Math tips & study guides
Problem-solving strategies, exam tips and step-by-step guides, each with worked examples you can check.
How to Use Desmos on the Digital SAT — Complete 2026 Guide
The built-in Desmos calculator is the single biggest score multiplier on the digital SAT — if you know the right moves. Here's the 2026 guide to using Desmos for equations, systems, quadratics, regression, and stats, plus the timing rule that keeps it from slowing you down.
Best Math Solver Apps in 2026 — Honest Comparison (Photomath, Mathway, Symbolab, Gauthmath & Solver AI)
Snap-and-solve math apps have multiplied since Photomath kicked off the category — and not all of them earn the install. We tested the five most-installed math solver apps of 2026 across OCR accuracy, step-by-step quality, topic coverage, free tier, and honesty of pricing. Here's what each one is actually best for.
How to Find Asymptotes — Horizontal, Vertical, and Slant Step by Step
Every rational function has a story told by its asymptotes. Learn how vertical asymptotes come from the denominator's zeros, the degree-comparison rule for horizontal asymptotes, when a slant asymptote appears, how to tell a hole from a vertical asymptote, and how all three connect to limits — with worked examples for Algebra 2, AP Precalc, and Calc 1.
Convergence Tests for Infinite Series — Ratio, Root, Integral, Comparison, Alternating
Every infinite series problem comes down to choosing the right test. Learn the nth-term divergence test, geometric and p-series benchmarks, the integral, comparison, limit comparison, ratio, root, and alternating series tests, the difference between absolute and conditional convergence, and a decision tree for picking the right tool the first time.
Fundamental Theorem of Calculus — Part 1, Part 2, and Worked Examples
The Fundamental Theorem of Calculus ties differentiation and integration together. Learn FTC Part 1 (derivatives of accumulation functions), FTC Part 2 (evaluating definite integrals with antiderivatives), the intuition behind why it works, common mistakes, and worked AP-style examples.
Bayes' Theorem — Formula, Intuition, and Worked Examples
Bayes' Theorem tells you how to update a probability when new evidence arrives. Learn the formula, the intuition behind priors and posteriors, why the base rate fallacy fools doctors and juries, and how to set up Bayes problems step by step with worked examples from medical testing and spam filtering.
Mean Value Theorem — Statement, Intuition, and Worked Examples
The Mean Value Theorem connects average rate of change to instantaneous rate of change. Learn the formal statement, geometric intuition, how to check hypotheses, find the c value, and apply MVT to physics and AP-style problems.
Quadratic Formula — Complete Guide with Derivation and Examples
The quadratic formula solves every quadratic equation. Learn the formula, see how it's derived from completing the square, use the discriminant to predict solutions, and work through real examples.
Cross Product and 3D Vectors — Formula and Examples
Master the cross product of 3D vectors. Covers the formula, determinant method, right-hand rule, geometric meaning, applications to area and torque, and the scalar triple product.
Hypothesis Testing — Step-by-Step Guide with Examples
Master hypothesis testing step by step. Learn to set up the null and alternative hypotheses, choose z-tests vs t-tests, interpret p-values, and avoid Type I and Type II errors.
Law of Sines and Law of Cosines — Formulas and Examples
Master the Law of Sines and Law of Cosines. Learn when to use each, the ambiguous SSA case, and how to solve any triangle — not just right triangles — step by step.
Taylor and Maclaurin Series — Formulas and Examples
Master Taylor and Maclaurin series from scratch. Covers the general formula, how to expand sin, cos, e^x, ln(1+x), radius of convergence, and polynomial approximations.
Conic Sections — Circles, Ellipses, Parabolas, and Hyperbolas
Master the four conic sections — circles, ellipses, parabolas, and hyperbolas — with this complete guide. Covers standard equations, key features, graphing, and real-world applications.
Exponential Growth and Decay — Formulas and Real-World Examples
Learn exponential growth and decay from scratch. Covers the general formula, discrete and continuous forms, doubling time, half-life, compound interest, and real-world applications.
Composite Functions — How to Compose and Decompose Functions
Learn composite functions from scratch. Covers notation, evaluation, domain restrictions, decomposition into simpler pieces, and the connection to inverse functions.
Vectors and the Dot Product — Magnitude, Direction, and Angles
Learn vectors from the ground up. Covers vector components, magnitude, addition, scalar multiplication, the dot product, and using it to find the angle between two vectors.
Complex Numbers — Operations, Polar Form, and Applications
Understand complex numbers from the ground up. Learn the imaginary unit i, arithmetic with complex numbers, the complex plane, polar form, and De Moivre's theorem.
Polar Coordinates — Conversion, Graphing, and Equations
Learn polar coordinates from the ground up. Covers the (r, θ) system, conversions to/from rectangular form, graphing polar equations, and common curves like cardioids and roses.
L'Hôpital's Rule — How to Evaluate Indeterminate Limits
Learn L'Hôpital's rule for evaluating tricky limits. Covers the 0/0 and ∞/∞ forms, seven indeterminate forms, when to apply the rule, and common mistakes.
Synthetic Division — Fast Way to Divide Polynomials
Synthetic division is the fastest way to divide a polynomial by a linear factor. This guide covers the method, worked examples, the remainder theorem, and when to use it.
Inverse Functions — How to Find and Verify Them
Master inverse functions with this complete guide. Learn how to find, verify, and graph inverse functions using the algebraic method, horizontal line test, and domain restrictions.
Partial Fractions Decomposition — How to Split Rational Expressions
Master partial fractions decomposition with this complete guide. Learn to split complex rational expressions into simple fractions for easier integration and algebra.
Matrix Operations — Addition, Multiplication & Properties
Master matrix operations with this complete guide. Learn how to add, subtract, and multiply matrices, understand their key properties, and see how identity matrices and transposes work with fully worked examples.
Optimization Problems in Calculus — How to Find Max & Min
Master calculus optimization problems with this complete guide. Learn the 6-step method and work through classic examples: fencing, maximum box volume, and minimum distance problems.
Function Transformations — Shifts, Reflections, Stretches & Compressions
Master function transformations with this complete guide. Learn how shifts, reflections, stretches, and compressions change the graph of any function, and how to combine multiple transformations.
Implicit Differentiation — When and How to Use It
Master implicit differentiation with this complete guide. Learn when to use it, the step-by-step method with chain rule, worked examples on circles and complex curves, and how to find tangent lines.
Normal Distribution & Z-Scores — How to Use the Bell Curve
Understand the normal distribution and z-scores with this complete guide. Learn the properties of the bell curve, how to calculate and interpret z-scores, use the z-table, and apply it all to real-world problems.
How to Solve Rational Equations — Step by Step
Master solving rational equations with the LCD method. This guide covers finding the LCD, clearing fractions, checking for extraneous solutions, and avoiding common mistakes with fully worked examples.
Arithmetic & Geometric Sequences — Formulas and Examples
Master arithmetic and geometric sequences with formulas for the nth term and series sums, clear explanations of common difference and common ratio, and fully worked examples.
Related Rates in Calculus — How to Solve Them Step by Step
Learn how to solve related rates problems with a reliable 5-step method. This guide walks through classic examples — the sliding ladder, inflating balloon, and filling cone — with every step explained.
Integration by Parts — Formula, Strategy, and Examples
Master integration by parts with the complete formula, the LIATE strategy for choosing u and dv, detailed worked examples from simple to advanced, and practice problems.
Logarithms Explained — Rules, Properties, and Examples
A complete guide to logarithms covering what they are, all the key rules and properties, how to solve logarithmic equations, and the change of base formula with fully worked examples.
Binomial Theorem — Formula, Pascal's Triangle & Examples
The binomial theorem turns the tedious expansion of (a+b)^n into a clean, predictable formula. Learn how Pascal's triangle supplies the coefficients, how the nCr formula works, how to expand quickly, and how to pick out any single term without expanding the whole thing.
Right Triangle Trigonometry — SOH CAH TOA Explained
SOH CAH TOA turns right triangle problems into a simple three-step process. Learn the three trig ratios, how to solve for missing sides and angles, the two special right triangles, and where trigonometry shows up in the real world.
Solving Systems of Equations with 3 Variables — Step by Step
Systems with three variables look intimidating, but the strategy is straightforward: reduce three equations to two, then two to one. Learn the elimination method, Gaussian elimination, and how to handle special cases.
U-Substitution in Integration — Step-by-Step Method
U-substitution is the most important integration technique after basic antiderivatives. Learn the step-by-step method, how to choose the right u, and work through examples for both indefinite and definite integrals.
Area and Volume Formulas — Complete Reference Guide
Every area and volume formula you need in one place. Covers 2D shapes, surface area, and volumes of prisms, cylinders, pyramids, cones, and spheres with worked examples.
Exponent Rules — Complete Guide with Examples
Master every exponent rule you need for algebra and beyond. Learn the product, quotient, and power rules plus zero, negative, and fractional exponents with worked examples.
How to Find Limits Algebraically — Techniques & Examples
Master the essential algebraic techniques for evaluating limits: direct substitution, factoring, rationalizing, special trig limits, and limits at infinity with worked examples.
Trigonometric Identities Cheat Sheet — All Formulas You Need
Every trigonometric identity you need in one place. Learn the Pythagorean, reciprocal, double angle, half angle, and sum/difference identities with examples showing how to verify and apply them.
Domain and Range Explained — How to Find Them for Any Function
Domain and range describe every function's inputs and outputs. Learn systematic methods to find them for polynomials, rationals, radicals, and more.
How to Graph Linear Equations — Slope, Intercepts & Examples
Graphing linear equations is a core algebra skill. Learn how to plot lines using slope-intercept form, intercepts, and tables of values with clear examples and tips.
Introduction to Probability — Rules, Formulas & Examples
Probability measures how likely events are. Master sample spaces, the addition and multiplication rules, conditional probability, and Bayes' theorem with clear examples.
Long Division of Polynomials — Step-by-Step Method & Examples
Polynomial long division follows the same logic as numeric long division. Learn the step-by-step process, when to use synthetic division instead, and practice with clear examples.
Mean, Median, Mode & Range — How to Find Them (With Examples)
Mean, median, mode, and range are the building blocks of statistics. Learn how to calculate each one, when to use which measure, and how outliers affect your results.
Order of Operations (PEMDAS) — Rules, Examples & Common Mistakes
PEMDAS governs how every math expression is evaluated. Master the correct order of operations with clear rules, tricky examples, and the most common mistakes students make.
How to Complete the Square — Method, Examples & When to Use It
Completing the square transforms any quadratic into vertex form. Learn the step-by-step method, when to choose it over factoring, and practice with clear worked examples.
Permutations and Combinations Explained — Formulas, Differences & Examples
Struggling to tell permutations from combinations? This guide breaks down when order matters, teaches both formulas, and walks through counting problems step by step.
Understanding Slope and Slope-Intercept Form — Complete Guide
Slope measures steepness and direction of a line. Master the slope formula, y = mx + b form, graphing techniques, and converting between standard and slope-intercept form.
How to Solve Absolute Value Equations and Inequalities — Step by Step
Absolute value problems require splitting into two cases. Learn the step-by-step method for equations and inequalities, with worked examples and common pitfalls to avoid.
How to Study for AP Calculus AB — Tips & Practice Strategy
Preparing for the AP Calculus AB exam? This guide covers everything from the exam format to FRQ strategies, study timelines, and the best ways to practice effectively.
Chain Rule vs Product Rule — When to Use Which in Calculus
Chain rule or product rule? Learn how to instantly identify which differentiation rule to apply, avoid common pitfalls, and work through examples that combine both.
5 Common Algebra Mistakes Students Make on Exams
These five algebra mistakes trip up students on nearly every exam. Learn to spot them before they cost you points, with clear examples showing what goes wrong and how to fix it.
Derivative Rules, Formulas, and Examples — Complete Reference
This is your one-stop reference for every derivative rule you need in calculus. Covers power, product, quotient, and chain rules plus trig, exponential, and log derivatives.
How to Factor Any Quadratic Equation — Step by Step
Factoring quadratics is a core algebra skill. Learn five reliable methods — from GCF extraction to the AC method — so you can factor any quadratic you encounter.
How to Solve Word Problems in Math — A Step-by-Step Framework
Word problems are the most feared part of math for many students. This guide gives you a repeatable framework and applies it to the five most common word problem types.
Integration by Parts — When and How to Use It
Integration by parts is essential for integrals involving products of functions. Learn the formula, the LIATE mnemonic, the tabular method, and how to avoid common mistakes.
Limits in Calculus — A Complete Beginner's Guide
Limits are the foundation of all of calculus. This beginner-friendly guide covers everything from the intuitive definition to L'Hopital's rule and limits at infinity.
Pythagorean Theorem Explained — Formula, Proofs & Practice Problems
The Pythagorean theorem is one of the most important formulas in math. Learn the formula, see a visual proof, and practice with worked examples.
Simplifying Radicals and Rational Exponents — Rules You Need
Radicals and exponents follow clear rules that, once mastered, make simplification fast and reliable. Learn the key rules, see worked examples, and practice.
Solving Inequalities — Linear, Quadratic, and Absolute Value
Inequalities are everywhere in algebra. Master the techniques for solving linear, compound, absolute value, quadratic, and rational inequalities with this complete guide.
Understanding Logarithms — Properties, Rules, and Equations
Logarithms can seem abstract, but they follow clear rules. This guide explains what logs really mean, their key properties, and how to solve log and exponential equations.
How to Use the Unit Circle — Complete Guide with Examples
The unit circle is the key to unlocking trigonometry. Learn how to find exact values of sin, cos, and tan for any standard angle with clear explanations and examples.
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