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Complete and Continue
Year 1 Pure
Proof
Set and Interval Notation (17:02)
Proof by deduction (18:22)
Proof by exhaustion (9:28)
Disproof by counterexample (3:07)
Stage 3: Mixed Exam Questions on Proof
Indices
Basic indices (fractional and negative indices) (13:22)
Writing one number as the power of another (9:31)
Stage 3: Mixed Exam Questions on Indices
Surds
Arithmetic with surds (8:19)
Simplifying surds (12:20)
Rationalising the denominator of surds (15:35)
Stage 3: Mixed Exam Questions on Surds
Quadratic Equations
Completing the square (17:00)
Simultaneous equations involving quadratics (6:21)
Stealth quadratics (equations reducible to quadratics) (11:37)
Stage 3: Mixed Exam Questions on Quadratic Equations
Inequalities and the Discriminant
Quadratic Inequalities (16:16)
The Discriminant (17:10)
Stage 3: Mixed Exam Questions on Inequalities and the Discriminant
Polynomials and the Factor Theorem
Polynomial Division (20:38)
The Factor Theorem (22:00)
Stage 3: Polynomials and the Factor Theorem Exam Questions
Transformations
Identifying and Describing Transformations (14:57)
Transformations of Graphs (8:18)
Equations of Transformed Functions (5:06)
Transformations of Standard Curves (19:02)
Stage 3: Mixed Exam Questions on Transformations
Straight Line Geometry
Length, Gradient and Midpoint of a Straight Line (15:58)
General Equation of a Straight Line (17:41)
Stage 3: Straight Line Geometry Mixed Exam Practice
Circle Geometry
Equation of a Circle (8:50)
Tangents and Normals to Circles (5:28)
Stage 3: Circle Geometry Mixed Exam Practice
Exponentials and Logarithms
Basic Logarithms and Laws of Logarithms (16:29)
Inverse Logarithms and Solving Logarithmic Equations (14:06)
Solving Exponential Equations (11:10)
Exponential and Logarithmic Graphs (10:44)
The Number e and Natural Logarithms (6:21)
Modelling Exponential Growth and Decay (14:03)
Reduction to Linear Form (15:36)
Stage 3: Exponentials and Logarithms Mixed Exam Practice
Trigonometry
Multiple Solutions to Trigonometric Equations (36:33)
Trigonometric Identities (38:49)
The Sine Rule, Cosine Rule and Area of a Triangle (8:49)
Stage 3: Trigonometry Mixed Exam Practice
Binomial Expansion
Binomial Expansion (28:03)
Stage 3: Binomial Expansion Mixed Exam Practice
Differentiation
Differentiation from First Principles (22:30)
Basic Differentiation (11:16)
Tangents and Normals to Curves (16:02)
Finding and Classifying Stationary Points (22:36)
Practical Applications of Differentiation (Optimisation Problems) (17:55)
Stage 3: Differentiation Mixed Exam Practice
Integration
Definite and Indefinite Integration (20:21)
Area Between a Curve and the x-axis (14:00)
Differential Equations (Finding the Equation of a Curve Given dy/dx) (2:33)
Stage 3: Integration Mixed Exam Practice
Vectors
Properties of Vectors (Addition, Magnitude and Direction) (27:58)
Parallel and Perpendicular Vectors (15:48)
Geometrical Problems Involving Vectors (21:01)
Stage 3: Vectors Mixed Exam Questions
Proof by exhaustion
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