Bedok View 4E AM PRELIM P2 2021

[Turn Over BEDOK VIEW SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 CANDIDATE NAME REGISTER NUMBER CLASS ADDITIONAL MATHEMATICS Secondary 4 Express Paper 2 Candidates answer on the Question Paper. No Additional Materials are required. 4049/02 31 August 2021 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your index number and name in the spaces at the top of this page. 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 the 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. 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. Setter: Ms S. Ang Parent’s / Guardian’s Signature: ……………………..… This document consists of 20 printed pages.

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

3 [Turn Over 1 Prove that for all real values of x. Hence, or otherwise, find the range of values of x for which . [7]

4 2 (a) By considering the general term in the binomial expansion of , explain why the power is a multiple of 5. [3]

5 [Turn Over 2 (b) Find the coefficient of in the expansion of . [3]

6 3 In the figure below, line BFE is a tangent to the circle at B. FA is a angle bisector of angle BAC and cuts the circle at D. (a) Show that angle DBC = angle DBF. [3] (b) Explain whether . [2] D B C A F E

7 [Turn Over 4 The diagram below shows a rectangle ABCD inside a semicircle with centre O and radius 6 cm. The angles AOB and COD are each equal to , where is measured in degrees. (a) Show that the perimeter, P cm, of the rectangle is given by . [2] (b) Express P in the form . [2] O A D B C

8 4 (c) State the maximum value of P and find the corresponding value of . [2] (d) Show that the area of the shaded region is cm2. [3]

9 [Turn Over 5 The table below shows the values of y corresponding to the values of x. x 1 2 3 4 5 y 1 1.6 2 2.28 2.5 It is known that x and y are related by an equation of the form , where a and b are constants. (a) Draw a straight line graph of against on the graph paper in the next page. [2] (b) Use the graph to estimate the value of a and of b. [3] (c) It is found that the value of is rather small. Another straight line graph is proposed by plotting the values of x in the horizontal axis. (i) State the variable to be plotted in the vertical axis. [2] (ii) Explain what does b represent in this new straight line graph. [1]

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