Math Formulas For Class 11

Maths is a subject that deals with different mathematical operations. It requires a systematic way to operate any kind of question. To solve the math problems, different ranges of formulas were discovered. Maths is a complex subject and not everyone wants to opt for it. 

• The students can find a wide range of mathematical formulas in each chapter of class 11. 
• The formulas are very helpful for all the students.
• Maths is usually a complex yet very interesting subject. 
• The different theorems, as well as formulas, are proposed in Maths Class 11 chapters. 

Key Terms: Formula, Set, Algebra, Trigonometry, Coordinate geometry.

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What is Formula?

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Maths is an operational subject. It is based on different logic and reasons. The questions in Maths are needed to be understood with the help of practical examples. Then, the formulas are introduced for solving the numerical questions. There is a list of formulas that are used in class 11 Math. 

• The formulas are divided into different chapters. 
• The chapters are Sets, Trigonometric Functions, Relations and Functions, Complex Numbers and Quadratic Equations, Permutations and Combinations, Binomial Theorem, Sequence and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, and Statistics. 
• These chapters are included in the class 11 Mathematics book.

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List of Class 11 Formulas

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The students can use different formulas which are related to different chapters. They can solve mathematical problems on the basis of given formulas. It reduces the complexity and toughness of the questions. So, the students can easily solve the questions. Some chapters and their formulas are given here. 

Sets - Formulas

A set is considered the collection of different objects. It possesses definite and proper elements. 

For any two sets A and B, the formula is given.

• (A∪B)′=A′∩B′
• (A∩B)′=A′∪B′

If the finite sets A and B are given such that (A∩B)= ϕ, then: 

• n(A∪B)=n(A)+n(B)

If (A∪B)= ϕ, then: 

• n(A∪B)=n(A)+n(B)−n(A∩B)

Other important formulas are as follows– 

• A – A = Ø
• B – A = B⋂ A’
• B – A = B – (A⋂B)
• (A – B) = A if A⋂B = Ø
• (A – B) ⋂ C = (A⋂ C) – (B⋂C)
• A ΔB = (A-B) U (B- A)
• n(A∪B) = n(A) + n(B) – n(A⋂B)
• n(A∪B∪C)= n(A) +n(B) + n(C) – n(B⋂C) – n (A⋂ B)- n (A⋂C) + n(A⋂B⋂C)
• n(A – B) = n(A∪B) – n(B)
• n(A – B) = n(A) – n(A⋂B)
• n(A’) = n(∪) – n(A)
• n(U) = n(A) + n(B) + – n(A⋂B) + n((A∪B)’)
• n((A∪B)’) = n(U) + n(A⋂B) – n(A) – n(B)

Algebra - Formulas

This is a chapter which also deals with the different ranges of formulas for the students.

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

Trigonometry - Formulas

• sin (- θ) = - sin θ 
• cos (- θ) = cos θ 
• tan (- θ) = - tan θ 
• cosec (- θ) = - cosec θ 
• sec (- θ) = sec θ 
• cot (- θ) = - cot θ

The Reciprocal Identities of trigonometry are given below.

• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• cot θ = 1/tan θ
• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ

Coordinate Geometry - Formulas

• General Form of a Line: Ax + By + C = 0
• Slope Intercept Form of a Line: y = mx + c
• Point-Slope Form: y − y₁= m(x − x₁)
• The slope of a Line Using Coordinates: m = Δy/Δx = (y₂ − y₁)/(x₂ − x₁)
• The slope of a Line Using General Equation: m = − (A/B)
• Intercept-Intercept Formula: x/a + y/b = 1
• Distance Formula: |P₁P₂| = √[(x₂ − x₁)² + (y₂ − y₁)²]
• For Parallel Lines: m₁ = m₂
• For Perpendicular Lines: m₁m₂ = – 1
• Midpoint Formula : M (x, y) = [½ (x₁ + x₂), ½ (y₁ + y₂)]
• Angle Formula : tan θ = [(m₁ – m₂)/ 1 + m₁m₂]
• Area of a Triangle Formula: ½ |x₁(y₂−y₃)+x₂(y₃–y₁)+x₃(y₁–y₂)|
• Distance from a Point to a Line: d = [|Ax₀ + By₀ + C| / √(A₂ + B₂)]
• Section Formula (Internal division): P(x, y) = [(m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)]
• Section Formula (External division): P(x, y) = [(m₁x₂ – m₂x₁)/(m₁ – m₂), (m₁y₂ – m₂y₁)/(m₁ – m₂)]

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Things to Remember

• Slope Intercept Form of a Line formula is y = mx + c.
• Distributive Property formula is a × (b + c) = a × b + a × c.
• Commutative Property of Addition formula is a + b = b + a.
• Commutative Property of Multiplication formula is a × b = b × a. 
• Associative Property of Addition formula is a + (b + c) = (a + b) + c.
• Associative Property of Multiplication formula is a × (b × c) = (a × b) c.
• Additive Identity Property formula is a + 0 = a.
• Multiplicative Identity Property formula is a × 1 = a.