Solving $\log(y)+\log(x)=\frac{1}{n}\log(ay^n)$ for $x$, where $a$ and $n$ are positive integers.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_a\left(\frac{1}{x}\right) = b$, where $a$ is a positive integer and $b$ is a negative integer.

Finding $x$ from a logarithmic equation of the form $\log_x \left(\frac{1}{\sqrt(a)}\right) = \frac{1}{2}$, for a positive integer $a$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ is a positive integer and $b$ is a positive fraction.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_xa = b$, where $a$ and $b$ are positive integers.

Solving $e^{\ln(x)}+\ln(e^x)=a$ for $x$.

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

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

Solving a differential equation of the form $\frac{dy}{dx}=ax^n e^{-y}$ using separation of variables.

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.

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.

Solve simple two step linear equations with feedback.

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

This question will test the ability of test taker to distinguish between solving mean and solving weighted mean problem

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

Some quadratics are to be solved by factorising

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Exercises in solving simultaneous equations with 2 variables.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

No description given