Index Laws

Expanding Brackets

Factorising

Negative and Fractional Indices

Surds

Rationalising Denominators

Cubic Graphs

Quartic Graphs

Reciprocal Graphs

Points of Intersection

Translating Graphs

Stretching Graphs

Transforming Functions

Algebraic Fractions

Dividing Polynominals

The Factor Theorem

Mathematical Proof

Methods of Proof

Angles in all four quadrants

Exact values of trigonometrical ratios

Trigonometric Identities

Trigonometric Equations

Harder Trigonometric Equations

Equations and Identities

Integrating x^{n}

Indefinite Integrals

Finding Functions

Definite Integrals

Areas Under Curves

Areas under the x-axis

Areas Between Curves and Lines

Solving Quadratic Equations

Completing the Square

Functions

Quadratic Graphs

The Discriminant

Modelling with Quadratics

Y = mx + c

Equations of Straight Lines

Parallel and Perpendicular Lines

Length and Area

Modelling with Straight Lines

Pascal's Triangle

Factorial Notation

The Binomial Expansion

Solving Binomial Problems

Binomial Estimation

Vectors

Representing Vectors

Magnitude and Direction

Position Vectors

Solving Geometric Problems

Modelling with Vectors

Exponential Functions

Y = e^{x}

Exponential Modelling

Logarithms

Laws of Logarithms

Solving Equations using Logarithms

Working with Natural Logarithms

Logarithms and Non-Linear Data

Linear Simultaneous Equations

Quadratic Simultaneous Equations

Simultaneous Equations on Graphs

Linear Inequalities

Quadratic Inequalities

Inequalities on Graphs

Regions

Midpoints and Perpendicular Bisectors

Equation of a Circle

Intersections of Straight Lines and Circles

Use Tangent and Chord Properties

Circles and Triangles

The Cosine Rule

The Sine Rule

Areas of Triangles

Solving Triangle Problems

Graphs of sine, cosine and tangent

Transforming Trigonometric Graphs

Gradients of Curves

Finding the Derivative

Differentiating X^{n}

Differentiating Quadratics

Differentiating Functions With 2+ Terms

Gradients, Tangents, and Normals

Increasing and Decreasing Functions

Second Order Derivatives

Stationary Points

Sketching Gradient Functions

Modelling with Differentiation

Populations and Samples

Sampling

Non-random Sampling

Types of Data

The Large Data Set

Measures of Central Tendency

Other Measures of Location

Measures of Spread

Variance and Standard Deviation

Coding

Outliers

Box Plots

Cumulative Frequency

Histograms

Comparing Data

Correlation

Linear Regression

Calculating Probabilities

Venn Diagrams

Mutually Exclusive and Independent Events

Tree Diagrams

Probability Distributions

The Binomial Distribution

Cumulative Probabilities

Hypothesis Testing

Critical Values

One-Tailed Tests

Two-Tailed Tests

Constructing a Model

Modelling Assumptions

Quantities and Units

Working with Vectors

Displacement-Time Graphs

Velocity-Time Graphs

Constant Acceleration Formulae 1

Constant Acceleration Formulae 2

Vertical Motion Under Gravity

Force Diagrams

Forces as Vectors

Forces and Acceleration

Motion in 2 Dimensions

Connected Particles

Pulleys

Functions of Time

Using Differentiation

Maxima and Minima Problems

Using Integration

Constant Acceleration Formulae

Proof by Contradiction

Partial Fractions

Repeated Factors

Algebraic Division

Expanding (1 + x)^{n}

Expanding (a + bx)^{n}

Using Partial Fractions

Addition Formulae

Using the Angle Addition Formulae

Double-angle Formulae

Solving Trigonometric Equations

Simplifying acosx +/- bsinx

Proving Trigonometric Identities

Modelling with Trigonometric Function

Locating Roots

Iteration

The Newton-Raphson Method

Applications to Modelling

The Modulus Function

Functions and Mapping

Composite Functions

Inverse Functions

y = |f(x)| and y = f(|x|)

Combining Transformations

Solving Modulus Problems

Radian Measure

Arc Length

Areas of Sectors and Segments

Small Angle Approximations

Parametric Equations

Using Trigonometric Identities

Curve Sketching

Modelling with Parametric Equations

Integrating Standard Functions

Integrating f(ax + b)

Reverse Chain Rule

Integration by Substitution

Integration by Parts

Finding Areas

The Trapezium Rule

Solving Differential Equations

Modelling with Differential Equations

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Sum to Infinity

Sigma Notation

Recurrence Relations

Modelling with Series

Secant, Cosecant, and Cotangent

Graphs of sec x, cosec x, and cot x

Using sec x, cosec x, and cot x

Inverse Trigonometric Functions

Differentiating sin x and cos x

Differentiating Exponentials and Logarithms

The Chain Rule

The Product Rule

The Quotient Rule

Differentiating Trigonometric Functions

Parametric Differentiation

Implicit Differentiation

Using Second Derivatives

Rates of Change

3D Coordinates

Vectors in 3D

Application to Mechanics

Exponential Models

Measuring Correlation

Hypothesis Testing for Zero Correlation

Moments

Resultant Moments

Equilibrium

Centres of Mass

Tilting

Static Particles

Modelling with Statics

Friction and Static Particles

Static Rigid Bodies

Dynamics and Inclined Planes

Set Notation

Conditional Probability

Probability Formulae

Resolving Forces

Inclined Planes

Friction

Vectors in Kinematics

Vector Methods with Projectiles

Variable Acceleration in One Dimension

Differentiating Vectors

Integrating Vectors

The Normal Distribution

Finding Probabilities for Normal Distributions

Inverse Normal Distribution Function

Standard Normal Distribution

Finding μ and σ

Approximating a Binomial Distribution

Hypothesis Testing with the Normal Distribution

Horizontal Projection

Horizontal & Vertical Components

Projection at Any Angle

Projection Motion Formulae

Solve

1. Questions?

2. Question?

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