RVHS P1 ANNEX

1 ANNEX B RVHS H2 Maths Preliminary Examination Paper 1 Qn/No Topic Set Answers 1 Complex Numbers 18a , 45b , 1 2iz , 1 2iz , 3iz , 3iz 2 Integration Techniques 3 0 or 3xx    2 18ln 3 1 9ln(4 ) 2 nn   As 0n , I 3 Vectors (i) 2 2 4 OQ     (ii)  a c c is the projection vector of a onto b . (iii) 02 p (iv) | a b| is the area of the rhombus OAQB. 4 Maclaurin’s Series ...4 2 2  xxy  (i) 4 2  xy (ii) 2x 5 Sequence & Series (i) 83.2 (iii) 9 (iv) 200 6 Functions (i) A horizontal line y = k where 40 k   cuts the graph of y = f(x) twice, thus f is not one-to-one. Therefore f −1 does not exist. (ii) Largest value of 1a . (iii) 1 13 2x  (iv) Rg = (0,2) & Df = ( ,1] Since Rg  Df . Thus, fg does not exist. (v) Dg = [1.2,3) fg ( 3,0]R  7 Curve Sketching (ii) 27yx and 3x (iv) 481 481or33kk  . 8 Application of Differentiation (Tangent & Normal) (i) d d y x = tcosec (iii) 0.75 (iv) 22 11 144xy

2 9 Summation, MI (a) (ii) 5 2ln(3628800)12 10 Vectors (i) 26.6o  , 45 5 (ii) 4 0 : 2 18 1 p     r or 4 0 : 2 6 1 p     r (iii) l : r = 02 1 , 22             (iv) 5 , 1 