Topics
Number Systems
Real Numbers
Algebra
Pair of Linear Equations in Two Variables
- Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient
Arithmetic Progressions
Quadratic Equations
- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Quadratic Equations Examples and Solutions
Polynomials
Geometry
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem Or Thales Theorem
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity Triangle Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity
- Ratio of Sides of Triangle
Constructions
Trigonometry
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Statistics and Probability
Probability
Statistics
Coordinate Geometry
Lines (In Two-dimensions)
Mensuration
Areas Related to Circles
Surface Areas and Volumes
notes
Number can be classified into Imaginary Number and Real Number.
- Imaginary Numbers- are those number who have i as its part eg. 12i, 98i, 71i, etc.'i' stands for iato where i= √-1 and 'i' is an imaginary constant. In the cartesian system the y-axis represents imaginary number line and the x-axis represents real number line in the complex number system.
- Real Numbers- is any number without imaginary part eg. 8, `3/94,` `sqrt52,` etc. Real Number is again classified into Irrational Numbers and Rational Numbers.
- Irrational Numbers- these are the numbers which can not be written in `p/q` form eg. π, `sqrt55`, `sqrt1378`, etc.
- Rational Numbers- they can be expressed in the form of `p/q`, where q is not eqaul to 0 eg. `6/7, 27/4, 883/95`, etc.
- Integers- Integers are part of Rational Numbers. The numbers that lie on number line with a denominator of 1. They can't have decimal points. Integers can be both positive or negative eg. -45, -8, 2, 509, etc.
- Whole Numbers- Whole Numbers are numbers on number line starting from 0. Every number to the right side of 0 is whole number. Whole numbers are always positive eg. 1, 2, 9738, etc.
- Natural Numbers- Natural Numbers are all positive numbers excluding zero. Natural numbers are never in decimals eg. 1, 2, 3, 37, etc.
- Prime Numbers- The numbers that are divisible only by itself and 1 eg. 2, 3, 97, 101, etc.
- Composite Numbers- Composite Numbers can be represented as product of two Prime numbers eg. 64, 27, 119. 1 is neither Prime nor Composite number.
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