Worked solutions
SAT Worked Solutions: Original Math and Grammar Problems
Study 12 original SAT-style worked problems with verified math, alternate methods, distractor explanations and transfer exercises.
Reviewed
The short answer
Use these original teaching problems to understand a method, diagnose a wrong turn and apply the idea again. Each solution explains the answer, gives a second check and includes a related exercise. Choose a problem, attempt it first and then compare your reasoning with the worked steps.
Math worked examples
- SAT Linear Systems: Solve an Adult and Student Ticket Problem: Solve an original two-variable ticket problem by elimination, check both totals and try a related problem.
- SAT Quadratics: Find the Maximum Height of a Model: Use vertex form and the vertex formula to solve an original quadratic maximum problem and check the domain.
- SAT Percentages: An Increase Followed by a Decrease: Work through successive percentage changes with multipliers and explain why equal rates do not cancel.
- SAT Circles: Find the Center and Radius by Completing the Square: Rewrite a circle equation in standard form, find its center and radius, and verify a point on the circle.
- SAT Probability: Choose the Correct Denominator in a Two-Way Table: Use an original club survey table to calculate conditional probability and explain the denominator.
- SAT Trigonometry: Read Sine from a Right Triangle: Identify opposite, adjacent and hypotenuse in an original labeled right triangle, then calculate sine.
- SAT Equivalent Expressions: Cancel a Factor and Keep the Domain: Simplify a rational expression, explain the excluded input and check the result by factoring.
- SAT Scatterplots: Predict a Value from a Linear Model: Find an exact line for an original data set and interpret a predicted value with appropriate limits.
- SAT Student-Produced Response: Enter an Exact Fraction: Solve an original linear equation and practice entering its fractional or decimal answer without answer choices.
Reading and Writing worked examples
- SAT Punctuation: Use a Semicolon Before However: Identify two independent clauses and choose the punctuation around a conjunctive adverb in an original example.
- SAT Grammar: Find the Subject Across an Intervening Phrase: Choose a verb that agrees with the main subject rather than a noun inside a prepositional phrase.
- SAT Transitions: Choose a Contrast After an Unexpected Result: Explain a concessive relationship in an original passage and eliminate transitions with the wrong logical role.
Sources
- College Board: Official Bluebook practicesatsuite.collegeboard.org
Sources are linked for reference; they do not endorse PeakSAT. How we prepare our guides