12th Class Math Sindh Board Video Tutorials watch now
12th Class Math Sindh Board
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1.1: Introduction Numbers Systems
Definition & Notation of Some Important Sets
1.2: Intervals
Defining Closed, Open, Half Open and Half Closed Interval
1.3: Modulus Function
1.4: Neighborhood
Introduction to Neighborhood in Intervals
1.5: Binary Relation
Introduction to Binary Relation
ProblemIntroduction to Binary Relation
Problem 1: Introduction to Binary Relation
Domain & Range of Binary Relation
ProblemDomain & Range of Binary Relation
Problem 1: Domain & Range of Binary Relation
1.6: Functions
Problem 1: Introduction to Function
More on Introduction to Functions
1.7: Inverse Function
1.8: Concept of Function in Terms of Variables
1.9: Algebra of Functions
1.10: Polynomial Function
1.11: Rational Function
Constant, Identity and Rational Functions
1.12: Composite Function
1.13: Even and Odd Function
1.14: Circular Trigonometric Function
1.15: Inverse Trigonometric Function
Introduction to Binary Operations
1.16: Formulization of Functions
1.17: Graph of a Relation and of a Function
Graphical Representation of Functions
1.18: Sequence
Defining Sequence and Limit of Sequence
1.19: Limit of Sequence
Defining Sequence and Limit of Sequence
1.20: Bounded Set and Monotonic Sequence
Bounded Set and Monotonic Sequence
1.21: Divergence
Convergent and Divergent Sequence
1.22: Exponential Function
Operations on Residue Classes Modulo n
1.23: Logarithmic Function
Properties of Binary Operations
1.24: Infinite Series
1.25: Meaning of the Phrase ‘x’ Tends to ‘a’
Meaning of Phrase x Approaches to a
1.26: Limit of Function
Concept of a Limit of a Function
1.27: Limits as x Tends Infinity
2.1: Cartesian Coordinate System
Cartesian Coordinate System & Cartesian Plane
2.2: Distance Between Two Given Points
Derivation of Distance formula
Problem 1: Use of Distance formula
2.3: Division of Given Line Segment in a Given Ratio
Points Dividing the Join of Two Points in Given Ratio
More on Points Dividing Join of Two Points in Given Ratio
Problem1aPoints Dividing the Join of Two Points in Given Ratio
Problem1bPoints Dividing the Join of Two Points in Given Ratio
2.4: Rules For the Choice of Axes
2.5: Curves and Equations
2.6: Slope or Gradient of a Line
Gradient of a Straight Line Joining Two Points
2.7: Slope of the Line Joining Two Given Points
Gradient of a Straight Line Joining Two Points
2.8: Condition For Three Points to be Collinear
Slope of Collinear Line Segments
2.9: Parallel and Perpendicular Lines
ProblemSlope of Parallel Lines
Problem2Slope of Parallel Lines
Relationship between Two and Three Straight Lines
2.10: Angle From One Line to Another in the Slope Form
Problem1Angle Between Two Lines
Problem2Angle Between Two Lines
2.11: Lines Parallel to the Axes of Coordinates
2.12: Various Forms of Equation of Straight Line
More on Equations of Straight Line
ProblemEquations of a Straight Line
Derivation of Slope Intercept form
Problem1Derivation of Slope Intercept form
Deriving Pointslope Form of Equation of Straight Line
Problem1Deriving Pointslope Form of Equation of Straight Line
Symmetric Form of Equation of Straight Line
Problem1Symmetric Form of Equation of Straight Line
Two Point form of Equation of Straight Line
Problem1Two Point form of Equation of Straight Line
Intercept Form of Equation of Straight Line
Problem1Intercept Form of Equation of Straight Line
Normal Form of Equation of Straight Line
Problem1Normal Form of Equation of Straight Line
2.13: Deduction of One Form of an Equation of a Line From Another
Transforming General Linear Equation to Standard Forms
Problem1Transforming General Linear Equation to Standard Forms
Transforming General Equation to Slope Intercept Form
Problem1Transforming General Equation to Slope Intercept Form
Transforming General Form of Equation to Intercept Form
Problem1Transforming General Form of Equation to Intercept Form
Transforming General Form of Equation to Normal Form
Problem1Transforming General Form of Equation to Normal Form
Transforming General Form of Equation to Point Slope Form
Problem1Transforming General Form of Equation to Point Slope Form
Transforming General Form of Equation to Symmetric Form
Problem1Transforming General Form of Equation to Symmetric Form
3.1: The General Linear Equation
How 2 Variabled Linear Equation Represent Straight Line
Problem1How 2 Variabled Linear Equation Represent Straight Line
3.2: Angle Between Two Lines From l2 to l1 in The General Form
Angle Between Two Lines in General Form
3.3: Points of Intersection of Two Straight Lines
The Point of Intersection of Straight Lines
Problem1The Point of Intersection of Straight Lines
3.4: Concurrency of Three Lines
Condition of Concurrency of Three Straight Lines
More on Condition of Concurrency of Three Straight Lines
Problem1Condition of Concurrency of Three Straight Lines
3.5: Equations of Lines in the Matrix Form
Equation of a Straight Line in Matrix Form
More on Equation of Straight Line in Matrix Form
Problem1Equation of a Straight Line in Matrix Form
Problem2Equation of a Straight Line in Matrix Form
3.6: Lines Through the Intersection of Two Given Lines
Equation of Lines Through Point of Intersecting 2 Lines
Problem1Equation of Lines Through Point of Intersecting 2 Lines
3.7: Position of a Point with Respect to a Given Straight Line
Position of Point with Respect to Line
More on Position of Point with Respect to Line
Problem1Position of Point with Respect to Line
3.8: Distance of a Point From a Line
Problem1Distance of Point From Line
Distance between Two Parallel Lines
Problem1Distance between Two Parallel Lines
3.9: Area of a Triangle
Area of Triangular Region With Given Vertices
More on Area of Triangular Region With Given Vertices
Problem1Area of Triangular Region With Given Vertices
3.10: Equation of a Pair of Straight Lines Through the Origin
Equation of a Pair of Straight Lines Through the Origin
3.11: The General Quadratic Equation
Homogeneous Equation of Second Degree in Two Variables
More on Homogeneous Equation of 2nd Degree in 2 Variables
Homogeneous Equation of Degree ‘n’
More on Homogeneous Equation of Degree ‘n’
Problem1Homogeneous Equation of Degree ‘n’
Problem2Homogeneous Equation of Degree ‘n’
Problem2More on Homogeneous Equation of Degree ‘n’
Problem3Homogeneous Equation of Degree ‘n’
4.1: Derivative of a Function at a Point
More on Derivative of a Function
More on Derivative by First Principle
Problem1Derivative by First Principle
Problem2Derivative by First Principle
Derivative of a Constant Function
Power Rule for Differentiation
More on Power Rule for Differentiation
ProblemPower Rule for Differentiation
Problem1Power Rule for Differentiation
Derivative of a sum or Difference of Functions
Problem1Derivative of a sum or Difference of Functions
Problem1Derivative of Product
More on Derivative of a Quotient
Problem1aDerivative of Quotient
Derivative of Trigonometric Functions
More on Derivative of Trigonometric Functions
More Stuff on Derivative of Trigonometric Functions
Problem1Derivative of Trigonometric Functions
Problem2Derivative of Trigonometric Functions
Problem3Derivative of Trigonometric Functions
4.2: Composite Function
More on Differentiation by Chain Rule
Problem1Differentiation by Chain Rule
Problem2Differentiation by Chain Rule
Derivative of Inverse Trigonometric Functions
More on Derivative of Inverse Trigonometric Functions
Problem1Derivative of Inverse Trigonometric Functions
Problem2Derivative of Inverse Trigonometric Functions
Problem3Derivative of Inverse Trigonometric Functions
Derivative of Exponential Functions
Problem1Derivative of Exponential Functions
Derivative of Logarithmic Functions
Problem1Derivative of Logarithmic Functions
Problem SolvingLogarithmic Functions
4.3: Implicit Function
ProblemImplicit Differentiations
ProblemImplicit Differentiations
4.4: Parametric Function
Derivative of Parametric Equations
Problem1Derivative of Parametric Equations
4.5: Higher Derivatives
Introducing Higher Order Differentiation
Problem1Introducing Higher Order Differentiation
Problem2Introducing Higher Order Differentiation
5.1: Geometrical Meaning of dy/dx
Geometrical Interpretation of a Derivative
More on Geometrical Interpretation of Derivative
5.2: dy/dx as a Rate Measurer
DifferentialApplication to Kinematics
5.3: Differential
Difference between Delta y and dy
5.4: Increasing and Decreasing Function
Increasing and Decreasing Functions
More on Increasing and Decreasing Functions
Problem1Increasing and Decreasing Functions
Problem1Introducing Relative Extrema
Problem2Relative Maxima and Minima
Critical Values and Critical Points
Second Derivative Test and Concavity
More on Second Derivative Test and Concavity
Problem SolvingSecond Derivative Test and Concavity
DifferentialMaxima and Minima Problems
Problem1aSecond Derivative and Its Applications
6.1: Antiderivation or Integration
Antidifferentiation and Indefinite Integral
Integral Language and Notation
Difference between Delta y and dy
Problem1Difference between Delta y and dy
Problem1Theorems on Antiderivative
Problem2Theorems on Antiderivative
Problem3Theorems on Antiderivative
Problem4Theorems on Antiderivative
To Integrate x Raise to Power n
Problem1To Integrate x Raise to Power n
To Integrate Secant Squared Fucntions
To Integrate Cosecant.Cotangent Functions
Integrating Exponential Functions
To Integrate Tangent Functions
To Integrate Cotangent Functions
To Integrate Cosecant Functions
Integrating Power Functions with Given Derivatives
More on Integrating Power Functions with Given Derivatives
6.2: Integration by Substitution
Some Useful Substitutions in Integration
More on Some Useful Substitions in Integration
Some More Useful Substitions in Integration
ProblemIntegration by Useful Substitution
Problem2Some More Useful Substitions in Integration
Prolem3Some More Useful Substitions in Integration
Prolem4Some More Useful Substitions in Integration
Prolem5Some More Useful Substitions in Integration
6.3: Integration by Completing the Squares
Integration by Completing Square
Integration by Completing Square
6.4: Integration by Parts
Problem2bIntegration by Parts
Integration by Parts of Trigonometric Functions
More on Integration by Parts of Trigonometric Functions
6.5: Partial Fractions
Integrating Partial Fractions with Nonrepeated Factors
Problem1Integrating Partial Fractions with Nonrepeated Factors
Problem1aIntegrating Partial Fractions with Nonrepeated Factors
More on Integrating Partial Fractions with Nonrepeated Factors
Integrating Partial Fractions with Nonrepeated Linear Factors
Problem1Integrating Partial Fractions with Nonrepeated Linear Facto
Problem1aIntegrating Partial Fractions with Nonrepeated Linear Fact
More on Integrating Partial Fractions with Nonrepeated Factors
Integrating Partial Fractions with NonRepeated Quadratic Factors
Problem1Integrating Partial Fractions with NonRepeated Quadratic Fa
Problem1aIntegrating Partial Fractions with NonRepeated Quadratic F
More on Integrating Partial Fractions with NonRepeated Quadratic Fac
Further to Integrating Partial Fractions with NonRepeated Quadratic
6.6: Integation of Rational Fractions
Integration of Rational Fractions
6.7: Area Under a Curve
Problem1The Definite Integral
Problem2The Definite Integral
Problem2aThe Definite Integral
Negative Area by Definite Integral
Symmetrical Area by Integration
Area Bounded by Two Curves by Integration
To Deal with Negative and Positive Areas in Integation
Area Bounded by Two Curves Above and Below xaxis
Application of Definite Integral
More on Application of Definite Integral
Problem1Application of Definite Integral
Problem2Application of Definite Integral
Problem2aApplication of Definite Integral
Problem3Application of Definite Integral
Problem3aApplication of Definite Integral
6.8: Differential Equations
Introduction to Differential Equation
More on Introduction to Differential Equation
Classification of Differential Equation
More on Classification of Differnetial Equation
Solving First Order Differential Equation
More on Solving First Order Differential Equation
Problem1Solving First Order Differential Equation
Problem2Solving First Order Differential Equation
Solving First Order Differential Equation by Initial Conditions
P1Solving First Order Differential Equation by Initial Conditions
P2Solving First Order Differential Equation by Initial Conditions
P3Solving First Order Differential Equation by Initial Conditions
Homogeneous Differential Equation
Differential Equation Reducible to Homogeneous Differential Equation
Differential Equation of Orthogonal Trajectories
More on Differential Equation of Orthogonal Trajectories
7.1: Introduction
More on Introduction to Conic Section
7.2: Equation of a Circle
Standard Form of Equation of Circle
General Form of Equation of Circle
More on General Form of Equation of Circle
7.3: Equation of a Circle with a Line Segment as its Diameter
Equation of Circle Passing Through 2 Points and its Centre on Line
7.4: Tangents and Normals to a Circle
More on Equation of Tangent to Circle
Problem1 Equation of Tangent to Circle
Problem2aEquation of Tangent to Circle
Problem2bEquation of Tangent to Circle
7.5: Equation of the Chord Joining Two Points on the Circle
Chords Perpendicular Passes Centre of Circle
More on Chords Perpendicular Passes Centre of Circle
7.6: Points of Intersection of the Straight Line and the Circle
Line Intersects Circle at Most 2 Points
7.7: Condition of Tangency of a Line to a Circle
Condition that Line may be Tangent to Circle
7.8: The Equation of Tangents and Normals Using Derivatives
More on Equation of Tangent to Circle
Problem1 Equation of Tangent to Circle
Problem2aEquation of Tangent to Circle
Problem2bEquation of Tangent to Circle
7.9: Length of the Tangent from the Point to the Circle
7.10: Condition of Normality
7.11: Some Geometrical Properties of the Circle
Proof2 Tangents can be Drawn to Circle from Point
More on Proof2 Tangents can be Drawn to Circle from Point
To Prove Circles Diameter is 2 Times its Radius
Chords Perpendicular Passes Centre of Circle
More on Chords Perpendicular Passes Centre of Circle
Line From Centre and Midpoint of Chord is Perp to it
More on Line From Centre and Midpoint of Chord is Perp to it
Congruent Chords are Equidistance from Centre of Circle
More on Congruent Chords are Equidistance from Centre of Circle
Angle in SemiCircle is Right Angle
More on Angle in SemiCircle is Right Angle
8.1: General Conic
More on Introduction to Conic Section
8.2: Parabola
More on Introduction to Parabola
General Form of Equation of Parabola
Graph of Parabola Facing Upward
Graph of Parabola Facing Downward
Graph of Parabola Facing Rightward
Graph of Parabola Facing Leftward
Parabola with Vertex not at Origin
More on Parabola with Vertex not at Origin
ProblemParabola with Vertex not at Origin
Graphing Parabola with Vertex not at Origin
More on Graphing Parabola with Vertex not at Origin
Finding Equation of Parabola with Focus and Vertex
Finding Equation of Parabola with Directrix and Vertex
Problem1Finding Equation of Parabola with Focus and Vertex
Problem2Finding Equation of Parabola with Focus and Vertex
Problem3Finding Equation of Parabola with Focus and Vertex
8.3: The Standard Equation of an Ellipse
Obtaining Standard Equation of Ellipse
More on Obtaining Standard Equation of Ellipse1
More on Obtaining Standard Equation of Ellipse2
More on Obtaining Standard Equation of Ellipse3
Circle as Special Case of Ellipse
Basic Terms Associated with Ellipse
More on Basic Terms Associated with Ellipse
Standard Form of Vertical and Horizontal Ellipses
Problem1Standard Form of Vertical and Horizontal Ellipses
Translation of Horizontal Ellipse
More on Translation of Horizontal Ellipse
Translation of Vertical Ellipse
More on Translation of Vertical Ellipse
Equation of Ellipse with Foci and Vertices
Problem1Equation of Ellipse with Foci and Vertices
Problem3Equation of Ellipse with Foci and Vertices
Ellipse Equation with Centre and Length of Axes
Ellipse Equation with Centre and Given Point
More on Ellipse Equation with Centre and Given Point
8.4: Hyperbola
Standard Form of Equation of Hyperbola
More on Standard Form of Equation of Hyperbola
More on Standard Form of Equation of Hyperbola
Hyperbola with Focus and Eccentricity
Graphing Hyperbola with Eccentricity and Latus Rectum
Graphing Hyperbola with Focus and Directrix
Translation of Hyperbola with Horizontally
More on Translation of Hyperbola with Horizontally
Translation of Hyperbola Vertically
8.5: Equation of Chords
Equation of Chords to Parabola
8.6: Equations of Tangents and Normals to Conics
Intersection of Line and Parabola
More on Intersection of Line and Parabola
Equation of Tangent Line to Parabola in Slope Form
Equation of Tangent Line to Parabola at Given Point
ProblemEquation of Tangent Line to Parabola at Given Point
Equation of Normal Line to Parabola at Given Point
Problem1Equation of Normal Line to Parabola at Given Point
Application of ParabolaSuspension Related Problem
Reflecting Property of Parabola
Use of Parabola on Everyday LifeProblem
Points of Intersection of Line and Ellipse
More on Points of Intersection of Line and Ellipse
Condition of Tangency of Line to Ellipse
Equation of Tangent to Ellipse at Point
More on Equation of Tangent to Ellipse at Point
Equation of Normal to Ellipse at Point
More on Equation of Normal to Ellipse at Point
Problem1aEquation of Normal to Ellipse at Point
Problem1bEquation of Normal to Ellipse at Point
Point of Intersection of Line with Hyperbola
Condition of Tangency of Line to Hyperbola
Problem Condition of Tangency of Line to Hyperbola
Equation of Tangent Line to Hyperbola at Point
More on Equation of Tangent Line to Hyperbola at Point
Problem Equation of Tangent Line to Hyperbola at Point
Equation of Normal Line to Hyperbola at Point
8.7: TwoTangents and Condition of Tangency to Conics
Equation of Tangent Line to Parabola in Slope Form
Equation of Tangent Line to Parabola at Given Point
ProblemEquation of Tangent Line to Parabola at Given Point
Equation of Normal Line to Parabola at Given Point
Problem1Equation of Normal Line to Parabola at Given Point
Condition of Tangency of Line to Ellipse
Equation of Tangent to Ellipse at Point
More on Equation of Tangent to Ellipse at Point
Equation of Normal to Ellipse at Point
More on Equation of Normal to Ellipse at Point
Problem1aEquation of Normal to Ellipse at Point
Problem1bEquation of Normal to Ellipse at Point
Condition of Tangency of Line to Hyperbola
Problem Condition of Tangency of Line to Hyperbola
Equation of Tangent Line to Hyperbola at Point
More on Equation of Tangent Line to Hyperbola at Point
9.1: Cartesian Coordinate System for 3D Space
ProblemIntroducing Vector Geometry
ProblemConcept of Vector in Space
9.2: Scalar and Vectors Quantities
ProblemScalar and Vector Quantities
Terminologies and Notations of Vectors
9.3: Equal Vectors
9.4: Position Vector and its Direction Cosines
Direction Angles and Direction Cosines of Vector
ProblemDirection Angles and Direction Cosines of Vector
9.5: Multiplication of a Vector by a Scalar
ProblemScalar Multiple of a Vector
9.6: Vector Addition
Vector Addition is Associative
ProblemVector Addition is Associative
ProblemSubtraction of Vectors
9.7: Components of a Vector in a Plane
Properties of Vectors in Plane
More on Properties of Vectors in Plane
A Unit Vector in the Direction of Another Vector
ProblemA Unit Vector in the Direction of Another Vector
Notation for Vectors in Coordinate System
ProblemNotation for Vectors in Coordinate System
9.8: Application to Analytic Geometry
Vectors Application to Geometry
Problem1Vectors Application to Geometry
Problem2Vectors Application to Geometry
9.9: The Scalar and Vector Products of Two Vectors
ProblemScalar Product of Two Vectors
More on Properties of Scalar Product
ProblemProperties of Scalar Product
Scalar Product of Vectors in Their Component Form
ProblemScalar Product of Vectors in Their Component Form
ProblemAngle Between Two Vectors
Projection of One Vector Upon Another Vector
ProblemProjection of One Vector Upon Another Vector
ProblemApplication of Scalar Product
Application of Scalar Product on Geometry
More on Application of Scalar Product on Geometry
ProblemApplication of Scalar Product on Geometry
ProblemCross Product of Two Vectors
Derivation of Useful Results of Cross Product
ProblemDerivation of Useful Results of Cross Product
Expression of Cross Product in Terms of Components
ProblemExpression of Cross Product in Terms of Components
ProblemProperties of Cross Product
More on Properties of Cross Product
Analytical Expression of Cross Product
Direction Numbers or Direction Ratios
ProblemDirection Numbers or Direction Ratios
Collinear and Coplanar Vectors
ProblemCollinear and Coplanar Vectors
Vectors Application to Geometry
Problem1Vectors Application to Geometry
Problem2Vectors Application to Geometry
Condition of Parallel Vectors in Cross Product
ProblemCondition of Parallel Vectors in Cross Product
Area of Parallelogram by Vectors
ProblemVector Equation of Line in 3D
Application of Vector Equation
Problem1Application of Vector Equation
Problem2Application of Vector Equation
9.10: Scalar Products of Three Vectors
Analytical Expression of Triple Product
ProblemAnalytical Expression of Triple Product
Volume of Parallelepiped by Triple Product
ProblemVolume of Parallelepiped by Triple Product
Volume of Tetrahedron by Triple Product
ProblemVolume of Tetrahedron by Triple Product
Properties of Triple Scalar Product
ProblemProperties of Scalar Triple Product
9.11: Applications of Vectors to Mechanics
Area of Parallelogram by Vectors
Application of Vector Equation
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