Find an integral by choosing a suitable substitution.

Add, subtract, multiply and divide numerical fractions.

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Tiny demo question for the polynomials extension.

It's important to wrap the student's answer in polynomial() in the marking script, otherwise the marking doesn't work.

Using differentiation to find the tangent and normal to a line at a given point

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Introduction to using the product rule

Introduction to using the product rule

A basic introduction to differentiation

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.

Converting decimals to percentages.

Given the vector equations of two straight lines, find the coordinates of the point of intersection

The javascript function edge(...) draws the edges of a triangle

Given the vector equations of two straight lines, find the angle between them

A sneak peek at a really clever integration of GeoGebra with Numbas.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

This is a test of the Numbas math question examiner

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

First- and second order recurrence equations, homogenous and nonhomogenous

In this question, a locally extreme value (and its location) of a function will be determined.

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Questions using Pythagoras' theorem involving integers and surds. 

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Assessment questions for First Order Differential Equations (1)