Simon Thomas

Find angle and side in a right angled triangle.

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Pythagoras' Theorem and naming sides of right angled triangle

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Pythagoras' Theorem and naming sides of right angled triangle

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Cos, Sin and Tan

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Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

To be used on the connected particles page under the Dynamics section of the Mechanics wiki page.

Connected particle involving a pulley system - can not treat whole system as a whole due to different directions.

Connected particle involving a pulley system - can not treat whole system as a whole due to different directions.

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.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

A particle is projected up a rough plane at a given speed. Given the angle of the slope and the coefficient friction, find the distance the particle travels before it comes to instantaneous rest.

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 $y$. 

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

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

Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

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.

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A ball is thrown vertically upwards from a position above ground level. Find its greatest height, and the total time its in the air.

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Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.

A variety of trigonometric equations which can be solved using inverse operations.

Directional derivative of a scalar field.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Cofactors Determinant and inverse of a 3x3 matrix.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Elementary Exercises in multiplying matrices. 

Multiplication of $2 \times 2$ matrices.