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.
PrefaceAcknowledgementsChapter 1: Real NumbersReal 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 NumbersChapter 2: PolynomialsPolynomials, 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 PolynomialsChapter 3: Linear Equations in Two VariablesLinear 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 AnglesChapter 4: Quadratic EquationsMeaning 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 AreaChapter 5: Arithmetic ProgressionSequence, Progression, Arithmetic Progression, General Term of an AP, Sum of ‘n’ Terms of an APChapter 6: TrianglesTriangle Basics, Problems Based on Similar Triangles, Basic Proportionality Theorem, Converse of Basic Proportionality Theorem, Area Theorem, Pythagoras’ Theorem, Converse of Pythagoras’ TheoremChapter 7: Coordinate GeometryDistance Formula, Properties of Types of Quadrilaterals, Section Formula, Mid-point Formula, Centroid of a Triangle, Area of a TriangleChapter 8: Introduction to TrigonometryRelationship 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 IdentitiesChapter 9: Some Applications of TrigonometryMeaning of Line of Sight, Meaning of Angle of Elevation, Meaning of Angle of DepressionChapter 10: CirclesDefinitions, Tangent Perpendicular to the Radius, Length of TangentsChapter 11: ConstructionsDivision 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 CircleChapter 12: Areas Related to CirclesImportant 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 FiguresChapter 13: Surface Areas and VolumesUseful 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 FrustumChapter 14: StatisticsDefinitions, Mean, Median, Mode, Cumulative Frequency Curve or OgiveChapter 15: ProbabilityDefinitions, Coins, Dice, Playing Cards, Miscellaneous Problems
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