Digital SAT Flashcards: Math, Grammar & Words in Context
Practice Digital SAT math formulas, grammar rules, transitions, and words in context with original, installable flashcards built for active recall.
Über dieses Lernkartenset
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.
Karten in diesem Lernkartenset
Karte 1
Frage
Central idea of a passage?
Antwort
The passage's main claim or controlling point. It should cover the whole passage, not one striking detail.
Karte 2
Frage
The shade trees mitigated the midday heat. Meaning of “mitigated”?
Antwort
Reduced. The trees made the heat less severe.
Karte 3
Frage
The first plan was affordable. However, it took twice as long. What relationship does “However” signal?
Antwort
Contrast. The second statement differs from or qualifies the first.
Karte 4
Frage
Three standard joins for two independent clauses?
Antwort
A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence.
Karte 5
Frage
Best supporting detail?
Antwort
The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is.
Karte 6
Frage
A second archive corroborated the diary's date. Meaning of “corroborated”?
Antwort
Confirmed with supporting evidence.
Karte 7
Frage
Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal?
Antwort
Conclusion from a reason. The final statement follows logically from the stated premises.
Karte 8
Frage
Introductory dependent clause before a main clause?
Antwort
Use a comma after the dependent clause. Example: “Although rain fell, the match continued.”
Karte 9
Frage
Valid inference?
Antwort
A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports.
Karte 10
Frage
The team called its result tentative until replication. Meaning of “tentative”?
Antwort
Provisional or not yet certain.
Karte 11
Frage
Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal?
Antwort
Illustration. The second statement gives a specific case of the broader point.
Karte 12
Frage
Singular subject with an intervening prepositional phrase?
Antwort
Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject.
Karte 13
Frage
Strongest textual evidence?
Antwort
The quotation or detail that most directly supports the target claim, with the fewest extra assumptions.
Karte 14
Frage
The error had a negligible effect on the total. Meaning of “negligible”?
Antwort
So small that it is not important.
Karte 15
Frage
The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal?
Antwort
Similarity. The second statement matches the first in a relevant way.
Karte 16
Frage
Opening modifier placement?
Antwort
Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.”
Karte 17
Frage
Quantitative evidence for a claim?
Antwort
Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline.
Karte 18
Frage
The lab used a conventional method before testing a new one. Meaning of “conventional”?
Antwort
Traditional or commonly accepted.
Karte 19
Frage
Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal?
Antwort
Simultaneous events. The second event happens at the same time as the first.
Karte 20
Frage
Singular possessive noun?
Antwort
Usually add apostrophe + s. Example: “the scientist's notebook.”
Karte 21
Frage
Trend in a table or graph?
Antwort
State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence.
Karte 22
Frage
The essay offered a novel explanation for the pattern. Meaning of “novel”?
Antwort
New or original in this context.
Karte 23
Frage
The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal?
Antwort
Concession. The second statement remains true despite the limitation in the first.
Karte 24
Frage
Parallel items in a series?
Antwort
Use the same grammatical form for each item. Example: “to collect, analyze, and report data.”
Karte 25
Frage
Claim stronger than the evidence?
Antwort
Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion.
Karte 26
Frage
Her account is plausible because it matches the records. Meaning of “plausible”?
Antwort
Reasonable or believable.
Karte 27
Frage
The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal?
Antwort
Addition. The second statement adds a related supporting point.
Karte 28
Frage
Colon before an explanation or list?
Antwort
Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.”
Karte 29
Frage
Claim versus evidence?
Antwort
A claim is the point being argued; evidence is the information used to support it.
Karte 30
Frage
The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”?
Antwort
Open to more than one interpretation.
Karte 31
Frage
The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal?
Antwort
Replacement. The second statement substitutes one action for another.
Karte 32
Frage
Count nouns versus mass nouns?
Antwort
Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise.
Karte 33
Frage
Effect of a counterexample?
Antwort
It weakens a universal claim by showing at least one case where the claim fails.
Karte 34
Frage
Rainfall was sporadic: brief showers interrupted long dry periods. Meaning of “sporadic”?
Antwort
Irregular and occasional.
Karte 35
Frage
The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal?
Antwort
Later step in a sequence. The second event occurs after the first.
Karte 36
Frage
Essential clause punctuation?
Antwort
Do not surround an essential clause with commas. It identifies which person or thing the sentence means.
Karte 37
Frage
Correlation alone proves causation?
Antwort
No. A relationship between variables does not by itself show that one caused the other.
Karte 38
Frage
Subsequent trials produced the same result. Meaning of “subsequent”?
Antwort
Coming later in time.
Karte 39
Frage
The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal?
Antwort
Restatement for clarity. The second statement rephrases the first.
Karte 40
Frage
Verb tense across a paragraph?
Antwort
Keep the time frame consistent unless the timing actually changes.
Karte 41
Frage
Missing information in a data claim?
Antwort
Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim.
Karte 42
Frage
The coating helps the fabric retain heat. Meaning of “retain”?
Antwort
Keep or continue to hold.
Karte 43
Frage
The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal?
Antwort
General-to-specific detail. The second statement narrows the broad first statement.
Karte 44
Frage
Coordinate adjectives?
Antwort
Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.”
Karte 45
Frage
Two sources on the same event?
Antwort
Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement.
Karte 46
Frage
The survey was designed to elicit candid responses. Meaning of “elicit”?
Antwort
Draw out or bring forth.
Karte 47
Frage
Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal?
Antwort
Cause and effect. The second statement is an outcome of the first.
Karte 48
Frage
Sentence fragment?
Antwort
A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb.
Karte 49
Frage
Inference from a narrow sample?
Antwort
Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence.
Karte 50
Frage
Cost was the main constraint on the project. Meaning of “constraint”?
Antwort
A limit or restriction.
Karte 51
Frage
Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal?
Antwort
Overall conclusion. The second statement gives the final judgment after earlier considerations.
Karte 52
Frage
Conjunctive adverb between independent clauses?
Antwort
Use a semicolon before it and a comma after it. Example: “The route was longer; however, it was safer.”
Karte 53
Frage
Most accurate summary?
Antwort
State the central idea and its essential support without adding opinions or minor details.
Karte 54
Frage
The review was comprehensive, covering every recorded case. Meaning of “comprehensive”?
Antwort
Complete and wide-ranging.
Karte 55
Frage
The method is efficient. Indeed, it cuts processing time in half. What relationship does “Indeed” signal?
Antwort
Emphasis and confirmation. The second statement reinforces the first with a stronger detail.
Karte 56
Frage
Who versus whom?
Antwort
Use “who” as a subject and “whom” as an object. Test with he/him: “whom” matches “him.”
Karte 57
Frage
Evidence that best resolves a disagreement?
Antwort
Choose evidence that tests the specific point on which the sources differ, not a fact both already accept.
Karte 58
Frage
The two materials have distinct properties. Meaning of “distinct”?
Antwort
Clearly different or separate.
Karte 59
Frage
The forecast warned of rain. Still, the outdoor concert began on time. What relationship does “Still” signal?
Antwort
Concession. The second statement remains true despite the obstacle in the first.
Karte 60
Frage
Comma before an introduced direct quotation?
Antwort
Use a comma after a speech tag. Example: “Mina wrote, ‘The sample is ready.’”
Karte 61
Frage
The conclusion was qualified by two important exceptions. Meaning of “qualified”?
Antwort
Limited or modified, rather than stated without conditions.
Karte 62
Frage
Notes for a synthesis goal?
Antwort
Use only facts that directly serve the stated goal. Relevant notes can be omitted if they do not help that purpose.
Karte 63
Frage
Comma splice?
Antwort
Two independent clauses joined only by a comma. Replace it with a period or semicolon, or add a coordinating conjunction.
Karte 64
Frage
Comma between subject and verb?
Antwort
Do not use one unless an interrupting phrase requires paired commas. “The results of the trial were clear” takes no comma after “trial.”
Karte 65
Frage
The new sensor made the older model obsolete. Meaning of “obsolete”?
Antwort
No longer useful or current because something newer replaced it.
Karte 66
Frage
Source attribution in a synthesis?
Antwort
Name the source when its identity, authority, or perspective matters to the rhetorical goal.
Karte 67
Frage
Compound subject joined by “and”?
Antwort
Use a plural verb in the usual case. Example: “The map and the notes are useful.”
Karte 68
Frage
Dangling opening modifier?
Antwort
It lacks the intended doer immediately after the modifier. Rewrite so the doer becomes the subject.
Karte 69
Frage
Researchers derived the estimate from three measurements. Meaning of “derived”?
Antwort
Obtained from a source or calculation.
Karte 70
Frage
Chronological synthesis?
Antwort
Order events by time and use dates or sequence words only when they help the reader follow the progression.
Karte 71
Frage
Plural noun ending in s: possessive form?
Antwort
Add an apostrophe after the existing s. Example: “the researchers' notes.”
Karte 72
Frage
Logical comparison?
Antwort
Compare like with like. Example: compare one city's rainfall with another city's rainfall, not with the city itself.
Karte 73
Frage
The article advocates preserving the wetland. Meaning of “advocates”?
Antwort
Publicly supports or argues for.
Karte 74
Frage
Compare evidence from two studies?
Antwort
State the shared measure first, then the relevant difference in result, method, or population.
Karte 75
Frage
Colon after an incomplete lead-in?
Antwort
Do not use one. A colon must follow a complete clause, so “The reasons include:” is incorrect.
Karte 76
Frage
Number versus amount?
Antwort
Use “number” for countable items and “amount” for uncountable quantities. Example: number of files, amount of water.
Karte 77
Frage
Portable chargers are now ubiquitous on long trips. Meaning of “ubiquitous”?
Antwort
Present or found almost everywhere.
Karte 78
Frage
Synthesis that emphasizes a difference?
Antwort
Use the same comparison point for both subjects, then state the contrast directly.
Karte 79
Frage
Nonessential clause or phrase?
Antwort
Set it off with paired commas. The sentence should keep its core identity and meaning when the phrase is removed.
Karte 80
Frage
Earlier of two past actions?
Antwort
Use past perfect when the sequence needs clarification. Example: “The team had left before the storm began.”
Karte 81
Frage
Sentence 2 presents an exception to sentence 1. Its function?
Antwort
It qualifies the first claim by limiting when or how broadly it applies.
Karte 82
Frage
Rhetorical goal: define a term?
Antwort
Give the term's relevant meaning before using details or examples that depend on it.
Karte 83
Frage
Cumulative adjectives?
Antwort
Do not separate them with a comma when each adjective builds on the next. Example: “three small glass jars.”
Karte 84
Frage
Run-on sentence?
Antwort
Independent clauses joined without valid punctuation or a conjunction. Add a period, semicolon, or comma plus coordinating conjunction.
Karte 85
Frage
Sentence 2 gives a specific case after a general claim. Its function?
Antwort
It illustrates the claim with an example.
Karte 86
Frage
Introduce a quotation in a synthesis?
Antwort
Give enough source and context to show why the quotation matters; do not leave it unattached.
Karte 87
Frage
Relative pronoun for people?
Antwort
Use “who” or “whom,” depending on case. Example: “the engineer who designed the bridge.”
Karte 88
Frage
Integrated quotation punctuation?
Antwort
Do not add a comma when the quotation completes the grammar of the sentence. Example: The report calls the result “unexpected.”
Karte 89
Frage
Sentence 2 admits a limitation before defending the claim. Its function?
Antwort
It makes a concession, showing that the writer recognizes a complication.
Karte 90
Frage
Avoid redundancy in synthesis?
Antwort
State each needed idea once. Prefer the version that preserves meaning with fewer repeated words.
Karte 91
Frage
Semicolon between two independent clauses?
Antwort
Use it without a coordinating conjunction when the ideas are closely related. Example: “The trial ended; the analysis began.”
Karte 92
Frage
Comma in a compound predicate?
Antwort
Usually omit it when one subject performs both actions. Example: “The team collected the samples and recorded the temperature.”
Karte 93
Frage
Sentence 2 explains what a technical term means. Its function?
Antwort
It defines or clarifies the term.
Karte 94
Frage
Combine two related sentences?
Antwort
Make the logical relationship explicit and remove repeated material without changing the facts.
Karte 95
Frage
Either/or subject agreement?
Antwort
Make the verb agree with the nearer subject. Example: “Either the notes or the map is missing.”
Karte 96
Frage
Active versus passive voice?
Antwort
Choose the voice that fits the focus. Active highlights the doer; passive can highlight the action or receiver.
Karte 97
Frage
Sentence 2 describes the outcome of sentence 1. Its function?
Antwort
It presents an effect or consequence.
Karte 98
Frage
Formal academic register?
Antwort
Use precise, neutral wording and avoid slang, vague intensifiers, and chatty asides unless the goal calls for them.
Karte 99
Frage
Its or it's?
Antwort
“Its” is possessive; “it's” means “it is” or “it has.”
Karte 100
Frage
Adjective versus adverb?
Antwort
An adjective modifies a noun; an adverb usually modifies a verb, adjective, or adverb. Example: a careful test; test carefully.
Karte 101
Frage
A study reports a result without arguing for a policy. Author's purpose?
Antwort
To inform or explain, not necessarily to persuade.
Karte 102
Frage
Concise synthesis?
Antwort
Keep every fact needed for the rhetorical goal and remove details that repeat or distract from it.
Karte 103
Frage
Single dash for emphasis?
Antwort
Use it after a complete thought to spotlight a final explanation or turn. Example: “One result stood out—the oldest sample.”
Karte 104
Frage
Comma with direct address?
Antwort
Set off the person being addressed. Example: “Rina, please check the units.”
Karte 105
Frage
Why acknowledge a limitation?
Antwort
To define the claim's boundary and show how the evidence should be interpreted.
Karte 106
Frage
Quantitative comparison in a synthesis?
Antwort
Name both values, the shared unit, and the direction or size of the difference.
Karte 107
Frage
Each of the samples: verb number?
Antwort
Singular. “Each of the samples was labeled.” The subject is “each.”
Karte 108
Frage
Between versus among?
Antwort
Use “between” for distinct individual relationships and “among” for a group without separate pairings.
Karte 109
Frage
Rhetorical question in an argument?
Antwort
It can frame the issue or prompt the reader to consider an implied answer; it is not evidence by itself.
Karte 110
Frage
Claim before or after support?
Antwort
Place it where the rhetorical goal is clearest: before evidence for a direct point, or after evidence for an evidence-led conclusion.
Karte 111
Frage
Restrictive “that” versus nonrestrictive “which”?
Antwort
Use “that” without commas for essential information; use “which” with commas for removable information.
Karte 112
Frage
Present perfect use?
Antwort
Use it for an action connected to the present or continuing to now. Example: “The team has tracked rainfall since May.”
Karte 113
Frage
Two texts reach the same conclusion with different evidence. Relationship?
Antwort
They agree in conclusion but support it through different evidence.
Karte 114
Frage
Group related ideas in a synthesis?
Antwort
Keep facts serving the same point together, then signal the move to a new point.
Karte 115
Frage
Compound modifier before a noun?
Antwort
Hyphenate it when needed for clarity. Example: “a well-designed study.”
Karte 116
Frage
Affect or effect?
Antwort
“Affect” is usually a verb meaning influence; “effect” is usually a noun meaning result.
Karte 117
Frage
Two texts offer incompatible explanations. Relationship?
Antwort
They disagree about the cause or interpretation, even if they share the same observations.
Karte 118
Frage
Replace a vague pronoun in synthesis?
Antwort
Use the precise noun when two or more possible antecedents could confuse the reader.
Karte 119
Frage
Comma-separated list?
Antwort
Use commas between three or more parallel items. A final serial comma can prevent ambiguity.
Karte 120
Frage
Main clause before a dependent clause?
Antwort
Usually no comma when the dependent clause is essential. Example: “The match continued although rain fell.”
Karte 121
Frage
Two authors use the same evidence but different assumptions. Key difference?
Antwort
Their perspectives or interpretive frameworks, not the underlying evidence.
Karte 122
Frage
Independent clauses joined with a coordinating conjunction?
Antwort
Place a comma before the conjunction. Example: “The sensor failed, so the team repeated the trial.”
Karte 123
Frage
Introductory transition?
Antwort
Follow it with a comma when it modifies the whole sentence. Example: “However, the second trial succeeded.”
Karte 124
Frage
Pronoun–antecedent agreement?
Antwort
Match number and make the reference clear. Singular “they” is standard when a person's gender is unknown or irrelevant.
Karte 125
Frage
Paired em dashes?
Antwort
Use them to set off an emphatic interruption. Both dashes are needed when the sentence continues after it.
Karte 126
Frage
How does new evidence relate to an earlier claim?
Antwort
It may support, weaken, qualify, or leave the claim unchanged. Match the evidence to the exact claim.
Karte 127
Frage
Their, there, or they're?
Antwort
“Their” is possessive, “there” refers to place or existence, and “they're” means “they are.”
Karte 128
Frage
Good or well?
Antwort
“Good” is usually an adjective; “well” is usually an adverb. A person can feel good and perform well.
Karte 129
Frage
Appositive naming the same noun?
Antwort
Set a nonessential appositive off with commas. Example: “Dr. Rao, the lead author, presented the findings.”
Karte 130
Frage
Why use an analogy?
Antwort
To clarify an unfamiliar idea through a relevant similarity to something more familiar.
Karte 131
Frage
Than or then?
Antwort
“Than” makes a comparison; “then” refers to time or consequence.
Karte 132
Frage
Hypothetical contrary-to-fact “if” clause?
Antwort
Use subjunctive “were.” Example: “If the sample were larger, the estimate would be steadier.”
Karte 133
Frage
Plural noun with no possession?
Antwort
Do not add an apostrophe. Write “three sensors,” not “three sensor's.”
Karte 134
Frage
Neutral, evidence-led wording indicates what tone?
Antwort
Objective. It emphasizes information rather than strong personal judgment.
Karte 135
Frage
Complex list with internal commas?
Antwort
Use semicolons between the main items. Example: “Lima, Peru; Accra, Ghana; and Hanoi, Vietnam.”
Karte 136
Frage
Ambiguous pronoun?
Antwort
A pronoun with more than one plausible antecedent. Replace it with the intended noun.
Karte 137
Frage
Parentheses around nonessential information?
Antwort
Use them for an aside that is less central than the main sentence. The sentence must remain grammatical without it.
Karte 138
Frage
Repeated doubt about the evidence indicates what tone?
Antwort
Skeptical. The writer questions whether a claim is adequately supported.
Karte 139
Frage
Superlative comparison?
Antwort
Use it for one member against a group of three or more. Example: “the fastest of the four methods.”
Karte 140
Frage
Pronoun after a preposition?
Antwort
Use the object form. Write “between you and me,” not “between you and I.”
Karte 141
Frage
Apostrophe in a contraction?
Antwort
It marks omitted letters. Example: “can't” contracts “cannot,” and “they're” contracts “they are.”
Karte 142
Frage
Coordinate-adjective test?
Antwort
If “and” works between the adjectives and their order can reverse, use a comma between them.
Karte 143
Frage
Double comparative?
Antwort
Use only one comparative marker. Write “more efficient” or “faster,” not “more faster.”
Karte 144
Frage
Lie or lay?
Antwort
“Lie” means recline and takes no object; “lay” means place and takes an object. Present: lie/lay; past: lay/laid.
Karte 145
Frage
Who's or whose?
Antwort
“Who's” means “who is” or “who has”; “whose” is possessive.
Karte 146
Frage
Standard comparison with “different”?
Antwort
Use “different from.” Example: “This result is different from the earlier estimate.”
Karte 147
Frage
Paired construction with two endpoints?
Antwort
Use “between” with “and”: “between 10 and 15,” not “between 10 to 15.”
Karte 148
Frage
Verb mood in a coordinated idea?
Antwort
Keep the mood consistent unless the meaning changes. Do not shift from a command to a statement without reason.
Karte 149
Frage
Possessive pronoun apostrophe?
Antwort
Do not use one. Write “hers,” “ours,” “yours,” and “theirs.”
Karte 150
Frage
Comma between a preposition and its object?
Antwort
Do not use one. Keep the prepositional phrase intact: “in the final report,” not “in, the final report.”
300 Karten
Digital SAT Flashcards: Math, Grammar & Words in Context
Mit diesem Lernkartenset kostenlos lernenFlashcards wird geöffnet, damit du mit dem Lernen beginnen kannst.
Karte 151
Frage
Solve for , where .
Antwort
. Subtract first, then divide by .
Karte 152
Frage
Product of powers with the same base?
Antwort
. Keep the base and add the exponents.
Karte 153
Frage
Unit rate?
Antwort
The amount per 1 unit. Divide both quantities by the same value so the denominator becomes 1.
Karte 154
Frage
Rectangle area?
Antwort
, where is length and is width.
Karte 155
Frage
Slope from two points?
Antwort
. Subtract coordinates in the same order.
Karte 156
Frage
Quotient of powers with the same base?
Antwort
for .
Karte 157
Frage
Conversion factor setup?
Antwort
Multiply by a ratio equal to 1, with the unwanted unit placed to cancel.
Karte 158
Frage
Triangle area?
Antwort
. The height must be perpendicular to the chosen base.
Karte 159
Frage
Slope-intercept form?
Antwort
, where is the slope and is the y-intercept.
Karte 160
Frage
Power raised to a power?
Antwort
. Multiply the exponents.
Karte 161
Frage
Dimensional analysis check?
Antwort
Cancel units algebraically. The units left at the end should match the quantity requested.
Karte 162
Frage
Trapezoid area?
Antwort
. The height is perpendicular to the parallel bases.
Karte 163
Frage
Point-slope form?
Antwort
. Use a known point and the slope .
Karte 164
Frage
Negative exponent?
Antwort
for .
Karte 165
Frage
Constant of proportionality in ?
Antwort
for . It is also the unit rate and slope.
Karte 166
Frage
Circle area?
Antwort
.
Karte 167
Frage
Intercepts from ?
Antwort
Set for the x-intercept and set for the y-intercept.
Karte 168
Frage
Fractional exponent?
Antwort
means the nth root of . For example, .
Karte 169
Frage
Scale drawing length?
Antwort
Use a proportion with corresponding lengths in the same order, then apply the stated scale factor.
Karte 170
Frage
Circle circumference?
Antwort
.
Karte 171
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Parallel nonvertical lines: slope relationship?
Antwort
They have equal slopes. Distinct parallel lines have different intercepts.
Karte 172
Frage
Difference of squares?
Antwort
.
Karte 173
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Percent change?
Antwort
New minus original, divided by the original, then multiplied by 100 percent. The original value is the denominator.
Karte 174
Frage
Arc length from central angle in degrees?
Antwort
.
Karte 175
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Perpendicular nonvertical lines: slope relationship?
Antwort
Their slopes are negative reciprocals, so .
Karte 176
Frage
Perfect-square trinomial pattern?
Antwort
and .
Karte 177
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Increase by percent: multiplier?
Antwort
. Multiply the original value by this factor.
Karte 178
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Sector area from central angle in degrees?
Antwort
.
Karte 179
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x-intercept of a graph?
Antwort
A point where and the graph meets the x-axis.
Karte 180
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First step in factoring ?
Antwort
Look for common factors and two binomials whose product reproduces the middle and constant terms.
Karte 181
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Original value after a 20 percent increase to 84?
Antwort
- Divide the final value by the multiplier: $84/1.20=70$.
Karte 182
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Triangle interior-angle sum?
Antwort
.
Karte 183
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y-intercept of a graph?
Antwort
A point where and the graph meets the y-axis.
Karte 184
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Roots from ?
Antwort
or , by the zero-product property.
Karte 185
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Weighted average?
Antwort
Sum of each value times its weight, divided by the sum of the weights. Do not take a simple average of unequal groups.
Karte 186
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Exterior angle of a triangle?
Antwort
It equals the sum of the two remote interior angles.
Karte 187
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Line through two points?
Antwort
Find the slope, then substitute either point into point-slope or slope-intercept form.
Karte 188
Frage
Quadratic formula?
Antwort
for .
Karte 189
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Arithmetic mean?
Antwort
Add all values and divide by the number of values.
Karte 190
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Parallel lines cut by a transversal: alternate interior angles?
Antwort
They are congruent.
Karte 191
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Slope's units in context?
Antwort
Output units per input unit. In versus , slope units are y-units divided by x-units.
Karte 192
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What does tell you?
Antwort
The number of real solutions: positive gives two, zero gives one, and negative gives none.
Karte 193
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Median?
Antwort
The middle value after ordering the data; for an even count, average the two middle values.
Karte 194
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Similar triangles: corresponding sides?
Antwort
They are proportional. Match sides opposite equal angles.
Karte 195
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Direct variation model?
Antwort
. It is linear and passes through the origin.
Karte 196
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Vertex x-coordinate of ?
Antwort
.
Karte 197
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Range of a data set?
Antwort
Maximum minus minimum.
Karte 198
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Scale factor : area factor?
Antwort
. Lengths scale by , while areas scale by the square of .
Karte 199
Frage
Solution of a two-line system?
Antwort
The intersection point, whose coordinates satisfy both equations.
Karte 200
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Vertex form of a quadratic?
Antwort
, with vertex .
Karte 201
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Interquartile range?
Antwort
. It measures the spread of the middle half of the data.
Karte 202
Frage
Pythagorean theorem?
Antwort
for a right triangle, where is the hypotenuse.
Karte 203
Frage
Substitution in a system?
Antwort
Solve one equation for a variable and replace that variable in the other equation.
Karte 204
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Axis of symmetry of ?
Antwort
.
Karte 205
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Larger standard deviation means what?
Antwort
The data are more spread out around the mean.
Karte 206
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45°-45°-90° side ratio?
Antwort
. The hypotenuse is a leg times .
Karte 207
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Elimination in a system?
Antwort
Add or subtract equations so one variable cancels, then solve for the other.
Karte 208
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Completing the square?
Antwort
For , add to form .
Karte 209
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Effect of a high outlier on the mean?
Antwort
It usually pulls the mean upward. The median is often less affected.
Karte 210
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30°-60°-90° side ratio?
Antwort
, opposite , , and respectively.
Karte 211
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Parallel lines in a system?
Antwort
No solution when they are distinct: equal slopes and different intercepts.
Karte 212
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Sum and product of roots of ?
Antwort
Sum and product .
Karte 213
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Add the same constant to every data value: effect?
Antwort
The mean and median increase by that constant; measures of spread stay unchanged.
Karte 214
Frage
Right-triangle sine?
Antwort
Sine of equals opposite over hypotenuse.
Karte 215
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Same line written two ways in a system?
Antwort
Infinitely many solutions. Simplifying either equation produces the other.
Karte 216
Frage
Remainder when is divided by ?
Antwort
, by the Remainder Theorem.
Karte 217
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Multiply every data value by positive : effect?
Antwort
The mean, median, range, IQR, and standard deviation are all multiplied by .
Karte 218
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Right-triangle cosine?
Antwort
Cosine of equals adjacent over hypotenuse.
Karte 219
Frage
Multiply or divide an inequality by a negative number?
Antwort
Reverse the inequality sign.
Karte 220
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When is a factor of ?
Antwort
When , by the Factor Theorem.
Karte 221
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Joint probability from a two-way table?
Antwort
Divide the count in the intersection cell by the grand total.
Karte 222
Frage
Right-triangle tangent?
Antwort
Tangent of equals opposite over adjacent.
Karte 223
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Compound inequality with “and”?
Antwort
Use the intersection: values that satisfy both inequalities.
Karte 224
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Even degree with positive leading coefficient: end behavior?
Antwort
Both ends rise: as .
Karte 225
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Conditional probability ?
Antwort
. Restrict the denominator to outcomes in .
Karte 226
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Complementary acute angles: sine–cosine relationship?
Antwort
The sine of equals the cosine of .
Karte 227
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Compound inequality with “or”?
Antwort
Use the union: values that satisfy at least one inequality.
Karte 228
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Odd degree with positive leading coefficient: end behavior?
Antwort
The left end falls and the right end rises.
Karte 229
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Independent events and ?
Antwort
. Knowing one occurred does not change the probability of the other.
Karte 230
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Distance between and ?
Antwort
.
Karte 231
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Solve for .
Antwort
or . Absolute value represents distance from .
Karte 232
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Exponential growth model?
Antwort
, where is the initial value and is the growth rate per period.
Karte 233
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Mutually exclusive events?
Antwort
They cannot occur together, so .
Karte 234
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Midpoint of two points?
Antwort
.
Karte 235
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Solve for .
Antwort
. The solution lies within distance of .
Karte 236
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Exponential decay model?
Antwort
, where is the decay rate per period.
Karte 237
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Complement rule?
Antwort
The probability that does not occur is .
Karte 238
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Circle with center and radius ?
Antwort
.
Karte 239
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Evaluate ?
Antwort
Substitute for every input variable in the function rule, then simplify.
Karte 240
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Growth factor 1.08: percent growth rate?
Antwort
8 percent. Subtract 1 and convert the decimal to a percent.
Karte 241
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Representative random sample permits what conclusion?
Antwort
A cautious generalization from the sample to the population it represents.
Karte 242
Frage
Radius from ?
Antwort
, provided .
Karte 243
Frage
Linear table: constant slope check?
Antwort
Equal changes in must produce equal changes in ; compare across intervals.
Karte 244
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Decay factor 0.73: percent decrease?
Antwort
27 percent. Compute .
Karte 245
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Random assignment permits what causal claim?
Antwort
If the experiment is well controlled, differences between treatment groups can support a causal conclusion.
Karte 246
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Radius and tangent at the contact point?
Antwort
They are perpendicular.
Karte 247
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Positive slope means what for a linear function?
Antwort
The output increases as the input increases.
Karte 248
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Solve .
Antwort
. Equal positive bases other than 1 have equal exponents.
Karte 249
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Observational study supports causation?
Antwort
No. It can show association, but uncontrolled confounding variables may explain the pattern.
Karte 250
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Rectangular-prism volume?
Antwort
, or base area times height.
Karte 251
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Arithmetic sequence common difference?
Antwort
Subtract consecutive terms: .
Karte 252
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Compound interest formula?
Antwort
, where is the number of compounding periods per year.
Karte 253
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Larger random sample: effect on margin of error?
Antwort
It generally decreases the margin of error when the sampling method stays sound.
Karte 254
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Cylinder volume?
Antwort
.
Karte 255
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Arithmetic sequence nth term?
Antwort
.
Karte 256
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Rational expression: first domain check?
Antwort
Exclude values that make any original denominator zero, even if a factor later cancels.
Karte 257
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Slope of a line of best fit?
Antwort
The predicted change in the response variable for each 1-unit increase in the explanatory variable.
Karte 258
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Cone volume?
Antwort
.
Karte 259
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Solve a literal equation for one variable?
Antwort
Treat the other symbols as constants and use inverse operations to isolate the target variable.
Karte 260
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Why check rational-equation solutions?
Antwort
Clearing denominators can produce a value excluded from the original equation. Reject any value that makes an original denominator zero.
Karte 261
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Residual?
Antwort
Actual value minus predicted value. A positive residual means the point lies above the model.
Karte 262
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Sphere volume?
Antwort
.
Karte 263
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Boundary for a two-variable linear inequality?
Antwort
Replace the inequality with equality to draw the boundary line, then test a point for the shaded side.
Karte 264
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Why check a solution after squaring both sides?
Antwort
Squaring can introduce an extraneous solution. Substitute each candidate into the original radical equation.
Karte 265
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Positive correlation?
Antwort
Larger values of one variable tend to occur with larger values of the other. It does not prove causation.
Karte 266
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Rectangular-prism surface area?
Antwort
.
Karte 267
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Check a proposed system solution?
Antwort
Substitute the ordered pair into both original equations. It must make both true.
Karte 268
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Simplify .
Antwort
. Factor and take outside the radical.
Karte 269
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Extrapolation risk?
Antwort
A model may not keep the same pattern outside the observed data range.
Karte 270
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Area scale factor when lengths double?
Antwort
- Area scales with the square of the length factor: $2^2=4$.
Karte 271
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Horizontal line slope?
Antwort
- Its y-value does not change as x changes.
Karte 272
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Inverse function setup?
Antwort
Write , swap and , then solve for . Restrict the domain when needed to make the inverse a function.
Karte 273
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Percentage points versus percent change?
Antwort
A rate moving from 40 percent to 50 percent rises 10 percentage points but 25 percent relative to 40.
Karte 274
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y-intercept in a context?
Antwort
The predicted or initial output when the input is zero; check whether zero is meaningful in the situation.
Karte 275
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Quadratic maximum or minimum from vertex form?
Antwort
The vertex value is in ; it is a minimum if and a maximum if .
Karte 276
Frage
Line parallel to through ?
Antwort
. Parallel lines keep the same slope.
Karte 277
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Graph of ?
Antwort
Shift the graph of right units and up units.
Karte 278
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Population versus sample?
Antwort
The population is the full group of interest; a sample is the subset actually observed.
Karte 279
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Linear model from initial value and rate ?
Antwort
. The initial value is the output at input zero.
Karte 280
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Function composition ?
Antwort
. Evaluate the inner function first.
Karte 281
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Density?
Antwort
Mass divided by volume. Keep the units consistent.
Karte 282
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Vertical line slope?
Antwort
Undefined because , which would require division by zero.
Karte 283
Frage
Nonlinear system with one equation solved for ?
Antwort
Substitute that expression for into the other equation, solve for , then find each matching .
Karte 284
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Weighted percentage across unequal groups?
Antwort
Convert each percentage to a count or weight, add the successes, then divide by the combined total.
Karte 285
Frage
Line perpendicular to a nonzero finite slope through ?
Antwort
Use slope in , when is nonzero and finite.
Karte 286
Frage
Cancel a common factor in a rational expression?
Antwort
Cancel factors, not terms, and keep every restriction from the original denominator.
Karte 287
Frage
Solve a linear equation containing fractions?
Antwort
Multiply every term by the least common denominator first, then solve the resulting linear equation.
Karte 288
Frage
Rewrite using base .
Antwort
. This can turn an exponential expression into a quadratic form.
Karte 289
Frage
Rate units check?
Antwort
Write the numerator and denominator units explicitly, such as kilometers per hour, then convert only if the requested units differ.
Karte 290
Frage
Strict versus inclusive inequality endpoint?
Antwort
Use an open point for or and a closed point for or .
Karte 291
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Even-multiplicity zero on a graph?
Antwort
The graph touches the x-axis and turns around; it does not cross there.
Karte 292
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System word problem: first setup step?
Antwort
Define the variables with units, then translate two independent relationships into equations.
Karte 293
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When does a quadratic have exactly one real solution?
Antwort
When . The repeated root is the vertex's x-coordinate.
Karte 294
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Two-way table: denominator for “among group B”?
Antwort
Use the total for group B, not the grand total. The wording makes B the condition.
Karte 295
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Find an input when .
Antwort
Set the function rule equal to and solve for ; there may be zero, one, or several inputs.
Karte 296
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Graph of ?
Antwort
Reflect the graph of across the x-axis.
Karte 297
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Three consecutive integers starting with ?
Antwort
, , and .
Karte 298
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Line–parabola intersections from a substituted quadratic?
Antwort
Use its discriminant: positive means two intersections, zero one tangent intersection, and negative none.
Karte 299
Frage
Linear equation with no solution: coefficient pattern?
Antwort
After simplification, the variable terms cancel and leave a false statement, such as .
Karte 300
Frage
Zeros of a function on its graph?
Antwort
The x-coordinates where the graph meets the x-axis, so .
300 Karten
Digital SAT Flashcards: Math, Grammar & Words in Context
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