Every lesson, before you buy

A 10-minute briefing before your diagnostic. Pax walks you through the diagnostic's section timings and a pacing plan on the board, turns your target score into how many questions you can miss per section, and shows you how to start the timed diagnostic in the app. You take the diagnostic on your own after the session. The diagnostic itself is a short, timed sample (about 50 questions across English, Math, Reading, and Science) that sets a baseline. A full-length sitting is longer: English, Math, and Reading total 131 questions, and the optional Science section brings it to 171.

Build a solid grammar foundation: find the subject and verb and make them agree, tell independent clauses from dependent ones, and apply the verb tense rules the ACT tests most often. You also learn the first move for every English question: see what changes across the four choices.

• First move on every English item: look down the four choices, say what changes from one to the next, and name the error family it belongs to (sentence boundaries and punctuation, things that must match, clarity and meaning, or economy)
• Find the subject and the main verb of any sentence, even when long phrases separate them, and make the verb agree with that subject: in 'Each of the volunteers has signed' the subject is 'each' (singular), and the prepositional phrase 'of the volunteers' is never the subject
• Tell independent from dependent clauses, and recognize simple, compound, and complex sentences and how structure errors appear on the ACT

Review the number skills that appear throughout ACT Math: order of operations, converting between fractions, decimals, and percents, arithmetic with negative fractions, and exact number words such as prime, factor, and consecutive.

• Apply order of operations (PEMDAS) accurately in multi-step problems
• Convert between fractions, decimals, and percentages fluently
• Read number words exactly (integer, digit, distinct, consecutive, prime, factor and multiple, remainder, inclusive, even and odd) and use them to find greatest common factors and least common multiples

Work through one short passage on screen with a light active reading routine, and learn to answer the three most basic question types on it: main idea, summary, and key detail.

• Preview before reading: glance at the questions, mark line references and key terms, then pick a reading mode (a quick 2 to 3 minute skim, or reading chunk by chunk as the questions send you) and keep a one-line note per paragraph
• Key detail questions first: go back to the text and point to the line that proves the answer before locking it
• Summary questions: pick the choice that covers the whole paragraph or passage, and name the reason each wrong choice fails (not stated, too narrow, distorted detail, extreme wording)

Optional: only for students taking the Science section. Learn to read and interpret the graphs, tables, and charts that form the backbone of ACT Science passages.

• Read and interpret line graphs, bar charts, scatter plots, and data tables
• Identify independent and dependent variables in experiments
• Recognize trends, direct relationships, and inverse relationships in data

Master subject-verb agreement, one of the most frequently tested concepts on the ACT English section, including tricky cases with intervening phrases and compound subjects. Finish with two quick usage rules: adjective vs. adverb and comparative vs. superlative.

• Match singular subjects with singular verbs and plural subjects with plural verbs
• Identify the true subject when prepositional phrases or relative clauses intervene
• Handle compound subjects joined by 'and,' 'or,' and 'nor', and inverted sentences where the subject follows the verb

Review percentages, ratios, and proportions (high-frequency ACT topics) and practice modeling: turning a word problem into an equation, including rates and unit conversions. More on rates and units in the Scientific Notation and Rates lesson.

• Convert between fractions, decimals, and percentages and calculate percent increase and decrease, including two changes in a row
• Set up and solve proportion equations (cross-multiplication)
• Translate ratio word problems into algebraic expressions

Learn the rules for pronoun-antecedent agreement and clear pronoun reference, two of the ACT's favorite grammar traps.

• Match pronouns with their antecedents in number, including indefinite pronouns (each, everyone, nobody) and collective nouns (team, company)
• Identify and fix ambiguous or vague references (a pronoun that could point to two nouns, or a this/it/which with no clear referent) and keep person consistent (one/you)
• Write possessives correctly: singular (student's), plural (students'), irregular plural (children's), -y words (company's, companies'), and possessive pronouns with no apostrophe (its, whose, their), including its/it's, their/they're, and whose/who's

Master solving linear equations, linear inequalities, and absolute value equations, the most common algebra question types on the ACT. More on inequalities in the Absolute Value Inequalities lesson.

• Solve one-variable linear equations, including ones with variables on both sides, parentheses, and fractions
• Solve a linear inequality, flipping the sign when multiplying or dividing by a negative, show it on a number line, and translate 'at most' as ≤ and 'at least' as ≥
• Solve absolute value equations by splitting |ax + b| = c into two cases, and recognize when there is no solution

Learn the punctuation the ACT tests most heavily: how to join two clauses correctly, the four comma rules, and when a comma does not belong. Apostrophes, colons, and dashes continue in the Apostrophes, Colons, and Dashes lesson.

• Use the boundary test on marks that join or introduce: split the sentence at a period, semicolon, colon, single dash, or comma + FANBOYS and ask whether each side is a complete thought (period, semicolon, comma + FANBOYS need two complete sides). Commas inside one clause are not judged by this test; they need a named reason
• Spot a comma splice (two independent clauses joined by only a comma) and fix it
• Apply the comma rules the ACT tests (lists, introductory elements, nonessential information, compound sentences) and the no-comma rules, give every comma a reason you can name, and run a quick removable-or-not round before placing commas

Learn substitution and elimination methods for solving systems of linear equations, a frequently tested ACT Math topic.

• Solve systems of two equations using substitution
• Solve systems of two equations using elimination (addition/subtraction method)
• Interpret systems of equations in word problem contexts

Develop strategies for the literary narrative passage, which focuses on characters, relationships, tone, and narrative voice.

• Identify the narrator's point of view (first person, third person limited, omniscient)
• Track character emotions, motivations, and relationships throughout the passage
• Answer tone questions: name the narrator's attitude in one word, and say what a descriptive detail or a line of dialogue reveals about a character

Identify and fix sentence fragments, run-on sentences, parallelism errors, and misplaced or dangling modifiers, four structural issues the ACT tests repeatedly.

• Recognize sentence fragments in a quick complete-or-incomplete round of about ten short sentences, including long ones with no main verb and short ones that are complete
• Identify and correct run-on sentences and comma splices, using the same split-at-the-mark test as the Commas and Semicolons lesson
• Apply parallel structure to the items in a list or series

A short oral retrieval round on Week 2: six questions, two each for English, Math, and Reading, each shown on screen. Pax then names the weakest area and says which earlier lesson to revisit. The timed quiz happens in the app after the session, not during it.

• Run a six-question oral retrieval round, one question at a time, each shown on screen: two English, two Math, two Reading, all from Days 8 to 13
• English pair: one pronoun or punctuation item and one sentence structure item (fragment, run-on, parallelism, or modifier)
• Math pair: one linear equation or inequality and one system of two equations, preceded by a quick 'which tool fits?' round of three unscored items where the student names only the first move (algebra, Pick a Number, or Middle Choice First) without solving. Do not quiz graphing lines, which is not taught until Day 22

Learn how the ACT tests logical transitions between sentences and paragraphs, and how to answer organization/ordering questions.

• Identify the logical relationship between sentences (contrast, cause-effect, addition, example)
• Choose the correct transition word or phrase for a given context, including formal connectors (moreover, conversely, nonetheless, accordingly, likewise)
• Answer sentence-placement and paragraph-ordering questions

Learn to factor quadratics, use the quadratic formula, and solve quadratic equations, a high-frequency ACT Math topic. More on algebraic expressions in the Polynomials and Radicals lesson.

• Factor quadratic expressions of the form ax² + bx + c
• Solve quadratic equations by factoring and setting each factor to zero
• Apply the quadratic formula x = (−b ± √(b² − 4ac)) / 2a, and use the discriminant b² − 4ac to count the real solutions

Learn to identify and eliminate redundancy and wordiness, a skill the ACT English section tests again and again.

• Recognize redundant phrases (e.g., 'past history,' 'return back,' 'true fact')
• Choose the most concise answer that preserves meaning
• Distinguish between necessary detail and unnecessary wordiness

Understand function notation, domain and range, composition, and how the ACT tests function concepts.

• Evaluate f(x) for given values and expressions
• Determine domain and range from equations and graphs
• Perform function composition: (f ∘ g)(x) = f(g(x))

Develop strategies for social science passages, which present research findings, theories, and data from fields like psychology, economics, and political science.

• Identify the main argument or thesis in a social science passage
• Distinguish between facts, opinions, and research findings
• Interpret data references within the passage text

Optional: only for students taking the Science section. Learn to analyze experiment-based science passages, which describe experimental setups, variables, controls, and results.

• Identify the independent variable, dependent variable, and controlled variables in an experiment
• Understand the purpose of a control group
• Compare results across multiple experiments within a passage

A short oral retrieval round on Week 3: six questions, two each for English, Math, and Reading, each shown on screen. Pax then names the weakest area and says which earlier lesson to revisit. The timed quiz happens in the app after the session, not during it.

• Run a six-question oral retrieval round, one question at a time, each shown on screen: two English, two Math, two Reading, all from Days 15 to 19
• English pair: one transition or sentence-placement item and one conciseness item
• Math pair: one quadratic (factor and solve, or use the discriminant) and one function item (evaluate f(x) or a composition)

Master the coordinate plane concepts tested on the ACT: slope, the equation of a line, distance, midpoint, and parallel and perpendicular lines.

• Find and use slope: read it from y = mx + b, compute it from two points, and use equal slopes for parallel lines and negative reciprocal slopes for perpendicular lines
• Calculate the distance between two points and the midpoint of a segment
• Write and graph the equation of a line from two points or from a slope and a point, and find its x- and y-intercepts

Review the essential plane geometry facts for angle relationships, triangles (including the two special right triangles), and the area and circumference of a circle.

• Solve problems involving supplementary, complementary, and vertical angles
• Apply the triangle angle sum (180°) and the exterior angle theorem, and find a triangle's area with 1/2 × base × height
• Use the Pythagorean theorem and recognize special right triangles (30-60-90, 45-45-90)

Develop strategies for humanities passages (art, architecture, music, philosophy, personal essays), and learn two question types they feature heavily: the function of a paragraph within the passage's structure, and inference.

• Recognize the structure of humanities passages (often personal or reflective) and track how the author's perspective evolves
• Answer author's purpose questions and separate the author's views from those of people the author describes
• Text structure: name the job a paragraph does (introduce, give an example, concede, shift, conclude) and how the passage is organized overall

Tackle natural science passages, which present scientific topics in a way that tests reading comprehension, not science knowledge.

• Identify the main scientific concept or finding being discussed, including findings given as data in the prose
• Follow the logical structure of a scientific argument or process
• Answer detail and cause-and-effect questions by finding the line that states them, scanning for scientific terms and definitions

Learn to answer ACT English questions about word choice, tone, and style: pick the word that fits the passage's tone, audience, and meaning. The lesson opens with a quick spoken recall of percent change and inference.

• Retrieval warm-up (about 3 minutes, before new material): two quick spoken recall questions from earlier in Week 4, one on percent change (Percentages and Ratios) and one on making an inference (Humanities Passages)
• Choose words that match the passage's tone (formal vs. informal, serious vs. humorous) and its intended audience
• Select the most precise word for a given context, and handle the few confusable pairs the ACT really tests (its/it's, their/they're/there, fewer/less)

Learn the trigonometric ratios (SOH-CAH-TOA), radian measure, the two basic identities, and how right-triangle trigonometry appears on the ACT.

• Use SOH-CAH-TOA to find missing sides and angles in right triangles, including angle of elevation and depression problems
• Convert between degrees and radians, and rebuild unit-circle values from the 30-60-90 and 45-45-90 triangles plus the quadrant signs
• Apply sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ, and substitute into the Law of Sines or Law of Cosines when a question prints it

A 10-minute briefing before Practice Test #1. Pax walks you through the section timings and a pacing plan on the board, sets one goal per section, and shows you how to start the timed test in the app. You take the full-length timed test on your own after the session.

A review of your first practice test. Pax looks at your section scores and the three question types you missed most, reworks one problem of each type on the board with you, and finishes with a 3-item priority list for the coming week.

Master the statistics and probability basics the ACT tests most: mean, median, mode, range, weighted averages, simple probability, and two-way tables. Data displays, the line of best fit, expected value, and Venn diagrams follow in the Graphs and Data lesson.

• Calculate mean, median, mode, and range, and solve weighted average problems
• Calculate probability: favorable over total when outcomes are equally likely, the complement rule P(not A) = 1 − P(A), and P(A and B) = P(A) × P(B) for independent events
• Read a probability off a two-way frequency table (the row/column count divided by the relevant total), including a conditional probability ('given that' means divide by that row or column's total), and use a random sample to estimate a population (a survey proportion, tag and recapture) and spot a biased sample

Tackle the exponent, logarithm, and exponential growth topics that appear in the harder half of the ACT Math section. More on growth patterns in the Sequences lesson.

• Apply exponent rules (product, quotient, power, negative, and zero exponents)
• Interpret rational exponents as roots: x^(1/n) = the nth root of x, and x^(m/n) = the nth root of x^m
• Understand logarithms as the inverse of exponents: log_b(x) = y means b^y = x

Optional: only for students taking the Science section. Learn to analyze conflicting viewpoints passages, which present two or more scientists or students with different explanations for the same phenomenon.

• Identify each scientist's or student's main claim and supporting evidence
• Determine where the viewpoints agree and disagree
• Answer questions that ask which evidence would strengthen or weaken a viewpoint

Master the 'big picture' English questions that ask about the purpose, effectiveness, and strategy of the passage as a whole.

• Use a four-step routine on goal, add, delete, and revise questions: find the goal in the question, reread the paragraph and what comes next, reject each choice with a stated reason (off topic, too narrow, does not lead into what follows, repeats, wrong tone), and on Yes/No items test each reason clause by itself
• Evaluate whether the essay or a detail meets a stated goal, including why the author included a detail and whom the writing is for
• Choose the best introduction, transition between paragraphs, or conclusion, rejecting choices that are true but too specific

Practice two skills from the ACT Reading category Integration of Knowledge and Ideas: evaluating the evidence behind an argument and comparing paired passages. Reading a chart or table alongside a passage continues in the Charts and Tables lesson.

• Evaluate an argument: find the claim, list the evidence offered, and judge whether that evidence actually supports the claim
• Compare paired passages in order: read and answer Passage A, then Passage B, then the questions about both
• Describe how two authors relate: they agree, they disagree, or one qualifies the other's view

A short oral retrieval round on Week 5: six questions, two each for English, Math, and Reading, each shown on screen. Pax then names the weakest area and says which earlier lesson to revisit. The timed quiz happens in the app after the session, not during it.

• Run a six-question oral retrieval round, one question at a time, each shown on screen: two English, two Math, two Reading, all from Days 30 to 34
• English pair: one 'does the essay accomplish this goal' item and one add/delete relevance item
• Math pair: one statistics or probability item and one exponent, logarithm, or exponential growth item

A think-aloud sprint for English speed. Pax shows one item at a time, and you name the question type and the first move within about 10 seconds, without fully solving. Then a pacing debrief against the real section: 50 questions in 35 minutes, about 42 seconds per question. The full timed section is assigned in the practice area afterwards.

• Run a think-aloud sprint of 8 to 10 English items, shown one at a time on screen
• For each item, the student first says what changes across the four choices, then names the question type and the first move within about 10 seconds, without fully solving
• Correct any mislabeled type on the spot with the one-line cue for that type

A think-aloud sprint for Math speed. Pax shows one item at a time, and you name the question type and the first move within about 10 seconds, without fully solving, including whether a calculator would help or hurt. Then a pacing debrief against the real section: 45 questions in 50 minutes, four answer choices, about 67 seconds per question. The full timed section is assigned in the practice area afterwards.

• Run a think-aloud sprint of 8 to 10 Math items, shown one at a time on screen, mixing the types (systems, quadratics, functions, triangles, circles, percentages, probability) and ending with two or three from the hard end of the section, such as logarithms or matrices
• For each item, the student names the question type and the first move within about 10 seconds, without fully solving
• For each item, the student says whether a calculator helps (messy arithmetic) or hurts (algebra that is faster by hand), and whether backsolving from the four choices is the faster first move

A think-aloud sprint for Reading speed. Pax shows one question stem at a time (with a short excerpt when needed), and you name the question type and the first move within about 10 seconds, without fully solving. Then a pacing debrief against the real section: 36 questions in 40 minutes, four passages of 9 questions, about 10 minutes per passage. The full timed section is assigned in the practice area afterwards.

• Run a think-aloud sprint of 8 to 10 Reading question stems, shown one at a time on screen with a short excerpt when needed
• For each stem, the student names the question type and the first move (where in the passage to look) within about 10 seconds, without fully solving
• Sort the types into 'fast' (key detail, vocabulary in context) and 'slow' (inference, paragraph function, paired comparison) and agree to answer the fast ones first within a passage

Optional: only for students taking the Science section. A think-aloud sprint for Science speed. Pax shows one item at a time (a small table or graph with a question), and you name the passage type, the question type, and the first move within about 10 seconds, without fully solving. Then a pacing debrief against the real section: 40 questions in 40 minutes. The full timed drill is assigned in the practice area afterwards.

• Run a think-aloud sprint of 8 to 10 Science items, shown one at a time on screen with their table, graph, or short text
• For each item, the student names the passage type (Data Representation, Research Summaries, or Conflicting Viewpoints), the question type, and the first move within about 10 seconds, without fully solving
• Practice the first move of going to the figure or table before the text on data passages, and reading the text carefully on Conflicting Viewpoints

A light tune-up the day before a practice test. Pax runs a short English warm-up of five on-screen items, gives one pacing reminder, and finishes with a confidence check. Nothing new is taught; the goal is freshness, not drilling.

• Run a light English warm-up of 5 on-screen items, one at a time: a verb item (subject-verb agreement, or past vs. past perfect), joining clauses or commas, a transition, a conciseness item, and a pronoun item
• For each item, the student answers and names the rule in one sentence; Pax fixes any miss in one or two sentences
• Give ONE pacing reminder for tomorrow: check the clock at the agreed checkpoints, and when a question stalls, guess, mark it, and move on

A 10-minute briefing before your next practice test. Pax walks you through the section timings and the pacing plan on the board, sets one goal per section based on what went wrong in your previous practice test, and shows you how to start the timed test in the app. You take the full-length timed test on your own after the session.

A review of the practice test you just took. Pax looks at your section scores and the three question types you missed most, compares them with your previous practice test, reworks one problem of each type on the board with you, and finishes with a 3-item priority list for the days ahead.

A targeted review of your recorded weak areas: one worked problem per weak area, then one test-day strategy per section. This is the last day of new practice before the final review.

• Pull up the student's recorded weak areas (the 3-item priority list from the latest practice test review and the weak areas Pax already knows) and confirm the top three with the student
• Work one problem per weak area on the board, with the student doing the steps aloud
• After each problem, have the student state the rule or formula in one sentence

The final light review before test day. Pax builds a quick formula and rule recap on the board with you, runs four trap-spotting items, locks in your pacing plan, and sorts out test day logistics. Tomorrow is a rest day.

• Build a quick formula and rule recap on the board together: Pax names each one and the student supplies it (slope, distance, midpoint, quadratic formula, SOH-CAH-TOA, circle area and circumference; joining clauses, comma rules, subject-verb agreement, pronoun reference)
• Answer 4 on-screen trap-spotting items, one at a time: one English, one Math, one Reading, and a fourth from Science if the student is taking it, otherwise from the student's weakest section. For each, name the trap in the tempting wrong answer
• Review the student's own pacing plan and error budget for each section one final time

The day before the test. Rest your mind and body and trust your preparation. At most a brief look back at the formula and rule recap from your final review, a final logistics check, then relaxation and a normal bedtime.

• Limit studying to a brief (10-minute) look back at the formula and rule recap from the final review, with no practice questions
• Do the final logistics check: ID, ticket, calculator, route, alarm
• Use relaxation techniques: deep breathing, visualization, light exercise