JPJC_9649_2023_Prelim_Annex

Further Mathematics 9649 ANNEX Paper 1 QN TOPIC (Pls Select) ANSWERS (Exclude graphs and text answers) 1 Linear Algebra (b) 4 (c) P = 1 1 1 1 2 1 1 3 2    D = 216 0 0 0 64 0 0 0 27    2 Recurrence Relations (a) 1 0.72 14000nnpp  (b)  170000 0.72 50000 n np  Last part: 9 3 Complex Numbers (a) 14 8 2 4 2i i i i i15 15 15 15 32e , 2e , 2e , 2e , 2e        (b) 2i 152ez   4 Conics (a)  11y y m x x   (d) 22 3xy ; circle with centre O and radius 3 5 Linear Algebra (a) 1 1 1 1 4 7,,1 7 11 1 2 5                                 (b) 11 11,20 02                     (c) No (d) 3 6 Conics (a) 2at a (b) – (c) 1y x att 7 Complex Numbers (a) (ii)  1 10 15cos 2 6cos 4 cos632      8 Linear Algebra (c) Hyperbola (d) (i) 3 (ii)    3,0 and 3,0

(iii) 11 and 33 xx  9 Apps of Integration (incl. polar) (a) 22 units3 (b)   2 5 ln 3 8ln 3 43    (d) 0.441 units 10 Recurrence Relations (a) 4 (d) 4 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 Recurrence Relations 2 cos sin 33e n nnAB nX   2 Apps of Integration (incl. polar) (b) 3 8  (c)   1 2 3 36  (d)   4 2 3 39  3 Apps of Integration (incl. polar) (a)  ,2rr (b) 2264 units3 r 4 Differential Equations (a)  1 1 ky t tk   (b) 0.182y (c) Overestimation 5 Mathematical Induction (a) 3e sinx x (d) (i) 0.609 (ii)  1n  6 Discrete RV (b) 19 (c) 0.0226 7 Hypo Testing & Confidence Intervals p-value = 0.225 >  = 0.1, we do not reject 0H 8 Chi-square Tests (a) 22.5, 45, 112.5, 7.5, 15, 37.5 (b) 18, 42, 12, 18 (c) p-value = 0.0408 <  , we reject 0H .

9 Continuous RV (a)     2 0, 0.1, F 100 0.1 , 0.1 0.2, 1, 0.2 x x x x x        (c)   3 g( ) 40000 0.1yy ; 0.18 (d) 40,72 (e) p-value = 0.117 >  , we do not reject 0H . 10 Non-parametric Tests (a) p-value = 0.00440   = 0.01, we reject 0H (b) 1.34w  (c) p-value = 0.144 >  , we do not reject 0H (d) 16 11 FM P2 Q11 Topic 12 FM P2 Q12 Topic 13 FM P2 Q13 Topic 14 FM P2 Q14 Topic