2022 HS AMath Prelims P1

CANDIDATE CLASS: NAME: CENTRE INDEX NUMBER: NUMBER: S ADDITIONAL MATHEMATICS 4049/01 Paper 1 Friday 19 August 2022 2 hours 15mins Candidates answer on the Question Paper Instructions to students: • Write your name, index number and class clearly in the spaces at the top of this page. • Write in dark blue or black pen on spaces provided. • 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 in this paper. • The use of an approved scientific calculator is expected, where appropriate. ▪ Give non-exact numerical answers correct to 3 significant figures, or one decimal place in case of angles in degrees, unless a different level of accuracy is specified in the question. ▪ You are reminded of the need for clear presentation in your answers. Information for pupils • The number of marks is given in brackets [ ] at the end of each question or part question. • The total mark for this paper is 90. Calculator Model: ______________________ The Question Paper consists of 20 printed pages (including this cover page) HOUGANG SECONDARY SCHOOL PRELIMINARY EXAMINATION / 2022 SECONDARY FOUR (EXPRESS) 90

Mathematical Formulae 1. ALGEBRA ,0equationtheFor : 2 =++ cbxax EquationQuadratic a acbbx 2 42 −−= nrrnnnnn bbar nbanbanaba TheoremBinomial ++     ++     +     +=+ −−− ........21)( : 221 where n is appositive integer and !)!( ! rrn n r n −=      = ! )1.().........1( r rnnn +−− 2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin += += =+ BABABA sincoscossin)sin( = cos(𝐴 ± 𝐵) = cos 𝐴 cos 𝐵 ∓ sin 𝐴 sin 𝐵 tan tantan( ) 1 tan tan ABAB AB = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= Formulae for ABC C c B b A a sinsinsin == Abccba cos2222 −+= CabABC sin2 1=

3 2022 4E Additional Mathematics Prelim 4049/01 1 The line 2 3 7yx=− meets the curve 2 38y x x= + − at two points A and B. Find the distance between A and B. [4]

4 2022 4E Additional Mathematics Prelim 4049/01 2 Express ( )( ) 2 78 2 1 1 x xx + +− in partial fractions. [5]

5 2022 4E Additional Mathematics Prelim 4049/01 3 Without using the calculator, find the values of the integer a and b such that 4 3 2 3 3 4 3ab −+ = +− . [3] 4 The line of symmetry of a quadratic curve is 2x=− and the curve lies above the x-axis for all x. Gi