Basic Maths Formulas for Class 6 to 12

Basic math formulas for class 6 to 12 include a list of mathematical expressions from various important topics like algebra, percentage, trigonometry, mensuration etc. Basic math formulas help students to tackle any mathematical problems easier and faster. 

By applying basic math formulas, learners can solve complex mathematical problems through various ways and tactics. Math is not a difficult subject to study as with the right formulas; students can tackle any type of question.

Table of Contents

• Basic Math Formulas: Download PDF Links
• Class 6 Basic Math Formulas
• Class 7 Basic Math Formulas
• Class 8 Basic Math Formulas
• Class 9 Basic Math Formulas
• Class 10 Basic Math Formulas
• Class 11 Basic Math Formulas
• Class 12 Basic Math Formulas
• Why is Practicing Basic Math Formulas Necessary?

Basic Math Formulas: Download PDF Links

Students can download the basic math formulas for their respective class by clicking on the links provided below-

Particular	Download Link
Class 6 Basic Math Formulas	Click Here
Class 7 Basic Math Formulas	Click Here
Class 8 Basic Math Formulas	Click Here
Class 9 Basic Math Formulas	Click Here
Class 10 Basic Math Formulas	Click Here
Class 11 Basic Math Formulas	Click Here
Class 12 Basic Math Formulas	Click Here

Also Check: Career Options In Commerce With Maths

Class 6 Basic Math Formulas

Class 6 basic math formulas include topics like Integers, Decimals, Fractions, Number System, Mensuration, etc. Students can go through the math formulas listed below for class 6.

• 1,000,000,000 is called one billion in the numeric system.
• Anything divisible by zero is called ‘undefined’.
• A number is divisible by 2 if it has 0, 2, 4, 6 or 8 in one place.
• A number is divisible by 3 if the sum of the digits is a multiple of 3.
• A closed figure formed by line segments is a polygon. A triangle is a three-sided Polygon, while quadrilaterals are four-sided polygons.
• An equation is a state represented by a variable. An equation consists of two sides, known as the Left-Hand Side and Right Hand Side, divided by an equal (=) sign. 
• The perimeter of a Square = 4 × Length of one square side
• Perimeter of a Rectangle = 2 × (Length of rectangle Breadth of rectangle)
• The perimeter of an Equilateral triangle = 3 × Length of one side
• Area of a Rectangle = length of a rectangle × breadth of a rectangle
• Variable refers to a value that is not fixed. It can carry different values.
• An equation is a state represented by a variable.
• An equation consists of two sides, known as the Left-Hand Side and Right Hand Side, divided by an equal (=) sign.

Class 7 Basic Math Formulas

Class 7 basic math topics include profit loss, percentage, simple and compound interest, etc. Students can view class 7 basic math formulas stated below.

• Profit Percentage = (Profit Price / Cost price) × 100
• Loss Percentage = (Loss Price/ Cost price) × 100
• Simple Interest = (Principal × Rate × Time) / 100
• Amount = Principal + Interest
• Percentage Change= (Change Amount / Original Amount) × 100
• Product of rational numbers = (Product of Numerators) / (Product of Denominators)
• First Rational Number × (Reciprocal of other Rational Number)
• Law of Product: am × an = am+n
• Law of Quotient: am/an = am-n
• Law of Zero Exponent: a0 = 1
• Law of Negative Exponent: a-m = 1/am
• Law of Power of a Quotient: (a/b)m = am/bm
• Law of Power of a Power: (am)n = amn
• Law of Power of a Product: (ab)m = ambm
• Perimeter of a Rectangle = 2 × (Length of a rectangle + Breadth of a rectangle)
• Area of Rectangle = Length of a rectangle× Breadth of a rectangle
• Area of a Square = Side2
• Area of Triangle = 1/ 2 × Base of a triangle × Height of a triangle
• The perimeter of a Square = 4 × Side
• Area of a Parallelogram = Base × Height
• Area of a circle = πr2
• Circumference of a circle = π d, where ‘d’ is the diameter of a circle and π = 22/7 or 3.14

Class 8 Basic Math Formulas

Class 8 basic math formulas consist of rational numbers, distributives, probability, etc. Students must go through the given formulas to solve mathematical problems quickly.

• Additive inverse of rational number: a/b = -b/a
• Multiplicative Inverse of a/b = c/d , if a/b × c/d = 1
• Distributives a(b – c) = ab – ac
• Simple Interest = (Principal × Rate × Time) / 100
• Amount = Principal amount + Interest amount
• Compound Interest formula = Amount – Principal, Amount in case the interest is calculated annually = Principal ( 1 + Rate/100)n, where ‘n’ is the period.
• Probability of the happening of an event = number of outcomes that comprise an event/ Total number of outcomes.

Class 9 Basic Math Formulas

Class 9 basic math formulas consist of Algebra, Polynomials, geometry, real numbers, etc. Students can check the basic class 9 math formulas stated below.

Class 9 Basic Math Formulas

Topics	Math Formulas
Real Numbers	√ab = √a √b √(a/b) = √a / √b (√a + √b) (√a – √b) = a – b (√a + √b)2 = a + 2√ab + b (a + √b) (a – √b) = a2 – b (a + b) (a – b) = a2 – b2
Rectangle	Area of Rectangle A = Length x Width Perimeter of Rectangle P = 2(Length + Width)
Triangle	Area of Triangle, A = ½ x Breadth x Height Perimeter of Triangle, P = Sum of all the three sides of a triangle
Circle	Area of Circle, A = πr² The perimeter of circle, P = 2 πr
Parallelogram	Area of Parallelogram, A = Breadth x Height Perimeter of Parallelogram, P = 2( a+ b) (Here. a = side, b = base )
Trapezoid	Area of Trapezoid A = ½ x Height x (b₁ x b₂) Perimeter of Trapezoid, P = Sum of all the sides of a trapezoid
Cuboid	Surface Area (A) = (lb + bh + hl), ([l = length, b = Breadth, h = height] Volume V = Length x Breadth x Height
Cylinder	Surface area of Cylinder A = 2πr( h + r) [r = radius of the circular cylinder, H = height of a cylinder] The volume of Cylinder V = πr²H
Cube	The surface area of the Cube. A = 6 side² Volume of a Cube V = Side³
Sphere	Surface Area of a Sphere A = 4πr² The volume of a Cube V = 4/3πr³
Cone	Surface area of a Cone (A) = πr( L + r) [l = slant height , r = Radius of base] Volume of a Cone (V )= ½ πr²
Heron’s Formula	Area of Triangle with 3 sides = √s(s-a)(s-b)(s-c) Here, s = semi-perimeter, and A,b, and c are the sides of a triangle. Semi Perimeter, S = ( a + b + c)/2
Polynomial Formula	P (x) = anxn + an- 1xn- 1 – an- 2xn- 1 + …… ax + a0
Algebra Identities	(x + θ) (x – θ) = x² – θ² (x + β)² = x² + β² + 2 x β (x – β)² = x² + β² – 2 x β (x – α)(x + θ) = x² + (θ – α)x – xθ (x – α)(x – θ) = x² – (α + θ)x + αq (x + α)(x + θ) = x² + (α + θ)x + αθ (x + α)(x – θ) = x² + (α – θ)x – αθ (α + β + θ)² = α² + β² + θ² + 2αβ + 2βθ + 2αθ (α + β – θ)² = α² + β² + θ² + 2αβ – 2βθ – 2αθ (α – β + θ)² = α² + β² + θ²- 2αβ – 2βθ + 2αθ (α – β – θ)² = α² + β² + θ² – 2αβ + 2βθ – 2αθ (α + θ)³ = α³ + θ³ + 3αθ(α + θ) (x)³ + (β)³ = ( x + β) (x² – xβ + β) (x)³ – (β)³ = ( x + β) (x² – xβ + β)
Statistics	Mean : Total number of observations/sum of all observations Median: ((n+1)/2)th observations = odd observations ((n/2)th + ((n/2)+1)th)/2 observations for even observations Mode: The most often occurring value in a data set

Class 10 Basic Math Formulas

Class 10 basic math formulas contain various kinds of algebraic, geometric, and arithmetic formulas. Students can go through class 10 basic math formulas tabulated below.

Arithmetic Formulas 

• An = a + (n – 1) d, where an is the nth term.
• Sn= n/2 [2a + (n – 1)d]

Algebra Formulas

• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• (a + b) (a – b) = a2 – b2
• (x + a)(x + b) = x2 + (a + b)x + ab
• (x + a)(x – b) = x2 + (a – b)x – ab
• (x – a)(x + b) = x2 + (b – a)x – ab
• (x – a)(x – b) = x2 – (a + b)x + ab
• (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – b3 – 3ab(a – b)
• (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
• (x + y – z)2 = x2 + y2 + z2 + 2xy – 2yz – 2xz
• (x – y + z)2 = x2 + y2 + z2 – 2xy – 2yz + 2xz
• (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2xz
• x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – xz)

Area and Volume Formulas 

• The volume of Sphere = 4/3 ×π r3
• Lateral Surface Area of Sphere (LSA) = 4π r2
• Total Surface Area of Sphere (TSA) = 4πr2
• The volume of the Right Circular Cylinder = πr2h
• Lateral Surface Area of Right Circular Cylinder (LSA) = 2×(πrh)
• Total Surface Area of Right Circular Cylinder (TSA) = 2πr×(r + h)
• Volume of Hemisphere = ⅔ x (πr3)
• Lateral Surface Area of Hemisphere (LSA) = 2πr2
• Total Surface Area of Hemisphere (TSA) = 3πr2
• Volume of Prism = B × h
• Lateral Surface Area of Prism (LSA) = p × h

Circle Formula

• The tangent to a circle equation x2 + y2 = a2 for a line y = mx + c is given by the equation y = mx ± a √ [1+ m2].
• The tangent to a circle equation x2 + y2 = a2 at (a1,b1) is xa1 + yb1 = a2

Trigonometry Formulas

• sin(90° – A) = cos A
• cos(90° – A) = sin A
• tan(90° – A) = cot A
• cot(90° – A) = tan A
• sec(90° – A) = cosec A
• cosec(90° – A) = sec A
• sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos 2 θ ⇒ cos2 θ = 1 – sin 2 θ
• cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cos 2 θ – 1
• sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Class 11 Basic Math Formulas

Basic math formulas in class 11 include calculus, trigonometry, algebra, statistics, geometric formulas, etc. Students can dig into class 11 basic math formulas stated below.

Geometry and Lines Formulas 

• Slope m = rise/run = Δy/Δx = y2−y1/x2−x1
• Point-Slope Form y−y1 = m (x−x1)

Algebra Formulas

• a × (b + c) = a × b + a × c (Distributive property)
• a + b = b + a (Commutative Property of Addition)
• a × b = b × a (Commutative Property of Multiplication)
• a + (b + c) = (a + b) + c (Associative Property of Addition)
• a × (b × c) = (a × b) × c (Associative Property of Multiplication)
• a + 0 = a (Additive Identity Property)
• a × 1 = a(Multiplicative Identity Property)
• a + (-a) = 0 (Additive Inverse Property)
• a⋅(1/a) = 1 (Multiplicative Inverse Property)
• a × (0) =0 (Zero Property of Multiplication)

Calculus Formulas

• d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
• d/dx [f(x) – g (x)] = d/dx [f(x)] – d/dx [g(x)]
• d/dx [f(x) × g (x)] = d/dx [f(x)] × [g(x)] + [f(x)] × d/dx [g(x)]
• d/dx [f(x) / g (x)] = {d/dx [f(x)] × [g(x)] – [f(x)] × d/dx [g(x)]} / g(x)2

Trigonometry Formulas

• sin(90° – A) = cos A
• cos(90° – A) = sin A
• tan(90° – A) = cot A
• cot(90° – A) = tan A
• sec(90° – A) = cosec A
• cosec(90° – A) = sec A
• sin2 θ + cos2 θ = 1 ⇒ sin2 θ = 1 – cos 2 θ ⇒ cos2 θ = 1 – sin2 θ
• cosec 2θ – cot2 θ = 1 ⇒ cosec 2θ = 1 + cot2 θ ⇒ cot2 θ = cos 2 θ – 1
• sec2 θ – tan2 θ = 1 ⇒ sec2 θ = 1 + tan2 θ ⇒ tan2 θ = sec2 θ – 1
• sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

Class 12 Basic Math Formulas

Class 12 basic math formulas include formulas for trigonometry, matrices, vectors, 3D geometry, etc. Students can find the basic math formulas for class 12 given below.

Calculus Formulas

• ∫ f(x) dx = F(x) + C
• Power Rule: ∫ xn dx = (xn+1) / (n+1) + C. (Where n ≠ -1)
• Exponential Rules: ∫ ex dx = ex + C 
• ∫ ax dx = ax / ln(a) + C
• ∫ ln(x) dx = x ln(x) – x + C
• Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant. 
• Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C 
• Sum Rules: ∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx
• Difference Rules: ∫ [f(x) – g(x)] dx = ∫f(x) dx – ∫g(x) dx
• ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
• Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx – ∫[d/dx f(x) × ∫ g(x) dx]dx
• ∫cos x dx = sin x + C
• ∫ sin x dx = -cos x + C
• ∫ sec2 x dx = tan x + C
• ∫ cosec 2x dx = -cot x + C
• ∫ sec x tan x dx = sec x + C
• ∫ cosec x cot x dx = – cosec x + C

Vector Formulas

• A + B = B + A (Commutative Law)
• A + (B + C) = (A + B) + C (Associative Law)
• (A • B )= |P| |Q| cos θ ( Dot Product )
• (A × B )= |P| |Q| sin θ (Cross Product)
• k (A + B )= kA + kB
• A + 0 = 0 + A (Additive Identity)

Geometry Formulas 

• Cartesian equation of a plane: lx + my + nz = d 
• Distance between two points P(x1, y1, z1) and Q(x2, y2, z2): PQ = √ ((x1 – x2)2 + (y1 – y2)2 + (z1 – z2)2) 

Trigonometry Formulas

• sin-1(-x) = – sin-1x 
• tan-1x + cot-1x = π / 2
• sin-1x + cos-1 x = π / 2
• cos-1(-x) = π – cos-1x
• cot-1(-x) = π – cot-1x

Why is Practicing Basic Math Formulas Necessary?

There are various reasons to practice basic math formulas on a daily basis. Students can find the reasons stated below.

• Students will be able to understand the problem effectively.
• It will help students to solve problems faster and have the right answers.
• Practicing basic math formulas helps students score better on exams.
• Often, practicing basic math formulas helps students in real-life situations.
• Practicing basic math formulas helps students to develop their logical thinking ability, improve calculation skills and be confident.