Pure Maths Help
Listed below are tutorials that will offer pure maths help and core maths help with your course of study
I have also included some past paper exam questions with worked solutions which I hope offer you more pure maths help.
Prior Knowledge
Algebra Basics
 Expanding a single bracket
 Expanding two or more brackets
 Squaring a bracket
 Terms in expressions and equations
 Identity or equation  what is the difference?
 Linear equations with a positive xterm
 Linear equations with a negative xterm
 Linear equations with two xterms
 Linear equations with brackets
 Fractional linear equations
Trigonometry Introduction
Indices
 Introduction to indices (exponents)
 Multiplication rules for indices
 Division rule for indices
 Negative indices
 Fractions raised to a negative index
 Rational (fractional) indices
 Simplifying terms with negative powers
 Expressing terms in the form ax^{n}
 Equations in which the power has to be found
 Summary of indices
 Exam Questions  Indices
Algebra and Functions
Identity or Equation?
Solving Linear Equations
Indices
 Introduction to indices (exponents)
 Multiplication rules for indices
 Division rule for indices
 Negative indices
 Fractions raised to a negative index
 Rational (fractional) indices
 Simplifying terms with negative powers
 Expressing terms in the form ax^{n}
 Equations in which the power has to be found
 Summary of indices
 Exam Questions  Indices
Functions
Factorising
Completing the Square
Polynomials
Inequalities 1
Graph Transformations
Sequences and Series
Working with Sequences and Series
Arithmetic Progressions
Geometric Series
Binomial Expansion
 Binomial expansion
 Binomial expansion formula
 Exam Questions  Binomial expansion, basic expansions
 Exam Questions  Binomial expansion, comparing coefficients
 Exam Questions  Binomial expansion, estimating a value
 Exam Questions  Binomial expansion, other
 Binomial expansion for rational powers
 Validity
 Exam Questions  Binomial expansion
 Using partial fractions with the binomial expansion
 Exam Questions  Partial fractions with the binomial expansion
Algebra and Functions 2
Algebraic Long Division
Factor and Remainder Theorems
Working with Functions
Graph Transformations and Asymptotes
Even and Odd and Periodic Functions
Logarithmic and Exponential Functions
Exponential Functions and Logarithms
The Exponential Function e^{x} and Natural Log Functions
Modelling Curves of the form y=kx^{n} and y=ka^{x}
Trigonometry
Pythagoras’ Theorem
Trigonometry: RightAngled Triangles
Trigonometric Ratios
Trigonometric Graphs and Transformations
Applications of Trigonometry
Trigonometric Equations
Trigonometric Identities
Sec θ, Cosec θ and Cot θ
Inverse trigonometric functions
Identities & Equations – Pythagorean Type
Identities – Addition type
Identities & Equations – Double angle type
Identities – Half angle type
Identities – Triple angle type
Identities – Factor Formulae
Identities & Equations – Harmonic Formulae
Smallangle Approximations
Exam Questions – Mixed trigonometry
Differentiation 1
Differentiation – Introduction
Tangents and Normals
Stationary Points
Increasing and Decreasing functions
Standard Differentials
The Chain Rule
The Product and Quotient Rules
More Standard Differentials
The Reciprocal Function of dy/dx
Exam Questions – Differentiation
Exponential Functions
Parametric Functions
Implicit Functions
Integration 1
Integration – Introduction
Equations of Curves
Definite Integration
Integration – Common Functions
 Integration:(ax+b)^{n} types
 Exam Questions  Integration:(ax+b)^{n} types
 Integrating exponential functions e^{x}, e^{ax} and e^{(ax+b)}
 Exam Questions  Integrating exponential functions e^{x}, e^{ax} and e^{(ax+b)}
 Integrating reciprocal functions 1/x and 1/(ax+b)
 Exam Questions  Integrating reciprocal functions 1/x and 1/(ax+b)
 Integrals of the form : f '(x)/f(x)
 Integrals of the form : f'(x)e^{f(x)}
Integrals of Trigonometric Functions
Integrals involving Partial fractions
Integration by Substitution
Integrating Products of the form f[g(x)]g'(x) by inspection
Integration by Parts
Mixed Examples & Exam Question – Integration
Applications of Integration – Area bound by a curve
Applications of Integration – Volumes of revolution
 Volume of revolution about the xaxis
 Exam Questions  Volume of revolution about the xaxis
 Volume of revolution about the xaxis generated between curves
 Volume of Revolution about the yaxis
 Exam Questions  Volume of Revolution about the yaxis
 Volume of Revolution about the yaxis generated between curves
 Volume of revolution for a curve given in parametric form
 Exam Questions  Volume of revolution: parametric form
Numerical Solution of Equations
Solution of Equations by Numerical methods
 Graphical methods
 Change of sign
 Bisection method for locating a root in a given interval
 Exam Questions  Bisection Method
 Linear interpolation method for locating a root in a given interval
 Exam Questions  Linear Interpolation
 Iteration
 Exam Questions  Iteration
 NewtonRaphson method for locating a root in a given interval
 Exam Questions  NewtonRaphson
Rational Expressions
Rational Expressions – Simplifying
 Simplifying algebraic fractions
 Exam Questions  Simplifying a rational expression
 Addition and subtraction of algebraic fractions
 Exam Questions  Addition & subtraction
 Multiplication of algebraic fractions
 Further simplifying of 'stacked fractions'
 Division of algebraic fractions
 Exam Questions  Algebraic long division
First Order Linear Differential Equations
Separating the variables
Forming differential equations
Vectors
Vectors
Scalar Product (Dot Product)
Vector Equations of Lines
Exam Questions – Vectors
Permutations and Combinations
Permutations and Combinations
The Language of Mathematics
The Language of Mathematics
Sets
Venn Diagrams
Cartesian Product
Logic
Books that you may find useful for more maths help.
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