RVHS 2022 JC1 H2 MA CT Soln w Comments

River Valley High School 1 2022 JC1 H2 MA Common Test Markers Comments 1 Solution [4] MOD Let 2 (2 1)(2 1) (2 1) (2 1) AB r r r r     1 2 2 1(2 1) x A r    1 2 2 1(2 1) x B r    2 1 1 (2 1)(2 1) (2 1) (2 1)r r r r     This part is well -done by almost every student. 11 1 1 1 1 (2 1)(2 1) 2 2 1 2 1 nn rr r r r r        11 13 11 351 2 11 2 3 2 1 11 2 1 2 1 nn nn             ... 1112 2 1 n    The common mistake is missing out the 1 2 but most students recognize it is MOD.

River Valley High School 2 4 1 14 1 3 12 11 1 (2 3)(2 1) 1 (2( 1) 3)(2( 1) 1) 1 (2 1)(2 1) 11 (2 1)(2 1) (2 1)(2 1) 1 1 1 1112 2( 1) 1 2 2(2) 1 1112 n r kn k n k n kk rr kk kk k k k k n                                                      (let r = k+1) = 112( 1) 1 2(2) 1 1 1 1 2 5 2 1 n n         The challenging part of this question is letting 1rk and more imp ortantly considering the starting and ending values of k.

River Valley High School 3 2 Solution [4] SLEs Let b, s and f be the price per cup of butter, sugar and flour respectively. 200b + 50s + 200f = 129 40b + 40s + 40f = 32.4 100b + 50s + 300f = 88 From GC, b = 0.5, s = 0.22, f = 0.09 Therefore, the price of a cup of butter, sugar, and flour is $0.50, $0.22, and $0.09 respectively. Hence, the cost to produce the pastries is $81.25 Very well -done by almost all students

River Valley High School 4 3 Solution [5] Inequality (a) 1 2 1 2 23 23 22 1 21 1 1 1 1 11 1 21 2 2 2 2 2 2 2 21 ... (*)2 2! 3! 1 1 11 ... 22 x xx x x x x x xx                                              Expansion is valid for 22 1 1 2 xxx     2 or 2xx  Since 6 6 2   , 6x is valid for getting an estimate for 6 . 23 2 1 1 11 22 x x x x x      Let 6x 23 4 1 1 116 ( 6) 2( 6) 2( 6)         2 353 4326  8646 353 Most students are able to come out with the series; however some did not read the question clearly and attempt to expand in increasing order instead. Not many students can write down the range of values of x correctly and subsequently give a reason why -6 is a good estimate. There is another approximate value of 3536 144 . 2 353 3 432 2 3 353.3 3 432 6 353 3 432 3536 144    

River Valley High School 5 4 Solution [5] Summation (a) 11 1 1 1 u( ) u( 1) 2 4 2 u( ) u( 1) 2 4 2 u(1) u(0) u(2) u(1) 2