1 CLASS 8 (Mathematics) -EM 1.RATIONAL NUMBER - Natural, Whole, Integers (positive and negative), rational numbers. Properties of Rational Numbers- Closure, Commutativity, Associativity with example The role of zero (0), The role of zero (1)- ( Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well. ) and ( 1 is the multiplicative identity for rational numbers. ) Negative(additive inverse) of a number, Reciprocal(ex-21/8 is the reciprocal of 8/21), Distributivity of multiplication over addition and Subtraction for rational numbers. 1.3 Representation of Rational Numbers on the Number Line with example. 1.4 Rational Numbers between Two Rational Numbers with example. 2.Linear Equations in One Variable- - algebraic expressions and equations, linear equations in one variable, solutions of the equation. Solving Equations which have Linear Expressions on one Side and Numbers on the other Side with example as Find the solution of - 2x 3 = 7, 2y + 9 = 4 etc. Some Applications ( The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved using linear equations. ) as Q.1 If the smaller number is taken to be x, the larger number is 10 more than x, i.e., x + 10. The other condition says that the sum of these two numbers x and x + 10 is 74. Q.2The perimeter of a rectangle is 13 cm and its width is 11/4 cm. Find its length.
2 Q.3The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number? 3. Understanding Quadrilaterals- NOTE Discuss all topic with proper explanation and diagrammatic examples. Polygons Classification of polygons Diagonals Convex and concave polygons Regular and irregular polygons Angle sum property Sum of the Measures of the Exterior Angles of a Polygon Kinds of Quadrilateral Trapezium Kite Parallelogram Elements of a parallelogram Angles of a parallelogram Diagonals of a parallelogram Some Special Parallelograms Rhombus A rectangle A square 4.Practical Geometry NOTE Every student must come with their geometry box having scale, compass, protector and sharp pencil with eraser. Constructing a Quadrilateral When four sides and one diagonal are given. When two diagonals and three sides are given. When two adjacent sides and three angles are given.
3 When three sides and two included angles are given. When other special properties are known with proper example. 5.Data Handling Looking for Information - 1. A Pictograph 2. A bar graph 3. Double Bar Graph Organising Data Raw Data, frequency, frequency distribution table Grouping Data grouped, grouped frequency distribution, Class Interval, lower class limit, upper class limit, width or size of the class interval Bars with a difference Circle Graph or Pie Chart Drawing pie charts Chance and Probability - random experiment Equally likely outcomes Linking chances to probability Outcomes as events Chance and probability related to real life. 6. Squares and Square Roots - square numbers (Ex- Is 32 a square number?) Properties of Square Numbers Some More Interesting Patterns 1. Adding triangular numbers 2. Numbers between square numbers 3. Adding odd numbers 4. A sum of consecutive natural numbers 5. Product of two consecutive even or odd natural numbers 6. Some more patterns in square numbers Finding the Square of a Number Other patterns in squares Pythagorean triplets Square Roots Finding square roots Finding square root through repeated subtraction Finding square root through prime factorisation Finding square root by division method Square Roots of Decimals Estimating Square Root
4 7. Cubes and Cube Roots - Ramanujan Number Cubes Some interesting patterns 1. Adding consecutive odd numbers 2. Cubes and their prime factors Smallest multiple that is a perfect cube Cube Roots Cube root through prime factorisation method Cube root of a cube number. 8.Comparing Quantities Recalling Ratios and Percentages Finding the Increase or Decrease Per cent Finding Discounts 8.3.1 Estimation in percentages Prices Related to Buying and Selling (Profit and Loss) Finding cost price/selling price, profit %/loss% Sales Tax/Value Added Tax 8.6 Compound Interest Deducing a Formula for Compound Interest Rate Compounded Annually or Half Yearly (Semi Annually) Applications of Compound Interest Formula. 9. Algebraic Expressions and Identities - What are Expressions? Terms, Factors and Coefficients Monomials, Binomials and Polynomials Like and Unlike Terms (7x, 14x, 13x are like terms. ) Addition and Subtraction of Algebraic Expressions Multiplication of Algebraic Expressions: Introduction Multiplying a Monomial by a Monomial Multiplying two monomials Multiplying three or more monomials Multiplying a Monomial by a Polynomial
5 Multiplying a monomial by a binomial Multiplying a monomial by a trinomial Multiplying a Polynomial by a Polynomial Multiplying a binomial by a binomial Multiplying a binomial by a trinomial What is an Identity? Standard Identities Applying Identities. 10. Visualising Solid Shapes Views of 3D-Shapes Mapping Space Around Us Faces, Edges and Vertices polyhedrons, a prism, a pyramid 11. Mensuration Let us Recall area of Rectangle, square, triangular, circle, parallelogram. Area of Trapezium Area of a General Quadrilateral Area of special quadrilaterals Area of a Polygon Solid Shapes Surface Area of Cube, Cuboid and Cylinder Cuboid Cube Cylinders Volume of Cube, Cuboid and Cylinder Cuboid Cube Cylinder Volume and Capacity - (There is not much difference between these two words. (a) Volume refers to the amount of space occupied by an object. (b) Capacity refers to the quantity that a container holds.)
6 12. Exponents and Powers Powers with Negative Exponents Laws of Exponents Use of Exponents to Express Small Numbers in Standard Form Comparing very large and very small numbers. 13. Direct and Inverse Proportions - Direct Proportion Inverse Proportion with appropriate example. 14. Factorisation Factors of natural numbers Factors of algebraic expressions What is Factorisation? Method of common factors Factorisation by regrouping terms Factorisation using identities Factors of the form ( x + a) ( x + b) Division of Algebraic Expressions Division of a monomial by another monomial Division of a polynomial by a monomial Division of Algebraic Expressions Continued (Polynomial Polynomial) 15. Introduction to Graphs A Bar graph A Pie graph (or a circle-graph) A histogram A line graph Linear Graphs Location of a point Coordinates
7 Some Applications with example - independent variable(control variable), dependent variable. 16.Playing with Numbers Numbers in General Form Games with Numbers - (i) Reversing the digits two digit number, (ii) Reversing the digits three digit number. (iii) Forming threedigit numbers with given three-digits Letters for Digits Tests of Divisibility Divisibility by 10 Divisibility by 5 Divisibility by 2 Divisibility by 9 and 3