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Completing the Square (to find MAX and MIN values) Part 4Completing 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 5Completing 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 6Completing 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.
Trigonometric functionsThe sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The sum of an infinite seriesIn this unit we see how finite and infinite series are obtained from finite and infinite sequences. We explain how the partial sums of an infinite series form
a new sequence, and that the limit of this new sequence (if it exists) defines
the sum of the series. We also consider two specific examples of infinite
series that sum to e and pi respectively. (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.
The sum of an infinite seriesIn this unit we see how finite and infinite series are obtained from finite and infinite sequences. We explain how the partial sums of an infinite series form
a new sequence, and that the limit of this new sequence (if it exists) defines
the sum of the series. We also consider two specific examples of infinite
series that sum to e and pi respectively. (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.
Sine, cosine and tangent of an angle of any sizeKnowledge of the trigonometric ratios sine, cosine and tangent is vital in many fields of engineering, maths and science. This unit explains how the sine, cosine and tangent of an arbitrarily sized angle can be found. (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.
Cwrs Gloywi CalcwlwsA Calculus Refresher.
This booklet revises techniques in calculus (differentiation and integration).
This is a welsh language version
Limits of sequencesIn this unit, we recall what is meant by a simple sequence, and introduce
infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequences, and see that they might tend to plus or minus infinity, or to a real limit, or behave in some other way. (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.
Arithmetic and Geometric ProgressionsThis unit introduces sequences and series, and gives some simple examples
of each. It also explores particular types of sequence known as arithmetic
progressions (APs) and geometric progressions (GPs), and the corresponding series. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have a table of derivatives, we can read it backwards as a table of anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of Differentiation. (Mathtutor Video Tutorial)
The video 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 & maximaCompleting 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)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Trig ratios in a right angled triangleKnowledge of the trigonometric ratios of sine, cosine and tangent is vital in very many fields of engineering, science and maths. This unit introduces them and provides examples of how they can be used to solve problems. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Cartesian components of vectorsAny vector may be expressed in Cartesian components, by using unit vectors in
the directions of the coordinate axes. In this unit we describe these unit
vectors in two dimensions and in three dimensions, and show how they can be
used in calculations. (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.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (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.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (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.
Integrating algebraic fractions (2)Sometimes the integral of an algebraic fraction can be found by first
expressing the algebraic fraction as the sum of its partial fractions. In this
unit we look at the case where the denominator of the fraction involves an
irreducible quadratic expression. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Properties of Straight Line Segments Part 1IPOD VIDEO: In this unit we use a system of co-ordinates to find various properties of the straight line between two points. We find the distance between the two points and the mid-point of the line joining the two points.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Properties of Straight Line Segments Part 2IPOD VIDEO: In this unit we use a system of co-ordinates to find various properties of the straight line between two points. We find the distance between the two points and the mid-point of the line joining the two points.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Properties of Straight Line Segments Part 3IPOD VIDEO: In this unit we use a system of co-ordinates to find various properties of the straight line between two points. We find the distance between the two points and the mid-point of the line joining the two points.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Properties of Straight Line Segments Part 4IPOD VIDEO: In this unit we use a system of co-ordinates to find various properties of the straight line between two points. We find the distance between the two points and the mid-point of the line joining the two points.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Finding areas by integrationIntegration can be used to calculate areas. In simple cases, the area is given
by a single definite integral. But sometimes the integral gives a negative
answer which is minus the area, and in more complicated cases the correct
answer can be obtained only by splitting the area into several parts and adding
or subtracting the appropriate integrals. (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.
Properties of straight line segmentsIn this unit we use a system of co-ordinates to find various properties
of the straight line between two points. We find the distance between the two
points and the mid-point of the line joining the two points.
(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.
Properties of straight line segmentsIn this unit we use a system of co-ordinates to find various properties
of the straight line between two points. We find the distance between the two
points and the mid-point of the line joining the two points.
(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.
Limits of sequencesIn this unit, we recall what is meant by a simple sequence, and introduce
infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequences, and see that they might tend to plus or minus infinity, or to a real limit, or behave in some other way. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
