3E NV AM EOY 2021

NORTH VISTA SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2021 90 SUBJECT: ADDITIONAL MATHEMATICS DATE: 8 OCTOBER LEVEL/ STREAM: SECONDARY 3 EXPRESS CODE : 4049 TIME : 2 HOURS 15 MINUTES READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. 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. NAME: _____________________________( ) CLASS: ____________ For Examiner’s Use Category Question No. Accuracy Brackets Fractions Units Others Marks Deducted This question paper consists of 21 printed pages. [Turn over

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0,ax bx c   2 4 2 b b acx a    Binomial expansion 1 2 2( ) ... ... , 12 n n n n n r r nn n na b a a b a b a b b r                          where n is a positive integer and ! ( 1)...( 1) ( )! ! ! n n n n n r r n r r r      2. TRIGONOMETRY Identities 22sin cos 1AA 22sec 1 tanAA 22cosec 1 cotAA sin( ) sin cos cos sinA B A B A B   cos( ) cos cos sin sinA B A B A B tan tantan( ) 1 tan tan ABAB AB  sin 2 2sin cosA A A 2 2 2 2cos2 cos sin 2cos 1 1 2sinA A A A A      2 2tantan 2 1 tan AA A   Formulae for ABC sin sin sin a b c A B C 2 2 2 2 cosa b c bc A   1 sin2 ab C

3 [Turn over 1 Express 2 2 53 5 7 (3 1)( 10) xx xx   in partial fractions. [6]

4 2 (a) Variables x and y are connected by the equation 23y ax by , where a and b are constants. Explain clearly how a and b can be calculated when a graph of 2x y against 2y is drawn. [3] (b) The mass, m grams, of a radioactive substance decreases with time, t years. The observation started on 1 January 2021. Measured values of m and t are shown in the table below. m (grams) 53.6 35.9 24.1 16.2 t (years) 10 20 30 40 It is known that m and t are related by the equation 0 ktm m e  , where 0m and k are constants. (i) Dra