Tutor-written learning library
Math makes more sense when every step has a reason.
Choose a topic for a clear explanation, a visual model, several worked examples, common mistakes, and practice that helps the method stick.
Algebra
Equations, lines, functions, factoring, and polynomial skills.
How to Solve Systems of Equations
Learn how to solve systems of equations by graphing, substitution, and elimination, with step-by-step examples and checks.
Learn the method Algebra · Guide 02The Substitution Method
Use substitution to solve systems of equations with clear steps, worked examples, and special-case guidance.
Learn the method Algebra · Guide 03The Elimination Method
Solve linear systems by elimination, including multiplying equations and recognizing special cases.
Learn the method Algebra · Guide 04How to Find Slope
Find slope from two points, a graph, a table, or an equation and understand what the result means.
Learn the method Algebra · Guide 05Slope-Intercept Form
Understand y = mx + b, write linear equations, and graph a line from its slope and y-intercept.
Learn the method Algebra · Guide 06How to Graph Linear Equations
Graph linear equations using slope-intercept form, intercepts, and tables, with examples for each method.
Learn the method Algebra · Guide 07How to Solve Inequalities
Solve and graph linear inequalities, including the rule for multiplying or dividing by a negative.
Learn the method Algebra · Guide 08Factoring Trinomials
Factor quadratic trinomials when the leading coefficient is 1 or another integer, with reliable checking steps.
Learn the method Algebra · Guide 09Difference of Squares
Recognize and factor the difference-of-squares pattern, including expressions with common factors.
Learn the method Algebra · Guide 10Completing the Square
Complete the square to solve quadratic equations and convert quadratics to vertex form.
Learn the method Algebra · Guide 11The Quadratic Formula
Use the quadratic formula accurately, interpret the discriminant, and simplify real or complex solutions.
Learn the method Algebra · Guide 12Function Notation
Read and evaluate function notation, find inputs and outputs, and work with composite expressions.
Learn the method Algebra · Guide 13Polynomial Division
Divide polynomials using long division and synthetic division, and interpret quotients and remainders.
Learn the methodGeometry
Triangles, proofs, circles, measurement, and spatial reasoning.
Triangle Congruence Rules
Learn SSS, SAS, ASA, AAS, and HL triangle congruence rules—and why SSA and AAA do not prove congruence.
Learn the method Geometry · Guide 02SAS vs. SSS Triangle Congruence
Compare SAS and SSS congruence, identify included angles, and decide which theorem a diagram supports.
Learn the method Geometry · Guide 03Similar Triangles
Prove triangles similar and use proportions to find missing side lengths.
Learn the method Geometry · Guide 04How to Write a Geometry Proof
Build two-column and paragraph geometry proofs from givens to a precise conclusion.
Learn the method Geometry · Guide 05Pythagorean Theorem Examples
Use the Pythagorean theorem to find missing sides and solve distance problems with step-by-step examples.
Learn the method Geometry · Guide 06Special Right Triangles
Use 45-45-90 and 30-60-90 triangle ratios to find exact side lengths quickly.
Learn the method Geometry · Guide 07Circle Formulas
Use circumference, area, arc length, and sector area formulas with radians and degrees.
Learn the method Geometry · Guide 08Area and Volume Formulas
Choose and use the most common area, surface area, and volume formulas with correct units.
Learn the methodAlgebra 2 / Precalculus
Polynomials, logarithms, sequences, trigonometry, and modeling.
Logarithm Rules
Understand the product, quotient, and power rules for logarithms and use them to expand or condense expressions.
Learn the method Algebra 2 / Precalculus · Guide 02How to Solve Logarithmic Equations
Solve logarithmic equations by rewriting exponential form, combining logs, and rejecting extraneous solutions.
Learn the method Algebra 2 / Precalculus · Guide 03Exponential Functions
Graph and model exponential growth and decay, identify rates, and solve practical examples.
Learn the method Algebra 2 / Precalculus · Guide 04Polynomial End Behavior
Predict polynomial end behavior from degree and leading coefficient, with graph and equation examples.
Learn the method Algebra 2 / Precalculus · Guide 05Polynomial Multiplicity
Understand repeated polynomial zeros and predict whether a graph crosses, touches, or flattens at each intercept.
Learn the method Algebra 2 / Precalculus · Guide 06Arithmetic Sequences
Find terms and sums of arithmetic sequences using common differences and explicit formulas.
Learn the method Algebra 2 / Precalculus · Guide 07Geometric Sequences
Find terms and sums of geometric sequences using common ratios and exponential structure.
Learn the method Algebra 2 / Precalculus · Guide 08The Unit Circle
Understand unit-circle coordinates, radians, reference angles, and exact sine and cosine values.
Learn the method Algebra 2 / Precalculus · Guide 09How to Memorize the Unit Circle
Memorize the unit circle by patterns, reference angles, and quadrant signs instead of 16 disconnected points.
Learn the method Algebra 2 / Precalculus · Guide 10Law of Sines
Use the Law of Sines for non-right triangles, including the ambiguous SSA case.
Learn the method Algebra 2 / Precalculus · Guide 11Law of Cosines
Use the Law of Cosines for SAS and SSS triangles and connect it to the Pythagorean theorem.
Learn the methodCalculus
Derivatives, applications, integrals, and volumes of revolution.
What Is a Derivative?
Understand derivatives as slopes, rates of change, and limits through visual and numerical examples.
Learn the method Calculus · Guide 02Derivative Rules
Learn the constant, power, sum, product, quotient, and chain rules with examples.
Learn the method Calculus · Guide 03Chain Rule Examples
Differentiate composite functions with the chain rule, from powers to trig and exponential expressions.
Learn the method Calculus · Guide 04Product Rule Examples
Differentiate products of functions with the product rule and simplify the result.
Learn the method Calculus · Guide 05Quotient Rule Examples
Differentiate quotients with the quotient rule, manage signs, and recognize when rewriting is easier.
Learn the method Calculus · Guide 06Implicit Differentiation
Differentiate equations where y is not isolated, including tangent slopes and second derivatives.
Learn the method Calculus · Guide 07Related Rates
Solve related-rates problems by connecting changing quantities, differentiating with respect to time, and tracking units.
Learn the method Calculus · Guide 08Optimization Problems
Solve calculus optimization problems by building an objective function, finding critical points, and verifying extrema.
Learn the method Calculus · Guide 09What Is an Integral?
Understand definite and indefinite integrals as accumulation, signed area, and reverse differentiation.
Learn the method Calculus · Guide 10U-Substitution
Use u-substitution to reverse the chain rule in indefinite and definite integrals.
Learn the method Calculus · Guide 11Integration by Parts
Apply integration by parts, choose u strategically, and handle repeated applications.
Learn the method Calculus · Guide 12Disk vs. Washer Method
Set up volumes of revolution with disks and washers, including correct radii and bounds.
Learn the method