Basic solving of linear equations.

Basic calculation exercise using distance, mpg and cost per litre (with the conversion factor for gallons to litres given).

Based on a generic test QTS question.

These 5 questions will introduce the student to the Numbas system-

1. Input 1          

2. Input 2

3. Input 3

4. Input 4     

5. Input 5                                           

This question allows you to practice identifying the coordinates of points on graphs.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Another example of finding the $x$ and $y$ components when multiple forces are applied at different angles to a particle.

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ direction but the positive $y$. 

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

A mass is inside a box which is suspended vertically by a cord. Question uses $F=ma$ for different accelerations.

A caravan pulled along by a car. Question uses SUVAT equations and $F=ma$.

A mass attached to a vertical rope. Finding the tension in the rope for different accelerations. Using $F=ma$.

Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

A particle is in equilibrium on an incline. Four forces are acting on it. You're given the angle of the incline and three forces. Resolve the forces to find the angle and magnitude of the other force.

Find the acceleration, distance moved and magnitude of the normal reaction of a particle being pulled along a rough horizontal plane.

Find the weight of a particle when the mass and acceleration due to gravity is known. Using $F=ma$ to find the acceleration of the particle when it is acted on by a resultant force.

Solving questions using $F=ma$ and $W=mg$.

Two particles collide. Given the masses and final speeds of the particles, as well as the impulse imparted on each, find their initial speeds.

Collisions question involving principle of conservation of momentum.

Finding speeds and impulses 

Use the Impulse-Momentum principle to find the change in speed of an object after a constant force is applied for a given period of time.

A block lies on rough horizontal ground. The coefficient of friction is given and students find the maximum value of friction $F_{\text{MAX}} = \mu R$. This is then used to determine the magnitude of force that must be exceeded to achieve movement when the force is applied horizontally and at two different angles to the horizontal.

A block lies on rough horizontal ground. The coefficient of friction is given and students find the maximum value of friction $F_{\text{MAX}} = \mu R$ to determine if the block will move when three different magnitudes of force act on the block horizontally.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Ball projected vertically within water of a swimming pool. Find the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Simplifying indices.

Finding factors and taking out composite roots.

Adapted from 'Surds 1' by Joshua Boddy.

Practice rationalising a binomial denominator which contains surds.

Adapted from 'Surds 3' by Joshua Boddy.

Practice rationalising a single-term, surd denominator.

Adapted from 'Surds 2' by Joshua Boddy.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).