Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Find the unit vector parallel to a given vector.

Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Calculate a speed in m/s given distance and time taken, then convert that to km/hour

A collection of questions on working with units of measurement, mainly in the SI/metric system.

Several 'real-world' examples.

Convert from km to metres and miles, and miles to km.

Convert a height given in feet and inches into cm and then metres.

Convert figures for car engine sizes between cc (cm^3), litres, and m^3.

Convert weights of babies between kg and lb and oz.

This question assesses the student's ability to use some given information involving two different units of measurement to rewrite the information as a compound measure.

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
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$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.)

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

A test of basic concepts to do with SI units and concentrations of solutions.

Unit circle definition of sin, cos, tan using degrees

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\cos\theta$ given $\sin\theta$ and the quadrant theta is in.

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\sin\theta$ given $\cos\theta$ and the quadrant theta is in.

Unit circle definition of sin, cos, tan using degrees

Often students need practice re-indexing series, these are three questions that give them that opportunity.

Often students need practice re-indexing series, these are three questions that give them that opportunity.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Conversions of units

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

Conversions of units

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.