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