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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 to substitute values for variables in algebraic expressions and how to evaluate the expressions to give a numerical answer.
Expand brackets: (a+b)(c+d)
How to expand algebraic expressions with brackets.
Factorise expressions like: ab + ac
How to factorise expressions by finding common factors.Factorise quadratic expressions
How to factorise quadratic expressions using 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 to calculate the roots of a quadratic equation algebraically after 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 to simplify algebraic expressions where no preparation is necessary. Several examples are discussed.Advanced simplifying techniques
How to simplify algebraic expressions where some expansion of brackets or factorising is necessary before 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 of substitution.Solve simultaneous equations by elimination
How to solve simultaneous equations algebraically by the method of elimination.Solve simultaneous equations graphically
How to solve simultaneous equations by finding intersection points of plotted graph lines.Solve systems of linear equations
How to use your computer to automatically solve simultaneous linear equations in any 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 is very 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 to find 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 to find 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 to find the point 'P' that divides the line segment AB in a given ratio. This topic covers both internal and external division. The download file solves problems of this type, displaying working steps and a diagram.
Area of triangles,
˝b×h
How to find areas of
triangles using the formula: A
= ˝base×height. The download document displays working steps and a labelled
diagram for this problem type.
Area of
triangles, ˝ab×sinC
How to find areas of
triangles using the formula: A
= ˝ab×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 = pr2,
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.
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.
Complex
number operations
This topic shows you how to add, subtract, multiply and divide
complex numbers. It also shows how to display full working steps for complex
number operations in Maths Helper Plus.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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