AMKSS_Prelim_2024_AMath_P2_MS

2024 AMKSS 4E5N Prelim AMP2 Marking Scheme Qn Solution Marks 1   1 2 100 10 24 0 10 10 10 24 0 x x x x       Let 10xy    2 10 24 0 12 2 0 y y y y       12y or 2y   10 12 rejected x  10 2x  lg10 lg 2x  lg 2x B1 (correct quadratic) M1 (factorise or quadratic formula) A1 (reject 10 12x  , do not accept if reject 12y ) A1 2 Let   3f 3 5 2x x x         3 f 1 3 1 5 1 2 0    By factor theorem, 1x is a factor of 33 5 2x x  .    3 23 5 2 1 3 2x x x x Ax      Comparing coefficient of x, 5 2 3 A A        21 3 3 2 0x x x    1x or        2 3 3 4 3 2 2 3x      3 33 6x   B1 M1 (or long division: must see 23x ) M1 (factors equate to 0) A1 (for 1x ) A1 (for exact values) 3(a)                   1 1 2 2 1 2 1 4 1 d 1 4 1 1 1 4 1 4d 2 4 1 4 1 2 1 4 1 2 2 4 1 6 1 4 1 y x x y x x xx x x x x x x x x                        M1 (for chain rule), M1 (product rule) M1 (factorise or combine to single fraction) A1

Qn Solution Marks 3(b)     66 2 2 66 6 2 2 2 6 1 d 1 4 1 4 1 6 1 d d 1 4 1 4 1 4 1 x x x x x x x x x x x x                                        6 1 266 2 2 2 6 6 2 2 6 2 4 16 d 1 4 1 14 1 42 1 4 1 d 1 4 16 24 1 4 6 16 1 4 6 1 21 d 64 1 4 2 12 1 4 2 1 2 53 6 xx x x x x x x x x x x x x x                                                         M1 (using (i)) M1 (integrate their 4 1 q x correctly) A1 (correct 6 2 d 4 1 x x x including 1 6 ) M1 (substitute correct values in correct order) A1 4(a) 2x or 3x   2 3 0x x    2 2 6 0 3 3 18 0 x x x x         3p 18q M1 (accept   2 3 0x x   ;   3 2 3y x x   ) A1 A1 4(b) (i)           2 2 2 2 2 1 3 3 1 1 0 1 4 3 1 0 2 1 12 12 0 10 11 0 11 1 0 qx x x q x q x q q q q q q q q q q                         11q or 1q M1 (eliminate x or y) M1 (correct D and = 0) M1 (factorise or quadratic formula) A1 4(b) (ii)     2 2 2 3 12 12 0 4 4 0 2 0 2 21 2, 21 x x x x x x y R            M1 (factorise or quadratic formula A1 (correct x) A1 (correct y)

Qn Solution Marks 5(a) (i) T 2.2 5.0 7.8 10 12.8 lg t 0.146 0.283 0.420 0.526 0.662 B2 (minus 1 for each incorrect point; minus 1 if axes not labelled) 5(a) (ii) (a) When 0T  lg 0.04 1.10 (accept 1.07 to 1.13) t t   M1 (equate vertical intercept to lg t) A1 (both marks only given if graph is extended to find lg t -intercept) 5(a) (ii) (b)     lg lg lg 1.064 lg lg lg 1.064 kT t a t a kT     Gradient = 0.0487       lg 1.064 0.0487 0.0487 lg 1.064 1.807611629 1.81 acce