Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Questions on transposition

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Finding the stationary points of a cubic with two turning points

This exercise will help you solve equations of type ax-b = c.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.

Also find the 95% confidence interval for the population mean.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.

Convert a metric measurement to another order of magnitude, e.g. g to kg.

Just what the title says, I guess.

This question shows how to load a GeoGebra applet in JavaScript, avoiding the JME functions. This allows you to do some more complicated manipulation of the worksheet than simply redefining objects.

Introductory exercise about set equality

Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Write expressions for the moment of inertia of simple shapes about various axes.

An A-frame structure supporting a load at the top.  Simple because both legs are two force bodies.

An A-frame structure supporting a load at the top.  Simple because both legs are two force bodies.

A fill-in-the-blank style question to test vocabulary within the topic of Algebra.

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