Notes & formula sheets.

Concept notes, formula sheets and worked examples for JEE and Olympiad mathematics.

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Complex Numbers in Coordinate Geometry Complete JEE Notes

Every locus JEE sets on complex numbers, read as a sentence about distance or angle instead of an equation to expand: rotation, section formula, quadrilaterals, the perpendicular bisector, circles and their nature, the Apollonius circle, constant-angle arcs, ellipse and hyperbola with their degenerate cases, and maximum-minimum modulus. Worked with IIT-JEE, JEE Advanced 2022-2023 and all thirteen JEE Main 2026 complex-number questions.

24 min · 13 sectionsRead

Concept

Solution of Triangles for JEE: Every Formula, Proved and Solved

A triangle has six elements, and any three of them that include a side fix the whole thing. This note builds the machinery in order: the sine and cosine rules with proofs, the half angle formulae that turn any angle condition into a statement about s, a, b and c, the four centres, the four circles and the Euler line, with thirty-one worked examples and sixteen JEE Main 2025 and 2026 past papers among them.

38 min · 19 sectionsRead

Concept

Area Bounded by Curves: Complete Notes with Illustrations

Every area question asks the same three things: which curve is on top, over what stretch, and where they cross. This note builds the machinery in order, from the sign convention that costs most students a mark to the six question types that cover the syllabus. Seventeen worked JEE Main 2026 questions, every region drawn, every answer re-derived from scratch.

21 min · 14 sectionsRead

Concept

Straight Line in Space Complete JEE Notes with examples.

The straight line in space built from its definition: direction cosines and ratios, the four forms of the equation, the angle between lines, and the one linear equation that gives the foot of a perpendicular. Includes the image of a point, the "measured along" trap, skew lines and shortest distance, worked on JEE Main 2024, 2025 and 2026 past questions.

17 min · 12 sectionsRead

Concept

Differential Equations for JEE: All Nine Methods, Worked Examples

Every differential equation JEE sets is solved by one of nine standard moves, and all nine are short. This note is a catalogue: each type gets the shape that triggers it, the substitution or integrating factor it wants, and a recent JEE question worked in full. Twelve examples, eleven of them from JEE Main 2026.

29 min · 28 sectionsRead

Concept

Properties of Definite Integrals: The Complete JEE Method

A definite integral is a number, not an antiderivative, and that single fact is what most JEE questions on this chapter test. This note works through all six properties with proofs and geometric meaning, then the eight question types they generate: king, odd and even, greatest integer, modulus, periodic, integral-as-constant, Newton-Leibnitz and bounds. Twenty-nine worked examples, every answer independently re-derived.

23 min · 18 sectionsRead

Concept

Conditional Probability, Total Probability and Bayes' Theorem

Conditional probability is the machinery for what happens when the sample space shrinks. This note builds it from the definition, proves the multiplication theorem, the law of total probability and Bayes' theorem, and draws every idea as a Venn diagram or a tree. Six of the nineteen JEE Main 2026 shifts asked a question from this family, and all of them are worked here.

28 min · 15 sectionsRead

Concept

Family of Circles: Complete JEE Notes

One parameter does the work of a whole page of algebra. This note builds every family form JEE uses, from L1 + λL2 = 0 for lines to S + λL = 0, S1 + λS2 = 0 and the tangency families for circles, then applies them to common chords, contact, common tangents, orthogonality and locus questions. Twenty-four worked examples, including thirteen JEE Main 2026 circle questions solved in class 11 and 12 steps.

30 min · 12 sectionsRead

Concept

Monotonic Functions Increasing, Decreasing, Concavity and Inflection

Increasing and decreasing functions built up from the definition: the derivative test with its mean value theorem reasoning, the f'>0 statement that is false and costs marks every year, concavity, points of inflection, and the six question types JEE actually sets worked with JEE Main 2026 questions.

17 min · 15 sectionsRead

Concept

Applications of Newton-Leibnitz Formula.

The formula that appeared in ten JEE Main 2026 questions filed under six different chapter headings, and in JEE Advanced 2014 and 2025 besides. Built from the fundamental theorem, then walked through limits, continuity, monotonicity, maxima and minima, tangents, root location and integral equations with the one decision (where does x appear?) that settles every question. 38 worked examples, every answer re-derived independently.

29 min · 14 sectionsRead

Concept

Maxima and Minima Complete JEE Notes

Local and global extrema built from the definition: the first derivative test, the nth order test and why an even power never flips the sign, extrema where the function is not differentiable, and the Newton-Leibnitz formula for functions defined by an integral. Worked with IIT-JEE and JEE Main 2026 past questions.

14 min · 10 sectionsRead

Concept

Relation Between AM, GM and HM Complete JEE Notes with Proofs

The three means built from scratch, the chain A >= G >= H proved two ways including the classic semicircle picture, inserting n means between two numbers, and the standard inequalities that follow. Then the six shapes the question takes in a paper, worked with IIT-JEE and JEE Main 2026 past questions.

14 min · 16 sectionsRead