The Mathcentre website www.mathcentre.ac.uk was set up in the early 2000s to provide a universal set of teaching and learning resources. From the site, handouts can be downloaded, that usually contain a tutorial on the topic, examples and practice exercises and solutions. It also contains further resources and videos. It is aimed at the post 16 education and it contains material that a continuing student studying maths post-16 and STEM 18-19 could typically undertake, ie levels 3-4 in UK education terms.
The material in the sections on arithmetic and algebra, will normally be met pre-16, but these also provide useful recap material. However the section on algebraic fractions would normally be post-16.
Topics: decimals, fractions, percentages, ratios, rules of arithmetic, surds and roots.
Basic Mathematics:
Introduction to Mathematical Language,
Expanding and removing brackets,
Powers or Indices,
Logarithms.
Introduction to Equations and Formulae:
Substitution and Formulae,
Simultaneous Linear Equations,
Transposition of Formulae.
Understanding Quadratics:
Factorizing Quadratic Expressions,
Completing the Square,
Solving Quadratic Equations.
Understanding Algebraic Fractions:
Simplifying Algebraic Fractions,
Partial Fractions,
Polynomial Division.
The material in the sections on trigonomery and functions, will normally be partially met pre-16, but these also provide useful recap material
and extend the topics to areas usually covered post-16..
Basic: Angles - Degrees and Radians, Pythagoras' Theorem,
Trigonometric Ratios: Sine, Cosine & Tangent,
Trigonometric Identities based on Pythagoras Theorem,
Trigonometric Ratios in All Quadrants. Trigonometrical Formulae:
Triangle Formulae: Sine & Cosine,
Addition Formulae,
Double Angle Formulae. Introduction to functions, Equations of Straight Lines,
Polynomial Functions,
Exponential and Logarithm Functions,
Trigonometric Functions, Hyperbolic Functions, Limits of Functions,
Inverse Functions,
Polar co-ordinates. Trigonometry
Functions and Graphs
Differentiation from First Principles, Differentiation Using a Table, Product Rule, Quotient Rule, Chain Rule, Maxima and Minima of Functions.
Integration Using a Table, Integration by parts, Integration by substitution, Integration by partial fractions, Finding areas by integration, Volumes of solids of revolution.
Understanding Complex Numbers: Definition of Complex Numbers,
The Complex Conjugate,
Argand Diagram,
Polar Form,
Exponential Form,
Conversion between Cartesian and Polar/Exponential Form.
Arithmetic with Complex Numbers: Arithmetic in Cartesian Form,
Multiplication and Division in Polar Form,
Addition and Subtraction in Polar Form.
Matrices - what is a matrix ?, Symmetric matrices and the transpose of a matrix, Addition, subtraction and scalar multiplication of matrices, Multiplying matrices, Determinants, Inverse of a Matrix, Solving a system of equations using the inverse, Cramer’s Rule.
Introduction to vectors, The scalar product, The vector product.
Arithmetic and Geometric Progressions, Sigma Notation, Pascal's Triangle and the Binomial Expansion, Sum of an Infinite Series.
Arithmetic and Geometric Progressions, First and second order ODEs.