NJC_JC2_H2_Maths_2012_Paper_1_Annex_B

ANNEX B 2012 NJC H2 Maths Preliminary Examination Paper 1 Qn/No Topic Set Answers 1 System of Linear Equations   324 10 56f 1; 2.527 9 9 x x xxx     2 Vectors (ii) 109 Since P is on BA produced, AP k AB for a negative value of k. 3 Maclaurin Series 23131 22  x x x (a) 13 (b) 251 2xx 4 Differential Equation (ii) 216 256; or 3.9416 1 65 tx t  (iii) The particular solution of the DE suggests that the amount of bacteria in the Petri dish will grow indefinitely as time passes. 5 Differentiation and Application of Integration involving Parametric Equations (ii) b = 4.5 6 Vectors (a) 7 or 1aa  (b) 1/ 3 1/ 3 2 / 3 or 2 / 3 1/ 3 1/ 3 ON                   (c) 1 2a , 7b 7 Arithmetic and Geometric Progressions (a)(ii) 125 3 a (b)(i) 5, 305pq  (ii) 9n 8 Complex Numbers 1m (i) 1 2 3 2 i, 2 i, 3z z z     (iii) Since 1 5,z  3 3z  , 13zz . The locus of complex numbers satisfying the

equation wa , for some positive constant a, will not pass through all the points representing the complex numbers 1z , 2z and 3z . 9 Sequences and Series/ Method of Difference/ Mathematical Induction (ii) 1 1 1 2 2 ( 1)( 2)NN    (iv) 11 144 2 ( 1)NN  10 Curve Sketching/ Graph Transformations (a) (i) Vertical asymptotes: xa or xa Horizontal asymptote: 2y 3h 11 Functions/ Inequalities (i) 2 2x (ii) k = (1  e9/8)/2 or 1.04 (iii) 1 1 or 2.5 <34 xx  