In this video we discuss how we can chose the scale for drawing the bar graph and also why choosing the scale is important.

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Created by Devahsish Phadnis

In this video we discuss what is an altitude of a triangle and how we can draw/identitfy different altitudes of the triangle

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


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Created by Devashish Phadnis

We look at the exterior angle property of the triangle and a quick problem on how to apply it.

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


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Created by Devashish Phadnis

In this video, Supriya uses various concepts of trigonometry to solve the given word problem (involving two right-angled triangles). She also talks about the angle of elevation and angle of depression.

Unit: Some Applications of Trigonometry, NCERT Class 10th (CBSE curriculum).

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

In this video, Supriya uses various concepts of trigonometry to solve the given word problem (involving one right-angled triangle). She also talks about the angle of elevation and angle of depression.

Unit: Some Applications of Trigonometry, NCERT Class 10th (CBSE curriculum).

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

Let's learn how we can find the lowest common multiple (LCM) of three numbers using prime factorization.

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Anmol.

In this video, Supriya explains how to find the trigonometric ratios (sin, cos, tan, cosec, sec, and cot) of some special angles: 30 degrees, 45 degrees, and 60 degrees.

For more details on 30-60-90 triangle, watch: https://youtu.be/SFL4stapeUs
For more details on 45-45-90 triangle, watch: https://youtu.be/McINBOFCGH8
To watch the next video, click: https://youtu.be/zGm7Z9v2Vds

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

Let's learn how we use the concept of complementary angles to find the value of the unknown angle asked in the question.

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

Let's see how we can find the value of the given trigonometric expression using the side lengths of the right-angled triangle given to us.

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

In this video, Supriya discusses how we can find the cosecant of an angle of a right-angled triangle when two of its sides are given.

For more free lessons & practice - https://www.khanacademy.org/ma....th/in-in-grade-10-nc

Khan Academy is a nonprofit organization with the mission of providing free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help!

Created by Supriya.

How to find the mean of the grouped data when the frequency is given? FInd out in this video, which covers the comprehensive understanding of the concept with an example.

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


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Created by
Devashish Phadnis

Description
In this video students will learn about finding the values corresponding to pie slices from a pie chart. The skill covered is an application level skill on the pie chart.

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


Experience the joy of easy, seamless, accessible learning anywhere, anytime with Khan Academy.


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Created by
Devashish Phadnis

http://www.rootmath.org | Algebra

This is the second example of finding a least common denominator by first finding a Least Common Multiple. This technique is useful for 'small' or 'easy' numbers.

http://www.rootmath.org | Algebra

In this video we find a least common denominator by first finding a Least Common Multiple. This technique is useful for 'small' or 'easy' numbers.

http://www.rootmath.org | Algebra

An introduction to adding fractions. We'll look at the easy case of adding fractions with a common denominator and we'll also see why we can't add fractions with different denominators.

http://www.rootmath.org | Algebra

In this video we learn that certain fractions are equal to 1. This will be very useful later when we want to find common denominators.

http://www.rootmath.org | Algebra

In this video we learn how to multiply fractions. Multiplying fractions is the easiest thing you can do with fractions so it's the first thing we'll learn.

http://www.rootmath.org | Algebra

In this video we get a basic understanding of fractions. We learn what a numerator and denominator is and what pieces of information they tell us.

In this video, we discuss the formal proof of the theorem which says that the equal chords that is the chords with same length subtend equal chord at the center of the circle.

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


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Created by Devashish Phadnis

In this video we prove the statement for PA x PB = PT^2 or in other words,
Proof: If from an external point P of a circle a tangent segment PT and a secant PAB are drawn, then PA.PB=PT^2

Khan Academy is a free learning platform for Class 1-12 students with videos, exercises, and tests for maths, science, and more subjects. Our content is aligned to CBSE syllabus and available in Hindi, English, and many more regional languages.


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Created by Devashish Phadnis

This videos elaborates how to work with composite functions

Welcome to our S.2 Mathematics lesson where we dive into the intriguing world of Linear Inequalities. 📈

In this lesson, we will explore two key aspects:

1. **Solving Linear Inequalities:** We will unravel the art of solving linear inequalities, providing you with the tools and techniques to handle a variety of inequality problems.

2. **Representing Linear Inequalities Graphically:** Discover the power of visualization as we learn how to represent linear inequalities graphically. This graphical representation adds a whole new dimension to understanding inequalities.

📋 **Lesson Highlights:**
- Understanding the basics of linear inequalities.
- Step-by-step problem-solving techniques for solving linear inequalities.
- Introduction to the number line and its role in representing inequalities.
- Drawing and interpreting graphs of linear inequalities.

📊 **Why Learn Linear Inequalities?**
Linear inequalities play a crucial role in various fields, from economics and engineering to everyday decision-making. Mastery of this topic is a valuable skill in problem-solving.

📚 **Additional Resources:**
- Practice exercises to reinforce your understanding.

Join us in this engaging lesson to build a strong foundation in linear inequalities. Stay tuned for more math insights and don't forget to hit the "Subscribe" button to keep up with our lessons. Your mathematical journey begins here! 🧮📚

⁣Linear inequalities are mathematical expressions that compare two quantities using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). These inequalities involve linear functions, meaning every term in the inequality has a degree of 1.

For example, consider the linear inequality 2x + 3 < 7. This inequality states that the expression 2x + 3 is less than 7. To solve this inequality, we can follow these steps:

1. Subtract 3 from both sides: 2x + 3 - 3 < 7 - 3
Simplified: 2x < 4

2. Divide both sides by 2: (2x) / 2 < 4 / 2
Simplified: x < 2

Therefore, the solution to the linear inequality 2x + 3 < 7 is x < 2. This means that any value of x less than 2 would satisfy the inequality.

Linear inequalities can also involve variables on both sides of the inequality symbol. For example, consider the linear inequality 3x - 2 ≥ 5x + 1. To solve this inequality, we can follow similar steps:

1. Subtract 5x from both sides: 3x - 2 - 5x ≥ 5x + 1 - 5x
Simplified: -2x - 2 ≥ 1

2. Add 2 to both sides: -2x - 2 + 2 ≥ 1 + 2
Simplified: -2x ≥ 3

3. Divide both sides by -2 and reverse the inequality symbol: (-2x) / -2 ≤ 3 / -2
Simplified: x ≤ -3/2

Therefore, the solution to the linear inequality 3x - 2 ≥ 5x + 1 is x ≤ -3/2. This means that any value of x less than or equal to -3/2 would satisfy the inequality.

Definition of a function
Examples of functions
Solving functions

⁣Mappings and relations are concepts in mathematics that involve the relationship between two sets or groups of elements.

A mapping, also known as a function, is a relation between two sets in which each element from the first set (domain) is paired with exactly one element from the second set (codomain). In other words, a mapping assigns each element of the domain to a unique element in the codomain.

For example, consider the mapping f: {1, 2, 3} -> {a, b, c}, where f(1) = a, f(2) = b, and f(3) = c. This mapping assigns each element in the domain {1, 2, 3} to a unique element in the codomain {a, b, c}.

Mappings can also be represented using tables, graphs, or algebraic expressions. They are widely used in various mathematical concepts, such as calculus, algebra, and discrete mathematics.

A relation, on the other hand, is a general concept that describes any connection or association between elements of two sets. Relations do not necessarily have to be one-to-one or onto like mappings. They can be many-to-one, one-to-many, or even many-to-many.

For example, consider the relation R = {(1, a), (1, b), (2, c), (3, a)}. This relation represents the connections between elements of the set {1, 2, 3} and the set {a, b, c}. In this case, the element 1 is related to both a and b, and hence, it is a many-to-many relation.

Relations can also be represented using tables, graphs, or algebraic expressions. They are used in various areas of mathematics, such as number theory, algebraic structures, and set theory.

In summary, mappings and relations are essential concepts in mathematics that describe the relationships between elements of two sets. Mappings, also known as functions, assign each element of the domain to a unique element in the codomain, while relations describe general connections or associations between elements of two sets, which can be one-to-one, onto, many-to-one, one-to-many, or even many-to-many.

⁣Mappings and relations are concepts in mathematics that involve the relationship between two sets or groups of elements.

A mapping, also known as a function, is a relation between two sets in which each element from the first set (domain) is paired with exactly one element from the second set (codomain). In other words, a mapping assigns each element of the domain to a unique element in the codomain.

For example, consider the mapping f: {1, 2, 3} -> {a, b, c}, where f(1) = a, f(2) = b, and f(3) = c. This mapping assigns each element in the domain {1, 2, 3} to a unique element in the codomain {a, b, c}.

Mappings can also be represented using tables, graphs, or algebraic expressions. They are widely used in various mathematical concepts, such as calculus, algebra, and discrete mathematics.

A relation, on the other hand, is a general concept that describes any connection or association between elements of two sets. Relations do not necessarily have to be one-to-one or onto like mappings. They can be many-to-one, one-to-many, or even many-to-many.

For example, consider the relation R = {(1, a), (1, b), (2, c), (3, a)}. This relation represents the connections between elements of the set {1, 2, 3} and the set {a, b, c}. In this case, the element 1 is related to both a and b, and hence, it is a many-to-many relation.

Relations can also be represented using tables, graphs, or algebraic expressions. They are used in various areas of mathematics, such as number theory, algebraic structures, and set theory.

In summary, mappings and relations are essential concepts in mathematics that describe the relationships between elements of two sets. Mappings, also known as functions, assign each element of the domain to a unique element in the codomain, while relations describe general connections or associations between elements of two sets, which can be one-to-one, onto, many-to-one, one-to-many, or even many-to-many.