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Notes
Mathematics
Pure Mathematics 1
Mathematics 9709
Pure Mathematics 1 — Revision Notes
Hover a chapter to open it, then pick a topic to start reading.
1
Quadratics
8 topics
1.1
Solving by factorising
1.2
Completing the square
1.3
The quadratic formula
1.4
The quadratic graph
1.5
The discriminant
1.6
Quadratic inequalities
1.7
Where a line meets a curve
1.8
Hidden quadratics
2
Functions
5 topics
2.1
Definition of a function (domain and range)
2.2
Composite functions
2.3
Inverse functions
2.4
The graph of a function and its inverse
2.5
Transformations of functions
3
Coordinate Geometry
5 topics
3.1
Length of a line segment and midpoint
3.2
Parallel and perpendicular lines
3.3
Equations of straight lines
3.4
The equation of a circle
3.5
Problems involving intersections of lines and circles
4
Circular Measure
4 topics
4.1
Radians and converting
4.2
Length of an arc
4.3
Area of a sector and a segment
4.4
Applications: shaded-region problems
5
Trigonometry
5 topics
5.1
Exact values and angles of any size
5.2
Graphs of sin, cos and tan
5.3
Inverse trigonometric functions
5.4
Trigonometric identities
5.5
Solving trigonometric equations
6
Series
4 topics
6.1
The binomial expansion
6.2
Arithmetic progressions
6.3
Geometric progressions
6.4
Infinite geometric series
7
Differentiation
6 topics
7.1
Derivatives and the gradient function
7.2
The chain rule
7.3
Tangents and normals
7.4
Stationary points and the second-derivative test
7.5
Increasing and decreasing functions
7.6
Rates of change
8
Integration
5 topics
8.1
Reversing differentiation & the constant
8.2
Integrating (ax + b)ⁿ
8.3
Definite integrals
8.4
Area under a curve
8.5
Area between curves & volumes of revolution
Mathematics Pure Mathematics 1 — Revision Notes · Conquer Your A Levels