
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
Start Topic

Find a particular term in an arithmetic sequence
Start Topic

How many terms in this arithmetic sequence?
Start Topic

Show that the sequence is arithmetic
Start Topic

Solving arithmetic sequences simultaneously
Start Topic

Summing up arithmetic sequences
Start Topic

Is this an arithmetic sequence?
Start Topic

Example (b)
Start Topic

Example (c)
Start Topic

Example (d)
Start Topic


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
Start Topic

Finding the sum of an arithmetic series
Start Topic

Finding the sum of an arithmetic sequence
Start Topic


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
Start Topic

Is this a geometric sequence?
Start Topic

Find a term in an increasing geometric sequence
Start Topic

Find a term in a decreasing geometric sequence
Start Topic

Which term has that value?
Start Topic

Example (b)
Start Topic

Example (c)
Start Topic

Example (d)
Start Topic


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
Start Topic

Infinite geometric series
Start Topic

Find the sum of an increasing geometric sequence
Start Topic

Find the sum of a decreasing geometric sequence
Start Topic

How many terms until the sum exceeds 2000?
Start Topic

Find the sum of an infinite geometric series
Start Topic

Sum a geometric series to infinity
Start Topic


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
Start Topic

Making rungs for a ladder
Start Topic

Growing Town
Start Topic


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
Start Topic

Generating a sequence from a difference equation
Start Topic

Difference equations that represent arithmetic sequences
Start Topic

Difference equations that represent geometric sequences
Start Topic

Generate the first 4 terms of a sequence
Start Topic

Generate the first 4 terms of another sequence
Start Topic

Find a general expression for the nth term
Start Topic

Find a general expression for the nth term
Start Topic


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
Start Topic

Solving difference equations
Start Topic

Find a general expression for the nth term
Start Topic

Find the first term from a given term
Start Topic

Find the first term from the second term
Start Topic


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
Start Topic

Finding maximum and minimum values
Start Topic

Solving linear and programming problems
Start Topic

Solving linear programming problems  example
Start Topic

Example part (b)
Start Topic


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
Start Topic

The general equation of a straight line
Start Topic

Finding the equation of a line
Start Topic

Simultaneous equations
Start Topic

Method 1  elimination
Start Topic

Method 2  substitution
Start Topic

Sketching linear equations
Start Topic

Break even analysis
Start Topic

Straight line graphs  gradient
Start Topic

Finding the gradient given the coordinates of two points
Start Topic

Elimination examples
Start Topic

The break even example
Start Topic

Sketching linear equations  example 1
Start Topic

Sketching linear equations  example 2
Start Topic

Straight line graphs  gradient example
Start Topic


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
Start Topic

Step graphs
Start Topic

Distancetime graphs
Start Topic


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
Start Topic

Linear representation of nonlinear graphs
Start Topic


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
Start Topic

Rightangled triangles
Start Topic

Solving non rightangled triangles
Start Topic

The sine rule
Start Topic

The cosine rule
Start Topic

The area of a triangle
Start Topic

Example
Start Topic

Example 2
Start Topic

Cosine rule – Example 1
Start Topic

Cosine rule – Example 2
Start Topic


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
Start Topic

Pythagoras in 3 dimensions
Start Topic

Similar figures
Start Topic

Surface area and volume
Start Topic

Similar figures example
Start Topic

Surface area and volume: example 1
Start Topic

Surface area and volume: example 2
Start Topic


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
Start Topic

Angles of elevation and depression
Start Topic

Directions and bearings
Start Topic

Contour maps
Start Topic

Traverse surveys
Start Topic

Compass bearings
Start Topic

True Bearings
Start Topic

Bearings application example
Start Topic

Field survey example
Start Topic

Field survey example continued
Start Topic

Bearings yachting example
Start Topic


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
Start Topic

Simplifying ratios
Start Topic

Expressing ratios as a percentage
Start Topic

Dividing quantities in a given ratio
Start Topic

Applications of ratio and proportion
Start Topic

Map scales
Start Topic

Dilution factors
Start Topic

Photography
Start Topic

Gears
Start Topic

Finding x values in ratios
Start Topic

Map scales: how far is that?
Start Topic

Dilution: drug strength
Start Topic

Photographing a tree
Start Topic

Gearing up... gearing down
Start Topic


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
Start Topic


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
Start Topic


Assessment

Assessment

Core Mathematics 2 Assessment
Start Topic
