11th class Math Sindh Board video tutorials

11th class Math Sindh Board

11th class Math Sindh Board all chapters video tutorials are available here. We managed all in one place, so you can watch it easily without going anywhere for a single video. Watch 11th class Math Sindh Board video tutorials from below list.

Chapter 1: Sets (128 videos)

1.1: Revision

Set Definition

Problem-Set Definition

Set Notation & its Characteristics

Problem-Set Notation & its Characteristics

Definition & Notation of Some Important Sets

Order of a Set

Problem-Order of a Set

Interval Notation of a Set

1.2: A Few Definitions

Equal & Equivalent Sets

Problem 1: Equal & Equivalent Sets

Subset Definition

Problem 1: Subset Definition

Problem-Subset Definition

Proper Subset & Improper Subset

Problem 1: Proper Subset & Improper Subset

Properties of Subset

Problem 1: Properties of Subset

Power Set

Problem 1: Power Set

Universal Set

Introduction to Ordered Pairs

1.3: Operations on Sets

Union of Two Sets

Problem 1: Union of Two Sets

Exhaustive Sets and Cells

Intersection of Set

Problem 1: Intersection of Set

Difference of Sets

Problem 1: Difference of Sets

Symmetric Difference of two sets

Problem 1: Symmetric Difference of two sets

The complement of a Set

Problem 1: Complement of a Set

Double Complementation Law

Problem-Double Complementation Law

Cartesian Product of Sets

Problem 1: Cartesian Product of Sets

1.4: Properties of Operations on Sets

Commutative Law of Union of Sets

Problem 1: Commutative Law of Union of Sets

Commutative Law of Intersection of Sets

Problem 1: Commutative Law of Intersection of Sets

Intersection Associativity for Overlapping Sets

Problem 1: Intersection Associativity for Overlapping Sets

Intersection Associativity for Disjoint Sets

Problem 1: Intersection Associativity for Disjoint Sets

Intersection Associativity for Sets

More on Intersection Associativity for Sets

Problem 1: Intersection Associativity for Sets

Problem 1: More on Intersection Associativity for Sets

Union Associativity for Overlapping Sets

Problem 1: Union Associativity for Overlapping Sets

Union Associativity for Disjoint Sets

Problem 1: Union Associativity for Disjoint Sets

Union Associativity for Sets

Problem 1: Union Associativity for Sets

More on Union Associativity for Set

Problem 1: More on Union Associativity for Set

Distributivity of Union Over Intersection of Sets

Problem 1: Distributivity of Union Over Intersection of Sets

Distributivity of Intersection Over Union of Sets

Problem 1: Distributivity of Intersection Over Union of Sets

Introducing Field

Problem-Introducing Field

Distributive Property of Cartesian Product Over Union

Problem-Distributive Property of Cartesian Product Over Union

Distributive Property of Cartesian Product Over Intersection

Problem-Distributive Property of Cartesian Product Over Intersection

Distributive Property of Cartesian Product Over Difference

Problem-Distributive Property of Cartesian Product Over Difference

Identity With Respect to Intersection

Problem-Identity With Respect to Intersection

1.5: Some Important Laws

Identity Laws

Problem-Identity Laws

Laws of Complement

Problem-Laws of Complement

Some Important Laws

Problem-Some Important Laws

Demorgans Law for Overlapping Sets

Problem 1: Demorgans Law for Overlapping Sets

Demorgans Law for Disjoint Sets

Problem 1: Demorgans Law for Disjoint Sets

Demorgans Law for Set & its Subset

Problem 1: Demorgans Law for Set & its Subset

Introduction to Binary Relation

Problem-Introduction to Binary Relation

Problem 1: Introduction to Binary Relation

Domain & Range of Binary Relation

Problem 1: Domain & Range of Binary Relation

Problem-Domain & Range of Binary Relation

Introduction to Binary Operations

Problem-Introduction to Binary Operations

Multiplication Table

Problem-Multiplication Table

Operations on Residue Classes Modulo n

Problem-Operations on Residue Classes Modulo n

Properties of Binary Operations

Problem-Properties of Binary Operations

Theorems on Binary Operation

More on Theorems on Binary Operation

Problem-Theorems on Binary Operation

Introduction to Function

More on Introduction to Functions

Problem 1: Introduction to Function

Problem-Introduction to Function

Problem3-Introduction to Function

Problem4-Introduction to Function

Implied Domain

Finding Domain and Range of Functions

Types of Relations

Operations on Functions

Into Function

Problem 1: Into Function

Problem-Into Function

Onto Function

Problem 1: Onto Function

Problem-Onto Function

One to One Function

Problem 1: One to One Function

Problem-One to One Correspondence

Bijective Function

Problem 1: Bijective Function

Problem-Bijective Function

Injective Function

Problem 1: Injective Function

Problem-Injective Function

One-One Function

Problem-One-One Function

Set Builder Notation for a Function

Problem-Set Builder Notation for a Function

Chapter 2: Real and Complex Number Systems (143 videos)

2.1: Introduction

Introduction to Real Numbers

Problem-Introduction to Real Numbers

Depiction of Real Number on Number Line

2.2: Development of Number Systems

Negative Numbers

Integers

Introduction to Rational Numbers

Problem 1: Introduction to Rational Numbers

Introduction to Irrational Numbers

Problem 1: Introduction to Irrational Numbers

Introduction to Real Numbers

Problem-Introduction to Real Numbers

2.3: Distinction of Between Rational and Irrational Numbers

Presenting Rational Numbers on Number Line

Problem-Decimal Representation of Rational Number

Presenting Irrational Numbers on Number Line

Problem-Decimal Representation of Irrational Number

Problem 1: Presenting Irrational Numbers on Number Line

Proving Square Root of Prime Number is Irrational Number

Problem-Proving Square Root of Prime Number is Irrational Number

2.4: The Real Number System

Closure law of Whole Numbers Addition and Multiplication

Closure law of Whole Numbers Subtraction and Division

Closure law of Integers Addition, Multiplication & Subtraction

Closure law of Integers Division

Problem 1: Closure law of Integers Addition, Multiplication & Subtrac

Closure Law of Rational Numbers

Closure law of Rational Numbers Subtraction and Division

Problem-Closure Law of Rational Numbers

Problem 1: Closure Law of Rational Numbers

Closure law of Irrational Numbers Addition and Subtraction

Closure law of Irrational Numbers Multiplication and Division

Commutative Law

Commutative law under Subtration and Division

Problem-Commutative Law

Associative Law

Associative law of Subtraction and Division

Problem-Associative Law

Problem 1: Associative Law

Additive Identity & Additive Inverse

Problem-Additive Identity & Additive Inverse

Problem 1: Additive Identity & Additive Inverse

Multiplicative Identity & Inverse

Problem-Multiplicative Identity & Inverse

Problem 1: Multiplicative Identity & Inverse

Distributive Law

Distributive Property of Multiplication over Subtraction

Problem-Distributive Law

Problem 1: Distributive Law

Problem 1: Distributive law of Multiplication over Subtraction

Trichotomy Property of Inequality

Problem-Trichotomy Property of Inequality

Problem 1: Trichotomy Property of Inequality

Reflexive And Symmetric Property of Equality

Problem-Reflexive And Symmetric Property of Equality

Transitive Property of Equality

Problem-Transitive Property of Equality

Problem 1: Transitive Property of Equality

Additive Property of Equality

Problem-Additive Property of Equality

Multiplicative Property of Equality

Problem-Multiplicative Property of Equality

Cancellation Property of Equality

Problem-Cancellation Property of Equality

Problem 1: Cancellation Property of Equality

Density Property

Problem-Density Property

Archimedian Property of Inequality

Problem-Transitive Property of Inequality

Problem 1: Transitive Property of Inequality

Additive Property of Inequality

Problem-Additive Property of Inequality

Multiplicative Property of Inequality

Problem 1: Multiplicative Property of Inequality

Inequality Multiplicative Inverse

Problem-Inequality Multiplicative Inverse

Indeterminate Form

Golden Rule of Fractions

Principle of Equality of Fractions

Rule for Quotient of Fractrions

2.5: The System C of Complex Numbers

Complex Number Introduction

Problem-Complex Number Introduction

Problem 1: Complex Number Introduction

Definition of Complex Number

Problem 1: Definition of Complex Number

Problem-Definition of Complex Number

Equality of Complex Number

Problem 1: Equality of Complex Number

Problem-Equality of Complex Number

Addition of Complex Number

Problem 1: Addition of Complex Number

Problem-Addition of Complex Number

Multiplication of Complex with Scalar Numbers

Problem 1: Multiplication of Complex with Scalar Numbers

Problem-Scalar Multiplication of Complex Numbers

Multiplication of Complex Numbers

Problem 1: Multiplication of Complex Numbers

Problem-Multiplication of Complex Numbers

2.6: Properties of Complex Numbers

Commutative Property of Complex Numbers

Problem-Commutative Property of Complex Numbers

Associative Property of Complex Numbers

Problem-Associative Property of Complex Numbers

The Distributive Property of Complex Numbers

Problem-The Distributive Property of Complex Numbers

Additive Identity and Multiplicative Identity of Complex Numbers

Problem-Additive Identity and Multiplicative Identity of Complex Numb

Additive Inverse and Multiplicative Inverse of Complex Numbers

Problem-Additive Inverse and Multiplicative Inverse of Complex Numbers

Solution of Simultaneous Linear Equations with Complex Co-efficients

Problem-Solution of Simultaneous Linear Equations with Complex Co-eff

Expression of the Polynomial P ( z ) as a Product of Linear Factors

Problem-Expression of the Polynomial P ( z ) as a Product of Linear F

Quadratic Equation of Complex Variables

Problem-Quadratic Equation of Complex Variables

2.7: Definition of Imaginary Numbers

Complex Numbers as Ordered Pairs of Real Numbers

Problem 1: Definition of Complex Number

2.8: Conjugate of Complex Numbers

Conjugate of Complex Number

Problem 1: Conjugate of Complex Number

Problem 2: Conjugate of Complex Number

Problem-Conjugate of Complex Number

2.9: Modulus of a Complex Number

Modulus of Complex Number

Problem-Modulus of Complex Number

Theorems on Complex Number

More on Theorems on Complex Numbers

Problem-Theorems on Complex Number

2.10: The Subtraction of Complex Numbers

Subtraction of Complex Numbers

Problem 1: Subtraction of Complex Numbers

Problem-Subtraction of Complex Numbers

Chapter 3: Equations (92 videos)

3.1: Quadratic Equations

Introduction to Polynomials

Problem 1: Introduction to Polynomials

Linear Equations in one, two and three variables

Problem 1: Linear Equations in one, two and three variables

Quadratic Equations in One Variable

Problem 1: Quadratic Equations in One Variable

3.2: Factor Theorem of Polynomials

Remainder Theorem

Problem 1: Remainder Theorem

Factor Theorem

Problem 2: Factor Theorem

Problem 1: Factor Theorem

3.3: Synthetic Division

Synthetic Division Method

3.4: Solution of Quadratic Equations

Solving Quadratic Equations by Factorization

Problem 1: Solving Quadratic Equations by Factorization

Solving Quadratic Equations by Completing the Squares

Problem 1: Solving Quadratic Equations by Completing the Squares

Problem 2: Solving Quadratic Equations by Completing the Squares

Derivation of Quadratic formula

Problem 1: Derivation of Quadratic formula

Solving Quadratic Equation by Quadratic formula

Problem1-Solving Quadratic Equation-Quadratic Formula

Problem 2: Solving Quadratic Equation by Quadratic formula

Problem-Solving Involving Quadratic Equations

3.5: The Cube Roots of Unity

The Cube Roots of Unity

Problem 1: The Cube Roots of Unity

3.6: Properties of the Cube Roots of Unity

Recognise Complex Cube Roots of Unity

Properties of Cube Roots of Unity

Problem 1: Properties of Cube Roots of Unity

3.7: Equations Reducible to the Quadratic Form

Solving Equation Having Degree 2n

Problem-Solving Equation Having Degree 2n

Problem2-Solving Equation Having Degree 2n

Solving Equation Having Degree Four

Solving Rational Equations

Solving Reciprocal Algebraic Equation

Problem 1: Solving Reciprocal Algebraic Equation

Solving Exponential Equations

Solving Algebraic Equations in Products Factors

Equations with Different Exponential Functions

More on Equations with Different Exponential Functions

Problem-Equations with Different Exponential Functions

Equations with Special Base e

Problem-Equations with Special Base e

Exponential Modelling

Problem1-Exponential Modelling

Problem2-Exponential Modelling

Equations Containing Logarithms

Problem-Equations Containing Logarithms

Disguised Quadratic Equations

Problem-Disguised Quadratic Equations

3.8: The Theory of Quadratic Equations

The Theory of Quadratic Equations

More on the Theory of Quadratic Equations

Problem-The Theory of Quadratic Equations

3.9: Nature of the Roots of a Quadratic Equation

Discriminant of Quadratic Expression

Problem 1: Discriminant of Quadratic Expression

Finding Discriminant of Quadratic Equation

Problem 1: Finding Discriminant of Quadratic Equation

Nature of the Roots of a Quadratic Equation

Problem 1: Nature of the Roots of a Quadratic Equation

Quadratic Function

Geometrical Interpretation and the Discriminant

Problem1-Geometrical Interpretation and the Discriminant-1

Problem1-Geometrical Interpretation and the Discriminant-2

Problem2-Geometrical Interpretation and the Discriminant-1

Verification of Nature of Roots of Equation

Finding s when Nature of Roots is given

Finding s when Nature of Roots is given

Problem 1: Finding s when Nature of Roots is given

3.10: Relaltions Between the Roots and the Coefficient of a Quadratic Equation

Roots & Coefficients of Quadratic Equation

Problem 1: Roots & Coefficients of Quadratic Equation

3.11: To Form a Quadratic Equation When its Roots are Given

Finding Sum of Roots from Their Product

Problem 1: Finding Sum of Roots from Their Product

Roots Satisfy a Given Relation

Sum & Product of Roots Equal to a Number.

Find a Quadratic Equation from Given Roots

Form Quadratic Equations Whose Roots are Given

Problem 1: Form Quadratic Equations Whose Roots are Given

3.12: Problems Involving Quadratic Equations

Problem Leading to Quadratic Equations.

Problem 1: Problem Leading to Quadratic Equations.

3.13: System of Two Equations Involving Two Variables

Solving Simultaneaous Quadratic Equations

Solving Linear and Quadratic Equations

Problem-Solving Linear and Quadratic Equations

System of Two Equations Involving Two Variables

Problem-System of Two Equations Involving Two Variables

3.14: Solution of Different Types of Systems of Equations

Solving Linear and Quadratic Equations

Problem-Solving Linear and Quadratic Equations

Solving 2nd Degree Equations in General Form Type 1

Problem-Solving 2nd Degree Equations in General Form Type 1

Solving 2nd Degree Equations in General Form Type 2

Case2-Solving 2nd Degree Equations in General Form Type 2

Case3-Solving 2nd Degree Equations in General Form Type 2

Case4-Solving 2nd Degree Equations in General Form Type 2

Case5-Solving 2nd Degree Equations in General Form Type 2

Chapter 4: Matrices and Determinants (139 videos)
4.1: Introduction

Introduction to Matrix

More on Introducing Matrix

Problem 1: Introduction to Matrix

4.2: Matrices

More on Introducing Matrix

Order of Matrix

Problem 1: Order of Matrix

Location of elements in Matrix

Problem 1: Location of elements in Matrix

Row Matrix and Column Matrix

Problem 1: Row Matrix and Column Matrix

Square Matrix and Rectangular Matrix

Problem 1: Square Matrix and Rectangular Matrix

4.3: Notation

Introduction to Matrix

Problem 1: Introduction to Matrix

Transpose of a Matrix

Problem 1: Transpose of a Matrix

4.4: Special Types of Matrices

Null Matrix or Zero Matrix

Problem 1: Null Matrix or Zero Matrix

Practical Application of Matrices

Symmetric and Skew-Symmetric Matrices

Problem 1: Symmetric and Skew-Symmetric Matrices

Problem2-Symmetric & Skew-Symmetric Matrices

Hermitian and Skew Hermitian Matrix

Problem-Hermitian and Skew Hermitian Matrix

Triangular Matrices

Problem-Triangular Matrices

Diagonal Matrix

Problem 1: Diagonal Matrix

Scalar Matrix

Problem 1: Scalar Matrix

Identity Matrix

Problem 1: Identity Matrix

Adjoint of a Matrix

Problem 1: Adjoint of a Matrix

4.5: Algebra of Matrices

Equal Matrices

Problem 1: Equal Matrices

Problem 2: Equal Matrices

Addition of Matrices

Problem 1: Addition of Matrices

Subtraction of Matrices

Problem 1: Subtraction of Matrices

Multiplication of Matrix by a Real Number

Problem 1: Multiplication of Matrix by a Real Number

Multiplication of Matrices

More on Multiplication of Matrices

Problem 1: Multiplication of Matrices

Problem 2: Multiplication of Matrices

Problem3-Multiplication of Matrices

4.6: Properties of Matrix Operation

Property for whole transpose of product of Matrices

Property for Whole Inverse of Product of Matrices

More on Property for Whole Inverse of Product of Matrices

Problem 1: Property for whole transpose of product of Matrices

Commutative Law under Addition for Matrices

Problem 1: Commutative Law under Addition for Matrices

Associaitve Law under Addition for Matrices

Problem 1: Associaitve Law under Addition for Matrices

Additive Identity of a Matrix

Problem 1: Additive Identity of a Matrix

Additive Inverse of a Matrix

Problem 1: Additive Inverse of a Matrix

Commutative Law of Multiplication of Matrices

Problem 1: Commutative Law of Multiplication of Matrices

Negative of Matrix

Problem 1: Negative of Matrix

Prove That c(AB) = (cA)B = A(cB)

Problem-Prove That c(AB) = (cA)B = A(cB)

Properties of Scalar Multiplication

Associative law under Multiplication of matrices

Problem 1: Associative law under Multiplication of matrices

Distributive Law of Multiplication over Addition for Matrices

Problem 1: Distributive Law of Multiplication over Addition for Matri

Multiplicative Identity of a Matrix

Problem 1: Multiplicative Identity of a Matrix

Properties of Transposed Matrices

Problem-Properties of Transposed Matrices

4.7: Determinant of a Square Matrix

Determinant of 2-by-2 Matrix

Problem1-Singular and Non-Singular Matrix

Problem2-Singular and Non-Singular Matrix

4.8: Determinants of Order Two and Three

Determinant of a Sqaure Matrix of Order 3 or greater

Problem-Determinant of a Sqaure Matrix of Order 3 or greater

4.9: Properties of Determinants of Order Two

Properties of Determinants

More on Properties of Determinants

Problem 1-Properties of Determinants

Problem 2-Properties of Determinants

Problem 3-Properties of Determinants

Problem 4-Properties of Determinants

4.10: Alternate Method For Expanding a Third Order Determinant

Alternate Method For Expanding a Third Order Determinant

Problem-Alternate Method For Expanding a Third Order Determinant

4.11: Properties of Determinants of Order Three

Properties of Determinants of Order Three

Problem-Properties of Determinants of Order Three

4.12: Minors and Cofactors of Elements of a Given Matrix A

Minor of an Element of a Matrix or Its Determinant

Problem-Minor of an Element of a Matrix or Its Determinant

Cofactor of an Element of a Matrix

Problem-Cofactor of an Element of a Matrix

More on Matrix Inverse Using Adjoint

Problem2-Matrix Inverse Using Adjoint

Adjoint of a Square Matrix of Order n = 3 or n > 3

Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3

4.13: The Multiplicative Inverse of a Square Matrix

Multiplicative Inverse of a Non-Singular Matrix

Problem 1: Multiplicative Inverse of a Non-Singular Matrix

Inverse of Matrix using Adjoint

More on Matrix Inverse Using Adjoint

Problem 1: Inverse of Matrix using Adjoint

Problem2-Matrix Inverse Using Adjoint

Problem3-Matrix Inverse Using Adjoint

Problem4-Matrix Inverse Using Adjoint

Adjoint of a Square Matrix of Order n = 3 or n > 3

Problem-Adjoint of a Square Matrix of Order n = 3 or n > 3

Deriving a Method For Determining Inverses

Problem-Deriving a Method For Determining Inverses

Inverse of Matrix by Row Operation

Problem-Inverse of Matrix by Row Operation

Problem-More on Inverse of Matrix by Row Operation

Inverse of Matrix by Column Operation

Problem-Inverse of Matrix by Column Operation

Problem-More on Inverse of Matrix by Column Operation

Echelon and Reduced Echelon Form of Matrix

Problem-Echelon and Reduced Echelon Form of Matrix

Echelon Form of Matrix

Problem-Echelon Form of Matrix

Reduced Echelon Form of Matrix

Problem-Reduced Echelon Form of Matrix

Rank of a Matrix

Problem-Rank of a Matrix

Invertible Matrix

Problem-Invertible Matrix

Theorems on Invertible Matrix

More Theorems on Invertible Matrix

4.14: Distinction Between Homogeneous and Non-Homogeneous Systems of Linear Equations

Solution of Homogeneous Linear Equations

More on Solution of Homogeneous Linear Equations

Problem-Solution of Homogeneous Linear Equations

More on Problem-Solution of Homogeneous Linear Equations

4.15: olving a System of Three Non-Homogeneous Linear Equations in Three Unknowns

System of Linear Equations

More on System of Linear Equations

Problem-System of Linear Equations

Consistency and Inconsistency of a System

Problem-Consistency and Inconsistency of a System

Solving a System of Three Non-Homogeneous Linear Equations

Problem-Solving a System of Three Non-Homogeneous Linear Equations

Chapter 6: Sequences and Series (102 videos)
6.1: Introduction

Introduction to Sequence and Series

Problem-Introduction to Sequence and Series

Convergent, Divergent and Periodic Sequences

Problem-Convergent, Divergent and Periodic Sequences

Types of Sequences

Problem-Types of Sequences

6.2: Arithmetic Sequences or Arithmetic Progression ( A.P )

Concept of Arithmetic Progression

Problem-Concept of Arithmetic Progression

6.3: Standard Form of an A.P

Concept of Arithmetic Progression

Problem-Concept of Arithmetic Progression

6.4: Arithmetic Series

Concept of Series

Problem1-Concept of Series

Problem2-Concept of Series

Sum of First n Terms of an Arithmetic Series

Problem-Sum of First n Terms of an Arithmetic Series

6.5: Arithmetic Means

Concept of Arithmetic Mean

Problem-Concept of Arithmetic Mean

6.6: To Insert Arithmetic Means

n Arithmetic Means Between Two Given Numbers

6.7: To Find the Sum of n A.M

To Find the Sum of n A.M

Problem-To Find the Sum of n A.M

To Find the Sum of p A.M

Problem-To Find the Sum of p A.M

Word Problems on Arithmetic Progression

More on Word Problems on Arithmetic Progression

Problem1-Word Problems on Arithmetic Progression

Problem2-Word Problems on Arithmetic Progression

6.8: Geometric Sequence or Geometric Progression ( G.P )

Concept of Geometric Progression

Problem1-Concept of Geometric Progressions

Problem2-Concept of Geometric Progressions

6.9: Standard Form of a G.P

Concept of Geometric Progression

Problem1-Concept of Geometric Progressions

Problem2-Concept of Geometric Progressions

6.10: Geometric Series

Introduction to Geometric Series

Problem-Introduction to Geometric Series

Sum of n Terms of a Geometric Series

Problem-Sum of n Terms of a Geometric Series

6.11: Infinite Geometric Series

The Infinite Geometric Series

More on The Infinite Geometric Series

Problem1-The Infinite Geometric Series

Problem2-The Infinite Geometric Series

Recurring Decimals

6.12: Geometric Means

Concept of Geometric Mean

Problem-Concept of Geometric Means

6.13: To Insert Geometric Mean

Concept of Geometric Mean

Problem-Concept of Geometric Means

n Geometric Means Between Two Given Numbers

Problem-n Geometric Means Between Two Given Numbers

Word Problems on Geometric Series

More on Word Problems on Geometric Series

Problem1-Word Problems on Geometric Series

Problem2-Word Problems on Geometric Series

Problem3-Word Problems on Geometric Series

6.14: Harmonic Sequences or Harmonic Progression ( H.P )

Concept of Harmonic Progression

Problem-Concept of Harmonic Progression

6.15: General Term of an H.P

General Term of Harmonic Progression

Problem-General Term of Harmonic Progression

6.16: The Characteristic Relation for an H.P

The Characteristic Relation for H.P

Problem-The Characteristic Relation for H.P

6.17: An Important Theorem

An Important Theorem

More on An Important Theorem

Problem-An Important Theorem

6.18: Harmonic Means

Concept of Harmonic Mean

Problem-Concept of Harmonic Mean

6.19: To Insert Harmonic Mean

Concept of Harmonic Mean

Problem-Concept of Harmonic Mean

n Harmonic Means Between Two Numbers

Problem-n Harmonic Means Between Two Numbers

6.20: Relation Between Means

Relations Between A.M, G.M & H.M

More on Relations Between A.M, G.M & H.M

Problem-Relations Between A.M, G.M & H.M

Alternate Formula For sum of n Numbers

Problem-Alternate Formula For sum of n Numbers

Alternate Formula For Sum of n Squares

More on Alternate Formula For Sum of n Squares

Problem-Alternate Formula For Sum of n Squares

Alternate Formula For Sum of n Cubes

More on Alternate Formula For Sum of n Cubes

Problem1-Alternate Formula For Sum of n Cubes

Problem2-Alternate Formula For Sum of n Cubes

Arithmetical-Geometric Series

Problem-Arithmetical-Geometric Series

Sum of n Terms of Arithmetical-Geometric Series

More on Sum of n Terms of Arithmetical-Geometric Series

Further on Sum of n Terms of Arithmetical-Geometric Series

Problem-Sum of n Terms of Arithmetical-Geometric Series

Sum to Infinity of Arithmetico-Geometric Series

Problem-Sum to Infinity of Arithmetico-Geometric Series

The Method of Differences

Problem-The Method of Differences

A Series Each Term Having r Factors in A.P

More on A Series Each Term Having r Factors in A.P-1

More on A Series Each Term Having r Factors in A.P-2

More on A Series Each Term Having r Factors in A.P-3

Problem-A Series Each Term Having r Factors in A.P

Introduction to Reciprocal Series

More on Introduction to Reciprocal Series1

More on Introduction to Reciprocal Series2

More on Introduction to Reciprocal Series3

Problem-Introduction to Reciprocal Series1

Problem-Introduction to Reciprocal Series2

Summation of Series By Partial Fractions

Problem-Summation of Series By Partial Fractions

Chapter 8: Mathematical Induction and Binomial Theorem (39 videos)
8.1: The Principle of Mathematical Induction

Introduction to Mathematical Induction

Problem-Introduction to Mathematical Induction

8.2: Sum of Positive Integral Powers of Natural Numbers

Principle of Mathematical Induction

More on Principle of Mathematical Induction

Problem1-Principle of Mathematical Induction

Problem2-Principle of Mathematical Induction

Sum of Positive Integral Powers of Natural Numbers

Principle of Extended Mathematical Induction

Problem1-Principle of Extended Mathematical Induction

Problem2-Principle of Extended Mathematical Induction

8.3: Binomial Theorem

Introduction to Binomial Theorem

Problem1-Introduction to Binomial Theorem

Problem2-Introduction to Binomial Theorem

Pascal’s Triangle

Problem1-Pascal’s Triangle

Problem2-Pascal’s Triangle

8.4: The Binomial Theorem for a Positive Integral Index

Proof of Binomial Theorem

More on Proof of Binomial Theorem

Problem1-Proof of Binomial Theorem

Problem2-Proof of Binomial Theorem

8.5: Some Important Observations

Some Important Observations

8.6: The General Term

Deductions From Binomial Theorem

Problem1-Deductions From Binomial Theorem

Problem2-Deductions From Binomial Theorem

8.7: The Middle Terms

The Middle Term in the Expansion of ( a + x ) ^2

Problem1-The Middle Term in the Binomial Expansion

Problem2-The Middle Term in the Binomial Expansion

More on Problem2-The Middle Term in the Binomial Expansion

Problem3-The Middle Term in the Binomial Expansion

8.8: The Binomial Series

Some Deductions From the Binomial Expansion of ( a + x ) ^n

Problem1-Some Deductions From the Binomial Expansion

Problem2-Some Deductions From the Binomial Expansion

Problem3-Some Deductions From the Binomial Expansion

8.9: Approximations

Some Deductions From the Binomial Expansion of ( a + x ) ^n

Applications of the Binomial Theorem

Problem1-Applications of the Binomial Theorem

8.10: Application to Summation of Series

Some Deductions From the Binomial Expansion of ( a + x ) ^n

More on Applications of the Binomial Theorem

Problem2-Applications of the Binomial Theorem

Chapter 9: Fundamentals of Trigonometry (32 videos)
9.1: Introduction

Introduction to an Angle

Measuring an Angle in Sexagesimal System

Problem1-Measuring an Angle in Sexagesimal System

Sexagesimal System into Decimal form & Vice Versa

Problem-Sexagesimal System into Decimal form & Vice Versa

9.2: Radian Measure

Radian Measure of an Angle

Problem-Radian Measure of an Angle

Problem2-Radian Measure of an Angle

9.3: General and Its Measure in Degree and Radians

General Angles

Problem-General Angles

9.4: Relation Between Radian and Degree Measure

Relationship Between Radians & Degrees.

9.5: Relation Between Arc-Length, Radius and General Angle

Relationship of Radius-Central Angle-Arc Length

Problem 1: Relationship of Radius-Central Angle-Arc Length

Problem2-Relationship of Radius-Central Angle-Arc Length

Area of a Circular Sector.

Problem 1: Area of a Circular Sector.

Problem2-Area of a Circular Sector.

Problems Using Arcs and Sectors

More on Problems Using Arcs and Sectors

9.6: The Radian Function

The Radian Function

9.7: Signs of the Trigonometric Function in the Four Quadrants

Signs of Trigonometric Ratios in Different Quadrants

Problem-Signs of Trigonometric Ratios in Different Quadrant

Problem2-Signs of Trigonometric Ratios in Different Quadrant

Trigonometric Functions for a Unit Circle

Values of Remaining Trigonometric Ratios

Values of Trigonometric Ratios at Quadrantal Angle

Problem-Values of Trigonometric Ratios at Quadrantal Angle

9.8: Values of Trigonometric Functions

Trigonometric ratios of 45 degree

Problem 1: Trigonometric ratios of 45 degree

Trigonometric ratios of 30 degree and 60 degree

Problem 1: Trigonometric ratios of 30 degree and 60 degree

Problem 2: Trigonometric ratios of 30 degree and 60 degree

Chapter 10: Trigonometric Identities (43 videos)
10.1: Trigonometric Identities and Their Applications

Proof of Fundamental Trigonometric Identity

Problem 1: Proof of Fundamental Trigonometric Identity

More on Fundamental Trigonometric Identity

Problem 2: More on Fundamental Trigonometric Identity

Problem 3: More on Fundamental Trigonometric Identity

Problem 4: More on Fundamental Trigonometric Identity

Problem5-Proof of Fundamental Trigonometric Identity

10.2: The Distance Formula

Derivation of Distance formula

Problem 1: Derivation of Distance formula

Problem-Derivation of Distance formula

Use of Distance formula

Problem 1: Use of Distance formula

Problem-Use of Distance formula

10.3: A Fundamental Law

Fundamental Law of Trigonometry

Problem-Fundamental Law of Trigonometry

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Proof of Angle Addition Formula for Cosine

Problem-Proof of Angle Addition Formula for Cosine

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10.4: Deductions From the Funndamental Law

Trigonometric Ratios and Allied Angles

Problem1-Trigonometric Ratios and Allied Angles

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Problem2-Trigonometric Ratios and Allied Angles

10.5: The Sum and Difference Identities

Deductions From Fundamental Law

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More on Deductions From Fundamental Law2

Problem1-Deductions From Fundamental Law

Problem2-Deductions From Fundamental Law

Problem3-Deductions From Fundamental Law

10.6: Applications

Further Application of Basic Identities

Problem1-Further Application of Basic Identities

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Problem2-Further Application of Basic Identities

10.7: Identities for Sin2A, Cios2A and Tan2A

Double Angle Identities

Problem-Double Angle Identities

10.8: Identities For Sin A/2, Cos A/2 and Tan A/2

Half Angle Identities

Problem-Half Angle Identities

10.9: Sum and Product Identities For Trigonometric Functions

Product to Sum or Difference of Sines and Cosines

Problem-Product to Sum or Difference of Sines and Cosines

Sum or Difference to Product of Sines and Cosines

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Problem-Sum or Difference to Product of Sines and Cosines

10.10: Applications

Applications of Product of Sines and Cosines

Chapter 11: Graphs of Trigonometric Functions (43 videos)
11.1: Trigonometric Functions

Domain and Ranges of Trigonometric Functions and Fundamental Identiti

Problem1-Domain and Ranges of Trigonometric Functions and Fundamental

Problem2-Domain and Ranges of Trigonometric Functions and Fundamental

Problem3-Domain and Ranges of Trigonometric Functions and Fundamental

Domain and Ranges of Sine and Cosine Functions

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Problem-Domain and Ranges of Sine and Cosine Functions

Domain and Ranges of Tangent and Cotangent Functions

More on Domain and Ranges of Tangent and Cotangent Functions

Problem-Domain and Ranges of Tangent and Cotangent Functions

Domain and Ranges of Secant Function

More on Domain and Ranges of Secant Function

Problem-Domain and Range of Secant Function

Domain and Ranges of Cosecant Function

More on Domain and Ranges of Cosecant Function

Problem-Domain and Range of Cosecant Function

11.2: Periods of Trigonometric Functions

Introduction to Period of Trigonometric Functions

Problem-Introduction to Period of Trigonometric Functions

Periodic Properties of the Graph of SinA, CosA and TanA

11.3: Graphs of Trigonometric Functions

Graphs of Trigonometric Functions

Problem-Graphs of Trigonometric Functions

Graph of y = Sin x From – 360 to 360 Degree

Problem1-Graph of y = Sin x From – 360 to 360 Degree

Problem1-Graph of y = Sin x From – 360 to 360 Degree

Graph of y = Cos x From – 360 to 360 Degree

Problem1-Graph of y = Cos x From – 360 to 360 Degree

Problem2-Graph of y = Cos x From – 360 to 360 Degree

Graph of y = Tan x From – 180 to 180 Degree

Problem-Graph of y = Tan x From – 180 to 180 Degree

Graph of y = Cot x From – 360 to 180 Degree

Problem-Graph of y = Cot x From – 360 to 180 Degree

Graph of y = Sec x From – 360 to 360 Degree

Problem-Graph of y = Sec x From – 360 to 360 Degree

Graph of y = Cosec x From – 360 to 360 Degree

Problem-Graph of y = Cosec x From – 360 to 360 Degree

Graph of Sin2A and Cos2A Where A is a Positive Constant

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Symmetric Properties of the Graph of SinA, CosA and TanA

Periodic Properties of the Graph of SinA, CosA and TanA

Translation Property of the Graph of SinA, CosA and TanA

More on Translation Property of the Graph of SinA, CosA and TanA

Maximum and Minimum Values of Certain Trigonometric Functions

Graphical Solution of Some Trigonometric Equations

Chapter 12: Solutions of Triangles (59 videos)
12.1: The Law of Sines

The Sine Rule

Problem-The Sine Rule

Examples on Sine Rule

12.2: The Laws of Cosines

The Cosine Rule

More on The Cosine Rule

Problem1-The Cosine Rule

Problem2-The Cosine Rule

12.3: The Laws of Tangents

The Law of Tangents

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Problem-The Law of Tangents

12.4: Solutions of Triangles

When measures of one side and one angle are given

Problem 1: When measures of one side and one angle are given

when measures of hypotenuse and one Acute angle are given

Problem 1: when measures of hypotenuse and one angle are given

When measures of two sides are given

Problem 1: When measures of two sides are given

When measures of hypotenuse and one side are given

Problem 1: When measures of hypotenuse and one side are given

Concept of Angle of Elevation & Depression

Problem 1: Concept of Angle of Elevation & Depression

Engineering and Heights and Distances

More on Engineering and Heights and Distances

Problem1-Engineering and Heights and Distances

Problem2-Engineering and Heights and Distances

Application of the Sine Rule

Problem2-The Cosine Rule

12.5: Half Angle Formulae in Terms of the Lengths of the Sides of a Triangle

Half Angle Formulas

Problem-The Sine of Half the Angle Formula

The Cosine of Half the Angle in Terms of the Sides

Problem-The Cosine of Half the Angle in Terms of the Sides

The Tangents of Half the Angle in Terms of the Sides

Problem-The Tangents of Half the Angle in Terms of the Sides

Bearing

Compass and True Bearing

Concept of Oblique Triangles

Problem-Concept of Oblique Triangles

When Measures of One Side and Two Angles are Given

Problem-When Measures of One Side and Two Angles are Given

When Measures of Two Side and Their Included Angles are Given

Problem-When Measures of Two Side and Their Included Angles are Given

When Measures of Three Sides are Given

12.6: Area of a Triangle

Area of Triangle

Area of Triangle by Measuring One Side and Two Angle

Area of Triangle by Measuring Three Sides

Problem-Area of Eqilateral Triangle With Given Sides

Area of Equilateral Triangle with Given Sides

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12.7: Circles Associated with a Triangle

Circles Connected With Triangles

Problem-Circles Connected With Triangles

12.8: Circum-Radius in Terms of the Measure of a Side and the Measure of the Opposite

Relation Among Radius, Circum-Angle & Chord of a Circum-Circle

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Problem1-Relation Among Radius, Circum-Angle & Chord of a Circum-Circ

12.9: Circum-Radius r in Terms of the Measure of three Sides of a Triangle

Relation Among Radius, Circum-Angle & Chord of a Circum-Circle

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Problem1-Relation Among Radius, Circum-Angle & Chord of a Circum-Circ

12.10: The In-Radius of a Triangle

Relation Among In-Radius, Perimeter & Area of Triangle

Problem-Relation Among In-Radius, Perimeter & Area of Triangle

12.11: Radii of e-Circles of a Triangle

Relation Among ex-Radius, Perimeter & Area of Triangle

Problem-Relation Among ex-Radius, Perimeter & Area of Triangle

Chapter 13: Inverse Trigonometric Functions and Trigonometric Equations (53 videos)
13.1: Inverse Trigonometric Functions and Their Domains and Ranges

Introduction to Inverse Trigonometric Functions

Vertical and Horizontal Line Tests

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The Inverse Sine Function

Problem1-The Inverse Sine Function

Problem2-The Inverse Sine Function

Inverse Relation of General Sine Functions

The Inverse Cosine Function

Problem1-The Inverse Cosine Function

Problem2-The Inverse Cosine Function

The Inverse Tangent Function

Problem1-The Inverse Tangent Function

Problem2-The Inverse Tangent Function

Inverse Cotangent, Secant and Cosecant Functions

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Further on Inverse Cotangent, Secant and Cosecant Functions

Problem1-Inverse Cotangent, Secant and Cosecant Functions

Problem2-Inverse Cotangent, Secant and Cosecant Functions

Domains and Ranges of Principal and Inverse Trigonometric Functions

Problem1-Domains and Ranges of Principal andInverse Trigonometric Fun

Problem2-Domains and Ranges of Principal andInverse Trigonometric Fun

Problem3-Domains and Ranges of Principal andInverse Trigonometric Fun

Problem4-Domains and Ranges of Principal andInverse Trigonometric Fun

Problem5-Domains and Ranges of Principal andInverse Trigonometric Fun

Problem6Domains and Ranges of Principal andInverse Trigonometric Func

Inverse Trigonometric Identities

More on Inverse Trigonometric Identities

Further on Inverse Trigonometric Identities

Addition and Subtraction Formulas

More on Addition and Subtraction Formulas

Problem-Addition and Subtraction Formulas

Problem-More on Addition and Subtraction Formulas

13.2: Applications

Introduction to Solutions of Trigonometric Equations

Problem-Introduction to Solutions of Trigonometric Equations

Solution of the Type SinA = k, Cos A = k and TanA = k

13.3: Solutions of Trigonometric Equations

Solution of General Trigonometric Equations

Problem1-Solution of General Trigonometric Equations

Problem2-Solution of General Trigonometric Equations

Problem3-Solution of General Trigonometric Equations

Solution of General Trigonometric Equations

Solution of General Trigonometric Equations by Factorization

Problem-Solution of General Trigonometric Equations by Factorization

Solution of Trigonometric Equations by Trigonometric Identities

Problem-Solution of Trigonometric Equations by Trigonometric Identiti

Solution of Trigonometric Equations by Quadratic Formula

Problem-Solution of Trigonometric Equations by Quadratic Formula

Writing aSinA + bCosA in the Form r Sin(A + B )

Solving aSinA + bCosA = c

Trigonometric Equations Containing Principal Functions

Problem-Trigonometric Equations Containing Principal Functions

Applications of Inverse Trigonometric Functions

Problem-Applications of Inverse Trigonometric Functions-1

Problem-Applications of Inverse Trigonometric Functions-2