A Level Mathematics

CIE A Level Maths revision notes made for the CIE (Cambridge International Examination) exam board. This covers all the topics and modules. 

Textbooks :

mechanics (m1 and m2)

statistics (s1 and s2)

pure maths(p1)

pure maths advanced(p2 and p3)

Summarise and concise notes:

P1

P3

S1

M1

Notes by topic 

year     Paper                      Chapter

1	Pure	Proof	Implication and Proof By Deduction
1	Pure	Proof	Sets and Interval Notation
1	Pure	Indices and Surds	Intro to Indices
1	Pure	Indices and Surds	Writing One Number as a Power of Another
1	Pure	Indices and Surds	Basic Surd Operations
1	Pure	Indices and Surds	Rationalising the Denominator
1	Pure	Quadratics	Factorising and Solving Quadratic Equations
1	Pure	Quadratics	Completing the Square
1	Pure	Quadratics	Simultaneous Equations
1	Pure	Quadratics	Linear Inequalities
1	Pure	Quadratics	Quadratic Inequalities
1	Pure	Quadratics	Stealth Quadratics
1	Pure	Polynomials	Polynomial Division and Factor Theorem
1	Pure	Graphs and Functions	Standard Graphs
1	Pure	Graphs and Functions	Sketching Cubic Graphs
1	Pure	Graphs and Functions	Sketching Quartic Graphs
1	Pure	Graphs and Functions	Transformations of Graphs and Functions
1	Pure	Straight Lines	Introduction to Straight Lines
1	Pure	Straight Lines	Parallel and Perpendicular Lines
1	Pure	Circles	Equations of Circles
1	Pure	Circles	Tangents and Normals To Circles
1	Pure	Exponentials and Logarithms	Intro to Logarithms
1	Pure	Exponentials and Logarithms	Laws of Logarithms
1	Pure	Exponentials and Logarithms	Solving Exponential Equations
1	Pure	Exponentials and Logarithms	Solving Logarithmic Equations
1	Pure	Exponentials and Logarithms	Logarithmic Graphs
1	Pure	Exponentials and Logarithms	Modelling with Exponentials
1	Pure	Exponentials and Logarithms	e and Natural Logarithms
1	Pure	Exponentials and Logarithms	Exponential Growth
1	Pure	Exponentials and Logarithms	Differential of exp(kx)
1	Pure	Binomial Expansion	Intro to Binomial Expansion
1	Pure	Binomial Expansion	Further Binomial Expansion
1	Pure	Trigonometry	Equations and Trig Identities
1	Pure	Trigonometry	Finding a Trigonometric Quantity Given Another
1	Pure	Trigonometry	Further Solving Trig Equations
1	Pure	Trigonometry	Solving Trig Equations
1	Pure	Vectors	Collinear Vectors
1	Pure	Vectors	Geometric Problems Using Vectors
1	Pure	Vectors	Magnitude and Direction of a Vector
1	Pure	Differentiation	Basic Differentiation of Powers of x
1	Pure	Differentiation	Differentiation (Tangents and Normals)
1	Pure	Differentiation	Differentiation from First Principles
1	Pure	Differentiation	Finding and Classifying Stationary Points
1	Pure	Differentiation	Further Differentiation from First Principles
1	Pure	Differentiation	Successive Approximatons in Differentiation
1	Pure	Differentiation	Modelling with Differentiation
1	Pure	Differentiation	Practical Differentiation Problems
1	Pure	Integration	Area Between a Curve and the x-Axis
1	Pure	Integration	Definite Integrals
1	Pure	Integration	Introduction to Integration
1	Pure	Integration	Solving Differential Equations
1	Mech	Kinematics	Variable Acceleration
1	Mech	Kinematics	S-T and V-T Graphs
1	Mech	Kinematics	Deriving SUVAT Equations
1	Mech	Kinematics	Intro to SUVAT
1	Mech	Kinematics	Motion Under Gravity
1	Mech	Forces and Motion	Newton’s Second Law (F=ma) in One and Two Dimensions
1	Mech	Forces and Motion	Resolving Perpendicular Forces
1	Mech	Connected Particles	Particles Over a Pulley
1	Mech	Connected Particles	Horizontally Connected Particles
1	Stats	Sampling	Sampling Techniques
1	Stats	Statistical Diagrams	Cumulative Frequency Diagrams
1	Stats	Statistical Diagrams	Histograms
1	Stats	Measures of Location and Spread	Outliers and Cleaning Data
1	Stats	Measures of Location and Spread	Averages and Spread
1	Stats	Correlation and Regression	Correlation and Regression
1	Stats	Discrete Random Variables	Discrete Random Variables
1	Stats	Discrete Random Variables	Calculating Binomial Probabilities
1	Stats	Discrete Random Variables	Cumulative Binomial Probabilities
1	Stats	Hypothesis Testing	One Tail Binomial Hypothesis Testing
1	Stats	Hypothesis Testing	Two Tail Binomial Hypothesis Testing
1	Stats	Hypothesis Testing	Critical Regions in Hypothesis Testing
1	Stats	Hypothesis Testing	Exam Questions Involving Trial and Improvement
2	Pure	Sequences and Series	Arithmetic Sequences
2	Pure	Sequences and Series	Geometric Sequences
2	Pure	Sequences and Series	Sum To Infinity of Geometric Sequences
2	Pure	Sequences and Series	Inductive Sequences
2	Pure	Rational Functions and Partial Fractions	Further Polynomial Division
2	Pure	Rational Functions and Partial Fractions	Rational Functions
2	Pure	Rational Functions and Partial Fractions	Partial Fractions
2	Pure	General Binomial Expansion	General Binomial Expansion
2	Pure	Functions	Composite Functions
2	Pure	Functions	Domain and Range
2	Pure	Functions	Mappings
2	Pure	Functions	Inverse of a Function
2	Pure	Functions	Multiple Transformations of Functions
2	Pure	Functions	Sketching Modulus Functions
2	Pure	Functions	Modulus Inequalities
2	Pure	Trigonometry	Radians, Circle Sectors and Triangles
2	Pure	Trigonometry	Inverse Trig Functions
2	Pure	Trigonometry	Compound Angle Formulae
2	Pure	Trigonometry	Double Angle Formulae
2	Pure	Trigonometry	Rcos(x+a) and Rsin(x+a)
2	Pure	Trigonometry	Small Angle Approximations
2	Pure	Trigonometry	Solving Equations With Reciprocal Trig Functions
2	Pure	Trigonometry	Further Reciprocal Trig Functions and Proofs
2	Pure	Differentiation	Chain Rule
2	Pure	Differentiation	Product Rule
2	Pure	Differentiation	Quotient Rule
2	Pure	Differentiation	Differentiating Trig Functions
2	Pure	Differentiation	Chain Rule
2	Pure	Differentiation	Implicit Differentiation
2	Pure	Integration	Standard Integrals
2	Pure	Integration	Methods for Trig Integration
2	Pure	Integration	Integration by Substitution
2	Pure	Integration	Integration by Parts
2	Pure	Integration	Integration Using Partial Fractions
2	Pure	Integration	Further Integration With Partial Fractions
2	Pure	Integration	Standard Integrals
2	Pure	Integration	Integration – Choosing the Correct Method
2	Pure	Integration	Area Between a Curve and the y-Axis
2	Pure	Integration	Area Between Two Curves
2	Pure	Proof	Proof By Contradiction
2	Pure	Differentiation	Convexity, Concavity and Points of Inflection
2	Pure	Parametric Equations	Intro to Parametric Equations
2	Pure	Parametric Equations	Parametric Differentiation
2	Pure	Parametric Equations	Parametric Integration
2	Pure	Differentiation	Connected Rates of Change
2	Pure	Integration	Further Integration and Area
2	Pure	Integration	Differential Equations – Separating the Variables
2	Pure	Numerical Methods	Fixed Point Iteration
2	Pure	Numerical Methods	Locating Roots with a Change of Sign
2	Pure	Numerical Methods	Newton Raphson Method
2	Pure	Numerical Methods	Trapezium Rule and Numerical Integration
2	Pure	Vectors	Vectors in 3d
2	Mech	Kinematics	Constant Acceleration in 2d
2	Mech	Kinematics	Variable Acceleration in 2d
2	Mech	Kinematics	Particles Projected Horizontally
2	Mech	Kinematics	Trajectory of a Projectile
2	Mech	Forces and Motion	Vectors in 3d
2	Mech	Forces and Motion	Resolving Non-Perpendicular Forces
2	Mech	Forces and Motion	Static Bodies in 2d
2	Mech	Forces and Motion	Forces on a Slope with Friction
2	Mech	Moments	Intro to Moments
2	Mech	Moments	Non-Uniform Rods
2	Stats	Conditional Probability	Probabilities and Venn Diagrams
2	Stats	Conditional Probability	Conditional Probabilities on Venn Diagrams
2	Stats	Conditional Probability	Conditional Probability on Tree Diagrams
2	Stats	Conditional Probability	Further Conditional Probability
2	Stats	Normal Distribution	Normal Distribution – Calculating Probabilities
2	Stats	Normal Distribution	Normal Distribution – Calculating Unknown Mean and Variance
2	Stats	Normal Distribution	Inverse Normal Distribution
2	Stats	Normal Distribution	Hypothesis Test for Sample Mean
2	Stats	Normal Distribution	Normal Approximation to Binomial Distribution
2	Stats	Correlation and Regression	Hypothesis Tests for Correlation

         

Some useful links that will surely help :

The Best site for detail learning will surely be:http://www.a-levelmathstutor.com/

For Past Papers and Marking Scheme visit: https://papacambridge.com/cie/sy-qp-ms/a-as-level/mathematics-9709/

The above resources will be more than enough to pass your a level exam with flying colors.Happy Studying. :)