XMSS E Math Prelim P2 Mark Scheme

Solution/ Mark Scheme 1 (a) ( ) ( ) 2 7 7 025 2 7 7 25 5 2 7 2 7 --- [M1] 10 35 14 2 12 21 37 1 (also accept ) --- [A1]44 xx xx xx xx x x +− −= +− = + = − + = − =− =− − Alternative 2 7 7 0 25 5(2 7) 2(7 ) 0 --- [M1] 10 35 14 2 0 12 21 37 1 (also acce pt ) --- [A1]44 xx xx xx x x +− −= + − − = + − + = =− =− − (b) (c) 22 2 2 2 15 3 28 15 8 23 20 --- [B1] x x y y x y x y y  = = 2 2 2 (2 3)( 4) 2 2 11 12 2 2 11 10 0 ---[M1] ( 11) ( 11) 4(2)(10) ---[M1]2(2) 11 41 4 1.15 or 4.35 --- [A1, A1] xx xx xx x x x − − = − + = − + = − −  − −= = =

(d) ( ) 22 22 3 2 6 6 3 2( 3 ) 6 ( 3 )( 2) --- [M1 for numerator; M1 for denominator]( 3 )( 2 ) 2 --- [A1]2 ax bx a b a ab b x a b a b a ab b a b x a b a b x ab + − − +− + − += +− +−= +− −= −

Solution/ Mark Scheme 2 (a) Each compound increases the principal amount, which in turn leads to greater interest being generated. Cody should invest in account A as it provides more frequent compounding than account B, hence, generating greater interest. OR Cody should invest in account A because the interest is calculated 12 times each year as compared to only once a year for Account B. Each time, the interest is calculated on a larger amount of money. Therefore, account A will generate greater interest. *Do not accept if students provide a calculated example and arrive at a conclusion just based on calculation. Key idea of more frequent compounding in account A, which will lead to more interest generated, should be featured in students’ explanation. (b) 3 3 3 3 20000 1 22823.32 --- [M1]100 22823.32 1 100 20000 22823.32 1 --- [M1]100 20000 22823.32 1100 20000 4.4999 (5 s x x x x x += += += =− = .f.) 4.5 (1 d.p.) --- [A1] (c)(i) 40 $156000 36 $2800 --- [M1]100 $163200 --- [A1]  +  =

(c)(ii) 3 $156000(0.92) --- [M1] $121475.328 (3 d.p.)= Method 1 $121475.328 100% 74.433% --- [M1]$163200 100% 74.433% 25.6% (3 s.f.) --- [A1] = −= Method 2 loss incurred: $163200 $121475.328 $41724. 672 $41724.672% loss: 100% --- [M1]$163200 25.566% 25.6% (3 s.f.) ---[A1] −=  = =

(d) [A1] for either Amount of S$ spent in America: $368 2 1.35 $993.60 [M1 for finding cost of hotel in US in SGD] 1Amount of S$ spent in Canada: $250 3 $735. 2941 (4 d.p.) 1.02   =   = [M1 for finding cost of hotel in Canada in SGD] 1.5Total amount spent: $993.60 $735.2941 ($99 3.60 $735.2941) $1754.82 100 OR 101.5 ($993.60 $735.2941) $1754.82 100 + +  + = +  =

Solution/ Mark Scheme 3 (a)(i) Median mark = 35 (a)(ii) 38 30 --- [M1] 8 --- [A1] − = (a)(iii) 60th percentile: 60 80 48100= From graph, 60th percentile: 36 --- [B1] (b)