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A graphical introduction to the concept of even functions a symmery

Ferrous Metals

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.

Area of circle

Calculating particular harmonic components of a Fourier series expansion.

Solve a Differential equation with an irreducible quadratic factor 

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Calculating rates and scaling rates. Drops per mL and drops per minute questions equivalent rate to unit rate.

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Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

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This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

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Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

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Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

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A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

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Converting a percentage to a fraction and decimal.

Is this number divisible by 100? Half the time the number is, half the time it isn't. Steps give the divisibility test and how to count the number of 100s.