Year 1 Pure
(Just click on the picture above for the full pdf to download)
(1) Indices
(2) Expanding Brackets
(3) Factorising Expressions
(4) More Indices (Negative and Fractional)
(5) Working with Surds
(6) Solving Quadratic Equations
(7) Completing the Square for Quadratics Expressions
(8) Function Notation
(9) Sketching Quadratic Graphs
(10) The Discriminant for Quadratic Equations
(11) Applications of Quadratics Equations
(12) Solving Linear Simultaneous Equations
(13) Linear & Non-Linear Simultaneous Equations
(14) Graphing Simultaneous Equations
(15) Linear Inequalities
(16) Quadratic Inequalities
(17) Graphing Inequalities
(18) Shading Inequalities
(19) Cubic Graphs
(20) Quartic Graphs
(21) Reciprocal Graphs
(22) The Intersection of Graphs
(23) Transforming Graphs (Translations)
(24) Transforming Graphs (Stretching/Reflecting)
(25) Straight Line Graphs in the form
(26) More Straight Line Graphs
(27) Straight Line Graphs (Parallel & Perpendicular)
(28) The Geometry of Straight Lines
(29) The Application of Linear Graphs
(30) Circle Geometry Midpoint & Perpendicular
(31) The Equation of a Circle
(32) Circles and Straight Lines (Intersections)
(33) Circles (Tangents and Chords)
(34) Circles and Triangles
(35) Algebraic Fractions
(36) Polynomial Division
(37) The Factor and Remainder Theorem
(38) An Introduction to Mathematical Proof
(39) Methods of Proof
(40) Binomial Expansion (Using Pascal’s Triangle)
(41) Binomial Expansion (Factorial Notation)
(42) Binomial Expansion (The Method)
(43) Binomial Expansion (Problem Solving)
(44) Binomial Expansion (Estimations and Approximations)
(45) The Cosine Rule
(46) The Sine Rule
(47) Areas of a Triangles
(48) Triangles (Problem Solving)
(49) Sine, Cosine & Tangent Graphs
(50) Transforming Graphs (Trigonometry)
(51) The ‘CAST’ Diagram for Trig Ratios
(52) Trigonometry (Exact Values)
(53) Proving Trigonometric Identities
(54) Solving Basic Trigonometric Equations
(55) More Challenging Trigonometric Equations
(56) Using Identities to Solve Trig Equations
(57) Vectors (Introduction)
(58) Vector Notation (Column and i and j form)
(59) Vectors (Magnitude and Direction)
(60) Vectors (Position and Direction Vectors)
(61) Vector Geometry
(62) Application of Vectors
(63) Differentiation (Gradients of Curves)
(64) Differentiation from 1st Principles
(65) Differentiating (Basic Powers of x)
(66) Differentiation (Quadratic Expression)
(67) Differentiation (Multiple Terms)
(68) Differentiation (Gradients, Tangents and Normals)
(69) Differentiation (Increasing and Decreasing Functions)
(70) Differentiation (Stationary Points)
(71) Differentiation (Gradient Functions
(72) The Applications of Differentiation
(73) Integration (Basic Expressions)
(74) Indefinite Integrals
(75) Integration (Finding c and Finding Functions)
(76) Integration (Definite Integrals)
(77) Integration (Basic Areas Under Curves)
(78) Integration (‘Negative and Positive Areas’)
(79) Integration (Areas between Curves and Lines)
(80) Basic Exponential Functions
(81) ‘The’ Exponential Function
(82) Applications of Basic Exponential Models
(83) Logarithms (Simplifying & Evaluating)
(84) Logarithms (The Log Laws)
(85) Logarithms (Log and Exponential Equations)
(2) Expanding Brackets
(3) Factorising Expressions
(4) More Indices (Negative and Fractional)
(5) Working with Surds
(6) Solving Quadratic Equations
(7) Completing the Square for Quadratics Expressions
(8) Function Notation
(9) Sketching Quadratic Graphs
(10) The Discriminant for Quadratic Equations
(11) Applications of Quadratics Equations
(12) Solving Linear Simultaneous Equations
(13) Linear & Non-Linear Simultaneous Equations
(14) Graphing Simultaneous Equations
(15) Linear Inequalities
(16) Quadratic Inequalities
(17) Graphing Inequalities
(18) Shading Inequalities
(19) Cubic Graphs
(20) Quartic Graphs
(21) Reciprocal Graphs
(22) The Intersection of Graphs
(23) Transforming Graphs (Translations)
(24) Transforming Graphs (Stretching/Reflecting)
(25) Straight Line Graphs in the form
(26) More Straight Line Graphs
(27) Straight Line Graphs (Parallel & Perpendicular)
(28) The Geometry of Straight Lines
(29) The Application of Linear Graphs
(30) Circle Geometry Midpoint & Perpendicular
(31) The Equation of a Circle
(32) Circles and Straight Lines (Intersections)
(33) Circles (Tangents and Chords)
(34) Circles and Triangles
(35) Algebraic Fractions
(36) Polynomial Division
(37) The Factor and Remainder Theorem
(38) An Introduction to Mathematical Proof
(39) Methods of Proof
(40) Binomial Expansion (Using Pascal’s Triangle)
(41) Binomial Expansion (Factorial Notation)
(42) Binomial Expansion (The Method)
(43) Binomial Expansion (Problem Solving)
(44) Binomial Expansion (Estimations and Approximations)
(45) The Cosine Rule
(46) The Sine Rule
(47) Areas of a Triangles
(48) Triangles (Problem Solving)
(49) Sine, Cosine & Tangent Graphs
(50) Transforming Graphs (Trigonometry)
(51) The ‘CAST’ Diagram for Trig Ratios
(52) Trigonometry (Exact Values)
(53) Proving Trigonometric Identities
(54) Solving Basic Trigonometric Equations
(55) More Challenging Trigonometric Equations
(56) Using Identities to Solve Trig Equations
(57) Vectors (Introduction)
(58) Vector Notation (Column and i and j form)
(59) Vectors (Magnitude and Direction)
(60) Vectors (Position and Direction Vectors)
(61) Vector Geometry
(62) Application of Vectors
(63) Differentiation (Gradients of Curves)
(64) Differentiation from 1st Principles
(65) Differentiating (Basic Powers of x)
(66) Differentiation (Quadratic Expression)
(67) Differentiation (Multiple Terms)
(68) Differentiation (Gradients, Tangents and Normals)
(69) Differentiation (Increasing and Decreasing Functions)
(70) Differentiation (Stationary Points)
(71) Differentiation (Gradient Functions
(72) The Applications of Differentiation
(73) Integration (Basic Expressions)
(74) Indefinite Integrals
(75) Integration (Finding c and Finding Functions)
(76) Integration (Definite Integrals)
(77) Integration (Basic Areas Under Curves)
(78) Integration (‘Negative and Positive Areas’)
(79) Integration (Areas between Curves and Lines)
(80) Basic Exponential Functions
(81) ‘The’ Exponential Function
(82) Applications of Basic Exponential Models
(83) Logarithms (Simplifying & Evaluating)
(84) Logarithms (The Log Laws)
(85) Logarithms (Log and Exponential Equations)
Year 2 Pure
(Just click on the picture above for the full pdf to download)
(1) Proof by Contradiction
(2) Algebraic Fractions (Simplifying)
(3) Partial Fractions
(4) Partial Fractions with Repeated Factors
(5) Partial Fractions Requiring Algebraic Division
(6) Introduction to the Modulus Function
(7) Mappings and Functions
(8) Composite Functions
(9) Inverse Functions
(10) modulus functions
(11) Multiple Graph Transformations
(12) Solving Modulus Equations and Inequalities
(13) Arithmetic Sequences
(14) Arithmetic Series
(15) Geometric Sequences
(16) Geometric Series
(17) Geometric Series. The Sum to Infinity
(18) Sigma Notation for Series
(19) Recurrence Relations and Periodic Sequences
(20) Application of Series
(21) Binomial Expansion of the form (1+ax)
(22) Binomial Expansion of the form (A+BX)
(23) Binomial Expansions Using Partial Fractions
(24) Using Radians as a Measurement of Angles
(25) Arc Lengths (Radians)
(26) Areas of Sectors and Segments (Radians)
(27) Solving Trigonometric Equations (Using Radians)
(28) Small Angle Approximations in Trig
(29) Secant, Cosecant and Cotangent Ratios in Trig
(30) Sketching the Graphs of sec, cosec and cot
(31) Equations and Identities using sec, cosec and cot
(32) Reciprocal Trigonometric Identities
(33) Inverse Trig Functions
(34) Addition Formulae
(35) Applying the Addition Formulae in Trig
(36) Double Angle Formula
(37) Solving Trigonometric Equations
(38) acos(x) + Bsin(x)
(39) Proving Trigonometric Identities
(40) Applications of Trigonometric Functions
(41) Parametric Equations Evaluating and Converting
(42) Trigonometric Identities for Parametric Equations
(43) Sketching Parametric Curves
(44) Points of Intersection of Parametric Curves
(45) Applications of Parametric Equations
(46) Differentiating sin and cos Functions
(47) Differentiating Exponentials & Logs
(48) Differentiation using the Chain Rule
(49) Differentiation using the Product Rule
(50) Differentiation using the Quotient Rule
(51) Differentiating other Trigonometric Functions
(52) Differentiating Parametric Equations
(53) Implicit Differentiation
(54) Using the 2nd Derivative
(55) Rates of Change (Differentiation)
(56) Numerical Methods Locating Roots
(57) Numerical Methods Iteration to Locate Roots
(58) Numerical Methods Newton-Raphson Method
(59) Applications of Numerical Methods
(60) Integrating Standard Functions (Logs and Trig)
(61) Integrating Functions of the form f(ax+b)
(62) Integrating using Trigonometric Identities
(63) Integration by Inspection (Reverse Chain Rule)
(64) Integration by Substitution
(65) Integration by Parts
(66) Integration using Partial Fractions
(67) Integration to Find Areas
(68) Integration using the Trapezium Rule
(69) Solving Differential Equations
(70) The Applications of Differential Equations
(71) 3D Coordinates
(72) Vectors in 3D
(73) Vector Geometry
(74) Vectors in Mechanics
(2) Algebraic Fractions (Simplifying)
(3) Partial Fractions
(4) Partial Fractions with Repeated Factors
(5) Partial Fractions Requiring Algebraic Division
(6) Introduction to the Modulus Function
(7) Mappings and Functions
(8) Composite Functions
(9) Inverse Functions
(10) modulus functions
(11) Multiple Graph Transformations
(12) Solving Modulus Equations and Inequalities
(13) Arithmetic Sequences
(14) Arithmetic Series
(15) Geometric Sequences
(16) Geometric Series
(17) Geometric Series. The Sum to Infinity
(18) Sigma Notation for Series
(19) Recurrence Relations and Periodic Sequences
(20) Application of Series
(21) Binomial Expansion of the form (1+ax)
(22) Binomial Expansion of the form (A+BX)
(23) Binomial Expansions Using Partial Fractions
(24) Using Radians as a Measurement of Angles
(25) Arc Lengths (Radians)
(26) Areas of Sectors and Segments (Radians)
(27) Solving Trigonometric Equations (Using Radians)
(28) Small Angle Approximations in Trig
(29) Secant, Cosecant and Cotangent Ratios in Trig
(30) Sketching the Graphs of sec, cosec and cot
(31) Equations and Identities using sec, cosec and cot
(32) Reciprocal Trigonometric Identities
(33) Inverse Trig Functions
(34) Addition Formulae
(35) Applying the Addition Formulae in Trig
(36) Double Angle Formula
(37) Solving Trigonometric Equations
(38) acos(x) + Bsin(x)
(39) Proving Trigonometric Identities
(40) Applications of Trigonometric Functions
(41) Parametric Equations Evaluating and Converting
(42) Trigonometric Identities for Parametric Equations
(43) Sketching Parametric Curves
(44) Points of Intersection of Parametric Curves
(45) Applications of Parametric Equations
(46) Differentiating sin and cos Functions
(47) Differentiating Exponentials & Logs
(48) Differentiation using the Chain Rule
(49) Differentiation using the Product Rule
(50) Differentiation using the Quotient Rule
(51) Differentiating other Trigonometric Functions
(52) Differentiating Parametric Equations
(53) Implicit Differentiation
(54) Using the 2nd Derivative
(55) Rates of Change (Differentiation)
(56) Numerical Methods Locating Roots
(57) Numerical Methods Iteration to Locate Roots
(58) Numerical Methods Newton-Raphson Method
(59) Applications of Numerical Methods
(60) Integrating Standard Functions (Logs and Trig)
(61) Integrating Functions of the form f(ax+b)
(62) Integrating using Trigonometric Identities
(63) Integration by Inspection (Reverse Chain Rule)
(64) Integration by Substitution
(65) Integration by Parts
(66) Integration using Partial Fractions
(67) Integration to Find Areas
(68) Integration using the Trapezium Rule
(69) Solving Differential Equations
(70) The Applications of Differential Equations
(71) 3D Coordinates
(72) Vectors in 3D
(73) Vector Geometry
(74) Vectors in Mechanics