RI DHS HCI TMJC 9649 2023 Prelim Annex

Further Mathematics 9649 ANNEX Paper 1 QN TOPIC (Pls Select) ANSWERS (Exclude graphs and text answers) 1 Numerical Methods (b) 1.2 (c) 1.276 2 Recurrence Relations 3 Recurrence Relations (a) 11 22 nn n iix A B aa            (b) 1 3cos sin446 n n nnx               (c) 1 ,2   4 Linear Algebra (c) 1 1 0 1       (d) Least k = 26, 0.80 1 1 0.44       5 Linear Algebra (a)    ba ba (b) 2 2 2 0 0 b b   A , 1 2 1 a b a b a ab     A (c) 1 2 if is odd if is even n n n bn bn   AA I 6 Conics (a) cos , sinm A B n B    (b)(ii)  11 cos cose r a a      7 Complex Numbers (a) 22 11Re( ) cos , Im( ) sinkkzz kk           , 2 2 1 k k  (b)(iii) 3π 4 or 3π 4 (b)(iv) 5 8 Linear Algebra (d) 2 3 3 1 43 10 v           (f) 1 2 1,,333   9 Apps of Integration (incl. polar) (a) 30, , 3 , 0 3y y x y x x    (b)(ii) 29.52 units (c) 245 10 Conics (a) Rre Rr   (b)(i) 11600 km (b)(ii) 4.85 hrs (c) 0.267 AU 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 Complex Numbers 2 Linear Algebra (c) 12 (d) 1 3 yx , 3yx 3 Differential Equations (i) 1ee ttb A B      (ii) 0.2 0.71.4e 1.2e 5ttb    (iii) 4.07 hours 4 Apps of Integration (incl. polar) (ii) 2   (iii)  tan  ,  (iv) cotsec e 1   5 Numerical Methods (a)     22 2 4 28cos 8 cos3 722          (b)(ii) 2 245 5 3 1( ) e 4 4 4 8y        6 Hypo Testing & Confidence Intervals 91.5 7 Chi-square Tests p-value = 59.37 10  , reject 0H 8 Continuous RV (a)  (b) 2 (d)   22 1 10 c   , 0, 1 9 Discrete RV (iii) 0.110 (iv) 0.0294 (v) 148 seconds 10 Non-parametric Tests (iii) p-value 0.172 , do not reject 0H (iv) T = 23, do not reject 0H 11 FM P2 Q11 Topic 12 FM P2 Q12 Topic 13 FM P2 Q13 Topic 14 FM P2 Q14 Topic