21 chapter playbooks behind 47.5 of the 50 questions

191 q - 4.96/paper - 40% HARD. The single heaviest chapter on recent papers. Seven subtopics, and the HARD is spread rather than concentrated (top two carry only 47%), so there is no cherry-pick here: you own the whole chapter or you lose ten marks.

214 q - 4.83/paper - 56% HARD. The largest chapter in the bank and the hardest of the cornerstones. Scalar Triple Product (68 q, 74% HARD) and Cross Product (63 q, 63%) carry 74% of its HARD between them, so this chapter DOES cherry-pick: secure Dot Product (46 q, 26% HARD) first.

207 q - 5.08/paper - 38% HARD. The Std XII trigonometry chapter and the second-largest in the bank, in three parts over six notes pages: equations (47 q), solution of triangle (69 q: the rules, then half-angle and area) and inverse trigonometry (91 q: values, identities, equations). The parts cost about the same; the one expensive page is inverse-trig identities at 63% HARD. Solution of triangle is rising (1.64 to 2.13 a paper) while equations are falling (1.12 to 0.83).

174 q - 3.88/paper - 21% HARD. The cheapest cornerstone by some distance, and the best marks-per-hour chapter on the paper. Seven subtopics, none above 31% HARD; Approximations using Differentials is 12 q at 0% HARD.

135 q - 3.38/paper - 36% HARD. Six subtopics that split cleanly by SOLUTION METHOD, which is exactly how the questions are set. Order/Degree/Formation (31 q, 23% HARD) is recognition work and near-free; Linear (Integrating Factor) at 63% HARD is where the chapter gets expensive.

151 q - 3.42/paper - 52% HARD. A cornerstone you cannot skip and cannot rush. Substitution alone is 52 q; Trigonometric Integrals (Rational forms) runs 75% HARD, the highest of any subtopic in the subject. Foundations plus Trig Powers are 21 q at ~14% HARD - take those first.

135 q - 3.21/paper - 47% HARD. Method-pure subtopics, each drilling one technique. Inverse-trig differentiation (39 q) is the biggest single block. Derivative of One Function with respect to Another is only 7 q but 71% HARD - the worst marks-per-minute cell in the chapter.

43 q - 1.00/paper - 5% HARD. The lowest-HARD chapter in the subject: three of its four notes pages have NEVER produced a HARD question, and both HARD ones are reading constraints off a figure. Two marks that should take under a minute. Do this first, every time.

107 q - 2.67/paper - 21% HARD. The highest-weight Quick-Win, worth over five marks a paper at a fifth the HARD rate of the calculus chapters. Classical Probability (21 q) runs 10% HARD; only Bayes and Conditional (24 q, 33%) has any real teeth.

84 q - 1.96/paper - 29% HARD. The one chapter in MHT-CET Maths with its own execution mode: 70% of its stems ask which statement is true, against roughly 0% everywhere else. Its 31% HARD overstates the cost, because the difficulty is front-loaded into learning ONE technique (build the truth table) that then applies to every question - and it is not spread evenly: Switching Circuits is 10 q at 60% HARD while Negation is 14 q at 14%.

57 q - 1.29/paper - 21% HARD. A small, closed chapter with four subtopics and no surprises. Mean, Variance and Standard Deviation of a binomial variable (15 q) runs 13% HARD and is pure formula recall.

43 q - 0.96/paper - 19% HARD. Four notes pages of routine coordinate geometry; every HARD question sits on the slope-and-angle page (15 q, 33%), and the distance page shares its whole toolkit with Line and Plane, so it costs almost nothing on top of a cornerstone you already own.

86 q - 2.04/paper - 55% HARD. The hardest chapter in the subject by rate, and unusually it does NOT cherry-pick: the limit pages and the continuity pages sit at the same difficulty. Four limit toolkits (existence and infinity, algebraic, trigonometric, exponential-logarithmic) feed three continuity pages (a single point, piecewise junctions, the [x] and |x| discontinuities).

67 q - 1.75/paper - 46% HARD. Five pages: the evaluation toolkit (standard forms, substitution with changed limits, by parts), the trigonometric block (tan x = t, half-angle forms), then the three properties that collapse a question in a line - odd/even symmetry, King's property with the f/(f + g) family, and modulus/greatest-integer splitting. The property pages are 43 of the 69 q and the highest-leverage recognition in the calculus block.

47 q - 1.13/paper - 47% HARD. Small and expensive. The determinant and adjoint identities page is 15 q at 67% HARD - the chapter's hardest corner and its most learnable, since three recalled identities answer most of it. The compensation is that its identities are memorisable and reusable, unlike most of the long tail.

43 q - 1.00/paper - 33% HARD. Five notes pages. Tangents (13 q, 46% HARD) and Two Circles (7 q, 43%) are the expensive corners; the equation page is the cheap entry and the distance page is the greatest-and-least move shared with Complex Numbers.

43 q - 1.00/paper - 33% HARD. Three pages in notes order. Modulus and Argument (17 q, 29% HARD) is the half worth owning; Algebra with the cube roots of unity (15 q, 47%) is the expensive corner; Locus (11 q, 18%) is one geometric idea - a modulus is a distance.

44 q - 1.04/paper - 32% HARD. Three pages: area under one curve (14 q, 14% HARD - the cheapest page in the strand), area between two curves once the intersections are found (21 q, 38%), and the circle, ellipse and hyperbola regions that need the standard root integrals (9 q, 44%). One well-defined skill, which makes it a cheaper page than its HARD rate suggests.

42 q - 1.00/paper - 43% HARD. A closed, formula-driven chapter in four notes pages. Every question reduces to reading a, h and b out of a combined equation and applying one of a short list of conditions, which makes it more learnable than its 41% suggests; the angle page (11 q, 64%) carries the cost.

40 q - 1.00/paper - 40% HARD. The least mechanical chapter on the paper: no formula rescues a misread constraint. Five pages in notes order; Circular Arrangements is 6 q at 83% HARD, the densest corner in the chapter. One question a paper, and the one most likely to eat five minutes.

38 q - 0.92/paper - 47% HARD. The Std XI identity chapter, in three notes pages: compound angles, multiple angles, and sum-to-product. Eight of its 19 HARD questions are evaluations at 18°, 20° and π/8 that fall to a memorised value rather than to algebra; learn those values and the compound-angle list first, and leave the conditional identities for the second pass.