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Algebra Analytical geometry Angles Area and Surface Area |
Calculus Complex numbers Co-ordinates Fractions |
Functions Gradient Money Trigonometry |

Evaluate algebraic expressions

How tosubstitute values for variables in algebraic expressionsand how toevaluate the expressionsto give a numerical answer.

Expand brackets: (a+b)(c+d)

How toexpand algebraic expressions with brackets.

Factorise expressions like: ab + ac

How to factorise expressions byfinding common factors.Factorise quadratic expressions

How tofactorise quadratic expressionsusing several methods.Splitting the middle term of a quadratic

How to split the middle term of a quadratic expression so that it can be factorised.Other factorising techniques

How to use Algematics to do these operations:difference of squares,sum and difference of cubes,split middle term of quadratic,group and factorise four terms.

Finding roots by factorising

How tocalculate the roots of a quadratic equation algebraicallyafter the quadratic expression is factorised.Using the quadratic formula

How to find roots of a quadratic equation by using the quadratic formula.

Simplify algebraic expressions

How tosimplify algebraic expressions where no preparation is necessary. Several examples are discussed.Advanced simplifying techniques

How to simplify algebraic expressionswhere some expansion of brackets or factorising is necessarybefore the expression can be simplified.

Solve simultaneous equations by substitution

This topic explains the concept of simultaneous equations, and explains how to solve simultaneous equations algebraically by the method ofsubstitution.Solve simultaneous equations by elimination

How to solve simultaneous equations algebraically by the method ofelimination.Solve simultaneous equations graphically

How to solve simultaneous equations by findingintersection points of plotted graph lines.Solve systems of linear equations

How to use your computer to automatically solve simultaneous linear equations inany number of variables. (A powerful numerical method called 'partial pivoting' is used.)

Solve linear equations with algebra

How to solve several common types of linear equations using algebraic techniques. Ten worked examples explain the methods clearly.Solve equations graphically

How to solve implicit functions in one variable using a graphical technique. The method isvery accurate, and works on very difficult equations.Changing the subject of a Formula

Uses two worked examples and the principle of inverse operations to explain how to change the subject of a formula.

Distance formula

How to use the distance formula tofind distances between (x,y) points. The download file displays the working steps and a diagram for your distance formula problems.Midpoint formula

How to use the midpoint formula tofind the midpoint of a line between two (x,y) points. The download file solves midpoint formula problems. Enter two points to display working steps and a diagram.Divide a line in a given ratio

How to tofind the point 'P' that divides the line segment AB in a given ratio.Â This topic covers both internal and external division. The download file solves problems of this type, displaying working steps and a diagram.

This topic explains the concept of radian measure, as well as how to convert between radians and degrees. The download file converts between radians and degrees, showing full working steps and a labelled diagram.

How to convert area measurements between 10 common units. Includes tables of conversion factors and worked examples. The download file converts areas in any of the ten area units to any of the remaining 9 types.

Area of triangles,
½b×h

How to find areas of
triangles using the formula: A
= ½base×height. The download document displays working steps and a labelled
diagram for this problem type.

Area of
triangles, ½ab×sinC

How to find areas of
triangles using the formula: A
= ½ab×sinC. The download document displays working steps and a labelled
diagram for this problem type.

Area of
triangles, Heron's formula

How to find areas of triangles using Heron's formula. The download document
displays working steps and a labelled diagram for solving a triangle using
Heron's formula.

Area of parallelograms

How to find areas of
parallelograms using the formula: A
= base×height. The formula is explained pictorially, and the download document
allows you to experiment with the formula, while displaying working steps and a
labelled diagram.

Area of circles

How to **find areas** of
circles using the formula: A = pr^{2},
or to **find the radius** if the area is given. The download document solves
both kind of problem, and also displays a labelled diagram.

Surface area
and volume of prisms

How to find the surface area and volume of prisms. Several prism types are
discussed. The download document calculates the volume and surface area of
rectangular prisms, showing all working steps. The labelled diagram shows a **3d
model** of the prism, as well as the 2d net of the prism.

Surface area of a sphere

How to ** find
the surface area** of a sphere, or the ** radius if the surface area is given**.
The download document solves both problem types, and displays both the working
steps and a labelled diagram.

This topic

Calculate
definite integrals

A **detailed introduction to definite integrals**. Includes helpful
diagrams and examples. Shows you how to calculate definite integrals using a
variety of numerical methods.

Area under a curve

An introduction to finding ** areas under curves using definite integrals**.
Helpful diagrams and examples are included.

Area
between two curves

A brief introduction and diagram explain the concept, then the rest of the
article shows you how to find areas between graphs using Maths Helper Plus. The
download file is set up for the worked example from the article, but you can
easily edit the example functions to calculate your own areas.

Stationary
points

This article discusses both **turning points** and points of **horizontal
inflection** of functions. Helpful worked examples and diagrams are given. The
download file is a starting point for your own problem solutions.

Tangents
and normals

Worked examples and diagrams explain **how to find tangent and normal
equations** to functions at a given point. The steps for calculating and
plotting tangent and normal equations in Maths Helper Plus are explained, and
the download file is a starting point for your own problem solutions.

This topic

Complex
number operations

This topic shows you ** how to add,Â subtract, multiply and divide
complex numbers**. It also shows how to display full working steps for complex
number operations in Maths Helper Plus.

This topic introduces

Plotting polar coordinates

This topic
introduces the concept of polar coordinates, and shows you ** how to plot polar
coordinates** on a graph. The download file displays a polar grid and marks in
the angle and radius for a given plotted polar point.

Converting between rectangular and polar coordinates

This topic uses diagrams and examples to explain how to convert between
polar and rectangular coordinates. The download file displays full working steps
and a labelled diagram to help you convert your own coordinates.

Explains one way of

Adding
and subtracting common fractions

This topic explains how to add and subtract common fractions, and also how
to use Algematics to create a worked solution for problems of this type.

Converting
decimals to common fractions

How to convert decimal fractions to common fractions, and also how to use
Algematics to create a worked solution for problems of this type.

Multiplying
and dividing common fractions

How to multiply or divide common fractions, and also how to use Algematics
to create a worked solution for problems of this type.

This topic

Find the tangent or normal to a function at a given point

Worked examples and diagrams explain how to find tangent and normal
equations to functions at a given point.

Linear
functions: y = mx + c, gradient and y intercept

This topic
** introduces the straight line function, y = mx + c, discusses 'm' and
'c'**, and
shows you how to draw graphs of some different forms of this function.

Learn about
polynomial functions

An **introduction to polynomial functions**, and how to draw graphs of polynomials, as well as find
** zeros** and ** turning points**.

Learn about trigonometric functions

An **introduction to ****sine and cosine functions**, and
how to draw their graphs. The download file graphs sine functions and does the
calculations involving period and phase shift, showing the working steps.

How to find the gradient of a line through the origin and another fixed point. The download file displays complete working and a labelled diagram.

Gradient of line segment between two fixed points

How to find the gradient of a line through
two fixed points. The download file displays complete working and a labelled
diagram.

This topic shows you

Profit and loss

This topic
shows you ** how to solve profit and loss problems**. The
download file solves a wide range of profit and loss problems with detailed
working and helpful diagrams.

Simple interest

This topic
shows you ** how to solve simple interest problems**. Several
worked examples and a powerful download file will help you solve your own simple
interest problems easily.

Compound interest

This topic
shows you ** how to solve compound interest problems** based
on the compound interest formula. The worked examples and download file help you
solve your own compound interest problems easily.

This topic introduces you to the

Using
the rule of Pythagoras to find unknown triangle sides

How
to use the Rule of Pythagoras to ** find unknown sides of right
triangles**. Worked examples and the download file show you all of the steps
and include labelled diagrams.

This topic introduces the 'tangent ratio' for right angled triangles, and

Using the tangent ratio to find unknown angles

This topic shows you
how to find unknown angles in right triangles using tangent ratios.
The download file calculates tangent ratios for a given angle, and also finds an
angle when the tangent ratio is given.

Finding unknown opposite or adjacent sides with the tangent ratio

This topic shows you how to find unknown opposite or adjacent sides in right triangles using tangent ratios.
Worked examples and diagrams explain the mathematics, then the download file
displays the complete working and a labelled diagram for solving your own
problems.

This topic

Finding an unknown opposite side or hypotenuse with the sine ratio

This topic shows you how to find an unknown opposite side or hypotenuse in a right
triangle using sine ratios. The download file shows full working steps and a
diagram to help you solve your own problems of this type.

This topic

Finding an unknown adjacent side or hypotenuse with the
cosine ratio

How to find an unknown adjacent side or hypotenuse in a right
triangle using cosine ratios. The worked examples and diagrams show you the
steps, while the download file solves your problems showing full working and a
labelled diagram.

given three sides

**How**** to find the unknown angles of a triangle when given the three side
lengths**. The working steps are fully explained, and the download file
creates full working steps and a labelled diagram for your own problems.

given two angles and one side

**How**
** to find the unknown angle and sides of a triangle when given the
two angles and one side**. The working steps are fully explained, and the
download file creates full working steps and a labelled diagram for your own
problems.

given two sides and the included angle

**How**
** to find the unknown side and angles of a triangle when given
two sides and the angle between them**. The working steps are fully explained,
and the download file creates full working steps and a labelled diagram for your
own problems.

given two sides and a non-included angle

**How**
** to find the unknown side and angles of a triangle when given
two sides and an angle not between them**. In this case there may be two
possible solutions. The working steps are fully explained, and the download file
creates full working steps and a labelled diagram for your own problems.