MHT-CET Maths — Teaching Notes

Indefinite Integration is one of the densest MHT-CET Maths chapters — 121 PYQs across 2021–2025, and the HARDEST by difficulty mix (about 60% are HARD). It is pure technique: there is no theory to memorise, only a toolbox of methods and the judgement to pick the right one. The chapter teaches in six movements, each one resting on the tools laid down before it: (1) Foundations — what an antiderivative is, the +C, the standard-formula table, the linear-argument (1/a) rule, and the algebra you do BEFORE integrating; (2) Substitution — the single highest-yield method (44 PYQs), built on the f'(x)/f(x) → log pattern and the reciprocal / take-out-the-power substitutions that dominate the hard end; (3) Trigonometric Integrals I — the standard tan/cot/sec/cosec results, power-reduction, identity simplification, and reducing an inverse-trig argument to a linear function of x; (4) Rational Functions and Partial Fractions — standard quadratic forms, completing the square, the numerator split, and decomposition (the arctan/arcsin/log machinery the next movement leans on); (5) Trigonometric Integrals II — the chapter's hard core: the half-angle (Weierstrass) substitution, the product-of-sines split, the trig-to-partial-fraction bridge, the divide-by-cos-squared move, and the fractional-power tan trick; (6) Integration by Parts — LIATE, the cyclic integrals, and the recurring eˣ[f(x)+f'(x)] family. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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Differentiation is the single most-tested calculus chapter in MHT-CET Maths — 103 PYQs across 2021–2025, and the HARDEST by difficulty mix (about 45% are HARD). It is almost pure technique: a small toolbox of rules, and the judgement to pick the right one for the shape in front of you. The chapter teaches in six movements, each resting on the tools laid before it: (1) Foundations, Chain Rule & Differentiability — the standard-derivative table, the product/quotient/chain rules, iterated compositions f(f(x)), simplify-before-you-differentiate, and where a derivative fails to exist; (2) Logarithmic Differentiation — take logs first when y is a product, quotient, or variable power, with the signature [(x+1)(2x+1)⋯(nx+1)] "value at x=0" pattern that the paper loves; (3) Implicit Differentiation & Special Forms — F(x,y)=0, the recurring log(x+y)=2xy, prove-the-relation problems, self-referential infinite expressions, and functional equations; (4) Inverse Functions & Inverse Trigonometric Differentiation — the chapter's biggest pool (29 q): the inverse-function rule, the inverse-trig derivative table, the substitution-collapse that turns a scary inverse-trig into a multiple of an angle, the tan⁻¹ addition formula, and one inverse-trig differentiated with respect to another; (5) Parametric, Higher-Order Derivatives & Relations — the dy/dx = ẏ/ẋ recipe, the second-derivative chain, proving a given differential relation, and the nth-derivative standard results; (6) Derivative of One Function with Respect to Another — the du/dv = (du/dx)/(dv/dx) move. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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A vector carries both magnitude AND direction — an arrow, not a number. Vectors is one of MHT-CET Maths's heaviest scorers and also its hardest single chapter: nearly six in ten questions are HARD. This chapter builds from the fundamentals — magnitude, components, unit vectors, the section formula — to the four products that do the real work: the DOT product (angle, projection, perpendicularity), the CROSS product (area, the perpendicular direction), and the SCALAR & VECTOR triple products (volume, coplanarity). Lock down the determinant forms and the |a+b|² magnitude expansion and most of the paper falls out. New to vectors? Start with Magnitude & Unit Vectors below; everything after it is an application.

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Line and Plane is the largest 3-D Geometry chapter in MHT-CET Maths and one of its hardest — nearly half the questions are HARD. Almost everything reduces to two engines: writing a line or plane in the right form, and taking a DOT or CROSS product of direction vectors and normals. This chapter builds in teaching order: first how to write a LINE (direction cosines, symmetric and vector form), then a PLANE (normal, Cartesian, intercept and family forms), then the ANGLES and parallel/perpendicular conditions between them. From there the applications follow — DISTANCES in 3-D, the FOOT of a perpendicular with its IMAGE and PROJECTION, the INTERSECTION / coplanarity / shortest-distance machinery, and finally TETRAHEDRON centroid and volume. New to 3-D? Start with the Line page; every later page leans on the direction-vector and cross-product habits it builds.

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Applications of Derivative is the largest single chapter in MHT-CET Maths — 183 PYQs across 2021–2025 — and it is where the derivative stops being an abstract limit and starts doing work: finding slopes, estimating values, tracking rates, and locating the best-possible answer. Everything rests on one idea — dy/dx is the slope of the curve at a point — read seven ways. The chapter teaches in seven movements, each building on the tools before it: (1) Tangents, Normals & the Slope of a Curve — the tangent/normal line equations, parametric slopes, the recurring "normal parallel to a given line" and "curve touches an axis" problems; (2) Angle Between Curves & Orthogonality — the tanθ = |(m₁−m₂)/(1+m₁m₂)| formula and the m₁m₂ = −1 right-angle condition; (3) Approximations using Differentials — dy = f'(x)dx and f(a+h) ≈ f(a) + h·f'(a) for roots, powers, trig and log values; (4) Rate of Change & Related Rates — the chain dQ/dt = (dQ/dx)(dx/dt), the sphere/cone/ladder templates, and rectilinear motion; (5) Increasing & Decreasing Functions — the sign of f'(x), the discriminant test for monotone-everywhere, and rational/trig/composite sign analysis; (6) Maxima, Minima & Optimisation — the first- and second-derivative tests, the extreme-value-at-a-given-point family, constrained-set extrema, and the classic optimisation word problems (tank, poster, wire-cut, number-splitting, AM-GM); (7) Rolle's Theorem & the Mean Value Theorem — the two existence theorems, finding c, and solving for parameters from the hypotheses. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

Open chapter notes

Differential Equations is one of the largest chapters in MHT-CET Maths — 144 PYQs across 2021–2025 — and it is almost pure method: recognise the type of first-order equation in front of you, then apply the matching recipe. The whole chapter turns on that recognition step. It teaches in six movements, each building on the last: (1) Order, Degree, Formation & Verification — read a DE's structure (order = highest derivative, degree = its power after clearing radicals), form the DE of a curve family by eliminating its arbitrary constants (n constants ⇒ order n), and verify a given solution; (2) Variable-Separable Equations — the workhorse: get all the y's on one side, all the x's on the other, and integrate; (3) Homogeneous & Reducible Equations — the y = vx substitution for same-degree equations, plus the v = x + y / v = y/x substitutions that reduce a disguised equation to separable; (4) Linear Equations (Integrating Factor) — the standard form dy/dx + P(x)y = Q(x), the integrating factor IF = e^∫P dx, the reciprocal 'linear in x' form, Bernoulli's substitution, and exact grouping; (5) Growth, Decay & Continuous Models — dP/dt = kP for population/bacteria/radioactive-decay/continuous-compounding, plus the special-rate models; (6) Newton's Law of Cooling — the dθ/dt = −k(θ − θₛ) model and its two-stage problems. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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Probability Distribution is a high-yield MHT-CET Maths chapter (126 PYQs across 2021–2025) that runs from first principles all the way to random variables. It teaches in four movements, each resting on the one before: (1) Classical Probability, Addition Theorem & Odds — the foundation: favourable ÷ total on equally-likely outcomes, counting with permutations and combinations, the addition theorem P(A∪B) = P(A)+P(B)−P(A∩B), the complement and 'at least one' shortcut, and converting odds to probabilities; (2) Conditional Probability, Independence & Bayes' Theorem — restricting the sample space with P(A|B), the multiplication rule for sequential draws, independent-event algebra, the total-probability theorem, and Bayes' theorem for bags, urns and diagnostic tests; (3) Discrete Random Variables, PMF & CDF — defining a distribution, finding the constant k (finite, quadratic, exponential and infinite-series PMFs), reading probabilities of ranges, building a distribution from an experiment, the cumulative distribution function, and the continuous (density) analogue; (4) Expectation, Variance & Standard Deviation — E(X), the variance formula Var(X) = E(X²) − [E(X)]², expected winnings in games, the uniform-distribution formulas E = (n+1)/2 and Var = (n²−1)/12, and back-solving for unknown probabilities from a given mean. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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Binomial Distribution is a compact, high-yield MHT-CET Maths chapter (60 PYQs across 2021–2025) built on one model: n independent trials, each a success (probability p) or failure (q = 1 − p). Almost every question reduces to spotting n, p and q, then reaching for the right tool. It teaches in four movements: (1) The Binomial Setting & PMF — recognise the Bernoulli-trial setup, fix p and q, and read off a single probability with P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ; (2) Computing Binomial Probabilities — 'at least', 'at most', ranges, and the workhorse 'at least one' = 1 − qⁿ, plus the even-count and expected-frequency variants; (3) Mean, Variance & Standard Deviation — mean = np, variance = npq, SD = √(npq), and inverting them to recover n and p; (4) Parameter Estimation & the Probability Ratio — pinning down n or p from a probability condition (P(X=a) = c·P(X=b)), the identity ⁿCₐ = ⁿC_b, and the successive-term ratio P(X=k)/P(X=k−1). Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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