Topics
Angle and Its Measurement
- Directed Angle
- Angles of Different Measurements
- Angles in Standard Position
- Measures of Angles with Various Systems
- Area of a Sector
- Length of an Arc
Trigonometry - 1
- Trigonometric Ratios
- Trigonometric Functions with the Help of a Circle
- Signs of Trigonometric Functions in Different Quadrants
- Range of Cosθ and Sinθ
- Trigonometric Functions of Specific Angles
- Trigonometric Functions of Negative Angles
- Important Identities and Standard Results
- Periodicity of Trigonometric Functions
- Domain and Range of Trigonometric Functions
- Graphs of Trigonometric Functions
- Polar Co-ordinate System
Trigonometry - 2
Determinants and Matrices
- Definition and Expansion of Determinants
- Minors and Cofactors of Elements of Determinants
- Properties of Determinants
- Application of Determinants
- Determinant Method (Cramer’s Rule)
- Consistency of Three Equations in Two Variables
- Area of Triangle and Collinearity of Three Points
- Concept of Matrices
- Types of Matrices
- Operation on Matrices
- Properties of Matrix Multiplication
- Transpose of a Matrix
Straight Line
- Locus of a Points in a Co-ordinate Plane
- Equations of Line in Different Forms
- Family & Concurrent Lines
Circle
Conic Sections
Measures of Dispersion
- Meaning and Definition of Dispersion
- Measures of Dispersion
- Quartiles and Range in Statistics
- Variance
- Standard Deviation
- Change of Origin and Scale of Variance and Standard Deviation
- Standard Deviation for Combined Data
- Coefficient of Variation
Probability
Complex Numbers
Sequences and Series
- Sequence, Series, and Progression
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Harmonic Progression (H. P.)
- Arithmetico Geometric Series
- Power Series
Permutations and Combination
Methods of Induction and Binomial Theorem
- Principle of Mathematical Induction
- Binomial Theorem for Positive Integral Index
- General Term in Expansion of (a + b)n
- Middle term(s) in the expansion of (a + b)n
- Binomial Theorem for Negative Index Or Fraction
- Binomial Coefficients
Sets and Relations
- Sets and Their Representations
- Classification of Sets
- Fundamental Concepts of Ordered Pairs and Relations
- Intervals
Functions
Limits
Continuity
Differentiation
- Definition of Derivative and Differentiability
- Rules of Differentiation (Without Proof)
- Derivative of Algebraic Functions
- Derivatives of Inverse Trigonometric Functions
- Derivative of Logarithmic Functions
- Derivatives of Exponential Functions
- L' Hospital'S Theorem
Formula: Trigonometric Functions
1. \[\lim_{x\to0}\frac{\sin x}{x}=1=\lim_{x\to0}\frac{x}{\sin x}\]
2. $$\lim_{x\to0}\frac{\tan x}{x}=1=\lim_{x\to0}\frac{x}{\tan x}$$
3. \[\lim_{x\to0}\frac{\sin^{-1}x}{x}=1=\lim_{x\to0}\frac{x}{\sin^{-1}x}\]
4. \[\lim_{x\to0}\frac{\tan^{-1}x}{x}=1=\lim_{x\to0}\frac{x}{\tan^{-1}x}\]
5. \[\lim_{x\to0}\frac{\sin x^{\circ}}{x}=\frac{\pi}{180}\]
6. \[\lim_{x\to0}\cos x=1\]
7. \[\lim_{x\to0}\frac{\sin\mathrm{k}x}{x}=\lim_{x\to0}\frac{\tan\mathrm{k}x}{x}=\mathrm{k}\]
8. \[\lim_{x\to\infty}\frac{\sin x}{x}=\lim_{x\to\infty}\frac{\cos x}{x}=0\]
9. \[\lim_{x\to\infty}\frac{\sin\left(\frac{1}{x}\right)}{\frac{1}{x}}=1=\lim_{x\to\infty}\frac{\tan\left(\frac{1}{x}\right)}{\frac{1}{x}}\]
10. \[\lim_{x\to a}\frac{\sin\left(x-a\right)}{x-a}=1=\lim_{x\to a}\frac{\tan\left(x-a\right)}{x-a}\]
