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.
Exam Questions – Small Angle Approximations
Exam Questions – Functions
Exam Questions – Double Angles
Harmonic identities – Max and Min
Identities – Addition type – Equations
Exam Questions – Simplifying a rational expression
Exam Questions – Algebraic long division
Exam Questions – Exponential rates of change
Exam Questions – Differentiation: tangents, normals and stationary points
Exam Questions – Differentiation methods
Exam Questions – Mixed trigonometry
Exam Questions – Harmonic identities and equations
Exam Questions – Modulus equations
Exam Questions – Modulus functions graphing
Exam Questions – Domain and range
Exam Questions – Iteration
Exam Questions – Natural log functions
Exam Questions – Modulus inequalities
Exam Questions – Graph transformations
Exam Questions – Inverse functions
Exam Questions – Addition & subtraction
The reciprocal function of dy/dx
Further simplifying of ‘stacked fractions’
Multiplication of algebraic fractions
The trig functions, sec(x), cosec(x) and cot(x)
The trig functions sin(x), cos(x) and tan(x)
The natural log function, ln(x)
Asymptotes – horizontal and vertical types
Iteration
Change of sign
Graphical methods
The quotient rule
The product rule
Chain rule: Trigonometric types
Chain rule: Natural log types
Chain rule: Exponential types
Chain rule: Polynomial to a rational power
Exponential function ex
Equations using harmonic identities
Harmonic Identities Rsin(x ± α), Rcos(x ± α)
Proving identities using the factor formulae
Here I introduce you to the factor formulae. These are identities, given without proof are useful when adding or subtracting two sine angles or cosine angles and creating one term from the two. Hence, factor formulae. The examples which follow are typical of the kind of questions you can get that uses the factor formulae. […]
Identity for cos 3θ and sin 3θ
Examples using half angle identities
Solving equations using double angle identities
Examples using double angle identities
Identities for sin2A, cos2A and tan2A
Proving identities using the addition formulae
Using the Addition formulae to get exact values
sin(A±B), cos(A±B) and tan(A±B)
Solving equations using Pythagorean identities
sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x
Examples using Inverse trigonometric functions
Inverse trigonometric functions – arcsin x, arccos x, arctan x
Graphs of sec θ, cosec θ and cot θ
Trig functions sec θ, cosec θ and cot θ
The natural logarithmic function, ln x
Sketching exponential graphs based on transformations
The exponential function ex
Modulus inequalities
Modulus equations
Graphing y=f(|x|)
Remember: f(|x|) reflects the graph to the right of the y-axis in the y-axis. Ignore the left hand side part of the graph In this video I show you how to draw graphs of the form y=f(|x|) using the modulus function and give you three graphs to try. Examples in the video: Sketch the following