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Complete MATHS Class 10 Formula Sheet in 60 mins πŸ“ MUST WATCH for Last Minute Revision πŸ”₯

BYJU'S - Class 9 & 10・63 minutes read

The session covers key math concepts and formulas for both Basic and Standard students, emphasizing understanding and application. Topics include polynomials, linear and quadratic equations, sequence formulas, similarity of triangles, trigonometry, geometry, and statistics/probability. Practical applications, definitions, and formula explanations are provided to aid in exam preparation.

Insights

  • The session covers various mathematical concepts, from Real Numbers to Trigonometry, emphasizing the importance of understanding formulas and concepts for both Basic and Standard students.
  • Detailed explanations are provided on topics such as polynomials, linear equations, and geometry, with a focus on practical applications like calculating the area and volume of shapes and understanding statistical measures like median and probability.

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Recent questions

  • What is the significance of the Fundamental Theorem of Arithmetic?

    The Fundamental Theorem of Arithmetic is crucial as it helps in understanding composite numbers and their prime factorization. It states that every integer greater than 1 can be expressed uniquely as a product of prime numbers.

  • How are HCF and LCM related in mathematics?

    The relationship between HCF (Highest Common Factor) and LCM (Least Common Multiple) is essential in mathematics, especially when dealing with two positive integers. The HCF is the largest number that divides both numbers without leaving a remainder, while the LCM is the smallest number that is a multiple of both numbers.

  • What is the significance of the degree of a polynomial?

    The degree of a polynomial is crucial as it indicates the highest power of the variable present in the polynomial. Understanding the degree helps in determining the behavior of the polynomial, such as the number of zeros it may have and the shape of its graph.

  • How are linear equations in two variables typically solved?

    Linear equations in two variables involve two unknowns, usually represented by x and y. To solve such equations, methods like substitution and elimination are commonly used to find the values of x and y that satisfy both equations simultaneously.

  • What is the formula for calculating the median of a set of data?

    The median of a set of data is the middle value when the data is arranged in ascending order. The formula to calculate the median is L + N/2 - Kf/F * h, where L is the lower boundary of the median class, N is the total number of data points, Kf is the cumulative frequency of the class before the median class, F is the frequency of the median class, and h is the class interval.

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Summary

00:00

"Mastering Math: Formulae and Polynomials Explained"

  • The session covers the Formal Formula Sheet and all concepts in 60 minutes, focusing on formulae available in all chapters.
  • The session is for both Basic and Standard students, emphasizing the importance of understanding formulae concepts.
  • Instructions are given to quickly subscribe to the channel for new students to receive notifications about upcoming sessions and exams.
  • The session starts with Real Numbers, discussing the Fundamental Theorem of Arithmetic and composite numbers.
  • The session delves into the Theorem of Arithmetic, explaining its significance in proving irrational numbers.
  • The relationship between HCF and LCM is highlighted, emphasizing its applicability to two positive integers.
  • The session moves on to Polynomials, defining terms like monomial, binomial, and trinomial based on the number of terms.
  • Different types of polynomials are discussed based on the degree, such as linear polynomials with the highest power as the degree.
  • The standard form of a polynomial is explained, focusing on arranging terms from the highest to the lowest degree.
  • The process of finding the value of a polynomial by replacing the variable with a specific value is detailed, highlighting the concept of zero of a polynomial.

14:34

Understanding Polynomial Degrees and Linear Equations

  • Degree of a polynomial indicates the highest power of the variable present.
  • A cubic polynomial has a degree of three, with three as the highest power of the variable.
  • Zeros of a polynomial are the values that make the polynomial equal to zero.
  • The graph of a polynomial intersects the x-axis at the zeros.
  • Quadratic polynomials form parabolas, with the graph intersecting at one or two points.
  • The relationship between the sum and product of zeros of a quadratic polynomial is discussed.
  • Linear equations in two variables involve two variables, typically represented by x and y.
  • A and B in linear equations cannot be zero to maintain linearity.
  • Methods like substitution and elimination are used to solve linear equations.
  • Quadratic equations can be solved using the quadratic formula, considering the nature of the roots.

29:38

Sequences, Formulas, and Geometry Theorems Explained

  • The sequence formula is given as A + D, A + 2D, A + 3D, and so on, where A is the first term and D is the common difference.
  • There are two formulas: the term formula and the sum of N terms formula.
  • The sum of N terms formula is given as Sn = n/2 * (2A + (n-1)D).
  • The last term formula is applicable when given the first term, last term, and number of terms.
  • The focus is on NCERT and practicing basic concepts.
  • Similarity of triangles is discussed, based on corresponding sides and angles.
  • The ratio of corresponding sides of similar triangles is highlighted.
  • The proof of theorems in coordinate geometry is emphasized.
  • The distance formula is explained as √((X2 - X1)^2 + (Y2 - Y1)^2).
  • The section formula for dividing a line segment in a given ratio is detailed as M1X2 + M2X1 / M1 + M2 and M1Y2 + M2Y1 / M1 + M2.

43:03

Trigonometry: Key Formulas and Practical Applications

  • Activation is not required, move on to voting.
  • Derivations are not necessary for the syllabus, focus on the midpoint formula.
  • The midpoint formula involves a ratio of 1:1 and inserting values into a specific formula.
  • The sum of angles in a circle is 180 degrees.
  • Different sets of triangles depend on the four points.
  • Preparation for the paper includes revising Introduction to Trigonometry.
  • Understanding trigonometric ratios involves remembering specific formulas.
  • Three key trigonometric identities need to be thoroughly prepared.
  • Practical applications of trigonometry involve understanding terminologies like line of sight and elevation.
  • Detailed instructions on drawing figures and understanding the geometry of 3D objects are crucial.

56:22

Geometry, Statistics, and Probability Explained

  • The slant height of a cone is the square root of the sum of the radius squared and the height squared.
  • The total surface area of a cone includes the circular base area (Ο€rΒ²) and the lateral area (Ο€r√(rΒ²+hΒ²)).
  • The volume of a cone is one-third of the volume of a cylinder with the same base and height (1/3Ο€rΒ²h).
  • Combining a cone with a cylinder results in a solid figure with different dimensions for each shape.
  • Calculating the area and volume of combined shapes depends on the information provided.
  • Statistics and probability involve understanding data averages, methods for calculating median, mode, and probability.
  • The median is the middle value in a set of data, calculated using the formula L + N/2 - Kf/F * h.
  • Probability is determined by the number of favorable outcomes divided by the total number of outcomes, with impossible events having a probability of zero.
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