2022 SCGS AMath Prelims P2 w Ans

SINGAPORE CHINESE GIRLS’ SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY FOUR O-LEVEL PROGRAMME CANDIDATE NAME Solution CLASS 4 REGISTER NUMBER CENTRE NUMBER INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 Paper 2 Wednesday 31 August 2022 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class, register number, centre number and index number 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 electronic 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. FOR EXAMINERS USE Q1 Q5 Q9 Q2 Q6 Q10 Q3 Q7 Q11 90 Q4 Q8 Q12 The Question Paper consists of 17 printed pages and 1 blank page. [Turn over

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c   , a acbbx 2 42 Binomial Theorem   nrrnnnnn bbar nbanbanaba                  221 21 , where n is a positive integer and ! )1()1( )!(! ! r rnnn rnr n r n        2. TRIGONOMETRY Identities 22 22 22 2 2 2 2 2 sin cos 1 sec 1 tan cosec 1 cot sin( ) sin cos cos sin cos( ) cos cos sin sin tan tantan( ) 1 tan tan sin 2 2sin cos cos 2 cos sin 2cos 1 1 2sin 2 tantan 2 1 tan AA AA AA A B A B A B A B A B A B ABAB AB 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 1. The equation of a curve is 2 8y x kx k    , where k is a constant. (a) Find the range of values of k for which the curve intersects the x-axis. [3] (b) In the case where k = 2, show that the line 43yx is a tangent to the curve. [2] (a) (b) 2 80x kx k          2 4 1 8 0kk     2 4 32 0kk     8 4 0kk   8 or 4kk  2 2 6 4 3x x x     2 6 9 0xx   Discriminant =      2 6 4 1 9    = 0  line is a tangent to the curve OR 2 6 9 0xx     2 30x line touches the x-axis at only one point where x = –3  line is a tangent to the curve

4 2. [The volume of a cone of height h and base radius r is 21 π3 rh .] An empty, inverted cone has a