SAJC ANNEX

Annex B SAJC H2 Maths Prelim : Qn/No Topic Set Paper Number Answers Marks 1 Binomial Expansion 9740/01 a = 1 3 , b = 1 3  , c = 5 63 4 2 Mathematical Induction 9740/01 6 3 Inequalities + Integration 9740/01 (i) 0 or 2xx<³ (ii) a = 4 6 4 Complex Numbers (Loci) 9740/01 (ii)(a) 3 2 | 3 3 | 6zi    (ii)(b) 3 arg( (3 3 ))4 zi     6 5 Maclaurin's Series 9740/01 (ii) 31 3xx- (iii) 16 3 9 (iv) 0 7 6 Tangent and Normal 9740/01 (i) 60 16 125x y a (ii) 25 125,16 64aa  (iii) 3 277 ,33aa     and 3 277 ,33aa     8 7 Functions 9740/01 (i) { : 1 }aa  (ii) 51[ 3, )7 (iii) 22 3 3h : , 1 xx x eex e   ,0xx 8 8 Maxima-Minima + Rate of Change 9740/01 (a) 22A x a x (b) 1 rad/s 12 10

9 Vectors (lines) 9740/01 (ii) 4.5 1 0    (iii) 0 8 11   (iv) 14.9; 53.6; Perpendicular/shortest distance from point X to line AB. 11 10 Vectors (planes) 9740/01 (i) 1 3 1   ; 35 (ii) 1 55 (iii) 2 19 2 r   11 11 Area & Volume 9740/01 (a)(i) 2.76 units2 (a)(ii) 31 4ln 2 units2 æö ÷çp - + ÷ç ÷çèø (b)(ii) 1tan 3- 11 12 Integration 9740/01 (a) 4 ( 1) 1 4 13 x x x C     (b) 1ln(tan ) xC  (c)(i) 21 21 xxe x    (c)(ii) 1 12 Pure Maths 1 Summation/Method of Difference 9740/02 (ii) 11 2 (2 2)!n  6 2 AP & GP 9740/02 (ii) 5 (iii)56 7 3 Transformations 9740/02 (b) 1. Translate the graph of 2 1y x= by 2 units in the positive x direction 2. S tretch the resulting graph parallel to the y-axis with a scale factor of -4. 3. Translate the resulting graph by 1 unit in the positive y 6

direction. 4 Differential Equations 9740/02 (ii)k < 0 A vaccination had been found to eliminate the virus OR The people infected by the virus had passed away 8 5 Complex Numbers 9740/02 (a) k = 2 (b) 11 5( ) ( ) ( )15 15 15 1 2 3 7 13( ) ( )15 15 45 2 , 2 , 2 , 2 , 2 i i i ii z e z e z e z e z e          13 Statistics 6 P & C 9740/02 31 3 7 Sampling 9740/02 (ii) Quota Sampling 6 8 Normal Distribution 9740/02 (i) 275 (ii) 344 5 9 Probability 9740/02 (i) 14 55 (ii) 11 21 7 10 Poisson Distribution 9740/02 1 2  ; 0.392; 0.714 7 11 Hypothesis Testing 9740/02 (i) -value 0.00882p  ; reject H0 (ii) conclusion in (i) does not change (ii) 60 10 12 Linear Regression and Correlation 9740/02 (ii) From the scatter diagram, the regression line of y on x should have negative gradient. Therefore 79 2yx is the correct regression line of y on x. (iii) (35, 18) (iv) -0.933 (v) 581.75 10a=´ ; b =  33.6 10 13 Binomial Distribution 9740/02 (ii) 0.923 (iii) 0.299 (iv) 11 0.00242 12