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Higher Mathematics
Exponentials & Logarithms
Exponential Functions (5:01)
Graphs of Exponential Functions (8:01)
Logarithmic Functions (5:42)
Graphs of Logarithmic Functions (6:57)
āeā and the Natural Logarithm (5:33)
Rules of Logarithms (7:22)
Switching Between Exponential and Log Form (7:02)
Exponential and Logarithmic Equations 1 (9:57)
Exponential and Logarithmic Equations 2 (9:53)
Exponential and Logarithmic Word Problems (11:06)
Quick Practice Questions
Full Practice Questions
Reference Notes
Trigonometry
The CAST Method (8:57)
Trigonometric Functions Overview (9:47)
Exact Values for Common Angles ā 30, 45, 60 & 90 (10:16)
Exact Values for Multiples of Common Angles (9:54)
Understanding Radians (11:43)
Exact Values for Angles Given in Radians (7:18)
The Addition Formulas (9:43)
The Wave Function (13:27)
The Double Angle Formulas (8:49)
Proving Trigonometric Identities (10:49)
Quick Practice Questions
Full Practice Questions
Reference Notes
Functions
Graph Transformations ā General Rules (12:14)
Graph Transformations for Trigonometric Functions (15:14)
Graphs of Quadratic Functions in Completed Square Form (13:57)
The Domain & Range of a Function (15:56)
Composite Functions (9:14)
Inverse Functions (8:38)
Quick Practice Questions
Full Practice Questions
Reference Notes
Vectors
Vectors Review (5:51)
Unit Vectors (6:53)
Vector Pathways (6:59)
Parallel Vectors (7:54)
Collinear Points (10:41)
The Co-ordinates of the Internal Division of a Line (9:11)
Scalar Product & Angle Between Vectors (13:39)
Quick Practice Questions
Full Practice Questions
Reference Notes
Polynomials
Polynomial Expressions (8:01)
Polynomial Factors (8:47)
Factorising using Synthetic Division with a Given Factor (9:06)
Factorising using Synthetic Division without a Given Factor (9:19)
The Remainder Theorem for Polynomials (8:25)
The Graph of a Cubic Function (9:37)
Intersection of a Polynomial with the X-Axis and the Y-Axis (10:49)
Determining Where a Straight Line and Polynomial Intersect (9:34)
Using the Discriminant to Determine Unknown Coefficients (8:55)
Quick Practice Questions - Polynomials
Quick Practice Questions - Quadratics
Full Practice Questions
Reference Notes
Trigonometric Equations
Solving Trigonometric Equations in Degrees (Calculator) (11:06)
Solving Trigonometric Equations in Degrees (Non-Calculator) (10:44)
The CAST Method in Radians (7:38)
Solving Trigonometric Equations in Radians (Calculator) (10:44)
Solving Trigonometric Equations in Radians (Non-Calculator) (12:42)
Solving Trigonometric Equations Involving Double Angles (12:31)
Quick Practice Questions
Full Practice Questions
Reference Notes
Differentiation
Introduction to Differentiation (6:23)
The Power Rule for Differentiation (9:22)
The Gradient Function (11:26)
The Equation of a Tangent to a Curve (9:48)
The Chain Rule for Differentiation (8:38)
Differentiating Trigonometric Functions (6:00)
Rates of Change (8:16)
Determining Where a Function is Increasing or Decreasing (8:32)
Determining the Stationary Points of a Function (10:38)
Determining the Nature of the Stationary Points of a Function (12:50)
Sketching the Graph of a Function (17:37)
Quick Practice Questions - Power Rule & Chain Rule
Quick Practice Questions - Stationary Points
Full Practice Questions
Reference Notes
Integration
Introduction to Integration (8:07)
The Power Rule for Integration (9:53)
The Chain Rule for Integration (10:32)
Integrating Trigonometric Functions (7:49)
Solving Simple Differential Equations (11:18)
Definite Integrals and the Fundamental Theorem of Calculus (12:33)
Quick Practice Questions - Power Rule & Chain Rule
Quick Practice Questions - Definite Integrals
Full Practice Questions
Reference Notes
Straight Lines
Parallel and Perpendicular Lines (12:45)
Collinearity Using Gradients (11:04)
Gradient and Angles (12:50)
Medians, Altitudes and Perpendicular Bisectors (12:41)
Finding Medians, Altitudes and Perpendicular Bisectors (9:52)
Quick Practice Questions
Full Practice Questions
Reference Notes
Circles
Introduction to Circles (6:15)
The Basic Equation of a Circle (12:49)
The General Equation of a Circle (11:30)
The Equation of a Tangent to a Circle (15:52)
Intersecting Circles (9:38)
Lines Intersecting Circles (12:03)
Quick Practice Questions
Full Practice Questions
Reference Notes
Recurrence Relations
Introduction to Recurrence Relations (8:39)
Determining a Recurrence Relation (10:46)
Calculating a Term from a Recurrence Relation (7:38)
Determining Whether a Recurrence Relation has a Limit (9:12)
Finding the Limit of a Recurrence Relation (12:36)
Quick Practice Questions
Full Practice Questions
Reference Notes
Applications
Maximum and Minimum Values on a Closed Interval (14:09)
Determining Optimal Solutions (Optimization) (12:52)
Finding the Area Under a Curve (12:08)
Finding the Area Between Two Curves (17:43)
Quick Practice Questions - Optimization
Quick Practice Questions - Area Under a Curve
Full Practice Questions
Additional Resources
Formula List
2023 Paper 1 Video Solutions (46:34)
2023 Paper 2 Video Solutions (69:36)
2022 Paper 1 Video Solutions (76:59)
2019 Paper 1 Video Solutions (86:17)
2019 Paper 2 Video Solutions (96:38)
2018 Paper 1 Video Solutions (69:03)
2018 Paper 2 Video Solutions (79:02)
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Graph Transformations for Trigonometric Functions
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