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.

This exercise will help you solve equations of type ax-b = c.

Solving quadratic equations using a formula,

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

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

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

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Find the solution of a first order separable differential equation of the form $(a+y)y'=b+x$.

Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

This exercise will help you solve equations of type ax-b = c.

Apply and combine logarithm laws in a given equation to find the value of $x$.

Given an equation or a worded formula determine if it is a function or not

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

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

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

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Solve a system of linear equations using Gaussian elimination.

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Two questions on solving systems of simultaneous equations.

Solve a pair of linear equations by writing an equivalent matrix equation.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

25 questions on solving quadratic equations

A variety of trigonometric equations which can be solved using inverse operations.