Class 12 Maths Formula Sheet 2026-27 — All 13 Chapters in One Page
Every formula from all 13 chapters, memory tricks that actually stick, and the exact question patterns CBSE repeats every year.
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Formulas Bhool Jaate Ho? Chill, Hum Hain Na 🎸
Exam se ek raat pehle formula yaad karne ki tension har back bencher jaanta hai. Isliye ye page bana hai — Class 12 Maths ke 13 chapters ke formulas, ek hi jagah, bina kisi bhaari-bharkam jargon ke. Scroll karo, jo chapter revise karna hai wahan jump karo, aur exam hall mein confidently likho.
Quick Jump — All Chapters
Chapter-Wise Formulas, Tricks & Exam Patterns
Relations and Functions — All Formulas
Remember 'RST' for equivalence relation — Reflexive, Symmetric, Transitive, all three needed together, missing even one disqualifies it.
Check whether a given relation is reflexive/symmetric/transitive, or check if a function is one-one and onto — 3-5 marks.
Inverse Trigonometric Functions — All Formulas
Always check the principal value range before writing your final answer — inverse trig functions have restricted ranges, and giving an answer outside that range is a very common mark deduction.
Simplify expressions or prove identities involving inverse trigonometric functions, or find the principal value — 2-3 marks.
Matrices — All Formulas
To check symmetric vs skew-symmetric quickly, just look at the diagonal — a skew-symmetric matrix must have ALL zeroes on its main diagonal, an instant giveaway.
Express a square matrix as the sum of a symmetric and a skew-symmetric matrix, or perform matrix operations (addition, multiplication) — 3-5 marks.
Determinants — All Formulas
If |A| = 0 in a system of linear equations, don't assume 'no solution' — it means either no solution or infinite solutions, you must check further (consistency), this exact trap appears almost every year.
Find the inverse of a matrix using adjoint, and use it to solve a system of linear equations (very frequent 5-mark question).
Continuity and Differentiability — All Formulas
For continuity questions at a specific point, always check THREE things separately — left hand limit, right hand limit, and the function's value at that point — all three must be equal, checking only two is the most common half-mark loss.
Check continuity/differentiability at a point, or find derivatives using chain rule, implicit differentiation, or logarithmic differentiation — 3-5 marks, very frequent.
Application of Derivatives — All Formulas
After solving f'(x)=0, always run the second derivative test (or sign-change test) before declaring a point as maximum or minimum — stopping at f'(x)=0 alone is an incomplete answer.
Find maxima/minima in optimisation word problems (maximum area, minimum cost, etc.), or find intervals where a function is increasing/decreasing — 5 marks, high-value chapter.
Integrals — All Formulas
For integration by parts, remember the order 'ILATE' (Inverse, Log, Algebraic, Trig, Exponential) to decide which function is 'u' — picking u in the wrong order makes the integral far harder to solve.
Evaluate indefinite integrals using substitution, by parts, or partial fractions — one of the most calculation-heavy, highest-weightage chapters (5 marks, appears multiple times).
Application of Integrals — All Formulas
Always sketch a rough graph FIRST before setting up the integral — this single step prevents the most common mistake in this chapter, which is choosing wrong limits of integration.
Find the area bounded by a curve and the x-axis, or the area between two curves (like a line and a parabola) — 5 marks.
Differential Equations — All Formulas
Always make sure the equation is in the standard 'dy/dx + Py = Q' form (coefficient of dy/dx must be 1) BEFORE identifying P and finding the integrating factor — skipping this step is the most common setup error.
Solve a first-order linear differential equation using the integrating factor method, or solve variable-separable equations — 5 marks.
Vector Algebra — All Formulas
Dot product gives a SCALAR (a number, uses cos), cross product gives a VECTOR (has direction, uses sin) — say 'Dot = number, Cross = vector' to never confuse the two under exam pressure.
Find the angle between two vectors using dot product, or find a vector perpendicular to two given vectors using cross product — 3-5 marks.
Three-Dimensional Geometry — All Formulas
Direction ratios and direction cosines are proportional, not identical — direction cosines are the ones that specifically satisfy l²+m²+n²=1, always normalise before using them in the angle formula.
Find the equation of a line/plane given specific conditions, or find the angle between two lines/planes, or the shortest distance between skew lines — 5 marks.
Linear Programming — All Formulas
You never need to check every point in the feasible region — the optimal value ALWAYS occurs at one of the corner points, so just evaluate Z at each corner and compare.
Formulate a linear programming problem from a word problem (maximise profit/minimise cost) and solve graphically by testing corner points — 5 marks.
Probability — All Formulas
Bayes' Theorem questions always give you 'effect' information (like a test result) and ask you to find the 'cause' probability — spot this reversed direction first, then set up the theorem, rather than trying to memorise it mechanically.
Solve conditional probability problems, or a full Bayes' Theorem word problem (like disease testing, factory defective items) — 5 marks, high-value and frequently asked.
⚡ 5-Minute Quick Revision Cheatsheet
High-yield summary — scan this table one last time before you walk into the exam hall.
| Chapter | Key Formula | Quick Trick |
|---|---|---|
| 1. Relations and Functions | A relation R is reflexive if (a,a)∈R for all a | Remember 'RST' for equivalence relation — Reflexive, Symmetric, Transi... |
| 2. Inverse Trigonometric Functions | sin⁻¹x + cos⁻¹x = π/2 | Always check the principal value range before writing your final answe... |
| 3. Matrices | A matrix is symmetric if A' = A, skew-symmetric if A' = -A | To check symmetric vs skew-symmetric quickly, just look at the diagona... |
| 4. Determinants | For 2x2: |A| = ad-bc (matrix [[a,b],[c,d]]) | If |A| = 0 in a system of linear equations, don't assume 'no solution'... |
| 5. Continuity and Differentiability | f is continuous at x=a if lim(x→a) f(x) = f(a) | For continuity questions at a specific point, always check THREE thing... |
| 6. Application of Derivatives | Rate of change: dy/dx as rate | After solving f'(x)=0, always run the second derivative test (or sign-... |
| 7. Integrals | ∫xⁿ dx = xⁿ⁺¹/(n+1) + C | For integration by parts, remember the order 'ILATE' (Inverse, Log, Al... |
| 8. Application of Integrals | Area under a curve y=f(x) from x=a to b: ∫[a to b] y dx | Always sketch a rough graph FIRST before setting up the integral — thi... |
| 9. Differential Equations | Order = highest derivative present; Degree = power of the highest order derivative (after removing radicals/fractions) | Always make sure the equation is in the standard 'dy/dx + Py = Q' form... |
| 10. Vector Algebra | Magnitude of vector a = xi+yj+zk: |a| = √(x²+y²+z²) | Dot product gives a SCALAR (a number, uses cos), cross product gives a... |
| 11. Three-Dimensional Geometry | Direction cosines: l²+m²+n² = 1 | Direction ratios and direction cosines are proportional, not identical... |
| 12. Linear Programming | Objective function: Z = ax+by (to be maximised/minimised) | You never need to check every point in the feasible region — the optim... |
| 13. Probability | Conditional probability: P(A|B) = P(A∩B)/P(B), P(B)≠0 | Bayes' Theorem questions always give you 'effect' information (like a ... |
⚠️ Common Mistakes to Avoid in the Exam Hall
- Stopping at f'(x)=0 in maxima/minima problems without applying the second derivative test to confirm the nature of the point.
- Choosing the wrong function as 'u' in integration by parts — not following the ILATE priority order.
- Ignoring |A| = 0 cases in matrix/determinant questions — this means no solution OR infinite solutions, not automatically 'no solution'.
- Skipping the graph sketch before setting integration limits in Application of Integrals, leading to wrong bounds.
- Confusing direction ratios with direction cosines in 3D Geometry — only direction cosines satisfy l²+m²+n²=1.
❓ FAQs — Class 12 Maths Maths Formulas
How many chapters are there in CBSE Class 12 Maths for 2026-27?
There are 13 chapters in the current CBSE Class 12 Maths syllabus, organised into 6 units — Relations & Functions, Algebra, Calculus, Vectors & 3D Geometry, Linear Programming, and Probability.
Which Class 12 Maths chapters carry the highest weightage?
Calculus (Continuity & Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations) carries the maximum combined weightage in the board exam.
How to memorise Class 12 Calculus formulas fast?
Group formulas by pattern instead of memorising each in isolation — for example, learn the standard derivative and integral pairs together, since they mirror each other.
Is NCERT enough for Class 12 Maths board exam preparation?
Yes, NCERT textbook examples and exercises are the primary source for CBSE board questions — exemplar problems and previous year papers are recommended as additional practice.
Which Class 12 Maths chapters are considered most scoring?
Matrices, Determinants, Vectors, and Linear Programming are generally considered scoring since they involve structured, formula-based questions with fewer conceptual traps.
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