Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Obtain the equation of a straight line that passes through 2 points.

Given one point and the gradient determine the equation of the line.

Graphs are given and students are required to match them with their equation.

Graphs are given and students are required to match them with their equation.

Graphs are given and students are required to match them with their equation.

Solving quadratic equations using a formula,

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!

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.

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

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

Given a graph, the student is asked to determine the quadratic function.

Solving quadratic equations using a formula,

Solve a system of three simultaneous linear equations

Cramers Rule applied to 3 simultaneous equations

Cramers Rule applied to 3 simultaneous equations

Solve a logarithmic equation

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Find a regression equation.

Now includes a graph of the regression line and another interactive graph gives users the opportunity to move the regression line around. Could be used for allowing users to experiment with what they think the line should be and see how this compares with the calculated line.

Some impossible-looking questions about quadratic equations which can be solved with a bit of thinking.

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

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.

Solving linear equations to find the value of x.

Given a graph of some function $f(x)$ (a cubic), the student is asked to write the coordinates of the maximum and minimum points. The student then finds the maximum and minimum points of a second cubic function without using a graph, by finding the derivative, solving the quadratic equation that results from setting the derivative equal to zero, and finally testing the value of the second derivative.

Solve a system of three simultaneous linear equations

Basic solving of linear equations.