# Digital SAT Flashcards: Math, Grammar & Words in Context ![An open study book surrounded by punctuation marks, a coordinate graph, a right triangle, a circle, and a data chart\.]() Practice Digital SAT math formulas, grammar rules, transitions, and words in context with original, installable flashcards built for active recall\. By author [Open Study Contributor]() [Study this deck for free]() Nibomo opens so you can start studying\. ## Deck details - Cards: 300 cards - Version: 1 - Published: September 1, 2026 - Last updated: September 10, 2026 - License: Common knowledge · CC0 1\.0 - Audience languages: [en]() - Subject: General aptitude - Level: Digital SAT - Tags: digital\-sat, rw, math ## About this deck ### Digital SAT Flashcards: Math, Grammar & Words in Context Practice the recall-worthy foundations behind all eight current SAT content domains: math formulas and setup cues, grammar and punctuation rules, transition logic, rhetorical choices, evidence checks, and high-utility words used in original sentence contexts. The 300 cards are ready to install and review offline. #### What the cards practice The deck maps short rule or task cues to a rule, distinction, formula, or setup. Original sentence contexts map to tested word meanings and grammar decisions. Original transition microcontexts name each transition and ask for the relationship it signals. Selected representation-to-interpretation prompts cover ideas such as slope as a rate of change and a residual as actual minus predicted. A few reverse prompts are included when recall in both directions prevents a common setup error. #### What is deliberately left out This is not a bank of SAT questions. It leaves out full passages, timed-test simulation, answer-choice elimination drills, copied questions, answer keys, mark schemes, official diagrams, arbitrary vocabulary lists, formula-symbol permutations, and automatic reversal of every fact. Use College Board's official practice for full reasoning, timing, and the adaptive test experience. #### Coverage and learning order Reading and Writing covers Information and Ideas, Craft and Structure, Expression of Ideas, and Standard English Conventions. Math covers Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. The 15 transition microcontexts stay in their fixed Expression of Ideas slots. Prerequisites appear before dependent ideas inside each topic. Related variants are separated by unrelated cards, while long-term spacing and interleaving stay with the review scheduler. #### Scope, provenance, and reuse The current College Board assessment framework and content-domain pages were used only as a scope and fact-check map. The prompts, answers, microcontexts, examples, selection, organization, sequence, metadata, and generated cover are independently written. Public pages from three current study tools were reviewed only to compare learner expectations; no competitor cards or examples were copied. The `Common knowledge · CC0 1.0` label applies to the original wording, examples, organization, metadata, and generated cover to the extent applicable rights exist. It does not claim ownership of mathematical facts, grammar rules, SAT domain names, College Board names, or third-party source material. Source review date: September 1, 2026. This deck is independent and unofficial. It is not affiliated with, endorsed by, or approved by College Board. No exam questions, mark schemes, or official specifications text were copied; see [College Board's official SAT content requirements](https://satsuite.collegeboard.org/higher-ed-professionals/sat-validity/content-domains). ## Similar decks - [ASVAB Flashcards: Verbal, Math, Science & Technical Review]() - [Academic Vocabulary Flashcards: 300 Words in Context]() - [FE Exam Flashcards: Engineering Equations, Units & Handbook Skills]() - [Spanish Preterite vs\. Imperfect Flashcards: Tense Choice in Context]() - [Spanish A1 Vocabulary Flashcards: Beginner Words & Phrases]() - [GRE Vocabulary Flashcards: 300 Words with Definitions & Examples]() ## Cards in this deck ### Card 1 **Question** Central idea of a passage? **Answer** The passage's main claim or controlling point. It should cover the whole passage, not one striking detail. ### Card 2 **Question** The shade trees mitigated the midday heat. Meaning of “mitigated”? **Answer** Reduced. The trees made the heat less severe. ### Card 3 **Question** The first plan was affordable. However, it took twice as long. What relationship does “However” signal? **Answer** Contrast. The second statement differs from or qualifies the first. ### Card 4 **Question** Three standard joins for two independent clauses? **Answer** A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence. ### Card 5 **Question** Best supporting detail? **Answer** The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is. ### Card 6 **Question** A second archive corroborated the diary's date. Meaning of “corroborated”? **Answer** Confirmed with supporting evidence. ### Card 7 **Question** Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal? **Answer** Conclusion from a reason. The final statement follows logically from the stated premises. ### Card 8 **Question** Introductory dependent clause before a main clause? **Answer** Use a comma after the dependent clause. Example: “Although rain fell, the match continued.” ### Card 9 **Question** Valid inference? **Answer** A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports. ### Card 10 **Question** The team called its result tentative until replication. Meaning of “tentative”? **Answer** Provisional or not yet certain. ### Card 11 **Question** Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal? **Answer** Illustration. The second statement gives a specific case of the broader point. ### Card 12 **Question** Singular subject with an intervening prepositional phrase? **Answer** Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject. ### Card 13 **Question** Strongest textual evidence? **Answer** The quotation or detail that most directly supports the target claim, with the fewest extra assumptions. ### Card 14 **Question** The error had a negligible effect on the total. Meaning of “negligible”? **Answer** So small that it is not important. ### Card 15 **Question** The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal? **Answer** Similarity. The second statement matches the first in a relevant way. ### Card 16 **Question** Opening modifier placement? **Answer** Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.” ### Card 17 **Question** Quantitative evidence for a claim? **Answer** Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline. ### Card 18 **Question** The lab used a conventional method before testing a new one. Meaning of “conventional”? **Answer** Traditional or commonly accepted. ### Card 19 **Question** Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal? **Answer** Simultaneous events. The second event happens at the same time as the first. ### Card 20 **Question** Singular possessive noun? **Answer** Usually add apostrophe + s. Example: “the scientist's notebook.” ### Card 21 **Question** Trend in a table or graph? **Answer** State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence. ### Card 22 **Question** The essay offered a novel explanation for the pattern. Meaning of “novel”? **Answer** New or original in this context. ### Card 23 **Question** The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal? **Answer** Concession. The second statement remains true despite the limitation in the first. ### Card 24 **Question** Parallel items in a series? **Answer** Use the same grammatical form for each item. Example: “to collect, analyze, and report data.” ### Card 25 **Question** Claim stronger than the evidence? **Answer** Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion. ### Card 26 **Question** Her account is plausible because it matches the records. Meaning of “plausible”? **Answer** Reasonable or believable. ### Card 27 **Question** The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal? **Answer** Addition. The second statement adds a related supporting point. ### Card 28 **Question** Colon before an explanation or list? **Answer** Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.” ### Card 29 **Question** Claim versus evidence? **Answer** A claim is the point being argued; evidence is the information used to support it. ### Card 30 **Question** The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”? **Answer** Open to more than one interpretation. ### Card 31 **Question** The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal? **Answer** Replacement. The second statement substitutes one action for another. ### Card 32 **Question** Count nouns versus mass nouns? **Answer** Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise. ### Card 33 **Question** Effect of a counterexample? **Answer** It weakens a universal claim by showing at least one case where the claim fails. ### Card 34 **Question** Rainfall was sporadic: brief showers interrupted long dry periods. Meaning of “sporadic”? **Answer** Irregular and occasional. ### Card 35 **Question** The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal? **Answer** Later step in a sequence. The second event occurs after the first. ### Card 36 **Question** Essential clause punctuation? **Answer** Do not surround an essential clause with commas. It identifies which person or thing the sentence means. ### Card 37 **Question** Correlation alone proves causation? **Answer** No. A relationship between variables does not by itself show that one caused the other. ### Card 38 **Question** Subsequent trials produced the same result. Meaning of “subsequent”? **Answer** Coming later in time. ### Card 39 **Question** The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal? **Answer** Restatement for clarity. The second statement rephrases the first. ### Card 40 **Question** Verb tense across a paragraph? **Answer** Keep the time frame consistent unless the timing actually changes. ### Card 41 **Question** Missing information in a data claim? **Answer** Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim. ### Card 42 **Question** The coating helps the fabric retain heat. Meaning of “retain”? **Answer** Keep or continue to hold. ### Card 43 **Question** The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal? **Answer** General-to-specific detail. The second statement narrows the broad first statement. ### Card 44 **Question** Coordinate adjectives? **Answer** Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.” ### Card 45 **Question** Two sources on the same event? **Answer** Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement. ### Card 46 **Question** The survey was designed to elicit candid responses. Meaning of “elicit”? **Answer** Draw out or bring forth. ### Card 47 **Question** Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal? **Answer** Cause and effect. The second statement is an outcome of the first. ### Card 48 **Question** Sentence fragment? **Answer** A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb. ### Card 49 **Question** Inference from a narrow sample? **Answer** Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence. ### Card 50 **Question** Cost was the main constraint on the project. Meaning of “constraint”? **Answer** A limit or restriction. ### Card 51 **Question** Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal? **Answer** Overall conclusion. The second statement gives the final judgment after earlier considerations. ### Card 52 **Question** Conjunctive adverb between independent clauses? **Answer** Use a semicolon before it and a comma after it. Example: “The route was longer; however, it was safer.” ### Card 53 **Question** Most accurate summary? **Answer** State the central idea and its essential support without adding opinions or minor details. ### Card 54 **Question** The review was comprehensive, covering every recorded case. Meaning of “comprehensive”? **Answer** Complete and wide-ranging. ### Card 55 **Question** The method is efficient. Indeed, it cuts processing time in half. What relationship does “Indeed” signal? **Answer** Emphasis and confirmation. The second statement reinforces the first with a stronger detail. ### Card 56 **Question** Who versus whom? **Answer** Use “who” as a subject and “whom” as an object. Test with he/him: “whom” matches “him.” ### Card 57 **Question** Evidence that best resolves a disagreement? **Answer** Choose evidence that tests the specific point on which the sources differ, not a fact both already accept. ### Card 58 **Question** The two materials have distinct properties. Meaning of “distinct”? **Answer** Clearly different or separate. ### Card 59 **Question** The forecast warned of rain. Still, the outdoor concert began on time. What relationship does “Still” signal? **Answer** Concession. The second statement remains true despite the obstacle in the first. ### Card 60 **Question** Comma before an introduced direct quotation? **Answer** Use a comma after a speech tag. Example: “Mina wrote, ‘The sample is ready.’” ### Card 61 **Question** The conclusion was qualified by two important exceptions. Meaning of “qualified”? **Answer** Limited or modified, rather than stated without conditions. ### Card 62 **Question** Notes for a synthesis goal? **Answer** Use only facts that directly serve the stated goal. Relevant notes can be omitted if they do not help that purpose. ### Card 63 **Question** Comma splice? **Answer** Two independent clauses joined only by a comma. Replace it with a period or semicolon, or add a coordinating conjunction. ### Card 64 **Question** Comma between subject and verb? **Answer** Do not use one unless an interrupting phrase requires paired commas. “The results of the trial were clear” takes no comma after “trial.” ### Card 65 **Question** The new sensor made the older model obsolete. Meaning of “obsolete”? **Answer** No longer useful or current because something newer replaced it. ### Card 66 **Question** Source attribution in a synthesis? **Answer** Name the source when its identity, authority, or perspective matters to the rhetorical goal. ### Card 67 **Question** Compound subject joined by “and”? **Answer** Use a plural verb in the usual case. Example: “The map and the notes are useful.” ### Card 68 **Question** Dangling opening modifier? **Answer** It lacks the intended doer immediately after the modifier. Rewrite so the doer becomes the subject. ### Card 69 **Question** Researchers derived the estimate from three measurements. Meaning of “derived”? **Answer** Obtained from a source or calculation. ### Card 70 **Question** Chronological synthesis? **Answer** Order events by time and use dates or sequence words only when they help the reader follow the progression. ### Card 71 **Question** Plural noun ending in s: possessive form? **Answer** Add an apostrophe after the existing s. Example: “the researchers' notes.” ### Card 72 **Question** Logical comparison? **Answer** Compare like with like. Example: compare one city's rainfall with another city's rainfall, not with the city itself. ### Card 73 **Question** The article advocates preserving the wetland. Meaning of “advocates”? **Answer** Publicly supports or argues for. ### Card 74 **Question** Compare evidence from two studies? **Answer** State the shared measure first, then the relevant difference in result, method, or population. ### Card 75 **Question** Colon after an incomplete lead-in? **Answer** Do not use one. A colon must follow a complete clause, so “The reasons include:” is incorrect. ### Card 76 **Question** Number versus amount? **Answer** Use “number” for countable items and “amount” for uncountable quantities. Example: number of files, amount of water. ### Card 77 **Question** Portable chargers are now ubiquitous on long trips. Meaning of “ubiquitous”? **Answer** Present or found almost everywhere. ### Card 78 **Question** Synthesis that emphasizes a difference? **Answer** Use the same comparison point for both subjects, then state the contrast directly. ### Card 79 **Question** Nonessential clause or phrase? **Answer** Set it off with paired commas. The sentence should keep its core identity and meaning when the phrase is removed. ### Card 80 **Question** Earlier of two past actions? **Answer** Use past perfect when the sequence needs clarification. Example: “The team had left before the storm began.” ### Card 81 **Question** Sentence 2 presents an exception to sentence 1. Its function? **Answer** It qualifies the first claim by limiting when or how broadly it applies. ### Card 82 **Question** Rhetorical goal: define a term? **Answer** Give the term's relevant meaning before using details or examples that depend on it. ### Card 83 **Question** Cumulative adjectives? **Answer** Do not separate them with a comma when each adjective builds on the next. Example: “three small glass jars.” ### Card 84 **Question** Run-on sentence? **Answer** Independent clauses joined without valid punctuation or a conjunction. Add a period, semicolon, or comma plus coordinating conjunction. ### Card 85 **Question** Sentence 2 gives a specific case after a general claim. Its function? **Answer** It illustrates the claim with an example. ### Card 86 **Question** Introduce a quotation in a synthesis? **Answer** Give enough source and context to show why the quotation matters; do not leave it unattached. ### Card 87 **Question** Relative pronoun for people? **Answer** Use “who” or “whom,” depending on case. Example: “the engineer who designed the bridge.” ### Card 88 **Question** Integrated quotation punctuation? **Answer** Do not add a comma when the quotation completes the grammar of the sentence. Example: The report calls the result “unexpected.” ### Card 89 **Question** Sentence 2 admits a limitation before defending the claim. Its function? **Answer** It makes a concession, showing that the writer recognizes a complication. ### Card 90 **Question** Avoid redundancy in synthesis? **Answer** State each needed idea once. Prefer the version that preserves meaning with fewer repeated words. ### Card 91 **Question** Semicolon between two independent clauses? **Answer** Use it without a coordinating conjunction when the ideas are closely related. Example: “The trial ended; the analysis began.” ### Card 92 **Question** Comma in a compound predicate? **Answer** Usually omit it when one subject performs both actions. Example: “The team collected the samples and recorded the temperature.” ### Card 93 **Question** Sentence 2 explains what a technical term means. Its function? **Answer** It defines or clarifies the term. ### Card 94 **Question** Combine two related sentences? **Answer** Make the logical relationship explicit and remove repeated material without changing the facts. ### Card 95 **Question** Either/or subject agreement? **Answer** Make the verb agree with the nearer subject. Example: “Either the notes or the map is missing.” ### Card 96 **Question** Active versus passive voice? **Answer** Choose the voice that fits the focus. Active highlights the doer; passive can highlight the action or receiver. ### Card 97 **Question** Sentence 2 describes the outcome of sentence 1. Its function? **Answer** It presents an effect or consequence. ### Card 98 **Question** Formal academic register? **Answer** Use precise, neutral wording and avoid slang, vague intensifiers, and chatty asides unless the goal calls for them. ### Card 99 **Question** Its or it's? **Answer** “Its” is possessive; “it's” means “it is” or “it has.” ### Card 100 **Question** Adjective versus adverb? **Answer** An adjective modifies a noun; an adverb usually modifies a verb, adjective, or adverb. Example: a careful test; test carefully. ### Card 101 **Question** A study reports a result without arguing for a policy. Author's purpose? **Answer** To inform or explain, not necessarily to persuade. ### Card 102 **Question** Concise synthesis? **Answer** Keep every fact needed for the rhetorical goal and remove details that repeat or distract from it. ### Card 103 **Question** Single dash for emphasis? **Answer** Use it after a complete thought to spotlight a final explanation or turn. Example: “One result stood out—the oldest sample.” ### Card 104 **Question** Comma with direct address? **Answer** Set off the person being addressed. Example: “Rina, please check the units.” ### Card 105 **Question** Why acknowledge a limitation? **Answer** To define the claim's boundary and show how the evidence should be interpreted. ### Card 106 **Question** Quantitative comparison in a synthesis? **Answer** Name both values, the shared unit, and the direction or size of the difference. ### Card 107 **Question** Each of the samples: verb number? **Answer** Singular. “Each of the samples was labeled.” The subject is “each.” ### Card 108 **Question** Between versus among? **Answer** Use “between” for distinct individual relationships and “among” for a group without separate pairings. ### Card 109 **Question** Rhetorical question in an argument? **Answer** It can frame the issue or prompt the reader to consider an implied answer; it is not evidence by itself. ### Card 110 **Question** Claim before or after support? **Answer** Place it where the rhetorical goal is clearest: before evidence for a direct point, or after evidence for an evidence-led conclusion. ### Card 111 **Question** Restrictive “that” versus nonrestrictive “which”? **Answer** Use “that” without commas for essential information; use “which” with commas for removable information. ### Card 112 **Question** Present perfect use? **Answer** Use it for an action connected to the present or continuing to now. Example: “The team has tracked rainfall since May.” ### Card 113 **Question** Two texts reach the same conclusion with different evidence. Relationship? **Answer** They agree in conclusion but support it through different evidence. ### Card 114 **Question** Group related ideas in a synthesis? **Answer** Keep facts serving the same point together, then signal the move to a new point. ### Card 115 **Question** Compound modifier before a noun? **Answer** Hyphenate it when needed for clarity. Example: “a well-designed study.” ### Card 116 **Question** Affect or effect? **Answer** “Affect” is usually a verb meaning influence; “effect” is usually a noun meaning result. ### Card 117 **Question** Two texts offer incompatible explanations. Relationship? **Answer** They disagree about the cause or interpretation, even if they share the same observations. ### Card 118 **Question** Replace a vague pronoun in synthesis? **Answer** Use the precise noun when two or more possible antecedents could confuse the reader. ### Card 119 **Question** Comma-separated list? **Answer** Use commas between three or more parallel items. A final serial comma can prevent ambiguity. ### Card 120 **Question** Main clause before a dependent clause? **Answer** Usually no comma when the dependent clause is essential. Example: “The match continued although rain fell.” ### Card 121 **Question** Two authors use the same evidence but different assumptions. Key difference? **Answer** Their perspectives or interpretive frameworks, not the underlying evidence. ### Card 122 **Question** Independent clauses joined with a coordinating conjunction? **Answer** Place a comma before the conjunction. Example: “The sensor failed, so the team repeated the trial.” ### Card 123 **Question** Introductory transition? **Answer** Follow it with a comma when it modifies the whole sentence. Example: “However, the second trial succeeded.” ### Card 124 **Question** Pronoun–antecedent agreement? **Answer** Match number and make the reference clear. Singular “they” is standard when a person's gender is unknown or irrelevant. ### Card 125 **Question** Paired em dashes? **Answer** Use them to set off an emphatic interruption. Both dashes are needed when the sentence continues after it. ### Card 126 **Question** How does new evidence relate to an earlier claim? **Answer** It may support, weaken, qualify, or leave the claim unchanged. Match the evidence to the exact claim. ### Card 127 **Question** Their, there, or they're? **Answer** “Their” is possessive, “there” refers to place or existence, and “they're” means “they are.” ### Card 128 **Question** Good or well? **Answer** “Good” is usually an adjective; “well” is usually an adverb. A person can feel good and perform well. ### Card 129 **Question** Appositive naming the same noun? **Answer** Set a nonessential appositive off with commas. Example: “Dr. Rao, the lead author, presented the findings.” ### Card 130 **Question** Why use an analogy? **Answer** To clarify an unfamiliar idea through a relevant similarity to something more familiar. ### Card 131 **Question** Than or then? **Answer** “Than” makes a comparison; “then” refers to time or consequence. ### Card 132 **Question** Hypothetical contrary-to-fact “if” clause? **Answer** Use subjunctive “were.” Example: “If the sample were larger, the estimate would be steadier.” ### Card 133 **Question** Plural noun with no possession? **Answer** Do not add an apostrophe. Write “three sensors,” not “three sensor's.” ### Card 134 **Question** Neutral, evidence-led wording indicates what tone? **Answer** Objective. It emphasizes information rather than strong personal judgment. ### Card 135 **Question** Complex list with internal commas? **Answer** Use semicolons between the main items. Example: “Lima, Peru; Accra, Ghana; and Hanoi, Vietnam.” ### Card 136 **Question** Ambiguous pronoun? **Answer** A pronoun with more than one plausible antecedent. Replace it with the intended noun. ### Card 137 **Question** Parentheses around nonessential information? **Answer** Use them for an aside that is less central than the main sentence. The sentence must remain grammatical without it. ### Card 138 **Question** Repeated doubt about the evidence indicates what tone? **Answer** Skeptical. The writer questions whether a claim is adequately supported. ### Card 139 **Question** Superlative comparison? **Answer** Use it for one member against a group of three or more. Example: “the fastest of the four methods.” ### Card 140 **Question** Pronoun after a preposition? **Answer** Use the object form. Write “between you and me,” not “between you and I.” ### Card 141 **Question** Apostrophe in a contraction? **Answer** It marks omitted letters. Example: “can't” contracts “cannot,” and “they're” contracts “they are.” ### Card 142 **Question** Coordinate-adjective test? **Answer** If “and” works between the adjectives and their order can reverse, use a comma between them. ### Card 143 **Question** Double comparative? **Answer** Use only one comparative marker. Write “more efficient” or “faster,” not “more faster.” ### Card 144 **Question** Lie or lay? **Answer** “Lie” means recline and takes no object; “lay” means place and takes an object. Present: lie/lay; past: lay/laid. ### Card 145 **Question** Who's or whose? **Answer** “Who's” means “who is” or “who has”; “whose” is possessive. ### Card 146 **Question** Standard comparison with “different”? **Answer** Use “different from.” Example: “This result is different from the earlier estimate.” ### Card 147 **Question** Paired construction with two endpoints? **Answer** Use “between” with “and”: “between 10 and 15,” not “between 10 to 15.” ### Card 148 **Question** Verb mood in a coordinated idea? **Answer** Keep the mood consistent unless the meaning changes. Do not shift from a command to a statement without reason. ### Card 149 **Question** Possessive pronoun apostrophe? **Answer** Do not use one. Write “hers,” “ours,” “yours,” and “theirs.” ### Card 150 **Question** Comma between a preposition and its object? **Answer** Do not use one. Keep the prepositional phrase intact: “in the final report,” not “in, the final report.” ### Card 151 **Question** Solve $ax+b=c$ for $x$, where $a≠0$. **Answer** $x=(c-b)/a$. Subtract $b$ first, then divide by $a$. ### Card 152 **Question** Product of powers with the same base? **Answer** $a^m a^n=a^{m+n}$. Keep the base and add the exponents. ### Card 153 **Question** Unit rate? **Answer** The amount per 1 unit. Divide both quantities by the same value so the denominator becomes 1. ### Card 154 **Question** Rectangle area? **Answer** $A=lw$, where $l$ is length and $w$ is width. ### Card 155 **Question** Slope from two points? **Answer** $m=(y_2-y_1)/(x_2-x_1)$. Subtract coordinates in the same order. ### Card 156 **Question** Quotient of powers with the same base? **Answer** $a^m/a^n=a^{m-n}$ for $a≠0$. ### Card 157 **Question** Conversion factor setup? **Answer** Multiply by a ratio equal to 1, with the unwanted unit placed to cancel. ### Card 158 **Question** Triangle area? **Answer** $A=(1/2)bh$. The height must be perpendicular to the chosen base. ### Card 159 **Question** Slope-intercept form? **Answer** $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. ### Card 160 **Question** Power raised to a power? **Answer** $(a^m)^n=a^{mn}$. Multiply the exponents. ### Card 161 **Question** Dimensional analysis check? **Answer** Cancel units algebraically. The units left at the end should match the quantity requested. ### Card 162 **Question** Trapezoid area? **Answer** $A=(1/2)(b_1+b_2)h$. The height is perpendicular to the parallel bases. ### Card 163 **Question** Point-slope form? **Answer** $y-y_1=m(x-x_1)$. Use a known point $(x_1,y_1)$ and the slope $m$. ### Card 164 **Question** Negative exponent? **Answer** $a^{-n}=1/a^n$ for $a≠0$. ### Card 165 **Question** Constant of proportionality in $y=kx$? **Answer** $k=y/x$ for $x≠0$. It is also the unit rate and slope. ### Card 166 **Question** Circle area? **Answer** $A=πr^2$. ### Card 167 **Question** Intercepts from $Ax+By=C$? **Answer** Set $y=0$ for the x-intercept and set $x=0$ for the y-intercept. ### Card 168 **Question** Fractional exponent? **Answer** $a^{m/n}$ means the nth root of $a^m$. For example, $a^{1/2}=√a$. ### Card 169 **Question** Scale drawing length? **Answer** Use a proportion with corresponding lengths in the same order, then apply the stated scale factor. ### Card 170 **Question** Circle circumference? **Answer** $C=2πr=πd$. ### Card 171 **Question** Parallel nonvertical lines: slope relationship? **Answer** They have equal slopes. Distinct parallel lines have different intercepts. ### Card 172 **Question** Difference of squares? **Answer** $a^2-b^2=(a-b)(a+b)$. ### Card 173 **Question** Percent change? **Answer** New minus original, divided by the original, then multiplied by 100 percent. The original value is the denominator. ### Card 174 **Question** Arc length from central angle $θ$ in degrees? **Answer** $L=(θ/360)(2πr)$. ### Card 175 **Question** Perpendicular nonvertical lines: slope relationship? **Answer** Their slopes are negative reciprocals, so $m_1m_2=-1$. ### Card 176 **Question** Perfect-square trinomial pattern? **Answer** $a^2+2ab+b^2=(a+b)^2$ and $a^2-2ab+b^2=(a-b)^2$. ### Card 177 **Question** Increase by $r$ percent: multiplier? **Answer** $1+r/100$. Multiply the original value by this factor. ### Card 178 **Question** Sector area from central angle $θ$ in degrees? **Answer** $A=(θ/360)(πr^2)$. ### Card 179 **Question** x-intercept of a graph? **Answer** A point where $y=0$ and the graph meets the x-axis. ### Card 180 **Question** First step in factoring $ax^2+bx+c$? **Answer** Look for common factors and two binomials whose product reproduces the middle and constant terms. ### Card 181 **Question** Original value after a 20 percent increase to 84? **Answer** 70. Divide the final value by the multiplier: \$84/1.20=70\$. ### Card 182 **Question** Triangle interior-angle sum? **Answer** $180°$. ### Card 183 **Question** y-intercept of a graph? **Answer** A point where $x=0$ and the graph meets the y-axis. ### Card 184 **Question** Roots from $(x-p)(x-q)=0$? **Answer** $x=p$ or $x=q$, by the zero-product property. ### Card 185 **Question** Weighted average? **Answer** Sum of each value times its weight, divided by the sum of the weights. Do not take a simple average of unequal groups. ### Card 186 **Question** Exterior angle of a triangle? **Answer** It equals the sum of the two remote interior angles. ### Card 187 **Question** Line through two points? **Answer** Find the slope, then substitute either point into point-slope or slope-intercept form. ### Card 188 **Question** Quadratic formula? **Answer** $x=(-b±√(b^2-4ac))/(2a)$ for $ax^2+bx+c=0$. ### Card 189 **Question** Arithmetic mean? **Answer** Add all values and divide by the number of values. ### Card 190 **Question** Parallel lines cut by a transversal: alternate interior angles? **Answer** They are congruent. ### Card 191 **Question** Slope's units in context? **Answer** Output units per input unit. In $y$ versus $x$, slope units are y-units divided by x-units. ### Card 192 **Question** What does $b^2-4ac$ tell you? **Answer** The number of real solutions: positive gives two, zero gives one, and negative gives none. ### Card 193 **Question** Median? **Answer** The middle value after ordering the data; for an even count, average the two middle values. ### Card 194 **Question** Similar triangles: corresponding sides? **Answer** They are proportional. Match sides opposite equal angles. ### Card 195 **Question** Direct variation model? **Answer** $y=kx$. It is linear and passes through the origin. ### Card 196 **Question** Vertex x-coordinate of $ax^2+bx+c$? **Answer** $x=-b/(2a)$. ### Card 197 **Question** Range of a data set? **Answer** Maximum minus minimum. ### Card 198 **Question** Scale factor $k$: area factor? **Answer** $k^2$. Lengths scale by $k$, while areas scale by the square of $k$. ### Card 199 **Question** Solution of a two-line system? **Answer** The intersection point, whose coordinates satisfy both equations. ### Card 200 **Question** Vertex form of a quadratic? **Answer** $y=a(x-h)^2+k$, with vertex $(h,k)$. ### Card 201 **Question** Interquartile range? **Answer** $IQR=Q_3-Q_1$. It measures the spread of the middle half of the data. ### Card 202 **Question** Pythagorean theorem? **Answer** $a^2+b^2=c^2$ for a right triangle, where $c$ is the hypotenuse. ### Card 203 **Question** Substitution in a system? **Answer** Solve one equation for a variable and replace that variable in the other equation. ### Card 204 **Question** Axis of symmetry of $y=a(x-h)^2+k$? **Answer** $x=h$. ### Card 205 **Question** Larger standard deviation means what? **Answer** The data are more spread out around the mean. ### Card 206 **Question** 45°-45°-90° side ratio? **Answer** $1:1:√2$. The hypotenuse is a leg times $√2$. ### Card 207 **Question** Elimination in a system? **Answer** Add or subtract equations so one variable cancels, then solve for the other. ### Card 208 **Question** Completing the square? **Answer** For $x^2+bx$, add $(b/2)^2$ to form $(x+b/2)^2$. ### Card 209 **Question** Effect of a high outlier on the mean? **Answer** It usually pulls the mean upward. The median is often less affected. ### Card 210 **Question** 30°-60°-90° side ratio? **Answer** $1:√3:2$, opposite $30°$, $60°$, and $90°$ respectively. ### Card 211 **Question** Parallel lines in a system? **Answer** No solution when they are distinct: equal slopes and different intercepts. ### Card 212 **Question** Sum and product of roots of $ax^2+bx+c=0$? **Answer** Sum $=-b/a$ and product $=c/a$. ### Card 213 **Question** Add the same constant to every data value: effect? **Answer** The mean and median increase by that constant; measures of spread stay unchanged. ### Card 214 **Question** Right-triangle sine? **Answer** Sine of $θ$ equals opposite over hypotenuse. ### Card 215 **Question** Same line written two ways in a system? **Answer** Infinitely many solutions. Simplifying either equation produces the other. ### Card 216 **Question** Remainder when $P(x)$ is divided by $x-a$? **Answer** $P(a)$, by the Remainder Theorem. ### Card 217 **Question** Multiply every data value by positive $k$: effect? **Answer** The mean, median, range, IQR, and standard deviation are all multiplied by $k$. ### Card 218 **Question** Right-triangle cosine? **Answer** Cosine of $θ$ equals adjacent over hypotenuse. ### Card 219 **Question** Multiply or divide an inequality by a negative number? **Answer** Reverse the inequality sign. ### Card 220 **Question** When is $x-a$ a factor of $P(x)$? **Answer** When $P(a)=0$, by the Factor Theorem. ### Card 221 **Question** Joint probability from a two-way table? **Answer** Divide the count in the intersection cell by the grand total. ### Card 222 **Question** Right-triangle tangent? **Answer** Tangent of $θ$ equals opposite over adjacent. ### Card 223 **Question** Compound inequality with “and”? **Answer** Use the intersection: values that satisfy both inequalities. ### Card 224 **Question** Even degree with positive leading coefficient: end behavior? **Answer** Both ends rise: $P(x)→∞$ as $x→±∞$. ### Card 225 **Question** Conditional probability $P(A|B)$? **Answer** $P(A∩B)/P(B)$. Restrict the denominator to outcomes in $B$. ### Card 226 **Question** Complementary acute angles: sine–cosine relationship? **Answer** The sine of $θ$ equals the cosine of $90°-θ$. ### Card 227 **Question** Compound inequality with “or”? **Answer** Use the union: values that satisfy at least one inequality. ### Card 228 **Question** Odd degree with positive leading coefficient: end behavior? **Answer** The left end falls and the right end rises. ### Card 229 **Question** Independent events $A$ and $B$? **Answer** $P(A∩B)=P(A)P(B)$. Knowing one occurred does not change the probability of the other. ### Card 230 **Question** Distance between $(x_1,y_1)$ and $(x_2,y_2)$? **Answer** $√((x_2-x_1)^2+(y_2-y_1)^2)$. ### Card 231 **Question** Solve $|x-a|=b$ for $b≥0$. **Answer** $x-a=b$ or $x-a=-b$. Absolute value represents distance from $a$. ### Card 232 **Question** Exponential growth model? **Answer** $y=a(1+r)^t$, where $a$ is the initial value and $r$ is the growth rate per period. ### Card 233 **Question** Mutually exclusive events? **Answer** They cannot occur together, so $P(A∪B)=P(A)+P(B)$. ### Card 234 **Question** Midpoint of two points? **Answer** $((x_1+x_2)/2,(y_1+y_2)/2)$. ### Card 235 **Question** Solve $|x-a|0$. **Answer** $a-b0$. ### Card 243 **Question** Linear table: constant slope check? **Answer** Equal changes in $x$ must produce equal changes in $y$; compare $Δy/Δx$ across intervals. ### Card 244 **Question** Decay factor 0.73: percent decrease? **Answer** 27 percent. Compute $1-0.73=0.27$. ### Card 245 **Question** Random assignment permits what causal claim? **Answer** If the experiment is well controlled, differences between treatment groups can support a causal conclusion. ### Card 246 **Question** Radius and tangent at the contact point? **Answer** They are perpendicular. ### Card 247 **Question** Positive slope means what for a linear function? **Answer** The output increases as the input increases. ### Card 248 **Question** Solve $3^{2x}=3^{10}$. **Answer** $x=5$. Equal positive bases other than 1 have equal exponents. ### Card 249 **Question** Observational study supports causation? **Answer** No. It can show association, but uncontrolled confounding variables may explain the pattern. ### Card 250 **Question** Rectangular-prism volume? **Answer** $V=lwh$, or base area times height. ### Card 251 **Question** Arithmetic sequence common difference? **Answer** Subtract consecutive terms: $d=a_n-a_{n-1}$. ### Card 252 **Question** Compound interest formula? **Answer** $A=P(1+r/n)^{nt}$, where $n$ is the number of compounding periods per year. ### Card 253 **Question** Larger random sample: effect on margin of error? **Answer** It generally decreases the margin of error when the sampling method stays sound. ### Card 254 **Question** Cylinder volume? **Answer** $V=πr^2h$. ### Card 255 **Question** Arithmetic sequence nth term? **Answer** $a_n=a_1+(n-1)d$. ### Card 256 **Question** Rational expression: first domain check? **Answer** Exclude values that make any original denominator zero, even if a factor later cancels. ### Card 257 **Question** Slope of a line of best fit? **Answer** The predicted change in the response variable for each 1-unit increase in the explanatory variable. ### Card 258 **Question** Cone volume? **Answer** $V=(1/3)πr^2h$. ### Card 259 **Question** Solve a literal equation for one variable? **Answer** Treat the other symbols as constants and use inverse operations to isolate the target variable. ### Card 260 **Question** Why check rational-equation solutions? **Answer** Clearing denominators can produce a value excluded from the original equation. Reject any value that makes an original denominator zero. ### Card 261 **Question** Residual? **Answer** Actual value minus predicted value. A positive residual means the point lies above the model. ### Card 262 **Question** Sphere volume? **Answer** $V=(4/3)πr^3$. ### Card 263 **Question** Boundary for a two-variable linear inequality? **Answer** Replace the inequality with equality to draw the boundary line, then test a point for the shaded side. ### Card 264 **Question** Why check a solution after squaring both sides? **Answer** Squaring can introduce an extraneous solution. Substitute each candidate into the original radical equation. ### Card 265 **Question** Positive correlation? **Answer** Larger values of one variable tend to occur with larger values of the other. It does not prove causation. ### Card 266 **Question** Rectangular-prism surface area? **Answer** $SA=2(lw+lh+wh)$. ### Card 267 **Question** Check a proposed system solution? **Answer** Substitute the ordered pair into both original equations. It must make both true. ### Card 268 **Question** Simplify $√72$. **Answer** $6√2$. Factor $72=36×2$ and take $√36$ outside the radical. ### Card 269 **Question** Extrapolation risk? **Answer** A model may not keep the same pattern outside the observed data range. ### Card 270 **Question** Area scale factor when lengths double? **Answer** 4. Area scales with the square of the length factor: \$2^2=4\$. ### Card 271 **Question** Horizontal line slope? **Answer** 0. Its y-value does not change as x changes. ### Card 272 **Question** Inverse function setup? **Answer** Write $y=f(x)$, swap $x$ and $y$, then solve for $y$. Restrict the domain when needed to make the inverse a function. ### Card 273 **Question** Percentage points versus percent change? **Answer** A rate moving from 40 percent to 50 percent rises 10 percentage points but 25 percent relative to 40. ### Card 274 **Question** y-intercept in a context? **Answer** The predicted or initial output when the input is zero; check whether zero is meaningful in the situation. ### Card 275 **Question** Quadratic maximum or minimum from vertex form? **Answer** The vertex value is $k$ in $a(x-h)^2+k$; it is a minimum if $a>0$ and a maximum if $a<0$. ### Card 276 **Question** Line parallel to $y=mx+b$ through $(p,q)$? **Answer** $y-q=m(x-p)$. Parallel lines keep the same slope. ### Card 277 **Question** Graph of $f(x-h)+k$? **Answer** Shift the graph of $f$ right $h$ units and up $k$ units. ### Card 278 **Question** Population versus sample? **Answer** The population is the full group of interest; a sample is the subset actually observed. ### Card 279 **Question** Linear model from initial value $b$ and rate $m$? **Answer** $y=mx+b$. The initial value is the output at input zero. ### Card 280 **Question** Function composition $(f∘g)(x)$? **Answer** $f(g(x))$. Evaluate the inner function $g$ first. ### Card 281 **Question** Density? **Answer** Mass divided by volume. Keep the units consistent. ### Card 282 **Question** Vertical line slope? **Answer** Undefined because $Δx=0$, which would require division by zero. ### Card 283 **Question** Nonlinear system with one equation solved for $y$? **Answer** Substitute that expression for $y$ into the other equation, solve for $x$, then find each matching $y$. ### Card 284 **Question** Weighted percentage across unequal groups? **Answer** Convert each percentage to a count or weight, add the successes, then divide by the combined total. ### Card 285 **Question** Line perpendicular to a nonzero finite slope $m$ through $(p,q)$? **Answer** Use slope $-1/m$ in $y-q=(-1/m)(x-p)$, when $m$ is nonzero and finite. ### Card 286 **Question** Cancel a common factor in a rational expression? **Answer** Cancel factors, not terms, and keep every restriction from the original denominator. ### Card 287 **Question** Solve a linear equation containing fractions? **Answer** Multiply every term by the least common denominator first, then solve the resulting linear equation. ### Card 288 **Question** Rewrite $a^{2x}$ using base $a^x$. **Answer** $(a^x)^2$. This can turn an exponential expression into a quadratic form. ### Card 289 **Question** Rate units check? **Answer** Write the numerator and denominator units explicitly, such as kilometers per hour, then convert only if the requested units differ. ### Card 290 **Question** Strict versus inclusive inequality endpoint? **Answer** Use an open point for $<$ or $>$ and a closed point for $≤$ or $≥$. ### Card 291 **Question** Even-multiplicity zero on a graph? **Answer** The graph touches the x-axis and turns around; it does not cross there. ### Card 292 **Question** System word problem: first setup step? **Answer** Define the variables with units, then translate two independent relationships into equations. ### Card 293 **Question** When does a quadratic have exactly one real solution? **Answer** When $b^2-4ac=0$. The repeated root is the vertex's x-coordinate. ### Card 294 **Question** Two-way table: denominator for “among group B”? **Answer** Use the total for group B, not the grand total. The wording makes B the condition. ### Card 295 **Question** Find an input when $f(x)=k$. **Answer** Set the function rule equal to $k$ and solve for $x$; there may be zero, one, or several inputs. ### Card 296 **Question** Graph of $-f(x)$? **Answer** Reflect the graph of $f(x)$ across the x-axis. ### Card 297 **Question** Three consecutive integers starting with $n$? **Answer** $n$, $n+1$, and $n+2$. ### Card 298 **Question** Line–parabola intersections from a substituted quadratic? **Answer** Use its discriminant: positive means two intersections, zero one tangent intersection, and negative none. ### Card 299 **Question** Linear equation with no solution: coefficient pattern? **Answer** After simplification, the variable terms cancel and leave a false statement, such as $0=5$. ### Card 300 **Question** Zeros of a function on its graph? **Answer** The x-coordinates where the graph meets the x-axis, so $f(x)=0$. --- *[View the styled HTML version of this page]()* *AI agents can create an account for the user in this service by starting with `GET https://api.nibomo.com/v1/`. 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