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NEB · IOE · 2026 EDITION

High school STEM,
from first principles.

A free study library for Class 11 and 12 — Mathematics, Physics and Chemistry. Every result is derived step-by-step from core definitions and aligned with NEB and IOE exam requirements.

8 SUBJECTS•58 CHAPTERS•STEP-BY-STEP DERIVATIONS•NEB & IOE CURRICULUM
WORKED DERIVATIONMATH · CLASS 11
THE QUESTION

Why is the derivative of sin x exactly cos x?

DEFINITION
f'(x) = lim h→0 [sin(x + h) - sin x] / h
1.
Start with the definition
f'(x) = lim h→0 [sin(x + h) - sin x] / h
2.
Expand the compound angle
sin(x + h) = sin x cos h + cos x sin h
Step 2 of 3 displayed
E² = (pc)² + (mc²)²•F = dp/dt•PV = nRT•ΔG° = -nFE°•∇ × E = -∂B/∂t•lim_{x→0} (sin x)/x = 1•PV^γ = CONSTANT•i = v/R + C(dv/dt)•λ = h / mv•HΨ = EΨ•∮ B · dl = μ₀I_enc•E² = (pc)² + (mc²)²•F = dp/dt•PV = nRT•ΔG° = -nFE°•∇ × E = -∂B/∂t•lim_{x→0} (sin x)/x = 1•PV^γ = CONSTANT•i = v/R + C(dv/dt)•λ = h / mv•HΨ = EΨ•∮ B · dl = μ₀I_enc•
7,209worked notesMaths · Physics · Chemistry
1,306recall flashcardsBuilt for spaced repetition
1,102practice MCQsPast-paper style, solved
100%free & open accessNo sign-up required
01 —— THE PREMISE

Textbooks hand you the last line.
We start at the first.

Most students meet calculus, mechanics and organic chemistry as a list of results to remember. We rebuild each one from the conditions that create it — so the result becomes obvious, not borrowed.

“You can only use a formula confidently if you could have found it yourself.”
FIRST-PRINCIPLES APPROACH
FIRST PRINCIPLESEXAM STRATEGY

The exam gap is not intelligence. It is the first move.

The difference appears in the first ninety seconds of a paper: one student recognizes a question, the other begins it. Recognition fails the moment the numbers are disguised. Reconstruction does not.

THE USUAL WAY
“Which formula fits?”
  • • Opens with a formula to memorize.
  • • Works while the question looks familiar.
  • • Falls apart when the numbers or wording change.
OUR WAY
“What is actually changing?”
  • • Opens with the definition or law it comes from.
  • • Asks what is changing, and what stays fixed.
  • • Survives an unfamiliar question, because you can restart it.
Same syllabus, 3 differences that matter.
02 —— THE SHELF

Start with a question
worth asking.

MATHEMATICS01 / 06
f'(x) = lim h→0

Derivatives by First Principles

Step-by-step differentiation of radical and trigonometric expressions.

06 DERIVATIONS · 22 MIN
PHYSICS02 / 06
P + ½ρv² = const

Bernoulli's Theorem & Fluid Flow

Conservation of energy in fluid dynamics and pressure-velocity relationships.

05 DERIVATIONS · 31 MIN
CHEMISTRY03 / 06
R-CHO → Aldol

Aldol Condensation Mechanism

Carbon-carbon bond formation in aldehydes and ketones with alpha-hydrogens.

04 DERIVATIONS · 19 MIN
PHYSICS04 / 06
η = 1 - T₂/T₁

Carnot Engine & Thermal Efficiency

Reversible thermodynamic cycles, heat engine operation, and maximum efficiency.

05 DERIVATIONS · 28 MIN
CHEMISTRY05 / 06
m = Z · I · t

Faraday's Laws of Electrolysis

Quantitative electrochemistry, electrochemical equivalents, and mass deposited.

04 DERIVATIONS · 42 MIN
MATHEMATICS06 / 06
d/dx(eˣ) = eˣ

Exponential & Trigonometric Calculus

Standard differentiation rules for exponential growth and trigonometric chains.

04 DERIVATIONS · 27 MIN
EVERY ENTRY INCLUDES DERIVATIONS, FORMULAS AND A SOLVED PRACTICE SET.
03 —— THE MODEL LAB

See the shape
before the formula.

Hybridisation and VSEPR are easier once the geometry is not an abstraction. Pick a molecule, rotate it, and check the bond angles against its electron domains.

EthanolC₂H₆O
Tetrahedral / Bent
Drag to Orbit 360°
The C–O–H dipole is what makes ethanol miscible with water, and the reason it hydrogen-bonds.
04 —— SYLLABUS DIRECTORY

The whole syllabus,
one page.

Six subjects across two years, each chapter mapped to the NEB curriculum with JEE and IOE extensions marked separately.

TRY A STARTING POINT
MATHEMATICS01

Limits, continuity & the derivative

UNIT 3 · CALCULUS42 MIN
PHYSICS02

Periodic motion & acceleration in SHM

UNIT 1 · MECHANICS58 MIN
CHEMISTRY03

Avogadro's hypothesis & molecular mass

UNIT 1 · STOICHIOMETRY36 MIN
MATHEMATICS04

Exponential & logarithmic derivatives

UNIT 2 · CALCULUS51 MIN
PHYSICS05

Transfer of heat & thermal conductivity

UNIT 2 · THERMODYNAMICS44 MIN
CHEMISTRY06

Stoichiometry & metal oxide calculations

UNIT 1 · STOICHIOMETRY38 MIN
MATHEMATICS07

Derivatives of trigonometric roots by definition

UNIT 4 · CALCULUS49 MIN
PHYSICS08

Fluid mechanics & Bernoulli theorem

UNIT 3 · MECHANICS52 MIN
CHEMISTRY09

Atomic mass & molar volume relations

UNIT 1 · STOICHIOMETRY45 MIN
05 —— THE METHOD

Mastering concepts is a
structured procedure.

The loop below guides you through reading, deriving on paper, and verifying on questions.

0110 MINUTES · ONE PASS

Pick a boundary

Choose one chapter and read only its first-principles note. Do not open the exercises yet. State plainly what is being calculated, and from what.

→ ONE CHAPTER, NOT FOUR
0225 MINUTES · BLANK SHEET

Derive it on paper

Close the page and rebuild the result. Check a step only when you are genuinely stuck, then close it again. A derivation you cannot restart is not finished.

→ NO HINTS OPEN WHILE WRITING
0315 MINUTES · TWO MCQS

Test it on a question

Open the solved set after, never before. When your answer breaks, return to the step that failed — not to the formula at the end of the page.

→ RETURN TO STEP 02 ON A MISS
Focused study session with active recall and practice
06 —— THE WORKBENCH

Tools for the parts
a textbook skips.

Built to be used between reading and rehearsing. Each one opens in place.

TOOLVISUALIZE

3D molecule viewer

Rotate exam-relevant molecules and analyze 3D geometry and functional groups.

Launch
TOOLBALANCE

Redox equation solver

Balance complex oxidation-reduction reactions step-by-step in acidic and basic media.

Launch
TOOLRECALL

Revision flashcards

Active recall decks spaced to review definitions, formulas, and laws before exams.

Launch
TOOLEXPERIMENT

Interactive molecule lab

Explore atomic configurations and 3D molecular representations interactively.

Launch
07 —— QUESTIONS

Asked plainly,
answered plainly.

If something is missing, ask. A teacher reads the inbox, and corrections make it into the next revision.

STILL STUCK?studynovo9@gmail.comUSUALLY ANSWERED WITHIN 24–48 HOURS
Yes. The full chapter library, flashcards and practice questions are open without an account or a payment screen. We don't hide worked derivations behind a preview.
FREE & OPEN ACCESS REFERENCE

Start with the why.

Choose a chapter, bring a blank page, and rebuild each derivation from first principles. Every note is organized chapter by chapter according to the NEB science curriculum.

CLASS 11 & 12•1,300+ FLASHCARDS•WORKED DERIVATIONS
ACTIVE RECALL & PRACTICE

Test your understanding,
chapter by chapter.

Review definitions, laws, and step-by-step numerical questions with active recall flashcards and solved MCQs.

COVERS PHYSICS · CHEMISTRY · MATHEMATICS