A-LEVEL PURE MATHEMATICS FULL COURSE

About Course

This A Level Pure Mathematics course is meticulously designed to prepare students for the Cameroon GCE and similar global examinations. The course covers essential topics such as quadratic functions, inequalities, sequences and series, functions and mappings, binary relations, and vector geometry. Through detailed lessons, practical examples, and interactive problem-solving sessions, students will develop a strong understanding of advanced mathematical concepts and their applications.

Theory of Quadratic Functions and Equations
Understanding and solving quadratic equations
Relationships between roots and coefficients
Graphical analysis and transformations of quadratic functions
Inequalities and Inequations
Solving linear and quadratic inequalities
Graphing absolute value functions and systems of inequalities
Sequences and Series
Mastery of arithmetic and geometric progressions
Summation techniques and applications
Functions and Mappings
Domain, codomain, and range of functions
Exploring different types of mappings and their properties
Binary Relations
Cartesian products, equivalence relations, and ordered pairs
Vector Geometry
Vector operations, dot products, and 3D geometry applications

Course Content

THEORY OF QUADRATIC FUNCTIONS AND QUADRATIC EQUATIONS

Quadratic expressions and Quadratic equations

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Solve quadratic equations

00:00
Relationship between roots and coefficients of a quadratic equation

00:00
Symmetric properties of the roots of a quadratic equation

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Graphs and properties of quadratic Functions

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Simple transformations

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Applications of nature of roots

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Practice Problems

INEQUALITIES AND INEQUATIONS

SEQUENCES AND SERIES

Introduction to Sequences and series

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Arithmetic progressions: The nth term of an A.P and Arithmetic Mean (AM)

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Arithmetic progressions: Sum of an A.P and the General term

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Geometric progressions: The nth term of a G.P and geometric mean (G.M

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Geometric progressions: Sum of a G.P and Geometric Series

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Geometric progressions: Sum to infinity and applications

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Convergence of geometric sequences

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Summation of simple finite series and use of partial fractions

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Practice problems

FUNCTIONS AND MAPPINGS

BINARY RELATIONS

VECTOR GEOMETRY

Algebraic operations, magnitude and direction in vectors

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Scalar and dot product of two vectors / angle between two vectors

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Equations of a line in 3D

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Intersection of lines

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Perpendicular distance on line from point

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Equations of planes

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Angle between planes and Intersection of planes

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Intersection of lines and planes / angle

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Perpendicular distance from point to plane

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FINAL EXAM

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About Course

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Course Content

THEORY OF QUADRATIC FUNCTIONS AND QUADRATIC EQUATIONS

Quadratic expressions and Quadratic equations

Solve quadratic equations

Relationship between roots and coefficients of a quadratic equation

Symmetric properties of the roots of a quadratic equation

Graphs and properties of quadratic Functions

Simple transformations

Applications of nature of roots

Practice Problems

INEQUALITIES AND INEQUATIONS

Basic Rules on solving Inequalities

Linear and Quadratic inequalities

Inequalities Involving rational functions

Absolute value inequalities

Graphs of absolute value functions and inequalities

System of inequalities

Practice problems

SEQUENCES AND SERIES

Introduction to Sequences and series

Arithmetic progressions: The nth term of an A.P and Arithmetic Mean (AM)

Arithmetic progressions: Sum of an A.P and the General term

Geometric progressions: The nth term of a G.P and geometric mean (G.M

Geometric progressions: Sum of a G.P and Geometric Series

Geometric progressions: Sum to infinity and applications

Convergence of geometric sequences

Summation of simple finite series and use of partial fractions

Practice problems

FUNCTIONS AND MAPPINGS

Domain, codomain and range of a function

Parity and Composition of functions

Periodicity and continuity of a function

Surjective, Injective and Bijective mappings

Practice Problems

BINARY RELATIONS

The notation of binary Relations and Ordered Pairs

Cartesian product of two sets and Properties of relations

Equivalence Relations and Equivalence classes

Ordered Relations i.e. Partial, Total Order and Strict Order

Practice problems

VECTOR GEOMETRY

Algebraic operations, magnitude and direction in vectors

Scalar and dot product of two vectors / angle between two vectors

Equations of a line in 3D

Intersection of lines

Perpendicular distance on line from point

Equations of planes

Angle between planes and Intersection of planes

Intersection of lines and planes / angle

Perpendicular distance from point to plane

FINAL EXAM

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