Class 12 Maths Formula Sheet 2026-27 — All 13 Chapters in One Page

Remember 'RST' for equivalence relation — Reflexive, Symmetric, Transitive, all three needed together, missing even one disqualifies it.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.