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Higher Maths Study Pack
Introduction
Higher Topic List
Unit 1 - Expressions and Functions
Exponentials and Logarithms
Trigonometric Functions Overview
Trigonometric Exact Values
Working with Radians
The Addition Formulas
The Wave Function
The Double Angle Formulas
Proving Trigonometric Identities
Graphs of Transformed Functions
Domain and Range of a Function
Composite Functions
Inverse Functions
Collinearity
Scalar Product and Angle Between Vectors
Unit 2 - Relationships
Polynomials
The Remainder Theorem
The Graph of a Cubic Function
X and Y Intercepts
Straight Line and Polynomial Intersection
Using the Discriminant
Trigonometric Equations in Degrees
Trigonometric Equations in Radians
Trigonometric Equations involving Identities
The Power Rule for Differentiating
The Chain Rule for Differentiation
Differentiating Trigonometric Functions
The Equation of a Tangent to a Curve
Rates of Change
The Stationary Points of a Function
The Nature of Stationary Points of a Function
Determining Where a Function is Increasing and Decreasing
The Power Rule for Integration
The Chain Rule for Integration
Integrating Trigonometric Functions
Solving Simple Differential Equations
Definite Integrals
Unit 3 - Applications
Parallel and Perpendicular Lines
Collinearity Using Gradients
Gradients and Angles
Medians, Altitudes and Perpendicular Bisectors
The Equation of a Circle
The Equation of a Tangent to a Circle
Intersection with Circles
Recurrence Relations
The Limit of a Recurrence Relation
Maximum and Minimum Values on a Closed Interval
Optimization
Finding the Area Under a Curve
Determining Where a Function is Increasing and Decreasing
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