Denis Flynn

Solve a system of linear equations using Gaussian elimination.

Shows how to define variables to stop degenerate examples.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by elimination 1 with parts' by Joshua Boddy.

Compute a table of values for an exponential function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

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.

Cramers Rule applied to 3 simultaneous equations

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a right hyperbola.

This quiz contains questions on functions, limits, logs, exponential functions, simultaneous equations and quadratic equations.

Practice dividing polynomials using the long division method.

3 questions on factorising quadratics. The second question also asks for the roots of the quadratic. The third question involves factorising quartic polynomials but which are quadratics in $x^2$.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

In the Gaussian integer ring $\mathbb{Z}[i]$ , find the remainder $r=r_1+r_2i$, where $a \gt 0,\;b \gt 0$ , on dividing $a+bi$ by $c+di$ .

Questions on linear programming techniques, with interactive graphics.

Questions about complex arithmetic; argument and modulus of complex numbers; 

Denis's copy of Nick's copy of Henrik Skov's copy of Complex numbers

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Find angle and side in a right angled triangle.

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2 Converting Radians to Degrees

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Converting Degrees to Radians

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