NSAA NSAA Mathematics - Calculus 3

Question 1

The product rule for differentiation states: d/dx[f(x)g(x)] =

Accepted Answer

f'(x)g(x) + f(x)g'(x)

Answer

The product rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x).

Question 2

Evaluate ∫ sin(x) dx

Accepted Answer

-cos(x) + C

Answer

∫ sin(x) dx = -cos(x) + C.

Question 3

A particle's position is given by s(t) = t³ - 6t. What is the velocity at t = 2?

Accepted Answer

6

Answer

v(t) = ds/dt = 3t² - 6; v(2) = 3(4) - 6 = 12 - 6 = 6.

Question 4

Find the x-coordinate of the stationary point of y = x² - 6x + 9.

Accepted Answer

x = 3

Answer

dy/dx = 2x - 6 = 0 → x = 3.

Question 5

The integral ∫ 1/x dx equals:

Accepted Answer

ln|x| + C

Answer

∫ 1/x dx = ln|x| + C.

NSAA - Natural Sciences Admissions Assessment Practice Test