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
Additional Resources
