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Factorisation Part 1 - Lecture 1
Factorisation
In this chapter we will discuss about different methods of factorisation
When a polynomial (an algebraic expression) is expressed as the product of two or more expressions, each of these expressions is called a factor of the polynomial.
The polynomial x² + 5x + 6 can be expressed as the product of the expressions (x + 3) and(x + 2).
The process of writing an expression in the form of terms or brackets multiplied together is called factorisation. Each term and each bracket is called a factor of the expression. e.g. 5x² + 15 = 5(x² + 3)
METHODS OF FACTORISATION :
Type 1: Taking out the common factors : When each term of a given expression contains a common factor, divide each term by this factor and enclose the quotient within brackets, keeping the common factor outside the bracket.
Steps: Find the H.C.F. of all the terms of the given expression.
For expression 6a² - 3ax, its terms are 6a² and -3ax.
Therefore H.C.F. of these terms is 3a.
6a2 - 3ax = 3a 6q² 3a 3ax 3a = 3a (2a - x).
Type 2: Grouping An expression of an even number of terms, may be resolved into factors, if the terms are arranged in groups such that each group has a common factor.
Steps: 1. Group the terms of the given expression in such a way that each group has a common factor.
2. Factorise each group formed.
3. From each group, obtained in step 2, take out the common factor.
Type 3: Trinomial of the form ax² + bx +c (By splitting the middle term) When a trinomial is of the form ax² + bx + c (or a + bx + cx2), split b (the coefficient of x in the middle term) into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to the product of a and c. Then factorize by the grouping method
Type 4: Difference of two squares
Since, the product of (x + y) and (x - y) = (x + y) (x - y) = x²-y2
i.e. x² − y² = (x + y) (x − y).
Type 5: The sum or difference of two cubes
We know, a³ + b³ = (a + b)³-3ab (a + b)
a³ - b³ =(a - b)³ + 3ab (a - b)
a³+b³ = (a + b) (a² - ab + b²)
a³-b³ = (a - b) (a² + ab + b²)
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14min
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Factorisation Part 2 - Lecture 2
Factorisation
In this chapter we will discuss about different methods of factorisation
When a polynomial (an algebraic expression) is expressed as the product of two or more expressions, each of these expressions is called a factor of the polynomial.
The polynomial x² + 5x + 6 can be expressed as the product of the expressions (x + 3) and(x + 2).
The process of writing an expression in the form of terms or brackets multiplied together is called factorisation. Each term and each bracket is called a factor of the expression. e.g. 5x² + 15 = 5(x² + 3)
METHODS OF FACTORISATION :
Type 1: Taking out the common factors : When each term of a given expression contains a common factor, divide each term by this factor and enclose the quotient within brackets, keeping the common factor outside the bracket.
Steps: Find the H.C.F. of all the terms of the given expression.
For expression 6a² - 3ax, its terms are 6a² and -3ax.
Therefore H.C.F. of these terms is 3a.
6a2 - 3ax = 3a 6q² 3a 3ax 3a = 3a (2a - x).
Type 2: Grouping An expression of an even number of terms, may be resolved into factors, if the terms are arranged in groups such that each group has a common factor.
Steps: 1. Group the terms of the given expression in such a way that each group has a common factor.
2. Factorise each group formed.
3. From each group, obtained in step 2, take out the common factor.
Type 3: Trinomial of the form ax² + bx +c (By splitting the middle term) When a trinomial is of the form ax² + bx + c (or a + bx + cx2), split b (the coefficient of x in the middle term) into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to the product of a and c. Then factorize by the grouping method
Type 4: Difference of two squares
Since, the product of (x + y) and (x - y) = (x + y) (x - y) = x²-y2
i.e. x² − y² = (x + y) (x − y).
Type 5: The sum or difference of two cubes
We know, a³ + b³ = (a + b)³-3ab (a + b)
a³ - b³ =(a - b)³ + 3ab (a - b)
a³+b³ = (a + b) (a² - ab + b²)
a³-b³ = (a - b) (a² + ab + b²)
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14min
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Factorisation Part 3 - Lecture 3
Factorisation
In this chapter we will discuss about different methods of factorisation
When a polynomial (an algebraic expression) is expressed as the product of two or more expressions, each of these expressions is called a factor of the polynomial.
The polynomial x² + 5x + 6 can be expressed as the product of the expressions (x + 3) and(x + 2).
The process of writing an expression in the form of terms or brackets multiplied together is called factorisation. Each term and each bracket is called a factor of the expression. e.g. 5x² + 15 = 5(x² + 3)
METHODS OF FACTORISATION :
Type 1: Taking out the common factors : When each term of a given expression contains a common factor, divide each term by this factor and enclose the quotient within brackets, keeping the common factor outside the bracket.
Steps: Find the H.C.F. of all the terms of the given expression.
For expression 6a² - 3ax, its terms are 6a² and -3ax.
Therefore H.C.F. of these terms is 3a.
6a2 - 3ax = 3a 6q² 3a 3ax 3a = 3a (2a - x).
Type 2: Grouping An expression of an even number of terms, may be resolved into factors, if the terms are arranged in groups such that each group has a common factor.
Steps: 1. Group the terms of the given expression in such a way that each group has a common factor.
2. Factorise each group formed.
3. From each group, obtained in step 2, take out the common factor.
Type 3: Trinomial of the form ax² + bx +c (By splitting the middle term) When a trinomial is of the form ax² + bx + c (or a + bx + cx2), split b (the coefficient of x in the middle term) into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to the product of a and c. Then factorize by the grouping method
Type 4: Difference of two squares
Since, the product of (x + y) and (x - y) = (x + y) (x - y) = x²-y2
i.e. x² − y² = (x + y) (x − y).
Type 5: The sum or difference of two cubes
We know, a³ + b³ = (a + b)³-3ab (a + b)
a³ - b³ =(a - b)³ + 3ab (a - b)
a³+b³ = (a + b) (a² - ab + b²)
a³-b³ = (a - b) (a² + ab + b²)
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12min
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Factorisation Part 4 - Lecture 4
Factorisation
In this chapter we will discuss about different methods of factorisation
When a polynomial (an algebraic expression) is expressed as the product of two or more expressions, each of these expressions is called a factor of the polynomial.
The polynomial x² + 5x + 6 can be expressed as the product of the expressions (x + 3) and(x + 2).
The process of writing an expression in the form of terms or brackets multiplied together is called factorisation. Each term and each bracket is called a factor of the expression. e.g. 5x² + 15 = 5(x² + 3)
METHODS OF FACTORISATION :
Type 1: Taking out the common factors : When each term of a given expression contains a common factor, divide each term by this factor and enclose the quotient within brackets, keeping the common factor outside the bracket.
Steps: Find the H.C.F. of all the terms of the given expression.
For expression 6a² - 3ax, its terms are 6a² and -3ax.
Therefore H.C.F. of these terms is 3a.
6a2 - 3ax = 3a 6q² 3a 3ax 3a = 3a (2a - x).
Type 2: Grouping An expression of an even number of terms, may be resolved into factors, if the terms are arranged in groups such that each group has a common factor.
Steps: 1. Group the terms of the given expression in such a way that each group has a common factor.
2. Factorise each group formed.
3. From each group, obtained in step 2, take out the common factor.
Type 3: Trinomial of the form ax² + bx +c (By splitting the middle term) When a trinomial is of the form ax² + bx + c (or a + bx + cx2), split b (the coefficient of x in the middle term) into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to the product of a and c. Then factorize by the grouping method
Type 4: Difference of two squares
Since, the product of (x + y) and (x - y) = (x + y) (x - y) = x²-y2
i.e. x² − y² = (x + y) (x − y).
Type 5: The sum or difference of two cubes
We know, a³ + b³ = (a + b)³-3ab (a + b)
a³ - b³ =(a - b)³ + 3ab (a - b)
a³+b³ = (a + b) (a² - ab + b²)
a³-b³ = (a - b) (a² + ab + b²)
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10min
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Simultaneous Linear Equations Part 1 - Lecture 5
Simultaneous Linear Equations
An equation of the form ax + by + c = 0 is called a linear equation in which a, b and c are constants (real numbers) and x and y are variables each with degree 1 (one).
Consider the two linear equations: 3x + 4y = 6 and 8x + 5y = 3. These two equations contain same two variables (x and y in this case). Together such equations are called simultaneous (linear) equations.
METHODS OF SOLVING SIMULTANEOUS EQUATIONS
To solve two simultaneous linear equations means, to find the values of variables used in the given equations.
Out of the different algebraic methods for solving simultaneous equations, we shall be discussing the following three methods only:
1. Method of elimination by substitution.
2. Method of elimination by equating coefficients.
3. Method of cross-multiplication.
Type 1 : METHOD OF ELIMINATION BY SUBSTITUTION :
Steps: 1. From any of the given two equations, find the value of one variable in terms of the other. 2. Substitute the value of the variable, obtained in step (1), in the other equation and solve it. 3. Substitute the value of the variable obtained in step (2), in the result of step (1) and get the value of the remaining unknown variable.
Type 2 : METHOD OF ELIMINATION BY EQUATING COEFFICIENTS
Steps: 1. Multiply one or both of the equations by a suitable number or numbers so that either the coefficients of x or the coefficients of y in both the equations become numerically equal.
2. Add both the equations, as obtained in step 1, or subtract one equation from the other, so that the terms with equal numerical coefficients cancel mutually.
3. Solve the resulting equation to find the value of one of the unknowns.
4. Substitute this value in any of the two given equations and find the value of the other unknown.
Type 3. Method of cross-multiplication. Please see our lecture
In this chapter we wil also discuss about the problem based on simultaneous Equations.
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7min
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Simultaneous Linear Equation Part 2 - Lecture 6
Simultaneous Linear Equations
An equation of the form ax + by + c = 0 is called a linear equation in which a, b and c are constants (real numbers) and x and y are variables each with degree 1 (one).
Consider the two linear equations: 3x + 4y = 6 and 8x + 5y = 3. These two equations contain same two variables (x and y in this case). Together such equations are called simultaneous (linear) equations.
METHODS OF SOLVING SIMULTANEOUS EQUATIONS
To solve two simultaneous linear equations means, to find the values of variables used in the given equations.
Out of the different algebraic methods for solving simultaneous equations, we shall be discussing the following three methods only:
1. Method of elimination by substitution.
2. Method of elimination by equating coefficients.
3. Method of cross-multiplication.
Type 1 : METHOD OF ELIMINATION BY SUBSTITUTION :
Steps: 1. From any of the given two equations, find the value of one variable in terms of the other. 2. Substitute the value of the variable, obtained in step (1), in the other equation and solve it. 3. Substitute the value of the variable obtained in step (2), in the result of step (1) and get the value of the remaining unknown variable.
Type 2 : METHOD OF ELIMINATION BY EQUATING COEFFICIENTS
Steps: 1. Multiply one or both of the equations by a suitable number or numbers so that either the coefficients of x or the coefficients of y in both the equations become numerically equal.
2. Add both the equations, as obtained in step 1, or subtract one equation from the other, so that the terms with equal numerical coefficients cancel mutually.
3. Solve the resulting equation to find the value of one of the unknowns.
4. Substitute this value in any of the two given equations and find the value of the other unknown.
Type 3. Method of cross-multiplication. Please see our lecture
In this chapter we wil also discuss about the problem based on simultaneous Equations.
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18min
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Simultaneous Linear Equations Part 3 - Lecture 7
Simultaneous Linear Equations
An equation of the form ax + by + c = 0 is called a linear equation in which a, b and c are constants (real numbers) and x and y are variables each with degree 1 (one).
Consider the two linear equations: 3x + 4y = 6 and 8x + 5y = 3. These two equations contain same two variables (x and y in this case). Together such equations are called simultaneous (linear) equations.
METHODS OF SOLVING SIMULTANEOUS EQUATIONS
To solve two simultaneous linear equations means, to find the values of variables used in the given equations.
Out of the different algebraic methods for solving simultaneous equations, we shall be discussing the following three methods only:
1. Method of elimination by substitution.
2. Method of elimination by equating coefficients.
3. Method of cross-multiplication.
Type 1 : METHOD OF ELIMINATION BY SUBSTITUTION :
Steps: 1. From any of the given two equations, find the value of one variable in terms of the other. 2. Substitute the value of the variable, obtained in step (1), in the other equation and solve it. 3. Substitute the value of the variable obtained in step (2), in the result of step (1) and get the value of the remaining unknown variable.
Type 2 : METHOD OF ELIMINATION BY EQUATING COEFFICIENTS
Steps: 1. Multiply one or both of the equations by a suitable number or numbers so that either the coefficients of x or the coefficients of y in both the equations become numerically equal.
2. Add both the equations, as obtained in step 1, or subtract one equation from the other, so that the terms with equal numerical coefficients cancel mutually.
3. Solve the resulting equation to find the value of one of the unknowns.
4. Substitute this value in any of the two given equations and find the value of the other unknown.
Type 3. Method of cross-multiplication. Please see our lecture
In this chapter we wil also discuss about the problem based on simultaneous Equations.
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12min
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Simultaneous Linear Equations Part 4 - Lecture 8
Simultaneous Linear Equations
An equation of the form ax + by + c = 0 is called a linear equation in which a, b and c are constants (real numbers) and x and y are variables each with degree 1 (one).
Consider the two linear equations: 3x + 4y = 6 and 8x + 5y = 3. These two equations contain same two variables (x and y in this case). Together such equations are called simultaneous (linear) equations.
METHODS OF SOLVING SIMULTANEOUS EQUATIONS
To solve two simultaneous linear equations means, to find the values of variables used in the given equations.
Out of the different algebraic methods for solving simultaneous equations, we shall be discussing the following three methods only:
1. Method of elimination by substitution.
2. Method of elimination by equating coefficients.
3. Method of cross-multiplication.
Type 1 : METHOD OF ELIMINATION BY SUBSTITUTION :
Steps: 1. From any of the given two equations, find the value of one variable in terms of the other. 2. Substitute the value of the variable, obtained in step (1), in the other equation and solve it. 3. Substitute the value of the variable obtained in step (2), in the result of step (1) and get the value of the remaining unknown variable.
Type 2 : METHOD OF ELIMINATION BY EQUATING COEFFICIENTS
Steps: 1. Multiply one or both of the equations by a suitable number or numbers so that either the coefficients of x or the coefficients of y in both the equations become numerically equal.
2. Add both the equations, as obtained in step 1, or subtract one equation from the other, so that the terms with equal numerical coefficients cancel mutually.
3. Solve the resulting equation to find the value of one of the unknowns.
4. Substitute this value in any of the two given equations and find the value of the other unknown.
Type 3. Method of cross-multiplication. Please see our lecture
In this chapter we wil also discuss about the problem based on simultaneous Equations.
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25min
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Indices Part 1 - Lecture 9
Indices
Here we will discuss about exponents expressions to solve
If m is a positive integer, then ax ax ax a----- upto m terms, is written as am; where 'a is called the base and 'm' is called the power (or exponent or index).
am is read as a power m' or 'a raised to the power m'.
Thus ax ax ax ---- upto 10 terms = a10 [a raised to the power 10]
LAWS OF INDICES
Ist Law (Product Law): am x an = am+n
2nd Law (Quotient Law): am / an = am-n
3rd Law (Power Law) : (am)" = amn
HANDLING POSITIVE, FRACTIONAL, NEGATIVE AND ZERO INDICE
SOLVING EXPONENTIAL EQUATIONS
For solving an exponential equation, express both of its sides into terms with the same base. Then the exponents on both the sides of the equation are equal. i.e. if am = an ⇒ m = n.
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13min
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Indices Part 2 - Lecture 10
Indices
Here we will discuss about exponents expressions to solve
If m is a positive integer, then ax ax ax a----- upto m terms, is written as am; where 'a is called the base and 'm' is called the power (or exponent or index).
am is read as a power m' or 'a raised to the power m'.
Thus ax ax ax ---- upto 10 terms = a10 [a raised to the power 10]
LAWS OF INDICES
Ist Law (Product Law): am x an = am+n
2nd Law (Quotient Law): am / an = am-n
3rd Law (Power Law) : (am)" = amn
HANDLING POSITIVE, FRACTIONAL, NEGATIVE AND ZERO INDICE
SOLVING EXPONENTIAL EQUATIONS
For solving an exponential equation, express both of its sides into terms with the same base. Then the exponents on both the sides of the equation are equal. i.e. if am = an ⇒ m = n.
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16min
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Indices Part 3 - Lecture 11
Indices
Here we will discuss about exponents expressions to solve
If m is a positive integer, then ax ax ax a----- upto m terms, is written as am; where 'a is called the base and 'm' is called the power (or exponent or index).
am is read as a power m' or 'a raised to the power m'.
Thus ax ax ax ---- upto 10 terms = a10 [a raised to the power 10]
LAWS OF INDICES
Ist Law (Product Law): am x an = am+n
2nd Law (Quotient Law): am / an = am-n
3rd Law (Power Law) : (am)" = amn
HANDLING POSITIVE, FRACTIONAL, NEGATIVE AND ZERO INDICE
SOLVING EXPONENTIAL EQUATIONS
For solving an exponential equation, express both of its sides into terms with the same base. Then the exponents on both the sides of the equation are equal. i.e. if am = an ⇒ m = n.
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11min
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Indices Part 4 - Lecture 12
Indices
Here we will discuss about exponents expressions to solve
If m is a positive integer, then ax ax ax a----- upto m terms, is written as am; where 'a is called the base and 'm' is called the power (or exponent or index).
am is read as a power m' or 'a raised to the power m'.
Thus ax ax ax ---- upto 10 terms = a10 [a raised to the power 10]
LAWS OF INDICES
Ist Law (Product Law): am x an = am+n
2nd Law (Quotient Law): am / an = am-n
3rd Law (Power Law) : (am)" = amn
HANDLING POSITIVE, FRACTIONAL, NEGATIVE AND ZERO INDICE
SOLVING EXPONENTIAL EQUATIONS
For solving an exponential equation, express both of its sides into terms with the same base. Then the exponents on both the sides of the equation are equal. i.e. if am = an ⇒ m = n.
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14min
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Mid-Point Theorem & its Convert Part 1 - Lecture 13
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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27min
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Mid-Point Theorem & its Convert Part 2 - Lecture 14
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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35min
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Mid-Point Theorem & its Convert Part 3 - Lecture 15
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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20min
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Mid-Point Theorem & its Convert Part 4 - Lecture 16
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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26min
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Mid-Point Theorem & its Convert Part 5 - Lecture 17
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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23min
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Mid-Point Theorem & its Convert Part 6 - Lecture 18
Mid Point theorem and its converse
The midpoint theorem states that the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
The converse of Mid Point Theorem
The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.
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21min
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Pythagorus Theorem Part 1 - Lecture 19
Pythagoras Theorem
Pythagoras Theorem Statement
Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called Pythagorean triple.
Pythagoras Theorem Formula:
Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
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16min
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Pythagorus Theorem Part 2 - Lecture 20
Pythagoras Theorem
Pythagoras Theorem Statement
Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called Pythagorean triple.
Pythagoras Theorem Formula:
Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
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15min
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Pythagorus Theorem Part 3 - Lecture 21
Pythagoras Theorem
Pythagoras Theorem Statement
Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called Pythagorean triple.
Pythagoras Theorem Formula:
Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
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15min
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Pythagorus Theorem Part 4 - Lecture 22
Pythagoras Theorem
Pythagoras Theorem Statement
Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called Pythagorean triple.
Pythagoras Theorem Formula:
Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
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16min
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Pythagorus Theorem Part 5 - Lecture 23
Pythagoras Theorem
Pythagoras Theorem Statement
Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called Pythagorean triple.
Pythagoras Theorem Formula:
Consider the triangle
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
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17min
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Rectlinear Figures Part 1 - Lecture 24
Rectilinear Figures
What is a rectilinear figure?
Rectilinear means along a straight line or in a straight line or forming a straight line. Basically, it is a plane figure bounded by line segments.
Polygon
Polygon is a closed rectilinear figure. The line segments by which it is bounded are called its sides, the points of intersection of consecutive sides are called its vertices, and the angle formed by the intersection of two consecutive sides is called an interior angle or simply an angle.
Quadrilaterals
A quadrilateral can be defined as a closed, two-dimensional shape that has four straight sides.
Concave and Convex Polygons:
We know that each side of a polygon is connected by two consecutive vertices of the polygon.A diagonal is a line segment
that connects the non-consecutive vertices of a polygon.If a diagonal lies outside a polygon, then the polygon is called a concave polygon.If all the diagonals lie inside the polygon, then the polygon is said to be a convex polygon.
Regular and Irregular Polygons:
A regular polygon is equiangular and equilateral. The word equiangular means, the interior angles of the polygon are equal to one another. The word equilateral means, the lengths of the sides are equal to one another.
The polygon with unequal sides and unequal angles is called an irregular polygon.
Quadrilaterals:
A quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides.
Here we will discuss Special kinds of Quadrilaterals and their Properties.
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28min
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Rectlinear Figures Part 2 - Lecture 25
Rectilinear Figures
What is a rectilinear figure?
Rectilinear means along a straight line or in a straight line or forming a straight line. Basically, it is a plane figure bounded by line segments.
Polygon
Polygon is a closed rectilinear figure. The line segments by which it is bounded are called its sides, the points of intersection of consecutive sides are called its vertices, and the angle formed by the intersection of two consecutive sides is called an interior angle or simply an angle.
Quadrilaterals
A quadrilateral can be defined as a closed, two-dimensional shape that has four straight sides.
Concave and Convex Polygons:
We know that each side of a polygon is connected by two consecutive vertices of the polygon.A diagonal is a line segment
that connects the non-consecutive vertices of a polygon.If a diagonal lies outside a polygon, then the polygon is called a concave polygon.If all the diagonals lie inside the polygon, then the polygon is said to be a convex polygon.
Regular and Irregular Polygons:
A regular polygon is equiangular and equilateral. The word equiangular means, the interior angles of the polygon are equal to one another. The word equilateral means, the lengths of the sides are equal to one another.
The polygon with unequal sides and unequal angles is called an irregular polygon.
Quadrilaterals:
A quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides.
Here we will discuss Special kinds of Quadrilaterals and their Properties.
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22min
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Rectlinear Figures Part 3 - Lecture 26
Rectilinear Figures
What is a rectilinear figure?
Rectilinear means along a straight line or in a straight line or forming a straight line. Basically, it is a plane figure bounded by line segments.
Polygon
Polygon is a closed rectilinear figure. The line segments by which it is bounded are called its sides, the points of intersection of consecutive sides are called its vertices, and the angle formed by the intersection of two consecutive sides is called an interior angle or simply an angle.
Quadrilaterals
A quadrilateral can be defined as a closed, two-dimensional shape that has four straight sides.
Concave and Convex Polygons:
We know that each side of a polygon is connected by two consecutive vertices of the polygon.A diagonal is a line segment
that connects the non-consecutive vertices of a polygon.If a diagonal lies outside a polygon, then the polygon is called a concave polygon.If all the diagonals lie inside the polygon, then the polygon is said to be a convex polygon.
Regular and Irregular Polygons:
A regular polygon is equiangular and equilateral. The word equiangular means, the interior angles of the polygon are equal to one another. The word equilateral means, the lengths of the sides are equal to one another.
The polygon with unequal sides and unequal angles is called an irregular polygon.
Quadrilaterals:
A quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides.
Here we will discuss Special kinds of Quadrilaterals and their Properties.
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19min
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Circles Part 1 - Lecture 27
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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21min
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Circles Part 2 - Lecture 28
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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20min
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Circles Part 3 - Lecture 29
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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24min
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Circles Part 4 - Lecture 30
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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26min
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Circles Part 5 - Lecture 31
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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26min
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Circles Part 6 - Lecture 32
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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13min
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Circles Part 7 - Lecture 33
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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21min
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Circles Part 8 - Lecture 34
In this chapter we will discuss about Circle properties and chord properties as well as theorem related with them .
We will also discuss about Arc and Chord Properties together.
And also find the angle subtended by each arm of n – side of regular polygon inscribe in circle at the centre of circle by using formula 360® /n
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16min
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Statistics Part 1 - Lecture 35
The word Statistics came into existence towards the middle of the eighteenth century. It seems to have been derived from the Latin word 'Status' or the Italian word 'Statista' or the German word 'Statistik'; each of which means a Political State'.
Statistics is a branch of mathematics that is concerned with how information is collected, organized, presented, summarized and then analyzed so the conclusions may be drawn from the information.
Statistics is used in two different senses singular and plural. When used as singular, it refers to the whole subject as a branch of knowledge which deals with statistical principles and methods used in collecting, analysing and interpreting data.
When used as plural, it refers to the numerical data, collected in a systematic manner, with some definite object in view, in any field of enquiry
Here we will also discuss about Graphical Representation of Data with the help of Histogram , Frequency polygon with using histogram , , Frequency polygon without using histogram.
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22min
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Statistics part 2 - Lecture -36
The word Statistics came into existence towards the middle of the eighteenth century. It seems to have been derived from the Latin word 'Status' or the Italian word 'Statista' or the German word 'Statistik'; each of which means a Political State'.
Statistics is a branch of mathematics that is concerned with how information is collected, organized, presented, summarized and then analyzed so the conclusions may be drawn from the information.
Statistics is used in two different senses singular and plural. When used as singular, it refers to the whole subject as a branch of knowledge which deals with statistical principles and methods used in collecting, analysing and interpreting data.
When used as plural, it refers to the numerical data, collected in a systematic manner, with some definite object in view, in any field of enquiry
Here we will also discuss about Graphical Representation of Data with the help of Histogram , Frequency polygon with using histogram , , Frequency polygon without using histogram.
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17min
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Statistics part 3 - Lecture 37
The word Statistics came into existence towards the middle of the eighteenth century. It seems to have been derived from the Latin word 'Status' or the Italian word 'Statista' or the German word 'Statistik'; each of which means a Political State'.
Statistics is a branch of mathematics that is concerned with how information is collected, organized, presented, summarized and then analyzed so the conclusions may be drawn from the information.
Statistics is used in two different senses singular and plural. When used as singular, it refers to the whole subject as a branch of knowledge which deals with statistical principles and methods used in collecting, analysing and interpreting data.
When used as plural, it refers to the numerical data, collected in a systematic manner, with some definite object in view, in any field of enquiry
Here we will also discuss about Graphical Representation of Data with the help of Histogram , Frequency polygon with using histogram , , Frequency polygon without using histogram.
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21min
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Mean -Median Mode Part 1 - Lecture 38
Here In this chapter we will discuss about mean of ungrouped data and their properties based on four fundamental operations
And median of ungrouped for even number of terms as well as for odd number of terms.
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27min
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Mean -Median Mode Part 2 - Lecture 39
Here In this chapter we will discuss about mean of ungrouped data and their properties based on four fundamental operations
And median of ungrouped for even number of terms as well as for odd number of terms.
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18min
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Mean -Median Mode Part 3 - Lecture 40
Here In this chapter we will discuss about mean of ungrouped data and their properties based on four fundamental operations
And median of ungrouped for even number of terms as well as for odd number of terms.
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24min
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Area & Perimeter - Part 1 - Lecture 41
Here in this chapter we will find the area and perimeter of plane figures like Triangle , Quadrilaterals
We will also discuss about the Area and Circumference of Circle and we will also discuss about some mix questions in which combination is involved like where we require area of square and circle to calculate remaining area.
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18min
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Area & Perimeter - Part 2 - Lecture 42
Here in this chapter we will find the area and perimeter of plane figures like Triangle , Quadrilaterals
We will also discuss about the Area and Circumference of Circle and we will also discuss about some mix questions in which combination is involved like where we require area of square and circle to calculate remaining area.
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23min
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Area & Perimeter - Part 3 - Lecture 43
Here in this chapter we will find the area and perimeter of plane figures like Triangle , Quadrilaterals
We will also discuss about the Area and Circumference of Circle and we will also discuss about some mix questions in which combination is involved like where we require area of square and circle to calculate remaining area.
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19min
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Area & Perimeter - Part 4 - Lecture 44
Here in this chapter we will find the area and perimeter of plane figures like Triangle , Quadrilaterals
We will also discuss about the Area and Circumference of Circle and we will also discuss about some mix questions in which combination is involved like where we require area of square and circle to calculate remaining area.
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29min
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Area & Perimeter - Part 5 - Lecture 45
Here in this chapter we will find the area and perimeter of plane figures like Triangle , Quadrilaterals
We will also discuss about the Area and Circumference of Circle and we will also discuss about some mix questions in which combination is involved like where we require area of square and circle to calculate remaining area.
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19min
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Solids - Part 1 - Lecture 46
Here in this chapter we will discuss about Surface area and volume of three – dimensional figures like cube , cuboids by using different formulas.
Also we will discuss about Area of Cross- Section and Flow of Liquid
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28min
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Solids Part 2 - Lecture 47
Here in this chapter we will discuss about Surface area and volume of three – dimensional figures like cube , cuboids by using different formulas.
Also we will discuss about Area of Cross- Section and Flow of Liquid
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23min
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Solids Part 3 - Lecture - 48
Here in this chapter we will discuss about Surface area and volume of three – dimensional figures like cube , cuboids by using different formulas.
Also we will discuss about Area of Cross- Section and Flow of Liquid
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24min
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Trigonometrical Ratios part 1 - Lecture 49
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc.
How you can remember these ratios and can find different values for given problems or when one ratio is given to find remaining trigonomertrical ratio.
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22min
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Trigonometrical Ratios part 2 - Lecture 50
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc.
How you can remember these ratios and can find different values for given problems or when one ratio is given to find remaining trigonomertrical ratio.
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17min
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Trigonometrical Ratios part 3 - Lecture 51
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc.
How you can remember these ratios and can find different values for given problems or when one ratio is given to find remaining trigonomertrical ratio.
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23min
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Trigonometrical Ratios part 4 - Lecture 52
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc.
How you can remember these ratios and can find different values for given problems or when one ratio is given to find remaining trigonomertrical ratio.
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24min
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Trigonometrical Ratios of Standard Angles Part 1 - Lecture 53
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
How you can remember these standard angle values and can find different values for given problems or when one ratio is given to solve trigonomertrical equations.
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24min
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Trigonometrical Ratios of Standard Angles Part 2 - Lecture 54
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
How you can remember these standard angle values and can find different values for given problems or when one ratio is given to solve trigonomertrical equations.
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13min
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Trigonometrical Ratios of Standard Angles Part 3 - Lecture 55
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
How you can remember these standard angle values and can find different values for given problems or when one ratio is given to solve trigonomertrical equations.
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18min
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Solution of Right Triangles - Part 1 -Lecture 56
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
How you can remember these standard angle values and can find different values for given problems or when one ratio is given to solve trigonomertrical equations.
And Here with the help of above said concept we will solve Simple 2-D Problems Involving One Right- angled Triangle
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30min
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Solution of Right Triangles - Part 2 -Lecture 57
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
How you can remember these standard angle values and can find different values for given problems or when one ratio is given to solve trigonomertrical equations.
And Here with the help of above said concept we will solve Simple 2-D Problems Involving One Right- angled Triangle
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19min
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Complementary Angles Part 1 -Lecture 58
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
Here we will mainly discuss the Concept of Trigonometric Ratio Of Complementary Angles how these ratios are convertible to each other.
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19min
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Complementary Angles Part 2 -Lecture 59
Here we will discuss about concept of perpendicular ,base , Hypotenuse in right Triangle , Notation of Angles , Trigonomertrical ratios like Sin , cos , tan etc. and their standard angles values
Here we will mainly discuss the Concept of Trigonometric Ratio Of Complementary Angles how these ratios are convertible to each other.
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14min
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Graphical Solutions part 1 - Lecture 60
Here we will discuss about Graphs of Linear Equations in two Variables.
We will also discuss about to find linear equation.
And Solution of Simultaneous Linear Equations Graphically. We will also learn how we can draw graphs when different conditions are given and how to find the Area and Perimeter of different figures under different conditions.
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29min
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Graphical Solutions part 2 - Lecture 61
Here we will discuss about Graphs of Linear Equations in two Variables.
We will also discuss about to find linear equation.
And Solution of Simultaneous Linear Equations Graphically. We will also learn how we can draw graphs when different conditions are given and how to find the Area and Perimeter of different figures under different conditions.
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24min
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Distance Formula part 1 - Lecture 62
Here we will discuss about for any two known (given) points in a co-ordinate (Cartesian) plane, the knowledge of co-ordinate geometry may be used to find :
(a) the distance between the given points.
(b) the co-ordinates of a point which divides the line joining the given points in a given ratio.
(c) the co-ordinates of the mid-point of the line segment joining the two given points.
(d) equation of the straight line through the given points etc.
And we will also learn how we can show that given quadrilateral is a parallelogram, rectangle, rhombus etc. and also same for Right Triangle, Isosceles Triangle etc.
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28min
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Distance Formula Part 2 - Lecture 63
Here we will discuss about for any two known (given) points in a co-ordinate (Cartesian) plane, the knowledge of co-ordinate geometry may be used to find :
(a) the distance between the given points.
(b) the co-ordinates of a point which divides the line joining the given points in a given ratio.
(c) the co-ordinates of the mid-point of the line segment joining the two given points.
(d) equation of the straight line through the given points etc.
And we will also learn how we can show that given quadrilateral is a parallelogram, rectangle, rhombus etc. and also same for Right Triangle, Isosceles Triangle etc.
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26min
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