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.

A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Introductory exercise about power sets.

Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

Slightly harder introductory exercises about the power set.

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