2020 J2 YIJC H2 Math Prelim P1 Answers

1 Qn Solution 1(i) (ii) 33  2(i)     3 4 1 2 1 2 3 2 5 8 28 2 1 2 3 2 5 r r r r r r r        (ii) 2 1 1 3 3 4 2 5 2 3nn    (iii) When 13, 0, 02 5 2 3n nn   ,     0 2 7 2 2 1 2 3 2 5 3 r r r r r       which is a finite number. Therefore the series is convergent. Sum to infinity = 2 3 3(i) , 3 , 5b a c a d a   (ii) 1.63 or 3dd  (iii) 4(i)    210 10 4 3 551 (rejected 0) or or 36 10 40 6 5 10 33 x x x      x y O xk O 0y O 10, k   O

2 (ii)      54 36 1 4 5 32 45 32 x xx x xx x xx       From the graphs, 5 10 33x or 5 5 10 2 or 23 3 3xx     5(i) (ii) 3 = 2 hL xR 6(i) (ii) Equation of tangent at y = 2 4 2ln 2 2 y kx   (iii) Angle between y-axis and the tangent in (ii) 14.0 7(i) (ii)   11f g( ) f 3 3 17 24 x x xe e         1 gfgDD  (iii) 1k  8(a) (i) x = 2 O x y

3 8(a) (ii) 1 2tan 2 2 11e1 2 2! 4 11 1 ... 28 x xx xx                   (b) 2 2 1g( ) 2 cos 4 131 2 x x a xxa a       9(i) (ii) 14 3 a (iii) 73tan 90 ab 10(i) (a) Distance she runs in the 15th session 2937.19 metres (b) Least n = 32 She needs a minimum of 32 sessions. O x y O x y

4 (c) Wendie’s average speed of the 33rd session first exceeds 220 metres per minute. (ii) =16.02x (iii) 11(i)   d 0.008 15 25d x xxt    (ii)   0.08 0.08 75 1 e 3 5e t tx    OR   0.08 0.08 75 e 1 3e 5 t tx      (iii) (iv) 4.2059 4.21(3 s.f.)t (v) Method 1: From graph, when , 15tx  For large values of t, the mass of X increases and approaches to a limit of 15 grams Method 2:   0.08 0.08 75 e 1 3e 5 t tx      When , 15tx  For large values of t, the mass of X increases and approaches to a limit of 15 grams x=15 O