Algebra
Bank ~35–40 /100 Math (~full Algebra share)
~37% of Math tags (2020–2026)
MathematicsCommon notes
One page per chapter
Mathematics · common notes
Independent portion pages built for 60–90 second answers and transferable methods — Algebra, Calculus, Coordinate, Trigonometry, and Vectors & 3D. Depth-upgraded for Advanced process, not formula dumps. Each topic below is its own page — methods with impact copy, processed sample questions, and reusable question families.
Study path: open a topic page (not only the portion hub). Read official syllabus + trends (why it matters) → scan mixed joins → method impact → sample → question family. Formulas come last.
How to use
Common practice principle
- 01Principle 1
Do not memorize isolated tricks. Automate 4–6 universal moves that work on every paper type (SC, MC, NUM, MATCH).
- 02Principle 2
First 20 seconds decide the method; the next 40–70 seconds only execute.
- 03Principle 3
Write one-line reasons on rough sheet — that is what converts accuracy into 100%.
- 04Principle 4
Open the matching topic page for full methods, samples, and families — this hub is the routing layer.
Portion overview pages
Hubs (protocol + links)
Calculus
Bank ~28–32 /100 Math (~full Calculus share)
~28–30% of Math tags (2020–2026)
Coordinate Geometry
Bank ~12–16 /100 Math (full Coordinate share + joins)
~13% of Math tags (2020–2026) — still every-year & high accuracy if templated
Trigonometry
Bank formulas + equations + inverse; keep SOT ready for joins
Official Trig unit + frequent Calculus/Complex joins; SOT as join toolkit
Vectors & 3D Geometry
Bank Basics → Dot/Cross → Triple → Lines → Planes as five topic pages
Official Vectors + Analytical Geometry (3D) — high accuracy if templated
Primary study surface
Math topic notes (complete)
Independent pages for Algebra, Calculus, Coordinate, Trigonometry, and Vectors & 3D — each with official syllabus mapping, paper trends, mixed joins, and a 60–90s process drawn from the JEE Advanced 2026 syllabus map.
Algebra · open a topic page
Matrices & Determinants
Matrices · independent page
Matrices full marks come from structure first: order → trace/det → reduce (Cayley–Hamilton / nilpotent / adjoint) → only then multiply. Same process for systems and matching.
Complex Numbers
Complex · independent page
Complex full marks come from form choice: polar for powers/Arg, x+iy for lines/circles, ω-toolkit for cube roots of unity — with principal Arg locked before options.
Probability & Statistics
Probability · independent page
Probability full marks come from modelling: define events → partition/tree → apply definition/Bayes/counting → keep exact fractions. Statistics (mean/variance) uses the same clean table habit.
Quadratic Equations
Quadratic · independent page
Quadratic full marks come from symmetric functions first: write ∑α, ∑αβ, αβ before expanding — then nature of roots, formation of equations, and location of roots.
Binomial Theorem
Binomial · independent page
Binomial full marks come from coefficient extraction and identities: write general term T_{r+1}, apply nCr symmetries, and verify small-n when matching looks heavy.
Permutations & Combinations
P&C · independent page
P&C full marks come from one habit: write a counting model sentence (order? replacement? constraints?) before any nPr/nCr — then finish in 60–90 seconds.
Sets
Sets · independent page
Sets full marks come from a fixed toolkit: roster/set-builder clarity → Venn or algebra of sets → De Morgan / inclusion-exclusion → verify with a 2–3 element test set.
Relations
Relations · independent page
Relations full marks come from independent property checks: reflexive, symmetric, transitive (and equivalence ⇒ partition) — never ‘two out of three feels like equivalence’.
Sequences & Series
Sequences · independent page
Sequences full marks come from naming the type (AP/GP/HP/special) → writing a,d or a,r → applying the matching term/sum formula → sanity-checking the last term.
Calculus · open a topic page
Limits · Continuity · Differentiability
Limits · independent page
Full marks here mean: one-sided limits table → continuity vs differentiability as separate verdicts → simplify before L’Hôpital → never apply L’Hôpital without 0/0 or ∞/∞.
Applications of Derivatives
AOD · independent page
AOD full marks: simplify → differentiate → critical points + sign chart (and endpoints on closed intervals) → translate to tangent/normal/increasing language.
Integrals · Properties · Area
Integrals · independent page
Integrals full marks: property glance (King/even-odd) before expanding → technique if needed → for area, intersections first then ∫|f−g|.
Differential Equations
DE · independent page
DE full marks: rewrite standard form → stamp SEP / HOM / LIN → apply only that recipe → use IC → optionally differentiate to verify.
Coordinate · open a topic page
Straight Lines
Lines · independent page
Lines full marks: write a convenient form → apply distance/angle/bisector/family toolkit with sign care → verify with a known point.
Circle
Circle · independent page
Circle full marks: complete square → centre/radius → one tool (tangent length, chord of contact, S₁−S₂) → verify with a point.
Parabola
Parabola · independent page
Parabola full marks: standardise to y²=4ax (or x²=4ay) → write a, focus, directrix → parametric/tangent tool → eliminate t for locus.
Ellipse
Ellipse · independent page
Ellipse full marks: standardise → identify a>b or major-axis orientation → e²=1−b²/a² → foci/directrices/tangent dictionary → verify 0<e<1.
Hyperbola
Hyperbola · independent page
Hyperbola full marks: standardise → e²=1+b²/a² → foci → asymptotes y=±(b/a)x → tangent dictionary — never borrow ellipse’s e formula.
Trigonometry · open a topic page
Trig Formulas & Applications
Formulas · independent page
Sin / cos / tan marks come from a fixed toolkit: A±B → multiple/sub-multiple → factor (sum↔product) → apply to a value or simplify — never from re-deriving identities mid-paper.
Trigonometric Equations
Equations · independent page
Equation full marks = reduce to one function → find α → stamp the correct general template (sin/cos/tan) → reject extraneous roots. Listing only [0,2π] when ℝ is asked is a mark killer.
Inverse Trigonometry
Inverse · independent page
Inverse Trig full marks = lock principal range first, then evaluate or apply elementary identities. Same discipline as Arg in Complex — wrong branch is a designed distractor.
Solution of Triangles
Triangles · independent page
SOT full marks (when it appears as a tool) come from Law of Sines / Cosines + area formulas first — then half-angle / projection only if needed. Treat this as a bridge chapter, not a formula museum.
Vectors & 3D · open a topic page
Vector Algebra (Basics)
Basics · independent page
Basics full marks come from components + magnitude + unit vector + linear combination discipline — before any product is touched.
Dot & Cross Products
Dot · Cross · independent page
Dot/Cross full marks = meaning first: angle/⊥ → · , area/normal/∥ → × — then compute. Wrong product is the #1 Vectors mark killer.
Scalar & Vector Triple Products
Triple · independent page
Triple-product full marks = STP as determinant for volume/coplanar, and BAC–CAB for a×(b×c) — never expand nested cross in raw components first.
Lines in Three Dimensions
3D Lines · independent page
3D Lines full marks = write direction vector b first, then choose angle / intersect / skew-SD / coplanar gate — never use 2D distance intuition on skew lines.
Planes in Three Dimensions
3D Planes · independent page
Planes full marks = write normal n first, then distance/angle/foot templates. Cross product from two edges beats expanding giant determinants mid-paper.