
Free Course

XSIQ

34 Hours

Assessment

Certification

50 Pts
Sequences, Series and Equations in Mathematics

Description

Outcome

Certification

This free online course is the second of our UpperSecondary Mathematics suite of courses. It covers ratio and proportion, geometric sequences, arithmetic series, difference equations, linear programming, geometry, trigonometry, and graphs. This course is suitable for all math students revising for exams. It is also suitable for anyone with an interest in Mathematics.

On completing of this course you will be able to calculate arithmetic sequences, geometric sequences, geometric series, difference equations and more successfully. You will understand the positive and negative gradient in straight line graphs. You will be able to find the equation of a straight line and know how to interpret graphs effectively. You will gain a good knowledge of trigonometry such as rightangled triangles, area of a triangle, the sine rule, cosine rule, Pythagoras' theorem, surface area, and volume. You will know how to simplify ratios and much more.

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, Certificate or PDF.
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( 18 )

Module
1 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
2 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
3 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
4 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
5 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
6 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
7 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
8 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
9 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
10 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
11 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
12 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
13 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
14 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
15 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
16 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
17 Further Maths Glossary
Further Maths GlossaryThis free online course is a glossary for maths.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.

Glossary


Assessment

Assessment

Core Mathematics 2 Assessment
