Modelling exponential growth and decay
In this tutorial I show you what an exponential function [...]
In this tutorial I show you what an exponential function [...]
The Newton-Raphson method is another numerical method for solving equations [...]
Sometimes you will have integrals that approach asymptotes for certain [...]
Here I show you how to handle integrals which take [...]
I am of often asked, "What method do we [...]
What is a Radian? As well as measuring angles in [...]
Try the exercise in the video of mixed questions on [...]
You are expected to be able to find the maximum [...]
In this tutorial I show you how you can calculate [...]
Integrals of the form eaxsin(bx) and eaxcos(bx) are handled in [...]
How to Solve a Cubic Equation In this tutorial [...]
In this tutorial I show you how we can use [...]
Changing the base of a logarithm is useful when it [...]
A quick simple way to find the acute angle between [...]
Finding the shortest distance from a point to a line [...]
Here I show you 3 examples involving simultaneous equations that [...]
In this video, I show you the the meaning behind [...]
De Morgan's Laws are two results relating intersection, union and [...]
I now consider problems using Venn diagrams involving 3 sets. [...]
Some integrals contain square roots. In these you can have [...]
Here I introduce you to Sets and the algebra of [...]
Finding the shortest distance of a point to a line [...]
So often I am asked what is the difference between [...]
When an angle is small and in radians we can [...]
By using logs we can transform curves into straight lines [...]
Integration can be used to find the area bounded by [...]
Mid-ordinate Rule is another method used to find the approximate [...]
In this video I show you how to handle [...]
Simpson's rule is used to find the approximate area under [...]
I now extend the the basic volume of revolution about [...]
I now extend the the basic volume of revolution about [...]
I now introduce you to the volume of revolution about [...]
I have selected these questions to reflect various factorising [...]
This is a summary of all the rules for indices [...]
You may want to know how to prove the formula [...]
In some circumstances a fraction may need to be expressed [...]
In my ExamSolutions Beasties I try to give you a [...]
In this video I show introduce you to what [...]
In this video I demonstrate the method of handling [...]
In this video I introduce you to how we solve [...]
In this first video, you are shown how to integrate [...]
Example 1 This is first in a series of [...]
In this video I demonstrate the use of the relationship [...]
Sometimes you will get what I call 'stacked fractions' and [...]
In this video I show you how to multiply algebraic [...]
In this video, I show you how to differentiate the [...]
In this video, I show you how to differentiate the [...]
In this video, I show you how to differentiate the [...]
Nature of a stationary point using the first differential In [...]
Here you are shown two basic identities that hold for [...]
When solving trig. equations with multiple angles in a given [...]
I now extend the work by looking at solving trig. [...]
In this section I show you stretches of the trigonometric [...]
You will often find that you need to find the [...]
Another common question is that you are given three consecutive [...]
One common question is to find the first term a, [...]
In this tutorial I show you what a sequence is [...]
When sketching graphs you may need to draw in asymptotes [...]
I now move on to reciprocal curves of the form, [...]
In this video, I show you how to sketch cubic [...]
The Newton-Raphson method is another numerical method for solving equations [...]
The linear interpolation method for locating a root in a [...]
The bisection method is a simple extension to the change [...]
In this video, I show you how to find the [...]
In this video you are shown the vector triangle for [...]
In this video, I tell you about the properties of [...]
In this video I show you how to find the [...]
If two lines are not parallel then they will either [...]
In this video you are shown the conditions for two [...]
In this video you are shown how to find the [...]
This tutorial will show you how to get to any [...]
The scalar product can be used to test if two [...]
In this video I show you how the scalar product [...]
You will need to know how to find the magnitude [...]
Unit vectors have a magnitude of 1 unit. In this [...]
In this video, I show you the difference between a [...]
In this video, I show you many of the different [...]
In this video, I show you what we mean by [...]
The trapezium rule is used to find the approximate area [...]
In this video I look at how a differential equation [...]
In this video I look at how a differential equation [...]
In this video I look at how a differential equation [...]
In this video I look at exponential and trig [...]
In this tutorial I show you how to find the [...]
In the first video in this series, I show you [...]
In this tutorial I show you how to find the [...]
To be really confident with integration you must try mixed [...]
This tutorial will show you how to integrate functions that [...]
This tutorial shows you how to do integration by parts [...]
It is important that you can recognise what types of [...]
In this tutorial you are shown how to handle [...]
Some integrals have limits (definite integrals). Make sure you [...]
You can use substitution on some exponential types as [...]
You can use substitution on some trigonometric type integrals. [...]
Integration by substitution, sometimes called changing the variable, is used [...]
Some integrals require you to split a fraction into [...]
In this video, I show you how to integrate functions [...]
In this video, I show you how to integrate functions [...]
In this tutorial you are shown how to do integrals [...]
In this tutorial you are shown how to do integrals [...]
In this tutorial you are shown how to do integrals [...]
In this video, I show you how to integrate exponential [...]
In this video I show you how to integrate terms [...]
Problems on cones can be quite tricky so I would [...]
This next question is more involved - don't take the [...]
I now show you how we can apply the chain [...]
In this tutorial I show you how to find stationary [...]
In this tutorial I show you how to find the [...]
Here I introduce you to differentiating implicit functions. These are [...]
In this video you are shown how to find the [...]
In this video you are shown how to find the [...]
First order differentiation for a Parametric Equation In this video [...]
In this video I show you how to differentiate exponential [...]
You will be expected to sketch simple parametric curves. In [...]
In this video, I show you how to convert a [...]
In this video I introduce you to what parametric equation [...]
The Binomial Expansion (1 + a)n is not always [...]
Up until now the power 'n' was a positive integer. [...]
Some algebraic fractions are improper (top heavy). In this [...]
In this tutorial you are shown how to split an [...]
Denominator contains 2 linear factors In this video tutorial [...]
This tutorial will show you how to write down the [...]
In this video, you are introduced to the method of [...]
Change of Sign Method for Locating a Root in a [...]
In this video you are shown how to find roots [...]
The quotient rule is used to differentiate fractions which contain [...]
The product rule is used to differentiate products of two [...]
In this tutorial I show you how to differentiate trigonometric [...]
In this tutorial you are shown how to differentiate composite [...]
In this tutorial I show you how to differentiate composite [...]
In this tutorial I introduce the chain rule as a [...]
In this video, I show you how to differentiate the [...]
The Harmonic Identities are useful when solving equations with the [...]
The following identities, known as the harmonic identities, are very [...]
Here I introduce you to the factor formulae. These are [...]
A common question is to express cos3θ in terms of [...]
Proving Identities - Half angles based on the Double Angle [...]
When the angles are different. Is One angle Double the [...]
You will be expected to be able to prove a [...]
In this video you are shown how the double angle [...]
You will be expected to be able to prove [...]
You will be asked to find exact values say for [...]
You are introduced to the trigonometric sum and difference (addition) [...]
If the equation contains trig functions with the same angle [...]
In this video you are shown the Pythagorean identities and [...]
In this video I show you how to find the [...]
The graphs of the inverse trigonometric functions arcsin(x), arccos(x) and [...]
In this video, I show you how to sketch the [...]
In this video, I introduce you to the definitions of [...]
In this video I introduce you to the natural log [...]
Reflections In this tutorial I show you how to transform [...]
In this tutorial I introduce you to exponential functions and [...]
In the following videos I introduce you to solving modulus [...]
WARNING: CARE MUST BE TAKEN WHEN SOLVING MOD EQUATIONS. There [...]
Remember: f(|x|) reflects the graph to the right of the [...]
Remember: |f(x)| reflects any part of the original f(x) [...]
In this video I introduce you to the modulus function. [...]
In this video I show you the graphical relationship [...]
If you are not sure what an inverse function is [...]
You will be asked to combine functions. In this tutorial [...]
I am often asked what is the domain and range [...]
In these two videos I introduce you to addition and [...]
A single fraction can often be simplified by cancelling out [...]
Integration - Area under a graph Integration can be used [...]
In this tutorial I show you how to handle integrals [...]
In this tutorial I show you what we mean by [...]
You can often be asked to state the range of [...]
In this example I demonstrate how we can apply stationary [...]
Stationary Points - What are they? In the first of [...]
Can it be written in the same trig. function? [...]
Two important identities They are very important and should be [...]
Once you have grasped the quadrant rule it is time [...]
The quadrant rule or CAST diagram is very useful to [...]
Arc length and sector area I will show you how [...]
Finding the length of a side of a non right [...]
Finding the length of a side of a non right [...]
When finding the area of a segment you will often [...]
Now I show you how transformations can be combined to [...]
In this section I show you reflections of the trigonometric [...]
In this section I show you translations of the trigonometric [...]
Here I show you how the graphs of sin θ [...]
In this tutorial I show you how you can calculate [...]
The Binomial Expansion formulaIn the tutorial I explain why and [...]
Section 1 : Introduction 0:00:55 Section 2 : [...]
If the common ratio 'r' of a geometric series is [...]
Here I show you how to prove the formula for [...]
What is a Geometric Progression? In this video you are [...]
In this video I show you some of the common [...]
In this tutorial I show you how you can find [...]
In this tutorial you are shown how to find the [...]
You should be aware of the alternative form of the [...]
In this tutorial you are shown how the equation of [...]
In this tutorial you are shown how to solve inequalities [...]
There are different types of equations that involve logs in [...]
In this tutorial you are shown you how simplify and [...]
In the next tutorial I show you the basic rules [...]
In this tutorial you are shown what a log is [...]
In this tutorial I show you what an exponential function [...]
The Remainder Theorem Rule to remember: If a polynomial f(x) [...]
So what is the factor theorem? The factor theorem is [...]
Algebraic long division can be useful in factorising polynomials. In [...]
Finding the equation of the curve given dy/dx In [...]
Integration in calculus can be considered as the inverse [...]
You are expected to be able to find the equation [...]
In this video you are shown how to do 2nd [...]
Differentiating terms where the power is a positive integer [...]
In this video you are introduced to the gradient function [...]
In this video you are shown how to find the [...]
Nature of the intersection of a straight line and curve [...]
In this video you are shown how to find the [...]
In this video, I show you how to find the [...]
In this next example, I show you how to find [...]
In this next example, I show you how to find [...]
In this video I show you how to find the [...]
As part of my series on coordinate geometry I show [...]
In the first tutorial I introduce you to the equation [...]
In this video you are shown the relationship that exists [...]
In this video you are shown the relationship that exists [...]
In this tutorial you are given the definition of the [...]
Some exam boards expect you to be able to prove [...]
In this tutorial you are shown what an arithmetic progression [...]
In this video you are introduced to the difference between [...]
In this video you are shown how to define by [...]
Quadratic inequalities are tackled in a different way to solving [...]
In this tutorial you shown how to solve a double [...]
In this tutorial you are given two linear inequalities to [...]
Before you start to solve linear inequalities, it is essential [...]
In this tutorial you are shown how inequalities are written [...]
In these tutorials you are shown how to solve a [...]
Tutorials on this page: Introduction to solving simultaneous equations [...]
In this next section I start to work with [...]
In this tutorial I show you how to find an [...]
Missing Side on the Top of the Trig Ratio [...]
Naming the Sides of a Right-Angled Triangle In this [...]
In this video I explain Pythagoras' theorem inside 10 minutes. [...]
I now start to extend the work covered so far [...]
In this video, I now show you how to handle [...]
In this video, I now show you how to handle [...]
This is the first in a series of videos to [...]
When working with expressions and equations it is important to [...]
It is useful to be able to square a bracket [...]
In the video tutorial you are shown how to [...]
In the video tutorial you are shown how to [...]
Being able to transform basic graphs is an essential skill [...]
Being able to transform basic graphs is an essential skill [...]
Being able to transform basic graphs is an essential skill [...]
In this video you are shown some of the basic [...]
In this tutorial I show you what a polynomial [...]
I am often asked how to sketch quadratic graphs. In [...]
In video I explain what we mean by roots and [...]
In this video I show you how to solve quadratic [...]
Some quadratic equations cannot be solved by factorising and so [...]
In this tutorial you are shown how to solve a [...]
All quadratic equations have the form ax2 + bx + [...]
In these tutorials I show you how we can use [...]
I am assuming that you are familiar with squaring a [...]
Quadratic expressions have a distinct look about them. They have [...]
Sometimes when there is no common factor, by grouping several [...]
The first step in factorising is: ALWAYS check to see [...]
In this short video I show you what we mean [...]
In this tutorial I go through an alternative notation for [...]
You are going to need to know how to combine [...]
You will also need to know how to rationalise [...]
You will need to look at simplifying the division [...]
Surds are numbers that cannot be square rooted exactly. [...]
In this video, you are shown how we combine surds [...]
Next you are shown how to solve equations where [...]
You will need to be able to simplify terms [...]
In the next video you are shown how to [...]
In this tutorial I introduce you to fractions which [...]
Next I introduce you to negative indices [...]
Next you are shown how to handle [...]
Multiplication Rule (1) In this tutorial you [...]
You will also need to express terms in the [...]
Indices (or exponents) are used to write statements in shorthand [...]