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

Posted by Strategic Communications, JGI Group on on 22 July 2024

Memorising mathematical formulas can be a challenging task for many students. Nonetheless, understanding these formulas is crucial for solving problems and achieving good grades. The fundamentals of mathematics illustrate how to use various equations to address problems related to forces, accelerations, and work done. These equations are vital tools for solving real-world problems. Mathematical equations come in many forms and appear across different areas of math. The methods to understand and implement these equations vary depending on their types. While some equations might involve straightforward addition, others require more complex processes such as integration and differentiation. Let us look at some of the basic math formulas and some tips to remember them!

What are Basic Math Formulas?

A formula is a mathematical expression or rule derived from the relationship between two or more quantities, represented using symbols. In math, formulas typically include constants (specific numbers), variables (letters representing unknown values), mathematical symbols (such as plus or minus signs), and sometimes exponential powers. Mathematics is divided into various branches based on the methods of calculation and the topics they cover. Each branch has its own set of formulas used to solve different types of problems. Some of these branches include geometry, algebra, arithmetic, percentages, and exponential functions. Let us look at some of the basic maths formulas used extensively:

BODMAS Formula

• B = Bracket
• O = Of
• D = Division
• M = Multiplication
• A = Addition
• S = Subtraction

Basic Algebraic 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 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 Maths Formula Table

We have listed some basic maths formulas in a tabular format for our students:

Basic Maths Formula from Grade VI to XII

A thorough understanding of maths formulas significantly enhances students' performance in various exams, whether they are class tests, final exams, or board exams. Many chapters in the math syllabus are interconnected. Mastering the formulas from one chapter can make it easier to grasp subsequent chapters. For instance, understanding the relationship between percentages and profit-loss or between percentages and fractions can simplify related topics. Similarly, understanding real numbers can ease the study of complex numbers. Students should dedicate ample time and effort to methodically analyse and understand these formulas. By doing so, they can better navigate the interconnected topics within the math curriculum. This approach will provide a solid foundation for studying basic math formulas from grades 6 to 12.

Basic Math Formulas for Grade VI

• 1,000,000,000 is known as one billion.
• Division by zero results in an 'undefined' value.
• A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
• A number is divisible by 3 if the sum of its digits is a multiple of 3.
• A polygon is a simple closed figure made up of line segments. For example, a triangle is a three-sided polygon, and a quadrilateral is a four-sided polygon.
• An equation represents a condition involving a variable and consists of two sides, separated by an equal (=) sign.
• The perimeter of a square is calculated as 4 times the length of one side.
• The perimeter of a rectangle is given by 2 times the sum of its length and breadth.
• The perimeter of an equilateral triangle is 3 times the length of one side.
• The area of a rectangle is found by multiplying its length by its breadth.
• A variable is a value that can change and is not fixed.

Basic Math Formulas for Grade VII

• Product of Rational Numbers: To multiply rational numbers, multiply the numerators to get the new numerator and the denominators to get the new denominator.
• Total Amount: The total amount is the sum of the principal and interest.
• Increase in Percentage = (Change / Original Amount) × 100
• Profit Percentage = (Profit / Cost price) × 100
• Simple Interest = (Principal × Rate × Time) / 100
• Amount = Principal + Interest
• Multiplying Rational Numbers: When multiplying a rational number by the reciprocal of another, multiply the numerators together and the denominators together.
• Area of a Square: The area is found by squaring the length of one side.
• Perimeter of a Square: To find the perimeter, multiply the length of one side by 4.
• Area of a Rectangle: Multiply its length by its breadth to get the area.
• Perimeter of a Rectangle: The perimeter is twice the sum of its length and breadth.
• Area of a Parallelogram: Multiply the base by the height to find the area.
• Area of a Triangle: The area is half of the product of the base and height.
• Circumference of a Circle: Multiply the diameter by π\piπ (approximately 3.14 or 227\frac{22}{7}722).
• Area of a Circle: Square the radius and multiply by π\piπ to get the area.
• Law of Product: When multiplying two numbers with the same base, add their exponents.
• Law of Quotient: When dividing two numbers with the same base, subtract the exponent of the denominator from the exponent of the numerator.
• Law of Zero Exponent: Any non-zero number raised to the power of zero equals 1.
• Law of Negative Exponent: For a negative exponent, find the reciprocal of the base and change the sign of the exponent.
• Law of Power of a Power: When raising an exponent to another exponent, multiply the exponents.
• Law of Power of a Product: When raising a product to an exponent, apply the exponent to each factor within the product.
• Law of Power of a Quotient: When raising a quotient to an exponent, apply the exponent to both the numerator and the denominator.
• Expanding (a−b)2(a-b)^2(a−b)2: To expand, square the first term, subtract twice the product of the terms, and then add the square of the second term.
• Expanding (a−b−c)2(a-b-c)^2(a−b−c)2: To expand, square each term, add the squares of all terms, subtract twice the product of each pair of terms, and then add the results.

Basic Math Formulas for Grade VIII

• 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.

Basic Math Formulas for Grade IX

1. 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

2. Geometry Formulas – Geometry Shapes Formulas for Class 9

Basic Math Formulas for Grade X

Algebra Formulas For Class 10

• (a+b)2 = a2 + b2 + 2ab
• (a-b)2 = a2 + b2 – 2ab
• (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)
• x2 + y2 =½ [(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 = ½ [(x-y)2 + (y-z)2 + (z-x)2]

Basic Formulas For Powers For Class 10

• pm x pn = pm+n
• {pm}⁄{pn} = pm-n
• (pm)n = pmn
• p-m = 1/pm
• p1 = p
• P0 = 1
• 3. Arithmetic Formulas For Class 10
• an = a + (n – 1) d, where an is the nth term.
• Sn= n/2 [2a + (n – 1)d]

Trigonometry Formulas For Class 10

• 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 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
• cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 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

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
• Area and Volume Formulas
• 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

Basic Maths Formulas for Grade XI

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)

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 – cos2 θ ⇒ cos2 θ = 1 – sin2 θ
• cosec2 θ – cot2 θ = 1 ⇒ cosec2 θ = 1 + cot2 θ ⇒ cot2 θ = cosec2 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

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

Geometry and Lines Formulas

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

Basic Maths Formulas for Grade XII

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)

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

Calculus Formulas

Tips to Remember Basic Maths Formulas

Mastering advanced math formulas and logarithms becomes much easier with a solid understanding of the concepts. Before diving into memorisation, students should ensure they grasp the meaning, function, and derivation of each formula. Here are some smart techniques to help students remember basic math formulas effectively:

Create a Mental Image of the Formula

Visual aids can make memorising complex formulas more engaging. Follow these steps:

• Break Down the Formula: Identify all constants, variables, and operations involved.
• Assign Visual Symbols: Convert each component into a visual element. For instance, in
• 𝐸 = 𝑚𝑐2 , students could imagine 𝐸 as an elephant, 𝑚 as a mountain, and 𝑐2 as two cars racing at the speed of light.
• Craft a Storyline: Develop a vivid story incorporating these elements. Picture a balance scale with an elephant on one side and a mountain with two race cars zooming at light speed on the other.
• Make It Outrageous: The more unique and memorable the story, the better. Students should rehearse the story and practice converting it back into the formula.

Use a Mnemonic Device

Mnemonics simplify memorisation through catchy sentences. For example, “Some Officers Have Curly Auburn Hair Til Old Age” helps recall Sine = Opposite Over Hypotenuse, Cosine = Adjacent Over Hypotenuse, and Tangent = Opposite Over Adjacent. Students can create their own mnemonic by using the first letters of each element in the formula to form memorable words.

Use Flashcards

Flashcards, whether paper or digital are effective for memorisation. Students should write the formula name on one side and the formula itself on the other. Regularly testing themselves and using apps like Anki, which utilise spaced repetition to optimise learning, can be highly beneficial.

Write the Formulas Repeatedly

For kinesthetic learners, writing formulas repeatedly helps reinforce memory. Students should utilise spare moments to jot down formulas, such as before or during class. Regular practice, even in short bursts, can significantly improve retention.

Practice Using the Formulas

Memorising formulas is just the beginning; applying them is crucial. Students should solve numerous practice problems to familiarise themselves with real-world applications. If preparing for tests like the SAT, engaging with practice tests will help in effectively using the formulas.

Sing or Recite the Formulas Aloud

Setting formulas to music or simply reciting them can aid memorisation, especially for auditory learners. Students can explore existing songs for formulas online or create their own. Even if not musically inclined, reciting formulas aloud can be highly effective.

In a Nutshell

Mastering mathematical formulas is integral to understanding the vast landscape of mathematics and solving a variety of problems effectively. While memorisation of these formulas may initially seem daunting, understanding their derivations and applications significantly enhances problem-solving abilities and overall mathematical competence. Effective strategies for retaining these formulas include practicing their application in diverse problems, visualising their geometric interpretations, and relating them to real-world scenarios. Additionally, understanding the underlying principles behind each formula can make it easier to recall and apply them accurately.