1. Mathematics for Entry Tests

2. How to Prepare Notes for Quick Revision

3. Introduction to Numbers

4. Terminating and Recurring Decimals

5. Properties of Real Numbers

6. Complex Numbers and Powers of Iota

7. Operations and Properties of Complex Numbers

8. Modulus and Properties

9. Polar Form and Argument

10. Cartesian Product and Polar Coordinates

11. DeMoivre's Theorem

12. Examples Discussion 1

13. Examples Discussion 2

14. Examples Discussion 3

1. Sets and Discription

2. Equivalent Sets and Order

3. Subset, Power Set and Universal Set

4, Union, Intersection and Difference

5. Venn Diagrams and Useful Results

6. Operations on Three Sets

7. Properties of Union and Intersection

8. Logics

9. Symbolic Logics

10. Logics and Truth Tables

11. Relations and Functions

12. Functions and Types

13. Linear, Quadratic and Inverse Functions

14. Binary Operation

15. Operations on Residue Classes Modulo

16. Group, Semi Group, Monoid and Others

17. Short Tricks and Useful Results

18. Examples Discussion 1,2

19. Examples Discussion 2,2

1. Introduction to Matrices

2. Rectangular, Diagonal and Identity

3. Addition, Subtraction and Multiplication

4. Determinants, Inverse of 2 x 2 Matrices

5. Simultaneous Linear Equations

6. Properties of Matrices

7,8. Determinant of Higher Order Matrices

9. Minors and Cofactors

10. Properties of Determinants

11. Inverse of Higher Order Matrices

12. Row and Column Operations

13. Triangular Matrices and Trace

14. Symmetric and Hermitian Matrices

15. Echelon and Reduced Echelon Form

16. Systems of Equations

17. Important Short Tricks

18. Useful Results and Properties

18b. Short Tricks for Finding Rank

19. Examples Discussion 1, 2

20. Examples Discussion 2, 2

1. Solution of Quadratic Equations

2. Equations Reducible to Quadratic Equations

3. Equations Reducible to Quadratic Equations

4. Cube Roots of Unity

5. Fourth Roots of Unity

6. Polynomials and Remainder Theorem

7. Roots and Coefficients of Quadratic Equations

8. Formation of Equation using Roots

9. Nature of Roots using Discriminant

10. System of 2nd Order Equations

11. Word Problems

12. Important Short Tricks

13. Examples Discussion 1,3

14. Examples Discussion 2,3

15. Examples Discussion 3,3

1. Rational and Partial Fractions

2. Resolving Rational Into Partial Fractions Case 1

3. Resolving Rational Into Partial Fractions Case 2

4. Resolving Rational Into Partial Fractions Case 3

5. Resolving Rational Into Partial Fractions Case 4

6. Short Methods for Partial Fractions

7. Examples Discussion

1. Sequences and General Terms

2. Arithmetic Progression

3. Arithmetic Mean

4. Arithmetic Series

5. Word Problems on Arithmetic Progressions

6. Geometric Progression

7. Geometric Mean

8. Geometric Series

9. Recurring Decimals Into Vulgar Fraction

10. Word Problems on Geometric Progressions

11. Harmonic Progression and Mean

12. Relation Between A.P, H.P and H.p

13. Sigma Notation for Series

14. Short Tricks

15. Short Tricks

16. Examples Discussion

17. Examples Discussion

1. Factorial Notation

2. Fundamental Counting Principle

3. Applying Restrictions on FCP

4. Permutations

5. Arranging Objects in Permutations

6. Permutation of Things Not All Different

7. Permutation of Things Not All Different

8. Circular Permutations

9. Combinations

10. Permutations vs Combinations vs FCP

11. Calculating Combinations

12. Probability Concepts

13. Complements in Probability

14. Probability of Event A OR Event B

15. Probability of Event A AND Event B

16. Short Methods and Useful Results

17. Examples Discussion 1,3

18. Examples Discussion 2,3

19. Examples Discussion 3,3

1. Mathematical Induction Introduction

2. Principle of Mathematical Induction

3. Binomial Theorem

4. Using Binomial Theorem

5. Middle Term in Expansion

6. Index os Negative for Fraction

7. Application of Binomial Theorem

8. Short Ticks and useful Results

9. Finding Term Involving Power of X

10. Short Methods for Binomial Theorem

11. General Terms Questions

12. Conversion to Binomial Expansion n

13. Short Tricks and useful results

14. Examples Discussions

15. Example Discussions 2

1. Trigonometry Introduction

2. Sexagesimal System (Degree, Minute, Second)

3. Circle Systems and Length of an Arc of Circle

4. Degree and Radian Conversion

5. Area of a Sector of a Circle

6. Coterminal Angles and Angles in Standard Position

7. Trigonometric Functions

8. Fundamental Identities

9. Signs of Trigonometric Functions

10. Trigonometric Functions for Acute and Common Angles

11. Clock Problems

12. Clock Problems Techniques

13. Short Tricks and Useful Results

14. Examples Discussion 1,2

15. Examples Discussion 2,2

1. Distance Formula and Fundamental Law of Trigonometry

2. Trigonometric Ratios for Allied Angles

3. Sum and Difference of Angles

4. Half, Double and Triple Angle Identities

5. Sum,Difference and Product of Sines and Cosines

6. Short Tricks and Useful Results

7. Short Tricks and Useful Results

8. Examples Discussion 1

9. Examples Discussion 2

1. Domain and Range of Trigonometric Functions

2. Period of Trigonometric Functions

3. Graphs of Sine and Cosine

4. Graphs of Tangent and Cotangent

5. Graphs of Secant and Cosecant

6. Amplitude, Phase Shift, Period and Frequency

7. Short Tricks and Useful Results

8. Short Tricks and Useful Results

9. Examples Discussion

1. Types of Angles and Triangles

2. Solution of Right Triangles

3. Isosceles and Equilaterial Triangles

4. Pythagorean Triplets

5. Special Right Triangles and Similar Triangles

6. Angle of Elevation and Depression

7. Solution of Oblique Triangles

8. Areas Of Oblique Triangles

9. Circles Connected with Triangles

10. Short Tricks and Useful Results

11. Examples Discussion

12. Examples Discussion

1. Inverse Sine and Cosine Functions

2. Inverse Tangent, Secant and Cosecant Functions

3. Domain and Range of Inverse Functions

4. Inverse Trigonometric Formulas

5. Examples Discussion 1

6. Examples Discussion 2

1. Solution of Trigonometric Equations

2. General Solutions

3. Equations Having More than One Trigonometric Functions

4. Equations Having Extraneous Roots

5. Examples Discussion

6. Examples Discussion

1. Functions Introduction

2. Functions, Domain and Range

3. Graphs of Algebraic Functions

4. Piece wise Defined Functions

5. Types of Functions

6. Types of Functions

7. Checking Odd and Even Functions

8. Composition of Functions

9. Inverse of a Function

10. Limit of a Function

11. Theorems on Limits of Functions

12. Limits for Zero and Infinity Forms

13. Evaluating Limits at Zero and Infinity

14. Special Theorems

15. Continuity and Discontinuity

16. Graphs of Explicit Functions

17. Graphs of Implicit Functions

18. Graphs of Discontinuous Functions

19. Short Tricks and Useful Results

20. Finding Inverse and Checking Symmetry

21. L Hospital Rulle For Limits

22. Short Tricks and Useful Results

23. Examples Discussion 1

24. Examples Discussion 2

25. Examples Discussion 3

26. Examples Discussion 4

1. Dependent and Independent Variables

2. Finding Derivative of a Function

3. Power Rule

4. Theorems of Differentiation

5. The Chain Rule

6. Derivative of Parametric, Trigonometric Functions

7. Logarithmetic Functions

8. Hyperbolic and Inverse functions

9. Higher Order Derivatives

10. Series Expansion of Functions

11. Relative Maxima and Minima

12. Summary

13. Short Tricks and Useful Results

14. Short Tricks

15. Examples Discussion 1

16. Examples Discussion 2

17. Examples Discussion 3

1. Integration as Antiderivative

2. Theorems of Integration

3. Integration by Parts

4. Definite Integrals & Ares Under Curve

5. Application of Definite Integrals

6. Short Tricks and Useful Results

7. Short Tricks and Useful Results

8. Summary

9. Examples Discussion 1

10. Examples Discussion 1

1. Geometry Introduction

2. Rectangular Coordinate System

3. Distance Formula Concepts

4. Point Dividing Line Segment in Ratio

5. Translation and Rotation of Axes

6. Slopes of Lines

7. Slopes of Line Segments

8. Equation of Lines Parallel to X and Y Axes

9. Standard Equations of Straight Lines

10. Standard Equations of Straight Lines

11. General Equations of Straight Lines

12. Transform General Equations to Straight Lines

13. Transform General Equations to Straight Lines

14. Position of Point and Line

15. Two and Three Straight Lines

16. Distances of Points and Lines

17. Angles between Lines

18. Equations of Lines in Matrix Form

19. Summary

20. Short Tricks and Useful Results

21. Examples Discussion 1

22. Examples Discussion 1

4. Feasible Region and Solution Set

1. Linear Inequalities

2. Graphing Linear Inequalities

3. Region Bounded By Inequalities

5. Linear Programming

6. Summary

7. Examples Discussion

1. Introduction to Conics

2. Equation of Circle

3. Equation of Circle with Conditions

4. Circle Equations in Special Form

5. Tangents and Normals to Circles

6. Position of Point w.r.t Circle

7. Lines Intersecting Circles

8. Length of Tangents

9. Theorems and Properties of Circles

10. Eccentricity of Cone

11. Parabolas

12. Graph of Parabola

13. Solving Parabolas

14. Theorems and Properties of Parabolas

15. Ellipse and It's Elements

16. Solving Ellipse

17. Hyperbola and It's Elements

18. Solving Hyperbolas

19. Tangents and Normals for Conics

20. Conditions of Tangents to Conics

21. Intersection of Two Conics

22. Translation and Rotation of Axes

23. General Equation of Conics

24. Conics Classification

25. Summary

26. Short Methods for Parabolas

27. Short Methods for Ellipse

28. Short Methods for Hyperbolas

29. Examples Discussion 1

30. Examples Discussion 2

31. Examples Discussion 3

32. Examples Discussion 4

33. Examples Discussion 5

34. Examples Discussion 6

1. Introduction to Vectors

2. Multiplication,Addition,Subtraction of Vectors

3. Vectors in Plane

4. Unit Vectors

5. Ratio Formula and Vector Geometry

6. Vectors in Space

7. Distance Formula in Space

8. Direction Angles and Direction Cosines

9. Scalar Product of Vectors

10. Angle Between Vectors

11. Projection of One Vector on Another

12. Cross Product of Vectors

13. Properties of Cross Product

14. Application of Cross Product

15. Finding Areas in Vector Product

16. Scalar Triple Product

17. Properties of Triple Product

18. Application in Physics

19. Short Tricks and Useful Results

20. Summary

21. Examples Discussion