Statistics
Chi-Square Test of Independence: Expected Counts and Worked Example
Work through a chi-square test of independence from observed and expected counts to the statistic, degrees of freedom, p-value, and conclusion.
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Worked examples for the geometry, physics and statistics problems students meet most often—written to make the reasoning reusable.
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Statistics
How to Find a P-Value From a Z-Score: One- and Two-Tailed Examples
Convert a z-test statistic to a p-value for left-, right-, or two-tailed tests, with z-table steps, three worked examples, and practice answers.
Physics
Newton's Second Law Problems With Solutions: Net Force to Acceleration
Solve four F=ma problems step by step, including friction, an elevator, and an incline. Learn to draw forces, choose signs, and check your answer.
Geometry
Parallel Lines and Transversals: Solve for x Step by Step
Solve for x in parallel-line angle problems with four worked examples, a visual angle-pair guide, practice answers, and a check for when lines are parallel.
Physics
Series and Parallel Circuit Problems With Solutions
Solve series, parallel, and mixed resistor circuits step by step with current and voltage checks, four worked examples, and practice answers.
Geometry
Similar Triangles Word Problems With Solutions
Learn to match corresponding sides and solve shadow, distance, and algebra word problems with similar triangles, complete checks, and practice answers.
Geometry
How to Teach Geometry Proofs: Find and Fix Student Mistakes
Teach geometry proofs with three worked error-and-repair examples, a student checklist, and a classroom routine for finding unsupported reasoning.
Physics
Physics Problem Solving: How to Choose the Right Method
Choose forces, kinematics, energy or momentum before calculating. Follow three worked physics problems, common mistakes and teacher feedback prompts.
Statistics
Probability Distribution Problems: Step-by-Step Examples
Solve probability distribution problems with tables, expected value, binomial, Poisson and normal examples, plus common mistakes and teaching prompts.
Geometry
Coordinate Geometry Problems: Which Formula Should I Use?
Solve coordinate geometry problems with slope, distance, midpoint, line equations and intersections, then prove rectangles and rhombuses step by step.
Statistics
Confidence Intervals Explained With Examples
Learn what a 95% confidence interval means, calculate intervals for a mean and proportion, and avoid the most common interpretation mistakes.
Physics
Kinematics Equations: Which One to Use and When
Choose the right kinematics equation from the variables you know, then follow worked constant-acceleration examples with signs, units and checks.
Geometry
Pythagorean Theorem Word Problems With Answers
Solve Pythagorean theorem word problems step by step, including ladders, diagonals, navigation and distance, with answers and common-error checks.
Geometry
Circle Theorem Problems: Angles, Tangents & Secants
Choose the right circle theorem for tangents, chords, arcs, inscribed angles, secants and cyclic quadrilaterals, with worked examples and practice.
Physics
Free Body Diagram Problems and How to Read Them
Learn how to draw free-body diagrams through three worked examples involving a table, a frictionless incline and a mass supported by two ropes.
Statistics
Standard Deviation Step by Step (With Real Data)
Calculate standard deviation by hand in six steps with contextual data, and learn exactly when to divide by N or n−1.
Geometry
Geometry Proofs: Triangle Congruence, Similarity & More
Stuck on a geometry proof? Learn how to start, choose a theorem, and write triangle congruence, similarity, parallel-line and circle proofs.
Statistics
Hypothesis Testing Explained Step by Step
Follow the five hypothesis-testing steps through two complete numerical examples, from hypotheses and conditions to p-values and conclusions.
Physics
Projectile Motion Problems With Solutions
Solve horizontal and angled projectile motion problems step by step, including time of flight, maximum height, range and final velocity.