NBSS 4E AMath Prelim P2 2021 v3

NAVAL BASE SECONDARY SCHOOL PRELIMINARY EXAMINATION, 2021 O Name ______________________________( ) Class ______________ ADDITIONAL MATHEMATICS 4049/02 Paper 2 30 August 2021 Candidates answer on the Question Paper No Additional Materials are required 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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 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 marks for this paper is 90. Item For Examiner’s Use Presentation Accuracy Units Total Parent’s Signature ______________________________________________________________________________________ [Turn over This paper consists of 21 printed pages and 3 blank pages.

2 [Turn over Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ,02  cbxax a acbbx 2 42  Binomial expansion ,......21)( 221 nrrnnnnn bbar nbanbanaba                  where n is a positive integer and ! )1(...)1( )!(! ! r rnnn rnr n r n       2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin    BA BABA BABABA BABABA tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin(      2 2 2 2 2 sin 2 2sin cos cos 2 cos sin 2cos 1 1 2sin 2 tantan 2 1 tan A A A A A A A A AA A          Formulae for ABC 2 2 2 sin sin sin 2 cos 1 sin2 a b c A B C a b c bc A bc A     

3 [Turn over Answer all the questions. 1 Express 2 2 20 3 2 (2 3)( 1) xx xx   in partial fractions. [6]

4 [Turn over 2 The table shows experimental values of two variables x and y. x 1.5 2 3 4 5 y 10.9 14.1 24.0 41.7 76.4 It is known that x and y are related by an equation xy ab e , where a and b are constant. (i) Explain how a straight line graph may be drawn to represent the given data. [2] (ii) On the grid on page 5, draw this graph for the given data and use it to estimate the value of a and of b. [4]

5 [Turn over

6 [Turn over (iii) By inserting another suitable line on your graph, solve the equation 24 x xab e   . [2]

7 [Turn over 3 (a) Find the range of values of k for which the curve ( 2)( 3)y x x   and the line 5y kx do not intersect. [3]

8 [Turn over (b) The above sketch shows part of the graph of 2y px qx r   . For each of the following expressions state, with a reason, whether it is positive, zero or negative. (i) r, [2] (ii) 2 4q pr , [2] (iii) 2 2 d d y x . [2] x y

9 [Turn over 4 (i) Express 8 41 x x in the form 41 ba x  , where a and b are integers. [2] (ii) Given that 2 ln(4 1)y x x , find an expression for d d y x . [3]

10 [Turn over (iii) Using the results in part (i) and (ii), determine ln(4 1) dxx . [4]