Practise VCE with a tutor that doesn’t bluff.

Differentiate $y = (3x^2 + 1)^5$ with respect to $x$.

Find $\dfrac{dy}{dx}$ for $y = x^2 e^{x}$.

Differentiate $y = \dfrac{2x + 1}{x - 3}$.

Differentiate $y = \sin(2x^2)$.

Differentiate $y = \ln(5x)$, for $x > 0$.

Find $\dfrac{dy}{dx}$ for $y = x(2x - 1)^3$, and give your answer in fully factorised form.

Evaluate $\displaystyle\int_0^2 3x^2 \, dx$.

Evaluate $\displaystyle\int_0^{\pi/2} \cos x \, dx$.

Which of the following is $\displaystyle\int (4x^3 - 2)\, dx$?

If $y = e^{3x}$, then $\dfrac{dy}{dx}$ equals:

The curve $y = x^2 - 4x + 3$ has a tangent at the point where $x = 1$.

Differentiate $y = e^{x^2}$.

Differentiate $y = \dfrac{x}{x^2 + 1}$.

Find $\displaystyle\int (6x^2 - 4x + 1)\, dx$. (You may omit the constant of integration.)

Evaluate $\displaystyle\int_1^3 2x \, dx$.

Differentiate $y = \cos(3x)$.

Find the $x$-coordinate of the stationary point of $y = x^2 - 6x + 5$.

A car travels in a circle of radius $r = 5\ \text{m}$ at a constant speed $v = 10\ \text{m/s}$. Find the magnitude of its centripetal acceleration, in $\text{m/s}^2$.

A car of mass $m = 1500\ \text{kg}$ moves at $v = 20\ \text{m/s}$. Find its momentum, in $\text{kg}\,\text{m/s}$.

A constant force $F = 20\ \text{N}$ pushes a box $d = 3\ \text{m}$ in the direction of the force. Find the work done, in joules.

An ideal transformer has $N_p = 100$ turns on the primary and $N_s = 500$ turns on the secondary. If the primary voltage is $V_p = 12\ \text{V}$, find the secondary voltage $V_s$, in volts.

A $2\ \text{kg}$ object moves at $3\ \text{m/s}$. What is its kinetic energy?

How many moles are in $18\ \text{g}$ of water ($M = 18\ \text{g/mol}$)?

How many moles are in $8\ \text{g}$ of oxygen gas, $\text{O}_2$ ($M = 32\ \text{g/mol}$)?

What is the concentration of a solution containing $0.5\ \text{mol}$ of solute in $2\ \text{L}$ of solution, in $\text{mol/L}$?

A solution has a hydrogen ion concentration $[\text{H}^+] = 1 \times 10^{-3}\ \text{mol/L}$. Find its pH.

What is the mass of $2\ \text{mol}$ of carbon dioxide, $\text{CO}_2$ ($M = 44\ \text{g/mol}$)?