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Number Systems
Number Systems
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Polynomials
Linear Equations in Two Variables
Coordinate Geometry
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Coordinate Geometry
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Introduction to Euclid’S Geometry
Lines and Angles
 Introduction to Lines and Angles
 Basic Terms and Definitions
 Intersecting Lines and Nonintersecting Lines
 Parallel Lines
 Pairs of Angles
 Parallel Lines and a Transversal
 Lines Parallel to the Same Line
 Angle Sum Property of a Triangle
Statistics and Probability
Triangles
Quadrilaterals
 Concept of Quadrilaterals  Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
 Angle Sum Property of a Quadrilateral
 Types of Quadrilaterals
 Another Condition for a Quadrilateral to Be a Parallelogram
 Theorem of Midpoints of Two Sides of a Triangle
 Property: The Opposite Sides of a Parallelogram Are of Equal Length.
 Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
 Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
 Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
 Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
 Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
 Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
 Concept of Circle  Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
 Angle Subtended by a Chord at a Point
 Perpendicular from the Centre to a Chord
 Circles Passing Through One, Two, Three Points
 Equal Chords and Their Distances from the Centre
 Angle Subtended by an Arc of a Circle
 Cyclic Quadrilateral
Areas  Heron’S Formula
Surface Areas and Volumes
Statistics
Algebraic Expressions
Algebraic Identities
Area
Constructions
 Introduction of Constructions
 Basic Constructions
 Some Constructions of Triangles
Probability
Definition
 Linear Equation in One Variable: If there is only one variable in the equation then it is called a linear equation in one variable.
Notes
Linear Equation in One Variable:
If there is only one variable in the equation then it is called a linear equation in one variable. These are called linear equations in one variable because the highest degree of the variable is one.
These are linear expressions:
2x, 2x + 1, 3y – 7, 12 – 5z, `5/4(x  4) + 10`
These are not linear expressions:
x^{2} + 1, y + y^{2}, 1 + z + z^{2} + z^{3}. ....(since highest power of variable > 1)
The general form is ax + b = c, where a, b and c are real numbers and a ≠ 0.
Example:
x + 5 = 10, y – 3 = 19.
Some Important points related to Linear Equations:

There is an equality sign in the linear equation. The expression on the left of the equal sign is called the LHS (lefthand side) and the expression on the right of the equal sign is called the RHS (righthand side).

In the linear equation, the LHS is equal to RHS but this happens for some values only and these values are the solution of these linear equations.
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