Maths Formula for Class 11 with Examples

#Formula
TL;DR
Every maths formula for class 11 gathered in one place, covering sequences, trigonometry, the binomial theorem, permutations, complex numbers and conics.
BT
Bhanzu TeamLast updated on November 7, 20266 min read

Key Points

  • The maths formula for class 11 set is the largest of any school year, spanning sequences, trigonometry, counting, complex numbers and conic sections.

  • Trigonometric identities make up the biggest single group, and most of them derive from the compound-angle formulas.

  • Permutations count arrangements where order matters, while combinations count selections where it does not, and dividing out the orderings converts one into the other.

  • The binomial theorem generalises the class 8 identities to any positive integer power.

  • Class 11 formulas are the direct prerequisites for class 12 calculus, so gaps here surface immediately next year.

What Formulas Does Class 11 Maths Cover?

The maths formula for class 11 list is where school mathematics broadens sharply. Six groups account for nearly all of it: sequences and series, trigonometry, permutations and combinations, the binomial theorem, complex numbers, and conic sections.

The volume is large, but the structure is not. Most groups rest on two or three results from which the rest follow.

Sequences and Series

Quantity

Arithmetic

Geometric

nnth term

a+(n−1)da + (n-1)d

arn−1ar^{n-1}

Sum of nn terms

n2[2a+(n−1)d]\frac{n}{2}[2a+(n-1)d]

a(rn−1)r−1\frac{a(r^n-1)}{r-1}, r≠1r \neq 1

Infinite sum

does not converge

a1−r\frac{a}{1-r} for ∣r∣<1\lvert r \rvert < 1

The arithmetic sequence and geometric sequence pages cover each in full, and sum of arithmetic sequence handles the summation.

Trigonometric Identities

Group

Formula

Pythagorean

sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1

Compound angle

sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B

Compound angle

cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B

Double angle

sin⁡2θ=2sin⁡θcos⁡θ\sin 2\theta = 2\sin\theta\cos\theta

Double angle

cos⁡2θ=cos⁡2θ−sin⁡2θ\cos 2\theta = \cos^2\theta - \sin^2\theta

Half angle

sin⁡2θ2=1−cos⁡θ2\sin^2\frac{\theta}{2} = \frac{1-\cos\theta}{2}

Setting B=AB = A in the compound-angle formulas produces the double-angle ones directly, which is why the compound pair is worth learning first. The double angle and half angle pages carry the detail.

Permutations, Combinations and the Binomial Theorem

Quantity

Formula

Permutations

nPr=n!(n−r)!^nP_r = \frac{n!}{(n-r)!}

Combinations

nCr=n!r!(n−r)!^nC_r = \frac{n!}{r!(n-r)!}

Relationship

nPr=nCr×r factorial^nP_r = {}^nC_r \times r \text{ factorial}

Binomial theorem

(a+b)n=∑r=0nnCran−rbr(a+b)^n = \sum_{r=0}^{n} {}^nC_r a^{n-r}b^r

General term

Tr+1=nCran−rbrT_{r+1} = {}^nC_r a^{n-r} b^r

The nCr, nPr and binomial expansion pages cover these individually.

Complex Numbers and Conics

Topic

Formula

Modulus

∣z∣=x2+y2\lvert z \rvert = \sqrt{x^2+y^2}

Polar form

z=r(cos⁡θ+isin⁡θ)z = r(\cos\theta + i\sin\theta)

Power of a complex number

zn=rn(cos⁡nθ+isin⁡nθ)z^n = r^n(\cos n\theta + i \sin n\theta)

Circle

(x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

Parabola

y2=4axy^2 = 4ax

Ellipse

x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

The power rule is the de moivre formula, which also generates the multiple-angle identities.

Example 1

Find the 12th term of an arithmetic progression with first term 5 and common difference 3.

a12=5+(12−1)(3)=5+33=38a_{12} = 5 + (12-1)(3) = 5 + 33 = 38

Final answer: 38

Example 2

How many ways can 3 students be chosen from 8 for a committee, using permutations?

Permutations give 8P3=336^8P_3 = 336, from 8×7×68 \times 7 \times 6.

But a committee has no order: choosing Amir, Bina and Chen is the same committee however they are listed. The permutation count has counted each committee 66 times over, once per ordering of three names.

8C3=3366=56^8C_3 = \frac{336}{6} = 56

Final answer: 56. Ask whether order matters before choosing between PP and CC.

Example 3

Find the coefficient of x3x^3 in (1+x)7(1+x)^7.

The general term gives 7C3=7×6×53×2×1=35^7C_3 = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35.

Final answer: 35

Example 4

Find the modulus of z=3+4iz = 3 + 4i and write it in polar form.

∣z∣=9+16=5,θ=arctan⁡43≈53.13∘\lvert z \rvert = \sqrt{9+16} = 5, \qquad \theta = \arctan\frac{4}{3} \approx 53.13^\circ

Final answer: ∣z∣=5\lvert z \rvert = 5, so z=5(cos⁡53.13∘+isin⁡53.13∘)z = 5(\cos 53.13^\circ + i\sin 53.13^\circ)

Example 5

Find sin⁡75∘\sin 75^\circ exactly, using a compound-angle formula.

Write 75∘75^\circ as 45∘+30∘45^\circ + 30^\circ:

sin⁡75∘=sin⁡45cos⁡30+cos⁡45sin⁡30=22⋅32+22⋅12=6+24\sin 75^\circ = \sin 45 \cos 30 + \cos 45 \sin 30 = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2}\cdot\frac{1}{2} = \frac{\sqrt{6}+\sqrt{2}}{4}

Final answer: 6+24\frac{\sqrt{6}+\sqrt{2}}{4}

Where Class 11 Students Trip Up

Mistake 1: Using permutations where combinations are wanted

Where it slips in: Both count selections from a group, and the formulas look similar.

Don't do this: 8P3^8P_3 for a committee of 3 from 8.

The correct way: Use nCr^nC_r when order does not matter. The two differ by rr factorial, so dividing a permutation answer by that gives the combination.

Students who ask whether rearranging the chosen items gives a different outcome settle this in one step. A committee does not change when its members are listed differently; a podium of first, second and third does.

Mistake 2: Memorising every trig identity separately

Where it slips in: The list is long, and each identity looks self-contained.

Don't do this: Learn the double and half angle formulas independently of the compound-angle ones.

The correct way: Learn the two compound-angle formulas and derive the rest. Setting B=AB = A gives the double-angle pair immediately.

Mistake 3: Using the geometric sum formula when r=1r = 1

Where it slips in: The formula is applied mechanically without checking the ratio.

Don't do this: a(rn−1)r−1\frac{a(r^n-1)}{r-1} with r=1r = 1, which divides by zero.

The correct way: When r=1r = 1 every term is aa, so the sum is simply nana. The formula carries the condition r≠1r \neq 1 for exactly this reason.

The Short Version

  • The maths formula for class 11 set covers sequences, trigonometry, counting, the binomial theorem, complex numbers and conics.

  • The two compound-angle formulas generate most of the trigonometric list.

  • Permutations and combinations differ by a factor of rr factorial, and the deciding question is whether order matters.

  • The geometric sum formula requires r≠1r \neq 1, since the ratio appears in its denominator.

  • To work through the class 11 syllabus with a teacher, explore a high school math tutor or math tuition.

Practice These Three Before Moving On

Find the sum of the first 20 terms of an arithmetic progression with a=4a=4 and d=5d=5. Then compute 10C4^{10}C_4, and find cos⁡15∘\cos 15^\circ using a compound-angle formula.

Want a live Bhanzu trainer to walk through the class 11 formulas? Book a free demo class.

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Frequently Asked Questions

What is the full maths formula for class 11 list?
Sequences and series, trigonometric identities, permutations and combinations, the binomial theorem, complex numbers, and the conic sections.
Which maths formula for class 11 group is largest?
Trigonometry, though most of its identities derive from the two compound-angle formulas, so the learning load is smaller than the list suggests.
What is the difference between nPr and nCr?
Permutations count arrangements where order matters; combinations count selections where it does not. They differ by a factor of rr factorial.
How do class 11 formulas connect to class 12?
Directly. Trigonometric identities, sequences and complex numbers are all assumed by class 12 calculus, so gaps show up immediately.
✍️ Written By
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Bhanzu Team
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Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.
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