AH Maths CfE Course Documents
Here are the latest versions of the CfE documents for the Advanced Higher Mathematics course :
AH Maths Course Specification (May 2019, Version 2.0) |
AH Exam Paper Information
AH Maths Specimen QP 1 |
AH Maths Specimen QP 2 |
AH Maths Lessons
M. Patel
Methods in Algebra and Calculus Lessons
Partial Fractions Lessons
001 - Rational Functions and Partial Fractions |
002 - Long Division and Partial Fractions |
Differential Calculus Lessons
001 - Chain Rule Revision |
002 - Product and Quotient Rules |
003 - Derivatives of Tan x and Reciprocal Trigonometric Functions |
004 - Derivatives of Exponential and Logarithmic Functions |
005 - Derivatives of Inverse (Trigonometric) Functions |
006 - Higher-Order Derivatives |
007 - Implicit Differentiation |
008 - Logarithmic Differentiation |
009 - Parametric Differentiation |
010 - Planar Motion |
011 - Related Rates |
Integral Calculus Lessons
001 - Standard Integrals |
002 - Integration by Substitution |
003 - Integration of Rational Functions |
004 - Integration by Parts |
005 - Reduction Formulae |
Differential Equations Lessons
001 - Separable Differential Equations |
002 - Integrating Factor Differential Equations |
003 - 2nd-Order Homogeneous Differential Equations |
004 - 2nd-Order Non-Homogeneous Differential Equations |
Applications of Algebra and Calculus Lessons
Binomial Theorem Lessons
001 - Binomial Coefficients |
002 - The Binomial Theorem |
Arithmetic and Algebra of Complex Numbers Lessons
001 - Arithmetic of Complex Numbers |
002 - Solving Complex Quadratics and Other Simple Equations |
003 - Solving Complex Polynomials |
Sequences and Series Lessons
001 - Arithmetic Sequences |
002 - Arithmetic Series |
003 - Geometric Sequences |
004 - Finite Geometric Series |
005 - Infinite Series, Partial Sums and Infinite Geometric Series |
006 - Power Series |
007 - Maclaurin Series from First Principles |
008 - Combinations and Compositions of Maclaurin Series |
009 - Differentiation and Integration of Maclaurin Series |
010 - Finite Sums |
Proof by Mathematical Induction Lessons
001 - Mathematical Induction 1 (Finite Sums) |
002 - Mathematical Induction 2 (Divisibility) |
003 - Mathematical Induction 3 (Inequalities) |
004 - Mathematical Induction 4 (Differentiation) |
Properties of Functions Lessons
Even, Odd and Neither Functions |
The Second Derivative Test, Concavity and Points of Inflexion |
Inverse Functions |
Modulus Graphs, Critical Points and Extrema |
Asymptotes and Sketching Rational Functions |
Applications of Calculus Lessons
Rectilinear Motion |
Areas and Volumes |
Geometry, Proof and Systems of Equations Lessons
Matrices and Systems of Equations Lessons
001 - Gaussian Elimination |
002 - Ill-Conditioned Systems |
003 - Basic Matrix Algebra |
004 - Matrix Multiplication |
005 - Determinants and Inverses of 2 x 2 Matrices |
006 - Determinants and Inverses of 3 x 3 Matrices |
007 - Transformation Matrices |
Vectors, Lines and Planes Lessons
001 - The Vector Product and Scalar Triple Product |
002 - Equations of Planes |
003 - Equations of Lines and Their Intersection |
004 - Intersections of Lines and Planes |
Further Proof Techniques Lessons
001 - Direct Proof |
002 - Proof by Counterexample (aka Disproof) |
003 - Proof by Contraposition and Proof by Contradiction |
Number Theory Lessons
001 - The Euclidean Algorithm and the GCD |
002 - The Fundamental Theorem of Arithmetic and Number Bases |
Geometry of Complex Numbers Lessons
001 - Polar Form, Multiplication and Division |
002 - Complex Loci |
003 - De Moivre's Theorem and Powers |
004 - nth Roots of a Complex Number |
AH Maths Questions
AH Maths Practice Unit Assessments
M. Patel
Methods in Algebra and Calculus Practice Assessments
Methods in Algebra and Calculus - Practice 1 |
Methods in Algebra and Calculus - Practice 1 Solns |
Methods in Algebra and Calculus - Practice 2 |
Methods in Algebra and Calculus - Practice 2 Solns |
Methods in Algebra and Calculus - Practice 3 |
Methods in Algebra and Calculus - Practice 3 Solns |
Applications of Algebra and Calculus Practice Assessments
Applications of Algebra and Calculus - Practice 1 |
Applications of Algebra and Calculus - Practice 1 Solns |
Applications of Algebra and Calculus - Practice 2 |
Applications of Algebra and Calculus - Practice 2 Solns |
Applications of Algebra and Calculus - Practice 3 |
Applications of Algebra and Calculus - Practice 3 Solns |
Geometry, Proof and Systems of Equations Practice Assessments