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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)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Inverse functionsAn inverse function is a second function which undoes the work of the first
one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist. (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.
Substitution & FormulaeIn 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)
The video 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)
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 expansionA 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)
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)
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 Gradient of a Straight Line Segment Part 3IPOD VIDEO:
In this unit we find the gradient of a straight line segment, and the relationships between the gradients of parallel lines and of perpendicular 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.
The Gradient of a Straight Line Segment Part 2IPOD VIDEO:
In this unit we find the gradient of a straight line segment, and the relationships between the gradients of parallel lines and of perpendicular 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.
Integrating algebraic fractions (1)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 will illustrate this idea. We will see that it is also necessary to
draw upon a wide variety of other techniques such as completing the square,
integration by substitution, using standard forms, and so on. (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.
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)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Maths E.G.An e-assessment system containing almost 2000 mathematics questions with random parameters and feedback spanning topics from GCSE to undergraduate level 2. Each question in the database will generate thousands of examples, each with fully-worked solutions. The MSOR Network supported the development of questions in elementary discrete mathematics (sets, logic and graph theory) as part of the National HE STEM Programme. Maths E.G. is delivered under a Creative Commons BY-SA licence.
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)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Tangents and NormalsThis unit explains how differentiation can be used to calculate the equations of the tangent and normal to a curve.
The tangent is a straight line which just touches the curve at a given point. The normal is a straight line which is
perpendicular to the tangent. (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)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
At-a-Glance 01: Units & StrengthsAt a Glance - Pharmacy Calculations (Leaflet 1) covering units of measure, prefixes and strengths.
This resource has been contributed under a Creative Commons licence to the mathcentre Community Project by Dr Matthew Copping, University of Kent and reviewed by Dr Scott Wildman, Medway School of Pharmacy. It is one of a series of 17 resources funded by a sigma Resource Development grant.
Trig functions: cosecant, secant and cotangentIn this unit we see how the three trigonometric ratios cosecant, secant and cotangent can appear in trigonometric identities and in the solution of trigonometric equations. Graphs of the functions are obtained from a knowledge of sine, cosine and tangent. (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 (to find MAX and MIN values) Part 1Completing 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 2Completing 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 3Completing 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 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.
