2019 CCHY MYE AMath 4047_P2 sol

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 1 of 20 Mid-Year Examination (2019) Secondary 4 Express / 5 Normal (Academic) Candidate Solutions Name Register No Class Additional Mathematics Paper 2 4047 / 2 Date : 14th May 2019 Duration : 2 hours 30 minutes Additional Materials : Graph Paper READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. 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 marks for this paper is 100. Setter : Ang Wee Hoon Fyn This paper consists of 20 printed pages, INCLUDING the cover page. For examiner’s use / 100 CHUNG CHENG HIGH SCHOOL YISHUN 义 顺 [Turn over

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 2 of 20 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation a 2x + bx + c = 0, x = 2 4 2 b b ac a    Binomial Expansion nba = na + 1 n    1na b + 2 n    2na 2b +    +    r n rna  rb +    + nb , where n is a positive integer and    r n =  !! ! rnr n  = 1 1 ! n n n r r     2. Trigonometry Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin ( A  B ) = sin A cos B  cos A sin B cos ( A  B ) = cosA cos B  sin A sin B tan ( A  B ) = BA BA tantan1 tantan   sin 2A = 2 sin A cos A cos 2A = cos2 A - sin2 A = 2 cos2 A – 1 = 1 – 2 sin2 A tan 2A = 2 2 tan 1 tan A A Formulae for ABC sin a A = sin b B = sin c C a2 = b2 + c2 – 2bc cos A area of ABC = 1 2 ab sin C

CCHY Mid-Year Examination (2019) Additional Mathematics Sec 4E/5N Page 3 of 20 1. The table below shows the experimental values of two variables x and y. x 0.5 1.0 1.5 2.0 2.5 3.0 y 1.20 1.00 0.86 0.74 0.66 0.59 It is known that x and y are related by an equation of the form ay x b  , where a and b are constants. (i) Using a scale of 4cm to 1 unit on the x axis, and 4cm to 0.5units on the 1 y axis, draw a straight line graph. [3] (ii) Use your graph to estimate the value of a and of b. [2] (iii) Find the value of x where 10 9y [2] From another set of experimental data, it is found that x and y are related by the equation 7 28 25xy y  .