2022 TKSS AMath Prelims P1 Ans

2 Marking Scheme Additional Mathematics Paper 1 CANDIDATE NAME ADDITIONAL MATHEMATICS 4049/01 Paper 1 Thursday 11 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 and index number on 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, highlighters, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal in the case of angles in degree, unless a different level of accuracy is specified in the question. The use of a 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. TANJONG KATONG SECONDARY SCHOOL Preliminary Examination 2022 Secondary 4 MARKING SCHEME CLASS INDEX NUMBER

2 4049/1/Sec4Prelim2022 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = a acbb 2 42  . Binomial Theorem (a + b)n = an +       1 n an  1 b +       2 n an  2 b2 + . . . +       r n an  r br + . . . + bn, where n is a positive integer and       r n = !)!( ! rrn n  = ! )1).......(1( r rnnn  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 tan (A ± B) = tan tan 1 tan tan A B A B   sin 2A = 2 sin A cos A cos 2A = cos2 A  sin2 A = 2 cos2 A  1 = 1  2 sin2 A tan 2A = A A 2tan1 tan2  Formulae for ABC C c B b A a sin sin sin  a2 = b2 + c2  2bc cos A  = 2 1 bc sin A

3 4049/1/Sec4Prelim2022 2(i) 3 2 2d 3 2d y x ax bx c y x ax bx        B1 (ii) For decreasing function, 2 2 d 0d 3 2 0 From 1 3, 3( 1)( 3) 0 3 6 9 0 y x x ax b x x x x x              By comparison, a= −3 and b = −9 B1 M1 B1 AG Their (i) < 0 Form eqn with factors (x+1)(x-9) ignore 3 Both correct Total: 4m 1 2 2 2 2 2 2 2 2 2 2 2 3 (2 ) (2 ) 1 0 6 3 4 4 1 0 5 10 4 1 0 0 ( 10 ) 4(5)(4 1) 0 20( 1) 0 20( 1)( 1) 0 x x m x m x x mx x m mx x x mx m D m m m m m                            m < −1 or m > 1 M1 B1 M1 A1 B1 Remove / substitute to 1 variable factorisation Total:5m -1 1

4 4049/1/Sec4Prelim2022 3a 2 3 2 32 2 2 2 3 2 2 2 3 51 2 2 7 1 2 2 100 5 56 2 2 5 2 52 3 5 2 3 2 52 5 5 2 3 5 2 3 5                 