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Class 12 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

Functions and limits

Functions, domain and range, composite and inverse functions, the idea of a limit, limit theorems, important limits and continuity, with worked examples. Chapter notes

Differentiation

The derivative as a limit and as a rate of change, rules of differentiation, derivatives of trigonometric, exponential and logarithmic functions, implicit and parametric differentiation, higher derivatives, and maxima and minima. Chapter notes

Integration

Integration as the reverse of differentiation, standard integrals, substitution, integration by parts, partial fractions, definite integrals with properties, and the area under a curve. Chapter notes

Analytic geometry

Distance, midpoint and section formulas, slope of a line, forms of the equation of a straight line, angle between lines, parallel and perpendicular lines, distance from a point to a line, and the area of a triangle. Chapter notes

Conic sections

The circle, parabola, ellipse and hyperbola as sections of a cone: definitions, standard equations, centre, foci, vertices, directrix, eccentricity, latus rectum, and finding equations from given data. Chapter notes

Vectors

Scalars and vectors in two and three dimensions, unit vectors i, j, k, magnitude, addition, scalar product, vector product, angle between vectors, projection, work done, and area of a parallelogram and a triangle. Chapter notes

Inequalities and linear programming

Linear inequalities in one and two variables, graphing half planes, feasible regions and corner points, and the method of linear programming to find the greatest or least value of an objective function.

Class 12 Mathematics practice questions