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Gen-Math-IX
Chapter 1: Number Systems (12 videos) (Practice Test)
1.1: Decimal System and Base
- Introduction to Decimal System and Base
- Problem-Introduction to Decimal System and Base
1.2: Base Five System
- Introduction to Base Five System
- Problem-Introduction to Base Five System
1.3: Binay System or Base 2 System
- Introducing Base 2 System
- Problem-Introducing Base 2 System
1.4: Addition and Subtraction in Base 5
- Addition and Subtraction in Base-5
- Problem-Addition and Subtraction in Base-5
1.5: Multiplication in Base 5 System
- Multiplication in Base-5 System
- Problem-Multiplication in Base-5 System
1.6: Basic Operations in Base 2 System
- Basic Operations in Base-2 System
- Problem-Basic Operations in Base-2 System
Chapter 2: Real Numbers and Coordinate System (45 videos) (Practice Test)
2.1: Real Number System
- Introduction to Rational Numbers
- Problem 1: Introduction to Rational Numbers
2.2: Irrational Numbers
- Introduction to Irrational Numbers
- Problem 1: Introduction to Irrational Numbers
2.3: Real Numbers
- Introduction to Real Numbers
2.4: Properties of the Real Numbers (Practice Test)
- Closure law of Whole Numbers Addition and Multiplication
- Closure law of Whole Numbers Subtraction and Division
- Closure law of Irrational Numbers Addition and Subtraction
- Closure law of Irrational Numbers Multiplication and Division
- Commutative Law
- Commutative law under Subtration and Division
- Associative Law
- Associative law of Subtraction and Division
- Problem 1: Associative Law
- Additive Identity & Additive Inverse
- Multiplicative Identity & Inverse
- Problem 1: Additive Identity & Additive Inverse
- Distributive Law
- Distributive Property of Multiplication over Subtraction
- Problem 1: Multiplicative Identity & Inverse
- Trichotomy Property of Inequality
- Problem 1: Distributive Law
- Problem 1: Distributive law of Multiplication over Subtraction
- 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
- Inequality Multiplicative Inverse
- Problem 1: Multiplicative Property of Inequality
2.7: Ordered Pairs
- Introduction to Ordered Pairs
2.8: The Cartesian Product
- Cartesian Product of Sets
- Problem 1: Cartesian Product of Sets
2.9: Coordinate System
- Cartesian Coordinate System & Cartesian Plane
- Problem 1: Cartesian Coordinate System & Cartesian Plane
2.10: Catesian Coordinate System for Plane
- Cartesian Coordinate System & Cartesian Plane
- Problem 1: Cartesian Coordinate System & Cartesian Plane
Chapter 3: Laws of Exponents and Logarithms (61 videos) (Practice Test)
- Exponent or Index Definition
- Problem 1: Exponent or Index Definition
- Law of Sum of Power of Exponents
- Law of Power of Product of Exponent
- Problem 1: Law of Sum of Power of Exponents
- Law of Power of Power of Exponent
- Law of Quotient of Power with Same Base
- Problem 1: Law of Power of Product of Exponent
- Law of Power of a Fraction
- Problem 1: Law of Power of Power of Exponent
- Problem 1: Law of Quotient of Power with Same Base
- Problem 1: Law of Power of a Fraction
3.2: Square Root
- Square Root
- Problem 1: Square Root
- Properties of qth Root of x
- Problem 1: qth Root of x
- qth Root of x
- Problem 1: Properties of qth Root of x
3.4: Scientific Notation (Practice Test)
- Introduction to Scientific Notation
- Problem 1: Introduction to Scientific Notation
- Converting Scientific to Common form
- Movement of Decimal in Scientific Notation
- Problem 1: Converting Scientific to Common form
- Converting common to scientific form
- Logarithm Definition
- Converting Exponential to Log Form
- Problem 1: Logarithm Definition
- Converting Log to Exponential Form
- Problem 1: Converting Exponential to Log Form
- How to Find Unknown Base in Log Form
- How to Find Unknown Number in Log Form
- Problem 1: Converting Log to Exponential Form
- How to Find Unknown index in Log Form
- Law of Change of Base of Logarithm
- Product Law of Logarithm
- Problem 1: How to Find Unknown Base in Log Form
- Power Law of Logarithm
- Problem 1: How to Find Unknown Number in Log Form
- Quotient Law of Logarithm
- Problem 1: How to Find Unknown index in Log Form
- Problem 1: Law of Change of Base of Logarithm
- Problem 1: Product Law of Logarithm
- Problem 1: Power Law of Logarithm
- Problem 1: Quotient Law of Logarithm
- Common Logarithm
- Problem 1: Common Logarithm
- Reference Position in scientific notation
- Characteristic & Mantissa of Logarithm
- Problem 1: Reference Position in scientific notation
- How to Find Characteristic of Given Number
- Finding Mantissa of Number by Log Table
- Problem 1: Characteristic & Mantissa of Logarithm
- Problem 1: How to Find Characteristic of Given Number
- Problem 1: Finding Mantissa of Number by Log Table
3.7: Anti-Logarithm
- Introduction to Anti-Logarithms
- Problem 1: Introduction to Anti-Logarithms
3.8: Arithematical Computation With the Help of Logarithm
- Applications of Logarithm Laws in Calculations
- Problem 2: Applications of Logarithm Laws in Calculations
- Problem 1: Applications of Logarithm Laws in Calculations
- Problem 3: Applications of Logarithm Laws in Calculations
- Problem 4: Applications of Logarithm Laws in Calculations
Chapter 4: Statistics (53 videos) (Practice Test)
4.1: 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
- Introduction to Numerical Data
- Collection of Data Using a Questionnaire
- Collection of Data Through Observation
- Collection of Data Through Interviews
- Collection of Data by Measuring
- Collection of Data by Using electronic means and Internet
4.3: Ungrouped Data
- Types of Data
- Problem 1: Types of Data
4.4: Grouped Data
- Ungrouped & Grouped Data
- Problem 1: Ungrouped & Grouped Data
4.5: Classification of Data
- Classification & No. of Classes
- Problem 1: Classification & No. of Classes
4.6: Tabulation of Data
- Introduction to Tabulation
- Problem 1: Introduction to Tabulation
4.7: Class Interval
- Class interval & Class Limits
- Problem 1: Class interval & Class Limits
4.8: Class Frequency
- Class Frequency
- Problem 1: Class Frequency
4.9: Lower Limit and Upper Limit
- Class interval & Class Limits
- Problem 1: Class interval & Class Limits
4.10: Magnitude of Class Interval
- Class interval & Class Limits
- Problem 1: Class interval & Class Limits
4.11: Frequency Distribution (Practice Test)
- Construction of Continuous Frequency Table
- Problem 1: Construction of Continuous Frequency Table
4.12: To Prepare Frequency Distribution Table from Ungrouped Data
- Formation of Frequency Distribution byTally Bar Method
- Problem 1: Formation of Frequency Distribution by Tally Bar Method
4.13: Measures of Central Tendency (Practice Test)
- Measure of Location
- Problem 1: Measure of Location
- Types of Measures of Central Tendency
- Importance of Measure of Central Tendency
- Problem 2: Types of Measures of Central Tendency
- problem 3: Types of Measures of Central Tendency
- Problem 1: Types of Measures of Central Tendency
- 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
- Short formula for Computing Arithmetic Mean for Ungrouped Data
- Problem 1: A.M for Grouped Data by Direct Method
- Short formula for Computing Arithmetic Mean for Grouped Data
- Coding Method of Finding Arithmetic Mean
- Problem 1: A.M for Ungrouped Data by Short formula Method
- Finding A.M for Grouped Data-Coding Method
- Problem 1: A.M for Grouped Data by Short formula Method
- Problem 1: A.M for Ungrouped Data by Coding Method
- Problem 1: A.M for Grouped Data by Coding Method
4.15: Median
- Median for Ungrouped Data
- Problem 1: Median for Ungrouped Data
4.16: Mode
- Mode for Ungrouped Discrete Data
- Problem 1: Mode for Ungrouped Discrete Data
Chapter 5: Ratio, Proportion, Inheritance and Partnership (25 videos) (Practice Test)
- Concept of Ratio
- Problem 1: Concept of Ratio
- Properties of Ratio
- Problem 1: Properties of Ratio
- Introduction to Proportion
- Problem 1: Introduction to Proportion
- Law of Proportion
- Problem 1: Law of Proportion
5.3: Proportion Between Two Sets
- Direct Proportions
- Problem 2: Direct Variations
- Problem 1: Direct Variations
- Problem 3: Inverse Variations
- Inverse Proportion
- More on Inverse Proportion
5.5: Compound Proportion
- Introducing Compound Proportion
5.6: Continued Ratios
- Continued Proportional
- Problem-Introducing Continued Ratios
5.7: Proportional Division
- Introducing Proportional Division
- Problem-Introducing Proportional Division
5.8: Miscellaneous Problems
- Miscellaneous Proportional Problems
- Problem-Miscellaneous Proportional Problems
- Introducing Inheritance
- More on Introducing Inheritance
- Introducing Business Partnership
5.11: Compound Partnership (Practice Test)
- Introducing Business Partnership
Chapter 6: Percentage (34 videos) (Practice Test)
6.1: Percent
- Percentages, Fractions and Decimals
6.2: Problems on Percent
- Finding the Percentage of a Number
6.3: Zakat
- Zakat and Rate of Zakat
- Problem1-Zakat and Rate of Zakat
- Problem2-Zakat and Rate of Zakat
- Value-added Tax and GST
- Types of Taxation
- More on Types of Taxation
- Problem1-Taxation
- Problem2-Taxation
- Types of Taxation
- More on Types of Taxation
- Problem3-Taxation
- Types of Taxation
- More on Types of Taxation
- Problem4-Taxation
- Types of Taxation
- More on Types of Taxation
- Problem5-Taxation
6.9: Discount, Reduction
- Discount
- Problem1-Discount
6.10: Commission, Brokerage (Practice Test)
- Commission
6.11: Buying and Selling on Instalments
- Hire Purchased
6.12: Societies and Banks Loans (Practice Test)
- Profit on Deposit
- Markup on Loan
- Calculating Profit on Deposit
- Problem1-Calculating Profit on Deposit
- Calculating Markup on Loan
- Problem2-Calculating Profit on Deposit
- Problem3-Calculating Profit on Deposit
- Problem4-Calculating Profit on Deposit
- Problem1-Calculating Markup on Loan
- Problem2-Calculating Markup on Loan
- Problem3-Calculating Markup on Loan
Chapter 7: Fundamental Operations on Polynomials (17 videos) (Practice Test)
7.1: Variable
- Introducing Variable & Constant
7.2: Algebraic Expressions
- Introducing Algebraic Expression
7.3: Terms of an Expression
- Polynomials w.r.t Terms & Variables
- Problem 1: Polynomials w.r.t Terms & Variables
7.4: Co-efficients
- Introducing Coefficient & Exponent
- Problem 1: Introducing Coefficient & Exponent
7.5: Polynomial
- Introduction to Polynomials
- Problem 1: Introduction to Polynomials
7.6: Ordering a Polynomial
- Ordering of an Algebraic Expressions
7.7: Addition of Polynomials
- Addition of Algebraic Expression
- Problem 1: Addition of Algebraic Expression
7.8: Subtraction of Polynomials
- Equality Property of Rational Expression
- Subtraction of Polynomials
7.9: Multipllication of Polynomials
- Product of Algebraic Expression
- Problem 1: Product of Algebraic Expression
7.10: Division of Polynomials
- Division of Algebraic Expression
- Problem 1: Division of Algebraic Expression
Chapter 8: Formulae and Factors (32 videos) (Practice Test)
8.1: Formulae
- Square of Sum of Two Terms
- Problem 2: Square of Sum of Two Terms
- Problem 1: Square of Sum of Two Terms
8.2: Formula1
- K times Sum of Three Terms
- Problem-K times Sum of Three Terms
8.3: Factors and Factorization
- Introduction to Factorization
8.4: Factorization of Expressions of the Form ka+kb+kc
- Factorization of Expressions of the Form ka+kb+kc
- Problem-Factorization of Expressions of the Form ka+kb+kc
8.5: Formula 2
- Factoring Square of Sum Or Difference of Two Terms
- Problem 1: Factoring Square of Sum Or Difference of Two Terms
8.6: Use of Formulae 2 and 3
- Problem 1: Square of Sum of Two Terms
- Problem 1: Factoring Difference of Square of Two Terms
8.7: Factorization of Sum/Difference of Squares (Practice Test)
- Factoring Difference of Square of Two Terms
- Problem-Factoring Square of Difference of Two Terms
- Square of Sum of Two Terms
- Problem-Square of sum of two terms
8.8: Formula4
- Factoring Difference of Square of Two Terms
- Problem-Factoring Difference of Square of Two Terms
- Problem 2: Factoring Difference of Square of Two Terms
- Problem 1: Factoring Difference of Square of Two Terms
8.9: Factorization of Square of Difference of 2 Terms
- Factoring Difference of Square of Two Terms
- Problem-Factoring Square of Difference of Two Terms
8.10: Factorization of Expression Reducible to Sqaure of Difference
- Problem 2: Factoring Difference of Square of Two Terms
8.11: Formula5
- Factorization by Grouping
8.12: Factorization of product of two Linear Expression
- Factorization by Grouping
- Cube of Sum of Two Terms
- Problem 2: Cube of Sum of Two Terms
- Cube of Difference of Two Terms
8.14: Factorization of Sum/Difference of Cube
- Problem 1: Cube of Sum of Two Terms
- Problem 1: Cube of Difference of Two Terms
8.15: Formula8
- Sum & Differences of Cube
8.16: Factorization of Cube of Sum/Difference of 2 Terms
- Problem 1: Sum & Differences of Cube
Chapter 9: Algebraic Sentences, Matrices and Equations (50 videos) (Practice Test)
9.1: Linear Equation in 2 Variables; The Solution Set (Practice Test)
- Algebraic Expressions & Algebraic Sentences
- Problem 1: Algebraic Expressions & Algebraic Sentences
- Solution of Simple Linear Equations in two Variables
- Problem 1: Solution of Simple Linear Equations in two Variables
9.2: Graph of a Linear Equation in 2 Variable
- Graphical Solution of Simultaneous Linear Equations
- Introduction to Matrix
- Order of Matrix
- Problem 1: Introduction to Matrix
- Location of elements in Matrix
- Square Matrix and Rectangular Matrix
- Problem 1: Order of Matrix
- Problem 1: Location of elements in Matrix
- Problem 1: Square Matrix and Rectangular Matrix
9.4: Addition of Matrices (Practice Test)
- Null Matrix or Zero Matrix
- Negative of Matrix
- Problem 1: Null Matrix or Zero Matrix
- Addition of Matrices
- Subtraction of Matrices
- Problem 1: Negative of Matrix
- Commutative Law under Addition for Matrices
- Diagonal Matrix
- Problem 1: Addition of Matrices
- Scalar Matrix
- Identity Matrix
- Problem 1: Subtraction of Matrices
- Problem 1: Commutative Law under Addition for Matrices
- Problem 1: Diagonal Matrix
- Problem 1: Scalar Matrix
- Problem 1: Identity Matrix
9.5: Multiplication of Matrices (Practice Test)
- Multiplication of Matrices
- Multiplicative Identity of a Matrix
- Problem 1: Multiplication of Matrices
- Determinant of 2-by-2 Matrix
- Problem 2: Multiplication of Matrices
- Singular and Non-singular Matrix
- Multiplicative Inverse of a Non-Singular Matrix
- Problem 1: Multiplicative Identity of a Matrix
- Inverse of Matrix using Adjoint
- Problem1-Singular and Non-Singular Matrix
- Problem2-Singular and Non-Singular Matrix
- Problem 1: Singular and Non-singular Matrix
- Problem 1: Multiplicative Inverse of a Non-Singular Matrix
- Problem 1: Inverse of Matrix using Adjoint
- Solving Simultaneous Equations-Inversion Method
- Solving Simultaneous Equations-Cramers Rule
- Use of Matrices in Solving Everyday Life Problems
9.7: Properties of Simulataneous Equations and Their Algebraic Solutions (Practice Test)
- Solving Simultaneous Linear Equations by Substitution
- Problem 1: Solving Simultaneous Linear Equations by Substitution
- Soving Simultaneous Lnear Equations by Comparison
- Solving Simultaneous Linear Equations-Equating-Co-efficient
Chapter 10: Geometry (56 videos) (Practice Test)
10.1: Fundamental Concepts of Geometry (Practice Test)
- Introduction to Point, Line, Line-segment and Ray
- Problem 1: Introduction to Point, Line, Line-segment and Ray
- Collinear and Non-collinear Points
- Coincident Points & Coincident Lines
- Problem 1: Collinear points and Non-collinear points
- Coincident points and coincident lines
- Between and Beyond the line segment
- Interior and exterioir of an angle
- Problem 1: Coincident points and coincident lines
- Problem 1: Between and Beyond the line segment
- Problem 1: Interior and exterioir of an angle
10.2: Some Properties of Points and Lines (Practice Test)
- Fundamental Concepts of Geometry
- Problem 1: Fundamental Concepts of Geometry
- Complementary and Supplementary angles
- Angles
- Problem 1: Complementary and supplementary anlges
- Different Kinds of Angles
- Acute, Obtuse and Congruent Angles
- Vertically Opposite Angles
- Problem 1: Acute, Obtuse and Congruent Angles
- Problem 1: Vertically Opposite Angles
10.3: Important Rules About Angles (Practice Test)
- If two lines intersect each other,than vertical angles are congruent
- Problem 1: If two lines intersect each other,than vertical angle are
- Alternate and Vertical Angles
- Interior and exterior of triangle
- Problem-Alternate and Vertical Angles
- Problem 1: Interior and exterior angles of traingle
- Parallel Lines
- Problem 1: Parallel Lines
- Intersecting Lines
- Similarly Directed and Opposite Directed Rays
- Problem 1: Parallel Lines Postulate
- Problem-Similarly Directed and Opposite Directed Rays
10.5: Alternate and Corresponding Angles
- Alternate and corresponding Angles
- Alternate and Vertical Angles
- Problem 1: Alternate and corresponding Angles
- Problem 1: Transversal, Interior and Exterior Angles
- Problem-Alternate and Vertical Angles
10.6: Playfairs Axioms and Parallel Lines (Practice Test)
- If a transversal intersects two coplanar lines
- Problem 1: If a transversal intersects two coplanar lines such that t
- If a transversal intersects two parallel lines
- Problem 1: If a transversal intersects two parallel lines
10.7: Congruent Triangles (Practice Test)
- Congruence of Other Polygons
- Congruency of Triangles
- Problem 1: Congruence of Polygons
- Congruent Figures and Objects
- Problem 1: Congruency of Triangles
- Congruency Tests
- Problem-Congruent Figures and Objects
- Problem-Congruency Tests
10.8: Theroem About Congruent Triangles (Practice Test)
- Angle-Side-Angle Postulate-1
- Problem 1: Angle-Side-Angle Postulate-1
- Side-Side-Side Postulate-3
- Hypotenuse Side Postulate-4
- Problem 1: Side-Side-Side Postulate-3
- Problem 1: Hypotenuse Side Postulate-4
Chapter 11: Practical Geometry (90 videos) (Practice Test)
11.1: Introduction to Pratical Geometry (Practice Test)
- The Protractor and Angle Measure
- Geometrical Constructions
- Use of Compass
- Bisecting Line Segment
- Introduction to Practical Geometry
- Problem 1: Introduction to Practical Geometry
- Constructing Triangle with Three Sides
- Construction of a Triangle when one angle and two sides
- Problem 1: Constructing Triangle with Three Sides
- Constructing Triangle with Side & Two Angles
- Problem 1: Constructing Triangle with Side & Two Angles
11.2: Pythagorus Theorem (Practice Test)
- Proof of Pythagoras Theorem
- Problem-Proof of Pythagoras Theorem
- More on Proof of Pythagoras Theorem 1
- More on Proof of Pythagoras Theorem 2
- Problem-More on Proof of Pythagoras Theorem 1
- Problem-More on Proof of Pythagoras Theorem 2
11.3: Two Special Right Angled Triangles (Practice Test)
- Two Special Right Angled Triangles
- More on Two Special Right Angled Triangles
- Problem-Two Special Right Angled Triangles
- Problem-More on Two Special Right Angled Triangles
11.4: Condtion of Similarity of 2 Polygons
- Condition of Similarity of 2 Polygons
- Problem-Condition of Similarity of 2 Polygons
11.5: Condition of Similarity of 2 Triangles (Practice Test)
- Similar Triangles
- Similarity and Enlargement
- Problem-Similar Triangles
- Proportional Parts of Similar Triangle-4
- Problem-Similarity and Enlargement
- Similar Triangles
11.6: Constructing Similar Triangles
- Constructing Similar Triangles
- Problem-Similarity and Enlargement
11.7: The Slope of a Line and Its Equation (Practice Test)
- Inclination of Line
- Slope or Gradient of a Line
- Problem-Slope or Gradient of a Line
- Slope of Collinear Line Segments
- Slope of Parallel Lines
- Equations of a Straight Line
- Derivation of Slope Intercept form
- Problem-Slope of Parallel Lines
- Deriving Point-slope Form of Equation of Straight Line
- Problem-Equations of a Straight Line
- Introduction to Circle & its Characteristics
- Problem 1: Introduction to Circle & its Characteristics
- Chord , Diameter & Circumference of a Circle
- Arc of a Circle
- Concept of Central Angle of an Arc
- Problem 1: Chord , Diameter & Circumference of a Circle
- Segment & Sector of a Circle
- Area of a Circle
- Problem 1: Arc of a Circle
- Length of Arc and Area of Sector
- The Radian
- Problem 1: Concept of Central Angle of an Arc
- Concept of Secant & Tangent Line
- Tangent Circles and Length of Tangent
- Problem 1: Segment & Sector of a Circle
- Concentric Circles and Common Internal and External Tangents to two C
- Concept of Inscribed Angle of an Arc
- Concept of Circum Circle of a Triangle
- Concept of Inscribed Circle of a Triangle
- Problem 1: Concept of Secant & Tangent Line
- Concept of Escribed Circle of a Triangle
- If Arcs Congruent, then Chords Congruent-1
- If Chords Congruent, then Arcs Congruent-2
- Problem 1: Tangent Circles and Length of Tangent
- If Chords Congruent, then Central Angles Congruent-3
- Problem 1: Concentric Circles,Common Internal & External Tangents of
- If Central Angles Congruent, then Arcs Congruent-4
- Axial Symmetry of the Circle
- Problem 1: Concept of Inscribed Angle of an Arc
- Problem 1: Concept of Circum Circle of a Triangle
- Problem 1: Concept of Inscribed Circle of a Triangle
- Problem 1: Concept of Escribed Circle of a Triangle
- Problem-If Arcs Congruent- then Chords Congruent
- Problem-If Chords Congruent- then Central Angles Congruent
11.9: Some Theorems About Circles (Practice Test)
- Perpendicular radius bisects chord
- Problem 1: Perpendicular radius bisects chord
- Converse of perpendicular radius bisects chord
- Congruent Chords Equidistance from Circle-4
- Chords Equidistance of Circle are Congruent-5
- Problem 2: Congruent Chords Equidistance from Circle-4
- Central angle theorem
- Problem 1: Congruent Chords Equidistance from Circle-4
- Tangent to Circle-1
- Converse of Tangent to Circle-2
- Problem 1: Chords Equidistance of Circle are Congruent-5
- Problem 1: Central angle theorem
- Problem 2: Central angle theorem
- Problem 1: Tangent to Circle-1
- Problem 1: Converse of Tangent to Circle-2