Mathematics Hip-Hop Academy
A-Level Pure Mathematics
Professional Mathematics Notes
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10 ChaptersStructured PartsWorked ExamplesExamination Practice
Explore Your Chapters
01 Chapter 01: Numerical Concepts Indices, logarithms, surds, fractional powers and numerical foundations ⌄
Study parts
- Part 1 — Indices Read lesson
- Part 2 — Logarithms Read lesson
- Part 3 — Surds and Fractional Surds Read lesson
02 Chapter 02: Differentiation Differentiation rules and applications, including product, quotient and chain rules ⌄
Study parts
- Part 1 — Introduction and First Principles Read lesson
- Part 2 — Chain Rule Read lesson
- Part 3 — Differentiation Read lesson
03 Chapter 03: Integration Elementary integration, substitution, trigonometric integrals, partial fractions, applications and differential equations ⌄
Study parts
- Part 1 — Foundations and Elementary Integration Read lesson
- Part 2 — Substitution Read lesson
- Part 3 — Trigonometric Integration Read lesson
- Part 4 — Partial Fractions and Integration by Parts Read lesson
- Part 5 — Applications of Integration Read lesson
- Part 6 — Differential Equations Read lesson
04 Chapter 04: Trigonometry Trigonometric functions, identities, equations, graphs and applications ⌄
Study parts
- Part 1 — Trigonometric Functions, Angles and Graphs Read lesson
- Part 2 — Trigonometric Identities and Formulae Read lesson
- Part 3 — Trigonometric Equations and General Solutions Read lesson
- Part 4 — Compound Angles, Double Angles and Multiple Angles Read lesson
- Part 5 — Trigonometric Applications and Examination Practice Read lesson
05Chapter 05: CirclesCircle equations, tangents, chords and circle geometry⌄
Study parts
06Chapter 06: Coordinate GeometryStraight lines, distances, ratios, intersections, areas, loci and mixed practice⌄
Study parts
- Part 1 — Straight Lines, Gradients and Equations Read lesson
- Part 2 — Circles, Equations, Centre and Radius Read lesson
- Part 3 — Lines and Circles: Intersections, Tangents and Chords Read lesson
- Part 4 — Applications and Examination Practice Read lesson
- Part 5 — Conic Sections: Introduction to Parabolas Read lesson
- Part 6 — Conic Sections: The Ellipse Read lesson
- Part 7 — Conic Sections: The Hyperbola Read lesson
- Part 8 — Conic Sections: General Review and Mixed Examination Practice Read lesson
07Chapter 07: Roots of EquationsRelationships between roots and coefficients, and numerical/graphical methods⌄
Study parts
- Part 1 — Introduction, Vector Notation and Basic Operations Read lesson
- Part 2 — The Scalar Product, Angles and Perpendicular Vectors Read lesson
- Part 3 — Vector Equations of Lines, Parallel Lines and Intersections Read lesson
- Part 4 — Further Applications of Vectors Read lesson
- Part 5 — Planes in Three Dimensions Read lesson
08Chapter 08: Sequences & SeriesArithmetic and geometric progressions, infinite series and sigma notation⌄
Study parts
- Part 1 — Introduction and Arithmetic Progressions Read lesson
- Part 2 — Geometric Progressions Read lesson
- Part 3 — Sum of a Finite Arithmetic Series Read lesson
- Part 4 — Sum of a Finite Geometric Series Read lesson
- Part 5 — Sum to Infinity of a Geometric Series Read lesson
09Chapter 09: VectorsVector notation, operations, geometry and applications⌄
Study parts
- Part 1 — Introduction and Fractional Indices Read lesson
- Part 2 — Further Problems and Simplification of Indices Read lesson
- Part 3 — Surds and Their Simplification Read lesson
- Part 4 — Further Applications of Surds and Rationalisation Read lesson
- Part 5: Applications and Consolidation of Indices and Surds
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