This book covers the entire CBSE syllabus for Mathematics for Class X. With this reader-friendly guide, students can expect to master the fundamental and important concepts of the subject and also learn how to apply these concepts to solve problems. Using a mix of definitions, worked-out examples, proofs and different types of exercises, this invaluable aid will help engage and develop the students' interest in Mathematics and also enable them to excel in the examination.

*Salient features:*

- Over 925 solved examples and practice problems
- Over 1,230 subjective questions
- More than 560 multiple choice, fill in the blank, assertion–reason and true/false questions
- Questions drawn from NCERT, NCERT Exemplar and previous years' CBSE question papers
- Hints and solutions to selected questions
- Android app with practice problems, additional exercises and more
- Video lectures available at www.universitiespress.com/mathsclassX

**Tarun Gulati** is an education professional from Delhi who has more than 25 years of teaching experience. He obtained his Bachelor’s and Master’s degrees in Mathematics from Madurai Kamaraj University. He has wide-ranging experience as a guest lecturer at various schools. He has been Director of his own coaching facility, Educare Academy, since 2000.

*Preface *

*Acknowledgements *

**Chapter 1: Real Numbers **

Real Numbers, Composite Numbers, Fundamental Theorem of Arithmetic, Computing the HCF and LCM of Two Positive Integers [Using Fundamental Theorem], Formulae for Finding the HCF and LCM of Two Numbers, Euclid’s Division Lemma, Irrational Numbers, Decimal Expansion of Rational Numbers

Chapter 2: Polynomials

Polynomials, Zeros of a Polynomial, Relationship between Zeros and Coefficients of a Quadratic Polynomial, Formation of Quadratic Polynomial, Division in Polynomials, Division Algorithm, Proof of Relationship between Zeros and Coefficients of Quadratic and Cubic Polynomials

Chapter 3: Linear Equations in Two Variables

Linear Equation, Solving Linear Equations, Solve the System of Equations Graphically, Word Problems, Problems Based on Simple Day-to-Day Life Problems, Problems Based on Fractions, Problems Based on Two-Digit Numbers, Problems Based on Age, Problems Based on Speed, Distance and Time, Problems Based on Area, Problems Based on Angles

Chapter 4: Quadratic Equations

Meaning of Quadratic Equations, Solution of Quadratic Equations, Solving a Quadratic Equation by Factorisation, Solving Quadratic Equations by the Method of Completing the Square, Solving a Quadratic Equation by Quadratic Formula, Finding the Roots of Equations using the Quadratic Formula, Word Problems, Problems Based on Numbers, Problems Based on Speed, Distance and Time, Problems Based on Simple Day-to-Day Life Problems, Problems Based on Age, Problems Based on Area

Chapter 5: Arithmetic Progression

Sequence, Progression, Arithmetic Progression, General Term of an AP, Sum of ‘n’ Terms of an AP

Chapter 6: Triangles

Triangle Basics, Problems Based on Similar Triangles, Basic Proportionality Theorem, Converse of Basic Proportionality Theorem, Area Theorem, Pythagoras’ Theorem, Converse of Pythagoras’ Theorem

Chapter 7: Coordinate Geometry

Distance Formula, Properties of Types of Quadrilaterals, Section Formula, Mid-point Formula, Centroid of a Triangle, Area of a Triangle

Chapter 8: Introduction to Trigonometry

Relationship between Perpendicular, Base and Hypotenuse of a Right Triangle, Problems Based on the Trigonometric Table, Complementary Angles Formulae, Trigonometric Identities, Problems Based on Complementary Angles, Problems Based on Trigonometric Identities

Chapter 9: Some Applications of Trigonometry

Meaning of Line of Sight, Meaning of Angle of Elevation, Meaning of Angle of Depression

Chapter 10: Circles

Definitions, Tangent Perpendicular to the Radius, Length of Tangents

Chapter 11: Constructions

Division of a Line Segment in a Given Ratio, To Construct a Triangle Similar to a Given Triangle as Per the Given Scale Factor, Construction of Tangents to a Circle

Chapter 12: Areas Related to Circles

Important Formulae, Circumference of a Circle, Area of a Circle, Length of an Arc, Area of Minor and Major Sectors, Area of Minor and Major Arcs, Area of Shaded Regions, Area Enclosed by Combination of Plane Figures

Chapter 13: Surface Areas and Volumes

Useful Formulae, Problems Based on Surface Area of Cube, Cuboid, Right Circular Cylinder and Cone, Sphere and Hemisphere, Surface Area and Volume of Combined Figures, Problems Based on Volume of Cube, Cuboid, Right Circular Cylinder and Cone, Sphere and Hemisphere, Problems Based on Melting, Change in Shape and Embankment, Problems Based on Frustum

Chapter 14: Statistics

Definitions, Mean, Median, Mode, Cumulative Frequency Curve or Ogive

Chapter 15: Probability

Definitions, Coins, Dice, Playing Cards, Miscellaneous Problems

*Hints and Solutions*