Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

Given a linear programming problem in standard form, write down the dual problem.

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Experimental question using JSXGraph to provide dynamic, interactive graphs.

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

No description given

Prove (by induction) that every value $\ge$ 44ct can be combined by using 5ct and 12ct stamps.

Idea seen in collection of exercises for preparing for the Putnam contest.

A set of Numbas exercises for students transitioning from school to University. Designed to help students gain familiarity with using Numbas to enter mathematics, and as revision for algebra, geometry and calculus. 

Using the IF to find the General Solution.

Try to solve some simultaneous equations using matrix inverses.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Semi-worked example of inverting a 3x3 matrix using cofactor, adjoint and determinant.

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.

It asks questions about

• finding sides and angles of right angle triangles,
• finding areas of triangles,
• using the sine rule,
• using the cos rule,
• bearings, and
• radial surveys.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Small demo using the JME implementation of JSXGraph inline in a multiple choice question. This version uses a JME variable to store the expressions and then calls a function wherever a plot is required.

Small demo using the JME implementation of JSXGraph inline in a multiple choice question.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

This question demonstrates sending commands to geogebra and getting geogebra values and using them as part of a marking algorithm.

Sketch a function graph by using fist and second derivatives.

This demonstrates how to construct a JSXGraph diagram in JME code.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS applied to integers. These questions only test IDMAS. That is Indices, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.