= AG N0 p –4 (c) evidence of integration (M1) = A1A1A1 f(x) substituting (2, 4) or into their expression (M1) correct equation A1 e.g. A1 N4 [14] 6. evidence of integrating the acceleration function (M1) e.g. correct expression ln cos 2t + A1A1 t c – evidence of substituting (1, 0) (M1) 0 = ln 1 cos 2 + e.g. c – = (A1) c –0.624 = ln (A1) v t – = 2.24 (accept the exact answer ln 5 1.5 cos 10 + 1.5 cos 2) A1 N3 v(5) – [7] 7. (a) (x) = 2x 2 f – (x) = 2x + (M1)(M1) x2 c – = 0 when = 3 x  0 = 9 6 + c – = (A1) c –3 (x) = 2x 3 (AG) f x2 – – (x) = 3x + (M1) f x2 d – – When = 3, (x) = x f –7  = 9 9 9 + (M1) d –7 – –  = 2 (A1) 6 d  (x) = 3x + 2 f x2 – – (b) (0) = 2 (A1) f (–1) = 1 + 3 + 2 f – – = 3 (A1) = 1 + 2 3 (–1) f – = 0 (A1) 3 (c) = 0 is a stationary point (–1)  f (A4) 4 Note: Award (A1) for maximum, (A1) for (0, 2) (A1) for (3, –7), (A1) for cubic. [13] 8. (a) finding derivative (A1) = e.g. f′(x) correct of derivative or its negative reciprocal (seen anywhere) A1 e.g. gradient of normal = (seen anywhere) A1 e.g. substituting into equation of line (for normal) M1
p = –4 AG N0 (c) evidence of integration (M1) f(x) = A1A1A1 substituting (2, 4) or into their expression (M1) correct equation A1 e.g. A1 N4 [14] 6. evidence of integrating the acceleration function (M1) e.g. correct expression ln t – cos 2t + c A1A1 evidence of substituting (1, 0) (M1) e.g. 0 = ln 1 – cos 2 + c c = –0.624 (A1) v = ln t – (A1) v(5) = 2.24 (accept the exact answer ln 5 – 1.5 cos 10 + 1.5 cos 2) A1 N3 [7] 7. (a) f (x) = 2x – 2 (x) = x2 – 2x + c (M1)(M1) = 0 when x = 3  0 = 9 – 6 + c c = –3 (A1) f (x) = x2 – 2x – 3 (AG) f (x) = – x2 – 3x + d (M1) When x = 3, f (x) = –7  –7 = 9 – 9 – 9 + d (M1)  d = 2 (A1) 6  f (x) = – x2 – 3x + 2 (b) f (0) = 2 (A1) f (–1) = – – 1 + 3 + 2 = 3 (A1) f (–1) = 1 + 2 – 3 = 0 (A1) 3 (c) f (–1) = 0  is a stationary point (A4) 4 Note: Award (A1) for maximum, (A1) for (0, 2) (A1) for (3, –7), (A1) for cubic. [13] 8. (a) finding derivative (A1) e.g. f′(x) = correct of derivative or its negative reciprocal (seen anywhere) A1 e.g. gradient of normal = (seen anywhere) A1 e.g. substituting into equation of line (for normal) M1
semester_1_review.docx