Basic Math Formulas, Important Math Formulas, Tips to Remember Formulas

Physics Wallah Academic Expert
July 04, 2024

Mathematics fundamentals show how we can solve problems using different equations, like those involving forces, accelerations, or work done. These equations are crucial tools for tackling real-world issues. Equations come in many types and are present in various areas of math. The methods used to understand them depend on their specific types. It can be as easy as adding numbers together or as complex as using integration and differentiation. Thus, to keep it organised, the Physics Wallah team has provided candidates with essential math formulas. Remembering these formulas is crucial not only for school exams but also for upcoming entrance exams.

BODMAS Formula 

B = Bracket 

O = Of

D = Division

M = Multiplication 

A = Addition

S = Subtraction 

Basic Algebraic Formula

  1. a2 – b2 = (a – b)(a + b)

  2. (a + b)2 = a2 + 2ab + b2

  3. a2 + b2 = (a + b)2 – 2ab

  4. (a – b)2 = a2 – 2ab + b2

  5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

  6. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca

  7. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)

  8. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)

  9. a3 – b3 = (a – b)(a2 + ab + b2)

  10. a3 + b3 = (a + b)(a2 – ab + b2)

  11. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

  12. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

  13. a4 – b4 = (a – b)(a + b)(a2 + b2)

  14. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

  15. (a +b+ c)2=a2+b2+c2+2ab+2bc+2ca

  16. (a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯

  17. (x+ y+ z)2=x2+y2+z2+2xy+2yz+2xz

  18. (x +y−z)2=x2+y2+z2+2xy−2yz−2xz

  19. (x− y+ z)2=x2+y2+z2−2xy−2yz+2xz

  20. (x−y−z)2=x2+y2+z2−2xy+2yz−2xz

  21. x3+y3+z3−3xyz=(x+ y+ z)(x2+y2+z2−xy−yz−xz)

  22. x2+y2=1/2[(x+ y)2+(x−y)2]

  23. (x +a)(x +b)(x +c)=x3+(a +b+ c)x2+(ab +bc+ ca)x+ abc

  24. x3+y3=(x+ y)(x2−xy+y2)

  25. x3−y3=(x−y)(x2+xy+y2)

  26. x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]

Basic Geometry Formula

  1. Perimeter of a square: P = 4a, where 'a' is the length of the sides of the square.

  2. Perimeter of a rectangle: P = 2(l + b), where 'l' is the length and 'b' is the breadth.

  3. Area of a square: A = a², where 'a' is the length of the sides of the square.

  4. Area of a rectangle: A = l × b, where 'l' is the length and 'b' is the breadth.

  5. Area of a triangle: A = ½ × b × h, where 'b' is the base and 'h' is the height.

  6. Area of a trapezoid: A = ½ × (b₁ + b₂) × h, where b₁ and b₂ are the bases and 'h' is the height.

  7. Area of a circle: A = π × r², where 'r' is the radius.

  8. Circumference of a circle: C = 2πr, where 'r' is the radius.

  9. Surface Area of a cube: S = 6a², where 'a' is the length of the sides.

  10. Curved surface area of a cylinder: 2πrh, where 'r' is the radius and 'h' is the height.

  11. Total surface area of a cylinder: 2πr(r + h), where 'r' is the radius and 'h' is the height.

  12. Volume of a cylinder: V = πr²h, where 'r' is the radius and 'h' is the height.

  13. Curved surface area of a cone: πrl, where 'r' is the radius and 'l' is the slant height.

  14. Total surface area of a cone: πr(r + l) = πr[r + √(h² + r²)], where 'r' is the radius, 'l' is the slant height, and 'h' is the height.

  15. Volume of a cone: V = ⅓ × πr²h, where 'r' is the radius and 'h' is the height.

  16. Surface Area of a sphere: S = 4πr², where 'r' is the radius.

  17. Volume of a sphere: V = 4/3 × πr³, where 'r' is the radius.

Basic Maths Formula Table

Candidates can go through the Basic Maths Formula Table from below: 

Basic Maths Formula Table

Area

  1. Square

  2. Rectangle

  3. Triangle

  4. Trapezoid

  5. Circle

  1. A = a2

  2. A = l x b

  3. A = ½(b x h)

  4. A = ((b1 +b2 ) x h) / 2

  5. A = π x r 2

Surface Area

  1. Cube

  2. Cylinder

  3. Cone

  4. Sphere

  1. S = 6l2

  2. CSA = 2 x π x r x h

  3. CSA = π x r x l

  4. S = 4 x π x r 2

Circumference

  1. Circle

  1. C = 2 (pi) r

Volume

  1. Cylinder

  2. Cone

  3. Sphere

  1. V = πr 2h

  2. V =1/3 πr 2h

  3. V = 4/3 x π x r3 

Perimeter

  1. Square

  2. Rectangle

  1. P = 4a

  2. P = 2(l+b)

Pythagoras Theorem

a2 + b2 = c2

Algebraic Formula

  1. Pythagorean theorem

  2. Slope-intercept form of the equation of a line

  3. Distance formula

  4. Total cost

  5. Quadratic formula

  6. Laws of Exponents

  7. Fractional Exponents

  1. a2 + b2 = c2

  2. y = mx + c

  3. d = rt

  4. total cost = (number of units) × (price per unit)

  5. X = [-b ± √(b2 – 4ac)] /2a

  6. am x b m = (a x b)m; am x a n = (a)m+n

  7. a1/2 = √a

Distance Formula

d = √[(x2 – x1)2 +(y2 – y1)2]

Slope of a line

m = y2 – y1 / x2 – x1

Mid- Point Formula

M = [(x1 + x2 )/ 2 , (y1 + y2 )/ 2]

Trigonometric Formulas

  1. Sine Function

  2. Cosine Function

  3. Tangent Function

  1. Sin x = Opposite Side/ Hypotenuse

  2. Cos X = Adjacent Side/ Hypotenuse

  3. Tan x = Opposite Side/ Adjacent Side

Basic Maths Formula from Class 6 to 12

Mastering math formulas significantly improves students' performance in exams at all academic levels. Chapters in the math syllabus are interconnected, making it crucial to understand one chapter's formulas for easier comprehension of others. Examples include percentage and profit-loss, percentages and fractions, and real numbers and complex numbers. Thus, here are some of the basic math formulas for classes 6 to 12.

Basic Maths Formula Class 6 

  1. A number is divisible by 3 if the sum of its digits is a multiple of 3.

  2. A simple closed figure formed by line segments is called a polygon. A triangle is a three-sided polygon, while quadrilaterals are four-sided polygons.

  3. An equation is a statement involving a variable. It consists of two sides, the Left-Hand Side and Right-Hand Side, separated by an equal (=) sign.

  4. 1,000,000,000 is known as one billion.

  5. Division by zero results in 'undefined.'

  6. A number is considered divisible by 2 if it contains 0, 2, 4, 6, or 8 in any place.

  7. The perimeter of a square is calculated as 4 times the length of its side.

  8. The perimeter of a rectangle is found by doubling the sum of its length and breadth.

  9. The perimeter of an equilateral triangle is determined by multiplying the length of one side by 3.

  10. The area of a rectangle is calculated as the product of its length and breadth.

  11. A variable is a value that is not fixed and can take on different values.

  12. An equation represents a condition involving a variable, consisting of two sides known as the Left-Hand Side and Right-Hand Side, separated by an equal (=) sign.

Basic Maths Formula Class 7

  1. Product of rational numbers: Multiply the numerators to get the new numerator and multiply the denominators to get the new denominator.

  2. Increase in Percentage = (Change / Original Amount) × 100

  3. Profit Percentage = (Profit / Cost price) × 100

  4. Simple Interest = (Principal × Rate × Time) / 100

  5. Amount = Principal + Interest

  6. Multiplying a rational number by the reciprocal of another rational number is equivalent to multiplying both numerators together and both denominators together.

  7. Area of a square: A Square is the length of one of its sides.

  8. Perimeter of a square: Multiply the length of one side by 4.

  9. Area of a rectangle: Find the product of its length and breadth.

  10. Perimeter of a rectangle: Double the sum of its length and breadth.

  11. Area of a parallelogram: Multiply the base by the height.

  12. Area of a triangle: Take half of the product of the base and height.

  13. Circumference of a circle: Multiply the diameter by π (approximately 3.14 or 22/7).

  14. Area of a circle: Square the radius and multiply by π.

  15. Law of Product: When you multiply two numbers with the same base, add the exponents.

  16. Law of Quotient: When you divide two numbers with the same base, subtract the exponents.

  17. Law of Zero Exponent: Any non-zero number raised to the power of zero is equal to 1.

  18. Law of Negative Exponent: To find the reciprocal of a number with a negative exponent, change the sign of the exponent.

  19. Law of Power of a Power: When you raise an exponent to another exponent, multiply the exponents.

  20. Law of Power of a Product: When you raise a product to an exponent, distribute the exponent to each factor.

  21. Law of Power of a Quotient: When you raise a quotient to an exponent, apply the exponent to both the numerator and denominator.

  22. (a-b) 2 = a2 – 2ab + b2: Square the first term, multiply twice the product of the terms, and square the second term.

  23. (a-b-c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ac: Square each term, multiply twice the product of each pair of terms and add the results.

Basic Maths Formula Class 8

  1. Additive inverse of a rational number: For any rational number a/b, its additive inverse is -b/a.

  2. Multiplicative Inverse of a/b: If a/b × c/d equals 1, then the multiplicative inverse of a/b is c/d.

  3. Distributive property: a(b – c) equals ab – ac.

  4. Probability of an event: The probability of an event occurring is the number of favourable outcomes divided by the total number of possible outcomes.

  5. Compound Interest formula: The compound interest is calculated as the difference between the amount and the principal. If the interest is calculated annually, the amount is given by Principal (1 + Rate/100)n, where 'n' is the period.

  6. (a – b)²: The square of the binomial (a – b) is given by a² – 2ab + b².

  7. (a + b)(a – b): The product of the sum and difference of two terms (a + b)(a – b) is equal to a² – b².

  8. Euler's Formula: For any polyhedron, the sum of the number of faces and vertices minus the number of edges equals 2.

  9. Volume of a Cone: The volume of a cone is calculated as (1/3)πr²h, where 'r' is the radius and 'h' is the height.

  10. Volume of a Sphere: The volume of a sphere is (4/3)πr³, where 'r' is the radius.

Tips to Remember Basic Maths Formula

A student's school life is filled with hundreds of formulas, making it challenging to remember them all. However, here are effective tips to memorize Basic Math Formulas:

  1. Gain a deep understanding of the formulas and their derivations.

  2. Practice applying the formulas to various questions, utilizing resources like Vedantu sample papers.

  3. Create concise revision sheets to quickly review the formulas before exams.

Basic Maths Formula FAQs

Q1. What is the formula for the perimeter of a square?

Ans. Formula: Perimeter = 4 × side length (P = 4a)

Q2. How do I calculate the area of a rectangle?

Ans. Formula: Area = length × breadth (A = l × b)

Q3. How can I find the circumference of a circle?

Ans. Formula: Circumference = 2πr (C = 2πr)

Q4. ow do I calculate the surface area of a cube?

Ans. Formula: Surface Area = 6 × side length squared (S = 6a²)

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