RVHS 2022 Lec Test 1 Ver 3

Q1 Solution MS (i) Let $x and $y be the price of each daily adult ticket and each student ticket respectively. Booth X : -----(1) Booth Y : -----(2) Booth Z : -----(3) From GC : x = 15 , y = 8 , Each adult ticket costs $15, and each student ticket costs $8 and . Alternatively: (And solve together with (2) from above) 5 5976nx ny 357 51 5763xy 7 2 8712nx ny 15 5976 0 (1)xy n     1357 51 0 5763 (2)xy n     17 2 8712 0 (3)xy n     11 72n  72n 5 5976 7 2 8712 xy xy    1728 3240 0xy

Q2 Solution MS (i) Since , + -3 - 2 + For Therefore, or (ii)     2 2 2 2 2 2 2 2 2 2 2 7 15 16 7 15 106 7 15 6 06 7 15 6 06 69 06 69 06 3 0( 2)( 3) x xx x xx x x x xx x x x xx xx xx xx xx x xx                         2 30x 1 0( 2)( 3)xx    2 2 , 3xx 32 x   3x 3 ln 2x   2 3 1 xee 

Q3 Solution MS (i) Sketch the graphs of : When (ii) By observation, the 2 graphs intersect at and 1 2xb . Hence, for (*), 10 2x or xb 2 2 1 and by x b y x    0, 2 1 10, 2 x y b y x b         2 2 2 2 1 22 2 2 1 0 (2 1)( ) 0 1 or 2 2 or 1 bxb x x bx x b x b x b x x b x x b y b y                   1 2x 2 2 1b xbx    (0, 2b-1) (-b, -1) by x 2 2 1y x b   1 ,02 b 

(iii) Replace x in (*) by : 2( ) 2 1 2 2 2 1 b x b bxb b x b bxb         110 22x b b x b        Or 2x b b x b    Q4 Solution MS (i) …….(*) Valid range: xb 2 4 1b xbxb    3 1 27 12 x   1 327 12 x     1 1 3 3 427 1 9 x     2 14 1 1 4 4 3313 3 9 2! 9 xx                            21 4 3213 27 729 xx    21 4 32 3 81 2187xx   4 19 99 44 x x    

(ii) 1Let 8x Since expansion is valid for , 1 3 3 33 2 33 33 33 3 1LHS: 27 12 8 1 28.5 1 19 1.5 1 1 4 1 32 1 3 81 8 2187 819 1.5 716 2187 1 716 218719 1.5 19 1.5 3.05447 1.5 1.145                         (*) 99:, 44x x x    