Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

Show a list of the factors of a number.

Works by testing each number up to $n$ for divisibility by $n$, so won't do well with really big numbers. Certainly fast enough for numbers up to 4 or 5 digits.

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years. 

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

A question made for the FYiMaths December meeting, to show off some of the more adventurous things you can do with Numbas.

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

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Made for my TALMO talk. This demonstrates how you can use a part with no marks as an oracle to perform calculations, to help the student check their working.

This question demonstrates a few ways of interacting with a Venn diagram drawn using JSXGraph.

This test will assess a students ability to work with piecewise and composite functions.

A line with random $x$- and $y$- intercepts is plotted, and you have to drag two dots over the points where the line crosses the $x$ and $y$ axes.

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

Denominators with linear factors, repeated factors and non-factorisable quadratics.

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Inverse and division of complex numbers.  Four parts.

Trigonometric equations with degrees

Simple trig equations with radians

Practice solving equations with integer solutions. 

A question that will allow students to check their understanding of the Caesar Cipher by encrypting a short message given a random key. May be updated with a decryption task later.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $af(x)$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(x)+a$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(ax)$.

Finding the transformation of a function with a modulus, from $f(x)=nx-m|x|$ to $f(x+a)$.

This question gives information for students on how to answer number entry parts, with some opportunities to try submitting answers.

Recall of common units, along with understanding multiplication.

Create a truth table with 3 logic variables to see if two logic expressions are equivalent.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Calculating the integral of a function of the form $\frac{cx+d}{(x+a)(x+b)}$ using partial fractions.