Class 11 Maths Formula Sheet (CBSE 2026-27)
How to memorise a formula sheet: do not read it top to bottom. Pick one chapter, cover the right-hand column with a sheet of paper, and write each formula from the name alone. Mark the ones you miss and revise only those the next day. Three short rounds beat one long reread.
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\n Sets
\n Sets and Functions · 23 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Subsets | 2ⁿ subsets, 2ⁿ − 1 proper subsets | n is the number of elements. |
| Union count | n(A ∪ B) = n(A) + n(B) − n(A ∩ B) | Subtract the overlap once. |
| Three sets | n(A ∪ B ∪ C) = Σn(A) − Σn(A ∩ B) + n(A ∩ B ∩ C) | Inclusion–exclusion. |
| Difference | n(A − B) = n(A) − n(A ∩ B) | Elements in A but not in B. |
| De Morgan | (A ∪ B)′ = A′ ∩ B′; (A ∩ B)′ = A′ ∪ B′ | Complement flips the operation. |
Watch out: Writing {∅} for the empty set instead of ∅.
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\n Relations and Functions
\n Sets and Functions · 23 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Cartesian product size | n(A × B) = n(A) × n(B) | Ordered pairs, so (a, b) ≠ (b, a). |
| Number of relations | 2^(mn) relations from A to B | Every subset of A × B is a relation. |
| Domain of a quotient | Denominator ≠ 0 | Exclude those x values. |
| Domain of a square root | Radicand ≥ 0 | For even roots. |
| Modulus | |x| = x if x ≥ 0; −x if x < 0 | Range is [0, ∞). |
Watch out: Calling any relation a function — a single input with two outputs is not a function.
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\n Trigonometric Functions
\n Sets and Functions · 23 marks\n\n \n
\n
\n | Formula / rule | Statement | Notes |
|---|---|---|
| Sum and difference | sin(A ± B) = sinA cosB ± cosA sinB; cos(A ± B) = cosA cosB ∓ sinA sinB | Watch the sign flip in cosine. |
| Double angle | sin2A = 2sinA cosA; cos2A = cos²A − sin²A = 1 − 2sin²A = 2cos²A − 1 | Three useful forms of cos2A. |
| Triple angle | sin3A = 3sinA − 4sin³A; cos3A = 4cos³A − 3cosA | Occasionally needed in proofs. |
| Sum to product | sinC + sinD = 2 sin((C+D)/2) cos((C−D)/2) | And the corresponding cosine and difference forms. |
| General solution | sinθ = sinα ⇒ θ = nπ + (−1)ⁿα | n ∈ ℤ for all three forms. |
| Arc and sector | arc = rθ; area = ½r²θ | θ must be in radians. |
Watch out: Using degrees in formulas that require radians.
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\n Complex Numbers and Quadratic Equations
\n Algebra · 25 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Powers of i | i² = −1, i³ = −i, i⁴ = 1 | Reduce any power modulo 4. |
| Modulus | |z| = √(a² + b²) | Always non-negative. |
| Conjugate | z̄ = a − ib; z·z̄ = a² + b² | Used to rationalise denominators. |
| Division | (a + ib)/(c + id) = ((a + ib)(c − id))/(c² + d²) | Multiply by the conjugate of the denominator. |
| Quadratic roots | x = (−b ± √(b² − 4ac))/2a | If b² − 4ac < 0, write √(negative) as i√(positive). |
Watch out: Writing √(−4) = −2 instead of 2i.
\nRead the full Complex Numbers and Quadratic Equations notes →
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\n Linear Inequalities
\n Algebra · 25 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Interval notation | (a, b), [a, b], (a, ∞), (−∞, b] | Round bracket excludes the endpoint. |
| Sign flip | −2x > 6 ⇒ x < −3 | Dividing by a negative reverses the sign. |
| Half-plane test | Substitute (0, 0) into the inequality | If true, shade the side containing the origin. |
Watch out: Forgetting to flip the inequality sign when dividing by a negative.
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\n Permutations and Combinations
\n Algebra · 25 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Factorial | n! = n(n − 1)(n − 2)…1, with 0! = 1 | Cancel factorials before multiplying. |
| Permutation | nPr = n!/(n − r)! | Order matters. |
| Combination | nCr = n!/(r!(n − r)!) | Order does not matter. |
| Symmetry | nCr = nC(n − r) | Choosing r is the same as rejecting n − r. |
| Pascal-type identity | nCr + nC(r − 1) = (n+1)Cr | Used when simplifying sums. |
| Circular arrangement | (n − 1)! | Divide by 2 if clockwise and anticlockwise are identical. |
Watch out: Using permutations when the question asks for a committee or a selection.
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\n Binomial Theorem
\n Algebra · 25 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Binomial expansion | (a + b)ⁿ = Σ(r=0 to n) nCr a^(n−r) b^r | Coefficients are nC0, nC1, …, nCn. |
| General term | T(r+1) = nCr a^(n−r) b^r | Set the exponent equal to the required power. |
| Middle term | n even ⇒ (n/2 + 1)th term | n odd ⇒ two middle terms. |
| Coefficient sum | nC0 + nC1 + … + nCn = 2ⁿ | Put a = b = 1 in the expansion. |
Watch out: Confusing the term number with the value of r — T(r+1) is the (r + 1)th term.
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\n Sequences and Series
\n Algebra · 25 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| AP nth term and sum | aₙ = a + (n − 1)d; Sₙ = n/2[2a + (n − 1)d] | Same as Class 10. |
| GP nth term | aₙ = ar^(n−1) | r is the common ratio. |
| GP sum | Sₙ = a(1 − rⁿ)/(1 − r), r ≠ 1 | Sum to infinity a/(1 − r) when |r| < 1. |
| Means | AM = (a + b)/2; GM = √(ab) | AM ≥ GM for positive a, b. |
| Standard sums | Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]² | Useful for series of the form n², n³. |
Watch out: Using the AP formula for a GP or the reverse.
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\n Straight Lines
\n Coordinate Geometry · 12 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Slope | m = (y₂ − y₁)/(x₂ − x₁) | Undefined for a vertical line. |
| Point-slope form | y − y₁ = m(x − x₁) | When a point and the slope are known. |
| Two-point form | y − y₁ = ((y₂ − y₁)/(x₂ − x₁))(x − x₁) | Directly from two points. |
| Slope-intercept | y = mx + c | c is the y-intercept. |
| Distance from a line | |ax₀ + by₀ + c|/√(a² + b²) | Straight-line distance, not horizontal distance. |
| Perpendicular condition | m₁m₂ = −1 | Parallel: m₁ = m₂. |
Watch out: Writing the slope as (x₂ − x₁)/(y₂ − y₁).
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\n Conic Sections
\n Coordinate Geometry · 12 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Circle | (x − h)² + (y − k)² = r² | Centre (h, k), radius r. |
| Parabola | y² = 4ax; focus (a, 0); directrix x = −a; latus rectum 4a | x² = 4ay opens upward instead. |
| Ellipse | x²/a² + y²/b² = 1, a > b; c² = a² − b²; e = c/a; latus rectum 2b²/a | Foci (±c, 0). |
| Hyperbola | x²/a² − y²/b² = 1; c² = a² + b²; e = c/a; latus rectum 2b²/a | e > 1; foci (±c, 0). |
| Eccentricity bounds | Ellipse: 0 < e < 1; hyperbola: e > 1; parabola: e = 1 | A quick check on your answer. |
Watch out: Using c² = a² − b² for a hyperbola instead of c² = a² + b².
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\n Introduction to Three Dimensional Geometry
\n Coordinate Geometry · 12 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Distance | √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²) | Three squared differences. |
| Section | ((m₁x₂ + m₂x₁)/(m₁ + m₂), same for y and z) | Ratio m₁ : m₂. |
| Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2) | Special case of 1 : 1. |
| Centroid | ((x₁ + x₂ + x₃)/3, same for y and z) | Average of the vertices. |
Watch out: Forgetting the z-term in the distance formula.
\nRead the full Introduction to Three Dimensional Geometry notes →
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\n Limits and Derivatives
\n Calculus · 8 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Standard limit | lim(x→a) (xⁿ − aⁿ)/(x − a) = n·a^(n−1) | Very common in exams. |
| Trigonometric limits | lim(x→0) sin x / x = 1; lim(x→0) (1 − cos x)/x² = ½ | Angles in radians. |
| Derivative definition | f′(x) = lim(h→0) (f(x + h) − f(x))/h | First principles. |
| Derivatives | d/dx(xⁿ) = nx^(n−1); d/dx(sin x) = cos x; d/dx(cos x) = −sin x; d/dx(tan x) = sec²x | Memorise the table. |
| Rules | Product: (uv)′ = u′v + uv′; Quotient: (u/v)′ = (u′v − uv′)/v² | Chain rule for composite functions. |
Watch out: Substituting x = a directly into an indeterminate form such as 0/0.
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\n Statistics
\n Statistics and Probability · 12 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Mean deviation | MD = (Σ|xᵢ − x̄|)/n | Or from the median. |
| Variance | σ² = (Σ(xᵢ − x̄)²)/n = (Σxᵢ²)/n − x̄² | The second form is easier for decimals. |
| Standard deviation | σ = √variance | Same units as the data. |
| Coefficient of variation | CV = (σ/x̄) × 100% | Used to compare consistency. |
| Grouped variance | σ² = (Σfᵢxᵢ²)/N − (Σfᵢxᵢ/N)² | N = Σfᵢ. |
Watch out: Forgetting to square deviations before averaging for variance.
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\n Probability
\n Statistics and Probability · 12 marks\n\n \n
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\n | Formula / rule | Statement | Notes |
|---|---|---|
| Probability | P(A) = n(A)/n(S) | S is the sample space. |
| Addition rule | P(A ∪ B) = P(A) + P(B) − P(A ∩ B) | For any two events. |
| Complement | P(A′) = 1 − P(A) | Useful for ‘at least one’. |
| Mutually exclusive | P(A ∩ B) = 0 | Then P(A ∪ B) = P(A) + P(B). |
| Independent | P(A ∩ B) = P(A)P(B) | Not the same as mutually exclusive. |
Watch out: Adding probabilities without subtracting the overlap.
\n \nFormula-sheet habits that save marks
- Write the formula before substituting numbers. Examiners give method marks for the correct formula even when the arithmetic slips.
- Keep units attached to every substituted value, and convert to a single unit before calculating.
- Check whether the question expects π = 22/7 or 3.14; the answer changes and so does the marking.
- For trigonometry, write the angle in every line. Dropping “θ” is the most common silent error.
- At the end, ask whether the answer is physically reasonable — a negative length or a probability above 1 is always wrong.
Last updated: 22 October 2026 · Author: Bazid Ahmed Laskar · Independent study material.