Finding Points of Intersection between a Parametric and Cartesian Equation
In this video tutorial I show you how to find [...]
Integrating products of the form f[g(x)]g'(x) by inspection
Here I show you how to handle integrals which take [...]
Integration – General Methods
I am of often asked, "What method do we [...]
eaxsin(bx) and eaxcos(bx) types
Integrals of the form eaxsin(bx) and eaxcos(bx) are handled in [...]
Identities – Addition type – Equations
In this tutorial I show you how we can use [...]
Position vectors 2d
In this video, I show you the difference between a [...]
Vector notation 2d
In this video, I show you many of the different [...]
Square root types
Some integrals contain square roots. In these you can have [...]
Shortest distance of a point to a line
Finding the shortest distance of a point to a line [...]
Parametric equations of circle, ellipse, parabola and hyperbola
Example: Parametric equation of a circleThe following example is used.A curve [...]
Simpson’s Rule
Simpson's rule is used to find the approximate area under [...]
Volume of revolution about the x-axis generated between curves
I now extend the the basic volume of revolution about [...]
Proof of the formula – Integration by parts
You may want to know how to prove the formula [...]
Working with constants in log types
In this video I demonstrate the method of handling [...]
Differential Equations – Finding a general and a particular solution
In this video I introduce you to how we solve [...]
sin2x and cos2x types
In this first video, you are shown how to integrate [...]
Integrals Using Trigonometric Identities
Example 1 This is first in a series of [...]
Further simplifying of ‘stacked fractions’
Sometimes you will get what I call 'stacked fractions' and [...]
Multiplication of algebraic fractions
In this video I show you how to multiply algebraic [...]
The trig functions sin(x), cos(x) and tan(x)
In this video, I show you how to differentiate the [...]
The natural log function, ln(x)
In this video, I show you how to differentiate the [...]
Stretches of trig graphs
In this section I show you stretches of the trigonometric [...]
Magnitude of a 2 dimensional vector
In this video, I show you how to find the [...]
Equal and negative vectors
In this video, I tell you about the properties of [...]
Closest point to a line and shortest distance from the origin
In this video I show you how to find the [...]
Intersecting and skew lines
If two lines are not parallel then they will either [...]
Parallel lines
In this video you are shown the conditions for two [...]
Angle between two lines
In this video you are shown how to find the [...]
Vector equation of a line
This tutorial will show you how to get to any [...]
Perpendicular vectors
The scalar product can be used to test if two [...]
Scalar product
In this video I show you how the scalar product [...]
Magnitude of a 3 dimensional vector
You will need to know how to find the magnitude [...]
Unit vectors
Unit vectors have a magnitude of 1 unit. In this [...]
Position vectors
In this video, I show you the difference between a [...]
Vector notation
In this video, I show you many of the different [...]
What is a vector and a scalar quantity?
In this video, I show you what we mean by [...]
Trapezium rule
The trapezium rule is used to find the approximate area [...]
Newton’s law of cooling
In this video I look at how a differential equation [...]
Inverse proportion type
In this video I look at how a differential equation [...]
Direct proportion type
In this video I look at how a differential equation [...]
Differential Equations – Exponential and trig type
In this video I look at exponential and trig [...]
Volume of revolution for a curve given in parametric form
In this tutorial I show you how to find the [...]
Volume of revolution about the x-axis
In the first video in this series, I show you [...]
Area under a graph : parametric type
In this tutorial I show you how to find the [...]
Mixed Examples – Integration
To be really confident with integration you must try mixed [...]
Integration by parts (ln types)
This tutorial will show you how to integrate functions that [...]
Integration by parts using limits
This tutorial shows you how to do integration by parts [...]
Integration by parts
It is important that you can recognise what types of [...]
Integration of trigonometric functions by substitution with limits
In this tutorial you are shown how to handle [...]
Integration by substitution using limits
Some integrals have limits (definite integrals). Make sure you [...]
Integration of exponential types by substitution
You can use substitution on some exponential types as [...]
Integration of trigonometric functions by substitution
You can use substitution on some trigonometric type integrals. [...]
Integration by substitution
Integration by substitution, sometimes called changing the variable, is used [...]
Integrals involving partial fractions
Some integrals require you to split a fraction into [...]
Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
In this video, I show you how to integrate functions [...]
Integrals of sin x, cos x, sec² x
In this video, I show you how to integrate functions [...]
Integrals of the form : f'(x)ef(x)
In this tutorial you are shown how to do integrals [...]
Integrals of the form : f ‘(x)/f(x)
In this tutorial you are shown how to do integrals [...]
Integrating reciprocal functions 1/x and 1/(ax+b)
In this tutorial you are shown how to do integrals [...]
Integrating exponential functions ex, eax and e(ax+b)
In this video, I show you how to integrate exponential [...]
Integration:(ax+b)n types
In this video I show you how to integrate terms [...]
Connected rates of change cone type problems
Problems on cones can be quite tricky so I would [...]
Using three connected rates of change
This next question is more involved - don't take the [...]
Connected rates of change
I now show you how we can apply the chain [...]
Stationary points
In this tutorial I show you how to find stationary [...]
Tangents and normals
In this tutorial I show you how to find the [...]
Implicit functions
Here I introduce you to differentiating implicit functions. These are [...]
Stationary points
In this video you are shown how to find the [...]
Tangents and normals
In this video you are shown how to find the [...]
Differentiation: Parametric functions
First order differentiation for a Parametric Equation In this video [...]
Differentiation: Exponential functions of the form y=ax
In this video I show you how to differentiate exponential [...]
Sketching parametric graphs
You will be expected to sketch simple parametric curves. In [...]
Converting to Cartesian form
In this video, I show you how to convert a [...]
Parametric equations
In this video I introduce you to what parametric equation [...]
Improper types
Some algebraic fractions are improper (top heavy). In this [...]
Denominator contains repeated factors
In this tutorial you are shown how to split an [...]
Denominator contains 2 or 3 linear factors
Denominator contains 2 linear factors In this video tutorial [...]
Partial fractions
This tutorial will show you how to write down the [...]
Iteration
In this video, you are introduced to the method of [...]
Change of sign
Change of Sign Method for Locating a Root in a [...]
Graphical methods
In this video you are shown how to find roots [...]
The quotient rule
The quotient rule is used to differentiate fractions which contain [...]
The product rule
The product rule is used to differentiate products of two [...]
Chain rule: Trigonometric types
In this tutorial I show you how to differentiate trigonometric [...]
Chain rule: Natural log types
In this tutorial you are shown how to differentiate composite [...]
Chain rule: Exponential types
In this tutorial I show you how to differentiate composite [...]
Chain rule: Polynomial to a rational power
In this tutorial I introduce the chain rule as a [...]
Exponential function ex
In this video, I show you how to differentiate the [...]
Equations using harmonic identities
The Harmonic Identities are useful when solving equations with the [...]
Harmonic Identities Rsin(x ± α), Rcos(x ± α)
The following identities, known as the harmonic identities, are very [...]
Proving identities using the factor formulae
Here I introduce you to the factor formulae. These are [...]
Identity for cos 3θ and sin 3θ
A common question is to express cos3θ in terms of [...]
Examples using half angle identities
Proving Identities - Half angles based on the Double Angle [...]
Solving equations using double angle identities
When the angles are different. Is One angle Double the [...]
Examples using double angle identities
You will be expected to be able to prove a [...]
Identities for sin2A, cos2A and tan2A
In this video you are shown how the double angle [...]
Proving identities using the addition formulae
You will be expected to be able to prove [...]
Using the Addition formulae to get exact values
You will be asked to find exact values say for [...]
sin(A±B), cos(A±B) and tan(A±B)
You are introduced to the trigonometric sum and difference (addition) [...]
Solving equations using Pythagorean identities
If the equation contains trig functions with the same angle [...]
sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x
In this video you are shown the Pythagorean identities and [...]
Examples using Inverse trigonometric functions
In this video I show you how to find the [...]
Inverse trigonometric functions – arcsin x, arccos x, arctan x
The graphs of the inverse trigonometric functions arcsin(x), arccos(x) and [...]
Graphs of sec θ, cosec θ and cot θ
In this video, I show you how to sketch the [...]
Trig functions sec θ, cosec θ and cot θ
In this video, I introduce you to the definitions of [...]
The natural logarithmic function, ln x
In this video I introduce you to the natural log [...]
Sketching exponential graphs based on transformations
Reflections In this tutorial I show you how to transform [...]
Graphical relationship between f(x) and its inverse
In this video I show you the graphical relationship [...]
The inverse of a function
If you are not sure what an inverse function is [...]
Combination of functions
You will be asked to combine functions. In this tutorial [...]
Domain and range
I am often asked what is the domain and range [...]
Addition and subtraction of algebraic fractions
In these two videos I introduce you to addition and [...]
Simplifying algebraic fractions
A single fraction can often be simplified by cancelling out [...]
Area bound by a curve and x-axis
Integration - Area under a graph Integration can be used [...]
Combining transformations
Now I show you how transformations can be combined to [...]
Reflections of trig graphs
In this section I show you reflections of the trigonometric [...]
Stretches of graphs
Being able to transform basic graphs is an essential skill [...]
Reflections of graphs
Being able to transform basic graphs is an essential skill [...]
Translations of graphs
Being able to transform basic graphs is an essential skill [...]
Basic graphs used in transformations
In this video you are shown some of the basic [...]
f(x) notation
In this tutorial I go through an alternative notation for [...]