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