Revising: an ending that answers the cause
Learn to choose the concluding sentence that responds to the specific problem, and the specific cause, that a short draft describes.
Start sample lessonSHSAT Course: Free Sample Lessons
Sample chapters from the full SHSAT course, grouped by section. Each one teaches a question type and ends with a practice question.
Updated October 3, 2026
English Language Arts
contextual revising and editing · sentence grammar and punctuation · literary and informational reading · poetry, evidence, inference and structure
Inference: what a revised procedure is designed to show
Learn to infer the purpose of a second attempt by comparing what changed and what stayed the same, and to reject answers that promise results or inflate small details.
Start sample lessonSentence boundaries: joining complete thoughts
Learn to spot complete thoughts, the correct ways to join them, and the comma splice, the error behind most wrong answers in this question type.
Start sample lessonAgreement, tense and parallel form
Learn to match each verb to its true subject, keep events in a logical time order, and give items in a list or comparison the same form.
Start sample lessonPronouns: the right case and a clear reference
Learn to choose subject, object and reflexive pronouns correctly, use who and whom, and fix pronouns that could point to more than one noun.
Start sample lessonModifiers: put each description next to its target
Learn to fix dangling and misplaced modifiers, place only where it gives the intended meaning, and avoid double negatives.
Start sample lessonPunctuation: commas, colons, semicolons and apostrophes
Learn to set off extra information with a pair of commas, use colons and semicolons where they belong, and form possessives and its correctly.
Start sample lessonConcise and precise expression
Learn to cut words that repeat meaning, choose the idiom or word that fits, and keep a writer's claim exactly as strong as it was.
Start sample lessonOrganizing a draft: place each sentence where it connects
Learn to map a numbered draft, place an added sentence right after the idea it refers to, and choose openings, paragraph breaks and conclusions that fit the whole sequence.
Start sample lessonConnections: combine sentences and choose transitions
Learn to name the relationship between two ideas, pick the transition or connecting word that states it, and combine sentences without adding a cause, an order or a claim the writer didn't make.
Start sample lessonFocus: keep, cut or add sentences that serve the purpose
Learn to name a draft's purpose, cut sentences that don't serve it, choose details that support a specific claim, and pick conclusions that sum up without overreaching.
Start sample lessonLiterary reading: motives, gestures and a changing character
Learn to explain why a character acts by pointing to what they say and do, read small gestures as signs of change, and state a theme the whole story supports.
Start sample lessonLiterary reading: a flaw, a turning point and a new view
Learn to explain why a character wants to hide a flaw, find the moment that changes their view, read key words in context, and see why an author orders events as they do.
Start sample lessonLiterary reading: competing motives and an open ending
Learn to read what a physical detail shows before anyone explains it, state each character's motive fairly, and describe an ending that leaves a conflict unsettled.
Start sample lessonTechnical reading: conditions, causes and failures
Learn to break an explanation of how something works into its conditions, trace each failure to the condition it breaks, and see what job a passage's opening does.
Start sample lessonInformational reading: the central idea and its limits
Learn to state a passage's central idea so that it covers every paragraph and keeps the author's limits, and to choose the details that best support a claim.
Start sample lessonInformational reading: how models are tested and revised
Learn the path that passages about models usually follow (purpose, simplification, test, mismatch, revision, limits) and use it to answer central-idea and purpose questions.
Start sample lessonPoetry reading: literal action first, then meaning
Learn to state what is literally happening in a poem before interpreting it, read word choice for what it suggests about the speaker, and track a shift in the speaker's attitude.
Start sample lessonPoetry reading: timeline, memory and a repeated image
Learn to separate a poem's present from what the speaker remembers, follow the order of events, and read a repeated sound or image that links the two.
Start sample lessonPaired passages: positions, examples and common ground
Learn to summarize each writer's position along with its limits, explain what an example is doing, and name where two passages agree and where they differ.
Start sample lessonMathematics
rational numbers and percentages · ratios, rates and proportions · equations and inequalities · geometry and measurement · statistics and probability · grade-9 linear functions, systems and transformations
Unit rate: find the amount for one, then scale
Find a unit rate from one pair of numbers, use it to scale to a new amount, and spot when a warm-up or starting amount breaks the proportion.
Start sample lessonEquations true for every x, for no x, or for one x
Tell whether a linear equation has one solution, no solution or infinitely many, and find a missing constant that makes it true for every x.
Start sample lessonSigned numbers and fractions: track every sign
Combine signed changes, separate net change from distance, and avoid common sign and fraction slips.
Start sample lessonFractions of a changing whole
Track which whole each fraction refers to, update it after every step, and work backward from a part to the whole.
Start sample lessonRatios: count the parts, then find one part
Split a total by a ratio, find shares from a difference, link two ratios, and scale lengths and areas.
Start sample lessonLinear equations: write them from words, then solve
Solve equations with variables on both sides, and turn word problems about consecutive numbers, ages, totals and rectangles into equations.
Start sample lessonInequalities with whole-number answers
Solve linear inequalities, turn the solution into the greatest or least integer the situation allows, and count the integers in a range.
Start sample lessonFactors, multiples and remainders
Choose between the GCF and the LCM, count divisors from a prime factorization, and solve remainder and divisibility questions.
Start sample lessonAngle relationships: write the total, then solve
Use straight-line, triangle, polygon and parallel-line angle facts to write and solve equations for unknown angles.
Start sample lessonArea of composite shapes
Find areas of L-shapes, borders and cut-outs by splitting them into rectangles, triangles, trapezoids and circles.
Start sample lessonVolume, capacity and displacement
Find volumes of boxes and prisms, convert cubic centimeters to liters, and solve displacement and packing questions.
Start sample lessonMean, median and range: think in totals
Find missing or added values from a mean, combine groups correctly, find medians, and predict how changes to the data affect each measure.
Start sample lessonProbability and counting: choose the right total
Find probabilities from counts, use the opposite event, handle draws without replacement, and count allowed combinations.
Start sample lessonTables and proportional relationships
Test whether a table is proportional, extend it with a constant of proportionality, read cumulative tables, and compare rates fairly.
Start sample lessonLinear functions: slope, intercepts and rates
Find slope from two points, write y = mx + b from a point or a story, and find intercepts and values.
Start sample lessonRates, unit conversions and average speed
Scale a rate to a new amount, convert minutes to hours, combine rates for teamwork and chases, and find average speed correctly.
Start sample lessonPercent change: know your base
Chain discounts, taxes and increases with multipliers, work backward to an earlier amount, and find percent change from the right base.
Start sample lessonExpressions: distribute, combine and model
Simplify expressions with parentheses and negative signs, evaluate them with negative numbers, and write expressions from word descriptions.
Start sample lessonSystems of linear equations
Solve systems by substitution or elimination, tell how many solutions a system has, and answer the exact quantity a question asks for.
Start sample lessonExponent rules and scientific notation
Use the product, quotient and power rules, handle zero and negative exponents, and compute with numbers in scientific notation.
Start sample lessonSquare roots and the Pythagorean theorem
Find missing sides of right triangles, distances between points, and estimates or simplified forms of square roots.
Start sample lessonTransformations and similar figures
Apply translations, reflections, rotations and dilations to coordinates, and scale perimeters and areas of similar figures.
Start sample lessonVolume of cylinders, cones and spheres
Find volumes of cylinders, cones and spheres in terms of π or with a given value of π, and predict how changing the radius or height changes the volume.
Start sample lessonScatter plots and lines of fit
Use a line of fit to make predictions, compare observed and predicted values, interpret slope, and judge which claims a model supports.
Start sample lesson