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Class X: Mathematics

Download NCERT Books for UPSC & State PSC Exams: Class X (Mathematics)

Real Numbers
Introduction
Euclid’s Division Lemma
The Fundamental Theorem of Arithmetic
Revisiting Irrational Numbers
Revisiting Rational Numbers and Their Decimal Expansions
Summary
Polynomials
Introduction
Geometrical Meaning of the Zeroes of a Polynomial
Relationship between Zeroes and Coefficients of a Polynomial
Division Algorithm for Polynomials
Summary
Pair of Linear Equations in Two Variables
Introduction
Pair of Linear Equations in Two Variables
Graphical Method of Solution of a Pair of Linear Equations
Algebraic Methods of Solving a Pair of Linear Equations
Substitution Method
Elimination Method
Cross-Multiplication Method
Equations Reducible to a Pair of Linear Equations in Two Variables
Summary
Quadratic Equations
Introduction
Quadratic Equations
Solution of a Quadratic Equation by Factorisation
Solution of a Quadratic Equation by Completing the Square
Nature of Roots
Summary
Arithmetic Progressions
Introduction
Arithmetic Progressions
nth Term of an AP
Sum of First n Terms of an AP
Summary
Triangles
Introduction
Similar Figures
Similarity of Triangles
Criteria for Similarity of Triangles
Areas of Similar Triangles
Pythagoras Theorem
Summary
Coordinate Geometry
Introduction
Distance Formula
Section Formula
Area of a Triangle
Summary
Introduction to Trigonometry
Introduction
Trigonometric Ratios
Trigonometric Ratios of Some Specific Angles
Trigonometric Ratios of Complementary Angles
Trigonometric Identities
Summary
Some Applications of Trigonometry
Introduction
Heights and Distances
Summary
Circles
Introduction
Tangent to a Circle
Number of Tangents from a Point on a Circle
Summary
Constructions
Introduction
Division of a Line Segment
Construction of Tangents to a Circle
Summary
Areas Related to Circles
Introduction
Perimeter and Area of a Circle — A Review
Areas of Sector and Segment of a Circle
Areas of Combinations of Plane Figures
Summary
Surface Areas and Volumes
Introduction
Surface Area of a Combination of Solids
Volume of a Combination of Solids
Conversion of Solid from One Shape to Another
Frustum of a Cone
Summary
Statistics
Introduction
Mean of Grouped Data
Median of Grouped Data
Graphical Representation of Cumulative Frequency Distribution
Summary
Probability
Introduction
Probability — A Theoretical Approach
Summary
Appendix A1 : Proofs in Mathematics
Introduction
Mathematical Statements Revisited
Deductive Reasoning
Conjectures, Theorems, Proofs and Mathematical Reasoning
Negation of a Statement
Converse of a Statement
Proof by Contradiction
Summary
Appendix A2 : Mathematical Modelling
Introduction
Stages in Mathematical Modelling
Some Illustrations
Why is Mathematical Modelling Important?
Summary
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