2022 J1 RVHS End of Year Revision Package Solutions Ch1-4

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 End-of-Year Revision Package (Solutions) 1 RIVER VALLEY HIGH SCHOOL 2022 JC 1 H2 Mathematics (9758) End-of-Year Revision Package (Solutions)

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 End-of-Year Revision Package (Solutions) 2 1 Inequalities & Equations Basic Skills 1. Find the discriminant of the following quadratic expressions. (a) 2 1x x  (b) 2 4 5x x  (c) 2 1x x   (d) 22 4 3x x   (e) 2 5 2 9 x x  (f) 2 63 xx   (a) 2 1x x   21 4 1 1 3 D   (b) 2 4 5x x   24 4 1 5 36 D    (c) 2 1x x    21 4 1 1 3 D     (d) 22 4 3x x    24 4 2 3 40 D     (e) 2 5 2 9 x x    2 1 51 4 2 9 19 9 D           (f) 2 63 xx      21 4 1 63 1249 D        2. Find the exact roots of the following quadratic equations. (a) 2 3 2 0x x   (b) 2 2 3 0x x    (c) 2 2 1 02 x x    (d) 22 1 03 4x x   (e) 2 1x x     (f) 2 6 3 02 x x   (a) 2 3 2 0x x   2 1 0 1or 2 x x x      (b) 2 2 3 0x x    1 3 0 1or 3 x x x      (c) 2 2 1 02 x x     12 4 4 1 2 12 2 2 2 2 21 x                 (d) 22 1 03 4x x   2 11 1 4 3 4 22 3 5 51 3 33 3 4 4 3 3 15 4 x                       (e) 2 1x x          2 2 2 1 0 1 1 4 1 2 1 1 4 4 2 1 2 1 2 1 2 1 1 2 1or2 2 11or x x x                                      (f) 2 6 3 02 x x    16 6 4 32 12 2 6 x            

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 End-of-Year Revision Package (Solutions) 3 Tutorial Review Tutorial 1 Questions 4 and 7. Revision Questions 1. NYJC Promo 9758/2020/Q2 (i) The first four terms of a sequence nu are given by 132.1u, 217u, 30.7u and 47.8u. Given that nu is a cubic polynomial in n, find nu in terms of n. [3] (ii) Find the least value of n for which nu is greater than 555. [2] (i) Let 3 2nu an bn cn d    132.1u a b c d     28 4 2 17u a b c d     327 9 3 0.7u a b c d     464 16 4 7.8u a b c d     Using GC, 1.5a, 9.6b, 3.2c, 37d 3 21.5 9.6 3.2 37nu n n n     (ii) 3 2555 1.5 9.6 3.2 518 0nu n n n      Method 1 From GC graphing, 9.7871n  least value of n10 Method 2 From GC Table,  least value of n10

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 End-of-Year Revision Package (Solutions) 4 2. YIJC Promo 9758/2020/Q1 Four families, namely Chan, Lee, Tan and Wong, purchase masks, hand sanitisers and thermometers at a pharmacy. The Tan family made their purchase using a vouche