Topics
Number Systems
Number Systems
Polynomials
Algebra
Coordinate Geometry
Linear Equations in Two Variables
Geometry
Coordinate Geometry
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Introduction to Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Properties of a Triangle
- Some More Criteria for Congruence of Triangles
- Inequalities in a Triangle
Quadrilaterals
- Concept of Quadrilaterals
- Properties 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
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
- Mean , Median , Mode
- Quartile , Inter quartile
Notes
The three measures of central tendency for ungrouped data are :
The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.
So, `bar x =
(sum_(i=1)^n x_i)/ n`.
For an ungrouped frequency distribution, it is `bar x = (sum_(i=1)^n f_ix_i)/(sum_(i=1)^n f_i)`
The median is that value of the given number of observations, which divides it into exactly two parts.
If n is an odd number, the median = value of the `((n + 1)/2)^(th)` observation.
If n is an even number, median = Mean of the values of the `(n/2)^(th)` and `(n/2 + 1)^(th)` observation.
The mode is that value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called the mode.
