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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)
‘e’ 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 – 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 – 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
Reference Notes
Exam Video Solutions
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)
Exam Written Solutions (download link at the end of each document)
2023 Higher Maths Solutions
2022 Higher Maths Solutions
2019 Higher Maths Solutions
2018 Higher Maths Solutions
2017 Higher Maths Solutions
2016 Higher Maths Solutions
2015 Higher Maths Solutions
2014 Higher Maths Solutions
2013 Higher Maths Solutions
Past Exam Papers (download link at the end of each paper)
2022 Higher Maths Papers
2019 Higher Maths Papers
2018 Higher Maths Papers
2017 Higher Maths Papers
2016 Higher Maths Papers
2015 Higher Maths Papers
2014 Higher Maths Papers
2013 Higher Maths Papers
Past Exam Questions by Topic (download link at the end of each document)
Circles
Composite Functions
Differentiation
Domain
Exponentials & Logarithms
Graph Transformations
Integration
Inverse Functions
Optimization
Polynomials
Quadratics
Rates of Change
Recurrence Relations
Straight Lines
Trigonometric Equations
Trigonometric Identities
Vectors
Additional Resources
Extended Formula List
Practice Paper A - Non-Calculator
Practice Paper B - Calculator
Key Skills Practice
Teach online with
The Chain Rule for Integration
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