In short: Class 11 Maths has roughly 180 formulas across 16 chapters - from Sets and Relations to Probability. This complete formula list covers every chapter with clear expressions, organised in tables you can scan quickly during revision. Whether you are preparing for school exams, JEE, or building foundations for Class 12, this is your one-stop reference.
Why Class 11 Maths Formulas Matter More Than You Think
Class 11 Maths is not just another year of school. It introduces the building blocks for Class 12 Calculus, Coordinate Geometry, and Probability - topics that carry the most marks in board exams and competitive tests.
The jump from Class 10 to Class 11 Maths is significant. You go from solving equations to proving identities, from basic geometry to conic sections, from simple probability to permutations and combinations. Each chapter brings new formulas, and they stack on top of each other.
This formula sheet follows the CBSE 2026-27 syllabus order. Bookmark it, print it, or save it on your phone for quick access.
Chapter 1 - Sets
| Formula | Expression |
|---|---|
| Union | A U B = {x : x in A or x in B} |
| Intersection | A ∩ B = {x : x in A and x in B} |
| Complement | A' = U - A |
| Difference | A - B = {x : x in A and x not in B} |
| De Morgan's Law 1 | (A U B)' = A' ∩ B' |
| De Morgan's Law 2 | (A ∩ B)' = A' U B' |
| Cardinal number | n(A U B) = n(A) + n(B) - n(A ∩ B) |
| Three sets | n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C) |
Chapter 2 - Relations and Functions
| Formula | Expression |
|---|---|
| Cartesian product | A x B = {(a, b) : a in A, b in B} |
| Number of relations | From A to B: 2^(m x n), where m = n(A), n = n(B) |
| Domain | Set of first elements in ordered pairs |
| Range | Set of second elements in ordered pairs |
| Identity function | f(x) = x |
| Constant function | f(x) = c for all x |
| Signum function | f(x) = 1 if x > 0, 0 if x = 0, -1 if x < 0 |
Chapter 3 - Trigonometric Functions
| Formula | Expression |
|---|---|
| sin^2(x) + cos^2(x) | = 1 |
| 1 + tan^2(x) | = sec^2(x) |
| 1 + cot^2(x) | = cosec^2(x) |
| sin(A + B) | = sinA cosB + cosA sinB |
| sin(A - B) | = sinA cosB - cosA sinB |
| cos(A + B) | = cosA cosB - sinA sinB |
| cos(A - B) | = cosA cosB + sinA sinB |
| tan(A + B) | = (tanA + tanB) / (1 - tanA tanB) |
| tan(A - B) | = (tanA - tanB) / (1 + tanA tanB) |
| sin 2A | = 2 sinA cosA |
| cos 2A | = cos^2 A - sin^2 A = 2cos^2 A - 1 = 1 - 2sin^2 A |
| tan 2A | = 2 tanA / (1 - tan^2 A) |
| sin 3A | = 3 sinA - 4 sin^3 A |
| cos 3A | = 4 cos^3 A - 3 cosA |
Product-to-sum formulas:
| Formula | Expression |
|---|---|
| 2 sinA cosB | = sin(A + B) + sin(A - B) |
| 2 cosA sinB | = sin(A + B) - sin(A - B) |
| 2 cosA cosB | = cos(A + B) + cos(A - B) |
| 2 sinA sinB | = cos(A - B) - cos(A + B) |
Sum-to-product formulas:
| Formula | Expression |
|---|---|
| sinC + sinD | = 2 sin((C+D)/2) cos((C-D)/2) |
| sinC - sinD | = 2 cos((C+D)/2) sin((C-D)/2) |
| cosC + cosD | = 2 cos((C+D)/2) cos((C-D)/2) |
| cosC - cosD | = -2 sin((C+D)/2) sin((C-D)/2) |
Chapter 4 - Complex Numbers
| Formula | Expression |
|---|---|
| Definition | i = sqrt(-1), i^2 = -1 |
| General form | z = a + bi |
| Modulus | |
| Conjugate | z-bar = a - bi |
| z x z-bar | = |
| Argument | theta = tan^-1(b/a) |
| Polar form | z = r(cos theta + i sin theta) |
| i^1 = i, i^2 = -1 | i^3 = -i, i^4 = 1 (cycle of 4) |
| Sum of conjugates | z + z-bar = 2 Re(z) |
| Difference of conjugates | z - z-bar = 2i Im(z) |
Chapter 5 - Linear Inequalities
| Formula | Expression |
|---|---|
| If a > b, then a + c > b + c | Adding same number preserves inequality |
| If a > b and c > 0, then ac > bc | Multiplying by positive preserves inequality |
| If a > b and c < 0, then ac < bc | Multiplying by negative reverses inequality |
| Solution of ax + b > 0 | x > -b/a (if a > 0) or x < -b/a (if a < 0) |
Chapter 6 - Permutations and Combinations
| Formula | Expression |
|---|---|
| Factorial | n! = n x (n-1) x (n-2) x ... x 1, and 0! = 1 |
| Permutation | nPr = n! / (n-r)! |
| Combination | nCr = n! / (r! (n-r)!) |
| nCr = nC(n-r) | Symmetry property |
| nC0 = nCn = 1 | - |
| nC1 = n | - |
| Circular permutation | (n-1)! |
| Permutation with repetition | n^r |
| Permutation with identical objects | n! / (p! q! r!...) where p, q, r are counts of identical objects |
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Chapter 7 - Binomial Theorem
| Formula | Expression |
|---|---|
| Binomial expansion | (a + b)^n = Sum from r=0 to n of nCr a^(n-r) b^r |
| General term | T(r+1) = nCr a^(n-r) b^r |
| Middle term (n even) | T(n/2 + 1) |
| Middle terms (n odd) | T((n+1)/2) and T((n+3)/2) |
| (1 + x)^n | = nC0 + nC1 x + nC2 x^2 + ... + nCn x^n |
| Sum of coefficients | Put x = 1: 2^n |
| Sum of even coefficients | 2^(n-1) |
| Sum of odd coefficients | 2^(n-1) |
Chapter 8 - Sequences and Series
Arithmetic Progression (AP):
| Formula | Expression |
|---|---|
| nth term | a(n) = a + (n-1)d |
| Sum of n terms | S(n) = n/2 [2a + (n-1)d] = n/2 [a + l] |
| Common difference | d = a(n) - a(n-1) |
| Arithmetic mean | AM = (a + b) / 2 |
Geometric Progression (GP):
| Formula | Expression |
|---|---|
| nth term | a(n) = a r^(n-1) |
| Sum of n terms | S(n) = a(r^n - 1) / (r - 1) if r > 1 |
| Sum of n terms | S(n) = a(1 - r^n) / (1 - r) if r < 1 |
| Sum to infinity | S = a / (1 - r) if |
| Geometric mean | GM = sqrt(ab) |
| Relation AM, GM | AM >= GM (equality when a = b) |
Special sums:
| Formula | Expression |
|---|---|
| Sum of first n natural numbers | n(n+1)/2 |
| Sum of squares | n(n+1)(2n+1)/6 |
| Sum of cubes | [n(n+1)/2]^2 |
Chapter 9 - Straight Lines
| Formula | Expression |
|---|---|
| Distance formula | d = sqrt((x2-x1)^2 + (y2-y1)^2) |
| Section formula (internal) | ((m x2 + n x1)/(m+n), (m y2 + n y1)/(m+n)) |
| Mid-point | ((x1+x2)/2, (y1+y2)/2) |
| Slope | m = (y2-y1)/(x2-x1) = tan(theta) |
| Slope-intercept form | y = mx + c |
| Point-slope form | y - y1 = m(x - x1) |
| Two-point form | (y-y1)/(y2-y1) = (x-x1)/(x2-x1) |
| Intercept form | x/a + y/b = 1 |
| Normal form | x cos(alpha) + y sin(alpha) = p |
| General form | ax + by + c = 0 |
| Distance from point to line | d = |
| Angle between two lines | tan(theta) = |
| Parallel lines | m1 = m2 |
| Perpendicular lines | m1 x m2 = -1 |
Chapter 10 - Conic Sections
Circle:
| Formula | Expression |
|---|---|
| Standard form | (x-h)^2 + (y-k)^2 = r^2, centre (h,k), radius r |
| General form | x^2 + y^2 + 2gx + 2fy + c = 0, centre (-g,-f), r = sqrt(g^2+f^2-c) |
Parabola:
| Formula | Expression |
|---|---|
| y^2 = 4ax | Focus (a,0), Directrix x = -a, Latus rectum = 4a |
| x^2 = 4ay | Focus (0,a), Directrix y = -a, Latus rectum = 4a |
Ellipse:
| Formula | Expression |
|---|---|
| Standard form | x^2/a^2 + y^2/b^2 = 1 (a > b) |
| Eccentricity | e = sqrt(1 - b^2/a^2), where 0 < e < 1 |
| Foci | (+-ae, 0) |
| Latus rectum | 2b^2/a |
Hyperbola:
| Formula | Expression |
|---|---|
| Standard form | x^2/a^2 - y^2/b^2 = 1 |
| Eccentricity | e = sqrt(1 + b^2/a^2), where e > 1 |
| Foci | (+-ae, 0) |
| Latus rectum | 2b^2/a |
Chapter 11 - Introduction to Three-Dimensional Geometry
| Formula | Expression |
|---|---|
| Distance formula | d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2) |
| Section formula | ((m x2 + n x1)/(m+n), (m y2 + n y1)/(m+n), (m z2 + n z1)/(m+n)) |
| Mid-point | ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2) |
Chapter 12 - Limits and Derivatives
| Formula | Expression |
|---|---|
| lim (x->a) [x^n - a^n] / (x - a) | = n a^(n-1) |
| lim (x->0) sin(x)/x | = 1 |
| lim (x->0) tan(x)/x | = 1 |
| lim (x->0) (1 - cos x)/x | = 0 |
| lim (x->0) (e^x - 1)/x | = 1 |
| lim (x->0) log(1+x)/x | = 1 |
| d/dx (x^n) | = n x^(n-1) |
| d/dx (sin x) | = cos x |
| d/dx (cos x) | = -sin x |
| d/dx (tan x) | = sec^2 x |
| d/dx (e^x) | = e^x |
| d/dx (ln x) | = 1/x |
| Product rule | d/dx (uv) = u(dv/dx) + v(du/dx) |
| Quotient rule | d/dx (u/v) = (v du/dx - u dv/dx) / v^2 |
Chapter 13 - Statistics
| Formula | Expression |
|---|---|
| Mean (direct) | x-bar = Sum(x_i) / n |
| Mean (grouped) | x-bar = Sum(f_i x_i) / Sum(f_i) |
| Variance | sigma^2 = Sum(f_i (x_i - x-bar)^2) / N |
| Standard deviation | sigma = sqrt(variance) |
| Shortcut for variance | sigma^2 = (Sum f_i x_i^2)/N - (x-bar)^2 |
| Coefficient of variation | CV = (sigma / x-bar) x 100 |
Chapter 14 - Probability
| Formula | Expression |
|---|---|
| Probability | P(E) = n(E) / n(S) |
| Complement | P(E') = 1 - P(E) |
| Addition rule | P(A U B) = P(A) + P(B) - P(A ∩ B) |
| Mutually exclusive | P(A U B) = P(A) + P(B) (when A ∩ B = empty) |
| P(A ∩ B') | = P(A) - P(A ∩ B) |
| Exhaustive events | P(S) = 1 |
How to Memorise 180+ Maths Formulas
1. Cluster by theme. Trigonometry alone has 30+ formulas, but they all derive from sin^2 + cos^2 = 1 and the compound angle formulas. Learn the 4-5 root formulas and derive the rest.
2. Practise, practise, practise. Every formula you use in a problem gets stored in long-term memory. Solve 3-5 problems per formula. By the third problem, you will write the formula without thinking.
3. Create a one-page cheat sheet per chapter. Writing formulas by hand is one of the strongest memory techniques. Condense each chapter to a single page and revise from your own handwritten sheet.
4. Test yourself with blanks. Print this formula list, white out the expressions, and fill them in from memory. Repeat every 3 days using spaced repetition.
5. Use Padhaao for targeted practice. Tell the AI tutor which chapter you are working on and it generates problems that test exactly the formulas you need. If you apply a formula incorrectly, it explains the error immediately.
Common Mistakes to Avoid
- nPr vs nCr confusion. Use permutation when order matters (arranging), combination when it does not (selecting). If the question says "how many ways to choose," it is nCr. If it says "how many arrangements," it is nPr.
- Sign errors in trigonometry. cos(A - B) has a plus sign between the terms, cos(A + B) has a minus. Getting this backwards ruins your entire solution.
- Forgetting the condition for GP sum to infinity. S = a/(1-r) only works when |r| < 1. If |r| >= 1, the series diverges.
- Wrong section formula. Internal division uses +, external division uses -. Draw a diagram before applying the formula.
- Mixing up parabola orientations. y^2 = 4ax opens rightward. x^2 = 4ay opens upward. Swapping them puts the focus in the wrong place.
Exam-Day Quick Revision Plan
Minutes 1-10: Trigonometric formulas - compound angles, double angles, sum-to-product. These appear in almost every paper.
Minutes 11-20: Sequences (AP/GP formulas), Permutations/Combinations, Binomial Theorem general term.
Minutes 21-30: Coordinate geometry - straight line forms, conic section standard equations and eccentricity formulas.
Minutes 31-35: Limits standard results and derivative formulas. Quick scan of probability addition rule.
FAQ
How many formulas are in Class 11 Maths?
About 180 formulas across 16 chapters. Trigonometry and Coordinate Geometry contribute the most. However, many formulas are variations - if you know the compound angle formula, you can derive double angle, triple angle, and half angle formulas.
Which chapter has the hardest formulas?
Conic Sections and Trigonometric Functions tend to have the most formulas that students struggle with. Conic sections require memorising standard forms for four curves, and trigonometry has dozens of identities.
Should I memorise all standard limits?
Yes. The six standard limits (sin x/x, tan x/x, etc.) are used directly in exam problems. They take 2 minutes to memorise and save you derivation time during the exam.
Are Class 11 Maths formulas useful for JEE?
Absolutely. JEE Main and Advanced test Class 11 and 12 equally. Trigonometry, Permutations and Combinations, and Conic Sections from Class 11 are heavily tested in JEE.
How do I remember the difference between AP and GP formulas?
AP formulas use addition (common difference d, nth term = a + (n-1)d). GP formulas use multiplication (common ratio r, nth term = a x r^(n-1)). The operation tells you which series you are dealing with.
Can I use this formula sheet for ISC/ICSE too?
Most formulas overlap since the topics are the same. ISC may have slight syllabus differences, but the core formulas for trigonometry, coordinate geometry, calculus introduction, and probability are identical.
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