Topics
Geometrical Constructions
 Constructing a Bisector of an Angle
 Drawing a Perpendicular to a Line at a Point on the Line
 The Property of the Angle Bisectors of a Triangle
 Perpendicular Bisectors of the Sides of an Acuteangled Triangle
 Perpendicular Bisectors of the Sides of an Obtuseangled Triangle
 Construction of Triangles
 Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
 Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
 Construct a Triangle Given Two Angles and the Included Side
 Construct a Rightangled Triangle Given the Hypotenuse and One Side
 Congruence Among Line Segments
 Congruence of Angles
 Congruence of Circles
Multiplication and Division of Integers
 Concept for Natural Numbers
 Concept for Whole Numbers
 Negative and Positive Numbers
 Concept of Integers
 Concept for Ordering of Integers
 Addition of Integers
 Addition of Integers on Number line
 Subtraction of Integers
 Multiplication of a Positive and a Negative Integers
 Multiplication of Two Negative Integers
 Multiplication of Two Positive Integers
 Division of Integers
HCF and LCM
Angles and Pairs of Angles
Operations on Rational Numbers
 Rational Numbers
 Addition of Rational Number
 Additive Inverse of Rational Number
 Subtraction of Rational Number
 Multiplication of Rational Numbers
 Division of Rational Numbers
 Rational Numbers Between Two Rational Numbers
 Decimal Representation of Rational Numbers
 BODMAS  Rules for Simplifying an Expression
Indices
 Concept of Exponents
 Concept of Square Number
 Concept of Cube Number
 Laws of Exponents
 Multiplying Powers with the Same Base
 Dividing Powers with the Same Base
 Taking Power of a Power
 Multiplying Powers with Different Base and Same Exponents
 Dividing Powers with Different Base and Same Exponents
 Numbers with Exponent Zero, One, Negative Exponents
 Miscellaneous Examples Using the Laws of Exponents
 Expressing Large Numbers in the Standard Form
 Finding the Square Root of a Perfect Square
Joint Bar Graph
Algebraic Expressions and Operations on Them
 Algebraic Expressions
 Terms, Factors and Coefficients of Expression
 Like and Unlike Terms
 Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
 Addition of Algebraic Expressions
 Subtraction of Algebraic Expressions
 Multiplication of Algebraic Expressions
 Multiplying Monomial by Monomials
 Multiplying a Monomial by a Binomial
 Multiplying a Binomial by a Binomial
 Equations in One Variable
Direct Proportion and Inverse Proportion
Banks and Simple Interest
Circle
Perimeter and Area
Pythagorasâ€™ Theorem
Algebraic Formulae  Expansion of Squares
Statistics
Definition
Arc of the Circle: A chord divides the circumference of a circle into two parts and each part is called an arc.
Minor Arc: The arc which is less than the semicircle is called minor arc.
Major Arc: The arc which is greater than the semicircle is called major arc.
Notes
Arc of the Circle:

An arc is a part of the circumference of a circle.

A chord divides the circumference of a circle into two parts and each part is called an arc.

In the figure, given above, chord PQ divides the circumference into two unequal arc PRQ and arc PQ.

The arc which is less than the semicircle is called minor arc.

The arc which is greater than the semicircle is called major arc.

If two arcs of a circle have common endpoints and the arcs make one complete circle, the arcs are said to be corresponding arcs. Here, arc PRQ and arc PQ are mutually corresponding arcs.

In the figure below, chord AB is a diameter of the circle. The diameter gives rise to two equal arcs. They are called semicircular arcs.