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Categories: Algebra Formulas

Important Formulas in Algebra

By allformula 0 Comment August 8, 2019

Here is a list of Algebraic formulas – a2 – b2 = (a – b)(a + b) (a+b)2 = a2 + 2ab + b2 a2 + b2 = (a – b)2 + 2ab (a – b)2 = a2 – 2ab + b2 (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc (a – b – c)2 = a2 + b2 + c2 – 2ab – […]

Factoring Formulas

By allformula 0 Comment August 8, 2019

Percentage Formula

By allformula 0 Comment August 8, 2019

Percentage = (Value ⁄ Total Value) × 100 Solved Example : Question 1: Express ⅘ as percentage. Solution: ⅘ = (4 × 20 ⁄ 5 × 20) = (80 ⁄ 100) = 80% Question 2: There are 150 students in a class. Out of them, 75 are girls. Find the percentage of girls in the class? Solution: […]

Ratio Formula

By allformula 0 Comment August 8, 2019

The ratio formula is a:b⇒ab Solved example Question: A and B went into partnership and started a business. They agreed to dived the profit in the ratio of 2 : 4. What is their part of profit at the end of the financial year, if they made Rs. 10,000 in profits? Solution: The ratio in which […]

Matrix Formula

By allformula 0 Comment August 8, 2019

If you see a 2×2 matrix, then that means the matrix has 2 rows and 2 columns.A=[a11a21a12a22] The adjoint of a 2×2 matrix is given as,adj(A)=[a22−a21−a12a11] The inverse of a 2×2 matrix is given as,A−1=1|A|×adj(A) Solved Examples Question: Find out the determinant of the matrix: [−2475]  Solution: The determinant is given by the formula: |A| = ad – bc −2×5−7×4=−38

Exponents Formulas

By allformula 0 Comment August 8, 2019

Here we will learn about various formulas of exponents The Exponents Formulas are a0 = 1 a1 = a a−−√ = a12 a−−√n = a1n a−n = 1an an = 1a−n aman = am+n aman = am−n (am)p = amp (amcn)p = ampcnp (amcn)p = ampcnp Solved Examples Question 1: Solve 14−3 Solution: As per the The Negative Exponent Rule – […]

Polynomial Formula

By allformula 0 Comment August 8, 2019

The general Polynomial Formula is written as, axn+bxn−1+…..+rx+s=0 If n is a natural number, an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1) If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1) If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1) […]

Standard Form Formula

By allformula 0 Comment August 8, 2019

Sometimes standard form is also known as exponential notation or scientific notation. Step one: Put a decimal point right after the first digit of a number from its right Step two: Count the number of places after the decimal, that will be the scientific notation. Step three: Drop the zeroes if any present after the decimal at the […]

Direction Of A Vector Formula

By allformula 0 Comment August 8, 2019

If we say that the rock is moving at 5meter per second, and the direction is towards the West, then it is represented as a vector. If x is the horizontal movement and y is the vertical movement, then the formula of direction isθ=tan−1yx If (x1,y1 ) is the starting point and ends with (x2,y2 ), then […]

Interpolation Formula

By allformula 0 Comment August 8, 2019

The following is  Linear Interpolation Formulay=y1+(x−x1)(x2−x1)×(y2−y1) The La-grange’s Interpolation Formula is given as,y=(x−x1)(x−x2)……(x−xn)(xo−x1)(x0−x2)….(x0−−xn)y+(x−x0)(x−xn)….(x−xn)(x1−x0)(x1−x2….((x1−xn)y1+(x−x1)(x−x2)….(x−xn)(xo−x1)(x0−x2)…..(xo−xn)yn  Some solved problems on interpolation are given below: Solved Examples Question 1: Using the interpolation formula, find the value of y at x = 8 given some set of values (2, 6), (5, 9) ?Solution:The known values are,x0=8,x1=2,x2=5,y1=6,y2=9 y=y1+(x−x1)(x2−x1)×(y2−y1) y=6+((8−2)(5−2)×(9−6)y = 6 + 6y = 12

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