Chapter 1

Sets and Functions

Sets and their representations

medium • 1 min read

Types of sets and Subsets

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Venn diagrams and operations on sets

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Relations and Functions

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Domain, Codomain, and Range

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Chapter 2

Trigonometry

Angles and their measures (radians/degrees)

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Trigonometric functions and their properties

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Trigonometric functions of sum and difference of two angles

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Trigonometric Equations

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Properties of Triangles

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Chapter 3

Algebra: Complex Numbers and Quadratic Equations

Concept of iota and complex numbers

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Algebra of complex numbers

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Argand plane and polar representation

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Fundamental Theorem of Algebra

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Roots of a quadratic equation

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Chapter 4

Algebra: Permutations and Combinations

Fundamental principle of counting

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Factorial notation

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Permutations calculation

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Combinations calculation

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Applications to simple problems

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Chapter 5

Sequence and Series

Arithmetic Progression (A.P.)

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Geometric Progression (G.P.)

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General term and sum to n terms

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Arithmetic Mean (A.M.) and Geometric Mean (G.M.)

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Sum to infinity of a G.P.

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Chapter 6

Coordinate Geometry: Straight Lines

Slope of a line and angle between two lines

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Various forms of equations of a line

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General equation of a line

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Distance of a point from a line

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Family of lines

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Chapter 7

Coordinate Geometry: Conic Sections

Sections of a cone

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Equations of Circle and Parabola

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Equations of Ellipse and Hyperbola

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Standard equations and properties

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Latus rectum and eccentricity

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Chapter 8

Calculus: Limits and Derivatives

Intuitive idea of limit

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Limits of polynomials and rational functions

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Limits of trigonometric functions

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Derivative introduced as rate of change

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Derivative of polynomials and trigonometric functions

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Chapter 9

Statistics

Measure of dispersion

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Mean deviation

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Variance

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Standard deviation

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Analysis of frequency distributions

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Chapter 10

Probability

Random experiments and sample space

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Events and occurrence of events

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Axiomatic approach to probability

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Addition theorem of probability

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Mutually exclusive and exhaustive events

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Chapter 11

Mathematical Reasoning

Statements and logical operations

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Implications and equivalence

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Validating statements

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Understanding truth tables

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Evaluating compound statements

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Chapter 12

Linear Inequalities

Linear inequalities in one variable

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Algebraic solutions and number line

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Graphical representation of inequalities

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Linear inequalities in two variables

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System of linear inequalities

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