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Class 10 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

Quadratic equations

The standard form, solving by factorisation, by completing the square and by the quadratic formula, equations that reduce to quadratics, and word problems. Chapter notes

Theory of quadratic equations

Solving quadratics, the discriminant and nature of roots, cube roots of unity, relations between roots and coefficients, symmetric functions, forming equations, and equations that reduce to quadratic form. Chapter notes

Variations

Ratio and proportion, properties of proportion such as componendo and dividendo, and direct, inverse and joint variation with the constant of variation, shown through word problems. Chapter notes

Partial fractions

Rational fractions, proper and improper forms, and splitting a fraction into partial fractions when the denominator has distinct linear factors, repeated linear factors, or an irreducible quadratic factor. Chapter notes

Sets and functions

Sets and their operations, Venn diagrams, De Morgan's laws, ordered pairs and Cartesian product, relations, and functions with domain, range, types and inverse of a function. Chapter notes

Basic statistics

Data and frequency distributions, measures of central tendency (mean, median, mode, weighted mean) and measures of dispersion (range, variance, standard deviation) for grouped and ungrouped data. Chapter notes

Introduction to trigonometry

Angles in degrees and radians, arc length and sector area, the six trigonometric ratios, values for 30°, 45° and 60°, fundamental identities, and simple problems on heights and distances. Chapter notes

Chords and tangents of a circle

Circle terms, theorems on chords and their distance from the centre, tangents and the radius, equal tangents from an external point, the tangent chord angle, and circles touching each other.

Class 10 Mathematics practice questions