Maths Formulas for Class 11 Session 2022-23: A Complete Guide

Maths Formulas for Class 11: Mathematics is a difficult and scoring subject if you have clearly understood formulas and concepts, but many students find it tricky to remember all these complex formulas. There are many formulas in Mathematics like the trikonmiti formula ( Trigonometry), straight lines class 11 formulas and more. Class 11 CBSE Maths formulas will help students secure good scores in maths and also help in building a base to clear competitive exams in the future. 

The article covers relations and functions, limits and derivatives class 11 formulas, formulas for permutation and combination, binomial theorem, trigonometric formulas, straight lines class 11 formulas and others. Embibe brings you the essential Maths formulas for Class 11 PDF download to help you in your preparation journey. Read the article to download all the math formulas and equations to help you solve problems quickly and score higher grades in your CBSE Class 11 exams.

Maths Formulas for Class 11

Maths is a subject of reason and logic. Students must have a clear understanding of the underlying theories. They must understand what the maths class 11 formulas mean. Only then will they be able to crack the Mathematics questions. Before getting into the list of the formulas, let’s check out the major chapters of Class 11 Maths for which formulas are needed:

1. Sets
2. Relations and Functions
3. Trigonometric Functions
4. Complex Numbers and Quadratic Equations
5. Permutations and Combinations
6. Binomial Theorem
7. Sequence and Series
8. Straight Lines
9. Conic Sections
10. Introduction to Three Dimensional Geometry
11. Limits and Derivatives
12. Statistics

Maths Class 11 Formulas – Sets

A set is a well-collaborated collection of objects. A set consisting of definite elements is a finite set. Otherwise, it is an infinite set. You can find the essential symbols and properties for Sets below:

1. The union of two sets A and B are said to be contained elements that are either in set A and set B. The union of A and B is denoted as: \(A\cup B\).
2. The intersection of two sets A and B are said to be contained elements that are common in both the sets. The intersection of A and B is denoted as: \(A\cap B\).
3. The complement of a set A is the set of all elements given in the universal set U that are not contained in A. The complement of A is denoted as \({A}’\).
4. For any two sets A and B, the following holds true:
   • (i) \({(A\cup B)}’={A}’\cap{B}’\)
   • (ii) \({(A\cap B)}’={A}’\cup{B}’\)
5. If the finite sets A and B are given such that \({(A\cap B)}=\phi\), then: \(n{(A\cup B)}=n(A)+n(B)\)
6. If \({(A\cup B)}=\phi\), then: \(n{(A\cup B)}=n(A)+n(B)-n(A\cap B)\)

Relations and Functions Class 11 Formulas

An ordered pair is a pair of elements grouped together in a certain order. A relation R towards a set A to a set B can be described as a subset of the cartesian product A × B which is obtained by describing a relationship between the first of its element x and the second of its element y given in the ordered pairs of A × B.

The below-mentioned properties will surely assist you in solving your Maths problems.

1. A cartesian product A × B of two sets A and B is given by:
   A × B = { \((a,b):a\epsilon A, b\epsilon B\) }
2. If (a , b) = (x , y); then a = x and b = y
3. If n(A) = x and n(B) = y, then n(A × B) = xy
4. A × \(\phi\) = \(\phi\)
5. The cartesian product: A × B ≠ B × A
6. A function f from the set A to the set B considers a specific relation type where every element x in the set A has one and only one image in the set B.
   A function can be denoted as f: A → B, where f(x) = y
7. Algebra of functions: If the function f: X → R and g: X → R; we have:
   • (i) \((f + g) (x) = f (x) + g(x), x\epsilon X\)
   • (ii) \((f – g) (x) = f (x) – g(x), x\epsilon X\)
   • (iii) \((f.g)(x) = f (x) .g (x), x\epsilon X\)
   • (iv) \((kf) (x) = k ( f (x) ), x\epsilon X\), where k is a real number
   • (v)\( \frac{f}{g}(x) = \frac{f(x)}{g(x)}, x\epsilon X, g(x)\neq 0\)

Trigonometric Functions – Maths Formulas for Class 11

In Mathematics, trigonometric functions/ trikonmiti formula is the real functions that relate to an angle of a right-angled triangle forming some finite ratios of two side lengths. Find the important Math formulas for Class 11 related to trigonometric functions below.

1. If in a circle of radius r, an arc of length l subtends an angle of θ radians, then \(l = r × θ\).
2. Radian Measure = \(\frac{\pi}{180}\) × Degree Measure
3. Degree Measure = \(\frac{180}{\pi}\) × Radian Measure
4. \(cos^2 x + sin^2 x = 1\)
5. \(1 + tan^2 x = sec^2 x\)
6. \(1 + cot^2 x = cosec^2 x\)
7. \(cos (2n\pi + x) = cos\: x\)
8. \(sin (2n\pi + x) = sin\: x\)
9. \(sin\: (-x) = -sin\: x\)
10. \(cos\: (-x) = -cos\: x\)
11. \(cos\:(\frac{\pi}{2}-x)=sin\:x\)
12. \(sin\:(\frac{\pi}{2}-x)=cos\:x\)
13. \(sin\: (x + y) = sin\: x\times cos\: y+cos\: x\times sin\: y\)
14. \(cos\: (x + y) = cos\: x\times cos\: y-sin\: x\times sin\: y\)
15. \(cos\: (x – y) = cos\: x\times cos\: y+sin\: x\times sin\: y\)
16. \(sin\: (x – y) = sin\: x\times cos\: y-cos\: x\times sin\: y\)
17. \(cos\:(\frac{\pi}{2}+x)=-sin\:x\)
18. \(sin\:(\frac{\pi}{2}+x)=cos\:x\)
19. \(cos\: (\pi-x) = -cos\: x\)
20. \(sin\: (\pi-x) = sin\: x\)
21. \(cos\: (\pi+x) = -cos\: x\)
22. \(sin\: (\pi+x) = -sin\: x\)
23. \(cos\: (2\pi-x) = cos\: x\)
24. \(sin\: (2\pi-x) = -sin\: x\)
25. If there are no angles x, y and (x ± y) is an odd multiple of (π / 2); then:
    • (i) \(tan\:(x+y)=\frac{tan\:x+tan\:y}{1-tan\:x\:tan\:y}\)
    • (ii) \(tan\:(x-y)=\frac{tan\:x-tan\:y}{1+tan\:x\:tan\:y}\)
26. If there are no angles x, y and (x ± y) is an odd multiple of π; then:
    • (i) \(cot\:(x+y)=\frac{cot\:x\:cot\:y-1}{cot\:y+cot\:x}\)
    • (ii) \(cot\:(x-y)=\frac{cot\:x\:cot\:y+1}{cot\:y-cot\:x}\)
27. \(cos\:2x=cos^2\:x-sin^2\:x=2\:cos^2\:x-1=1-2\:sin^2\:x=\frac{1-tan^2\:x}{1+tan^2\:x}\)
28. \(sin\:2x=2\:sin\:x:cos\:x=\frac{2\:tan\:x}{1+tan^2\:x}\)
29. \(sin\:3x=3\:sin\:x-4\:sin^3\:x\)
30. \(cos\:3x=4\:cos^3\:x-3\:cos\:x\)
31. \(tan\:3x=\frac{3\:tan\:x-tan^3\:x}{1-3\:tan^2\:x}\)
32. Addition and Subtraction of sin and cos
    • (i) \(cos\:x+cos\:y=2\:cos\frac{x+y}{2}\:cos\frac{x-y}{2}\)
    • (ii) \(cos\:x-cos\:y=-2\:sin\frac{x+y}{2}\:sin\frac{x-y}{2}\)
    • (iii) \(sin\:x+sin\:y=2\:sin\frac{x+y}{2}\:cos\frac{x-y}{2}\)
    • (iv) \(sin\:x-sin\:y=2\:cos\frac{x+y}{2}\:sin\frac{x-y}{2}\)
33. Multiplication of sin and cos
    • (i) \(2\:cos\:x\:cos\:y=cos\:(x+y)+cos\:(x-y)\)
    • (ii) \(-2\:sin\:x\:sin\:y=cos\:(x+y)-cos\:(x-y)\)
    • (iii) \(2\:sin\:x\:cos\:y=sin\:(x+y)+sin\:(x-y)\)
    • (iv) \(2\:cos\:x\:sin\:y=sin\:(x+y)-sin\:(x-y)\)
34. \(sin\: x = 0;\: gives\: x = n\pi,\: where\: n\: \epsilon\: Z\)
35. \(cos\: x = 0;\: gives\: x = (2n+1)\frac{\pi}{2},\: where\: n\: \epsilon\: Z\)
36. \(sin\: x = sin\: y;\: implies\: x = n\pi\:+(-1)^n\:y,\: where\: n\: \epsilon\: Z\)
37. \(cos\: x = cos\: y;\: implies\: x = 2n\pi\pm y,\: where\: n\: \epsilon\: Z\)
38. \(tan\: x = tan\: y;\: implies\: x = n\pi+y,\: where\: n\: \epsilon\: Z\)

Complex Numbers and Quadratic Equations

A number that can be expressed in the form a + ib is known as the complex number; where a and b are the real numbers and i is the imaginary part of the complex number.

1. Let z₁ = a + ib and z₂ = c + id; then:
   • (i) z₁ + z₂ = (a + c) + i (b + d)
   • (ii) z₁ . z₂ = (ac – bd) – i (ad + bc)
2. If there is a non-zero complex number; z = a + ib; where (a ≠ 0, b ≠ 0), then there exists a complex number \(\frac{a}{a^2+b^2}+i\frac{-b}{a^2+b^2}\); denoted by \(\frac{1}{z} or z^–1 is known as the multiplicative inverse of z; such that
   (a + ib) [ \(\frac{a^2}{a^2+b^2}+i\frac{-b}{a^2+b^2}\) ] = 1 + i 0 = 1
3. For every integer k, i^4k = 1, i^4k+1 = i, i^4k+2 = -1, i^4k+3 = -i
4. The conjugate of the complex number is \(\bar{z}=a-ib\)
5. The polar form of the complex number z = x + iy is \(r(cos\: \theta+i\:sin\:\theta)\); where \(r=\sqrt{x^2+y^2}\) (the modulus of z)
   \(cos\:\theta =\frac{x}{r}\) and \(sin\:\theta =\frac{y}{r}\) (θ is the argument of z)
6. A polynomial equation with n degree has n mysqladmins.
7. The solutions of the quadration equation ax² + bx + c = 0 are:
   \(x=\frac{-b\pm \sqrt{4ac-b^2i}}{2a}\) where a, b, c ∈ R, a ≠ 0, b² – 4ac < 0

Permutations and Combinations

If a certain event occurs in ‘m’ different ways followed by an event that occurs in ‘n’ different ways, then the total number of occurrences of the events can be given in m × n order. Find the important Maths formulas for class 11 as under:

1. The number of permutations of n different things taken r at a time is given by \({}^{n}\textrm{P}{r}\) \(=\frac{n!}{(n-r)!}\) where 0 ≤ r ≤ n
2. \(n!=1\times 2\times 3\times …\times n\)
3. \(n!=n\times (n-1)!\)
4. The number of permutations of n different things taken r at a time with repetition being allowed is given as: n^r
5. The number of permutations of n objects taken all at a time, where p₁ objects are of one kind, p₂ objects of the second kind, …., p_k objects of kth kind are given as: \(\frac{n!}{p_{1}!\:p_{2}!\:…\:p_{k}!}\)
6. The number of permutations of n different things taken r at a time is given by \({}^{n}\textrm{C}{r}\) \(=\frac{n!}{r!(n-r)!}\) where 0 ≤ r ≤ n

Binomial Theorem

A Binomial Theorem helps to expand a binomial given for any positive integer n.
\((a+b)^n={}^{n}\textrm{C}_{0}\:a^n+{}^{n}\textrm{C}_{1}\:a^{n-1}.b+{}^{n}\textrm{C}_{2}\:a^{n-2}.b^2+…+{}^{n}\textrm{C}_{n-1}\:a.b^{n-1}+{}^{n}\textrm{C}_{n}\:b^n\)

1. The general term of an expansion (a + b)ⁿ is \(T_{r+1}={}^{n}\textrm{C}_{r}\:a^{n-r}.b^r\)
2. In the expansion of (a + b)ⁿ; if n is even, then the middle term is \((\frac{n}{2}+1)^{th}\) term.
3. In the expansion of (a + b)ⁿ; if n is odd, then the middle terms are \((\frac{n+1}{2})^{th}\) and \((\frac{n+1}{2}+1)^{th}\) terms

Maths Formula For Class 11: Sequence And Series

An arithmetic progression (A.P.) is a sequence where the terms either increase or decrease regularly by the same constant. This constant is called the common difference (d). The first term is denoted by a and the last term of an AP is denoted by l.

1. The general term of an AP is \(a_{n}=a+(n-1)\:d\)
2. The sum of the first n terms of an AP is: \(S_{n}=\frac{n}{2}[2a+(n-1)\:d]=\frac{n}{2}(a+l)\)

A sequence is said to be following the rules of geometric progression or G.P. if the ratio of any term to its preceding term is specifically constant all the time. This constant factor is called the common ratio and is denoted by r.

1. The general term of an GP is given by: \(a_{n}=a.r^{n-1}\)
2. The sum of the first n terms of a GP is: S_{n}=\frac{a(r^n-1)}{r-1}\: or\: \frac{a(1-r^n)}{1-r}; if r ≠ 1
3. The geometric mean (G.M.) of any two positive numbers a and b is given by \(\sqrt{ab}\)

Straight Lines Class 11 Formulas

1. Slope (m) of the intersecting lines through the points (x₁, y₁) and x₂, y₂) is given by \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\); where x₁ ≠ x₂
2. An acute angle θ between lines L1 and L2 with slopes m1 and m2 is given by \(tan\:\theta =\left | \frac{m_{2}-m_{1}}{1+m_{1}.m_{2}} \right |\); 1 + m₁.m₂ ≠ 0.
3. Equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given by: \(y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})\)
4. Equation of the line making a and b intercepts on the x- and y-axis respectively is: \(\frac{x}{a}+\frac{y}{b}=1\)
5. The perpendicular distance d of a line Ax + By + C = 0 from a point (x₁, y₁) is: \(d=\frac{\left | Ax_{1}+By_{1}+C \right |}{\sqrt{A^2+B^2}}\)
6. The distance between the two parallel lines Ax + By + C₁ and Ax + By + C₂ is given by: d=\(\frac{\left | C_{1}-C_{2} \right |}{\sqrt{A^2+B^2}}\)

Conic Sections

A circle is a geometrical figure where all the points in a plane are located equidistant from the fixed point on a given plane.

1. The equation of the circle with the centre point (h, k) and radius r is given by (x – h)² + (y – k)² = r²
2. The equation of the parabola having focus at (a, 0) where a > 0 and directrix x = – a is given by: y² = 4ax
3. The equation of an ellipse with foci on the x-axis is \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
4. Length of the latus rectum of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is given by: \(\frac{2b^2}{a}\)
5. The equation of a hyperbola with foci on the x-axis is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)
6. Length of the latus rectum of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is given by: \(\frac{2b^2}{a}\)

Introduction to Three Dimensional Geometry

The three planes determined by the pair of axes are known as coordinate planes with XY, YZ and ZX planes. Find the important Maths formulas for Class 11 below:

1. The distance of two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is:
   \(PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)
2. The coordinates of a point R that divides the line segment joined by two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) internally as well as externally in the ratio m : n is given by:
   \(\left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n} \right )\:and\:\left ( \frac{mx_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n},\frac{mz_2-nz_1}{m-n} \right )\);
3. The coordinates of the mid-point of a given line segment joined by two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) are \(\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2} \right )\)
4. The coordinates of the centroid of a given triangle with vertices (x₁, y₁, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃) are \(\left ( \frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3} \right )\)

Limits and Derivatives Class 11 Formulas

A limit of a function at a certain point holds a common value of the left as well as the right-hand limits if they coincide with each other.

1. For functions f and g, the following property holds true:
   • (i) \(\lim\limits_{x \to a} \left [ f(x)\pm g(x) \right ]= \lim\limits_{x \to a}f(x) \pm \lim\limits_{x \to a}g(x)\)
   • (ii) \(\lim\limits_{x \to a} \left [ f(x) .g(x) \right ]= \lim\limits_{x \to a}f(x) . \lim\limits_{x \to a}g(x)\)
   • (iii) \(\large \lim\limits_{x \to a} \left [ \frac{f(x)}{g(x)} \right ] = \frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a}g(x)}\)
2. Standard Limits
   • (i) \(\lim\limits_{x \to a}\frac{x^n-a^n}{x-a}= n\:a^{n-1}\)
   • (ii) \(\lim\limits_{x \to a}\frac{sin\:x}{x}=1\)
   • (iii) \(\lim\limits_{x \to a}\frac{1-cos\:x}{x}=0\)
3. The derivative of a function f at a holds as: \({f}'(a)=\lim\limits_{x \to a}\frac{f(a+h)-f(a)}{h}\)
4. The derivative of a function f at a given point x holds as: \({f}'(x)=\frac{\partial f(x)}{\partial x}=\lim\limits_{x \to a}\frac{f(x+h)-f(x)}{h}\)
5. For the functions u and v, the following holds true:
   • (i) \((u\pm v)’=u’\pm v’\)
   • (ii) \((uv)’=u’v+uv’\)
   • (iii) \(\left ( \frac{u}{v} \right )’=\frac{u’v-uv’}{v^2}\)
6. Standard Derivatives
   • (i) \(\frac{\partial}{\partial x}(x^n)=nx^{n-1}\)
   • (ii) \(\frac{\partial}{\partial x}(sin\:x)=cos\:x\)
   • (iii) \(\frac{\partial}{\partial x}(cos\:x)=-sin\:x\)

Class 11 Maths Formulas: Statistics

You will find the essential maths formulas for Class 11 of Statistics given below:

1. Mean Deviation for the ungrouped data:
   • (i) \(M.D.(\bar x)=\frac{\sum \left | x_i-\bar x \right |}{n}\)
   • (ii) \(M.D.(M)=\frac{\sum \left | x_i-M \right |}{n}\)
2. Mean Deviation for the grouped data:
   • (i) \(M.D.(\bar x)=\frac{\sum f_i|x_i-\bar x|}{N}\)
   • (ii) \(M.D.(M)=\frac{\sum f_i|x_i-M|}{N}\)
3. Variance and Standard Deviation for the ungrouped data:
   • (i) \(\sigma ^2=\frac{1}{N}\sum (x_i-\bar x)^2\)
   • (ii) \(\sigma=\sqrt{\frac{1}{N}\sum (x_i-\bar x)^2}\)
4. Variance and Standard Deviation of a frequency distribution (discrete):
   • (i) \(\sigma ^2=\frac{1}{N}\sum f_i(x_i-\bar x)^2\)
   • (ii) \(\sigma=\sqrt{\frac{1}{N}\sum f_i(x_i-\bar x)^2}\)
5. Variance and Standard Deviation of a frequency distribution (continuous):
   • (i) \(\sigma ^2=\frac{1}{N}\sum f_i(x_i-\bar x)^2\)
   • (ii) \(\sigma=\frac{1}{N}\sqrt{N\sum f_ix_i^2-(\sum f_ix_i)^2}\)
6. Coefficient of variation (C.V.) = \(\frac{\sigma}{\bar x}\times 100\) ; where \(\bar x\neq 0\)

FAQs on Maths Formulas for Class 11

Here are some important frequently asked questions about the Class 11 Maths formulas answered by our experts.

Q.1: Are Class 11 & 12 math formulas and definitions enough to score good marks in the NATA?
Ans: Though many students might tell you the Maths section of NATA is easy to score, but underestimating it will be completely wrong. Apart from knowing Class 11 and 12 maths formulas, you should know all the properties and concepts. You should solve plenty of maths mock questions if you want to score good marks in NATA.

Q.2: How will these Maths formulae help me?
Ans: When you practice your Maths questions, there is a chance that you might get stuck in some questions. At this time, these Maths formulas and properties will help you go through a quick revision. Even if you understand what is asked of you in a problem and have figured out the solution, it will be impossible to arrive at the right solution, if you cannot recall the correct formula. This is why learning the formula becomes absolutely necessary from the preparation point of view to help you score better in your Maths exam.

Q.3: Where can I get formula sheet of Maths Class 11 for?
Ans: You can get 11th Maths formulas pdf download at Embibe.

Q.4: Which are the important topics for which I will have to memorize the formulae?
Ans: Below are the important chapters for which memorizing the formulae will find applications in the exams:

• Trigonometric Functions
• Relations and Functions
• Principles of Mathematical Induction
• Complex Numbers and Quadratic Equations
• Binomial Theorem
• Permutations and Combinations
• Introduction to 3D Geometry
• Straight Lines
• Mathematical Reasoning
• Limits and Derivatives
• Statistics
• Probability.

Q.5: How will these Class 11 Maths Formula help me get good scores in my Class 11 final exam?
Ans: Practicing the Class 11 Maths Formulae will give a strong foundation in mathematics. The formulae in the fingertip will also help students solve all the problems quickly and correctly. We have provided the formula for each topic in Class 11 Maths in the article. Students can practice the same.

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CHECK THE DETAILED CBSE SYLLABUS FOR CLASS 11