Mathematics important formulae Chapter wise part-1

[Virtual Presenter] Welcome to Your SSC Dost, the ultimate source for all updates related to SSC Board Class 10. Here, you can find career guidance and smart study tips to help you prepare for your exams in 2025 or plan your future after 10th grade. I am here to assist you every step of the way. Let's embark on this journey together and make sure to subscribe to stay ahead! Today's focus is on the important math formulas, which will be presented chapter by chapter to help you excel in your Class 10 exams with confidence. This is just Part 1, as we have a full series planned for you. Our first stop is to cover the essential formulae, presented chapter by chapter, to establish a strong foundation. This is where your journey truly starts. So sit back, take notes, and get ready to ace your math exams with ease. Let's immerse ourselves in the world of mathematics and master those formulas!.

[Audio] Chapter 1 of Your SSC Dost training video focuses on the fundamental concept of Real Numbers. These numbers are commonly used in our daily lives, including whole numbers, fractions, and numbers with roots. Real Numbers can be classified as either rational or irrational. Rational numbers can be written as simple fractions, such as 2 or ½, while irrational numbers cannot be expressed as fractions and are often represented by symbols like √2. This chapter also covers even, odd, prime, and composite numbers, all of which fall under the category of Real Numbers. Understanding the concept of Real Numbers is crucial in building a strong foundation in mathematics. Let's explore the fascinating world of Real Numbers..

[Audio] In this chapter, we will discuss the HCF (Highest Common Factor) of two numbers. It is an essential concept in mathematics that can be incredibly helpful in problem-solving. Two methods can be used to find the HCF - the Division Algorithm and Prime Factorization. The Division Algorithm involves dividing the numbers and checking the remainder until it becomes zero, while the Prime Factorization method breaks down the numbers into their prime factors and determines the common ones. This method is particularly useful for larger numbers. For example, if we want to find the HCF of 24 and 36, we can use the Prime Factorization method. 24 can be broken down into 2 x 2 x 2 x 3, and 36 into 2 x 2 x 3 x 3. The common prime factors are 2, 2, and 3, which, when multiplied, give us the HCF of 12. In conclusion, to find the HCF of two numbers, we can use either the Division Algorithm or Prime Factorization method. These methods can be applied to any set of numbers and can greatly aid in problem-solving. Thank you for choosing SSC Dost as your one-stop destination for SSC Board Class 10 updates and smart study tips. We hope you found this information useful. Stay tuned for more important math formulas in our upcoming chapters..

[Audio] In this chapter, we will discuss the topic of terminating and non-terminating decimals. It is important to understand the difference between the two as it is essential in solving math problems. Terminating decimals stop after a certain number of digits while non-terminating decimals continue infinitely. We also need to remember that if the denominator of a fraction is in the form of 2^m * 5^n, it will be a terminating decimal, with a finite number of digits. However, if the denominator is not in this form, it will be a non-terminating decimal with an infinite number of digits. It is important to keep in mind the Laws of Exponents while simplifying expressions with powers. This concludes slide number 4. Let's now move on to the next chapter, where we will work with a table of data to help us better understand terminating and non-terminating decimals. We hope you find this information useful in your preparation for the SSC Board Class 10 exams..

[Audio] In this segment, we will be discussing sets - an important topic in math. Essentially, a set is a collection of distinct objects or elements that have at least one characteristic in common. There are two forms in which sets can be represented: Roster form, where elements are listed inside curly brackets, and Set-builder form, where a property of the elements is given instead of listing them all. The first type of sets is the Empty set, which has no elements and is represented by empty curly brackets or the symbol for phi. For example, the set of natural numbers less than 1 is an empty set. Thank you for watching and stay tuned for the next chapter in our series, where we will be discussing another important topic in math..

[Audio] In this chapter, we will cover important concepts related to sets, including singleton sets, the universal set, and subsets. A singleton set is a set that contains only one element, such as or . The universal set, denoted by μ (mu), includes all elements under consideration in a particular discussion. For example, if we have sets A= and B=, the universal set would be μ=. Moving on, a set A is considered a subset of a set B (written A⊆B) if every element in A is also in B. In this case, B is referred to as the superset of A. This can be remembered with the phrase "B is the father, and A is the son", symbolized by superscript and subscript respectively. For example, in Example 1, if A= and B=, A is a subset of B (A⊆B), and the sets are equal (A=B). In Example 2, if A= and B=, A is still a subset of B (A⊆B), but the sets are not equal (A≠B). It should also be noted that the null set is a subset of every set, and every set is a subset of itself. To recap, we discussed singleton sets, the universal set, and subsets, and learned a trick to remember their relationship. The next slide will explore subsets in more detail, so stay tuned!.

[Audio] Slide number 7 of our presentation on Equal and Equivalent sets discusses the properties of sets and how they relate to each other. Two sets are equal if they have the exact same elements, regardless of their order. This can be demonstrated by the sets A= and B=, where A equals B. On the other hand, sets are considered equivalent if they have the same number of elements, even if the elements themselves are different. This is represented by n(A)=n(B), where n(X) represents the number of elements in set X. Moving on, there are finite and infinite sets. A finite set has a countable number of elements, such as A=, while an infinite set has an uncountable or never-ending number of elements, like A= or A=. It's important to understand the distinction between these types of sets as they have different properties and characteristics. To visually depict the relationships between sets, Venn diagrams can be used. These diagrams show the common elements between sets and can also demonstrate when sets are disjoint or when one is a proper subset of the other. For instance, if two sets have no elements in common, they are considered disjoint. In summary, equal sets have the same elements, equivalent sets have the same number of elements, finite and infinite sets have different properties, and Venn diagrams are a useful tool to comprehend the relationships between sets. Remember, cardinality represents the number of elements in a set and is denoted as n(X). Please proceed to the next slide for more information on sets..

[Audio] This slide will discuss the basic operations on sets, which are important for understanding and solving problems in set theory. These operations allow us to manipulate and analyze sets to determine relationships between them. There are three fundamental operations: Union, Intersection, and Difference. The first operation, Union, is denoted as A∪B and represents the combination of all elements from two sets without repetition. The second operation, Intersection, is denoted as A∩B and shows the common elements in both sets. The third operation, Difference, is denoted as A−B or B-A and represents the elements present in one set but not the other. Understanding these basic operations is crucial for solving more complex problems in set theory. In the next slide, we will explore examples of these operations in action..

[Audio] Today, we will be discussing slide number 9 out of 23 - 'Relationship between Cardinality of Union and Intersection of Sets'. First, let's understand the meaning of cardinality. It refers to the number of elements in a set and is denoted as n(A) for set A. Moving on to the formula, n(A∪B)=n(A)+n(B)−n(A∩B). This means that the cardinality of the union of two sets is equal to the sum of their individual cardinalities minus the cardinality of their intersection. For a better understanding, let's take an example. Consider set A= and set B=. We can see that the intersection of these two sets is and its cardinality is 1. Similarly, the union of the two sets is with a cardinality of 6. We already know that n(A)=3 and n(B)=4. Now, if we apply the formula, we get n(A∪B)=n(A)+n(B)−n(A∩B)=3+4−1=6. Moving on to Chapter 2 - Sets, we have a table with the following data: 6 3 + 4 – 1 7 – 1 6. This represents the cardinality of sets A, B, and their intersection. So now you have a better understanding of the relationship between the cardinality of union and intersection of sets. Keep studying and preparing for your exams with confidence and stay tuned for more useful information on Your SSC Dost. See you in the next slide!.

[Audio] In this section, we will be discussing types of experiments in probability. An experiment is an action or process that results in well-defined outcomes. Two common experiments in probability are tossing coins and rolling dice. Tossing a coin results in two possible outcomes - heads or tails - each with an equal chance of appearing. The total number of outcomes when tossing one coin is two, and when tossing two or three coins, the total number of outcomes increases to four and eight, respectively. The formula for calculating the total number of possible outcomes when tossing n coins is 2 to the power of n. Rolling a die, which is a cube with numbers 1 to 6 on its faces, results in six possible outcomes when rolling one die and 36 possible outcomes when rolling two dice. This is because for each outcome of the first die, there are six possibilities for the second die, resulting in a total of 36 possibilities. This pattern continues for all possible outcomes, from (1,1) to (6,6). The number of possible outcomes when rolling a die is equal to the number of faces on the die to the power of the number of dice rolled. In summary, the number of possible outcomes in an experiment in probability is calculated by raising the number of options for each outcome to the power of the number of experiments. This information on types of experiments in probability is important to understand as we continue to expand our knowledge on this topic. Please refer to slide 10 for a table summarizing all the data discussed..

[Audio] We will now be discussing the structure of a standard deck of cards. A standard deck has 52 cards in total, divided into four suits - Spades, Clubs, Diamonds, and Hearts. Each suit contains 13 cards, including 1 King, 1 Queen, 1 Jack, 1 Ace and numbers 2 to 10. The deck is also divided into two color groups - red and black - with 26 cards in each. Understanding the structure of a deck of cards is important for various card games and can also aid in developing problem-solving and analytical skills. Let's move on to the next slide for a deeper exploration of the world of cards..

CHAPTER 3-PROBABILITY:-. PROBABILITY.

[Audio] In Chapter 4 - Statistics, we will cover the fundamental concepts of mean and median. Before delving into these concepts, let's examine the data in the table on this slide, which will aid in our understanding. The mean is the average of all data points and is calculated by adding all values and dividing by the total number of values. This calculation gives us an overall value for the data. The median, on the other hand, is the middle value that divides the data into equal upper and lower halves. This helps us understand the central tendency of the data. Understanding mean and median is crucial in interpreting and analyzing data effectively. Remember to pay attention to the concepts and calculations in this chapter. On the next slide, we will discuss additional important concepts in statistics. So, stay tuned and continue learning with SSC Dost..

[Audio] Slide 14 contains a crucial data table for SSC Board Class 10 preparation. This table is well-structured and includes the Class Interval, Frequency, and Mid Value or Class Mark. Each category is important in understanding and analyzing data sets, making it an essential tool for exam preparation. The Class Interval (C.I) groups the data into intervals, while the Frequency (fi) represents the number of occurrences within each interval. The Mid Value (xi) is the midpoint or average of each interval, providing a better understanding of the data's distribution. This table will help you organize and analyze data effectively, making your exam preparation more efficient and accurate. Moving forward, make sure to consult this table while studying. This concludes our discussion for slide 14, but we will continue with the remaining slides shortly. We hope this table will be a valuable asset in your SSC Board Class 10 journey with SSC Dost. Stay tuned for more helpful tips and guidance in the upcoming slides..

[Audio] In today's training video, we will be discussing Chapter 4 - Statistics. Statistics is a crucial part of the math syllabus and understanding it is essential for success in the exams. Let's take a look at Slide 15, which features a table containing important data such as Class Interval, Frequency, Mid value/Class mark, and Deviation. These terms may be unfamiliar to you, so I will explain them in detail. Class Interval refers to the range of values in a specific group, and Frequency is the number of times a value appears in the data set. The Mid value or Class mark is the average value within a group, and Deviation is the difference between a data point and the assumed mean (a). It's important to have a good understanding of these terms as they are frequently used in problems related to statistics. After covering Slide 15, we will move on to Slide 16 to continue our discussion. Thank you for watching and see you in the next segment..

[Audio] In slide 16 of our presentation, we will discuss a crucial table for calculating the median class in your SSC Board Class 10 exams. This table contains key data such as the lower limit of the median class, the number of observations, cumulative frequency, frequency of the median class, and class size. This information is vital for accurately determining the median class, which is an important concept in statistics and essential for exam preparation. It also aids in understanding data distribution and making informed decisions when solving mathematical problems. Be sure to refer to this table as a helpful tool in your preparation. With the assistance of SSC Dost, you can approach your exams with confidence and achieve your academic goals. Stay tuned for more useful tips and formulas in our presentation..

[Audio] In this training video, we will now focus on slide number 17 which contains a table of crucial data for the SSC Board Class 10 exams. The table displays the modal class's lower limit, frequency, class before and after, and the class interval size. These numbers are essential for understanding data distribution and can aid in calculating mathematical formulas. Take note of this table and refer back to it during your study sessions to feel more confident and prepared for your exams. Stay tuned for the remaining slides in our presentation. See you in the next video!.

[Audio] This training video, Your SSC Dost, aims to help you prepare for your SSC Board Class 10 exams by discussing important math formulas in a chapter by chapter format. We are currently on slide number 18 out of 23, which covers the topic of polynomials. Polynomials are a crucial aspect of the math curriculum and require a thorough comprehension for success in exams. Let's delve into the details of polynomials. A polynomial is an expression that includes terms, variables, constants, and operators (+, −) arranged in a specific order. This can also be described as an algebraic expression with more than one term. The slide highlights the general form of a polynomial in one variable. Terms are the individual parts of the polynomial, separated by + or − signs. These terms can be numbers, variables, or a combination of both. The coefficient refers to the number multiplied by the variable, while the variable represents the alphabet used in the expression. The exponent indicates the power of the variable, and the constant term is the term without any variable. To better understand these components, refer to the examples on the slide. Moving on to Chapter 5 - Polynomials, the slide includes a table with various types of polynomials and their corresponding expressions. This table can serve as a helpful reference while studying polynomials. This concludes our discussion on polynomials. We hope this information has aided in your understanding of this topic and will assist in your exam preparations. Thank you for watching and stay tuned for the remaining chapters in this presentation. Have a great day!.

[Audio] This slide discusses the various types of polynomials, categorized by the number of terms and their degree. A polynomial is an algebraic expression with variables and coefficients, and can have one, two, three, or multiple terms. The first category is constant polynomials, with only one term, also known as degree zero polynomials. Binomials have two terms, such as ab4 - 5, and can be linear (degree 1) or quadratic (degree 2), like 3x2 - 7. Trinomials have three terms, such as 3x2 - 5x + 8, and can be linear, quadratic, or cubic (degree 3), like 2y3 - y + 4. Polynomials with multiple terms, like 2x3 - 6x2 - 5x + 8 and 203 + 3y2 + 4y + 8a - 7, can have various degrees, including higher degrees. The degree of a polynomial is determined by the highest exponent of the variable. Now, let's move on to the next slide for a closer examination of polynomial degrees..

[Audio] This is slide number 20 of our training video on SSC Dost, your ultimate guide for SSC Board Class 10 exams. We have provided a useful tool to help you excel in your math exams, a table with important information on linear polynomials. It is important to note that there is only one zero for a linear polynomial, represented by the variable x. This information is essential for solving various equations and we want to ensure that you are well-prepared for your upcoming exams. Please keep this table easily accessible and refer to it as needed. We hope this presentation has been helpful and we wish you all the best for your SSC Board Class 10 exams. Thank you for watching and we look forward to seeing you again on SSC Dost for more resources..

[Audio] This chapter will cover the topic of polynomials, which are algebraic expressions consisting of variables, coefficients, and exponents. They involve the four basic math operations and have practical applications in various fields such as physics, economics, and engineering. The content of this chapter includes the definition, types, and operations of polynomials, as well as key concepts like degree, leading terms, and standard form. Real-world examples and exercises will be used to enhance understanding, and practice problems will be provided to test and reinforce learning. Polynomials are fundamental in understanding more advanced math topics, making it imperative to fully grasp this chapter. Thank you for choosing SSC Dost as your source for SSC Board Class 10, and we hope you continue to find it helpful. See you in the next chapter!.

[Audio] In Chapter 6 of our training on Trigonometry, we will be learning about the basics of trigonometry, starting with right-angled triangles and moving on to various trigonometric formulas. It's important to follow the sequence of sin, cos, tan, cosec, sec, and cot when learning these formulas. Think of the phrase "silly cows take clothes so clean" to remember the sequence. Let's now look at the table on this slide, which contains important data related to our lesson on trigonometry. Make sure to study and review this information, as it will be crucial for understanding this topic. We appreciate you joining us for this training and wish you the best of luck on your exam preparations..

[Audio] As our presentation comes to a close, let us take a moment to recognize the valuable information we have collected from the previous 22 slides. Our goal was to equip you with the necessary tools to succeed in your SSC Board Class 10 exams through our training video. However, before we wrap up, we have one last vital topic to cover - Trigonometry. This chapter is essential in Mathematics and can be overwhelming to understand with its various formulas and concepts. To ease your understanding, we have created a comprehensive Trigonometric table. This table will not only assist you in solving problems effortlessly but also serve as a convenient resource during exams. And that's not all, we have also included triangles alongside the table to help you remember the Trigonometric values. No more last-minute cramming before exams, use these triangles as a quick reference and you will be well-prepared. As we conclude our presentation, we would like to express our gratitude for being a part of the SSC Dost community. Keep visiting our website for regular updates, career guidance, and helpful study tips to excel in your academic journey. We hope you found this training video informative and beneficial. We wish you all the best for your exams and remember, with SSC Dost by your side, you can conquer anything. Thank you for listening, and until next time, stay curious and keep learning..