1. For y = (2x2 - 1)5, what is dy/dx at x = 1?
By the chain rule, dy/dx = 5(2x2 - 1)4 x 4x. At x = 1, this is 5 x 14 x 4 = 20.
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Practice advanced functions, calculus, probability, statistics, and extended mathematical modelling.
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By the chain rule, dy/dx = 5(2x2 - 1)4 x 4x. At x = 1, this is 5 x 14 x 4 = 20.
Using the product rule, f'(x) = 2xex + x2ex. At x = 1, f'(1) = 2e + e = 3e.
Factor as (2sin x + 1)(sin x - 1) = 0. Thus sin x = 1 or sin x = -1/2. On 0 ≤ x < 2π, this gives π/2, 7π/6, and 11π/6, so there are 3 solutions.
Choose 2 of the 6 seniors and 2 of the 5 juniors: C(6, 2) x C(5, 2) = 15 x 10 = 150.
Set 320 = 80e0.18t, so 4 = e0.18t. Hence t = ln 4 / 0.18 = 7.70..., so 7.7 years.
The z-score is (59 - 52)/7 = 1. Therefore P(X < 59) = Φ(1) = 0.8413.
ACT BSSS Year 11 Specialist Methods practice should make advanced functions, calculus, probability, regression, and inference feel structured rather than guessable. These examples preview that style before the no-login Specialist Methods demo.
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