WACE Mathematics Methods calculus: exam-style practice quiz

Section One style (no calculator). If $f(x) = x^2 e^{3x}$, then $f'(x)$ equals:

Section One style. The gradient of $y = \ln(x^2 + 4)$ at $x = 2$ is:

For $f(x) = x^3 - 3x^2 - 9x + 2$, which statement about the stationary points is correct?

Squares of side $x$ cm are cut from the corners of a 30 cm by 30 cm sheet of card, and the sides are folded up to make an open box with volume $V = x(30 - 2x)^2$. The value of $x$ that maximises the volume, and the maximum volume, are:

Use the incremental formula $\delta y \approx \frac{dy}{dx}\,\delta x$ with $y = \sqrt{x}$ and $x = 25$ to estimate $\sqrt{25.3}$.

Given $f'(x) = 6x^2 - 2x$ and $f(1) = 5$, the function $f(x)$ is:

Section One style. If $G(x) = \int_1^{x} \sqrt{t^3 + 1}\,dt$, then $G'(2)$ equals:

The area of the region enclosed between $y = x^2$ and $y = x + 2$ is:

A particle moves in a straight line with velocity $v(t) = t^2 - 6t + 8$ m/s for $0 \le t \le 4$. The total distance it travels is:

Section Two style. A town's population grows at a rate of $\frac{dP}{dt} = 50e^{0.02t}$ people per year, where $t$ is in years. The increase in population over the first 10 years is closest to:

The derivative of $y = \sin^2(3x)$ is:

For $f(x) = x^4 - 4x^3$, which statement is correct?