Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

Simple substitution into an algebraic expression. Includes powers, division, mulitplication, brackets.  Includes subscripts.

A demo of the mathematical expression part and its options.

Factorising a quadratic expression of the form $ax^2+bx+c$ by completing the square.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

You can enter an expression and rearrange it in the following steps. Numbas checks that each arrangement is equivalent to the original expression.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

No description given

No description given

Basically expand an expression like "5y(-2z+3)" where the student types answer into a single gap.

The student has to write the general solution of a 2nd order PDE. They can choose the names of their arbitrary functions of $x$ and $y$.

The marking algorithm finds the names of the functions of $x$ and $y$ in the student's answer, and replaces them with $\sin(x)$ and $\cos(y)$ (these could be changed) so that the expression can be evaluated.

Simlify (expand) logarithmic expressions 

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land$.

For example $\neg q \to \neg p$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Inputting ratios of algebraic expressions. (Translation to German)

A basic introduction to differentiation

Using BODMAS within mathematical expressions

A basic introduction to differentiation

More work on differentiation with fractional coefficients

A basic introduction to differentiation

More work on differentiation with fractional coefficients

Using BODMAS within mathematical expressions

More work on differentiation with fractional coefficients

A basic introduction to differentiation

A basic introduction to differentiation

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers