CBSE Class 12 Maths (2026) has 13 chapters in 6 units, and its 80-mark theory paper is dominated by one unit: Calculus alone carries 35 marks (Ch 5–9). This page compiles the key formulas of every chapter — from relations to Bayes' theorem — in chapter-wise tables, with memory tricks for the heaviest formula sets. Priority order by weightage: Calculus (35) → Vectors & 3D (14) → Algebra (10) → Probability (8) = R&F (8) → LPP (5).
- Chapter weightage 2026
- 1. Relations & Functions · 2. Inverse Trigonometry · 3. Matrices · 4. Determinants
- 5. Continuity & Differentiability · 6. Applications of Derivatives · 7. Integrals
- 8. Applications of Integrals · 9. Differential Equations
- 10. Vector Algebra · 11. Three-Dimensional Geometry · 12. LPP · 13. Probability
- Memory tricks for the heaviest formulas · FAQs
Where the 80 marks live
The 2026 blueprint makes prioritisation brutally simple — nearly half the paper is Calculus:
| Unit (chapters) | Marks |
|---|---|
| Calculus (Ch 5–9) | 35 |
| Vectors & 3D Geometry (Ch 10–11) | 14 |
| Algebra: Matrices & Determinants (Ch 3–4) | 10 |
| Relations & Functions (Ch 1–2) | 8 |
| Probability (Ch 13) | 8 |
| Linear Programming (Ch 12) | 5 |
Theory = 80 marks; internal assessment = 20. Any revision plan that doesn't give Ch 5–9 daily time is fighting the blueprint.
Ch 1 — Relations & Functions 8-mark unit
| Formula / condition | Used for |
|---|---|
| Reflexive: (a,a) ∈ R ∀ a | Testing equivalence relations — the unit's standard 2–3 marker |
| Symmetric: (a,b) ∈ R ⇒ (b,a) ∈ R | |
| Transitive: (a,b), (b,c) ∈ R ⇒ (a,c) ∈ R | |
| One-one: f(x1) = f(x2) ⇒ x1 = x2 | Injectivity test |
| Onto: range = codomain | Surjectivity test; bijective = one-one + onto = invertible |
Ch 2 — Inverse Trigonometric Functions 8-mark unit
| Formula | Used for |
|---|---|
| sin−1x + cos−1x = π/2 | Complementary pairs — the chapter's most-used identities |
| tan−1x + cot−1x = π/2; sec−1x + cosec−1x = π/2 | |
| sin−1(−x) = −sin−1x; tan−1(−x) = −tan−1x | Odd-symmetric inverses |
| cos−1(−x) = π − cos−1x | The exception — cos−1 shifts by π instead of flipping sign |
| Principal ranges: sin−1 [−π/2, π/2]; cos−1 [0, π]; tan−1 (−π/2, π/2) | Every answer must land in the principal range — where MCQ traps live |
Ch 3 — Matrices 10-mark unit
| Formula | Used for |
|---|---|
| (A′)′ = A; (A + B)′ = A′ + B′ | Transpose basics |
| (AB)′ = B′A′ | Reversal law — order flips! |
| Symmetric: A′ = A; Skew: A′ = −A | Classification questions |
| A = ½(A + A′) + ½(A − A′) | Express any square matrix as symmetric + skew-symmetric — a repeated 3-marker |
Ch 4 — Determinants 10-mark unit
| Formula | Used for |
|---|---|
| |AB| = |A||B|; |A′| = |A| | Determinant algebra |
| |kA| = kn|A| | Scalar multiple of an n × n matrix — classic MCQ trap |
| A(adj A) = |A| I | Adjoint's defining property |
| A−1 = adj A / |A| | Inverse — exists only if |A| ≠ 0 |
| |adj A| = |A|n−1 | Adjoint determinant — another MCQ favourite |
| Area of Δ = ½|x1(y2−y3) + x2(y3−y1) + x3(y1−y2)| | Area via determinants |
| AX = B ⇒ X = A−1B | Solving linear systems — the unit's standard 5-marker |
Ch 5 — Continuity & Differentiability 35-mark unit
| Formula | Used for |
|---|---|
| Continuity at a: lim(x→a) f(x) = f(a) | LHL = RHL = value — continuity checks |
| (uv)′ = u′v + uv′; (u/v)′ = (u′v − uv′)/v² | Product and quotient rules |
| dy/dx = (dy/du)(du/dx) | Chain rule — the engine of the whole unit |
| d/dx: xn → nxn−1; ex → ex; ln x → 1/x; ax → ax ln a | Standard derivatives |
| d/dx: sin → cos; cos → −sin; tan → sec² | Trig and inverse-trig derivatives |
| d/dx: sin−1x → 1/√(1−x²); tan−1x → 1/(1+x²) | |
| y = f(x)g(x): take ln both sides | Logarithmic differentiation |
| Parametric: dy/dx = (dy/dt)/(dx/dt) | Parametric derivatives |
Ch 6 — Applications of Derivatives 35-mark unit
| Formula / test | Used for |
|---|---|
| Rate: dy/dt = (dy/dx)(dx/dt) | Related-rates word problems |
| Increasing: f′(x) > 0; Decreasing: f′(x) < 0 | Monotonicity on intervals |
| First-derivative test at critical points (f′ = 0) | Locating maxima/minima by sign change |
| Second-derivative test: f″ < 0 → max; f″ > 0 → min | The faster test when f″ is easy |
Note: tangents/normals and approximations are not in the current rationalized syllabus — don't spend revision time there.
Ch 7 — Integrals 35-mark unit
| Formula | Used for |
|---|---|
| ∫xn dx = xn+1/(n+1) + C; ∫(1/x)dx = ln|x| + C | Power rule and its exception |
| ∫dx/(x² + a²) = (1/a) tan−1(x/a) + C | The "special forms" — recognising which one applies is the exam skill |
| ∫dx/√(a² − x²) = sin−1(x/a) + C | |
| ∫dx/(x² − a²) = (1/2a) ln|(x−a)/(x+a)| + C | |
| ∫√(a² − x²) dx = (x/2)√(a²−x²) + (a²/2) sin−1(x/a) + C | Standard root integrals (all three √ forms follow this pattern) |
| ∫u·v dx = u∫v dx − ∫(u′∫v dx) dx | Integration by parts — choose u by ILATE |
| ∫ex[f(x) + f′(x)] dx = ex f(x) + C | The ex shortcut — free marks when spotted |
| ∫0a f(x) dx = ∫0a f(a − x) dx | King property — solves most definite-integral 3-markers |
| ∫−aa f(x) dx = 0 if f is odd; = 2∫0a if even | Odd/even property |
Ch 8 — Applications of Integrals 35-mark unit
| Formula | Used for |
|---|---|
| Area = ∫ab y dx = ∫ab f(x) dx | Area under a curve (above x-axis) |
| Area between curves = ∫ab [f(x) − g(x)] dx | Upper curve minus lower curve — sketch first, always |
Ch 9 — Differential Equations 35-mark unit
| Formula / method | Used for |
|---|---|
| Order = highest derivative; degree = its power (when polynomial) | 1-mark identification questions |
| Variable separable: ∫f(y)dy = ∫g(x)dx | The first method to try |
| Homogeneous: put y = vx, dy/dx = v + x dv/dx | When RHS is a degree-zero homogeneous function |
| Linear: dy/dx + Py = Q | The 5-marker pattern: find IF, then y·IF = ∫Q·IF dx + C |
| IF = e∫P dx |
Ch 10 — Vector Algebra 14-mark unit
| Formula | Used for |
|---|---|
| |a| = √(x² + y² + z²); â = a/|a| | Magnitude and unit vector |
| a·b = |a||b| cosθ | Dot product; a·b = 0 ⇔ perpendicular |
| Projection of a on b = (a·b)/|b| | Projection numericals — repeated every year |
| |a × b| = |a||b| sinθ | Cross product; a × b = 0 ⇔ parallel |
| Area of parallelogram = |a × b|; triangle = ½|a × b| | Vector areas |
Ch 11 — Three-Dimensional Geometry 14-mark unit
| Formula | Used for |
|---|---|
| l² + m² + n² = 1 | Direction cosines of a line |
| Line: r = a + λb; (x−x1)/a = (y−y1)/b = (z−z1)/c | Vector and Cartesian forms |
| cosθ = |b1·b2| / (|b1||b2|) | Angle between two lines |
| Skew lines: d = |(b1 × b2)·(a2 − a1)| / |b1 × b2| | Shortest distance — the unit's flagship 5-marker |
| Parallel lines: d = |b × (a2 − a1)| / |b| | Distance between parallel lines |
Note: the plane is not in the current rationalized syllabus — 3D questions come from lines only.
Ch 12 — Linear Programming 5-mark unit
| Method | Used for |
|---|---|
| Corner point method: evaluate Z = ax + by at every vertex of the feasible region | Max/min of the objective function — the entire chapter in one procedure |
| Unbounded region: check whether ax + by > M (or < m) has points in common with the region | Deciding if a max/min actually exists |
Ch 13 — Probability 8-mark unit
| Formula | Used for |
|---|---|
| P(A|B) = P(A ∩ B) / P(B) | Conditional probability — the chapter's foundation |
| P(A ∩ B) = P(A) P(B|A) | Multiplication theorem |
| Independent: P(A ∩ B) = P(A) P(B) | Independence test |
| P(A) = Σ P(Ei) P(A|Ei) | Total probability theorem |
| P(Ei|A) = P(Ei)P(A|Ei) / Σ P(Ej)P(A|Ej) | Bayes' theorem — a near-guaranteed 5-marker every year |
| E(X) = Σ xi pi | Mean of a random variable |
Memory tricks for the heaviest formula sets
ILATE decides "u" in by-parts: Inverse trig → Logarithmic → Algebraic → Trigonometric → Exponential. Whichever comes first in ILATE becomes u; the rest is dv. This one mnemonic settles every by-parts choice in the paper.
The special-form triangle in integrals: see (x² + a²) → think tan−1; see √(a² − x²) → think sin−1; see (x² − a²) → think ln. Pattern recognition, not memory, is what the examiner is testing in Ch 7.
Inverse-trig pairs always sum to π/2: sin−1+cos−1, tan−1+cot−1, sec−1+cosec−1 — one fact, three formulas. And remember cos−1 is the odd one out for negatives: it shifts by π while the others just flip sign.
Determinant power pattern: for an n × n matrix, everything scales by determinant powers — |kA| = kn|A| and |adj A| = |A|n−1. Memorise the pattern "n and n−1," not two separate formulas.
Derivatives and integrals are mirrors: every entry in the Ch 5 derivative table is a Ch 7 integral read backwards. Revise them as one combined table and you halve the memorisation load of the 35-mark unit.
The complete handwritten Maths formula sheet — every chapter, one compact set
This page gives you the core formulas. Our Class 12 Maths Formula Sheet is the wall-chart version for the last 30 days:
- Full 2026-27 syllabus — all 13 chapters, compact and complete
- Colour-coded formula boxes with diagrams for fast visual recall
- Real handwritten notes by toppers — IITians, NITians and district toppers
- Instant PDF or printed book (COD available, all-India delivery)
- Available in English and Hindi medium
FAQs
How many formulas are there in Class 12 Maths?
Roughly 120–140 core formulas across the 13 chapters, with Integrals, Continuity & Differentiability and 3D Geometry being the most formula-dense.
Which unit has the highest weightage in Class 12 Maths 2026?
Calculus (Chapters 5–9) carries 35 of the 80 theory marks — nearly half the paper — followed by Vectors & 3D Geometry at 14 marks.
Which chapters should I revise first for the Maths board exam?
Follow the weightage: Calculus daily (35 marks), then Vectors & 3D (14), Matrices & Determinants (10), and Probability's Bayes' theorem — a near-guaranteed 5-marker.
What is the ILATE rule in integration?
It decides which function becomes u in integration by parts: Inverse trig, Logarithmic, Algebraic, Trigonometric, Exponential — whichever appears first in that order is u.
Is the plane included in 3D Geometry for 2026?
No. Under the current rationalized syllabus, 3D Geometry covers lines only — direction cosines, equations of lines, angle between lines and shortest distance.
Is there a Class 12 Maths formula sheet in Hindi?
Yes — the formulas are universal symbols, and the handwritten formula sheet linked above is available in both English and Hindi medium versions.
How do I remember all the integration formulas?
Learn them as patterns: the special-form triangle (tan−1, sin−1, ln forms), ILATE for by-parts, the ex[f + f′] shortcut, and the king property for definite integrals — five patterns cover most of Chapter 7.
Do I lose marks for missing +C in integration?
Yes — marking schemes deduct for a missing constant of integration in indefinite integrals. Write +C as a habit the moment you begin any indefinite integral.