Exponentials & Logarithms
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Exponential Functions (5:01)
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Graphs of Exponential Functions (8:01)
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Logarithmic Functions (5:42)
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Graphs of Logarithmic Functions (6:57)
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‘e’ and the Natural Logarithm (5:33)
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Rules of Logarithms (7:22)
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Switching Between Exponential and Log Form (7:02)
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Exponential and Logarithmic Equations 1 (9:57)
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Exponential and Logarithmic Equations 2 (9:53)
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Exponential and Logarithmic Word Problems (11:06)
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Quick Practice Questions
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Full Practice Questions
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Reference Notes
Trigonometry
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The CAST Method (8:57)
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Trigonometric Functions Overview (9:47)
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Exact Values for Common Angles – 30, 45, 60 & 90 (10:16)
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Exact Values for Multiples of Common Angles (9:54)
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Understanding Radians (11:43)
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Exact Values for Angles Given in Radians (7:18)
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The Addition Formulas (9:43)
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The Wave Function (13:27)
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The Double Angle Formulas (8:49)
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Proving Trigonometric Identities (10:49)
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Quick Practice Questions
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Full Practice Questions
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Reference Notes
Functions
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Graph Transformations – General Rules (12:14)
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Graph Transformations for Trigonometric Functions (15:14)
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Graphs of Quadratic Functions in Completed Square Form (13:57)
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The Domain & Range of a Function (15:56)
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Composite Functions (9:14)
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Inverse Functions (8:38)
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Quick Practice Questions
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Full Practice Questions
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Reference Notes
Vectors
Polynomials
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Polynomial Expressions (8:01)
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Polynomial Factors (8:47)
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Factorising using Synthetic Division with a Given Factor (9:06)
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Factorising using Synthetic Division without a Given Factor (9:19)
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The Remainder Theorem for Polynomials (8:25)
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The Graph of a Cubic Function (9:37)
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Intersection of a Polynomial with the X-Axis and the Y-Axis (10:49)
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Determining Where a Straight Line and Polynomial Intersect (9:34)
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Using the Discriminant to Determine Unknown Coefficients (8:55)
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Quick Practice Questions - Polynomials
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Quick Practice Questions - Quadratics
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Full Practice Questions
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Reference Notes
Trigonometric Equations
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Solving Trigonometric Equations in Degrees (Calculator) (11:06)
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Solving Trigonometric Equations in Degrees (Non-Calculator) (10:44)
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The CAST Method in Radians (7:38)
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Solving Trigonometric Equations in Radians (Calculator) (10:44)
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Solving Trigonometric Equations in Radians (Non-Calculator) (12:42)
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Solving Trigonometric Equations Involving Double Angles (12:31)
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Quick Practice Questions
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Full Practice Questions
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Reference Notes
Differentiation
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Introduction to Differentiation (6:23)
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The Power Rule for Differentiation (9:22)
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The Gradient Function (11:26)
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The Equation of a Tangent to a Curve (9:48)
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The Chain Rule for Differentiation (8:38)
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Differentiating Trigonometric Functions (6:00)
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Rates of Change (8:16)
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Determining Where a Function is Increasing or Decreasing (8:32)
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Determining the Stationary Points of a Function (10:38)
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Determining the Nature of the Stationary Points of a Function (12:50)
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Sketching the Graph of a Function (17:37)
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Quick Practice Questions - Power Rule & Chain Rule
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Quick Practice Questions - Stationary Points
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Full Practice Questions
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Reference Notes
Integration
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Introduction to Integration (8:07)
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The Power Rule for Integration (9:53)
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The Chain Rule for Integration (10:32)
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Integrating Trigonometric Functions (7:49)
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Solving Simple Differential Equations (11:18)
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Definite Integrals and the Fundamental Theorem of Calculus (12:33)
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Quick Practice Questions - Power Rule & Chain Rule
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Quick Practice Questions - Definite Integrals
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Full Practice Questions
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Reference Notes
Straight Lines
Circles
Recurrence Relations
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Introduction to Recurrence Relations (8:39)
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Determining a Recurrence Relation (10:46)
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Calculating a Term from a Recurrence Relation (7:38)
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Determining Whether a Recurrence Relation has a Limit (9:12)
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Finding the Limit of a Recurrence Relation (12:36)
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Quick Practice Questions
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Full Practice Questions
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Reference Notes
Applications
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Maximum and Minimum Values on a Closed Interval (14:09)
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Determining Optimal Solutions (Optimization) (12:52)
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Finding the Area Under a Curve (12:08)
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Finding the Area Between Two Curves (17:43)
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Quick Practice Questions - Optimization
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Quick Practice Questions - Area Under a Curve
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Full Practice Questions
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Reference Notes
Exam Video Solutions
Exam Written Solutions (download link at the end of each document)
Past Exam Papers (download link at the end of each paper)
Past Exam Questions by Topic (download link at the end of each document)
Additional Resources
