Topics
Number Systems
Real Numbers
Algebra
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
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
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 (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
Constructions
- Division of a Line Segment
- Construction of Tangents to a Circle
- Constructions Examples and Solutions
Trigonometry
Heights and Distances
Trigonometric Identities
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
Statistics and Probability
Probability
Statistics
Coordinate Geometry
Lines (In Two-dimensions)
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
- 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
Internal Assessment
Definition
- Circle: The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.
- Centre of a circle: The fixed point is called the centre of the circle.
- Radius of a circle: The line segment joining the centre and any point on the circle is called the radius of the circle.
- Circumference of a circle: The Perimeter of the circle is called the circumference.
- Chord of a circle: The line segment, joining any two points on the circumference of the circle, is called a chord.
- Sector of a circle: A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
- Segment of a circle: A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.
- Semi-circle: A semi-circle is half of a circle, with the endpoints of diameter as part of the boundary.
Notes
Circles:
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The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.
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The fixed point is called the centre of the circle.
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The fixed distance is called the radius of the circle.
The line segment joining the centre and any point on the circle is also called a radius of the circle. That is, ‘radius’ is used in two senses in the sense of a line segment and also in the sense of its length. -
The Perimeter of the circle is called the circumference.
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The line segment, joining any two points on the circumference of the circle, is called a chord.
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A chord, which passes through the centre of the circle is called the diameter and is the largest chord of the circle which is equal to two times the radius.
- A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
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A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.
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A diameter of a circle divides it into two equal parts; each part is a semi-circle. A semi-circle is half of a circle, with the endpoints of diameter as part of the boundary.
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A circle divides the plane on which it lies into three parts.
They are:
(i) inside the circle, which is also called the interior of the circle;
(ii) the circle and
(iii) outside the circle, which is also called the exterior of the circle, which is also called the exterior of the circle. The circle and its interior make up the circular region.
