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

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Content:

1. Real Numbers

• Introduction
• Euclid’s Division Lemma
• The Fundamental Theorem of Arithmetic
• Revisiting Irrational Numbers
• Revisiting Rational Numbers and Their Decimal Expansions
• Summary

2. Polynomials

• Introduction
• Geometrical Meaning of the Zeroes of a Polynomial
• Relationship between Zeroes and Coefficients of a Polynomial
• Division Algorithm for Polynomials
• Summary

3. 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

4. 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

5. Arithmetic Progressions

• Introduction
• Arithmetic Progressions
• nth Term of an AP
• Sum of First n Terms of an AP
• Summary

6. Triangles

• Introduction
• Similar Figures
• Similarity of Triangles
• Criteria for Similarity of Triangles
• Areas of Similar Triangles
• Pythagoras Theorem
• Summary

7. Coordinate Geometry

• Introduction
• Distance Formula
• Section Formula
• Area of a Triangle
• Summary

8. Introduction to Trigonometry

• Introduction
• Trigonometric Ratios
• Trigonometric Ratios of Some Specific Angles
• Trigonometric Ratios of Complementary Angles
• Trigonometric Identities
• Summary

9. Some Applications of Trigonometry

• Introduction
• Heights and Distances
• Summary

10. Circles

• Introduction
• Tangent to a Circle
• Number of Tangents from a Point on a Circle
• Summary

11. Constructions

• Introduction
• Division of a Line Segment
• Construction of Tangents to a Circle
• Summary

12. 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

13. 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

14. Statistics

• Introduction
• Mean of Grouped Data
• Mode of Grouped Data
• Median of Grouped Data
• Graphical Representation of Cumulative Frequency Distribution
• Summary

15. 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

Answers/Hints

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Courtesy: NCERT