01Relations and Functions
8 marksOne-one and onto proofs, and inverse trigonometric functions. Almost always a five-marker asking you to prove a function bijective.
Class 12 · Mathematics · 041
Mathematics, put together properly
All of this exists free somewhere. It's spread across a syllabus PDF, a dozen blogs that copy each other's mistakes, and a hundred channels. Here it is in one place, with what I'd actually do.
What I got in this subject
91/10071 theory + 20 practical
The paper I got most out of per hour spent, and the one I bought no book for. 71 of 80, untouched by moderation. My whole script is published, including the question I abandoned halfway through.
Every unit, and what it's worth
80 marks of theory across 6 units · 38 questions · 3 hours
Calculus 35Foundations 18Vectors & 3D 14Applied 13
02Algebra
10 marksMatrices and determinants — inverse by adjoint, and solving a system of three equations as a matrix product.
03Calculus
35 marksNearly half the paper. Continuity and differentiability, applications of derivatives, indefinite and definite integrals, area under curves, and differential equations.
04Vectors and Three-Dimensional Geometry
14 marksDot and cross products, projections, and the shortest distance between two lines — which turns up nearly every year.
05Linear Programming
5 marksOne question, graphical method, corner points. The most predictable five marks in the paper and the reason the booklet has graph paper in it.
06Probability
8 marksConditional probability, Bayes, and a case study built around a real-sounding scenario.
Calculus is 35 of 80 and everything else is a rounding error
Nearly half the paper is one unit. Integration alone will out-mark Linear Programming, Probability and Relations combined. If your revision plan gives Calculus the same slot as everything else, your revision plan is wrong.
The corollary is the good news: Linear Programming is five marks for one graph and a table of corner points, and it is the same question every year in different clothes. Probability is eight more for a small, self-contained syllabus. Between them that is thirteen marks you can genuinely secure in an evening.
Calculus every day. Linear Programming and Probability in the last week — not before, they will keep.
Do not buy a book for this subject
I did not, and it is the paper I scored highest in relative to effort. NCERT exercises — all of them, including the miscellaneous ones everybody skips because they are harder — plus every past paper you can find, is genuinely enough.
A reference book mostly gives you a way to feel busy without solving anything. You already have more questions in the NCERT than you will finish.
NCERT miscellaneous exercises are the ones worth doing. They are harder than the chapter exercises, which is the point.
The most expensive thing you can do is stop halfway
Question 30 on my paper was integration by parts. I set it up correctly and took the first mark. Then the working simply stops mid-line. The chip reads "30 : 1 + 0 + 0 = 1".
The same thing happened on my Physics paper, on a five-mark electrostatics question that scored zero. Two papers, same failure: the marks were sitting there in the later steps and I did not put anything on the page to claim them.
Maths is marked in half marks and every step is a slot. A wrong final answer with correct working keeps most of the marks. An abandoned answer keeps almost none. If you are stuck, write the next line you are sure of anyway.
Never leave a question half-written. Wrong beats blank, every single time.
Who to learn it from
Two channels, not twenty. Both checked by hand — plenty of dead accounts carry exactly the name you'd expect.
Checked against CBSE Academic — curriculum and rationalised syllabus · NCERT textbooks. Weightage is CBSE's own and is checked at build time to sum to 80.
Now go and solve something
Reading a guide is the same trap as watching a one-shot — it feels like work and produces nothing on its own. Set a daily question target and start today; the number compounds much faster than it feels like it should.