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Math-X
Chapter 1: Sets (108 videos) (Practice Test)
1.1: Revision
- Set Definition
1.2: Some Important Sets of Numbers (Practice Test)
- Definition & Notation of Some Important Sets
- Set Notation & its Characteristics
- Presentation of a Set
- Problem 1: Presentation of a Set
- Set Builder Notation
- Problem 1: Set Builder Notation
- Empty set and Singleton Set
- Problem 1: Empty Set & Singleton Set
- Finite & Infinite Set
- Problem 1: Finite & Infinite Set
- Equal & Equivalent Sets
- Problem 1: Equal & Equivalent Sets
- Subset Definition
- Problem 1: 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
1.3: Operations on Two Sets (Practice Test)
- Union of Two Sets
- Problem 1: Union of Two Sets
- 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
- Universal Set
- Complement of a Set
- Problem 1: Complement of a Set
1.4: Operations of Union and Intersection on Three Sets
- Operations of Union and Intesection on three sets
1.5: Properties of Union and Intersection for Two or Three Sets (Practice Test)
- Commutative Property of Union
- Associative Property of Union of Sets
- Problem 1: Associative Property of Union of Sets
- Associative Property of Intersection of Sets
- Problem 1: Associative Property of Intersection of Sets
- Distributive Property of Union Over Intersection
- Problem 1: Distributive Property of Union Over Intersection
- Distributive property of Intersection over Union
- Problem 1: Distributive property of Intersection over Union
- Demorgan Law 1
- Problem 1: Demorgan Law 1
- Demorgan Law 2
- Problem 1: Demorgan Law 2
- Introduction to Venn Diagrams
- Problem 1: Introduction to Venn Diagrams
- 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
- Problem 1: Intersection Associativity for Sets
- More on 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
- Difference of Sets for Overlapping Sets
- Problem 1: Difference of Sets for Overlapping Sets
- Difference of Sets for Disjoint Sets
- Problem 1: Difference of Sets for Disjoint Sets
- Difference of Sets for a Set & its Subset
- Problem 1: Difference of Sets for a Set & its Subset
- Complement of Union for Overlapping Sets
- Problem 1: Complement of Union for Overlapping Sets
- Complement of Intersection for Overlapping Sets
- Problem 1: Complement of Intersection for Overlapping Sets
- Complement of Intersection for Disjoint Sets
- Problem 1: Complement of Intersection for Disjoint Sets
- Complement of Union for Disjoint Sets
- Problem 1: Complement of Union for Disjoint Sets
- Complement of Union for Set & its Subset
- Problem 1: Complement of Union for Set & its Subset
- Complement of Intersection for Set & its Subset
- Problem 1: Complement of Intersection for Set & its Subset
1.8: Ordered Pairs
- Introduction to Ordered Pairs
1.9: Cartesian Product of Sets
- Cartesian Product of Sets
- Problem 1: Cartesian Product of Sets
- Introduction to Binary Relation
- Problem 1: Introduction to Binary Relation
- Domain & Range of Binary Relation
- Problem 1: Domain & Range of Binary Relation
- Introduction to Function
- Problem 1: Introduction to Function
- Onto Function
- Problem 1: Onto Function
- One to One Function
- Problem 1: One to One Function
- Bijective Function
- Problem 1: Bijective Function
1.12: Cartesian Coordinate System for Plane
- Cartesian Coordinate System & Cartesian Plane
- Problem 1: Cartesian Coordinate System & Cartesian Plane
1.13: Graphical Representation of Cartesian Product
- Introduction to Graphs
Chapter 2: System of Real Numbers, Exponents and Radicals (70 videos) (Practice Test)
2.1: Properties of Rational Numbers
- Introduction to Rational Numbers
- Problem 1: Introduction to Rational Numbers
2.2: Decimal Fractions as Rational and Irrational Numbers (Practice Test)
- Decimal Representation of Rational Number
- Problem 1: Decimal Representation of Rational Number
- Decimal Representation of Irrational Number
2.3: Set of Real Numbers
- Introduction to Real Numbers
2.4: Properties of Real Numbers (Practice Test)
- Closure Law of Rational Numbers
- Problem 1: Closure Law of Rational Numbers
- Commutative Law
- Associative Law
- Problem 1: Associative Law
- Additive Identity & Additive Inverse
- Problem 1: Additive Identity & Additive Inverse
- Multiplicative Identity & Inverse
- Problem 1: Multiplicative Identity & Inverse
- Distributive Law
- Problem 1: Distributive Law
- Trichotomy Property of Inequality
- Problem 1: Trichotomy Property of Inequality
2.5: Properties of Equality of Real Numbers (Practice Test)
- Reflexive And Symmetric Property of Equality
- Transitive Property of Equality
- Problem 1: Transitive Property of Equality
- Additive Property of Equality
- Multiplicative Property of Equality
- Cancellation Property of Equality
- Problem 1: Cancellation Property of Equality
2.6: Properties of Inequality of Real Numbers (Practice Test)
- Archimedian Property of Inequality
- Transitive Property of Inequality
- Problem 1: Transitive Property of Inequality
- Additive Property of Inequality
- Multiplicative Property of Inequality
- Problem 1: Multiplicative Property of Inequality
2.7: Exponent
- Exponent or Index Definition
- Problem 1: Exponent or Index Definition
- Law of Sum of Power of Exponents
- Problem 1: Law of Sum of Power of Exponents
- Law of Power of Product of Exponent
- Problem 1: Law of Power of Product of Exponent
- Law of Power of Power of Exponent
- Problem 1: Law of Power of Power of Exponent
- Law of Quotient of Power with Same Base
- Problem 1: Law of Quotient of Power with Same Base
- Law of Power of a Fraction
- Problem 1: Law of Power of a Fraction
2.9: Radicals and Square Root of Positive Real Number (Practice Test)
- Introduction to Radical
- Square Root
- Problem 1: Square Root
- Properties of Square Root
- Problem 1: Properties of Square Root
- More on Properties of Square Root
2.10: The nth Root of a Positive Real Number (Practice Test)
- qth Root of x
- Problem 1: qth Root of x
- Properties of qth Root of x
- Problem 1: Properties of qth Root of x
2.11: Rational Exponents (Practice Test)
- Rational Exponents
- Problem 1: Rational Exponents
- Properties of Rational Exponents
- Problem 1: Properties of Rational Exponents
- Introduction to Surds
- Problem 1: Introduction to Surds
- Addition & Subtraction of Surds
- Problem 1: Addition & Subtraction of Surds
- Problem 2: Addition & Subtraction of Surds
- Multiplication & Division of Surds
- Problem 1: Multiplication & Division of Surds
- Problem 2: Multiplication & Division of Surds
- Introduction to Rationalization
- Rationalizing Denominator & its Types
- Problem 1: Rationalizing Denominator & its Types
- Problem 2: Rationalizing Denominator & its Types
Chapter 3: Logarithms (37 videos) (Practice Test)
3.1: Introduction
- Logarithm Definition
- Problem 1: Logarithm Definition
3.2: Secintific Notation (Practice Test)
- Introduction to Scientific Notation
- Problem 1: Introduction to Scientific Notation
- Adding & Subtracting Scientific Notation
- Problem 1: Adding & Subtracting Scientific Notation
- Multiplication of Numbers in Scientific Notation
- Problem 1: Multiplication of Numbers in Scientific Notation
- Division of Numbers in Scientific Notation
- Problem 1: Division of Numbers in Scientific Notation
- Converting Scientific to Common form
- Problem 1: Converting Scientific to Common form
3.3: Definition of Logarithm (Practice Test)
- Logarithm Definition
- Problem 1: Logarithm Definition
- Converting Log to Exponential Form
- Problem 1: Converting Log to Exponential Form
- Converting Exponential to Log Form
- Problem 1: Converting Exponential to Log Form
- Product Law of Logarithm
- Problem 1: Product Law of Logarithm
- Power Law of Logarithm
- Problem 1: Power Law of Logarithm
- Quotient Law of Logarithm
- Problem 1: Quotient Law of Logarithm
3.5: Change of Base in Logarithms
- Law of Change of Base of Logarithm
- Problem 1: Law of Change of Base of Logarithm
- Common Logarithm
- Problem 1: Common Logarithm
- Characteristic & Mantissa of Logarithm
- Problem 1: Characteristic & Mantissa of Logarithm
3.7: Antilogarithms
- Introduction to Anti-Logarithms
- Problem 1: Introduction to Anti-Logarithms
3.8: Applications of Logarithms in Computation
- Applications of Logarithm Laws in Calculations
- Problem 1: Applications of Logarithm Laws in Calculations
- Problem 2: Applications of Logarithm Laws in Calculations
- Problem 3: Applications of Logarithm Laws in Calculations
- Problem 4: Applications of Logarithm Laws in Calculations
Chapter 4: Algebraic Expression (39 videos) (Practice Test)
4.1: Varibales and Constants
- Introducing Variable & Constant
- Problem 1: Introducing Variable & Constant
4.2: Coefficient
- Introducing Coefficient & Exponent
- Problem 1: Introducing Coefficient & Exponent
4.3: Algebraic Expressions
- Introducing Algebraic Expression
4.4: Kinds of Algebraic Expressions (Practice Test)
- Introduction to Polynomials
- Problem 1: Introduction to Polynomials
- Rational & Irrational Expressions
4.5: Classification of Polynomials
- Polynomials w.r.t Terms & Variables
- Problem 1: Polynomials w.r.t Terms & Variables
4.6: Order of Algebraic Expressions
- Ordering of an Algebraic Expressions
4.7: Value of Algebraic Expression
- Value of an Algebraic Expression
- Problem 1: Value of an Algebraic Expression
- Problem 2: Value of an Algebraic Expression
4.8: Fundamental Operations on Algebraic Expressions (Practice Test)
- Addition of Algebraic Expression
- Problem 1: Addition of Algebraic Expression
- Equality Property of Rational Expression
- Product of Algebraic Expression
- Problem 1: Product of Algebraic Expression
- Division of Algebraic Expression
- Problem 1: Division of Algebraic Expression
4.9: Remainder Theorem
- Remainder Theorem
- Problem 1: Remainder Theorem
4.10: Formula and their Applications (Practice Test)
- Square of Sum of Two Terms
- Problem 1: Square of Sum of Two Terms
- Square of Difference of Two Terms
- Difference of Square of Two Terms
- Square of Sum of Three Terms
- Problem 1: Square of Sum of Three Terms
- Cube of Sum of Two Terms
- Problem 1: Cube of Sum of Two Terms
- Cube of Difference of Two Terms
- Problem 1: Cube of Difference of Two Terms
- Sum & Differences of Cube
- Problem 1: Sum & Differences of Cube
- Twice the Sum of Square of Two Terms
- Problem 1: Twice the Sum of Square of Two Termss
- Four Times Product of Two Terms
- Problem 1: Four Times Product of Two Terms
Chapter 5: Factorization, H.C.F, L.C.M, Simplification and Square Root (49 videos) (Practice Test)
- Factoring Trinomial & Tetranomial of Degree One
- Problem 1: Factoring Trinomial & Tetranomial of Degree One
- Problem 2: Factoring Trinomial & Tetranomial of Degree One
- Factoring Square of Sum Or Difference of Two Terms
- Problem 1: Factoring Square of Sum Or Difference of Two Terms
5.2: Factors of Expressions Reducible to Difference of Square of Two Terms (Practice Test)
- Factoring Difference of Square of Two Terms
- Problem 1: Factoring Difference of Square of Two Terms
- Problem 2: Factoring Difference of Square of Two Terms
- Factoring Polynomial of Degree Four
- Problem 1: Factoring Polynomial of Degree Four
- Problem 2 : Factoring Polynomial of Degree Four
5.3: Factors of the Quadratic Polynomial (Practice Test)
- Factoring Quadratic Equation-Leading Coefficient-1
- Problem 1: Factoring Quadratic Equation-Leading Coefficient-1
- Factoring Quadratic Polynomial-Non-1 Leading Coefficient
- Problem 1: Factoring Quadratic Polynomial-Non-1 Leading Coefficient
- Problem 2: Factoring Quadratic Polynomial-Non-1 Leading Coefficient
5.4: Factoring Sum or Difference of Cube of Two Terms
- Factoring Sum or Difference of Cube of Two Terms
- Problem 1: Factoring Sum or Difference of Cube of Two Terms
- Problem 2: Factoring Sum or Difference of Cube of Two Terms
5.5: Factoring Sum of Cube of Three Terms Difference Three Times their Combined Produ
- Factoring sum of cube of three temrs
- Problem 1: Factoring sum of cube of three terms
- Problem 2: Factoring sum of cube of three terms
5.6: Factoring Product of Difference of Two of All Three Terms
- Factoring product of difference of two of all three terms
- Problem 1: Factoring product of difference of two of all three terms
5.7: Factorization by Using Remainder theorem
- Factorization by using Remainder Theorem
- Problem 1: Factorization by using Remainder Theorem
5.8: Highest Common Factor (Practice Test)
- H.C.F or G.C.D of Algebraic Expressions
- Problem 1: H.C.F or G.C.D of Algebraic Expressions
- Problem 2: H.C.F or G.C.D of Algebraic Expressions
- H.C.F of Algebraic Expression by Division
- Problem 1: H.C.F of Algebraic Expression by Division
5.9: Least Common Multiple of Polynomials
- L.C.M of Algebraic Expression by Factorization
- Problem 1: L.C.M of Algebraic Expression by Factorization
- Problem 2: L.C.M of Algebraic Expression by Factorization
- Problem 3: L.C.M of Algebraic Expression by Factorization
- L.C.M of Algebraic Expression by formula
5.10: Simplification of Algebraic Fractions (Practice Test)
- Adding and Subtracting Algebraic Expressions
- Dividing & Multiplying Algebraic Expressions
- Problem 1: Dividing & Multiplying Algebraic Expressions
- Problem 2: Dividing & Multiplying Algebraic Expressions
5.11: Simplification of Algebraic Fractions Involving Four Fundamental Operations Toge
- Simplication of algebraic fraction with all four operations
5.12: The Square Root of an Algebraic Expression (Practice Test)
- Square Root of Algebraic Expression-Factorization
- Problem 1: Square Root of Algebraic Expression-Factorization
- Problem 2: Square Root of Algebraic Expression-Factorization
- Square Root of Algebraic Expression-Division
- Problem 1: Square Root of Algebraic Expression-Division
- Problem 2: Square Root of Algebraic Expression-Division
- Square Root of Rational Expression
- Problem 1: Square Root of Rational Expression
Chapter 6: Algebraic Sentences (28 videos) (Practice Test)
6.1: Solution of Simple Linear Equations in One or Two Variables (Practice Test)
- Solution of Simple Linear Equations in one Variables
- Problem 1: Solution of Simple Linear Equations in one Variables
- Solving Simultaneous Linear Equations by Substitution
- Problem 1: Solving Simultaneous Linear Equations by Substitution
6.2: Graphical Solution of Two Simultaneous Linear Equations
- Graphical Solution of Simultaneous Linear Equations
6.3: Solution of Equations Involving Radicals in One Variable
- Solving Radical Equations in One Variable
- Problem 1: Solving Radical Equations in One Variable
- Problem 1: Solving Radical Equations in One Variable
6.4: Solution of Equations in One Variable Involving Absolute Value (Practice Test)
- Introduction to absolute value equation
- Problem 1: Introduction to absolute value equation
- Solving Absolute Valued Equations “
- Problem 1: Solving Absolute Valued Equations
6.5: Inequalities or Inequations (Practice Test)
- Solution of Inequalities
- Problem 1: Solution of Inequalities
- Representing Solution of Inequalities on Number Line
- Problem 1: Representing Solution of Inequalities on Number Line
6.6: Quadratic Equations in One Variable
- Quadratic Equations in One Variable
- Problem 1: Quadratic Equations in One Variable
6.7: Solution of Quadratic Equations by Factorization
- Solving Quadratic Equations by Factorization
- Problem 1: Solving Quadratic Equations by Factorization
6.8: Solution of Quadratic Equations by Completing Squares
- 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
6.9: Derivation of Quadratic Formula
- Derivation of Quadratic formula
- Problem 1: Derivation of Quadratic formula
6.10: Solution of Quadratic Equations by Quadratic Formula
- Solving Quadratic Equation by Quadratic formula
- Problem1-Solving Quadratic Equation-Quadratic Formula
- Problem 2: Solving Quadratic Equation by Quadratic formula
Chapter 7: Matrices (63 videos) (Practice Test)
7.1: Introduction
- Introduction to Matrix
- Problem 1: Introduction to Matrix
7.2: Notation
- Location of elements in Matrix
- Problem 1: Location of elements in Matrix
7.3: Order of Matrix
- Order of Matrix
- Problem 1: Order of Matrix
7.4: Location of Elements or Entries
- Location of elements in Matrix
- Problem 1: Location of elements in Matrix
- Row Matrix and Column Matrix
- Problem1-Singular and Non-Singular Matrix
- Problem 1: Row Matrix and Column Matrix
- Square Matrix and Rectangular Matrix
- Problem2-Singular and Non-Singular Matrix
- Problem 1: Square Matrix and Rectangular Matrix
- Null Matrix or Zero Matrix
- Problem 1: Null Matrix or Zero Matrix
- Negative of Matrix
- Problem 1: Negative of Matrix
- Diagonal Matrix
- Problem 1: Diagonal Matrix
- Scalar Matrix
- Problem 1: Scalar Matrix
- Identity Matrix
- Problem 1: Identity Matrix
7.6: Transpose of Matrix
- Transpose of a Matrix
- Problem 1: Transpose of a Matrix
7.7: Equality of Matrices
- Equal Matrices
- Problem 1: Equal Matrices
- Problem 2: Equal Matrices
7.8: Addition of Matrices
- Addition of Matrices
- Problem 1: Addition of Matrices
7.9: Additive Identity
- Additive Identity of a Matrix
- Problem 1: Additive Identity of a Matrix
7.10: Additive Inverse of A Matrix
- Additive Inverse of a Matrix
- Problem 1: Additive Inverse of a Matrix
7.11: Commutative Property w.r.t Addition
- Commutative Law under Addition for Matrices
- Problem 1: Commutative Law under Addition for Matrices
7.12: Associative Property w.r.t Addition
- Associaitve Law under Addition for Matrices
- Problem 1: Multiplication of Matrices
- Problem 1: Associaitve Law under Addition for Matrices
- Problem 2: Multiplication of Matrices
7.13: Subtraction of Matrices
- Subtraction of Matrices
- Problem 1: Subtraction of Matrices
7.14: Multiplication of Matrix by Real Number
- Multiplication of Matrix by a Real Number
- Problem 1: Multiplication of Matrix by a Real Number
7.15: Matrix Multiplication
- Multiplication of Matrices
- Problem 1: Multiplication of Matrices
- Problem 2: Multiplication of Matrices
7.16: Properties of Multiplication of Matrices (Practice Test)
- 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
7.17: Identity Matrix w.r.t Multiplication
- Multiplicative Identity of a Matrix
- Problem 1: Multiplicative Identity of a Matrix
7.18: Determinant of Matrix
- Determinant of 2-by-2 Matrix
7.19: Singular & Non-Singular Matrices
- Singular and Non-singular Matrix
- Problem 1: Singular and Non-singular Matrix
7.20: Adjoint of Matrix
- Adjoint of a Matrix
- Problem 1: Adjoint of a Matrix
7.21: Multiplicative Inverse of Matrix
- Inverse of Matrix using Adjoint
- Problem 1: Inverse of Matrix using Adjoint
7.22: Solution of Two Simultaneous Linear Equations Using Matrices
- Solving Simultaneous Equations-Inversion Method
7.23: Cramers Rule
- Solving Simultaneous Equations-Cramers Rule
Chapter 8: Elimination (8 videos) (Practice Test)
8.1: Concept of Elimination
- Concept of Elimination
- Problem 1: Concept of Elimination
8.2: Elimination by Substitution Method
- Elimination by Substitution Method
8.3: Elimination by Comparison Method
- Elimination by Comparison Method
8.4: Elimination by Application of Formulae
- Elimination by the Application of Formulae
- Problem 1: Elimination by the Application of Formulae
8.5: Method of Cross-Multiplication
- Method of Cross-Multiplication
- Problem 1: Method of Cross-Multiplication
Chapter 9: Variations (38 videos) (Practice Test)
9.1: Ratio
- Concept of Ratio
- Problem 1: Concept of Ratio
9.2: Proportion
- Introduction to Proportion
9.3: Continued Proportion
- Continued Proportional
- Direct Variations
- Problem 1: Direct Variations
- Problem 2: Direct Variations
- Inverse Variations
- Problem 1: Inverse Variations
- Problem 2: Inverse Variations
- Problem 3: Inverse Variations
9.5: K-Method And theorems on Proportion
- K-Method and Theorem 1 on Proportion
- Problem 1: K-Method and Theorem 1 on Proportion
- K-Method and Theorem 2 on Proportion
9.6: Properties of Proportion (Practice Test)
- Law of Proportion
- Problem 1: Law of Proportion
- Duplicate Ratio
- Problem 1: Duplicate Ratio
- Invertendo Theorem
- Problem 1: Invertendo Theorem
- Alternando Theorem
- Problem 1: Alternando Theorem
- Componendo Theorem
- Problem 1: Componendo Theorem
- Dividendo Theorem
- Problem 1: Dividendo Theorem
- Componendo-Dividendo Theorem
- Transitive Property of Ratio
- Problem 1: Transitive Property of Ratio
- Word Problem of Ratio of Shadow & Height
- Problem 1: Word Problem of Ratio of Shadow & Height
- Word problem of Ratio between Two Numbers
- Problem 1: Word problem of Ratio between Two Numbers
- Word problem of Ratio of Sides of Polygons
- Problem 1: Word problem of Ratio of Sides of Polygons
- Word problem of Ratio of angles of Polygons
- Problem 1: Word problem of Ratio of angles of Polygons
- Word problem of Ratio of Income & Expenses
Chapter 10: Information Handling (114 videos) (Practice Test)
10.1: Introduction
- Concept of Information Handling
- Problem 1: Concept of Information Handling
- Data, Collection of Data, Presentation of Data
- Problem 1: Data, Collection of Data, Presentation of Data
- Constant & Variable.
- Problem 1: Constant & Variable.
- Population
- Problem 1:Population
10.3: Types of Variables
- Types of Variables
- Problem 1: Types of Variables
10.4: Types of Data
- Types of Data
- Problem 1: Types of Data
10.5: Collection of Data
- Data, Collection of Data, Presentation of Data
- Problem 1: Data, Collection of Data, Presentation of Data
10.6: Presentation of Data Or Information
- Data, Collection of Data, Presentation of Data
- Problem 1: Data, Collection of Data, Presentation of Data
10.7: Classification
- Classification & No. of Classes
- Problem 1: Classification & No. of Classes
- Ungrouped & Grouped Data
- Problem 1: Ungrouped & Grouped Data
- Classification & No. of Classes
- Problem 1: Classification & No. of Classes
- Specification of Classes
- Problem 1: Specification of Classes
- Class interval & Class Limits
- Problem 1: Class interval & Class Limits
- Class Mark & Class Boundaries.
- Problem 1: Class Mark & Class Boundaries.
- One way Tabulation
- Problem 1: One way Tabulation
- Two way Tabulation
- Problem 1: Two way Tabulation
10.10: Frequency Distribution (Practice Test)
- Construction of Continuous Frequency Table
- Problem 1: Construction of Continuous Frequency Table
10.11: Construction of Frequency Distribution (Practice Test)
- Formation of Frequency Distribution byTally Bar Method
- Problem 1: Formation of Frequency Distribution by Tally Bar Method
- Formation of Frequency Distribution by Direct Method
- Problem 1: Formation of Frequency Distribution by Direct Method
10.12: Graphs
- Advantages and Disadvantages of Graphs
- Problem 1: Advantages and Disadvantages of Graphs
- Construction of Graphs
- Problem 1: Construction of Graphs
- Graph of Frequency Distribution by Histogram
- Problem 1: Constructing Histogram with Equal Intervals
10.14: Frequency Polygon
- Construction of Frequency Polygon
- Problem 1: Construction of Frequency Polygon
10.15: Diagrams Representation (Practice Test)
- Simple Bar Diagram
- Problem 1: Simple Bar Diagram
- Multiple Bar Diagram
- Problem 1: Multiple Bar Diagram
- Pie Diagram
- Problem 1: Pie Diagram
10.16: Measures of Location ( Central Tendency ) (Practice Test)
- Measure of Location
- Problem 1: Measure of Location
- Importance of Measure of Central Tendency
- Problem 1: Importance of Measure of Central Tendency
10.17: Types of Measures of Central Tendency
- Types of Measures of Central Tendency
- Problem 1: Types of Measures of Central Tendency
10.18: Arithmetic Mean ( A.M ) (Practice Test)
- Arithmetic Mean (A.M) for Ungrouped Data
- Problem 1: A.M of Ungrouped Data by Direct Method
- Arithmetic Mean (A.M) for Grouped Data by Direct Method
- Problem 1: A.M for Grouped Data by Direct Method
- Short formula for Computing Arithmetic Mean for Ungrouped Data
- Problem 1: A.M for Ungrouped Data by Short formula Method
- Short formula for Computing Arithmetic Mean for Grouped Data
- Problem 1: A.M for Grouped Data by Short formula Method
- Coding Method of Finding Arithmetic Mean
- Problem 1: A.M for Ungrouped Data by Coding Method
- Finding A.M for Grouped Data-Coding Method
- Problem 1: A.M for Grouped Data by Coding Method
- Median for Ungrouped Data
- Problem 1: Median for Ungrouped Data
- Median for Grouped Continuous Data
- Problem 1: Median for Grouped Continuous Data
- Mode for Ungrouped Discrete Data
- Problem 1: Mode for Ungrouped Discrete Data
- Mode for Grouped Data
- Problem 1: Mode for Grouped Data
10.21: Merits And Demerits of Measures of Central Tendency (Practice Test)
- Properties of Arithmetic Mean
- Problem 1: Properties of Arithmetic Mean
- Merits and Demerits of Median
- Problem 1: Merits and Demerits of Median
- Merits and Demerits of Mode
- Problem 1: Merits and Demerits of Mode
10.22: Concept of Dispersion
- Concept of Dispersion
- Problem 1: Concept of Dispersion
10.23: Importance & Uses of Measures of Dispersion
- Importance & Uses of Measures of Dispersion
- Problem 1: Importance & Uses of Measures of Dispersion
10.24: Types of Measures of Dispersion (Practice Test)
- Calculation of Range for Raw or Ungrouped Data
- Problem 1: Calculation of Range for Raw or Ungrouped Data
- Calculation of Range for Grouped Data
- Problem 1: Calculation of Range for Grouped Data
- Uses and Properties of Range
- Problem 1: Uses and Properties of Range
- Limitations or Drawbacks of Range
- Problem 1: Limitations or Drawbacks of Range
- Calculation of Variance by Proper Mean Formula
- Calculation of Variance of Grouped Data by Proper Mean Formula
- Calculation of Variance by Short Cut Method
- Problem 1: Calculation of Variance by Short Cut Method
- Calculation of the Variance and Standard Deviation by Direct Method
- Problem 1: Calculation of Variance by Direct Method
10.26: Standard Deviation ( S.D ) (Practice Test)
- Calculation of Standard Deviation by Proper Mean Formula
- Problem 1: Calculation of S.D by Proper Mean formula
- Calculation of S.D by Short Cut Method
- Problem 1: Calculation of S.D by Short Cut Method
- Calculation of S.D by Direct Method
- Problem 1: Calculation of S.D by Direct Method
- Uses and Properties of Standard Deviation
- Problem 1: Uses and Properties of Standard Deviation
- Limitations of Variance and Standard Deviation
- Problem 1: Limitations of Variance and Standard Deviation
- Criteria for the measurement of spread of Observation
- Problem 1: Criteria for the measurement of spread of Observation
Chapter 11: Fundamental Concepts of Geometry (29 videos) (Practice Test)
11.1: Inductive & Deductive Reasoning
- Inductive and deductive reasoning
- Problem 1: Inductive and deductive reasoning
11.2: Characteristics of Deductive Method
- Analytical and Synthesis method to Prove theorem
- Introduction to Point, Line, Line-segment and Ray
- Problem 1: Introduction to Point, Line, Line-segment and Ray
- Collinear and Non-collinear Points
- Problem 1: Collinear points and Non-collinear points
- Between and Beyond the line segment
- Problem 1: Between and Beyond the line segment
- Line segment ray and half line
- Problem 1: Line segment ray and half line
- Convex Set
- Problem 1: Convex Set
- Opposite Rays
- Problem 1: Opposite Rays
- Interior and exterioir of an angle
- Anlge Construction Postulate
- Problem 1: Anlge Construction Postulate
- Adjacent Angles
- Problem 1: Adjacent Angles
- Side & Angle Bisector
- Problem 1: Side and Angle Bisector
- Complementary and Supplementary angles
- Problem 1: Complementary and supplementary anlges
- Acute, Obtuse and Congruent Angles
- Problem 1: Acute, Obtuse and Congruent Angles
- Vertically Opposite Angles
- Problem 1: Vertically Opposite Angles
- Right Angle and Perpendicular
Chapter 12: Demonstrative Geometry (74 videos) (Practice Test)
12.1: Theorems on Lines & Polygons (Practice Test)
- Introduction to Geometrical Theorems
- Elements in proving a geometrical theorem
- Problem 1: Elements in proving a geometrical theorem
- Problem 1: Analytical and Synthesis method to Prove theorem
- Reductio-Ad-Absurdum Method
- Problem 1: Reductio-Ad-Absurdum Method
- If two lines intersect each other,than vertical angles are congruent
- Interior and exterior of triangle
- Problem 1: Interior and exterior of triangle
- Triangluar Region and Triangular Area
- Interior and exterior angles of traingle
- Included Angle and Included Side of Triangle
12.4: Kinds of Triangle
- Kinds of Triangle
- Problem 1: Kinds of Triangle
12.5: One-One Correspondence between Two Triangles & Other Polygons
- Congruence of Other Polygons
12.6: Congruence of Triangles
- Congruency of Triangles
- Problem 1: Congruency of Triangles
12.7: Congruence of Other Polygons
- Congruence of Other Polygons
- Problem 1: Congruence of Polygons
12.8: Postulate 14- Side Angle Side Postulate (Practice Test)
- Side Angle Side Postulate
- Problem 1: side angle side postulate
- An exterior angle of a traingle is greater in measure than either of
- Problem 1:An exterior angle of a traingle is greater in measure than
12.9: Transversal, Interior & Exterior Angles
- Transversal, Interior and Exterior Angles
- Problem 1: Transversal, Interior and Exterior Angles
12.10: Alternate & Corresponding Angles
- Alternate and corresponding Angles
- Problem 1: Alternate and corresponding Angles
12.11: Corresponding Angles
- Alternate and corresponding Angles
- Problem 1: Alternate and corresponding Angles
12.12: Parallel Lines
- Parallel Lines
- Problem 1: Parallel Lines
12.13: Postulate 15. Parallel Lines Postulate (Practice Test)
- Parallel Lines Postulate
- Problem 1: Parallel Lines Postulate
- If a transversal intersects two coplanar lines
- If a transversal intersects two parallel lines
- Problem 1: If a transversal intersects two parallel lines
12.14: Parallelogram
- Kinds of Parallelogram
- Problem 1: Kinds of Parallelogram
12.15: Trapezoid & Trapezium (Practice Test)
- Trapezoid and Trapezium
- Problem 1: Trapezoid and Trapezium
- Sum of three angles of triangle is 180 degree
- Problem 1: Sum of three angles of triangle is 180 degree
- Angle opposite to equal sides are equal in triangle
- Angle-Side-Angle Postulate-1
- Side-Side-Side Postulate-3
- Sides Facing Equal Angles are Equal in Triangle-2
- Hypotenuse Side Postulate-4
- Diagonals of Parallelogram Bisects Each Other-1
- Parallelogram Opposite Sides – Congruent -Parallel-2
- Mid point Theorem-3
- All Medians of Triangle Trisect Each Other-4
- Proportional Segment Theorem-5
- Perpendicular Bisector Theorem-1
- Converse of Perpendicular Bisector Theorem-2
- Triangle Right Bisectors of Sides are Concurrent-3
- Angle Bisector Theorem-4
- Converse of Angle Bisector Theorem-5
12.16: Theorems on Inequalities (Practice Test)
- Longer Side Inequality Theorem-1
- Converse of Longer Side Inequality Theorem-1a
- Problem 1: Converse of Longer Side Inequality Theorem-1a
- Triangle Sum of Two Sides is Greater Than Third-2
- Problem 2: Triangle Sum of Two Sides is Greater Than Third-3
- Shortest Distance from Point to a Line-3
- Problem 2: Shortest Distance from Point to a Line-3
- Proportional Parts of Triangle by Side Splitter Theo-1
- Converse of Proportional Parts of Triangle -2
- Division of Opposite Side by Angle Bisector-3
- Proportional Parts of Similar Triangle-4
- Converse of Proportional parts of similar triangle
12.18: Pythagoras Theorem (Practice Test)
- Pythagoras Theorem-1
- Problem 1: Pythagoras Theorem-1
- Problem 2: Pythagoras Theorem-1
- Converse of Pythagoras Theorem-2
- Problem 1: Converse of Pythagoras Theorem-2
Chapter 13: Circle (49 videos) (Practice Test)
13.1: Circle
- Introduction to Circle & its Characteristics
- Problem 1: Introduction to Circle & its Characteristics
13.2: Circumference of a Circle
- Chord , Diameter & Circumference of a Circle
- Chord , Diameter & Circumference of a Circle
- Problem 1: Chord , Diameter & Circumference of a Circle
- Concept of Secant & Tangent Line
- Problem 1: Concept of Secant & Tangent Line
13.4: Diameter of Circle
- Chord , Diameter & Circumference of a Circle
13.5: Interior & Exterior of Circle
- Introduction to Circle & its Characteristics
13.6: Arc of a Circle
- Arc of a Circle
- Problem 1: Arc of a Circle
13.7: Semi-Circle
- Arc of a Circle
13.8: Minor Arc & Major Arc
- Arc of a Circle
13.9: Central Angle of An Arc
- Concept of Central Angle of an Arc
- Problem 1: Concept of Central Angle of an Arc
13.10: Congruent Circles
- Concept of Central Angle of an Arc
13.11: Congruent Arcs
- Concept of Central Angle of an Arc
13.12: Inscribed Angle of an Arc
- Concept of Inscribed Angle of an Arc
- Problem 1: Concept of Inscribed Angle of an Arc
13.13: Tangent & Point of Tangency
- Concept of Secant & Tangent Line
13.14: Common Tangents, Common Internal Tangents And Common External Tangents to Two Ci
- Concentric Circles and Common Internal and External Tangents to two C
- Problem 1: Concentric Circles,Common Internal & External Tangents of
13.15: Sector of a Circle
- Segment & Sector of a Circle
- Problem 1: Segment & Sector of a Circle
13.16: Segment of a Circle
- Segment & Sector of a Circle
13.17: Circum Circle of a Triangle
- Concept of Circum Circle of a Triangle
13.18: Inscribed Circle of a Triangle
- Concept of Inscribed Circle of a Triangle
- Problem 1: Concept of Inscribed Circle of a Triangle
13.19: Escribed Circle of a Triangle
- Concept of Escribed Circle of a Triangle
- Problem 1: Concept of Escribed Circle of a Triangle
13.20: Theorems on Circle (Practice Test)
- Perpendicular Radius Bisects Chord-3
- Perpendicular Bisector to a Chord Circle-2
- The perpendicular bisector of chord of circle passes through centre o
- Congruent Chords Equidistance from Circle-4
- Problem 2: Congruent Chords Equidistance from Circle-4
- Chords Equidistance of Circle are Congruent-5
- Problem 1: Chords Equidistance of Circle are Congruent-5
- Three Non-Collinear Points Form a Circle-1
- Problem 1: Three Non-Collinear Points Form a Circle-1
- Central angle theorem
- Problem 1: Central angle theorem
- Tangent to Circle-1
- Problem 1: Tangent to Circle-1
- Converse of Tangent to Circle-2
- Problem 1: Converse of Tangent to Circle-2
- Tangent and radial lines are perpendicular to each other
- Equal Tangent Segments from a Point to a Circle-3
- Distance of Centers of Externally Tangent Circles-4a
- Distance of Centers of internally Tangent Circles-4b
Chapter 14: Practical Geometry (23 videos) (Practice Test)
- Introduction to Practical Geometry
- Problem 1: Introduction to Practical Geometry
- Constructing Triangle with Three Sides
- Problem 1: Constructing Triangle with Three Sides
- Construction of a Triangle when one angle and two sides
- Constructing Triangle with Side & Two Angles
- Problem 1: Constructing Triangle with Side & Two Angles
14.2: The Ambiguous Case
- Constructing Triangle-Ambiguous Case
14.3: Concurrent Lines with Reference to a Triangle (Practice Test)
- Constructing Angler Bisectors of Triangle
- Constructing Perpendicular Bisectors of Triangle
- Constructing Medians of Triangle
- Constructing Altitudes of Triangle
14.4: To Draw the Circum-Circle of a Triangle
- Circumscribe a Circle About a Given Triangle
- Problem 1: Circumscribe a Circle About a Given Triangle
14.5: To Draw Incircle of a Triangle
- Inscribe a Circle in a Given Triangle
- Problem 1: Inscribe a Circle in a Given Triangle
14.6: To Draw Escribed Circle Opposite To a Vertex of a Triangle
- Escribe a Circle to a Given Triangle
14.7: To Draw the Tangent to a Circle at a Given Point on the Circle
- To Draw the Tangent to a Circle at a Given point on the Circle
14.8: To Draw Two Tangents to a Circle From a Point Outside the Circle
- Tangent from a Point Outside a Circle
14.9: To Draw the Direct Common Tangents to the Two Given Circles. (Practice Test)
- Direct Common Tangents to Circles
- Direct Common Tangents to circles by Method 2
- Direct Common Tangents of Circles with Same Radii
14.10: To Draw the Transverse Common Tangents to the Two Given Circles.
- Transverse Common Tangents to Circles1
Chapter 15: Trigonometry (36 videos) (Practice Test)
15.1: Introduction
- Meaning and Importance of Trigonometry
- Problem 1: Meaning and Importance of Trigonometry
15.2: Trigonometric Ratios of Acute Angles
- Trigonometric Ratios of an Acute Angle
- Problem 1: Trigonometric Ratios of an Acute Angle
15.3: Values of Trigonometric Ratios of Angles of 45, 30 And 60 Degree. (Practice Test)
- 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
15.4: Relations Between Trigonometric Ratios of the Complementary Angles.
- Trigonometric Ratios of an Complementary Angles
- Problem 1: Trigonometric Ratios of an Complementary Angles
15.5: Fundamental Trigonometric Identities (Practice Test)
- 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
- Problem 1: More on Fundamental Trigonometric Identity
15.6: Solution of Right Triangle (Practice Test)
- 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
15.7: Finding Heights and Distances by Using Trigonometric Ratios (Practice Test)
- Concept of Angle of Elevation & Depression
- Problem 1: Concept of Angle of Elevation & Depression
- when one Side & Angle of Elevation are Given
- Problem 1: when one Side & Angle of Elevation are Given
- when One Side & Angle of Depression are Given
- Problem 1: when One Side & Angle of Depression are Given
- when Hypotenuse & Angle of Elevation are Given
- Problem 1: when Hypotenuse & Angle of Elevation are Given
- when Given Sides-Angle of Elevation-Depression
- Problem 1: when Given Sides-Angle of Elevation-Depression