Polynomials

Coefficients
Nested form
Dividing polynomials
Factor theorem
Synthetic division
Solving equations
Interactive :Synthetic Division

Quadratics

Completing the square
Quadratic formula
Discriminant
Tangency

Sequences

nth term
Recurrence relations
Convergence
Linear recurrences
Solving recurrences

Exponentials

Exponentials
Growth functions
Decay functions

Logarithms

Logarithms
Converting bases
Logarithm laws
Log and Ln
Logarithmic equations

Graphs of Logs and Exponentials

Graphing exponential & logarithmic functions
Logarithmic–linear scales
Log–log graphs
Interactive Exponential / log functions - graphs Interactive Log/log and log/linear graphs

Basic Functions

Functions
Set notation
Domain, codomain & range
One‑to‑one correspondence
Inverse function
Inverse function (algebraic)
Inverse function (graphical)
Composite functions

Graphs

Simple graphs of functions
Reflections, translations, etc.
y = −f(x)
y = f(−x)
y = f(x ± c)
y = f(x) ± d
y = f(bx)
y = f(x)/b
y = a f(x)
y = f(x)/a
y = a f(bx ± c) ± d
y = x
y = |f(x)|
Sketching polynomial equations
Interactive - Reflection
y = −f(x)

Background & First Principles

Differentiation
Gradients
Notation
First principles (Adv Higher)

Main Differentiation

xⁿ
axⁿ
Derivatives of sums
Differentiating sin & cos
(x + a)ⁿ
(ax + b)ⁿ
Chain rule

Tangents

Tangent gradients
Tangent equations

Stationary Points

Increasing / decreasing
Stationary points
Finding stationary points
Nature tables
Second derivative test
Closed intervals (Adv Higher)

Curve Sketching

Curve sketching
Graphing derived functions
Interactive - Stationary Points

Applications of Differentiation

Applications
Optimisation problems
Rectilinear motion
Newton’s equations of motion

Basic Integration

Integral calculus
Basic rules
Indefinite integrals
Definite integrals
Area function
Fundamental theorem of calculus
Integrating trig functions
∫(ax + b)ⁿ dx
Differential equations

Area under Curves

Area under curve (x‑axis)
Area between two graphs
Formula for area between curves
Areas of graphs
Areas under curves

The Circle

x² + y² = r²
Centre & radius
Diameter method
General equation
Circle equation from chords

Circle – Other

Tangents
Touching circles
Intersections
Interactive - Touching Circles

Straight Line

y − b = m(x − a)
General equation of a line
Gradient = tanθ
Distance formula
Midpoint formula
Perpendicular lines
Collinearity

Straight Lines & Circles

Altitudes
Centroid
Circumcentre
Circumcircle
Concurrency
Median
Orthocentre
Perpendicular bisector
Interactive – Median, Altitude, Orthocentre etc.

Basic Vectors

Scalar & vector quantities
Components
Magnitude
Position vectors
Unit vector
Zero vector
Equal vectors
Adding vectors
Subtracting vectors
Perpendicular vectors
Interactive – Vector Magnitudes

Other Vectors

Collinearity
Angle between vectors
Scalar product
Section formula

General

Solving trig equations (algebra)
Amplitude & period
Sketching trig graphs
Compound angle examples
Interactive – CAST Diagram
Interactive – y = A sin(x + φ)
Interactive – Graphs y = a·sin/cos/tan(bx + c) + d
Interactive – Trig Function Grapher

Radians

Radians Degrees → radians
Exact values (deg & rad)
Using exact values
Conversion table
Interactive – Radians

Wave Theory

Adding two waves
Subtracting two waves
Express as cos(x + a)
Express as sin(x − a)
Express as sin(x + a)

Formulae

Trig refresher
Trigonometric identities
Compound formulae
Double angle
Half angle
Product formulae
Multiple angle formulae

Deriving Formulae

Deriving addition formulae
Deriving double angle formulae
Deriving multiple angle formulae
Deriving half angle formulae