Trig Identities Worth Memorizing
The Pythagorean, reciprocal, quotient, double-angle and sum identities, how to use them to find exact values, and a method for proving identities.
Study guides
Step-by-step guides to algebra, geometry, trigonometry, calculus, statistics and the SAT, with worked examples and practice problems. Plus study skills, and notes for teachers.
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The Distance and Midpoint Formulas
How to find the distance between two points and the midpoint of a segment, where the formulas come from, and how to find an endpoint from a midpoint.
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Z-Scores, the Normal Curve and the 68-95-99.7 Rule
What a z-score measures, how to calculate one, the 68-95-99.7 rule for normal distributions, and how to compare scores from different tests.
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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.
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The Chain Rule
How the chain rule works, how to spot the inside and outside functions, examples with powers, roots, trig, e^x and ln, and mixing it with the product rule.
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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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Solving Any Triangle With the Law of Sines and Law of Cosines
When to use the law of sines or the law of cosines, how to solve triangles that are not right triangles, the ambiguous case, and the SAS area formula.
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Similar Triangles and Missing Sides
What makes triangles similar, the AA, SAS and SSS similarity tests, how to set up proportions for missing sides, and how area and perimeter scale.
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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.