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.
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.
-
-
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.
-
Permutations vs. Combinations: Does Order Matter?
The counting principle, factorials, permutations vs combinations with nPr and nCr, repeated letters, and probability with combinations, with worked examples.
-
How to Find a Limit
What a limit means, how to evaluate one by substitution, factoring and rationalizing, one-sided limits, limits at infinity, and continuity, with examples.
-
How ACT Math Works, and How to Prepare for It
The ACT Math format after the 2025 update, the topics it tests, what it covers that the SAT does not, a pacing plan, and a four-week study schedule.
-
How to Solve Inequalities
Solve and graph inequalities: when to flip the sign, compound “and” and “or” inequalities, absolute value inequalities, and interval notation.
-
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.
-
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.
-
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.
-
Circle Formulas, From Area to the Equation of a Circle
Every circle formula you need: circumference, area, arc length, sector area in degrees and radians, inscribed angles, and the equation (x − h)² + (y − k)² = r².