PLGMS 4E_5NA_AM P1 Prelim 2017_FINAL

Name: ___________________________ ( ) Class: _______ Centre Number S Index Number ADDITIONAL MATHEMATICS 4047/01 Paper 1 17 August 2017 Additional Materials: Answer Paper (8 sheets) 2 hours Graph Paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name 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 a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers on the separate Answer Paper and Graph Paper provided. 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 80. This paper consists of 6 pages, including this cover page. Paya Lebar Methodist Girls’ School (Secondary) Preliminary Examination 2017 Secondary 4 Express / 5 Normal Academic My Target is:

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, a acbbx 2 42  Binomial Expansion ,21)( 221 nrrnnnnn bbar nbanbanaba                   where n is a positive integer and     ! 11 )!(! ! r rnnn rnr n r n        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) = cos A cos B  sin A sin B BA BABA tantan1 tantan)tan(   sin 2A = 2 sin A cos A cos 2A = cos2 A  sin2 A = 2cos2 A  1 = 1  2sin2 A A AA 2tan1 tan22tan  Formulae for ABC C c B b A a sinsinsin  a2 = b2 + c2 – 2bc cos A Abc sin2 1

3 [Turn over 1 State the values between which each of the following must lie (a) the principal value of tan  1 x, [1] (b) the principal value of cos  1 2x. [2] 2 The function f is defined, for all values of x, by f(x) = (x + 3)(1 – 2x)2. Find the range of values of x for which f is a decreasing function. [3] 3 In the expansion of (2x – 1)2 8 1       x p , where p is a positive constant, there is no term in .1 3x Find the possible values of the constant p. [5] 4 A curve has the equation y = 4x2 – 24x + 30. (i) Express 4x2 – 24x + 30 in the form [a (x + h)] 2 + k. [1] (ii) Show that the minimum point of the