Mappings, functions or both?
Mappings, functions, or both? In this tutorial, we understand the definition of a function and show examples of whether or not a mapping is a function.
Increasing and decreasing sequences
In this tutorial, we show you how to prove whether a sequence is increasing or decreasing using algebra.
Mappings – More examples
In this tutorial, we go through more examples of mappings and I show you how to draw piecewise mappings.
Mappings
In this tutorial, we understand what a mapping actually is, the different types of mappings you need to know, and different ways we can represent a mapping.
Finding Points of Intersection between a Parametric and Cartesian Equation
Exam Questions – Parametric to Cartesian equations
Integrating products of the form f[g(x)]g'(x) by inspection
Integration – General Methods
Multiplying a vector by a scalar
Square root types
Exam Questions – Partial fractions with the binomial expansion
Exam Questions – Simplifying a rational expression
Exam Questions – Algebraic long division
Shortest distance of a point to a line
Exam Questions – Vectors
Exam Questions – Parallel intersecting and skew lines
Exam Questions – Scalar product
Exam Questions – Integration
Proof of the formula – Integration by parts
Exam Questions – Trigonometric types
Using partial fractions with the binomial expansion
Exam Questions – Trapezium rule
Exam Questions – Forming differential equations
Exam Questions – Integration by parts
Exam Questions – Integration by substitution
Exam Questions – Integrals involving partial fractions
Exam Questions – Implicit functions
Exam Questions – Parametric functions
Exam Questions – Parametric equations
Exam Questions – Binomial expansion for rational and negative powers
Exam Questions – Partial fractions
Exam Questions – Addition & subtraction
Working with constants in log types
Differential Equations – Finding a general and a particular solution
sin2x and cos2x types
Integrals Using Trigonometric Identities
Further simplifying of ‘stacked fractions’
Multiplication of algebraic fractions
The trig functions sin(x), cos(x) and tan(x)
Magnitude of a 2 dimensional vector
Addition and subtraction of vectors
Equal and negative vectors
Closest point to a line and shortest distance from the origin
Intersecting and skew lines
Parallel lines
Angle between two lines
Vector equation of a line
Perpendicular vectors
Scalar product
Magnitude of a 3 dimensional vector
Unit vectors
Position vectors
Vector notation
What is a vector and a scalar quantity?
Trapezium rule
Newton’s law of cooling
Inverse proportion type
Direct proportion type
Differential Equations – Exponential and trig type
Mixed Examples – Integration
Integration by parts (ln types)
Integration by parts using limits
Integration by parts
Integration of trigonometric functions by substitution with limits
Integration by substitution using limits
Integration of exponential types by substitution
Integration of trigonometric functions by substitution
Integration by substitution
Integrals involving partial fractions
Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
Integrals of sin x, cos x, sec² x
Integrals of the form : f'(x)ef(x)
Integrals of the form : f ‘(x)/f(x)
Stationary points
In this tutorial I show you how to find stationary points to a curve defined implicitly and I discuss how to find the nature of the stationary points by considering the second differential. Both methods involve using implicit differentiation and the product rule. Example: Nature of the Stationary Points
Tangents and normals
Implicit functions
Stationary points
In this video you are shown how to find the stationary points to a parametric equation.