Topics
Number Systems
Algebra
Geometry
Trigonometry
Statistics and Probability
Coordinate Geometry
Mensuration
Internal Assessment
Real Numbers
Pair of Linear Equations in Two Variables
 Linear Equation 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 of a Quadratic Equation
 Relationship Between Discriminant and Nature of Roots
 Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
 Application of Quadratic Equation
Polynomials
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 (Thales Theorem)
 Criteria for Similarity of Triangles
 Areas of Similar Triangles
 Rightangled Triangles and Pythagoras Property
 Similarity of Triangles
 Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
 Triangles Examples and Solutions
 Angle Bisector
 Similarity of Triangles
 Ratio of Sides of Triangle
Constructions
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Probability
Statistics
Lines (In Twodimensions)
Areas Related to Circles
Surface Areas and Volumes
 Concept of Surface Area, Volume, and Capacity
 Surface Area of a Combination of Solids
 Volume of a Combination of Solids
 Conversion of Solid from One Shape to Another
 Frustum of a Cone
 Concept of Surface Area, Volume, and Capacity
 Surface Area and Volume of Different Combination of Solid Figures
 Surface Area and Volume of Three Dimensional Figures
definition
 Irrational numbers: Irrational numbers are numbers that cannot be written in the form `p/q`, where p and q are integers and q ≠ 0. Example, √2, √3, √15, π, 0.10110111011110.........etc.
notes
Irrational Numbers:
 Consider an isosceles rightangled triangle whose base and height are each 1 unit long. Using Pythagoras theorem, the hypotenuse can be seen having a length `sqrt(1^2 + 1^2) = sqrt2`. Greeks found that this `sqrt2` is neither a whole number nor an ordinary fraction. The belief of the relationship between points on the number line and all numbers were shattered! `sqrt2` was called an irrational number.

Irrational numbers are numbers that cannot be written in the form `p/q`, where p and q are integers and q ≠ 0.

Example, √2, √3, √15, π, 0.10110111011110.........etc.

An irrational number cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal. Instead, the numbers in the decimal would go on forever, without repeating.

Examples:
 Apart from √2, one can produce a number of examples for such irrational numbers. Here are a few: √5, √7, 2√3,......
 π, the ratio of the circumference of a circle to the diameter of that same circle is another example for an irrational number.
 e, also known as Euler’s number, is another common irrational number.
 The golden ratio, also known as the golden mean, or golden section, is a number often stumbled upon when taking the ratios of distances in simple geometric figures such as the pentagon, the pentagram, decagon, and dodecahedron, etc., it is an irrational number.
GOLDEN RATIO (1:1.6) The Golden Ratio has been heralded as the most beautiful ratio in art and architecture.
Take a line segment and divide it into two smaller segments such that the ratio of the whole line segment (a + b) to segment a is the same as the ratio of segment a to the segment b. This gives the proportion `(a + b)/a = a/b`. Notice that 'a' is the geometric mean of a + b and b. 