NSAA Mathematics - Calculus Flashcards

6 cards from real NSAA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 NSAA Mathematics - Calculus flashcards as text

What is the derivative of f(x) = 5x³ - 2x + 7?
Answer: 15x² - 2
Using power rule: d/dx(5x³) = 15x², d/dx(-2x) = -2, d/dx(7) = 0; so f'(x) = 15x² - 2.
Evaluate the integral ∫(4x³ - 2x) dx
Answer: x⁴ - x² + C
∫4x³dx = x⁴ and ∫-2x dx = -x²; result is x⁴ - x² + C.
Find the gradient of y = 3x² - x at x = 2.
Answer: 11
dy/dx = 6x - 1; at x = 2: 6(2) - 1 = 12 - 1 = 11.
A function has a stationary point where:
Answer: The first derivative equals zero
A stationary point occurs where dy/dx = 0, meaning the gradient of the curve is zero.
What is ∫₀² 3x² dx?
Answer: 8
∫3x² dx = x³; evaluated from 0 to 2: 2³ - 0³ = 8.
What is the second derivative of f(x) = x⁴ - 3x² + 5?
Answer: 12x² - 6
f'(x) = 4x³ - 6x; f''(x) = 12x² - 6.

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