Solving a differential equation of the form $\frac{dy}{dx}=\frac{a \cos(x)}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=x(y-a)$ using separation of variables.

Solving a pair of simultaneous equations of the form $y=mx+c_1$ and $y=ax^2+kx+c_2$ to find the possible values for the unknown coefficient $k$, when given the values of $m$, $a$, $c_1$ and $c_2$.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Solving a quadratic equation of the form $ax^2+bx+c=0$ using the quadratic formula.

Determining the number of real roots a quadratic equation has by evaluating and interpreting the discriminant.

Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, solve the equation $g(x)=2h(x)$, giving all possible solutions for $x$. 

Using Gaussian Elimination to solve 3X3 systems of equations

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Solve simple two step linear equations with feedback.

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.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

A quadratic and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

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

Solve for $x$: $\displaystyle ax+b = cx+d$

No description given

Shear and bending moment diagram for a beam loaded with an arbitrary parabolic distributed load described with a loading function.  Integrate to find reactions and equations for shear and bending moment.

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Differential equations.

rebelmaths

First- and second order recurrence equations, homogenous and nonhomogenous

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