Scientific Notation
How to write numbers in scientific notation, convert back to standard form, and multiply, divide, add and subtract in it, plus calculator E notation.
Algebra
From fractions and order of operations to quadratics, logarithms and rational expressions. Each guide has worked examples, common mistakes and practice with answers.
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Working With Rational Expressions
How to simplify rational expressions, state excluded values, multiply and divide them, add with a common denominator, and solve rational equations.
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Completing the Square, and When to Use It
Complete the square to solve quadratics, find a parabola’s vertex and write circle equations in standard form, with worked examples and common mistakes.
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Polynomial Long Division and Synthetic Division, Step by Step
How to divide polynomials with long division and synthetic division, handle missing terms, write the remainder, and use the remainder theorem.
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Absolute Value Equations and Inequalities
How to solve absolute value equations and inequalities: isolate the bars, split into two cases, use “and” or “or” correctly, and spot no-solution cases.
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Simplifying Radicals and Solving Radical Equations
Simplify square roots and cube roots, add and multiply radicals, rationalize denominators, convert to fractional exponents, and solve radical equations.
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How to Solve Inequalities
Solve and graph inequalities: when to flip the sign, compound “and” and “or” inequalities, absolute value inequalities, and interval notation.
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PEMDAS and the Order-of-Operations Traps That Catch Everyone
How PEMDAS really works: why multiplication and division tie, how to handle exponents, negatives and fraction bars, and worked examples with answers.
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Exponential Growth and Decay, Half-Life Included
Exponential growth and decay explained: the formula y = a(1 + r)^t, growth vs decay factors, compound interest, half-life, and linear vs exponential.
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Setting Up Ratios, Rates and Proportions
Ratios, unit rates and proportions explained: simplifying ratios, cross-multiplying, scale drawings, unit conversion, and direct and inverse variation.