RI 9758/01 2022

1 | P a g e Question 1 No. Suggested Solution Remarks for Student       i 2 1 ...(1) 2 i i 6 ...(2) (2) 2i : 2i 2 i 2 12i ...(3) (1)+(3): i 4i 2 1 12i 1 12i 2 5i 1 12i 2 5i 58 29i 2 i29 29 Sub back into (1): 1 i 2 i1 i i2 2 z w z w z w z z z z z zw                              This is a non-calculator question. Detailed working needs to be shown. Question 2 No. Suggested Solution Remarks for Student (a)            1 12 2 22 22 f tan 2 1f 1 2 1 2 2 2f 1 2 2 2 1 2 x x x x x xx x x x                               (b)        1 2 2 2 2 f 0 tan 2 0.95532 1 1f 0 0.33333 31 2 2 2 2 2f 0 0.31427 91 2 0.31427f 0.955 0.333 ... 2 0.955 0.333 0.157 ... x x x x x                     Note that all calculated values are to be in radians – check that you set calculator to the correct mode. Note the degree of accuracy for this question is 3 s.f. Raffles Institution H2 Mathematics (9758) Solution for 2022 A-Level Paper 1

2 | P a g e Question 3 No. Suggested Solution Remarks for Student (a)    3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 1 1 d 3e 2e e e e 3e2 2 d 2 1 1 d 3e 2e e e e 3e2 2 d 2 3e 3ed e 2e23d e 2ee 3e2 1 d 2 1ln 2, 33 d 2 1 t t t t t t t t t t t t t t t t t tt t xx t yy t y x yt x                                Gradient of normal = 1 3 lne for 0x x x  (b) 3 3 e 2e t t x y x y      3 3e 2et tx y x y       2 2 2 2 2 22 1, 2 2 2 x yx y x      Since question says state the restriction for x, we can use GC to draw  3 31 e 2e2 t tx   to get the restriction on x. (x as Y1 and t as X in GC)

3 | P a g e Question 4 No. Suggested Solution Remarks for Student (a)   2 2 2 2 2 2 2 d d coscotd d sin sin cos (using quotient rule)sin 1 (since sin cos 1)sin cosec xxx x x x x x x xx x            (b) Note that sin 2 2sin cosx x x and sintan cos xx x , therefore  2sinsin 2 tan 2sin cos 2sincos xx x x x x x  This is a “show” question (c)   9 18 9 18 9 2 18 29 18 9 18 cosec6 cot 3 d 1 dsin 6 tan 3 1 d (from (b))2sin 3 1 cosec 3 d2 1 cot 3 (from (a))6 1 cot cot6 3 6 1 1 36 3 1 1 3 6 3 1 3 or 93 3 x x x xx x xx x x x                                     Note that you are expected to simplify the answer. You can also use GC to verify whether your answer is correct.

4 | P a g e Question 5 No. Suggested Solution Remarks for Student (a)          2 2 2 2 2 2 2 2 2 2 2 2 2 8 14 52 16 64 28 196 52 1 16 28 208 0...(1) line is tangent to curve means (1) has one repeated root, 16 28 4 1 208 0 256 896 784 832 832 0 48 896 576 0 3 56 36 0 x mx x x m x mx m x m x m m m m m m m m m         