ACJC 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) 2k  2 Recurrence Relations 12 5 4 3 n n nx n    3 Differential Equations (a) 4() 2ln x x y x cy x y x   (b) 2.375 (c) over-estimate 4 Linear Algebra (ii)(a) 32 31 21 0 0 0 aa aa aa   M (b) No (c)    ker |T k k a ,   3R( ) | 0T    v a v 5 Linear Algebra (i) 1 and cos sin     ; –1 and sin cos     (ii) 110 01     T R R (iii) 31 2 13 2     6 Numerical Methods (i) 2 (ii) 2.11 (iii) over-estimate (v) 2.06 7 Apps of Integration (incl. polar) (i) 3π 2 (ii) 32 27 17 16 122π π 3πa   8 Differential Equations (a)  0 e kt mC C kvv k   (b) Cv k 9 Recurrence Relations (a)(i) 1 ππsin cos2 3 3 r r rru A B          (ii) 1 8  , 3 2 1 1 8 9 r r uu    

(b)(ii) 13( 1) (3)44 nn na    10 Conics (i) 0.365e , 2.56a (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 (b) No 3 Numerical Methods (i) 80 8 899 (ii) over-estimate (iii) 220 4 827 27 (iv) 80 1 9 ln 3   (vi) 0.706% 4 Differential Equations (b) 63 63 20 16 16 4e e ,27 27 9 3 20 8 32 4ee27 27 9 9 xx xx yx zx           5 Complex Numbers (a) 11π 5π π 7πi i i i12 12 12 12e , e , e , ez                       (d) 5πi 12e   6 Hypo Testing & Confidence Intervals (a)  0.7550, 0.8006 (b) 1169 7 Chi-square Tests 0.780p , do not reject H0 No change 8 Non-parametric Tests (b) do not reject H0 (c) 1.4 1.6b 9 Continuous RV (a)    2f 1 , 4 125y y y     (b) 7 3 10 Discrete RV (ii) 0.107 (iii) 0.655 (iv)   1 721f e , 0 72 t tt  

(v) 86 11 Hypo Testing & Confidence Intervals (i) 1-sample t-test (ii) 3.34 (iii) 0.750p , do not reject H0 12 FM P2 Q12 Topic 13 FM P2 Q13 Topic 14 FM P2 Q14 Topic