VCE Practice — exam practice for VCE Maths, Physics and Chemistry

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.

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?

A ball of mass $m = 0.25\ \text{kg}$ is whirled on a string in a horizontal circle of radius $r = 0.80\ \text{m}$ at a constant speed $v = 4.0\ \text{m/s}$. Find the magnitude of the net (centripetal) force acting on the ball, in newtons, correct to 2 significant figures.

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 $\text{mol/L}$?

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

In a calorimetry experiment, $200\ \text{g}$ of water rises in temperature by $5.0\ ^\circ\text{C}$. Given the specific heat capacity of water is $4.18\ \text{J}\,\text{g}^{-1}\,\text{K}^{-1}$, calculate the heat energy absorbed by the water, in $\text{J}$.

$1.50\ \text{kJ}$ of heat energy is transferred to $150\ \text{g}$ of water. Given $c = 4.18\ \text{J}\,\text{g}^{-1}\,\text{K}^{-1}$, calculate the temperature rise of the water, in $^\circ\text{C}$, correct to 2 significant figures.