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Mathematics
Revision Notes
Pure Mathematics 1
Mathematics · Cambridge 9709
Pure Mathematics 1
9 chapters · 116 lessons
Collection
Pure Mathematics 1
Pure Mathematics 2
Pure Mathematics 3
Mechanics
Probability & Statistics 1
Probability & Statistics 2
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01
Quadratics
13 lessons · 3 topic areas
01
Solving Quadratics
7 lessons
Solving Quadratic Equations
Factorising Quadratics by Hand
Fractions and Valid Roots
Completing the Square
Using the Completed Square Form
The Quadratic Formula
Quadratics in Another Form
02
The Quadratic Graph
3 lessons
The Graph and the Vertex
Quadratic Range and Restricted Domains
Quadratic Inequalities
03
Roots and Intersections
3 lessons
The Discriminant
Where a Line Meets a Curve
Tangency and Parameter Conditions
Practise this chapter
02
Functions
9 lessons · 3 topic areas
01
Function Language
3 lessons
Functions and Domains
One-One and Many-One Functions
The Range of a Function
02
Combining and Reversing Functions
3 lessons
Composite Functions
Inverse Functions
The graph of a function and its inverse
03
Transforming Graphs
3 lessons
The Four Function Transformations
Describing Function Transformations
Combined Function Transformations
Practise this chapter
03
Coordinate Geometry
10 lessons · 3 topic areas
01
Coordinates and Lines
4 lessons
Distance and Midpoint
Gradient and Line Relationships
Equations of Straight Lines
Perpendicular Bisectors
02
Circle Equations and Geometry
4 lessons
The Equation of a Circle
Expanded Circle Equations
Circles Through Three Points
Circle Geometry and Tangents
03
Line-Circle Problems
2 lessons
Line-Circle Intersections
Intersection and Tangency Conditions
Practise this chapter
04
Circular Measure
10 lessons · 3 topic areas
01
Radians and Sectors
3 lessons
Radians
Length of an Arc
Area of a Sector
02
Chords and Segments
2 lessons
Chords and Segment Perimeters
Area of a Circular Segment
03
Circular Geometry Problems
5 lessons
Exact Circular-Measure Problems
Shaded-Region Problems
Perimeters with Arcs and Straight Lines
Overlapping Circles
Fixed-Perimeter Sectors
Practise this chapter
05
Trigonometry
13 lessons · 3 topic areas
01
Ratios and Angles
3 lessons
Trig Ratios and the Unit Circle
Exact Values and Reference Angles
Finding Related Trig Ratios
02
Graphs and Inverses
5 lessons
Graphs of sin, cos and tan
Transforming Trigonometric Graphs
Reading Trigonometric Graphs
Inverse Trigonometric Functions
Inverses of Restricted Trig Functions
03
Equations and Identities
5 lessons
Solving Trigonometric Equations
Trigonometric Identities
Quadratic Trig Equations
Multiple-Angle Trig Equations
Equations with Trigonometric Identities
Practise this chapter
06
Series
15 lessons · 4 topic areas
01
Arithmetic Progressions
4 lessons
Arithmetic Progressions
Sums of Arithmetic Progressions
Finding Terms from Sums
Selecting and Counting AP Terms
02
Geometric Progressions
5 lessons
Geometric Progressions
Finite Geometric Series
Infinite Geometric Series
Selected Geometric Series
Modelling Geometric Series
03
Linked Progressions
1 lesson
Linked Progressions
04
Binomial Expansion
5 lessons
The Binomial Expansion
Finding Binomial Terms
Products of Binomial Expansions
Unknown Binomial Coefficients
Using Binomial Expansions
Practise this chapter
07
Differentiation
12 lessons · 3 topic areas
01
Derivatives and Gradients
2 lessons
Derivatives and the Gradient Function
Calculating Chord Gradients
02
Differentiation Rules
4 lessons
The Power Rule
Differentiating Roots and Fractions
The Chain Rule
Second Derivatives
03
Applying Derivatives
6 lessons
Finding Points with a Given Gradient
Tangents and Normals
Intersections of Tangents and Normals
Areas from Tangents and Normals
Unknown Coefficients from Gradients
Conditions on Derivatives
Practise this chapter
08
Further Differentiation
14 lessons · 3 topic areas
01
Function Behaviour
6 lessons
Increasing and Decreasing Functions
Stationary Points
Sketching Curves Using Stationary Points
Conditions from Stationary Points
Counting Stationary Points
Finding the Minimum Gradient
02
Optimisation
4 lessons
Optimisation
Maximising the Volume of a Box
Minimising Surface Area
Optimisation with Geometric Constraints
03
Rates of Change
4 lessons
Rates of Change
Connected Rates on a Curve
Finding Unknown Rates
Filling and Emptying Containers
09
Integration
20 lessons · 4 topic areas
01
Finding Original Functions
7 lessons
Reversing Differentiation
Preparing Expressions for Integration
Finding the Constant of Integration
Finding a Curve from Conditions
Integrating Twice
Integrating Powers of a Linear Bracket
Recognising Reverse Chain Rule
02
Definite Integrals and Area
6 lessons
Definite Integrals
Area Under a Curve
Integrating with Respect to y
Area Between Curves
Areas with Changing Boundaries
Finding an Unknown Integration Limit
03
Improper Integrals
2 lessons
Infinite Integration Limits
Integrals with Undefined Endpoints
04
Volumes of Revolution
5 lessons
Volumes of Revolution
Rotation About the y-axis
Hollow Solids of Revolution
Finding Unknowns from a Volume
Water Volumes in a Curved Container
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AS & A Level · 9709
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