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.
1.1: Revision
Set Notation & its Characteristics
ProblemSet Notation & its Characteristics
Definition & Notation of Some Important Sets
1.2: A Few Definitions
Problem 1: Equal & Equivalent Sets
Proper Subset & Improper Subset
Problem 1: Proper Subset & Improper Subset
Problem 1: Properties of Subset
1.3: Operations on Sets
Problem 1: Intersection of Set
Symmetric Difference of two sets
Problem 1: Symmetric Difference of two sets
Problem 1: Complement of a Set
ProblemDouble Complementation Law
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
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
Distributive Property of Cartesian Product Over Union
ProblemDistributive Property of Cartesian Product Over Union
Distributive Property of Cartesian Product Over Intersection
ProblemDistributive Property of Cartesian Product Over Intersection
Distributive Property of Cartesian Product Over Difference
ProblemDistributive Property of Cartesian Product Over Difference
Identity With Respect to Intersection
ProblemIdentity With Respect to Intersection
1.5: 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
ProblemIntroduction to Binary Relation
Problem 1: Introduction to Binary Relation
Domain & Range of Binary Relation
Problem 1: Domain & Range of Binary Relation
ProblemDomain & Range of Binary Relation
Introduction to Binary Operations
ProblemIntroduction to Binary Operations
Operations on Residue Classes Modulo n
ProblemOperations on Residue Classes Modulo n
Properties of Binary Operations
ProblemProperties of Binary Operations
More on Theorems on Binary Operation
ProblemTheorems on Binary Operation
More on Introduction to Functions
Problem 1: Introduction to Function
ProblemIntroduction to Function
Problem3Introduction to Function
Problem4Introduction to Function
Finding Domain and Range of Functions
Problem 1: One to One Function
ProblemOne to One Correspondence
2.1: Introduction
ProblemIntroduction to Real Numbers
Depiction of Real Number on Number Line
2.2: Development of Number Systems
Introduction to Rational Numbers
Problem 1: Introduction to Rational Numbers
Introduction to Irrational Numbers
Problem 1: Introduction to Irrational Numbers
ProblemIntroduction to Real Numbers
2.3: Distinction of Between Rational and Irrational Numbers
Presenting Rational Numbers on Number Line
ProblemDecimal Representation of Rational Number
Presenting Irrational Numbers on Number Line
ProblemDecimal Representation of Irrational Number
Problem 1: Presenting Irrational Numbers on Number Line
Proving Square Root of Prime Number is Irrational Number
ProblemProving 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
ProblemClosure 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 under Subtration and Division
Associative law of Subtraction and Division
Additive Identity & Additive Inverse
ProblemAdditive Identity & Additive Inverse
Problem 1: Additive Identity & Additive Inverse
Multiplicative Identity & Inverse
ProblemMultiplicative Identity & Inverse
Problem 1: Multiplicative Identity & Inverse
Distributive Property of Multiplication over Subtraction
Problem 1: Distributive law of Multiplication over Subtraction
Trichotomy Property of Inequality
ProblemTrichotomy Property of Inequality
Problem 1: Trichotomy Property of Inequality
Reflexive And Symmetric Property of Equality
ProblemReflexive And Symmetric Property of Equality
Transitive Property of Equality
ProblemTransitive Property of Equality
Problem 1: Transitive Property of Equality
ProblemAdditive Property of Equality
Multiplicative Property of Equality
ProblemMultiplicative Property of Equality
Cancellation Property of Equality
ProblemCancellation Property of Equality
Problem 1: Cancellation Property of Equality
Archimedian Property of Inequality
ProblemTransitive Property of Inequality
Problem 1: Transitive Property of Inequality
Additive Property of Inequality
ProblemAdditive Property of Inequality
Multiplicative Property of Inequality
Problem 1: Multiplicative Property of Inequality
Inequality Multiplicative Inverse
ProblemInequality Multiplicative Inverse
Principle of Equality of Fractions
Rule for Quotient of Fractrions
2.5: The System C of Complex Numbers
ProblemComplex Number Introduction
Problem 1: Complex Number Introduction
Problem 1: Definition of Complex Number
ProblemDefinition of Complex Number
Problem 1: Equality of Complex Number
ProblemEquality of Complex Number
Problem 1: Addition of Complex Number
ProblemAddition of Complex Number
Multiplication of Complex with Scalar Numbers
Problem 1: Multiplication of Complex with Scalar Numbers
ProblemScalar Multiplication of Complex Numbers
Multiplication of Complex Numbers
Problem 1: Multiplication of Complex Numbers
ProblemMultiplication of Complex Numbers
2.6: Properties of Complex Numbers
Commutative Property of Complex Numbers
ProblemCommutative Property of Complex Numbers
Associative Property of Complex Numbers
ProblemAssociative Property of Complex Numbers
The Distributive Property of Complex Numbers
ProblemThe Distributive Property of Complex Numbers
Additive Identity and Multiplicative Identity of Complex Numbers
ProblemAdditive Identity and Multiplicative Identity of Complex Numb
Additive Inverse and Multiplicative Inverse of Complex Numbers
ProblemAdditive Inverse and Multiplicative Inverse of Complex Numbers
Solution of Simultaneous Linear Equations with Complex Coefficients
ProblemSolution of Simultaneous Linear Equations with Complex Coeff
Expression of the Polynomial P ( z ) as a Product of Linear Factors
ProblemExpression of the Polynomial P ( z ) as a Product of Linear F
Quadratic Equation of Complex Variables
ProblemQuadratic 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
Problem 1: Conjugate of Complex Number
Problem 2: Conjugate of Complex Number
ProblemConjugate of Complex Number
2.9: Modulus of a Complex Number
ProblemModulus of Complex Number
More on Theorems on Complex Numbers
ProblemTheorems on Complex Number
2.10: The Subtraction of Complex Numbers
Subtraction of Complex Numbers
Problem 1: Subtraction of Complex Numbers
ProblemSubtraction of Complex Numbers
2.11: The Division of Complex Numbers
Problem 1: Division of Complex Numbers
ProblemDivision of Complex Numbers
Division Property of Complex Numbers
Problem 1: Division Property of Complex Numbers
ProblemDivision Property of Complex Numbers
2.12: Geometrical Representation of the Complex Number x + iy as Pair of Real Numbers
ProblemModulus of Complex Number
2.13: The Order Relations
2.14: Vector Interpretation of Complex Numbers
Vector Interpretation of Complex Numbers
ProblemVector Interpretation of Complex Numbers
2.15: The Triangle Inequality
ProblemThe Triangle Inequality
2.16: Real and Imaginary Parts of ( x + iy ) Power n
3.1: Quadratic Equations
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
3.3: Synthetic Division
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
Problem1Solving Quadratic EquationQuadratic Formula
Problem 2: Solving Quadratic Equation by Quadratic formula
ProblemSolving Involving Quadratic Equations
3.5: 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
ProblemSolving Equation Having Degree 2n
Problem2Solving Equation Having Degree 2n
Solving Equation Having Degree Four
Solving Reciprocal Algebraic Equation
Problem 1: Solving Reciprocal Algebraic Equation
Solving Algebraic Equations in Products Factors
Equations with Different Exponential Functions
More on Equations with Different Exponential Functions
ProblemEquations with Different Exponential Functions
ProblemEquations with Special Base e
Problem1Exponential Modelling
Problem2Exponential Modelling
Equations Containing Logarithms
ProblemEquations Containing Logarithms
ProblemDisguised Quadratic Equations
3.8: The Theory of Quadratic Equations
The Theory of Quadratic Equations
More on the Theory of Quadratic Equations
ProblemThe 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
Geometrical Interpretation and the Discriminant
Problem1Geometrical Interpretation and the Discriminant1
Problem1Geometrical Interpretation and the Discriminant2
Problem2Geometrical Interpretation and the Discriminant1
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
ProblemSolving Linear and Quadratic Equations
System of Two Equations Involving Two Variables
ProblemSystem of Two Equations Involving Two Variables
3.14: Solution of Different Types of Systems of Equations
Solving Linear and Quadratic Equations
ProblemSolving Linear and Quadratic Equations
Solving 2nd Degree Equations in General Form Type 1
ProblemSolving 2nd Degree Equations in General Form Type 1
Solving 2nd Degree Equations in General Form Type 2
Case2Solving 2nd Degree Equations in General Form Type 2
Case3Solving 2nd Degree Equations in General Form Type 2
4.1: Introduction
Problem 1: Introduction to Matrix
4.2: Matrices
Location of elements in Matrix
Problem 1: Location of elements in Matrix
Problem 1: Row Matrix and Column Matrix
Square Matrix and Rectangular Matrix
Problem 1: Square Matrix and Rectangular Matrix
4.3: Notation
Problem 1: Introduction to Matrix
Problem 1: Transpose of a Matrix
4.4: Special Types of Matrices
Problem 1: Null Matrix or Zero Matrix
Practical Application of Matrices
Symmetric and SkewSymmetric Matrices
Problem 1: Symmetric and SkewSymmetric Matrices
Problem2Symmetric & SkewSymmetric Matrices
Hermitian and Skew Hermitian Matrix
ProblemHermitian and Skew Hermitian Matrix
Problem 1: Adjoint of a Matrix
4.5: Algebra of Matrices
Problem 1: Addition of Matrices
Problem 1: Subtraction of Matrices
Multiplication of Matrix by a Real Number
Problem 1: Multiplication of Matrix by a Real Number
More on Multiplication of Matrices
Problem 1: Multiplication of Matrices
Problem 2: Multiplication of Matrices
Problem3Multiplication 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
Problem 1: Additive Identity of a Matrix
Problem 1: Additive Inverse of a Matrix
Commutative Law of Multiplication of Matrices
Problem 1: Commutative Law of Multiplication of Matrices
Prove That c(AB) = (cA)B = A(cB)
ProblemProve 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
ProblemProperties of Transposed Matrices
4.7: Determinant of a Square Matrix
Problem1Singular and NonSingular Matrix
Problem2Singular and NonSingular Matrix
4.8: Determinants of Order Two and Three
Determinant of a Sqaure Matrix of Order 3 or greater
ProblemDeterminant of a Sqaure Matrix of Order 3 or greater
4.9: Properties of Determinants of Order Two
More on Properties of Determinants
Problem 1Properties of Determinants
Problem 2Properties of Determinants
Problem 3Properties of Determinants
Problem 4Properties of Determinants
4.10: Alternate Method For Expanding a Third Order Determinant
Alternate Method For Expanding a Third Order Determinant
ProblemAlternate Method For Expanding a Third Order Determinant
4.11: Properties of Determinants of Order Three
Properties of Determinants of Order Three
ProblemProperties 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
ProblemMinor of an Element of a Matrix or Its Determinant
Cofactor of an Element of a Matrix
ProblemCofactor of an Element of a Matrix
More on Matrix Inverse Using Adjoint
Problem2Matrix Inverse Using Adjoint
Adjoint of a Square Matrix of Order n = 3 or n > 3
ProblemAdjoint of a Square Matrix of Order n = 3 or n > 3
4.13: The Multiplicative Inverse of a Square Matrix
Multiplicative Inverse of a NonSingular Matrix
Problem 1: Multiplicative Inverse of a NonSingular Matrix
Inverse of Matrix using Adjoint
More on Matrix Inverse Using Adjoint
Problem 1: Inverse of Matrix using Adjoint
Problem2Matrix Inverse Using Adjoint
Problem3Matrix Inverse Using Adjoint
Problem4Matrix Inverse Using Adjoint
Adjoint of a Square Matrix of Order n = 3 or n > 3
ProblemAdjoint of a Square Matrix of Order n = 3 or n > 3
Deriving a Method For Determining Inverses
ProblemDeriving a Method For Determining Inverses
Inverse of Matrix by Row Operation
ProblemInverse of Matrix by Row Operation
ProblemMore on Inverse of Matrix by Row Operation
Inverse of Matrix by Column Operation
ProblemInverse of Matrix by Column Operation
ProblemMore on Inverse of Matrix by Column Operation
Echelon and Reduced Echelon Form of Matrix
ProblemEchelon and Reduced Echelon Form of Matrix
ProblemEchelon Form of Matrix
Reduced Echelon Form of Matrix
ProblemReduced Echelon Form of Matrix
More Theorems on Invertible Matrix
4.14: Distinction Between Homogeneous and NonHomogeneous Systems of Linear Equations
Solution of Homogeneous Linear Equations
More on Solution of Homogeneous Linear Equations
ProblemSolution of Homogeneous Linear Equations
More on ProblemSolution of Homogeneous Linear Equations
4.15: olving a System of Three NonHomogeneous Linear Equations in Three Unknowns
More on System of Linear Equations
ProblemSystem of Linear Equations
Consistency and Inconsistency of a System
ProblemConsistency and Inconsistency of a System
Solving a System of Three NonHomogeneous Linear Equations
ProblemSolving a System of Three NonHomogeneous Linear Equations
5.1: Binary Operations
Introduction to Binary Operations
ProblemIntroduction to Binary Operations
5.2: Multiplication ( or Composition ) Table
Operations on Residue Classes Modulo n
ProblemOperations on Residue Classes Modulo n
5.3: Properties of Binary Operations
Properties of Binary Operations
ProblemProperties of Binary Operations
5.4: Algebraic Structure
ProblemIntroduction to SemiGroup
5.5: Groups
ProblemIntroduction to Groups
Introduction to Abelian and NonAbelian Group
ProblemIntroduction to Abelian and NonAbelian Group
Problem1Finite and Infinite Group
Problem2Finite and Infinite Group
Introduction to Reversal Laws of Inverses
6.1: Introduction
Introduction to Sequence and Series
ProblemIntroduction to Sequence and Series
Convergent, Divergent and Periodic Sequences
ProblemConvergent, Divergent and Periodic Sequences
6.2: Arithmetic Sequences or Arithmetic Progression ( A.P )
Concept of Arithmetic Progression
ProblemConcept of Arithmetic Progression
6.3: Standard Form of an A.P
Concept of Arithmetic Progression
ProblemConcept of Arithmetic Progression
6.4: Arithmetic Series
Sum of First n Terms of an Arithmetic Series
ProblemSum of First n Terms of an Arithmetic Series
6.5: Arithmetic Means
ProblemConcept 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
ProblemTo Find the Sum of n A.M
ProblemTo Find the Sum of p A.M
Word Problems on Arithmetic Progression
More on Word Problems on Arithmetic Progression
Problem1Word Problems on Arithmetic Progression
Problem2Word Problems on Arithmetic Progression
6.8: Geometric Sequence or Geometric Progression ( G.P )
Concept of Geometric Progression
Problem1Concept of Geometric Progressions
Problem2Concept of Geometric Progressions
6.9: Standard Form of a G.P
Concept of Geometric Progression
Problem1Concept of Geometric Progressions
Problem2Concept of Geometric Progressions
6.10: Geometric Series
Introduction to Geometric Series
ProblemIntroduction to Geometric Series
Sum of n Terms of a Geometric Series
ProblemSum of n Terms of a Geometric Series
6.11: Infinite Geometric Series
More on The Infinite Geometric Series
Problem1The Infinite Geometric Series
Problem2The Infinite Geometric Series
6.12: Geometric Means
ProblemConcept of Geometric Means
6.13: To Insert Geometric Mean
ProblemConcept of Geometric Means
n Geometric Means Between Two Given Numbers
Problemn Geometric Means Between Two Given Numbers
Word Problems on Geometric Series
More on Word Problems on Geometric Series
Problem1Word Problems on Geometric Series
Problem2Word Problems on Geometric Series
Problem3Word Problems on Geometric Series
6.14: Harmonic Sequences or Harmonic Progression ( H.P )
Concept of Harmonic Progression
ProblemConcept of Harmonic Progression
6.15: General Term of an H.P
General Term of Harmonic Progression
ProblemGeneral Term of Harmonic Progression
6.16: The Characteristic Relation for an H.P
The Characteristic Relation for H.P
ProblemThe Characteristic Relation for H.P
6.17: An Important Theorem
6.18: Harmonic Means
ProblemConcept of Harmonic Mean
6.19: To Insert Harmonic Mean
ProblemConcept of Harmonic Mean
n Harmonic Means Between Two Numbers
Problemn 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
ProblemRelations Between A.M, G.M & H.M
Alternate Formula For sum of n Numbers
ProblemAlternate Formula For sum of n Numbers
Alternate Formula For Sum of n Squares
More on Alternate Formula For Sum of n Squares
ProblemAlternate Formula For Sum of n Squares
Alternate Formula For Sum of n Cubes
More on Alternate Formula For Sum of n Cubes
Problem1Alternate Formula For Sum of n Cubes
Problem2Alternate Formula For Sum of n Cubes
ProblemArithmeticalGeometric Series
Sum of n Terms of ArithmeticalGeometric Series
More on Sum of n Terms of ArithmeticalGeometric Series
Further on Sum of n Terms of ArithmeticalGeometric Series
ProblemSum of n Terms of ArithmeticalGeometric Series
Sum to Infinity of ArithmeticoGeometric Series
ProblemSum to Infinity of ArithmeticoGeometric Series
ProblemThe Method of Differences
A Series Each Term Having r Factors in A.P
More on A Series Each Term Having r Factors in A.P1
More on A Series Each Term Having r Factors in A.P2
More on A Series Each Term Having r Factors in A.P3
ProblemA 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
ProblemIntroduction to Reciprocal Series1
ProblemIntroduction to Reciprocal Series2
7.1: The Counting Principles
7.2: The Factorial Notation
Introduction to Factorial Notation
ProblemIntroduction to Factorial Notation
7.3: Permutations and Combinations
ProblemIntroduction to Permutation
7.4: Number of Permutations
Permutation of Things Not All Different
ProblemPermutation of Things Not All Different
7.5: Circular ( or Cyclic ) Permutations
7.6: Number of Combinations
Problem1Introduction to Combinations
Problem2Introduction to Combinations
Problem1Complementary Combination
Problem2Complementary Combination
7.7: Introduction to Probability
ProblemIntroduction to Probabillity
7.8: Basic Terminology
7.9: Definition of Probability
ProblemDefinition of Probability
7.10: Addition Law of Probability
Addition of Probabilities and Mutually Exclusive Events
ProblemAddition of Probabilities of Mutually Exclusive Events
Probability as Long Term Relative Frequency
8.1: The Principle of Mathematical Induction
Introduction to Mathematical Induction
ProblemIntroduction to Mathematical Induction
8.2: Sum of Positive Integral Powers of Natural Numbers
Principle of Mathematical Induction
More on Principle of Mathematical Induction
Problem1Principle of Mathematical Induction
Problem2Principle of Mathematical Induction
Sum of Positive Integral Powers of Natural Numbers
Principle of Extended Mathematical Induction
Problem1Principle of Extended Mathematical Induction
Problem2Principle of Extended Mathematical Induction
8.3: Binomial Theorem
Introduction to Binomial Theorem
Problem1Introduction to Binomial Theorem
Problem2Introduction to Binomial Theorem
8.4: The Binomial Theorem for a Positive Integral Index
More on Proof of Binomial Theorem
Problem1Proof of Binomial Theorem
Problem2Proof of Binomial Theorem
8.5: Some Important Observations
8.6: The General Term
Deductions From Binomial Theorem
Problem1Deductions From Binomial Theorem
Problem2Deductions From Binomial Theorem
8.7: The Middle Terms
The Middle Term in the Expansion of ( a + x ) ^2
Problem1The Middle Term in the Binomial Expansion
Problem2The Middle Term in the Binomial Expansion
More on Problem2The Middle Term in the Binomial Expansion
Problem3The Middle Term in the Binomial Expansion
8.8: The Binomial Series
Some Deductions From the Binomial Expansion of ( a + x ) ^n
Problem1Some Deductions From the Binomial Expansion
Problem2Some Deductions From the Binomial Expansion
Problem3Some Deductions From the Binomial Expansion
8.9: Approximations
Some Deductions From the Binomial Expansion of ( a + x ) ^n
Applications of the Binomial Theorem
Problem1Applications of the Binomial Theorem
8.10: Application to Summation of Series
Some Deductions From the Binomial Expansion of ( a + x ) ^n
9.1: Introduction
Measuring an Angle in Sexagesimal System
Problem1Measuring an Angle in Sexagesimal System
Sexagesimal System into Decimal form & Vice Versa
ProblemSexagesimal System into Decimal form & Vice Versa
9.2: Radian Measure
ProblemRadian Measure of an Angle
Problem2Radian Measure of an Angle
9.3: General and Its Measure in Degree and Radians
9.4: Relation Between Radian and Degree Measure
Relationship Between Radians & Degrees.
9.5: Relation Between ArcLength, Radius and General Angle
Relationship of RadiusCentral AngleArc Length
Problem 1: Relationship of RadiusCentral AngleArc Length
Problem2Relationship of RadiusCentral AngleArc Length
Problem 1: Area of a Circular Sector.
Problem2Area of a Circular Sector.
Problems Using Arcs and Sectors
More on Problems Using Arcs and Sectors
9.6: The Radian Function
9.7: Signs of the Trigonometric Function in the Four Quadrants
Signs of Trigonometric Ratios in Different Quadrants
ProblemSigns of Trigonometric Ratios in Different Quadrant
Problem2Signs of Trigonometric Ratios in Different Quadrant
Trigonometric Functions for a Unit Circle
Values of Remaining Trigonometric Ratios
Values of Trigonometric Ratios at Quadrantal Angle
ProblemValues 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
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
Problem5Proof of Fundamental Trigonometric Identity
10.2: The Distance Formula
Derivation of Distance formula
Problem 1: Derivation of Distance formula
ProblemDerivation of Distance formula
Problem 1: Use of Distance formula
ProblemUse of Distance formula
10.3: A Fundamental Law
Fundamental Law of Trigonometry
ProblemFundamental Law of Trigonometry
More on Fundamental Law of Trigonometry
Proof of Angle Addition Formula for Cosine
ProblemProof of Angle Addition Formula for Cosine
More on Proof of Angle Addition Formula for Cosine
10.4: Deductions From the Funndamental Law
Trigonometric Ratios and Allied Angles
Problem1Trigonometric Ratios and Allied Angles
More on Trigonometric Ratios and Allied Angles
Problem2Trigonometric Ratios and Allied Angles
10.5: The Sum and Difference Identities
Deductions From Fundamental Law
More on Deductions From Fundamental Law1
More on Deductions From Fundamental Law2
Problem1Deductions From Fundamental Law
Problem2Deductions From Fundamental Law
Problem3Deductions From Fundamental Law
10.6: Applications
Further Application of Basic Identities
Problem1Further Application of Basic Identities
More on Further Application of Basic Identities
Problem2Further Application of Basic Identities
10.7: Identities for Sin2A, Cios2A and Tan2A
ProblemDouble Angle Identities
10.8: Identities For Sin A/2, Cos A/2 and Tan A/2
10.9: Sum and Product Identities For Trigonometric Functions
Product to Sum or Difference of Sines and Cosines
ProblemProduct to Sum or Difference of Sines and Cosines
Sum or Difference to Product of Sines and Cosines
More on Sum or Difference to Product of Sines and Cosines
ProblemSum or Difference to Product of Sines and Cosines
10.10: Applications
11.1: Trigonometric Functions
Domain and Ranges of Trigonometric Functions and Fundamental Identiti
Problem1Domain and Ranges of Trigonometric Functions and Fundamental
Problem2Domain and Ranges of Trigonometric Functions and Fundamental
Problem3Domain and Ranges of Trigonometric Functions and Fundamental
Domain and Ranges of Sine and Cosine Functions
More on Domain and Ranges of Sine and Cosine Functions
ProblemDomain 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
ProblemDomain and Ranges of Tangent and Cotangent Functions
Domain and Ranges of Secant Function
More on Domain and Ranges of Secant Function
ProblemDomain and Range of Secant Function
Domain and Ranges of Cosecant Function
More on Domain and Ranges of Cosecant Function
ProblemDomain and Range of Cosecant Function
11.2: Periods of Trigonometric Functions
Introduction to Period of Trigonometric Functions
ProblemIntroduction 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
ProblemGraphs of Trigonometric Functions
Graph of y = Sin x From – 360 to 360 Degree
Problem1Graph of y = Sin x From – 360 to 360 Degree
Problem1Graph of y = Sin x From – 360 to 360 Degree
Graph of y = Cos x From – 360 to 360 Degree
Problem1Graph of y = Cos x From – 360 to 360 Degree
Problem2Graph of y = Cos x From – 360 to 360 Degree
Graph of y = Tan x From – 180 to 180 Degree
ProblemGraph of y = Tan x From – 180 to 180 Degree
Graph of y = Cot x From – 360 to 180 Degree
ProblemGraph of y = Cot x From – 360 to 180 Degree
Graph of y = Sec x From – 360 to 360 Degree
ProblemGraph of y = Sec x From – 360 to 360 Degree
Graph of y = Cosec x From – 360 to 360 Degree
ProblemGraph of y = Cosec x From – 360 to 360 Degree
Graph of Sin2A and Cos2A Where A is a Positive Constant
More on Graph of Sin2A and Cos2A Where A is a Positive Constant
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
12.1: The Law of Sines
12.2: The Laws of Cosines
12.3: The Laws 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
Problem1Engineering and Heights and Distances
Problem2Engineering and Heights and Distances
12.5: Half Angle Formulae in Terms of the Lengths of the Sides of a Triangle
ProblemThe Sine of Half the Angle Formula
The Cosine of Half the Angle in Terms of the Sides
ProblemThe Cosine of Half the Angle in Terms of the Sides
The Tangents of Half the Angle in Terms of the Sides
ProblemThe Tangents of Half the Angle in Terms of the Sides
ProblemConcept of Oblique Triangles
When Measures of One Side and Two Angles are Given
ProblemWhen Measures of One Side and Two Angles are Given
When Measures of Two Side and Their Included Angles are Given
ProblemWhen 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 by Measuring One Side and Two Angle
Area of Triangle by Measuring Three Sides
ProblemArea of Eqilateral Triangle With Given Sides
Area of Equilateral Triangle with Given Sides
More on Area of a Triangle with Given Sides
12.7: Circles Associated with a Triangle
Circles Connected With Triangles
ProblemCircles Connected With Triangles
12.8: CircumRadius in Terms of the Measure of a Side and the Measure of the Opposite
Relation Among Radius, CircumAngle & Chord of a CircumCircle
More on Relation Among Radius, CircumAngle & Chord of a CircumCircle
Problem1Relation Among Radius, CircumAngle & Chord of a CircumCirc
12.9: CircumRadius r in Terms of the Measure of three Sides of a Triangle
Relation Among Radius, CircumAngle & Chord of a CircumCircle
More on Relation Among Radius, CircumAngle & Chord of a CircumCircle
Problem1Relation Among Radius, CircumAngle & Chord of a CircumCirc
12.10: The InRadius of a Triangle
Relation Among InRadius, Perimeter & Area of Triangle
ProblemRelation Among InRadius, Perimeter & Area of Triangle
12.11: Radii of eCircles of a Triangle
Relation Among exRadius, Perimeter & Area of Triangle
ProblemRelation Among exRadius, Perimeter & Area of Triangle
13.1: Inverse Trigonometric Functions and Their Domains and Ranges
Introduction to Inverse Trigonometric Functions
Vertical and Horizontal Line Tests
More on Vertical and Horizontal Line Tests
Problem1The Inverse Sine Function
Problem2The Inverse Sine Function
Inverse Relation of General Sine Functions
Problem1The Inverse Cosine Function
Problem2The Inverse Cosine Function
Problem1The Inverse Tangent Function
Problem2The Inverse Tangent Function
Inverse Cotangent, Secant and Cosecant Functions
More on Inverse Cotangent, Secant and Cosecant Functions
Further on Inverse Cotangent, Secant and Cosecant Functions
Problem1Inverse Cotangent, Secant and Cosecant Functions
Problem2Inverse Cotangent, Secant and Cosecant Functions
Domains and Ranges of Principal and Inverse Trigonometric Functions
Problem1Domains and Ranges of Principal andInverse Trigonometric Fun
Problem2Domains and Ranges of Principal andInverse Trigonometric Fun
Problem3Domains and Ranges of Principal andInverse Trigonometric Fun
Problem4Domains and Ranges of Principal andInverse Trigonometric Fun
Problem5Domains 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
ProblemAddition and Subtraction Formulas
ProblemMore on Addition and Subtraction Formulas
13.2: Applications
Introduction to Solutions of Trigonometric Equations
ProblemIntroduction 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
Problem1Solution of General Trigonometric Equations
Problem2Solution of General Trigonometric Equations
Problem3Solution of General Trigonometric Equations
Solution of General Trigonometric Equations
Solution of General Trigonometric Equations by Factorization
ProblemSolution of General Trigonometric Equations by Factorization
Solution of Trigonometric Equations by Trigonometric Identities
ProblemSolution of Trigonometric Equations by Trigonometric Identiti
Solution of Trigonometric Equations by Quadratic Formula
ProblemSolution of Trigonometric Equations by Quadratic Formula
Writing aSinA + bCosA in the Form r Sin(A + B )
Trigonometric Equations Containing Principal Functions
ProblemTrigonometric Equations Containing Principal Functions
Applications of Inverse Trigonometric Functions
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