2023 MI PreU1 (Soln)

1 © Millennia Institute 9758/01/PU1/EOY/23 Mark Scheme 2023 MI H2 Math Pre-U 1 Exam Solutions Qn Solution 1(i) [2] When 2n ,   1 22 22 41 4 1 42 1 4 4 23 nnnuSS nn n n nn nn n n         When n = 1, 2 11 14 ( 1 ) 5 2(1) 3 uS   Thus, 1u follows the form of 2 3nun when n = 1. So, 2 3nun 1(ii) [2]  1 23 2 (1 ) 3 23 21 2 nnuu n n nn        Since 1 2nnuu  is a constant independent of n, the sequence is an arithmetic progression. 2(i) [3] Let $x, $y and $z be the price of a short, tall and grande cup of coffee respectively. 3 12 8 147.9 4 8 7 120.10 2547 0 Using GC, 4.50, 6.20, 7.50 xy z xyz xyz xyz      The price of a short, tall and grande cup of coffee is $4.50, $6.20 and $7.50 respectively. 2(ii) [2] The required amount 0.9 4.50 4 6.20 2(7.50) 41.37 Andrew pays $41.37.    

2 © Millennia Institute 9758/01/PU1/EOY/23 Mark Scheme 3(i) [3] 3(ii) [3]      2222 22 22 2 2 1 1 I: replace by /4 1 1 4 1 1 II: replace by 2 1 1144 2 2 1 1 III: repl4 xxy x x y xy x yy y x y                      2 2 2 2 4 ace by 2 2 2 1 14 23 1x xyy y y          O (െ√2, 0) x y (√2, 0)  1y x  1yx    22 11xy   (0, െ1)

3 © Millennia Institute 9758/01/PU1/EOY/23 Mark Scheme   4 (ii) [3] 5(i) [2] 1 , and are collinear, is the common point (shown) OA OB OC OA OB OB OC OA OB OC OB BA BC AB C B                                   Qn Solution 4 (i) [3] x y 𝑦ൌ 3  ሺ4, 2ሻ ሺെ4, 2ሻ O x = 2𝑥ൌെ 2 f| | 1yx ሺ0, 2ሻ (4, 1) 2 𝑦ൌ 1 2  𝑥 𝑦 𝑥ൌ 1 𝑂   1 fy x (0, 1)

4 © Millennia Institute 9758/01/PU1/EOY/23 Mark Scheme 5 (ii) [3] Given 1 6  , 51 66OA OB OC       65 65              OA OB OC OC OA OB   Method 1: Sub and Eliminate OC    By Ratio Theorem, 4 5 65 4 5 2 01 2 2 1 02 1 5 2 OC OAOD OA OB OA OD OD OA OB OD OD                                       Method 2: Find OC   and Sub in 015 65 6 2 5 1 1 7 02 1 0       OC OA OB              By Ratio Theorem, 4 5 50 1 17 4 2 5 10 0 1 5 2          OC OAOD OD OD            

5 © Millennia Institute 9758/01/PU1/EOY/23 Mark Scheme 5 (iii) [3] 101 12 3 20 2 10