PHS 2024 Prelim A Math P1 (final)_Marking Scheme

Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL ADDITIONAL MATHEMATICS 4049/01 Paper 1 19 August 2024 Monday 2 hours 15 min PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2024 SECONDARY FOUR EXPRESS / FIVE NORMAL (ACADEMIC) PRELIMINARY EXAMINATIONS MARKING SCHEME

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0,ax bx c+ + = 2 4 2 b b acx a −  −= Binomial expansion 1 2 2( ) ... ... , 12 n n n n n r r nn n na b a a b a b a b b r − − −     + = + + + + + +           where n is a positive integer and 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cosec 1 cotAA=+ sin( ) sin cos cos sinA B A B A B =  cos( ) cos cos sin sinA B A B A B= tan tantan( ) 1 tan tan ABAB AB = sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formulae for sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − 1 sin2 bc A= ! ( 1)...( 1) ( )! ! ! n n n n n r r n r r r  − − +== − ABC

3 1 Express as the sum of 3 partial fractions. [5]

4 2 (a) State, in terms of π, (i) the principal value of , [1] (ii) the values between which the principal value of must lie. [1] (b) Given that A is a reflex angle and , find the exact value of without the use of a calculator. [3] (a) (i) [B1] (ii) [B1] (b) A lies in the 3rd quadrant.

5 3 (a) Find the set of values of the constant k for which the curve y = – kx2 – 2x + 2k – 3 does not intersect the x-axis. [3] (b) Using the answer in part (a), explain whether it is possible for – kx2 – 2x + 2k – 3 to be positive for all x. [2] Since , coefficient of x2 = – k < 0.