#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Polynomials

##### 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 Co-efficient

##### 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

##### Arithmetic Progressions

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Constructions

- Division of a Line Segment
- Construction of Tangents to a Circle
- Constructions Examples and Solutions

##### Geometry

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem (Thales Theorem)
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled 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

##### 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

##### Trigonometry

##### Introduction to Trigonometry

- Trigonometry
- Trigonometry
- Trigonometric Ratios
- Trigonometric Ratios and Its Reciprocal
- Trigonometric Ratios of Some Special Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Proof of Existence
- Relationships Between the Ratios

##### Trigonometric Identities

##### Some Applications of Trigonometry

##### Mensuration

##### Areas Related to Circles

- Perimeter and Area of a Circle - A Review
- Areas of Sector and Segment of a Circle
- Areas of Combinations of Plane Figures
- Circumference of a Circle
- Area of Circle

##### Surface Areas and Volumes

- 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

##### Statistics and Probability

##### Statistics

##### Probability

##### Internal Assessment

- Area of the Sector and Circular Segment
- Length of an Arc

## Notes

1) Sector- The portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Here, OAPB is the minor sector and OAQB is the major sector.

Let OAPB be a sector of a circle with centre O and radius r. Let the degree measure of ∠AOB be θ.

Now, area of a circle= `πr^2`

We can consider this circular region to be a sector forming an angle of 360° at the centre O.

When angle at the centre is 360, area of the sector= `πr^2`

when angle at the centre is 1, area of the sector= `(πr^2)/360`

So, when angle at the centre is θ.

area of the sector= `(πr^2)/360 xx θ`

area of the sector= `θ/360 xx πr^2`

2) Segment- The potion (or part) of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

arc APB is the minor segment and arc AQB is the major segment.

Here, in a circle with centre O and radius r, You can see that:

Area of the segment APB = Area of the sector OAPB- Area of ΔOAB

`"Area" "of" "the" "segment" "APB" =θ/360 xx πr^2- "Area" "of" "ΔOAB"`