# Gen-Math-IX

##### Chapter 1: Number Systems (12 videos) (Practice Test)

###### 1.1: Decimal System and Base

###### 1.2: Base Five System

###### 1.3: Binay System or Base 2 System

###### 1.4: Addition and Subtraction in Base 5

###### 1.5: Multiplication in Base 5 System

###### 1.6: Basic Operations in Base 2 System

##### Chapter 2: Real Numbers and Coordinate System (45 videos) (Practice Test)

###### 2.1: Real Number System

###### 2.2: Irrational Numbers

###### 2.3: 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

###### 2.8: The Cartesian Product

###### 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)

###### 3.1: Laws of Exponents (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

###### 3.3: qth Root of a (Practice Test)

- 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

###### 3.5: Logarithm (Practice Test)

- 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

###### 3.6: Common Logarithm (Practice Test)

- 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

###### 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

###### 4.2: Collection of Data (Practice Test)

- 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

###### 4.4: Grouped Data

###### 4.5: Classification of Data

###### 4.6: Tabulation of Data

###### 4.7: Class Interval

###### 4.8: Class Frequency

###### 4.9: Lower Limit and Upper Limit

###### 4.10: Magnitude of Class Interval

###### 4.11: Frequency Distribution (Practice Test)

###### 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

###### 4.14: Arithematic Mean (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
- 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

###### 4.16: Mode

##### Chapter 5: Ratio, Proportion, Inheritance and Partnership (25 videos) (Practice Test)

###### 5.1: Ratio (Practice Test)

###### 5.2: Proportion (Practice Test)

- Introduction to Proportion
- Problem 1: Introduction to Proportion
- Law of Proportion
- Problem 1: Law of Proportion

###### 5.3: Proportion Between Two Sets

###### 5.4: Inverse Proportion (Practice Test)

###### 5.5: Compound Proportion

###### 5.6: Continued Ratios

###### 5.7: Proportional Division

###### 5.8: Miscellaneous Problems

###### 5.9: Inheritance (Practice Test)

###### 5.10: Partnership (Practice Test)

###### 5.11: Compound Partnership (Practice Test)

##### Chapter 6: Percentage (34 videos) (Practice Test)

###### 6.1: Percent

###### 6.2: Problems on Percent

###### 6.3: Zakat

###### 6.4: Tax (Practice Test)

###### 6.5: Income-Tax (Practice Test)

###### 6.6: Property Tax (Practice Test)

###### 6.7: Custom Duty (Practice Test)

###### 6.8: Others Taxes (Practice Test)

###### 6.9: Discount, Reduction

###### 6.10: Commission, Brokerage (Practice Test)

###### 6.11: Buying and Selling on Instalments

###### 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

###### 7.2: Algebraic Expressions

###### 7.3: Terms of an Expression

###### 7.4: Co-efficients

###### 7.5: Polynomial

###### 7.6: Ordering a Polynomial

###### 7.7: Addition of Polynomials

###### 7.8: Subtraction of Polynomials

###### 7.9: Multipllication of Polynomials

###### 7.10: Division of Polynomials

##### 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

###### 8.3: Factors and 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

###### 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

###### 8.10: Factorization of Expression Reducible to Sqaure of Difference

###### 8.11: Formula5

###### 8.12: Factorization of product of two Linear Expression

###### 8.13: Formula6 (Practice Test)

###### 8.14: Factorization of Sum/Difference of Cube

###### 8.15: Formula8

###### 8.16: Factorization of Cube of Sum/Difference of 2 Terms

##### 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

###### 9.3: 2 by 2 Matrices (Practice Test)

- 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

###### 9.6: Use of Matrices (Practice Test)

- 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

###### 10.4: Parallel Lines (Practice Test)

- 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

###### 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

###### 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

###### 11.8: Circle (Practice Test)

- 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