Modular arithmetic. Find the following numbers modulo the given number $n$. Three examples to do.

This question tests the students ability to use the logarithm equivalence law to make x the subject of a given equation and to check which of a list of logarithmic expressions are equivalent to x.

Solve a quadratic equation by completing the square. The roots are not pretty!

Given sequences with missing terms, find the common difference between terms.

This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Draws a right angled triangle based on a length and an angle.

Draws a right angled triangle based on a length and an angle.

Shows how to define variables to stop degenerate examples.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Two questions on solving systems of simultaneous equations.

Rearrange equations to make $x$ the subject.

Question assessing the students understanding of linear sequences.

Students are assessed on their ability to find the common difference and first term in a linear sequence and then find the nth term of the sequence using the arithmetic formula.

Some clever variable-substitution trickery to randomly pick two sides of a right-angled triangle to give to a student, and ask for the other.

The sides are set up so they're always Pythagorean triples, and the opposite side is always odd.

As ever, most of the tricky stuff is in the advice. 

Because this was created quickly to show how to set up the randomisation, there's no diagram. It would benefit greatly from a diagram.

Some clever variable-substitution trickery to randomly pick two sides of a right-angled triangle to give to a student, and ask for the other.

The sides are set up so they're always Pythagorean triples, and the opposite side is always odd.

As ever, most of the tricky stuff is in the advice. 

Because this was created quickly to show how to set up the randomisation, there's no diagram. It would benefit greatly from a diagram.

Introductory exercise about set equality

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.

Working with BODMAS

Solve a quadratic equation by completing the square. The roots are not pretty!

This question asks you to place a point on a number line. The number is an integer.

This question asks you to place a point on a number line. The number is an integer.

This question asks you to place a point on a number line. The number is an integer.

This question asks you to place a point on a number line. The number is an integer.

This question asks you to place a point on a number line. The number is a non integer.

This question asks you to place a point on a number line. The number is not an integer.

This question asks you to place a point on a number line. The number is not an integer.

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

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

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