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Class 11 Mathematics notes

Written by Hassan Raza (Mathematics)

Chapter notes with key points, definitions, short questions and model answers. Each chapter links to practice questions.

Chapter notes

Number systems and complex numbers

Natural, integer, rational and irrational numbers, and complex numbers: the imaginary unit, operations, conjugate, modulus, and the properties of complex numbers. Chapter notes

Sets, functions and groups

Sets and their operations, Venn diagrams, relations, functions and their types, inverse and composite functions, binary operations, and the idea of a group with simple examples and properties. Chapter notes

Matrices and determinants

Matrices and their types, operations, transpose, determinants of order 2 and 3, minors and cofactors, adjoint and inverse, and solving linear equations by the matrix method and Cramer's rule. Chapter notes

Quadratic equations

Standard form, solving by factoring, completing the square and the quadratic formula, the discriminant and nature of roots, sum and product of roots, forming equations, cube roots of unity and simultaneous equations. Chapter notes

Sequences and series

Sequences and series, arithmetic and geometric progressions, nth terms and sums, means, harmonic progressions, relation between A.M., G.M. and H.M., and the sum to infinity of a geometric series. Chapter notes

Permutations, combinations and probability

The counting principle, factorials, permutations and combinations with their formulas, arrangements with repeated objects, sample space and events, the definition of probability, and the addition rule for events. Chapter notes

Mathematical induction and binomial theorem

The principle of mathematical induction with proofs of sums and divisibility, the binomial theorem for a positive integer index, the general term, middle terms, Pascal's triangle and the binomial series for approximations. Chapter notes

Fundamentals of trigonometry

Angles in degrees and radians, arc length and sector area, trigonometric ratios and functions, signs in quadrants, values at special angles, fundamental identities, and trigonometric functions of allied angles.

Class 11 Mathematics practice questions