5. (a) Show that 22sin( )sin( ) cos cosAB AB B A+ −= − . [3] (b) Hence, without using a calculator, show that sin 1sin 75 15 4 oo = . [2]

10 6. The diagram shows the frontal view of a rectangular block PQRS, with dimensions 20 cm by 8 cm. It is placed on a ramp, VS, tilted at an acute angle of θ to the horizontal surface ST and 90oVTS∠= . (a) Show that d, the perpendicular distance from Q to ST, can be expressed as 8cos 20sinθθ+ , in centimetres. [2] θ