How-to library
Method pages, one routine each: how to complete the square, how to integrate by parts, how to balance a redox equation. Every page runs a full worked example.
Statistics
How to run a chi-square test of independencePerform a chi-square test of independence to determine if two categorical variables are associated by comparing observed and expected frequencies.
Statistics
How to run a one-sample t-testLearn how to perform a one-sample t-test to compare a sample mean to a hypothesized population mean when standard deviation is unknown.
Statistics
How to construct a confidence interval for a meanLearn the exact procedure to construct a confidence interval for a population mean using the t-distribution or z-distribution.
Statistics
How to count outcomes with permutations and combinationsCalculate the total number of possible outcomes using permutations for ordered arrangements and combinations for unordered selections.
Statistics
How to use Bayes' theoremA step-by-step guide to calculating conditional probabilities using Bayes' theorem.
Statistics
How to calculate expected valueLearn how to calculate the expected value of a discrete random variable by summing the products of each possible outcome and its probability.
Statistics
How to find a probability with the normal distributionLearn how to find normal distribution probabilities by calculating z-scores and evaluating the standard normal cumulative distribution function.
Statistics
How to calculate a binomial probabilityLearn how to calculate the probability of exactly k successes in n independent Bernoulli trials using the binomial probability formula.
Statistics
How to calculate a weighted meanLearn how to calculate a weighted mean by multiplying each value by its weight and dividing by the sum of the weights.
Statistics
How to find quartiles and the interquartile rangeLearn to calculate the first, second, and third quartiles of a dataset and compute the interquartile range (IQR).
Statistics
How to calculate the standard deviation of a sampleA precise, step-by-step method to compute the sample standard deviation using the sum of squared deviations divided by n-1.
Calculus
How to find the radius of convergence of a power seriesFind the radius of convergence of a power series by applying the Ratio Test or Root Test to its general term.
Calculus
How to find a Taylor seriesA step-by-step guide to finding the Taylor series of a function centered at a specific point by calculating its derivatives and applying the general formula.
Calculus
How to find the sum of a geometric seriesCalculate the sum of finite or infinite geometric series using standard formulas and the common ratio.
Calculus
How to test a series for convergence with the ratio testApply the ratio test to determine absolute convergence of infinite series involving factorials and exponentials by evaluating the limit of adjacent terms.
Calculus
How to find arc lengthLearn how to calculate the arc length of a curve using definite integrals in calculus.
Calculus
How to find the volume with the shell methodLearn how to calculate the volume of a solid of revolution using the cylindrical shell method in calculus.
Calculus
How to find the volume of a solid of revolution with the disk methodLearn how to calculate the volume of a solid of revolution using the disk method by integrating the area of circular cross-sections.
Calculus
How to find the area between two curvesFind the area between two curves by integrating the difference of the upper and lower functions over the bounded interval.
Calculus
How to integrate a trigonometric productLearn how to evaluate integrals of trigonometric products using u-substitution and half-angle identities for sine and cosine.
Calculus
How to evaluate an improper integralEvaluate improper integrals by replacing infinite limits or discontinuities with a variable and taking the limit as the variable approaches the bound.
Calculus
How to evaluate a definite integralLearn how to evaluate a definite integral using the Fundamental Theorem of Calculus by finding an antiderivative and computing the difference at the boundaries.
Calculus
How to integrate using partial fractionsA step-by-step guide to evaluating integrals of rational functions using partial fraction decomposition.
Calculus
How to integrate by partsLearn how to evaluate integrals using the integration by parts formula, including setup, steps, and verification.