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 Coefficient
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
 Pythagoras Theorem
 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 Twodimensions)
Mensuration
Areas Related to Circles
Surface Areas and Volumes
notes
Basic Ideas of Probability:
1. Random Experiment:

The experiment in which all possible results are known in advance but none of them can be predicted with certainty and there is an equal possibility for each result is known as a ‘Random experiment’.

For example, Tossing a coin, throwing a die, picking a card from a set of cards bearing numbers from 1 to 50, picking a card from a pack of wellshuffled playing cards, etc.

We know all possible results of the above experiment in advance but none of them can be predicted with certainty and there is an equal possibility for each result.
2. Experiment:
 An operation which can produce some welldefined outcome is called an experiment.
 In a random experiment of tossing a coin – there is only two outcomes. Head (H) or Tail (T).
3. Outcome:

Outcomes of an experiment are equally likely if each has the same chance of occurring.

Result of a random experiment is known as an ‘Outcome’.
 In a random experiment of tossing a coin – there are only two outcomes. Head (H) or Tail (T)
 In a random experiment of throwing a die, there are 6 outcomes, according to the number of dots on the six faces of the die. 1 or 2 or 3 or 4 or 5 or 6.
 A card is drawn randomly from a pack of wellshuffled playing cards.
There are 52 cards in a pack as shown below.
In a pack of playing cards, there are 4 sets, namely heart, diamond, club and spade. In each set, there are 13 cards as King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4,3, 2 and Ace. King, Queen and Jack are known as face cards. In each pack of cards, there are 4 cards of the king, 4 cards of Queen and 4 cards of Jack. Thus total face cards are 12.
4. Equally Likely Outcomes:

A given number of outcomes are said to be equally likely if none of them occurs in preference to others.

We assume that objects used for random experiments are fair or unbiased.

If a die is thrown, any of the numbers from 1, 2, 3, 4, 5, 6 may appear on the upper face. It means that each number is equally likely to occur. However, if a die is so formed that a particular face comes up most often, then that die is biased. In this case, the outcomes are not likely to occur equally.
5. Trial:
 A trial is an action which results in one or several outcomes.

A trial is a single performance of the welldefined experiments, such as the flipping of a coin, the generation of a random number etc.
6. Sample Space:

The set of all possible outcomes of a random experiment is called the sample space.

In an experiment or any random trial, when we make a set of all the results or outcomes that are possible in that experiment or trial, that set is said to be a sample space of that particular experiment.

It is denoted by ‘S’ or ‘Ω’ (A Greek letter 'Omega').

Each element of sample space is called a ‘sample point’.

The number of elements in the set ‘S’ is denoted by n(S).

If n(S) is finite, then the sample space is said to be a finite sample space.
Following are some examples of finite sample spaces.
Sr. No  Random experiment  Sample space  Number of sample points in S 
1. 
One coin is tossed. 
S = {H, T} 
n(s) = 2 
2. 
Two coins are tossed. 
S = { HH, HT, TH, TT} 
n(s) = 4 
3. 
Three coins are tossed. 
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} 
n(s) = 8 
4. 
A die is thrown. 
S = {1, 2, 3, 4, 5, 6} 
n(s) = 6 
5. 
Two dice are thrown. 
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} 
n(s) = 36 
6. 
A card is drawn from a pack bearing numbers from 1 to 25 
S = {1, 2, 3, 4,..................., 25} 
n(s) = 25 
7. 
A card is drawn from a wellshuffled pack of 52 playing cards. 
Diamond: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King Spade: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King Heart: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King Club: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King 
n(s) = 52 