Basic Math Formulas

Arithmetic

The basic operations involved in arithmetic are addition, subtraction, multiplication, and division.

Arithmetic formula

Arithmetic mean (average)= Sum of values/Number of values.

Algebra

Algebra is an elementary subject of mathematics that deals with the study of the evaluation of numbers and symbols. The algebraic operations are carried out to determine the unknown values which are expressed by letters. Algebraic equations are the expressions formed by the combination of variables, constants, factors, and coefficients of variables.

Basic algebra formula

• 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 + 2bc + 2ca
• (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
• (a + b)3 = a3 + 3a2b + 3ab2 + b2
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)
• (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
• (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
• a4– b4 = (a – b)(a + b)(a2 + b2)
• (am)(an)= am + n
• (ab)m = ambm
• (am)n = amn

Geometry

Geometry is a part of mathematics that is concerned with the study of shapes, sizes, parameters, measurement, properties, and dimensions. There are generally three types of geometry. They are Euclidean geometry, Spherical geometry, and Hyperbolic geometry.

Basic geometry formula

• Rectangle

1. Perimeter of Rectangle = 2(l + b)
2. The area of Rectangle  = l × b

Where 'l' is Length and 'b' is Breadth

• Square

1. The area of Square = a2
2. The perimeter of Square = 4a

Where 'a' is the length of the sides of a Square

• Triangle

Area of Triangle= 1/2 × b × h

Where 'b' is the base of the triangle and 'h' is the height of the triangle

• Trapezoid

Area of Trapezoid = 1/2 × (b1 + b2)× h

Where b1 and b2 are the bases of the Trapezoid

And, h = height of the Trapezoid

• Circle

1. Area of Circle = π × r2
2. Circumference of Circle = 2πr

Where 'r' is the radius of a Circle

• Cube

Surface Area of Cube = 6a2

Where 'a' is the length of the sides of the Cube

• Cylinder

1. The curved surface area of Cylinder = 2πrh
2. The total surface area of Cylinder = 2πr(r + h)
3. The volume of Cylinder = V = πr2h

Where 'r' is the radius of the base of the Cylinder

And, 'h' is the height of Cylinder

• Cone

1. The curved surface area of a cone = πrl
2. Total surface area of cone = πr(r + l)= πr[r + √(h2 + r2)]
3. Volume of a Cone = V = 1/3× πr2h

Here, 'r' is the radius of the base of Cone and h = Height of the Cone

• Sphere

1. Surface Area of a Sphere = S = 4πr2
2. Volume of a Sphere = V = 4/3 × πr3

Where, r = Radius of the Sphere

Probability

Probability is the mathematical term used to determine the chance of occurring a particular event. Probability can simply be defined as the possibility of the occurrence of an event. It is expressed on a linear scale from 0 to 1.

There are three types of probability: theoretical probability, experimental probability, and subjective probability.

Basic probability formula

P(A)= n(A)/n(S)

Where,

P(A)is the probability of an event.

n(A)is the number of favorable outcomes

n(S)is the total number of events

Fraction

A fraction is a number expressed with integers in which a numerator is divided by the denominator. A fraction is basically the quotient of a division. 

Basic fractions formula

• (a + b/c)= (a × c)+ b/c
• (a/b + d/b)= (a + d)/b
• (a/b + c/d)= (a × d + b × c/b × d)
• a/b × c/d = ac/bd
• (a/b)/(c/d)= a/b × d/c

Percentage

A percentage is a numerical value or ratio expressed as a fraction of 100. It is generally symbolized by the sign %.

Basic percentage formula

Percentage = (Amount in the category/Total value)× 100