# Algebra resources

### Guides (1)

Just the Maths (A.J.Hobson)

"Just the Maths" authored by the late Tony Hobson, former Senior
Lecturer in Mathematics of the School of Mathematical and
Information Sciences at Coventry University, is a collection of separate mathematics units, in chronological
topic-order, intended for foundation level and first year
degree level in higher education where mathematics is a service discipline e.g. engineering.

### iPOD Video (135)

Completing the Square (to find MAX and MIN values) Part 1

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square (to find MAX and MIN values) Part 2

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square (to find MAX and MIN values) Part 3

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square (to find MAX and MIN values) Part 4

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square (to find MAX and MIN values) Part 5

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square (to find MAX and MIN values) Part 6

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 1

In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 2

In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 3

In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 4

In this iPOD video we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 5

In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square 6

In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 1

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 2

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 3

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 4

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 5

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 6

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 7

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Cubic Equations 8

All cubic equations have either one real root, or three real roots. In this video we explore why this is so.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding and Removing Brackets Part 1

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding and Removing Brackets Part 2

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding and Removing Brackets Part 3

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding and Removing Brackets Part 4

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding and Removing Brackets Part 5

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 1

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 10

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 11

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 12

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 13

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 2

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 3

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 4

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 5

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 6

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 7

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 8

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Expressions 9

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to Ã?Â¢??removeÃ?Â¢?? or 'multiply-outÃ?Â¢?? brackets from an expression.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 1

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 2

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 3

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 4

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 5

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 6

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 7

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 8

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Indices or Powers 9

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 1

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 2

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 3

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 4

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 5

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 6

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Linear Equations in One Variable Part 7

IPOD VIDEO: In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x squared, x cubed, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 1

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 10

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 2

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 3

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 4

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 5

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 6

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 7

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 8

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms 9

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 1

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 2

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 3

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 4

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 5

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 6

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 7

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical Language Part 8

IPOD VIDEO: This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 1

This video segment introduces partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 2

This video segment continues to develop partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 3

This video segment continues to develop partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 4

This video segment continues to develop partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 5

This video segment continues to develop partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions 6

This video continues to develop partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 1

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 2

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 3

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 4

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 5

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 6

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 7

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 8

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's Triangle & the Binomial Theorem 9

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Polynomial Division 1

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Polynomial Division 2

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Polynomial Division 3

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Polynomial Division 4

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 1

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Quadratic Equations 10

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Quadratic Equations 2

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Quadratic Equations 3

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 4

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs.
Quadratic Equations 5

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 6

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 7

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 8

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Quadratic Equations 9

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 1

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 2

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 3

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 4

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 5

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 6

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Rearranging Formulae Part 7

IPOD VIDEO: It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 1

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 2

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 3

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 4

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 5

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 6

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simplifying algebraic fractions Part 7

IPOD VIDEO: This video explains how algebraic fractions can be simplified by cancelling common factors.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 1

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 2

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 3

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 4

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 5

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 6

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 7

IPOD VIDEO: The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities 1

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities 2

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities 3

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities 4

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities 5

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 1

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 2

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 3

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 4

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 5

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 6

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 7

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Substitution and Formulae Part 8

IPOD VIDEO: In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

### Practice & Revision (3)

Algebra Refresher

A refresher booklet on Algebra with revision, exercises and solutions on fractions, indices, removing brackets, factorisation, algebraic frations, surds, transpostion of formulae, solving quadratic equations and some polynomial equations, and partial fractions. An interactive version and a welsh language version are available.

Algebra Refresher - Interactive version

An interactive version of the refresher booklet on Algebra including links to other resources for further explanation. It includes revision, exercises and solutions on fractions, indices, removing brackets, factorisation, algebraic frations, surds, transpostion of formulae, solving quadratic equations and some polynomial equations, and partial fractions. An interactive version and a welsh language version are available.

Cwrs Gloywi Algebra

An Algebra Refresher.
This booklet revises basic algebraic techniques.
This is a welsh language version.

### Quick Reference (12)

Equations of motion

This resource covering equations of constant acceleration has been contributed to the mathcentre Community Project by Josh Simpson and reviewed by Leslie Fletcher, Liverpool John Moores University.

Expanding or removing brackets

In this leaflet we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in.

Factorising complete squares

There is a special case of quadratic expression known as a complete square. This leaflet explains what this means and how such expressions are factorised.

Factorising quadratics

This leaflet shows how to take a quadratic expression and factorise it.
Special cases of complete squares and difference of two squares are dealt with on other leaflets.

Factorising the difference of two squares

There is a special case of quadratic expression known as the difference of two squares. This leaflet explains what this means and how such expressions are factorised.

Indices or Powers

A power, or index, is used when we want to multiply a number by itself several times. This leaflet explains the use of indices and states rules which must be used when you want to rewrite expressions involving powers in alternative forms.

Logarithms - changing the base

Sometimes it is necessary to find logs to bases other then 10 and e.
There is a formula which enables us to do this. This leaflet states
and illustrates the use of this formula.

Negative and fractional powers

This leaflet explains the use of negative powers and fractional powers.

Simple linear equations

This leaflet shows how simple linear equations can be solved by
performing the same operations on both sides of the equation.

Solving equations using logs

Logs can be used to solve equations when the unknown occurs as a power. This leaflet explains how.

The laws of logarithms

There are rules, or laws, which are used to rewrite expressions involving logs in different forms. This leaflet states and illustrates these rules.

What is a logarithm ?

Logarithms can be used to write expressions involving powers in alternative forms. This leaflet explains how.

### Teach Yourself (18)

Completing the square

It is often useful to be able write a quadratic expression in an alternative form - that is as a complete square plus or minus a number. The process for doing this is called completing the square. This booklet explains how this process is carried out.

Completing the square - maxima and minima

This is a workbook which describes how to complete the square for a quadratic expression. It goes on to show how the technique can be used
to find maximum or minimum values of a quadratic expression.

Cubic equations

This booklet explains what is meant by a cubic equation and discusses the nature of the roots of cubic equations.
It explains a process called synthetic division which can be used to locate further roots when one root is known.
The graphical solution of cubic equations is also described.

Expanding, or removing brackets

This is a complete workbook covering the removal of brackets
from expressions. It contains lots of examples and exercises.
It can be used as a free-standing resource, or can be read in conjunction with mathtutor - the companion on-disk resource.

Factorising quadratics

The ability to factorise a quadratic expression is an essential skill.
This booklet explains how this process is carried out.

Indices or Powers

This is a complete workbook on Indices covering definitions, rules and lots of examples and exercises.
It can be used as a free-standing resource, or can be read in conjunction with mathtutor - the companion on-disk resource.

Linear equations in one variable

This is a complete workbook introducing the solution of a single linear equation in one variable. It contains plenty of examples and exercises.
It can be used as a free-standing resource or in conjunction with the mathtutor DVD.

Logarithms

This booklet explains what is meant by a logarithm. It states and illustrates the laws of llogarithms. It explains the standard bases 10 and e.
Finally it shows how logarithms can be used to solve certain types of equations.

Mathematical language

This introductory booklet describes conventions used in mathematical work and gives information on the appropriate use of symbols.

Partial fractions

An algebraic fraction can often be broken down into the sum of simpler fractions called partial fractions. This process is required in the solution of a number of engineering and scientific problems.
This booklet explains how this is done.

Pascal's triangle and the binomial theorem

This unit explains how Pascal's triangle is constructed and then used to expand binomial expressions.
It then introduces the binomial theorem.

Polynomial division

Polynomial division is a process used to simplify certain sorts of algebraic fraction. It is very similar to long division of numbers. This booklet describes how the process is carried out.

Quadratic equations

This booklet explains how quadratic equations can be solved by factorisation, by completing the square, using a formula, and by
drawing graphs.

Simplifying Fractions

This booklet explains how an algebraic fraction can be expressed in its lowest terms, or simplest form.

Simultaneous linear equations

This is a complete workbook introducing the solution of a pair of simultaneous linear equations. It contains plenty of examples and exercises.
It can be used as a free-standing resource or in conjunction with the mathtutor DVD.

Solving inequalities

This booklet explains linear and quadratic inequalities and how they can be solved algebraically and graphically.
It includes information on inequalities in which the modulus symbol is used.

Substitution and formulae

Formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities we can calculate the values of others. This booklet discusses several formulae.

Transposition, or rearranging formulae

It is often necessary to rearrange a formula in order to write it in a different, yet equivalent form. This booklet explains how this is done.

### Test Yourself (55)

Combining algebraic fractions - Numbas

13 questions on combining algebraic fractions. An area in which students often need practice.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Combining algebraic fractions - Numbas

13 questions on combining algebraic fractions. An area in which students often need practice. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Completing the square - Numbas

Two questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Completing the square - Numbas

Two questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Diagnostic Test - Brackets

Diagnostic test for using brackets.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Completing the square 1

Diagnostic test for completing the square. (1 of 2).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Completing the square 2

Diagnostic test for completing the square. (2 of 2).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Cubics

Diagnostic test for cubic equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Factorising quadratics 1

Diagnostic test for factorising quadratics. (1 of 2).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Factorising quadratics 2

Diagnostic test for factorising quadratics. (2 of 2).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Inequalities

Diagnostic test for solving inequalities.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Linear equations

Diagnostic test for linear equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Logarithms

Diagnostic test for logs and logarithms.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Mathematical language

Diagnostic test for mathematical language
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Partial fractions

Diagnostic test for partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Pascal's Triangle and the binomial expansion

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Polynomial division

Diagnostic test for polynomial division.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Powers

Diagnostic test for powers and indices.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Simplifying fractions

Diagnostic test for simplifying fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Simultaneous equations

Diagnostic test for simultaneous equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Substitution

Diagnostic test for substituting formulae.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Diagnostic Test - Transposing formulae

Diagnostic test for transposing formulae.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Brackets

Online exercise on using brackets.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Completing the square

Online exercise on completing the square.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Completing the square - maxima and minima

Online exercise on completing the square using maxima and minima.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Cubics

Online exercise on cubic equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Factorising Quadratics 1

Online exercise on factorising quadratics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Factorising Quadratics 2

Online exercise on factorising quadratics (2).
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Fractions

Online exercise on partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Inequalities

Online exercise on inequalities.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Linear equations

Online exercise on linear equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Logarithms

Online exercise for logarithms.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Partial fractions

Online exercise on partial fractions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Pascal's Triangle and the binomial expansion

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Polynomial division

Online exercise on polynomial division.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Powers

Online exercise for powers.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Simultaneous equations

Online exercise on simultaneous equations.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Substitution

Online exercise on substitution.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Transposing formulae

Online exercise on transposing formulae.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding Brackets - Numbas

9 questions: Expanding out expressions such $(ax+b)(cx+d)$ etc.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Expanding brackets - Numbas

9 questions: Expanding out expressions such $(ax+b)(cx+d)$ etc. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Factorising quadratics - Numbas

3 questions on factorising quadratics. The second question also asks for the roots of the quadratic. The third question involves factorising quartic polynomials but which are quadratics in $x^2$.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Logarithms and solving equations - Numbas

8 questions using logarithms. 7 questions use logarithms to solve equations.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Logarithms and solving equations - Numbas

8 questions using logarithms. Of these 7 questions use logarithms to solve equations.

Maths EG

Computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University.

Partial fractions - Numbas

1 question on partial fractions.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Partial fractions - Numbas

1 question on partial fractions. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Polynomial division - Numbas

2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Polynomial division - Numbas

2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Rearranging equations - Numbas

Rearrange equations to make $x$ the subject. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Simultaneous equations - Numbas

Two questions on solving systems of simultaneous equations. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

Solving simple linear equations - Numbas

2 equations, both linear (the second needs a small amount of algebra to reduce to a linear equation).
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Solving simple linear equations - Numbas

2 equations, both linear (the second needs a small amount of algebra to reduce to a linear equation). Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

System of linear equations - Numbas

3 questions. First, two equations in two unknowns, second 3 equations in 3 unknowns, solved by Gauss elimination.
The third two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.

Systems of linear equations - Numbas

3 questions. First, two equations in two unknowns; second 3 equations in 3 unknowns, solved by Gauss elimination. The third, two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.

### Third Party Resources (1)

University of East Anglia (UEA) Interactive Mathematics and Statistics Resources

The Learning Enhancement Team at the University of East Anglia (UEA) has developed la series of interactive resources accessible via Prezi mind maps : Steps into Numeracy, Steps into Algebra, Steps into Trigonometry, Bridging between Algebra and Calculus, Steps into Calculus, Steps into Differential Equations, Steps into Statistics and Other Essential Skills.

### Video (20)

Completing the square - an Animation

This mathtutor animation shows how the quadratic equation for a parabola may be transformed by completing the square. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square - by Inspection

In this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Completing the Square - maxima & maxima

Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Expanding & Removing Brackets

In this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Factorising Quadratic Equations

An essential skill in many applications is the ability to factorise quadratic expressions. In this unit you will see that this can be thought of as reversing the process used to 'remove' or 'multiply-out' brackets from an expression.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Logarithms

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Mathematical language

This introductory section provides useful background material on the importance of symbols in mathematical work. It describes conventions used by mathematicians, engineers, and scientists.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Partial Fractions

After viewing this tutorial, you should be able to explain the meaning of the terms 'proper fraction' and 'improper fraction', and express an algebraic fraction as the sum of its partial fractions. (Mathtutor Video Tutorial) algebraic fraction as the sum of its partial fractions.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Pascal's triangle and the binomial expansion

A binomial expression is the sum or difference of two terms. For example, x+1 and 3x+2y are both binomial expressions. If we want to raise a binomial expression to a power higher than 2 it is very cumbersome to do this by repeatedly multiplying x+1 or 3x+2y by itself. In this tutorial you will learn how Pascal's triangle can be used to obtain the required result quickly. (mathtutor video)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Polynomial Division

In order to simplify certain sorts of algebraic fraction we need a process known as polynomial division. This unit describes this process.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Powers

A knowledge of powers, or indices as they are often called, is essential for an understanding of most algebraic processes. In this section you will learn about powers and rules for manipulating them through a number of worked examples.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simple Linear Equations

In this unit we give examples of simple linear equations and show you how these can be solved. In any equation there is an unknown quantity, x say, that we are trying to find. In a linear equation this unknown quantity will appear only as a multiple of x, and not as a function of x such as x

^{2}, x^{3}, sin x and so on. Linear equations occur so frequently in the solution of other problems that a thorough understanding of them is essential. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Simplifying Algebraic Fractions

This video explains how algebraic fractions can be simplified by cancelling common factors. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous linear equations - an Animation

This mathtutor animation shows how solutions to simultaneous linear equations may be found. This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Simultaneous Linear Equations Part 1

The purpose of this section is to look at the solution of simultaneous linear equations. We will see that solving a pair of simultaneous equations is equivalent to finding the location of the point of intersection of two straight lines.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Cubic Equations

All cubic equations have either one real root, or three real roots. In this video we explore why this is so. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Inequalities

This video explains linear and quadratic inequalities and how they can be solved algebraically and graphically. It includes information on inequalities in which the modulus symbol is used. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Solving Quadratic Equations

This unit is about the solution of quadratic equations. These take the form ax

^{2}+bx+c = 0. We will look at four methods: solution by factorisation, solution by completing the square, solution using a formula, and solution using graphs. (Mathtutor Video Tutorial) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Substitution & Formulae

In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities; we can calculate the values of others. In this video we discuss several formulae and illustrate how they are used.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Transposition or Re-arranging Formulae

It is often useful to rearrange, or transpose, a formula in order to write it in a different, but equivalent form. This unit explains the procedure for doing this.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.