Unit 1

1. Logarithm

1.1 Introduction

1.2 Laws of Logarithm

1.3 Types of Logarithm

2. Partial Fractions

2.1 Introduction

2.2 Partial Fraction of Proper fraction

2.3 Partial Fractions of Improper Fraction

3. Determinants

3.1 Introduction

3.2 Definition and Expansion of Determinants

3.3 Cramer’s Rule to Solve Simultaneous Equations in 2 and 3 unknowns

4. Matrices

4.1 Introduction

4.2 Algebra of Matrices

4.3 Transpose of Matrix

4.4 Adjoint of Matrix

4.5 Solution of Simultaneous Equations

5. Binomial Theorem

5.1 Introduction  3

5.2 Factorial Notation n! or

5.3 Binomial Theorem

5.4 General Term  12

5.5 Binomial Theorem for Negative Index

5.6 Use of Binomial Theorem for Approximate values

6. Trigonometric Ratio

6.1 Introduction

6.2 Angle

6.3 Standard Position of an Angle

6.4 Trigonometric Ratios of Acute Angle

6.5 Trigonometric Ratios of any Angle

6.6 Signs of Trigonometric Ratios

6.7 Trigonometric Ratios of Special Angles viz. 0°, 30°, 45°, 60° and Quadrantal angles 90°, 180°, 270°

6.8 Trigonometric Ratios at (– q)

6.9 Trigonometric Ratios at (90° – q)

7. Trigonometric Ratios of Allied and Compound Multiple and Submultiple Angles

7.1 Introduction

7.2 Compound Angles

7.3 Allied Angles

7.4 Trigonometric Ratios of Multiple Angles

7.5 Trigonometric Ratios of submultiple Angles

8. Factorization and Defactorization Formulae

8.1 Introduction

8.2 Factorization Formulae (or Product Formulae)

8.3 Defactorization Formula  

9. Inverse Trigonometric Function

9.1 Introduction

9.2 Principal Values

9.3 Properties of Inverse Trigonometric Functions

10. Points and Distance

10.1 Introduction

10.2 Distance Formula

10.3 Section Formula

10.4 Midpoint formula

10.5 Centroid of Triangle

10.6 Area of a Triangle

11. Straight Line

11.1 Introduction

11.2 Slope of a Line

11.3 Equation of line in Different forms

11.4 Angle between two lines

11.5 Intersection of two lines

11.6 Length of perpendicular from a point on the line and distance  between parallel lines

12. Circle

12.1 Definition of Circle

12.2 General Equation of Circle and its Centre and Radius

13. Vectors

13.1 Introduction

13.2 Product of 2 Vectors

13.3 Application of Vectors

solved papers of winter 12,winter 13...