SJI 2024 Year 6 HL MAA Prelim Examination Paper 2 (MS)

SJI Year 6 HL MAA Prelim Exam 2024/P2 (Markscheme) Page 1 of 11 Year 6 HL MAA Preliminary Examination 2024 Paper 2 (Markscheme) Section A Qn Suggested solution Markscheme 1 Normal distribution with conditional probability [Marks: 6] (a)       2~ 3.24, 0.375 0.1 0.9 W N P W w P W w     By GDC (invNorm or nSolve), 3.72 (3 sf)w (A1) – cumulative prob (M1) – invNorm or nSolve A1 (b)      4 44 | 0.1 0.1 0.021348 0.1 0.213 (3 sf) P W W w P WP W W w          M1 A1 – conditional prob A1 – no follow through as   0.1P W w  is given 2 Vectors [Marks: 4]   2 2 2 2 0                                  a ba v b = a b b b a b= a b b b b a ba b b b a b a b = Since   0  a v b ,   a v b   sin 2       a v b a v b a v b M1 – distributive M1 – 2 b b = b A1 R1 – dot prod 0, perpendicular AG

SJI Year 6 HL MAA Prelim Exam 2024/P2 (Markscheme) Page 2 of 11 Qn Suggested solution Markscheme 3 Counting Techniques [Marks: 5] (a) (choose female P/VP and choose male P/VP and choose other 4 EXCO members)   4 4 28 1 1 42 655200 C C C   M1 M1 – combination & multiplication principle A1 (Accept 655000) (b) (arrange P/VP in middle two seats and arrange other 4 EXCO members in remaining seats)   2! 4! 48 M1 – arrangement A1 4 Sum and Product of Roots [Marks: 5] (a)   3 4 3( 3)( 6 10)P x x x x x      roots 0 6 6A    (M1)A1 (b)   7 roots 1 ( 30) 30G     M1A1 (c)  roots 1 31G   A1 5 Arithmetic sequence & series (with horizontal scaling [Marks: 8] (a) 2k  A1 (b) Method 1 1 2From graph, 3 and 7 7 3 4 x x a      Method 2 Period of  2 siny x  is 2 M1 A1 – consecutive min. pts. A1 M1 – use period of graphs

SJI Year 6 HL MAA Prelim Exam 2024/P2 (Markscheme) Page 3 of 11 Qn Suggested solution Markscheme Period of   22 4y f x      4a  Method 3 1 2 difference in values when ( )=0n nx x x f x    sin 0 , 2 ,...2 2x x           1 2 4 2 4n nx x      M1 – scaling of period A1 M1 – use of x-intercepts M1 A1 (c)     1 1 3 4 1 6 4 1 2 N N n n n Nx n N                Method 1 By GDC Graph   1 3 4 1 x n y n       and Table, 15 1 16 1 465 500 528 500 n n n n x x         Least 16N  Method 2 By GDC Graph  6 4 1 5002 xy x      15.563N  Least 16N  M1 A1 – AP with first term 3 and common diff. 4 Follow through from part (a) R1 A1 M1 A1

SJI Year 6 HL MAA Prelim Exam 2024/P2 (Markscheme) Page 4 of 11 Qn Suggested solution Markscheme 6 Domain, Area between Curves and Volume of Solid of revolution [Marks: 6] (a) For  f x to