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1. Number Systems

Type of Numbers

Exponent and Factors

Terminating nd recurring

Properties of Real Numbers

Equalities and Inequalities

Inequalities Properties

Complex Numbers

Operations on Complex numbers

Properties of Mudulus

Polar Form of Complex Numbers

Argument

12. Cartesian Products

13. De Moivres Theorem

14. Short cut for De Moivries

15. Problems Discussion 1

16. Problems Discussion 2

17. Problems Discussion 3

18. Problems Discussion 4

19. Problems Discussion 5

Complex Number Quiz 1

Complex Numbers Quiz 1 Solution

Quiz 2 Solution (1)

Quiz 2 Solution (2)

Quiz 2 Solution (3)

Which of Following is Irrational

2. Sets, Functions and Groups

1. Sets

2. Type of Sets

3. Subset and Types

4. Operation on Sets

5. Compliment and Difference

6. Conjunction Disjunction

7. Implication Conditional

8. Tautologies

9. Binary Relations

10. Functions and Types

11. Linear Quadratic Inverse Functions

12. Binary Operations

13. Groupoid Monoid Group

14. Abelian Group

15. Summary of Groups

16. Problems Discussion 1

17. Problems Discussion 2

18. Problems Discussion 3

19. Problems Discussion 4

3. Matrices and Determinants

1. Matrices Base

2. Diagnol Matrices and Types

3. Addition and Subtraction

4. Multiplication of Matrices

5. Determinant and Inverse

6. Determinant of Higher Order

7. Minor and Co factor

8. Properties of Determinants

9. Properties Upper and Lower Traingular

10. Adjoint and Inverse

11. Symmetric and Hermitian

12. Rank of a Matrix

13. Cramer's Rule

14. Short Trick for Symmetric and Skew Symmetric

15. Short Trick for Hermitian

16. Short Trick for Rank

17. Short of Rank Square Matrix

18. Problems Duscussion 1-3

19. Problems Duscussion 2-3

20. Problems Duscussion 3-3

Matrices Quiz 1

Maths

4. Quadratric Equations

Quadratic Equations Quiz 1

5. Partial Fractions

1. Partial Fractions

2. Proper Rational

3. Resolving Rational to Fraction

4. Irreducible Factors

5. Repeated Irreducible

6. Problems Discussion 1

7. Problems Discussion 2

6. Sequences and Series

Sequence and Series 1

Sequence and Series 2

Sequence and Series 3

7. Permutation, Combination and Probability

1. Factorial Notation

2. Listings and Countings

3. FCP

4. Counting Principal

5. Counting with Restrictions

6. Permutations

7. FCP vs Permuations

8. Things not all different

Permutations Combinations Probability Quiz 1

8. Mathematical Inductions and Binomial Theorem

Mathematical Induction and Binomial Theorem

9. Fundamentals of Trigonometry

1. Concept of Angle

2. Degree Minute Second

3. DMS to Decimal

4. Length of Arc and Circle

5. Degree and Radian Conversion

6. Area of Sector of Circle

7. Co Terminal Angles

8. Triangles Basic Concepts

9. Trigonometric Ratios

10. Solution Of Right Triangles

11. Types Of Triangles

12. Areas & Pythagorean Triplets

13. Special Right Triangles

14. Similar Triangles

15. Angle Of Elevation & Depression

16. Examples Discussion

17. Examples Discussion

18. Trigonometic Functions

19. Sign in Quadrants

20. Value for Acute Angles

21. Useful Results

22. Lines & Angles

23. Vertical,alternate & Corresponding Angles

24. Line & Angles Properties

25. Clock Problems

26. Clock Problems

27. Examples Discussion

28. Examples Discussion

29. Problems Discission 1

30. Problems Discission 2

10. Trigonometric Identities, Sum and Difference of Angles

Trigonometry Quiz 1

1. Fundamental Law

2. Allied Angles

3. ASTC

4. Allied Angle Examples

5. Sum and Difference of Angles

6. Product of Trigonometric Functions

7. Short Trick 45 Degree

8. Short Trick Product Rule

9. Short Trick Sin Cos Tan

10. Short Trick Max Value

11. Short Trick Replacing Functions

12. Problems Discussion (1)

13. Problems Discussion (2)

14. Problems Discussion (3)

15. Problems Discussion (4)

16. Problems Discussion (5)

11. Trigonometric Functions and Their Graphs

1. Domain and Range of Sine Cosine

2. Domain and Range of Tangent Cotagent

3. Period of Trigonometric Functions

4. Graphs of Trigonometric Functions

5. Graphs of Tangent Cotagent

6. Amplitude Phase Shift Period Frequency

7. Short Tricks and Useful Results

8. Short Tricks for Domain Range

9. Short Tricks for Period

10. Problems Discussion

12. Application of Trigonometry

1. Solution and Types of Triangles

2. Triangles Basic Concepts

3. Trigonometric Ratios

4. Solution Of Right Triangles

5. Types Of Triangles

6. Areas & Pythagorean Triplets

7. Special Right Triangles

8. Similar Triangles

9. Angle Of Elevation & Depression

10. Examples Discussion

11. Examples Discussion

12. Solution of Oblique Triangles

13. Law of Sines Cosines Tangents

14. Area of Oblique Triangles

15. Circles Connected With Triangles

16. Useful Results

17. Rigid Rectilinear figure

18. Short Tricks for Equilateral Triangle

19. Problems Discussion 1-4

20. Problems Discussion 2-4

21. Problems Discussion 3-4

22. Problems Discussion 4-4

13. Inverse Trigonometric Functions

1. Inverse Trigonometric Functions

2. Domain Range of Inverse Functions

3. Useful Results

4. Problems Discussion 1-3

5. Problems Discussion 2-3

6. Problems Discussion 3-3

14. Solutions of Trigonometric Equations

Advanced Trigonometry 1

Advanced Trigonometry 2

Advanced Trigonometry 3

Advanced Trigonometry 4

15. Functions and Limits

1. Concept of Functions

2. Domain and Range of Functions

3. Graph of Algebraic Functions

4. Piece Wise Defined Functions

5. Types of Functions

6. Even and Odd Functions

7. Composition of Functions

8. Inverse of Functions

9. X Approaches to Zero and Infinity

10. Theorems on Limits

11. Limits for Zero by Zero Form

12. Limits at Infinity

13. Evaluate Limits at Infinity

14. Special Theorems

15. Continuous and Discontinuous Function

16. Continuty of a Function

17. Graphs of Functions

18. Trigonometric Functions

19. Short Tricks for Graphs

20. Short Cut to Find Inverse

21. Symmetry of Functions

22. Short Cut for Rational Functions

23. L Hospital Rule

24. Short Trick for Even and Odd Function

25. Problems Discussion 1-8

26. Problems Discussion 2-8

27. Problems Discussion 3-8

28. Problems Discussion 4-8

29. Problems Discussion 5-8

30. Problems Discussion 6-8

31. Problems Discussion 7-8

32. Problems Discussion 8-8

Functions and Limits Quiz 1

16. Differentiation

1. Power Rule

2. Theorems on Differentiation

3. Chain Rule

4. Parametric and Implicit Differentiation

5. Trigonometric and Logarithmic Differentiation

6. Exponential Differentiation

7. Derivative of Hyperbolic Functions

8. Higher Order Derivatives

9. Series Expansion of Functions

10. Maclaurin Series

11. Taylor Series Expansion

12. Increasing and Decreasing Functions

13. Stationary Point

14. Relative Extrema

15. 2nd Derivative Test

16. Short Tricks Higher Derivatives

17. Short Trick nth Derivative

18. Short Tricks for Extrema

19. Common Maclaurin Series

20. Problems Discussion 1

21. Problems Discussion 2

22. Problems Discussion 3

23. Problems Discussion 4

24. Problems Discussion 5

25. Problems Discussion 6

26. Problems Discussion 7

Differentiation Quiz 1

17. Integration

1. Integration as Anti Derivative

2. Formulas for Integration

3. Theorems on Integration

4. Integration By Parts

5. Definite Integrals and Area Under Curve

6. Theorems on Definite Integrals

7. Application of Definite Integrals

8. Short Tricks and Useful Results

9. Short Trick for Order and Degree

10. Short Trick for Integration By Parts

11. Problems Discussion 1

12. Problems Discussion 2

13. Problems Discussion 3

14. Problems Discussion 4

15. Problems Discussion 5

Integration Quiz 1

18. Introduction to Analytic Geometry

1. Coordinate System

2. Distance Formula

3. Point Dividing Line Segment

4. Theorems

5. Translation and Rotation of Axis

6. Equation and Slope of Line

7. Point slope form and Intercept

8. Two Point and Normal Form

9. General Equation of Straight Lines

10. Position of Point with Respect to Line

11. Two and Three Straight Lines

12. Equation of Lines Through Point of Intersection of Lines

13. Theorems

14. Distance of Point from Line

15. Area of Traingular Region

16. Angle between Two Lines

17. Homogenous Equation of 2nd Degree

18. Short Tricks and Useful Results

19. Problems Discussion 1-4

20. Problems Discussion 2-4

21. Problems Discussion 3-4

22. Problems Discussion 4-4

19. Linear Inequalities and Linear Programming

Vectors and Linear Inequalities 1

Vectors and Linear Inequalities 2

Vectors and Linear Inequalities 3

20. Conic Section

Conic Section Quiz 1

Conics Demonstration

1. Circles Questions

3. Concept of Conics

4. Equations of Circle

5. General Form of Circle with Conditions

6. Three Conditions of Eq. of Circle

Center of Circle

No. of Tangents

Circles Short Trick to Find Center

Ellipse Short Trick to Find Center

Hyperbola Short Trick to Find Center

Parabola (X) Short Trick to Find Center

Parabola (Y) Short Trick to Find Center

Conic Section 1

Conic Section 2

Conic Section 3

Conic Section 4

Conic Section 5

Conic Section 6

Conic Section 7

Conic Section 8

21. Vectors

1. Scalars and Vectors

2. Addition and Subtraction of Vectors

3. Vectors in Plane

4. Unit Vector and Ratio Formula

5. Vectors in Space

6. Direction angleas and Cosines

7. Scalar or Dot Product

8. Cross Product

9. Areas of Parallelogram and Traingle

10. Scalar Triple Product

11. Application of Vectors

12. Short Tricks and Useful Results

13. Problems Discussion 1-3

14. Problems Discussion 2-3

15. Problems Discussion 3-3

Vectors Maths Quiz 1

Vectors Maths Quiz 2

Preview - Mathematics for Entry Tests