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

Physics Wallah Academic Expert

November 22, 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 Mathematics Formula

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Basic Algebraic Mathematics 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 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
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)
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
(a +b+ c)2=a2+b2+c2+2ab+2bc+2ca
(a +b+ c+…)2=a2+b2+c2+⋯+2(ab +ac+ bc +⋯
(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)
x2+y2=1/2[(x+ y)2+(x−y)2]
(x +a)(x +b)(x +c)=x3+(a +b+ c)x2+(ab +bc+ ca)x+ abc
x3+y3=(x+ y)(x2−xy+y2)
x3−y3=(x−y)(x2+xy+y2)
x2+y2+z2−xy−yz−zx=1/2[(x−y)2+(y−z)2+(z−x)2]

Basic Geometry Mathematics Formula

Perimeter of a square: P = 4a, where 'a' is the length of the sides of the square.
Perimeter of a rectangle: P = 2(l + b), where 'l' is the length and 'b' is the breadth.
Area of a square: A = a², where 'a' is the length of the sides of the square.
Area of a rectangle: A = l × b, where 'l' is the length and 'b' is the breadth.
Area of a triangle: A = ½ × b × h, where 'b' is the base and 'h' is the height.
Area of a trapezoid: A = ½ × (b₁ + b₂) × h, where b₁ and b₂ are the bases and 'h' is the height.
Area of a circle: A = π × r², where 'r' is the radius.
Circumference of a circle: C = 2πr, where 'r' is the radius.
Surface Area of a cube: S = 6a², where 'a' is the length of the sides.
Curved surface area of a cylinder: 2πrh, where 'r' is the radius and 'h' is the height.
Total surface area of a cylinder: 2πr(r + h), where 'r' is the radius and 'h' is the height.
Volume of a cylinder: V = πr²h, where 'r' is the radius and 'h' is the height.
Curved surface area of a cone: πrl, where 'r' is the radius and 'l' is the slant height.
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.
Volume of a cone: V = ⅓ × πr²h, where 'r' is the radius and 'h' is the height.
Surface Area of a sphere: S = 4πr², where 'r' is the radius.
Volume of a sphere: V = 4/3 × πr³, where 'r' is the radius.

Basic Math Formulas Table

Candidates can go through the Basic Math Formulas Table from below:

Basic Math Formulas Table
Area	Square Rectangle Triangle Trapezoid Circle	A = a2 A = l x b A = ½(b x h) A = ((b1 +b2 ) x h) / 2 A = π x r 2
Surface Area	Cube Cylinder Cone Sphere	S = 6l2 CSA = 2 x π x r x h CSA = π x r x l S = 4 x π x r 2
Circumference	Circle	C = 2 (pi) r
Volume	Cylinder Cone Sphere	V = πr 2h V =1/3 πr 2h V = 4/3 x π x r3
Perimeter	Square Rectangle	P = 4a P = 2(l+b)
Pythagoras Theorem	a2 + b2 = c2
Algebraic Formula	Pythagorean theorem Slope-intercept form of the equation of a line Distance formula Total cost Quadratic formula Laws of Exponents Fractional Exponents	a2 + b2 = c2 y = mx + c d = rt total cost = (number of units) × (price per unit) X = [-b ± √(b2 – 4ac)] /2a am x b m = (a x b)m; am x a n = (a)m+n 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	Sine Function Cosine Function Tangent Function	Sin x = Opposite Side/ Hypotenuse Cos X = Adjacent Side/ Hypotenuse Tan x = Opposite Side/ Adjacent Side

Basic Maths Formula from Class 6 to 12

Mastering mathematics 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

A number is divisible by 3 if the sum of its digits is a multiple of 3.
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.
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.
1,000,000,000 is known as one billion.
Division by zero results in 'undefined.'
A number is considered divisible by 2 if it contains 0, 2, 4, 6, or 8 in any place.
The perimeter of a square is calculated as 4 times the length of its side.
The perimeter of a rectangle is found by doubling the sum of its length and breadth.
The perimeter of an equilateral triangle is determined by multiplying the length of one side by 3.
The area of a rectangle is calculated as the product of its length and breadth.
A variable is a value that is not fixed and can take on different values.
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

Product of rational numbers: Multiply the numerators to get the new numerator and multiply the denominators to get the new denominator.
Increase in Percentage = (Change / Original Amount) × 100
Profit Percentage = (Profit / Cost price) × 100
Simple Interest = (Principal × Rate × Time) / 100
Amount = Principal + Interest
Multiplying a rational number by the reciprocal of another rational number is equivalent to multiplying both numerators together and both denominators together.
Area of a square: A Square is the length of one of its sides.
Perimeter of a square: Multiply the length of one side by 4.
Area of a rectangle: Find the product of its length and breadth.
Perimeter of a rectangle: Double the sum of its length and breadth.
Area of a parallelogram: Multiply the base by the height.
Area of a triangle: Take half of the product of the base and height.
Circumference of a circle: Multiply the diameter by π (approximately 3.14 or 22/7).
Area of a circle: Square the radius and multiply by π.
Law of Product: When you multiply two numbers with the same base, add the exponents.
Law of Quotient: When you divide two numbers with the same base, subtract the exponents.
Law of Zero Exponent: Any non-zero number raised to the power of zero is equal to 1.
Law of Negative Exponent: To find the reciprocal of a number with a negative exponent, change the sign of the exponent.
Law of Power of a Power: When you raise an exponent to another exponent, multiply the exponents.
Law of Power of a Product: When you raise a product to an exponent, distribute the exponent to each factor.
Law of Power of a Quotient: When you raise a quotient to an exponent, apply the exponent to both the numerator and denominator.
(a-b) 2 = a2 – 2ab + b2: Square the first term, multiply twice the product of the terms, and square the second term.
(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

Additive inverse of a rational number: For any rational number a/b, its additive inverse is -b/a.
Multiplicative Inverse of a/b: If a/b × c/d equals 1, then the multiplicative inverse of a/b is c/d.
Distributive property: a(b – c) equals ab – ac.
Probability of an event: The probability of an event occurring is the number of favourable outcomes divided by the total number of possible outcomes.
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.
(a – b)²: The square of the binomial (a – b) is given by a² – 2ab + b².
(a + b)(a – b): The product of the sum and difference of two terms (a + b)(a – b) is equal to a² – b².
Euler's Formula: For any polyhedron, the sum of the number of faces and vertices minus the number of edges equals 2.
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.
Volume of a Sphere: The volume of a sphere is (4/3)πr³, where 'r' is the radius.

Importance of Learning Basic Formulas of Maths

Learning basic formulas of math is essential for building a strong foundation in mathematics. Students can check the importance below.

Enhances Problem-Solving Skills: Basic formulas serve as tools to solve mathematical problems efficiently. Whether students are working with geometry, algebra, or calculus, knowing these basic formulas allows them to approach problems with confidence and clarity. Without understanding basic formulas, solving even simple math problems becomes much more difficult.

Saves Time: By memorizing and understanding basic formulas, students can solve complex problems more quickly. When they’re familiar with the core formulas, they don’t have to derive them from scratch each time. This is especially valuable in exams, where time is limited, and students need to apply basic formulas swiftly to answer questions.

Builds Strong Mathematical Intuition: Basic formulas help students develop a deeper understanding of mathematical concepts. For instance, knowing the Pythagorean theorem allows students to solve geometry problems involving right triangles, but it also helps them understand the relationship between sides in more complex geometric shapes. These formulas are stepping stones to more advanced topics.

Prepares for Advanced Topics: Many advanced mathematical concepts build on basic formulas. For example, calculus, algebra, and trigonometry rely on fundamental principles such as the distributive property, the quadratic formula, and trigonometric identities. Mastering these basic formulas ensures students are well-prepared for more complex math.

Real-Life Applications: Basic formulas are not just limited to academic purposes—they are used in real-world applications as well. Whether students are calculating areas and volumes in construction, understanding financial models, or working with data in statistics, basic formulas are tools that can be applied in everyday situations.

Check out - CBSE Class 10 Sample Paper Maths

Tips to Remember Important Maths Formulas

Remembering important math formulas can be challenging, but with the right strategies, you can make them stick. Here are some effective tips to help you retain mathematics all formulas:

Understand the Concept: Before memorizing important math formulas, ensure you fully understand the concepts behind them. This understanding will make it easier to recall the formula when needed, as you’ll know how it works and why it’s used.
Practice Regularly: The more you practice using mathematics all formulas, the more likely you are to remember them. Try solving problems that require these formulas to reinforce them in your mind.
Use Mnemonics: Creating a mnemonic or a memory aid can help you recall important math formulas more easily. For example, for the quadratic formula, you might use a catchy phrase that corresponds to each part of the formula.
Write and Rewrite: Writing down mathematics all formulas repeatedly helps reinforce them. Each time you write them out, you create a visual memory that can aid in recall.
Create Flashcards: Use flashcards to test yourself on important math formulas. Write the formula on one side and the name or application of the formula on the other side. This active recall method is an effective way to strengthen your memory.
Group Formulas by Topic: Organize important math formulas by topic (e.g., algebra, geometry, calculus). Reviewing formulas by category can make them easier to digest and recall in context.
Teach Someone Else: Explaining mathematics all formulas to someone else is a great way to solidify your understanding and memory. Teaching forces you to recall the formula and its application, reinforcing it in your mind.