Advanced Higher

	SCHOLAR
Mathematics 1	Formulae: Trig Calculus
Use algebraic skills	Factorials
	Pascal’s triangle.
	Binomial theorem
	Partial Fractions
elementary differentiation	Differentiation refresher
	First Principles
	Chain Rule.
	Product Rule.
	Quotient Rule
	secA cosecA cotA
	Exponentials & logs
	Higher derivatives
	Rectilinear Motion
	Extrema of functions
	Approximating roots
Integration	Integration refresher
	e^x, 1/x, sec²x
	Integration by substitution.
	Infinite integrals (Discontinuities)
	Areas under curves
	Area between curve and the x-axis
	Area between curve and the y-axis
	Volumes of revolution
	Distance, velocity & acceleration
Refresher of functions	Find the vertical asymptote of a rational function.
	Modulus function
	Inverse functions
	Polynomials
	Extrema
	Concavity and points of inflexion
	Odd and Even functions
	Asymptotes
Use matrix methods to solve systems of linear equations	Augmented matrix
Use matrix methods to solve systems of linear equations	Gaussian Elimination
Mathematics 2
Use further differentiation techniques	Inverse functions
	Inverse trig functions
	Implicit & Explicit functions
	Logarithmic functions
	Parametric equations
Use further integration techniques	Inverse trig functions
	Integration by parts
	Integration of rational functions
	Differential equations
	Integration of rational functions
Understand and use complex numbers	Complex Numbers
	Argand Diagrams
	Polar Form
	De Moivre's Theorem
	Roots of a complex number
Understand and use sequences and series	Recurrence relations
	Arithmetic sequences
	Geometric sequences
	Infinite series
Use standard methods to prove results in elementary number theory.	Direct Proof
	Proof by Contradiction
	Proof by contrapositive
	Proof by Induction
Mathematics 3
Use vectors in three dimensions	Vector product
	Scalar triple product
	Planes
	Vector Equations
	Intersections
Use matrix algebra	Reminders
	Matrix multiplication
	Determinants
	Inverse Matrix
	Transformation Matrices
Understand and use further aspects of sequences and series	Power Series
	D'Alembert's ratio test
	Maclaurin expansion
	Maclaurin series
	Iteration
	Newton-Raphson iteration
Solve further ordinary differential equations	First-order differential equations
Solve further ordinary differential equations	Second-order differential equations
Use further number theory and direct methods of proof	The division algorithm
	The Euclidean algorithm
	Diophantine equations
	Number bases