MSHS 2025 AMATH PRELIM P2 MS

[Turn over For Examiners’ Use Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 / 7 / 7 / 9 / 7 / 12 / 9 / 8 / 11 Q9 Q10 SUBTOTAL / 9 / 11 Statement Presentation Units Rounding Off Class/ Index Number Centre Number/ ‘O’ Level Index Number Name / / MARIS STELLA HIGH SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR ADDITIONAL MATHEMATICS 4049/2 Paper 2 Solution 26 August 2025 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. Write in dark blue or black pen. 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 scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. 90

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax 2 + bx + c = 0, x = a ac b b 2 42 − ± − Binomial expansion (a + b) n = an +       1 n an − 1b +       2 n an − 2b2 + ... +       r n an − r br + ... + bn, where n is a positive integer and       r n = ! !( )! n rn r − = ! ) 1 )...( 1 ( r r n n n+ − − 2. TRIGONOMETRY Identities sin 2 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) = B A B A tan tan1 tan tan  ± sin2 2sin cosA AA= 22 2 2cos 2 cos sin 2cos 1 1 2sinA AA A A= − = −=− 2 2 tantan 2 1 tan AA A= − Formulae for ∆ABC A a sin = B b sin = C c sin 2 22 2 cosa b c bc A=+− 1 sin2 bc A∆=

3 1 (a) A polynomial f (x) has a remainder of −1 when divided by (2x + 3). (i) F ind the remainder when f(x) – 1 is divided by (2x+3) [1] ( ) ( ) ( ) () 2 3 () 1 () 1 2 3 () 1 1 2 3 () 2 Remainder 2 f x x hx f x x hx x hx = +− −= + −− = +− =− (ii) Find in terms of f (x), a polynomial which is divisible by (2x + 3). [1] () 1Polynomial f x= + (b) The cubic polynomial g( x) is such that the coefficient of x3 is 2 and the roots of g(x) = 0 are −1, m and 2m, where m is an integer. It is given that g(x) has a remainder of 12 when divided by x – 1. Find an expression of g( x) in descending powers of x. [5] ( )( ) ( )( ) ( )( ) ( ) ( ) ( ) ( ) 2 2 2 2 3 22 32 32 () 2 1 ( 2 ) (1) 2(2)(1 )(1 2 ) 12 4(1 3 2 ) 12 2 3 13 2 3 20 2 1 20 12 () 2 ( ) 2 1 2 ( 4) 2 24 2 4 428 2 5 28 2 10 4 16 gx x x m x m g mm mm mm mm