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:
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