A Level 2016 P1 Solutions for new syllabus (edited CSC)

2016 A-Level H2 Maths Paper 1 Solutions 1     22 22 2 4 4 14 4 4 14 ( 4)( 3)344 4 4 14 12 4 3 5 2 4 (3 1)( 2) 4 x x x x x x xxx x x x x x xx x xx x                            2 2 4 4 14 3, 44 4 4 14 304 3 1 2 04 3 1 2 4 0, 4 xx xxx xx xx xx x x x x x                1 32 or 4xx   2(i) cos2 xy When x = 0, d 0d y x  When 2 d, 0.693 (3 s.f.)d yx x   2(ii)     cos0 cos 02 2 22 When 0, 2 2 Tangent at (0,2): 2 (1) When , 2 2 1 Tangent at ,1 : 1 0.693 0.693 2.09 (2) Substitute (1) into (2): 2 0.693 2.09 0.128 The tangents meet at (0.128, 2 xy y xy yx yx x x                         ). -2 x 4 1/3

2016 A-Level H2 Maths Paper 1 Solutions 3 44 f ( ) () x y x y k x l m     By the way (question doesn’t ask for it), this is the sequence of transformations: units44 in the positive -direction units44 in the positive -direction translate translatescale by factor parallel to -axis () ( ) ( ) l x m y k y y x y x l y k x l y k x l m               (0,0) ( , ) lm ( , ) ( , )l m a b , so la , mb . (0, )c lies on f ( )yx graph 4(0 )c k l m    44 c m c bk la  4(i) Given that the for the Arithmetic series: first term = a, common difference = d, Geometric series: first term = b , common ratio, r, ,, ,a b d r are non-zero, 4 7 14 74 43 14 7 77 77 43 37 3 3 10 3 10 3 3 (1) 8 (2) 11 (3) (2) (1) : 5 5 ( 1) (4) (3) (2): 3 3 ( 1) (5) (5) 3 ( 1):(4) 5 ( 1) 3 ( 1) 5 ( 1) 3 3 5 5 5 8 3 0 a d br a d br a d br d br br d br r d br br d br r br r br r rr r r r r rr                                Using GC, 0.74 or 1 (reject since <1)r r r Aim: Eliminate a, then eliminate d and b, leaving r. 4yx ( , )ab (0, )c 1( , )ba 1(0, )c 1 f ( )y x f ( )yx

2016 A-Level H2 Maths Paper 1 Solutions 4(ii) Required sum 12nnuu   1 2 1 2( ) ( ) (1 ) 11 1 (0.74) or 3.85 (0.74)0.26 n n n n n n u u u u u SS b b r rr br r b b              5(i)     2 1 , 0 2 22 1 , 1 22 2 2 2 1 1 4 4 2 2 2 a b aa bb a a b ba b b a                                                                               uv u v u v u v u v 5(ii) As the i- and k- components are equal, 22ba i.e. ba     21 8 2 4 21 a aa a                        u v u v    u v u v is a vector of length 1, given that it is a unit vector. 2 2 2 11 2 18 6 2 21 1262 1 2 4 1 1 1 2 4 1 1 2 1 4 1 1 2 18 1 (or ) a a a a a a  