
Free Course

XSIQ

1520 Hours

Assessment

Certification

250 Pts
Diploma in Mathematics

Description

Outcome

Certification

Alison.com's free online Diploma in Mathematics course gives you comprehensive knowledge and understanding of key subjects in mathematics. This course covers calculus, geometry, algebra, trigonometry, functions, vectors, data distributions, probability and probability and statistics. Math qualifications are in great demand from employers and this math course will greatly enhance your career prospects.

ALISON.com's math course will greatly enhance your skills, giving you a greater understanding of core mathematics components such as geometry, trigonometry, calculus and more as well as expanding your knowledge base in areas such as chance, data distributions, statistics, probability, correlations and regression.
You will learn about using binomial expansions for problem solving and will understand the relationship between the graphs of functions and their antiderivatives.
You will be able to confidently create graphs and make advanced calculations such as straightline calculations, kinematics, motion, vectors, algebra, binomial expressions, and quadratic functions. 
All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma or Certificate.
Having an official Alison document is a great way to celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 98 )

Module 1: Geometry

Module
1 Introduction to triangles
Introduction to triangles This free online course covers topics related to triangles. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to triangles

Triangle letter names

Equilateral triangles

Isosceles triangles

Scalene triangles

Acuteangled triangles

Rightangled triangles

Obtuseangled triangles

Quiz on triangle names


Module
2 Angle types
Angle types This free online course covers topics related to angle types. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Angle types

Angles in a circle

Angles as numbers

Measuring angles with a protractor

Complementary and supplementary angles

Angles in circles, rectangles and triangles

Vertically opposite angles


Module
3 Angle sizes and sums in triangles
Angle sizes and sums in triangles This free online course covers topics related to angle sizes and sums in triangles. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Angle sizes and sums in triangles

Angle sum demonstration

Practice questions on sum of angles in a triangle

Quiz on sum of angles in a triangle

Exterior angles of a triangle

Quiz on exterior angles of triangles


Module
4 Triangles  Similiarity and congruence
Triangles  Similiarity and congruence This free online course covers topics related to triangles such as similarity and congruence. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Triangles  similarity and congruence

Quiz on similar triangles

Congruent triangles


Module
5 Corresponding angles
Corresponding angles This free online course is an introduction to corresponding angles over parallel lines. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Corresponding angles

Parallel lines

Alternate and cointerior angles

General angles quiz

Quiz on angles and parallel lines


Module
6 Introduction to quadrilaterals
Introduction to quadrilaterals This free online course covers topics related to quadrilateral triangles. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to quadrilaterals

Equal sides, equal angles and parallel lines

Properties of a square

Properties of a rectangle

Properties of a parallelogram

Properties of a rhombus

Properties of a trapezium

Properties of a kite

Properties of basic quadrilaterals

Quiz on properties of quadrilaterals

Properties of an isosceles trapezium

Properties of a rectangle

Properties of a parallelogram

Properties of a rhombus

Properties of a trapezium

Properties of an isosceles trapezium

Properties of a kite

Properties of basic quadrilaterals


Module
7 Quadrilaterals
Quadrilaterals This free online course covers topics related to angle size and measurement in quadrilaterals. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Quadrilaterals angle sum

Quadrilaterals sum of exterior angles

Quiz on angles in quadrilaterals


Module
8 Introduction to polygons
Introduction to polygons This free online course is an introduction to polygons. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to polygons

What are polygons?

Regular polygons

Naming of polygon types

Rotational symmetry in polygons

Line symmetry in polygons

Quiz on polygons


Module
9 Polygons
Polygons This free online course covers topics related to angle size in polygons. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Polygon interior angle sum

Regular polygon interior angle sizes

Sum of exterior angles of polygons

Regular polygon exterior angle sizes

Quiz on polygon angle sizes


Module
10 Geometrical solids
Geometrical solids This free online course covers topics related to geometrical solids. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Geometrical solids

Prisms

Prisms quiz

Pyramids and cones

Spheres, hemispheres and toruses

Quiz on geometrical solids


Module
11 Conics (elipses and hyperbolae)
Conics (elipses and hyperbolae) This free online course covers topics graphs of hyperbolae and ellipses and the transformation of hyperbolae. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Graphs of Ellipses

Examples

Graphs of Hyperbolae

Example 1

Example 2

Example 3

Example 4

Transformations of hyperbolae

Translations


Module
12 Transformations
Transformations This free online course covers topics related to transformations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to transformations

Translations, reflections and rotations

Translations and coordinate geometry

Translations and coordinate geometry quiz

Reflections

Reflections

Reflections and coordinate geometry

Rotations

Rotations and coordinate geometry

Quiz on transformations


Module
13 Geometry
GeometryThis free online course covers topics related to geometry.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Intersection of half planes

Finding maximum and minimum values

Solving linear and programming problems

Solving linear programming problems  example

Example part (b)


Module 2: Probability and Chance

Module
14 Summarising data
Summarising dataThis free online course is an introduction to summarising data and covers topics such as mean, mode, median, range, and interquartile range.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Summarising data  overview

Mode

Mean

Median

Mode, mean, median

Comparing mode, mean, median

Range of data

Interquartile range

Review  summarising data


Module
15 Frequency and graphs
Frequency and graphsThis free online course is an introduction to data types such as nominal data, discrete data, and continuous data, and how to summarise data using frequency tables and graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency


Module
16 Creating a frequency table from data
Creating a frequency table from data This free online course covers types of data such as nominal, discrete and continuous data, and how to create frequency tables from data. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency


Module
17 Graphs of all kinds
Graphs of all kindsThis free online course covers the use of different types of graphs such as pie charts, line graphs, and bar graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Graphs of all kinds

Ice cream pictograph

Column and bar graphs

Examples of column graphs

Pie charts

Examples of pie charts

Line graphs

Temperature line graphs

Types of graphs

Interpreting column graphs

Manchester flights bar graph

Movie line graph

Interpretation of a sports pie graph

Review  graphs


Module
18 Introduction to probability
Introduction to probabilityThis free online course is an introduction to probability and how to calculate probability.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to probability

Probability words

Words describing chance

Finding probabilities theoretically

Probability with equally likely outcomes


Module
19 Odds and probability
Odds and probabilityThis free online course covers odds and probability.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Odds and probability

Odds

Odds on

Odds and probability

Fair or unfair?

Deciding fairness using probability


Module
20 Probability and relative frequency
Probability and relative frequencyThis free online course is an introduction to probability and relative frequency.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Probability and relative frequency

Shortrun coin tossing

Shortrun dice rolling

Predicting from past experience

Towards probability with coins

Towards probability with dice

Probability as longrun relative frequency


Module 3: Data Distributions

Module
21 Discrete random variables
Discrete random variables This free online course covers topics related to random variables and discrete probability distribution. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Random variables

Discrete probability distribution

The mean and variance of a discrete random variable

Standard deviation as a measure of spread


Module
22 Normal distribution
Normal distribution This free online course covers topics related to random variables and the normal distribution . The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The normal curve

Continuous random variables and the normal distribution

Calculation of probabilities for a normal distribution

Approximating the binomial distribution with normal distribution


Module
23 Binomial distribution
Binomial distributionThis free online course covers topics related to the binomial distribution and the binomial probability function .The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Binomial probability function and distribution

The number of successes in a given number
of trials

The effect of changing the parameter p

The effect of changing the parameter n

The mean and variance of a binomial random variable


Module
24 Hypergeometric distribution
Hypergeometric distributionThis free online course covers topics related to the hypergeometric distribution and calculating the mean and variance of hypergeometric distributions.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Sampling without replacement

The mean of a hypergeometric random variable

The variance of a hypergeometric
random variable

The mean and variance of a hypergeometric
random variable example

The mean and variance of a hypergeometric random variable example 2

The formula for calculating probabilities

Calculating probabilities

Relationship between hypergeometric and binomial
distributions


Module 4: Statistics, Correlation & Regressio...

Module
25 Univariate data
Univariate dataThis free online course is an introduction to the types of univariate data.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Types of data

Types of univariate data

Numerical data


Module
26 Univariate data 2
Univariate data 2This free online course is an introduction to displaying data using bar graphs and stem and leaf graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Displaying data

Bar graphs

Stem and leaf diagrams 1

Stem and leaf diagrams 2


Module
27 Bivariate data
Bivariate dataThis course is an introduction to bivariate data and covers topics such as dependent and independent data, stemplots and boxplots.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Dependent and independent variables

Percentaged tables

Parallel boxplots

Backtoback stemplots

Graphical display of bivariate data – in summary


Module
28 Summary statistics
Summary statisticsThis free online course is an introduction to statistical method such as calculating the mean, median, and mode.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Summary statistics

The mean

The median – definition

Cumulative frequency

Cumulative frequency graph

The mode

Advantages and disadvantages of the mean

The median for even data sets

Advantages and disadvantages of the median

The mean  example

The median  example


Module
29 Range
RangeThis course covers topics such as the interquartile range and creating boxplots.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The soccer activity

The range

The interquartile range

The interquartile range  example 1

The interquartile range  example 2

The standard deviation

Boxplots

Boxplots  example

Using your calculator


Module
30 Symmetry
SymmetryThis free online course reviews the skewness of the distribution of data.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Symmetry and skew of a distribution

Negative skew

Positive skew

Probability intervals

Probability interval examples

Comparing sample and population


Module
31 Calculating a seasonal index
Calculating a seasonal indexThis course covers how to calculate and interpret seasonal indices and how deseasonalise data.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Calculating a seasonal index

Interpreting seasonal indices

Seasonal movements

Deseasonalising the data

Deseasonalising the data – example


Module
32 Coefficient
CoefficientThis course covers topics such as the coefficient of determination, scatterplots, and calculating r.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Scatterplots

Scatterplots: using your calculator

Pearson's product moment correlation coefficient, r

Calculating r

The coefficient of determination

Practice question

Strength of association


Module
33 Regression line
Regression lineThis free online course covers topics related to the regression line.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Finding the equation of a regression line

Interpretation of slope and intercept

Practice question

The threemedian regression line

Using your calculator

The threemedian regression example

The threemedian regression practice questions

The least squares regression line

Making predictions from a regression line


Module
34 Nonlinear data
Nonlinear dataThis course is an introduction to square, log, and reciprocal transformations.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Nonlinear data

Square transformation

Log transformations

Reciprocal transformation

Example 1

Example 2


Module
35 Residual analysis
Residual analysisThis free online course is an introduction to residual analysis.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Residual analysis  part 1

Plotting the residuals

Residual analysis  part 2

Residual analysis  part 3


Module
36 Trends
TrendsThis free online course covers topics such as seasonal, random, and cyclic trends.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Trends

Cyclic patterns

Random patterns

Describing patterns in time series data

Seasonal patterns

Smoothing a time series

Median smoothing

Smoothing using moving averages

Smoothing  example 1

Smoothing  example 2


Module 5: Sequences and Series

Module
37 Arithmetic sequences
Arithmetic Sequences This free online course covers topics related to arithmetic sequences.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Arithmetic sequences

Find a particular term in an arithmetic sequence

How many terms in this arithmetic sequence?

Show that the sequence is arithmetic

Solving arithmetic sequences simultaneously

Summing up arithmetic sequences

Is this an arithmetic sequence?

Example (b)

Example (c)

Example (d)


Module
38 Arithmetic series
Arithmetic seriesThis free online course covers the arithmetic series.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Arithmetic series

Finding the sum of an arithmetic series

Finding the sum of an arithmetic sequence


Module
39 Geometric sequences
Geometric sequencesThis free online course covers topics related to geometric sequences.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Geometric sequences

Is this a geometric sequence?

Find a term in an increasing geometric sequence

Find a term in a decreasing geometric sequence

Which term has that value?

Example (b)

Example (c)

Example (d)


Module
40 Geometric series
Geometric seriesThis free online course covers topics related to the geometric series.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Geometric series

Infinite geometric series

Find the sum of an increasing geometric sequence

Find the sum of a decreasing geometric sequence

How many terms until the sum exceeds 2000?

Find the sum of an infinite geometric series

Sum a geometric series to infinity


Module
41 The binomial theorem
The binomial theorem This free online course is an introduction to the binomial theorem. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Binomial theorem – Pascal's triangle

The binomial expansion

The binomial expansion  examples


Module
42 Difference equations 1
Difference equations 1This free online course covers topics related to difference equations.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Applications of sequences and series

Making rungs for a ladder

Growing Town


Module
43 Difference equations 2
Difference equations 2This free online course covers topics related to difference equations.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Difference equations

Generating a sequence from a difference equation

Difference equations that represent arithmetic sequences

Difference equations that represent geometric sequences

Generate the first 4 terms of a sequence

Generate the first 4 terms of another sequence

Find a general expression for the nth term

Find a general expression for the nth term


Module
44 Difference equations 3
Difference equations 3This free online course covers topics related number patterns.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Other first order difference equations

Solving difference equations

Find a general expression for the nth term

Find the first term from a given term

Find the first term from the second term


Module 6: Trigonometry

Module
45 Trigonometry 1
Trigonometry 1This free online course covers topics in trigonometry such as the sine rule and cosine rule.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Trigonometry introduction

Rightangled triangles

Solving non rightangled triangles

The sine rule

The cosine rule

The area of a triangle

Example

Example 2

Cosine rule – Example 1

Cosine rule – Example 2


Module
46 Trigonometry 2
Trigonometry 2 This free online course covers topics related to trigonometry, including surface area and volume, and Pythagoras' theorem. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Pythagoras' theorem

Pythagoras in 3 dimensions

Similar figures

Surface area and volume

Similar figures example

Surface area and volume: example 1

Surface area and volume: example 2


Module
47 Degrees and radians
Degrees and radians This free online course covers the conversion of radian and degree measures. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Exact Values

Conversions of Radian and Degree Measures


Module
48 Pythagoras and bearings
Pythagoras and bearingsThis free online course is an introduction to topics related to Pythagoras.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The tomb of Pythagoras activity

Angles of elevation and depression

Directions and bearings

Contour maps

Traverse surveys

Compass bearings

True Bearings

Bearings application example

Field survey example

Field survey example continued

Bearings yachting example


Module
49 Trigonometric identities
Trigonometric identities This free online course covers topics related to reciprocal circular functions, inverse circular functions, and trigonometric identities. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Reciprocal Circular Functions

Inverse Circular Functions

Trigonometric Identities


Module
50 Ratio and proportion
Ratio and proportionThis free online course covers topics related to ratios and proportions.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Ratio and proportion

Simplifying ratios

Expressing ratios as a percentage

Dividing quantities in a given ratio

Applications of ratio and proportion

Map scales

Dilution factors

Photography

Gears

Finding x values in ratios

Map scales: how far is that?

Dilution: drug strength

Photographing a tree

Gearing up... gearing down


Module
51 Ratio and proportion gears
Ratio and proportion gearsThis free online course contains a video relating to ratio and proportion gears.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The gears video


Module 7: Calculus

Module
52 Rules of integration
Rules of integration This free online course covers rules for integrating functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Antidifferentiation

Antiderivatives of basic functions

Finding specific functions based on given information

Indefinite integral

Using related derivatives to find an integral


Module
53 Integration applications
Integration applications This free online course covers topics related to integration. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Approximating an area

Definite integrals

Evaluating a definite integral


Module
54 Rules of differentiation
Rules of differentiation This free online course covers topics related to differentiation such as the rules of differentiation and how to calculate derivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Basic functions

Functions

Rules of differentiation

Rules for finding derivatives

Linear combination of functions

Product of two functions

Quotient of two functions

Function of a function


Module
55 Applications of differentiation
Applications of differentiation This free online course covers applications of differentiation such as calculating the stationary points, and the maxima and minima points. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Applications of Differentiation

Stationary Points

Maximum or Minimum

Maximum/Minimum Problems

Equations of Tangents and Normals

Examples


Module
56 Polynomial equations
Polynomial equations This free online course covers solutions to polynomial equations and the Fundamental Theorem of Algebra. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Solution of Polynomial Equations

Example

The Fundamental Theroem of Algebra

Equations

Examples


Module
57 Factors of polynomials
Factors of polynomialsThis free online course is an introduction to the techniques used to factorise cubic and quadratic polynomials.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Factorising polynomials

Polynomial notation and function manipulations

Factorising polynomials

Factorisation process for cubics

Factorisation process for quartics

Factor and remainder theorems

Long division

Synthetic division

Factorising polynomials: example


Module
58 Differentiation  Product rule
Differentiation  Product rule This free online course covers the product rule for antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Product Rule

Example 1

Example 2

Example 3


Module
59 Differential equations
Differential equations This free online course covers topics related to differential equations such as first order and second order differential equations and rates of change . The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Order and degree of differential equations

Verifying solutions

Rates of change

Rates of change  chain rule

The rates of change example

First order differential equations  type 1

First order differential equations  type 2

Second order differential equations


Module
60 Second derivatives
Second derivatives This free online course covers the use of the second derivative. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Use of the second derivative

Examples

Second derivatives


Module
61 Antiderivatives
Antiderivatives This free online course covers topics related to antiderivatives such as standard antiderivative types, hyperbolic functions, and partial fractions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Review of Standard Antiderivatives

Standard Antiderivative Types

Type 2  Hyperbolic Functions

Type 3  Partial Fractions

Example 2

Type 5  Linear Substitution


Module
62 Antiderivatives of circular functions
Antiderivatives of circular functions This free online course covers the topic of the antiderivatives of circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Type 4  Inverse Circular Functions

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6

Type 6  Odd and Even Powers

Odd Powers

Even Powers


Module
63 Antiderivatives and their graphs
Antiderivatives and their graphs This free online course covers the relationship between the graphs of functions and their antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Relationships Between Graphs of Functions and their Antiderivatives

Original and Antiderivative Functions

Graphs of Antiderivatives

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6


Module 8: Functions

Module
64 Graphs
GraphsThis free online course covers topics related to graphs such as timedistance graphs and step graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Interpreting graphs

Step graphs

Distancetime graphs


Module
65 Straight lines
Straight linesThis free online course covers topics related to the straight line.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Straight line graphs

The general equation of a straight line

Finding the equation of a line

Simultaneous equations

Method 1  elimination

Method 2  substitution

Sketching linear equations

Break even analysis

Straight line graphs  gradient

Finding the gradient given the coordinates of two points

Elimination examples

The break even example

Sketching linear equations  example 1

Sketching linear equations  example 2

Straight line graphs  gradient example


Module
66 Straight line graphs
Straight line graphs This free online course covers topics related to straight line graphs including graphs for polynomial functions and transformations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Activity

Graphs of polynomial functions: the garden activity

Introduction

Graphs of polynomial functions

Graphs derived from standard graphs

Other standard graphs

Certain special graphs

Transformations

Reflections

Dilations

Combinations of transformations

Addition of ordinates

Important graphs

Important graphs: Type 1

Important graphs: type 2

Important graphs: type 3

Important graphs: type 4

Graphs of inverse functions

Graphs of polynomial functions: examples


Module
67 Power graphs
Power graphsThis free online course is an introduction to the power graphs, and the linear representation of nonlinear graphs.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Power graphs

Linear representation of nonlinear graphs


Module
68 Graphs of ciruclar functions
Graphs of ciruclar functionsThis free online course is an introduction to the equations used for graphs of circular forms.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Graphs of the form y=Asin(a(x+b))+B and y=Acos(a(x+b))+B

Solution of trigonometric equations

Graphs of the form y = tan(ax)

Equations of the form sin(ax)=B and cos(ax)=B

Equations of the form sin(ax)=kcos(ax)


Module
69 Inverse functions
Inverse functionsThis free online course is an introduction to inverse functions.The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Inverse functions  manytoone and onetomany

Inverse functions

Further inverse functions

Examples


Module
70 Logarithms and index laws
Logarithms and index laws This free online course is an introduction to logarithms and index equations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Indices and logarithms

Solution of exponential and logarithmic equations

Examples


Module
71 Inverse circular functions
Inverse circular functions This free online course covers derivatives of inverse circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Derivatives of Inverse Circular Functions

Example 2

Example 3


Module
72 Reciprocal function graphs
Reciprocal function graphs This free online course covers graphs of reciprocal functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Graphs of Reciprocal Functions

Example 1

Example 2

Example 3


Module
73 Symmetry and periodicity
Symmetry and periodicity This free online course covers topics related to symmetry and periodicity. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Use of Symmetric, Periodic and Complementary Relationships of Circular Functions

Symmetry Example 1

Example 2

Example 3

Periodicity

Complementary Relationships

Complementary Relationship Examples


Module 9: Vectors

Module
74 Kinematics
Kinematics This free online course covers topics related to kinematics such as velocity and acceleration. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Finding displacement from velocity

Solving differential equations (rectilinear motion)
example

Finding acceleration or velocity from displacement

Constant acceleration  introduction

Constant acceleration  example 1

Velocity time graphs  introduction

Finding the acceleration from the velocity time
graph

Finding the distance travelled from a velocity
time graph

Velocity time graphs  example

Constant acceleration  example 2


Module
75 Motion
Motion This free online course covers topics related to motion such as motion under a constant force and motion under a variable force. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Newton's laws of motions

Forcesweight

Diagram of forces

Basic equation of motion

Resolution of forces

Horizontal and vertical

Equations of motion

Parallel and perpendicular to a plane

Equations of motion

Moving down the slope

Connected masses

Motion under a constant force

Motion under a constant force  example 1

Motion under a constant force  example 2

Motion under a variable force

Motion under a variable force  example 1

Motion under a variable force  example 2

Motion under a variable force  example 3

Momentum and impulse

Momentum and impulse example

Moving up the slope

Motion under a constant force  example 1 continued

Forcesnormal reaction

Forcesfriction

Forcestension


Module
76 Resolution of forces
Resolution of forces This free online course covers topics related to resolution of forces such as static friction, and angle of friction. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Resolution of forces

Three forces

Static friction

Angle of friction


Module
77 Scalar products of vectors
Scalar products of vectors This free online course covers topics such as scalar and vector resolutes, and finding the angle between two vectors. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Scalar and vector resolutes

Scalar resolutes

Vector resolutes

Vector resolute examples

Scalar (or dot) Product

Using the Dot Product in Vector Proofs

Example 1

Finding the Angle Between Two Vectors

Example 2 (midpoints)

Perpendicular Vectors

Inclination to the x or y axis

Example 3 (midpoints)

Example 4 (Colinear points)


Module
78 Vectors
Vectors This free online course covers topics related to vectors such as parametric equations The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Position vectors as functions of time (Parametric
Equations)

Finding cartesian equations from parametric equations

Example 1

Example 2

Collision

Example 3

Using a graphic calculator with parametric equations

Using a graphic calculator with two parametric
equations to show a collision

The closest distance to a path

Example 4


Module
79 Vectors 2
Vectors 2 This free online course covers the differentiation and antidifferentiation of vectors. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The garden activity

Notation used in vector calculus

Differentiation and anti differentiation of vectors

Example 1

Example 2


Module
80 Vectors in 2 and 3 dimensions
Vectors in 2 and 3 dimensions This free online course covers topics related to scalars. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Vector Definition

Symbols Used to Represent Vectors

Magnitude of a Vector

Zero Vector

Subtracting Vectors

Equal vectors

Parallel Vectors

Vectors in Cartesian Form

Position Vectors

The Cartesian Plane

Linear Dependence and Independence

Unit Vector

Multiplying by a Scalar

Linear Dependence and Independence Example


Module 10: Algebra

Module
81 Introduction to Algebra
Introduction to AlgebraThis course introduces you to algebra. It uses interactive presentation to explain the concepts. This is ideal for those learners seeking to learn how to manipulate algebraic expressions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to algebra

The language of algebra

Algebraic notation


Module
82 Using Formulae 1
Using Formulae 1Many realworld problems require a formula to be used for a solution to be achieved. This course covering using formulae to solve algebraic problems. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Using formulae

The XSIQ petrol pump

Petrol stations

Renting a car

Get real rentacar deal

Speed examples

Speed

Temperature

Temperature examples

Temperature converter


Module
83 Using Formulae 2
Using Formulae 2This free online course continues the use of formulae to solve algebraic problems. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

The using formulae speed video

The using formulae temperature video


Module
84 Algebraic Expressions 1
Algebraic Expressions 1 This free online course describes and explains algebraic equations. This is extremely useful for anyone interested in mathematics. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Simplifying algebraic expressions without using algebra blocks

Verifying the simplified form of an algebraic expression

Verifying the simplification using substitution  examples

Verifying the simplification using a spreadsheet

Adding and subtracting terms  practice questions 1

Adding and subtracting terms  practice questions 2

Mulitplying terms  Commutative Law

Multiplying terms  rearranging 1

Multiplying terms  rearranging 2

Dividing terms  rearranging 1

Dividing terms  rearranging 2

Adding and subtracting like terms without using algebra blocks


Module
85 Algebraic Expressions 2
Algebraic Expressions 2This free online course continues algabraic expressions. It covers expanding and simplifying algebraic equations. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Expanding and simplifying algebraic expressions

Distributive Law  algebra blocks

Distributive Law  expansion

Expanding and collecting like terms

Expanding and simplifying algebraic expressions


Module
86 Algebraic Fractions 1
Algebraic Fractions 1This free online course introduces algebraic fractions. It carefully explains the concepts and introduces basic operations, such as addition and subtraction. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction to algebraic fractions

Adding simple algebraic fractions

Subtracting algebraic fractions

Fractions with letters in the denominators

Binomials in denominator

Speed and algebraic fractions

The faster car takes less time

Calculating the time difference

Adding and subtracting algebraic fractions  practice questions


Module
87 Algebraic Fractions 2
Algebraic Fractions 2This free online course continues the lessons on algebraic fractions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Factorising algebraic expressions

Factorising algebraic expressions

Highest common factor

More complex highest common factors

Factorising algebraic expressions  practice questions


Module
88 Algebraic Fractions 3
Algebraic Fractions 3This free online course continues the lessons on algabraic fractions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Factorising algebraic expressions  grouping

Grouping two and two

Grouping three terms and one term


Module
89 Terminology for Algebraic Expressions
Terminology for Algebraic ExpressionsThis course covers the terminology used when talking about and explaining algebraic equations. This is extremely useful for anyone interested in mathematics. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Terminology for algebraic expressions


Module
90 Binomial Expressions 1
Binomial Expressions 1This free online course introduces you to binomial expressions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Binomial expressions

Binomial expansions with like and unlike terms

Binomial expansions

Binomial expansions and areas

Using binomial expansions for problem solving

Binomial expansions  reminder

Binomial expansion with two variables

Binomial expansions  practice questions


Module
91 Binomial Expressions 2
Binomial Expressions 2This interactive mathematics course continues the lessons on binomial expressions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Binomial expansions with perfect and nonperfect squares

Binomial expansions with nonperfect squares

Expanding perfect squares  practice questions

Binomial expansions with perfect squares

Binomial expansions with perfect squares


Module
92 Binomial Expressions 3
Binomial Expressions 3This free online course continues the lessons on binomial expressions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Binomial expansions  Difference of perfect squares

Difference of perfect squares (DOPS)

Expanding and simplifying algebraic expressions  practice questions

Expanding using the difference of perfect squares rule

Difference of perfect squares rule

Difference of perfect squares


Module
93 Completing the Square
Completing the SquareThis online course covers completing the square. It features hints and tips for expanding square algebraic expressions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Completing the square

Factorising quadratic trinomials using the method of completing the square

Process to factorise a quadratic trinomial by the method of completing the square


Module
94 Perfect Squares
Perfect SquaresThis free interactive course covers hints and tips for completing perfect squares. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Using the difference of perfect squares 1

Using the difference of perfect squares 2

Factorising using the difference of perfect squares (DOPS) expressions


Module
95 Quadratic Trinomials
Quadratic TrinomialsThis section covers quadratic trinomials. If you thought binomials were heavy, wait until you see this one!The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

What are quadratic trinomials?

Factorising the general form by inspection

Factorising quadratic trinomials

Factorising algebraic expressions  quadratic trinomials

Factorising quadratic trinomials

Factorising quadratic trinomials

Factorisation of quadratic trinomials


Module
96 Substitution into Algebraic Expressions
Substitution into Algebraic ExpressionsWhen pronumerals are replaced by numbers or expressions, the process is called substitution. This course covers substitution. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Substitution into algebraic expressions


Module
97 Summary of Factorisation
Summary of FactorisationThis course summarises the processes and procedures of factorisation. This provides great help in solving algebraic problems. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Summary of factorisation

Practice question  Sally's patio

Practice question  in the swim with algebra

Practice question  algebra can be fishy


Assessment

Assessment

Assessment Score 80% or more in the assessment and you can obtain a Diploma parchment for this course.

Diploma in Mathematics Assessment
