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Year 2 Pure
Rational Expressions
Simplifying Algebraic Fractions (11:50)
Higher Order Polynomial Division (5:47)
Partial Fractions (17:23)
Stage 3: Rational Expressions Exam Practice
General Binomial Expansion
Expanding expressions of the form (1+bx)^n (24:31)
Expanding expressions of the form (a+bx)^n (12:32)
Stage 3: Binomial Expansion Exam Practice
Sequences and Series
Nth Term of an Arithmetic Sequence (11:49)
Summing Arithmetic Sequences (22:49)
Finite Geometric Sequences (18:32)
Summing Infinite Geometric Sequences (9:31)
Inductive Sequences (6:34)
Sigma Notation and Mixed Sequence Problems (20:09)
Stage 3: Sequences Exam Practice
Functions
Domain and Range of Functions (13:24)
Inverses of Functions (24:07)
Composite Functions (7:49)
Multiple Transformations of Functions (6:11)
Stage 3: Functions Exam Practice
The Modulus Function
Sketching Curves of Modulus Functions (10:10)
Solving Equations and Inequalities Involving the Modulus Function (15:02)
Stage 3: Modulus Function Exam Practice
Trigonometry Radians, Circle Sectors and Triangles
Working With Radians (11:38)
Circle Sectors (7:08)
Stage 3: Radians, Circle Sectors and Triangles Exam Practice
Trigonometry: Small Angle Approximations and Inverse Trig Functions
Small Angle Approximations (6:41)
Inverse Trigonometric Functions (8:16)
Stage 3: Small Angle Approximation and Inverse Trig Functions Exam Practice
Trigonometry: The Compound and Double Angle Formulae
Sine and Cosine Addition and Subtraction Formulae (17:33)
Tangent Addition and Subtraction Formulae (7:18)
The Sine Double Angle Formula (8:38)
The Cosine Double Angle Formulae (9:05)
The Tangent Double Angle Formula (1:41)
The Form Rsin(x+a) and Rcos(x+a) (24:29)
Stage 3: Compound and Double Angle Formulae Exam Practice
Trigonometry: Secant, Cosecant and Cotangent
Introduction to the reciprocal trig functions (17:20)
Pythagorean trig identities (16:40)
Stage 3: Reciprocal Trig Functions Exam Practice
Differentiation
The Chain Rule for Differentiation (17:34)
Differentiating Exponentials and Natural Logarithms (9:26)
The Product and Quotient Rule (21:21)
dx/dy as the Reciprocal of dy/dx and Differentiating a^x (14:23)
Differentiating Trigonometric Functions (15:17)
Implicit Differentiation (23:42)
Stage 3: Rules for Differentiation Exam Practice
Concave and Convex Curves/Points of Inflection
Concave and Convex Curves/Points of Inflection (23:56)
Stage 3: Concave and Convex Curves/Points of Inflection Exam Practice
Further Integration
Standard Integrals and Using the Formulae Sheet (32:24)
Integrating the Squares of sin(x), cos(x), sec(x) and tan(x) (8:21)
Integrations Requiring Partial Fractions (8:40)
Integration By Parts (23:37)
Stage 3: Further Integration Mixed Exam Practice
Integration By Substitution
Introduction to Integration By Substitution (13:47)
Integration By Substitution (with Exponentials, Natural Logs and Trig) (5:11)
Definite Integration By Substitution (4:00)
Further Trigonometric Integration by Substitution (18:21)
Stage 3: Integration By Substitution Exam Practice
Parametric Equations
Working With Parametric Equations and Cartesian Equations (10:57)
Differentiating Parametric Equations (10:10)
Integrating Parametric Functions (8:27)
Stage 3: Parametric Equations Mixed Exam Questions
Connected Rates of Change
Connected Rates of Change (6:43)
Stage 3: Connected Rates of Change Exam Practice
Proof By Contradiction
Proof By Contradiction (20:11)
Stage 3: Proof By Contradiction Exam Practice
Differential Equations
Solving Differential Equations (10:14)
Forming and Solving Differential Equations (7:39)
Stage 3: Differential Equations Exam Practice
Numerical Methods
Locating Roots with Change of Sign Method (8:24)
Fixed Point Iteration (32:07)
Newton-Raphson Method (15:30)
Trapezium Rule (14:51)
Stage 3: Numerical Methods Exam Practice
Vectors in 3d
Basic Vector Properties in 3d (13:24)
3d Vectors and Angles (6:13)
The Cosine Double Angle Formulae
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