Did you know that I recently published 200 videos for Mathematics Advanced Year 12 as well? Click here if you’d like to check out year 12.

## MA-F1 Working With Functions

#### – F1.1 Algebraic Techniques

Introduction to index laws and using them to simplify algebraic expressions

Index Law 1 – multiplication of indices

Index Law 2 – dividing indices

Index Law 3 – raising to the power of zero

Index Law 4 – Raising a power to another power

Index Law 5 – worked examples using the fifth index law

Index Law 6 – expanding brackets around a fraction raised to a power

Index law 7 Negative Indices – converting Negative indices into positive indices using fractions

Index Law 8 Fractional Indices – moving from index form to radical form

Index Laws equating bases to solve for unknown exponent or power part 1

Index Laws equating bases to solve for unknown exponent or power part 2

Index Laws Negative bases

Index Laws Fractional indices

Harder Indicial Equations

Solving Indicial equations

Indicial equations super hard quadratic action

Indicial equations The hardest one

Surds what is a surd

Simplifying surds

Simplifying Surds

Surds simplifying algebraic surds

Surds adding and subtracting surds

Adding and subtracting surds

Multiplying surds

Multiplying surds and the distributive law

Surds square numbers

Surds dividing

Dividing Surds

Solving Quadratics 3 ways

The quadratic formula and the discriminant

Completing the square part 1

Completing the square part 2

Solving by completing the square

Algebraic fractions cancelling common factors

Algebraic fractions multiplying and dividing

Algebraic fractions adding and subtracting

Algebraic fractions adding and subtracting part 2

Algebraic fractions adding and subtracting part 3

#### – F1.2 Introduction to Functions

Relations, Functions and the vertical line test

Function Notation: Better ways of representing functions

Interval Notation and Number Lines

Domain and Range of functions and relations

Composite functions

#### – F1.3 Linear, Quadratic and Cubic Functions

Find x and y values from a graph

Plotting Linear graphs

Equations of horizontal and vertical lines

The equation of a line y = mx + c

Determining the rule of a linear graph

Anatomy of a linear graph

Finding the gradient of a line revision

Parallel lines and their gradients

Perpendicular lines and their gradients

3 forms of the quadratic equation

The quadratic formula and the discriminant

solving simultaneous equations using quadratic and linear graphs

Modelling and problem solving with quadratics

Cubics quartics and greater polynomials in Turning Point Form

Factor form of Quadratics cubics and Quartics

Factorise solve and sketch a cubic

#### – F1.4 Further Functions and Relations

Factor form of Quadratics cubics and Quartics

Cubics quartics and greater polynomials in Turning Point Form

Finding a linear factor of a polynomial

Intersecting Functions

Direct and Indirect Proportion

Equations of hyperbola and sketching

Sketching Hyperbolas and why there's an asymptote

Finding equation of reciprocal function from sketch

The modulus or absolute value function introduction

The modulus or absolute value solving equations

Absolute Value Functions

Sketch Absolute Value Functions with a vertical shift

Sketching an absolute value function worked example

Reflecting Functions in the y axis using absolute value functions

Function Transformations intro

Functions Transformation fx+a

Function transformation f(x+a)

Functions transformations f(ax)

Sketching circles and finding equations of circles

Equation of a circle sketching and finding coordinates

## MA-T1 Trigonometry And Measure of Angles

#### – T1.1 Trigonometry

Trig Ratios fast

The Sine Rule Fast

The sine rule ambiguous case

The cosine rule

Area of a triangle using trigonometry

True Bearings

Bearings and Trigonometry an example

How to Draw the Diagrams for Trig Applications Questions (Bearings and Elevation/Depression

#### – T1.2 Radians

Introduction to Radians

Converting Radians to Degrees and Degrees to Radians

Radians quick angles

Standard triangles

The Unit Circle

The Unit Circle The Tan Ratio

The Unit Circle and Symmetry

The unit circle CAST and why CAST works

Finding exact trig ratios involving negative angles

Finding exact values of trig ratios around the unit circle

The Unit Circle Finding exact values of negative trig ratios

The unit circle Boundary angles

The unit circle solving unknown angles

Solving Simple Trig Equations Worksheet (worksheet in Description)

The unit circle solving unknowns in trig equations

Sketching SinX and CosX

## MA-T2 Trigonometric Functions and Identities

Pythagorean identity

Pythagorean identity rearrangement

Using Pythagorean Identities Part 1

Solving trig identity equations using quadratics

Solving trig identity equations using quadratics part 2

Solving and simplifying using trig identities

Sketching f(x) = tan(x) and why it looks like that.

Solving Trig equations The Tricky 3 Quantum of Quadratics

Solving Trig equations The Tricky 3 Square or Die

Solving Trig equations The Tricky 3 Domain Domination

Reciprocals of Trigonometric Functions

Complementary Trigonometric Relationships

Exact values of reciprocal trigonometric functions

Solving reciprocal trig functions

The pythagorean Identity and reciprocal trigonometric functions

Proving Trigonometric identities

2 more pythagorean identities

## MA-C1 Introduction to Differentiation

Variable and constant rates of change

Average rates of change

Intro to instantaneous rates of change

The Gradient function

Differentiation from first principles

Differentiating polynomials by rule

Finding Stationary points

Nature of Stationary points

Optimisation when the function is unknown

Introduction to Kinematics

Finding the equation of a tangent

Finding the equation of a normal

Derivatives of polynomials, negative and fractional powers by rule

Composite functions and the chain rule

The chain rule the fast way

The product rule

The quotient rule

## MA-E1 Logarithms and Exponentials

Log laws as fast as possible

Logs 1 Intro to Logarithms

Logs 2 Log Law 1

Logs 3 Log Law 2

Logs 4 Log Law 3

Logs 5 Log Law 4

Logs 6 Log Law 5

Logs 7 Log Law 6

Logs 8 solving exponentials

Solving Indicial equations using logarithms

Logs 9 Solving logarithmic equations

Solving Log equations examples

Solving equations involving natural log

Solving logarithmic equations with an unknown power

Solving logarithmic equations with an unknown base

Logs 10 Solving logarithmic equations part 2

Logarithms 12 Simplifying Log equations

Logarithmic functions Basic shape

Logarithmic functions Sketching

Finding equations of log functions

Logarithmic functions 3 Find equation from a sketch

Logarithmic Functions 4 Regression analysis

Exponential and logarithmic modelling

Solving Indicial equations

Harder Indicial Equations

Indicial equations super hard quadratic action

Indicial equations The hardest one

Exponential Functions Basic shape and Translations

Exponential Functions Dilations

Exponential functions 2 Sketching

Exponential functions 2 Sketching

Exponential functions 3 Finding equation from a sketch

Exponential Model and Applications

Derivatives of Exponential, Logarithmic and Trigonmetric functions

## MA-S1 Probability & Discrete Probability Distributions

#### – S1.1: Probability and Venn diagrams

The Language of Sets

Theoretical Probability with sets

All Probabilities sum to 1

Venn Diagrams the complement

Experimental probability

simplified tree diagram

The Addition rule of probability

Probability Tables intro

Conditional Probability formula

Conditional Probability Do you watch the bachelorette

Conditional probability rearranging the formula

Conditional Probability and Tree Diagrams

Independent events intro and tests

Independent events 2

Pascal's Triangle and Selections

Binomial expansion using pascal's triangle

#### – S1.2: Discrete probability distributions

Discrete Random Variables: Introduction and Examples

Discrete Random Variables Uniform Distribution

Discrete Random Variable Worked Example

The Geometric Probability Distribution

Expected Value of discrete random distributions

Discrete random distributions Expected value challenging but important

Variance and Standard Deviation

Properties of Expected Value: aE(X)+b = E(aX + b)

The alternative Variance formula Proof

Alternative Variance Formula Worked Example