TOPICS. Integers Properties of addition and. Rational Numbers Need for rational numbers. Exponents or Powers Introduction to Exponents or

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1 TOPICS DETAILS Integers Properties of addition and subtraction of integers Multiplication of integers Properties of multiplication of integers Division of integers Properties of division of integers Introduction to Integers Rational Numbers Need for rational numbers Understanding Rational numbers -- Definition Positive and Negative Rational numbers. (Zero is neither positive, nor negative) Standard form of rational numbers Comparison of Rational Numbers Four basic operations on rational numbers Exponents or Powers Introduction to Exponents or Powers To express numbers in exponential form Laws of exponents To simplify exponential expressions Standard form of exponents To convert negative exponent into positive exponent To simplify exponential expressions Expanded form of numbers To write any number in standard form Review of Exponents Squares and Square Roots Introduction to Squares & Square Roots To find the square of a number To identify whether a number is perfect square or not Properties of perfect squares Various methods of finding square roots of a given number

2 Pythagorean triplets Square root of positive integers and decimal numbers Review of Squares & Square Roots

3 Cubes and Cube Roots Introduction to Cubes & Cube Roots To find the cube of a given number To identify whether a number is perfect cube or not Properties of perfect cubes Cube root of perfect cubes Methods of finding cube roots Review of Cubes & Cube Roots H.C.F and L.C.M Introduction to H.C.F and L.C.M Highest Common Factor (HCF) Lowest Common Multiple (LCM) Review of H.C.F and L.C.M Fractions Classification of fractions Conversion of Fractions Operations on Fractions and Using BODMAS Decimal Fractions Operations on decimal numbers Introduction to Decimal Numbers Conversion of Decimal Numbers Types of Decimals Rounding off and Significant Digits in Decimals Unitary Method Unitary method is a way of calculating the value of a number of items by first finding the cost of one of them Unitary method in used in business maths for different applications. Speed, Distance and Time Learn to calculate speed. Tackle various problems on the same Ratio and Proportion Introduction to Ratio and Proportion Concept of ratio as a comparison of two or more things To understand that only quantities of same unit can be compared Proportion as equality of two ratios Review of Ratio and Proportion

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5 Percentages Convert Fractions, Decimals, Ratios into Percentage and vice versa Application of Percentage To calculate increase or decrease in percentage Introduction to Percentage Review of Percentage Profit, Loss and Discount To calculate profit, loss, profit % and loss % using CP and SP and Discount Learn to deduce the profit and loss in different transactions. Simple Interest Calculate Simple Interest and how to calculate it for a given rate and period Averages The result obtained by adding several quantities together and then dividing the sum total by the number of quantities is called average Learn to calculate average. Algebraic Expressions Introduction to Algebraic Expressions To understand the difference between terms, factors & coefficient Types of algebraic expressions Addition and subtraction of algebraic expressions Multiplication and Division of algebraic expressions Simplifying algebraic expressions with integral Denominators and Brackets Review of Algebraic Expressions To find the value of an expression Using algebraic expressions formulae and rules Algebraic Products and Identities Some Special Products as Identity

6 Bar Graphs A bar graph is a graph or chart with rectangular bars whose lengths are proportional to the values that they represent. The bars can be plotted either vertically or horizontally Learn to plot and read bar graphs. Construction of Double bar graphs for comparative data Construction of Bar graphs Co - ordinate Geometry - Graphs Introduction to Cartesian Plane Representation of a Point on a Plane Graph of Linear Equation in Two variables Lines and Angles Introduction to Lines and Angles Related Angles - Complementary, Supplementary, Adjacent, Linear pair, Vertically Opposite Pairs of Lines - Intersecting, Transversal, Parallel Lines Angles made by transversal Transversal of Parallel Lines Properties of Parallel Lines - Checking for parallel lines Types of Angles Triangle and its Properties Introduction to Triangles and its properties Medians of a trianglealtitudes of a triangle Exterior angle of a triangle and its property Angle sum property of a triangle Equilateral and isosceles triangles Sum of the lengths of two sides of a triangle is greater than the third side. Right-angled triangles and Pythagoras property Classification of Triangles Symmetry Introduction to Symmetry Rotation Line symmetry

7 Differentiate between line symmetry and rotational symmetry Reflections

8 Congruence of Triangles Introduction to Congruence of Triangles Conditions for Congruency Congruence of figures like circle, square, rectangle, etc. Check whether triangles are congruent and list their corresponding parts Criteria for congruence of triangles - SSS, SAS, ASA, AAS, RHS Review of Congruence of Triangles Triangles-Pythagoras Theorem Polygons Introduction of Polygons To identify different types of polygons and their properties Angle sum property for polygons Exterior angle property of polygons Properties of various types of quadrilaterals Review of Polygons Practical Geometry - Constructions Introduction to Construction Construction of a quadrilateral for the given measurements Construction of special types of quadrilaterals like square, rectangle, parallelogram, rhombus, etc. Review of Construction of Quadrilaterals Construction of Parallel lines Construction of Angles To construct triangles with given measurements of sides and angles(sss, SAS, ASA, RHS) To identify whether it is possible to construct a triangle with 3 given measurements Circles Circles and its Components Perimeter and Area Introduction to Perimeter & Area Perimeter and Area of Squares and Rectangles

9 Area of Parallelogram Area of Triangle Review of Perimeter & Area Circumference and Area of Circle Application of the areas of different shapes together

10 Volume and Surface Area CONCEPT :The sum of areas of all the faces of a 3D solid figure (both plane and curved) is called its total surface area. The total amount of space occupied by a 3D solid figure is called its volume. In this lesson we will learn to find the Surface Area and Volume of 3D figures like Cube and Cuboid. Collection and organization of data Introduction to Collection and organization of data Types of Data - Primary and Secondary Review of Collection and organization of data Organization of data Understanding and Construction of Frequency Distribution Central Values Understanding the Central Value Measures of Central Value : Arithmetic Mean, Median and Mode Calculating Arithmetic Mean of ungrouped and grouped data Arithmetic Mean of Grouped Data Graphical Representation of Data Pie charts Bar Graphs Line Graphs Set Concepts and Venn Diagram Introduction to Set Concepts Equal & Equivalent sets Empty & Universal sets Finite and Infinite sets Cardinal property of a set Operations on Set :Union and Intersection properties of sets Disjoint sets Overlapping & Complement sets Venn Diagrams Review of Set Concepts Universal Set and Subsets Relations and Mapping Introduction to Relations and Mapping Ordered Pair

11 Relation and its representation Domain and Range of a Relation Mapping