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Class 11 and 12 Mathematics Formula Sheet
The mathematics results you are expected to recall rather than derive in the exam. Trigonometry and calculus carry the most marks per formula learned.
32 formulas across 6 sections.
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Trigonometry: standard values
| What | Formula | Symbols |
|---|---|---|
| sin | 0, ½, 1/√2, √3⁄2, 1 | at 0°, 30°, 45°, 60°, 90° |
| cos | 1, √3⁄2, 1/√2, ½, 0 | the sine row read backwards |
| tan | 0, 1/√3, 1, √3, ∞ | tan = sin / cos |
Trigonometric identities
| What | Formula | Symbols |
|---|---|---|
| Pythagorean | sin²θ + cos²θ = 1 | the identity everything else builds on |
| Secant form | 1 + tan²θ = sec²θ | divide the first by cos²θ |
| Cosecant form | 1 + cot²θ = cosec²θ | divide the first by sin²θ |
| Sum | sin(A+B) = sinA cosB + cosA sinB | cos(A+B) = cosA cosB − sinA sinB |
| Double angle | sin2A = 2 sinA cosA | cos2A = cos²A − sin²A = 1 − 2sin²A |
Algebra
| What | Formula | Symbols |
|---|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | discriminant D = b² − 4ac |
| Nature of roots | D > 0 real distinct, D = 0 real equal, D < 0 complex | always check D first |
| Sum and product of roots | α + β = −b/a, αβ = c/a | faster than solving |
| AP nth term | aₙ = a + (n − 1)d | d common difference |
| AP sum | Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l) | l last term |
| GP nth term | aₙ = arn−1 | r common ratio |
| GP sum | Sₙ = a(rⁿ − 1)/(r − 1) | for r ≠ 1 |
| Infinite GP | S∞ = a/(1 − r) | only when |r| < 1 |
| Binomial general term | Tr+1 = nCr an−r br | n + 1 terms in total |
Calculus: derivatives
| What | Formula | Symbols |
|---|---|---|
| Power rule | d/dx (xⁿ) = n xn−1 | the one you use most |
| Trigonometric | d/dx (sinx) = cosx, d/dx (cosx) = −sinx | note the minus sign |
| Exponential and log | d/dx (eˣ) = eˣ, d/dx (ln x) = 1/x | eˣ is its own derivative |
| Product rule | (uv)′ = u′v + uv′ | differentiate one at a time |
| Quotient rule | (u/v)′ = (u′v − uv′)/v² | numerator order matters |
| Chain rule | dy/dx = (dy/du)(du/dx) | for a function of a function |
Calculus: integrals
| What | Formula | Symbols |
|---|---|---|
| Power rule | ∫xⁿ dx = xn+1/(n+1) + c | for n ≠ −1 |
| Reciprocal | ∫(1/x) dx = ln|x| + c | the exception to the power rule |
| Trigonometric | ∫sinx dx = −cosx + c, ∫cosx dx = sinx + c | signs are the usual slip |
| Exponential | ∫eˣ dx = eˣ + c | unchanged again |
| Standard | ∫dx/(1 + x²) = tan⁻¹x + c | recognise the shape |
| By parts | ∫u dv = uv − ∫v du | choose u by ILATE |
Vectors and 3D
| What | Formula | Symbols |
|---|---|---|
| Dot product | a·b = |a||b| cosθ | zero when perpendicular |
| Cross product | |a × b| = |a||b| sinθ | zero when parallel |
| Distance formula | √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²) | in three dimensions |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Chapter by chapter
Every chapter on its own page.
Trigonometry
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Open 15 formulasSequences and Series
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Open 19 formulasMatrices and Determinants
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Open 16 formulasContinuity and Differentiability
This chapter supplies the rules used everywhere else in calculus. Learn the standard derivatives as a block, then the fo...
Open 15 formulasApplications of Derivatives
Derivatives stop being algebra here and start answering questions: how fast, how steep, and what is the best. Maxima and...
Open 19 formulasIntegrals and Their Applications
Integration is differentiation read backwards, and the marks come from recognising the shape of the integrand. The stand...
Open 13 formulasDifferential Equations
A short, highly patterned chapter. Identify the type, apply its method, and the marks follow. Variable separable and lin...
Open 20 formulasVectors and Three Dimensional Geometry
Vectors and 3D geometry are one chapter twice: every line and plane result is a vector identity written out. Learn the t...
Open 14 formulasProbability
Probability rewards reading the question carefully more than any other chapter. Conditional probability, Bayes' theorem ...
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