Viva ICSE Mathematics 8

Contents:

Unit 1: Number System

Chapter 1. Rational Numbers • Positive and Negative Rational Numbers, Comparison of Rational Numbers, Properties of Rational Numbers, Addition and Subtraction of Rational Numbers, Multiplication and Division of Rational Numbers, Rational Numbers on a Number Line, Rational Numbers Between Two Given Rational Numbers

Chapter 2. Exponents and Powers • Laws of Exponents of Rational Numbers, Negative Integral Exponents

Chapter 3. Squares and Square Roots • Square of a Number, Perfect Squares or Square Numbers, Prime Factorization Method, Properties and Patterns of Perfect Squares, Square Roots, Finding Square Root by Repeated Subtraction Method, Finding Square Root by Prime Factorization Method, Finding Square Root by Long Division Method, Square Root of a Fraction, Square Roots of Rational Numbers in Decimal Form, Approximating the Value of Square Roots by Long Division Method

Chapter 4. Cubes and Cube Roots • Cube of a Natural Number, Properties of Cubes of Natural Numbers, Cube Roots, Cube Root of a Natural Number, Finding Cube Root by Prime Factorization, Cube Root of a Negative Perfect Cube, Cube Root of the Product of Integers, Cube Root of a Rational Number, Patterns in Perfect Cubes

Chapter 5. Playing with Numbers • Numbers in Generalized Form, Reversing the Digits—2- and 3-Digit Numbers, Tests of Divisibility, Letters for Digits, Number Puzzles and Games

Chapter 6. Set Theory • Set, Representation of Sets, Types of Sets, Cardinal Number of a Set, Subset of a Set, Operations on Sets, Complement of a Set

Unit 2: Ratio, Proportion and Arithmetical Problems

Chapter 7. Percentage • Converting a Fraction or a Decimal to Percentage and Vice Versa, Expressing One Quantity as a Percentage of the Other, Finding Percentage of a Given Quantity, Finding the Number from a Given Percentage of the Number, Increase or Decrease in Percentage

Chapter 8. Ratio and Proportion • Comparison of Ratios, Dividing a Quantity in a Given Ratio, Continued Ratio, Proportion, Direct and Inverse Proportions, Rule of Three, Proportional Parts

Chapter 9. Direct and Inverse Variations • Variation, Direct Variation, Inverse Variation, Applications of Direct and Inverse Variations

Chapter 10. Profit, Loss, Discount and Tax • Profit and Loss, Overhead Expenses, Profit% and Loss%, Discount, Tax

Chapter 11. Simple Interest and Compound Interest • Simple Interest, Compound Interest, Computation of Compound Interest Using Formulae, Inverse Problems on Compound Interest, Appreciation, Depreciation

Unit 3: Algebra

Chapter 12. Fundamental Operations on Algebraic Expressions • Algebraic Expression, Polynomial in One Variable, Polynomial in Two or More Variables, Addition and Subtraction of Algebraic Expressions, Multiplication of Algebraic Expression, Division of Algebraic Expression, Simplification of Algebraic Expression

Chapter 13. Algebraic Identities • Standard Identities: (a + b)2 = a2 + 2ab + b2; (a – b)2 = a2 – 2ab + b2; a2 – b2 = (a – b)(a + b), Special Products

Chapter 14. Factorization of Algebraic Expressions • Factors, Factorization by Taking Out Common Monomials and Binomials, Factorization by Regrouping, Factorization of Difference of Squares, Factorization of a Perfect Square Trinomial, Factorization of Quadratic Polynomial By Splitting the Middle Term

Chapter 15. Linear Equations and Inequations in One Variable • Linear Equation in One Variable, Solution of Linear Equation, Solving Linear Equations with Variables on One Side and Numbers on the Other Side, Solving Linear Equations with Variables on Both Sides (Transposition Method), Solving Equations Reducible to Linear Equations (Cross-Multiplication Method), Application Linear Equations (Word Problems), Linear Inequations, Rules for Solving Inequations, Method of Solving Inequations, Graphical Representation of Solution

Unit 4: Geometry

Chapter 16. Understanding Quadrilaterals • Polygon and its Types, Classification of Polygons, Sum of Interior and Exterior Angles of a Polygon, Quadrilaterals, Angle Sum Property of Quadrilaterals, Types of Quadrilaterals

Chapter 17. Construction of Quadrilaterals • Construction of Quadrilaterals: Required Conditions, Construction of a Quadrilateral Given 4 Sides and a Diagonal, Construction of a Quadrilateral Given 3 Sides and 2 Diagonals, Construction of a Quadrilateral Given 4 Sides and an Angle, Construction of a Quadrilateral Given 3 Sides and 2 Included Angles, Construction of a Quadrilateral Given 3 angles and 2 Sides, Construction of Some Special Quadrilaterals

Chapter 18. Three-dimensional Figures • Polyhedron, Prism and Pyramid, Visualization of 3D shapes Through Nets, Nested or Combined Solids, Views of 3D Shapes

Chapter 19. Symmetry, Reflection and Rotation • Symmetry, Reflection, Rotation, Rotational Symmetry

Chapter 20. Circles • Circle, Angle Subtended by an Arc, Angles in a Semicircle

Unit 5: Mensuration

Chapter 21. Perimeter and Area of Plane Figures • Area and Perimeter of a Rectangle, Area and Perimeter of a Square, Area of a Triangle, Area of a Parallelogram, Area of a Trapezium, Area of a Polygon, Area of a Circle

Chapter 22. Volume and Surface Area of Solids • Volume of Solids, Surface Area of Solids, Cylinder, Volume of a Cylinder

Unit 6: Data Handling

Chapter 23. Graphical Representation of Data • Presentation of Data, Frequency Distribution, Construction of a Grouped Frequency Distribution, Bar Graph (or Column Graph), Pie Chart

Chapter 24. Probability • Theoretical Approach to Probability, Tossing One, Two or Three Coins, Throwing a Die Twice, Deck of Playing cards, Theoretical Probability

Self-Testing Exercises

Concepts’ Glimpse

Formula Sheet

Question Bank

Subject Integration

Answers

About the Authors:

Monicaa Abhijit, with teaching experience of over 25 years, is currently teaching in St. Thomas School, New Delhi.

Ajay Kumar, with teaching experience of over 15 years, is currently heading the Mathematics Department in St. Mary's School, New Delhi.