Study guides
Free study guides
Clear, step-by-step study guides with worked examples for algebra, geometry, calculus, physics, biology, chemistry, history, economics, writing, and study methods.
How to solve quadratic equations
Algebra · Factoring, completing the square, and the quadratic formula explained step by step, with worked examples and a quick way to check every answer.
Derivative rules, explained with examples
Calculus · What a derivative means, plus the power, product, quotient, and chain rules with short worked examples you can follow line by line.
Photosynthesis, explained simply
Biology · The balanced photosynthesis equation, what happens in the light-dependent reactions and the Calvin cycle, and the factors that limit the rate.
How to balance chemical equations
Chemistry · A repeatable method for balancing chemical equations, with worked examples for combustion and rusting and the mistakes that trip students up.
How to write a strong thesis statement
Writing · What makes a thesis arguable and specific, a simple formula to draft one, and weak-to-strong examples you can model.
Active recall and spaced repetition
Study skills · Why testing yourself beats rereading, how spacing reviews fights forgetting, and a simple weekly schedule you can start today.
The Pythagorean theorem, step by step
Geometry · How a² + b² = c² works, how to find a missing side, how to test whether a triangle is right, and how the same idea gives the distance formula.
How to solve systems of equations
Algebra · Substitution, elimination, and graphing for two-variable systems, with worked examples, answer checks, and how to tell when there is no solution.
Newton's three laws of motion
Physics · Inertia, F = ma, and action-reaction pairs explained in plain language, with worked force problems, mass versus weight, and the mistakes to avoid.
Mitosis vs. meiosis
Biology · What each type of cell division is for, the phases in order, how chromosome numbers change, and a side-by-side list of the differences that show up on tests.
Mole conversions and stoichiometry
Chemistry · Convert between grams, moles, and particles, use balanced equations to predict how much product forms, and find the limiting reactant, with every step shown.
The causes of World War I
History · Militarism, alliances, imperialism, and nationalism explained, plus the assassination in Sarajevo and the July 1914 chain of events that turned a crisis into a world war.
Supply and demand, explained
Economics · The laws of supply and demand, how to calculate equilibrium price and quantity, what causes shortages and surpluses, and how to tell a shift from a movement along a curve.
How to write a lab report
Science writing · What goes in each section of a science lab report, how to write a testable hypothesis, how to graph your data, and how to calculate percent error.