EJC 9649 2023 Prelim Annex

Further Mathematics 9649 ANNEX Paper 1 QN TOPIC (Pls Select) ANSWERS (Exclude graphs and text answers) 1 Apps of Integration (incl. polar)   62 416 π3 3k k , 2k  2 Recurrence Relations 12 5 4 3 n n nx n    3 Numerical Methods (a) 4() 2ln x x y x cy x y x   (b) 2.375 4 Apps of Integration (incl. polar) (i) 3π 32 2 0 2π ( sin )(1 cos ) da t t t t  (ii)   3 2 41 3π 81 7224 a   5 Linear Algebra (ii)(a) 32 31 21 0 0 0 aa aa aa    (ii)(c)    ker |T k k a ,   3R( ) | 0T    v a v 6 Linear Algebra (i) 1, cos sin     , sin cos     7 Numerical Methods (ii) 2.11  (v) 2.06 8 Differential Equations (a)  0 e kt mC C kvv k   9 Recurrence Relations (a)(i) 1 ππsin cos2 3 3 r r rru A B          (a)(ii) 1 8 9 u (b)(ii) 13( 1) (3)44 nn na    10 Conics (i) 2.56, 0.365ae (ii) 41.4 days (iii) 5.84 days; 287 days 11 FM P1 Q11 Topic 12 FM P1 Q12 Topic 13 FM P1 Q13 Topic 14 FM P1 Q14 Topic Paper 2 QN TOPIC (Pls Select) ANSWERS (Exclude graphs and text answers)

1 Mathematical Induction 1 2 2 Linear Algebra (ii)(a) yes (ii)(b) no 3 Numerical Methods (i) 80 9 (ii) overestimate (iii) 220 27 (iv) 80 9ln3 (vi) 0.705% 4 Differential Equations (b) 6320 16 16 4ee27 27 9 3 xxyx     , 6320 8 32 4ee27 27 9 9 xxzx     5 Complex Numbers (a) 11 5 7i i i i12 12 12 12e ,e ,e ,e                          (d) 5i 12e   6 Hypo Testing & Confidence Intervals (a) (0.7550,0.8006) (b) 1170 7 Chi-square Tests Do not reject. No change. 8 Non-parametric Tests (b) Do not reject (c) 1.4 1.6b 9 Continuous RV (a) 2 (1 ), 4 125 yy    (b) 7 3 10 Discrete RV (ii) 0.107 (iii) 0.655 (iv) 1 721 e , 072 t t   (v) 86 11 Hypo Testing & Confidence Intervals (i) (1-sample) t test (ii) 3.34 (iii) Do not reject 12 FM P2 Q12 Topic 13 FM P2 Q13 Topic 14 FM P2 Q14 Topic