#### 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 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
- 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 Two-dimensions)

##### Mensuration

##### Areas Related to Circles

##### Surface Areas and Volumes

#### notes

Recall that two angles are said to be complementary if their sum equals 90°. In

∆ABC, right-angled at B.

Let ∠A= θ

In ∆ABC,

∠A+∠B+∠C= 180° (Angle sum property)

θ+ 90°+∠C= 180°

∠C= 180°-90°-θ

∠C= (90°-θ)

Trigonometric ratios-

1) sin(90°-θ)= `"AB"/"AC"`= cosθ

2) cos(90°-θ)= `"BC"/"AC"`= sinθ

3)tan(90°-θ)= `"AB"/"BC"`= cotθ

4)cot(90°-θ)= `"BC"/"AB"`= tanθ

5)sec(90°-θ)= `"AC"/"BC"`= cosecθ

6)cosec(90°-θ)= `"AC"/"AB"`= secθ

Example: Evaluate `"sin18°"/"cos72°"`

solutioin- `"sin(90°-72°)"/"cos72°"`

sin(90°-θ)= cosθ= `"cos72°"/"cos72°"= 1`

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