Central idea of a passage?

The passage's main claim or controlling point. It should cover the whole passage, not one striking detail.

The shade trees mitigated the midday heat. Meaning of “mitigated”?

Reduced. The trees made the heat less severe.

The first plan was affordable. However, it took twice as long. What relationship does “However” signal?

Contrast. The second statement differs from or qualifies the first.

Three standard joins for two independent clauses?

A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence.

Best supporting detail?

The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is.

A second archive corroborated the diary's date. Meaning of “corroborated”?

Confirmed with supporting evidence.

Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal?

Conclusion from a reason. The final statement follows logically from the stated premises.

Introductory dependent clause before a main clause?

Use a comma after the dependent clause. Example: “Although rain fell, the match continued.”

A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports.

The team called its result tentative until replication. Meaning of “tentative”?

Provisional or not yet certain.

Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal?

Illustration. The second statement gives a specific case of the broader point.

Singular subject with an intervening prepositional phrase?

Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject.

Strongest textual evidence?

The quotation or detail that most directly supports the target claim, with the fewest extra assumptions.

The error had a negligible effect on the total. Meaning of “negligible”?

So small that it is not important.

The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal?

Similarity. The second statement matches the first in a relevant way.

Opening modifier placement?

Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.”

Quantitative evidence for a claim?

Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline.

The lab used a conventional method before testing a new one. Meaning of “conventional”?

Traditional or commonly accepted.

Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal?

Simultaneous events. The second event happens at the same time as the first.

Singular possessive noun?

Usually add apostrophe + s. Example: “the scientist's notebook.”

Trend in a table or graph?

State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence.

The essay offered a novel explanation for the pattern. Meaning of “novel”?

New or original in this context.

The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal?

Concession. The second statement remains true despite the limitation in the first.

Parallel items in a series?

Use the same grammatical form for each item. Example: “to collect, analyze, and report data.”

Claim stronger than the evidence?

Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion.

The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal?

Addition. The second statement adds a related supporting point.

Colon before an explanation or list?

Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.”

Claim versus evidence?

A claim is the point being argued; evidence is the information used to support it.

The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”?

Open to more than one interpretation.

The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal?

Replacement. The second statement substitutes one action for another.

Count nouns versus mass nouns?

Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise.

Effect of a counterexample?

It weakens a universal claim by showing at least one case where the claim fails.

The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal?

Later step in a sequence. The second event occurs after the first.

Essential clause punctuation?

Do not surround an essential clause with commas. It identifies which person or thing the sentence means.

Correlation alone proves causation?

No. A relationship between variables does not by itself show that one caused the other.

The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal?

Restatement for clarity. The second statement rephrases the first.

Verb tense across a paragraph?

Keep the time frame consistent unless the timing actually changes.

Missing information in a data claim?

Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim.

The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal?

General-to-specific detail. The second statement narrows the broad first statement.

Coordinate adjectives?

Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.”

Two sources on the same event?

Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement.

Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal?

Cause and effect. The second statement is an outcome of the first.

A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb.

Inference from a narrow sample?

Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence.

Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal?

Overall conclusion. The second statement gives the final judgment after earlier considerations.

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.

Por Open Study Contributor

Sobre este baralho

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.

Cartões deste baralho

Cartão 1
Pergunta
Central idea of a passage?
Resposta
The passage's main claim or controlling point. It should cover the whole passage, not one striking detail.
Cartão 2
Pergunta
The shade trees mitigated the midday heat. Meaning of “mitigated”?
Resposta
Reduced. The trees made the heat less severe.
Cartão 3
Pergunta
The first plan was affordable. However, it took twice as long. What relationship does “However” signal?
Resposta
Contrast. The second statement differs from or qualifies the first.
Cartão 4
Pergunta
Three standard joins for two independent clauses?
Resposta
A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence.
Cartão 5
Pergunta
Best supporting detail?
Resposta
The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is.
Cartão 6
Pergunta
A second archive corroborated the diary's date. Meaning of “corroborated”?
Resposta
Confirmed with supporting evidence.
Cartão 7
Pergunta
Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal?
Resposta
Conclusion from a reason. The final statement follows logically from the stated premises.
Cartão 8
Pergunta
Introductory dependent clause before a main clause?
Resposta
Use a comma after the dependent clause. Example: “Although rain fell, the match continued.”
Cartão 9
Pergunta
Valid inference?
Resposta
A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports.
Cartão 10
Pergunta
The team called its result tentative until replication. Meaning of “tentative”?
Resposta
Provisional or not yet certain.
Cartão 11
Pergunta
Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal?
Resposta
Illustration. The second statement gives a specific case of the broader point.
Cartão 12
Pergunta
Singular subject with an intervening prepositional phrase?
Resposta
Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject.
Cartão 13
Pergunta
Strongest textual evidence?
Resposta
The quotation or detail that most directly supports the target claim, with the fewest extra assumptions.
Cartão 14
Pergunta
The error had a negligible effect on the total. Meaning of “negligible”?
Resposta
So small that it is not important.
Cartão 15
Pergunta
The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal?
Resposta
Similarity. The second statement matches the first in a relevant way.
Cartão 16
Pergunta
Opening modifier placement?
Resposta
Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.”
Cartão 17
Pergunta
Quantitative evidence for a claim?
Resposta
Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline.
Cartão 18
Pergunta
The lab used a conventional method before testing a new one. Meaning of “conventional”?
Resposta
Traditional or commonly accepted.
Cartão 19
Pergunta
Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal?
Resposta
Simultaneous events. The second event happens at the same time as the first.
Cartão 20
Pergunta
Singular possessive noun?
Resposta
Usually add apostrophe + s. Example: “the scientist's notebook.”
Cartão 21
Pergunta
Trend in a table or graph?
Resposta
State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence.
Cartão 22
Pergunta
The essay offered a novel explanation for the pattern. Meaning of “novel”?
Resposta
New or original in this context.
Cartão 23
Pergunta
The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal?
Resposta
Concession. The second statement remains true despite the limitation in the first.
Cartão 24
Pergunta
Parallel items in a series?
Resposta
Use the same grammatical form for each item. Example: “to collect, analyze, and report data.”
Cartão 25
Pergunta
Claim stronger than the evidence?
Resposta
Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion.
Cartão 26
Pergunta
Her account is plausible because it matches the records. Meaning of “plausible”?
Resposta
Reasonable or believable.
Cartão 27
Pergunta
The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal?
Resposta
Addition. The second statement adds a related supporting point.
Cartão 28
Pergunta
Colon before an explanation or list?
Resposta
Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.”
Cartão 29
Pergunta
Claim versus evidence?
Resposta
A claim is the point being argued; evidence is the information used to support it.
Cartão 30
Pergunta
The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”?
Resposta
Open to more than one interpretation.
Cartão 31
Pergunta
The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal?
Resposta
Replacement. The second statement substitutes one action for another.
Cartão 32
Pergunta
Count nouns versus mass nouns?
Resposta
Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise.
Cartão 33
Pergunta
Effect of a counterexample?
Resposta
It weakens a universal claim by showing at least one case where the claim fails.
Cartão 34
Pergunta
Rainfall was sporadic: brief showers interrupted long dry periods. Meaning of “sporadic”?
Resposta
Irregular and occasional.
Cartão 35
Pergunta
The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal?
Resposta
Later step in a sequence. The second event occurs after the first.
Cartão 36
Pergunta
Essential clause punctuation?
Resposta
Do not surround an essential clause with commas. It identifies which person or thing the sentence means.
Cartão 37
Pergunta
Correlation alone proves causation?
Resposta
No. A relationship between variables does not by itself show that one caused the other.
Cartão 38
Pergunta
Subsequent trials produced the same result. Meaning of “subsequent”?
Resposta
Coming later in time.
Cartão 39
Pergunta
The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal?
Resposta
Restatement for clarity. The second statement rephrases the first.
Cartão 40
Pergunta
Verb tense across a paragraph?
Resposta
Keep the time frame consistent unless the timing actually changes.
Cartão 41
Pergunta
Missing information in a data claim?
Resposta
Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim.
Cartão 42
Pergunta
The coating helps the fabric retain heat. Meaning of “retain”?
Resposta
Keep or continue to hold.
Cartão 43
Pergunta
The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal?
Resposta
General-to-specific detail. The second statement narrows the broad first statement.
Cartão 44
Pergunta
Coordinate adjectives?
Resposta
Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.”
Cartão 45
Pergunta
Two sources on the same event?
Resposta
Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement.
Cartão 46
Pergunta
The survey was designed to elicit candid responses. Meaning of “elicit”?
Resposta
Draw out or bring forth.
Cartão 47
Pergunta
Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal?
Resposta
Cause and effect. The second statement is an outcome of the first.
Cartão 48
Pergunta
Sentence fragment?
Resposta
A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb.
Cartão 49
Pergunta
Inference from a narrow sample?
Resposta
Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence.
Cartão 50
Pergunta
Cost was the main constraint on the project. Meaning of “constraint”?
Resposta
A limit or restriction.
Cartão 51
Pergunta
Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal?
Resposta
Overall conclusion. The second statement gives the final judgment after earlier considerations.
Cartão 52
Pergunta
Conjunctive adverb between independent clauses?
Resposta
Use a semicolon before it and a comma after it. Example: “The route was longer; however, it was safer.”
Cartão 53
Pergunta
Most accurate summary?
Resposta
State the central idea and its essential support without adding opinions or minor details.
Cartão 54
Pergunta
The review was comprehensive, covering every recorded case. Meaning of “comprehensive”?
Resposta
Complete and wide-ranging.
Cartão 55
Pergunta
The method is efficient. Indeed, it cuts processing time in half. What relationship does “Indeed” signal?
Resposta
Emphasis and confirmation. The second statement reinforces the first with a stronger detail.
Cartão 56
Pergunta
Who versus whom?
Resposta
Use “who” as a subject and “whom” as an object. Test with he/him: “whom” matches “him.”
Cartão 57
Pergunta
Evidence that best resolves a disagreement?
Resposta
Choose evidence that tests the specific point on which the sources differ, not a fact both already accept.
Cartão 58
Pergunta
The two materials have distinct properties. Meaning of “distinct”?
Resposta
Clearly different or separate.
Cartão 59
Pergunta
The forecast warned of rain. Still, the outdoor concert began on time. What relationship does “Still” signal?
Resposta
Concession. The second statement remains true despite the obstacle in the first.
Cartão 60
Pergunta
Comma before an introduced direct quotation?
Resposta
Use a comma after a speech tag. Example: “Mina wrote, ‘The sample is ready.’”
Cartão 61
Pergunta
The conclusion was qualified by two important exceptions. Meaning of “qualified”?
Resposta
Limited or modified, rather than stated without conditions.
Cartão 62
Pergunta
Notes for a synthesis goal?
Resposta
Use only facts that directly serve the stated goal. Relevant notes can be omitted if they do not help that purpose.
Cartão 63
Pergunta
Comma splice?
Resposta
Two independent clauses joined only by a comma. Replace it with a period or semicolon, or add a coordinating conjunction.
Cartão 64
Pergunta
Comma between subject and verb?
Resposta
Do not use one unless an interrupting phrase requires paired commas. “The results of the trial were clear” takes no comma after “trial.”
Cartão 65
Pergunta
The new sensor made the older model obsolete. Meaning of “obsolete”?
Resposta
No longer useful or current because something newer replaced it.
Cartão 66
Pergunta
Source attribution in a synthesis?
Resposta
Name the source when its identity, authority, or perspective matters to the rhetorical goal.
Cartão 67
Pergunta
Compound subject joined by “and”?
Resposta
Use a plural verb in the usual case. Example: “The map and the notes are useful.”
Cartão 68
Pergunta
Dangling opening modifier?
Resposta
It lacks the intended doer immediately after the modifier. Rewrite so the doer becomes the subject.
Cartão 69
Pergunta
Researchers derived the estimate from three measurements. Meaning of “derived”?
Resposta
Obtained from a source or calculation.
Cartão 70
Pergunta
Chronological synthesis?
Resposta
Order events by time and use dates or sequence words only when they help the reader follow the progression.
Cartão 71
Pergunta
Plural noun ending in s: possessive form?
Resposta
Add an apostrophe after the existing s. Example: “the researchers' notes.”
Cartão 72
Pergunta
Logical comparison?
Resposta
Compare like with like. Example: compare one city's rainfall with another city's rainfall, not with the city itself.
Cartão 73
Pergunta
The article advocates preserving the wetland. Meaning of “advocates”?
Resposta
Publicly supports or argues for.
Cartão 74
Pergunta
Compare evidence from two studies?
Resposta
State the shared measure first, then the relevant difference in result, method, or population.
Cartão 75
Pergunta
Colon after an incomplete lead-in?
Resposta
Do not use one. A colon must follow a complete clause, so “The reasons include:” is incorrect.
Cartão 76
Pergunta
Number versus amount?
Resposta
Use “number” for countable items and “amount” for uncountable quantities. Example: number of files, amount of water.
Cartão 77
Pergunta
Portable chargers are now ubiquitous on long trips. Meaning of “ubiquitous”?
Resposta
Present or found almost everywhere.
Cartão 78
Pergunta
Synthesis that emphasizes a difference?
Resposta
Use the same comparison point for both subjects, then state the contrast directly.
Cartão 79
Pergunta
Nonessential clause or phrase?
Resposta
Set it off with paired commas. The sentence should keep its core identity and meaning when the phrase is removed.
Cartão 80
Pergunta
Earlier of two past actions?
Resposta
Use past perfect when the sequence needs clarification. Example: “The team had left before the storm began.”
Cartão 81
Pergunta
Sentence 2 presents an exception to sentence 1. Its function?
Resposta
It qualifies the first claim by limiting when or how broadly it applies.
Cartão 82
Pergunta
Rhetorical goal: define a term?
Resposta
Give the term's relevant meaning before using details or examples that depend on it.
Cartão 83
Pergunta
Cumulative adjectives?
Resposta
Do not separate them with a comma when each adjective builds on the next. Example: “three small glass jars.”
Cartão 84
Pergunta
Run-on sentence?
Resposta
Independent clauses joined without valid punctuation or a conjunction. Add a period, semicolon, or comma plus coordinating conjunction.
Cartão 85
Pergunta
Sentence 2 gives a specific case after a general claim. Its function?
Resposta
It illustrates the claim with an example.
Cartão 86
Pergunta
Introduce a quotation in a synthesis?
Resposta
Give enough source and context to show why the quotation matters; do not leave it unattached.
Cartão 87
Pergunta
Relative pronoun for people?
Resposta
Use “who” or “whom,” depending on case. Example: “the engineer who designed the bridge.”
Cartão 88
Pergunta
Integrated quotation punctuation?
Resposta
Do not add a comma when the quotation completes the grammar of the sentence. Example: The report calls the result “unexpected.”
Cartão 89
Pergunta
Sentence 2 admits a limitation before defending the claim. Its function?
Resposta
It makes a concession, showing that the writer recognizes a complication.
Cartão 90
Pergunta
Avoid redundancy in synthesis?
Resposta
State each needed idea once. Prefer the version that preserves meaning with fewer repeated words.
Cartão 91
Pergunta
Semicolon between two independent clauses?
Resposta
Use it without a coordinating conjunction when the ideas are closely related. Example: “The trial ended; the analysis began.”
Cartão 92
Pergunta
Comma in a compound predicate?
Resposta
Usually omit it when one subject performs both actions. Example: “The team collected the samples and recorded the temperature.”
Cartão 93
Pergunta
Sentence 2 explains what a technical term means. Its function?
Resposta
It defines or clarifies the term.
Cartão 94
Pergunta
Combine two related sentences?
Resposta
Make the logical relationship explicit and remove repeated material without changing the facts.
Cartão 95
Pergunta
Either/or subject agreement?
Resposta
Make the verb agree with the nearer subject. Example: “Either the notes or the map is missing.”
Cartão 96
Pergunta
Active versus passive voice?
Resposta
Choose the voice that fits the focus. Active highlights the doer; passive can highlight the action or receiver.
Cartão 97
Pergunta
Sentence 2 describes the outcome of sentence 1. Its function?
Resposta
It presents an effect or consequence.
Cartão 98
Pergunta
Formal academic register?
Resposta
Use precise, neutral wording and avoid slang, vague intensifiers, and chatty asides unless the goal calls for them.
Cartão 99
Pergunta
Its or it's?
Resposta
“Its” is possessive; “it's” means “it is” or “it has.”
Cartão 100
Pergunta
Adjective versus adverb?
Resposta
An adjective modifies a noun; an adverb usually modifies a verb, adjective, or adverb. Example: a careful test; test carefully.
Cartão 101
Pergunta
A study reports a result without arguing for a policy. Author's purpose?
Resposta
To inform or explain, not necessarily to persuade.
Cartão 102
Pergunta
Concise synthesis?
Resposta
Keep every fact needed for the rhetorical goal and remove details that repeat or distract from it.
Cartão 103
Pergunta
Single dash for emphasis?
Resposta
Use it after a complete thought to spotlight a final explanation or turn. Example: “One result stood out—the oldest sample.”
Cartão 104
Pergunta
Comma with direct address?
Resposta
Set off the person being addressed. Example: “Rina, please check the units.”
Cartão 105
Pergunta
Why acknowledge a limitation?
Resposta
To define the claim's boundary and show how the evidence should be interpreted.
Cartão 106
Pergunta
Quantitative comparison in a synthesis?
Resposta
Name both values, the shared unit, and the direction or size of the difference.
Cartão 107
Pergunta
Each of the samples: verb number?
Resposta
Singular. “Each of the samples was labeled.” The subject is “each.”
Cartão 108
Pergunta
Between versus among?
Resposta
Use “between” for distinct individual relationships and “among” for a group without separate pairings.
Cartão 109
Pergunta
Rhetorical question in an argument?
Resposta
It can frame the issue or prompt the reader to consider an implied answer; it is not evidence by itself.
Cartão 110
Pergunta
Claim before or after support?
Resposta
Place it where the rhetorical goal is clearest: before evidence for a direct point, or after evidence for an evidence-led conclusion.
Cartão 111
Pergunta
Restrictive “that” versus nonrestrictive “which”?
Resposta
Use “that” without commas for essential information; use “which” with commas for removable information.
Cartão 112
Pergunta
Present perfect use?
Resposta
Use it for an action connected to the present or continuing to now. Example: “The team has tracked rainfall since May.”
Cartão 113
Pergunta
Two texts reach the same conclusion with different evidence. Relationship?
Resposta
They agree in conclusion but support it through different evidence.
Cartão 114
Pergunta
Group related ideas in a synthesis?
Resposta
Keep facts serving the same point together, then signal the move to a new point.
Cartão 115
Pergunta
Compound modifier before a noun?
Resposta
Hyphenate it when needed for clarity. Example: “a well-designed study.”
Cartão 116
Pergunta
Affect or effect?
Resposta
“Affect” is usually a verb meaning influence; “effect” is usually a noun meaning result.
Cartão 117
Pergunta
Two texts offer incompatible explanations. Relationship?
Resposta
They disagree about the cause or interpretation, even if they share the same observations.
Cartão 118
Pergunta
Replace a vague pronoun in synthesis?
Resposta
Use the precise noun when two or more possible antecedents could confuse the reader.
Cartão 119
Pergunta
Comma-separated list?
Resposta
Use commas between three or more parallel items. A final serial comma can prevent ambiguity.
Cartão 120
Pergunta
Main clause before a dependent clause?
Resposta
Usually no comma when the dependent clause is essential. Example: “The match continued although rain fell.”
Cartão 121
Pergunta
Two authors use the same evidence but different assumptions. Key difference?
Resposta
Their perspectives or interpretive frameworks, not the underlying evidence.
Cartão 122
Pergunta
Independent clauses joined with a coordinating conjunction?
Resposta
Place a comma before the conjunction. Example: “The sensor failed, so the team repeated the trial.”
Cartão 123
Pergunta
Introductory transition?
Resposta
Follow it with a comma when it modifies the whole sentence. Example: “However, the second trial succeeded.”
Cartão 124
Pergunta
Pronoun–antecedent agreement?
Resposta
Match number and make the reference clear. Singular “they” is standard when a person's gender is unknown or irrelevant.
Cartão 125
Pergunta
Paired em dashes?
Resposta
Use them to set off an emphatic interruption. Both dashes are needed when the sentence continues after it.
Cartão 126
Pergunta
How does new evidence relate to an earlier claim?
Resposta
It may support, weaken, qualify, or leave the claim unchanged. Match the evidence to the exact claim.
Cartão 127
Pergunta
Their, there, or they're?
Resposta
“Their” is possessive, “there” refers to place or existence, and “they're” means “they are.”
Cartão 128
Pergunta
Good or well?
Resposta
“Good” is usually an adjective; “well” is usually an adverb. A person can feel good and perform well.
Cartão 129
Pergunta
Appositive naming the same noun?
Resposta
Set a nonessential appositive off with commas. Example: “Dr. Rao, the lead author, presented the findings.”
Cartão 130
Pergunta
Why use an analogy?
Resposta
To clarify an unfamiliar idea through a relevant similarity to something more familiar.
Cartão 131
Pergunta
Than or then?
Resposta
“Than” makes a comparison; “then” refers to time or consequence.
Cartão 132
Pergunta
Hypothetical contrary-to-fact “if” clause?
Resposta
Use subjunctive “were.” Example: “If the sample were larger, the estimate would be steadier.”
Cartão 133
Pergunta
Plural noun with no possession?
Resposta
Do not add an apostrophe. Write “three sensors,” not “three sensor's.”
Cartão 134
Pergunta
Neutral, evidence-led wording indicates what tone?
Resposta
Objective. It emphasizes information rather than strong personal judgment.
Cartão 135
Pergunta
Complex list with internal commas?
Resposta
Use semicolons between the main items. Example: “Lima, Peru; Accra, Ghana; and Hanoi, Vietnam.”
Cartão 136
Pergunta
Ambiguous pronoun?
Resposta
A pronoun with more than one plausible antecedent. Replace it with the intended noun.
Cartão 137
Pergunta
Parentheses around nonessential information?
Resposta
Use them for an aside that is less central than the main sentence. The sentence must remain grammatical without it.
Cartão 138
Pergunta
Repeated doubt about the evidence indicates what tone?
Resposta
Skeptical. The writer questions whether a claim is adequately supported.
Cartão 139
Pergunta
Superlative comparison?
Resposta
Use it for one member against a group of three or more. Example: “the fastest of the four methods.”
Cartão 140
Pergunta
Pronoun after a preposition?
Resposta
Use the object form. Write “between you and me,” not “between you and I.”
Cartão 141
Pergunta
Apostrophe in a contraction?
Resposta
It marks omitted letters. Example: “can't” contracts “cannot,” and “they're” contracts “they are.”
Cartão 142
Pergunta
Coordinate-adjective test?
Resposta
If “and” works between the adjectives and their order can reverse, use a comma between them.
Cartão 143
Pergunta
Double comparative?
Resposta
Use only one comparative marker. Write “more efficient” or “faster,” not “more faster.”
Cartão 144
Pergunta
Lie or lay?
Resposta
“Lie” means recline and takes no object; “lay” means place and takes an object. Present: lie/lay; past: lay/laid.
Cartão 145
Pergunta
Who's or whose?
Resposta
“Who's” means “who is” or “who has”; “whose” is possessive.
Cartão 146
Pergunta
Standard comparison with “different”?
Resposta
Use “different from.” Example: “This result is different from the earlier estimate.”
Cartão 147
Pergunta
Paired construction with two endpoints?
Resposta
Use “between” with “and”: “between 10 and 15,” not “between 10 to 15.”
Cartão 148
Pergunta
Verb mood in a coordinated idea?
Resposta
Keep the mood consistent unless the meaning changes. Do not shift from a command to a statement without reason.
Cartão 149
Pergunta
Possessive pronoun apostrophe?
Resposta
Do not use one. Write “hers,” “ours,” “yours,” and “theirs.”
Cartão 150
Pergunta
Comma between a preposition and its object?
Resposta
Do not use one. Keep the prepositional phrase intact: “in the final report,” not “in, the final report.”
300 cartões
Digital SAT Flashcards: Math, Grammar & Words in Context
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Cartão 151
Pergunta
Solve $ax+b=c$ for $x$ , where $a≠0$ .
Resposta
$x=(c-b)/a$ . Subtract $b$ first, then divide by $a$ .
Cartão 152
Pergunta
Product of powers with the same base?
Resposta
$a^m a^n=a^{m+n}$ . Keep the base and add the exponents.
Cartão 153
Pergunta
Unit rate?
Resposta
The amount per 1 unit. Divide both quantities by the same value so the denominator becomes 1.
Cartão 154
Pergunta
Rectangle area?
Resposta
$A=lw$ , where $l$ is length and $w$ is width.
Cartão 155
Pergunta
Slope from two points?
Resposta
$m=(y_2-y_1)/(x_2-x_1)$ . Subtract coordinates in the same order.
Cartão 156
Pergunta
Quotient of powers with the same base?
Resposta
$a^m/a^n=a^{m-n}$ for $a≠0$ .
Cartão 157
Pergunta
Conversion factor setup?
Resposta
Multiply by a ratio equal to 1, with the unwanted unit placed to cancel.
Cartão 158
Pergunta
Triangle area?
Resposta
$A=(1/2)bh$ . The height must be perpendicular to the chosen base.
Cartão 159
Pergunta
Slope-intercept form?
Resposta
$y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.
Cartão 160
Pergunta
Power raised to a power?
Resposta
$(a^m)^n=a^{mn}$ . Multiply the exponents.
Cartão 161
Pergunta
Dimensional analysis check?
Resposta
Cancel units algebraically. The units left at the end should match the quantity requested.
Cartão 162
Pergunta
Trapezoid area?
Resposta
$A=(1/2)(b_1+b_2)h$ . The height is perpendicular to the parallel bases.
Cartão 163
Pergunta
Point-slope form?
Resposta
$y-y_1=m(x-x_1)$ . Use a known point $(x_1,y_1)$ and the slope $m$ .
Cartão 164
Pergunta
Negative exponent?
Resposta
$a^{-n}=1/a^n$ for $a≠0$ .
Cartão 165
Pergunta
Constant of proportionality in $y=kx$ ?
Resposta
$k=y/x$ for $x≠0$ . It is also the unit rate and slope.
Cartão 166
Pergunta
Circle area?
Resposta
$A=πr^2$ .
Cartão 167
Pergunta
Intercepts from $Ax+By=C$ ?
Resposta
Set $y=0$ for the x-intercept and set $x=0$ for the y-intercept.
Cartão 168
Pergunta
Fractional exponent?
Resposta
$a^{m/n}$ means the nth root of $a^m$ . For example, $a^{1/2}=√a$ .
Cartão 169
Pergunta
Scale drawing length?
Resposta
Use a proportion with corresponding lengths in the same order, then apply the stated scale factor.
Cartão 170
Pergunta
Circle circumference?
Resposta
$C=2πr=πd$ .
Cartão 171
Pergunta
Parallel nonvertical lines: slope relationship?
Resposta
They have equal slopes. Distinct parallel lines have different intercepts.
Cartão 172
Pergunta
Difference of squares?
Resposta
$a^2-b^2=(a-b)(a+b)$ .
Cartão 173
Pergunta
Percent change?
Resposta
New minus original, divided by the original, then multiplied by 100 percent. The original value is the denominator.
Cartão 174
Pergunta
Arc length from central angle $θ$ in degrees?
Resposta
$L=(θ/360)(2πr)$ .
Cartão 175
Pergunta
Perpendicular nonvertical lines: slope relationship?
Resposta
Their slopes are negative reciprocals, so $m_1m_2=-1$ .
Cartão 176
Pergunta
Perfect-square trinomial pattern?
Resposta
$a^2+2ab+b^2=(a+b)^2$ and $a^2-2ab+b^2=(a-b)^2$ .
Cartão 177
Pergunta
Increase by $r$ percent: multiplier?
Resposta
$1+r/100$ . Multiply the original value by this factor.
Cartão 178
Pergunta
Sector area from central angle $θ$ in degrees?
Resposta
$A=(θ/360)(πr^2)$ .
Cartão 179
Pergunta
x-intercept of a graph?
Resposta
A point where $y=0$ and the graph meets the x-axis.
Cartão 180
Pergunta
First step in factoring $ax^2+bx+c$ ?
Resposta
Look for common factors and two binomials whose product reproduces the middle and constant terms.
Cartão 181
Pergunta
Original value after a 20 percent increase to 84?
Resposta
Divide the final value by the multiplier: $84/1.20=70$.
Cartão 182
Pergunta
Triangle interior-angle sum?
Resposta
$180°$ .
Cartão 183
Pergunta
y-intercept of a graph?
Resposta
A point where $x=0$ and the graph meets the y-axis.
Cartão 184
Pergunta
Roots from $(x-p)(x-q)=0$ ?
Resposta
$x=p$ or $x=q$ , by the zero-product property.
Cartão 185
Pergunta
Weighted average?
Resposta
Sum of each value times its weight, divided by the sum of the weights. Do not take a simple average of unequal groups.
Cartão 186
Pergunta
Exterior angle of a triangle?
Resposta
It equals the sum of the two remote interior angles.
Cartão 187
Pergunta
Line through two points?
Resposta
Find the slope, then substitute either point into point-slope or slope-intercept form.
Cartão 188
Pergunta
Quadratic formula?
Resposta
$x=(-b±√(b^2-4ac))/(2a)$ for $ax^2+bx+c=0$ .
Cartão 189
Pergunta
Arithmetic mean?
Resposta
Add all values and divide by the number of values.
Cartão 190
Pergunta
Parallel lines cut by a transversal: alternate interior angles?
Resposta
They are congruent.
Cartão 191
Pergunta
Slope's units in context?
Resposta
Output units per input unit. In $y$ versus $x$ , slope units are y-units divided by x-units.
Cartão 192
Pergunta
What does $b^2-4ac$ tell you?
Resposta
The number of real solutions: positive gives two, zero gives one, and negative gives none.
Cartão 193
Pergunta
Median?
Resposta
The middle value after ordering the data; for an even count, average the two middle values.
Cartão 194
Pergunta
Similar triangles: corresponding sides?
Resposta
They are proportional. Match sides opposite equal angles.
Cartão 195
Pergunta
Direct variation model?
Resposta
$y=kx$ . It is linear and passes through the origin.
Cartão 196
Pergunta
Vertex x-coordinate of $ax^2+bx+c$ ?
Resposta
$x=-b/(2a)$ .
Cartão 197
Pergunta
Range of a data set?
Resposta
Maximum minus minimum.
Cartão 198
Pergunta
Scale factor $k$ : area factor?
Resposta
$k^2$ . Lengths scale by $k$ , while areas scale by the square of $k$ .
Cartão 199
Pergunta
Solution of a two-line system?
Resposta
The intersection point, whose coordinates satisfy both equations.
Cartão 200
Pergunta
Vertex form of a quadratic?
Resposta
$y=a(x-h)^2+k$ , with vertex $(h,k)$ .
Cartão 201
Pergunta
Interquartile range?
Resposta
$IQR=Q_3-Q_1$ . It measures the spread of the middle half of the data.
Cartão 202
Pergunta
Pythagorean theorem?
Resposta
$a^2+b^2=c^2$ for a right triangle, where $c$ is the hypotenuse.
Cartão 203
Pergunta
Substitution in a system?
Resposta
Solve one equation for a variable and replace that variable in the other equation.
Cartão 204
Pergunta
Axis of symmetry of $y=a(x-h)^2+k$ ?
Resposta
$x=h$ .
Cartão 205
Pergunta
Larger standard deviation means what?
Resposta
The data are more spread out around the mean.
Cartão 206
Pergunta
45°-45°-90° side ratio?
Resposta
$1:1:√2$ . The hypotenuse is a leg times $√2$ .
Cartão 207
Pergunta
Elimination in a system?
Resposta
Add or subtract equations so one variable cancels, then solve for the other.
Cartão 208
Pergunta
Completing the square?
Resposta
For $x^2+bx$ , add $(b/2)^2$ to form $(x+b/2)^2$ .
Cartão 209
Pergunta
Effect of a high outlier on the mean?
Resposta
It usually pulls the mean upward. The median is often less affected.
Cartão 210
Pergunta
30°-60°-90° side ratio?
Resposta
$1:√3:2$ , opposite $30°$ , $60°$ , and $90°$ respectively.
Cartão 211
Pergunta
Parallel lines in a system?
Resposta
No solution when they are distinct: equal slopes and different intercepts.
Cartão 212
Pergunta
Sum and product of roots of $ax^2+bx+c=0$ ?
Resposta
Sum $=-b/a$ and product $=c/a$ .
Cartão 213
Pergunta
Add the same constant to every data value: effect?
Resposta
The mean and median increase by that constant; measures of spread stay unchanged.
Cartão 214
Pergunta
Right-triangle sine?
Resposta
Sine of $θ$ equals opposite over hypotenuse.
Cartão 215
Pergunta
Same line written two ways in a system?
Resposta
Infinitely many solutions. Simplifying either equation produces the other.
Cartão 216
Pergunta
Remainder when $P(x)$ is divided by $x-a$ ?
Resposta
$P(a)$ , by the Remainder Theorem.
Cartão 217
Pergunta
Multiply every data value by positive $k$ : effect?
Resposta
The mean, median, range, IQR, and standard deviation are all multiplied by $k$ .
Cartão 218
Pergunta
Right-triangle cosine?
Resposta
Cosine of $θ$ equals adjacent over hypotenuse.
Cartão 219
Pergunta
Multiply or divide an inequality by a negative number?
Resposta
Reverse the inequality sign.
Cartão 220
Pergunta
When is $x-a$ a factor of $P(x)$ ?
Resposta
When $P(a)=0$ , by the Factor Theorem.
Cartão 221
Pergunta
Joint probability from a two-way table?
Resposta
Divide the count in the intersection cell by the grand total.
Cartão 222
Pergunta
Right-triangle tangent?
Resposta
Tangent of $θ$ equals opposite over adjacent.
Cartão 223
Pergunta
Compound inequality with “and”?
Resposta
Use the intersection: values that satisfy both inequalities.
Cartão 224
Pergunta
Even degree with positive leading coefficient: end behavior?
Resposta
Both ends rise: $P(x)→∞$ as $x→±∞$ .
Cartão 225
Pergunta
Conditional probability $P(A|B)$ ?
Resposta
$P(A∩B)/P(B)$ . Restrict the denominator to outcomes in $B$ .
Cartão 226
Pergunta
Complementary acute angles: sine–cosine relationship?
Resposta
The sine of $θ$ equals the cosine of $90°-θ$ .
Cartão 227
Pergunta
Compound inequality with “or”?
Resposta
Use the union: values that satisfy at least one inequality.
Cartão 228
Pergunta
Odd degree with positive leading coefficient: end behavior?
Resposta
The left end falls and the right end rises.
Cartão 229
Pergunta
Independent events $A$ and $B$ ?
Resposta
$P(A∩B)=P(A)P(B)$ . Knowing one occurred does not change the probability of the other.
Cartão 230
Pergunta
Distance between $(x_1,y_1)$ and $(x_2,y_2)$ ?
Resposta
$√((x_2-x_1)^2+(y_2-y_1)^2)$ .
Cartão 231
Pergunta
Solve $|x-a|=b$ for $b≥0$ .
Resposta
$x-a=b$ or $x-a=-b$ . Absolute value represents distance from $a$ .
Cartão 232
Pergunta
Exponential growth model?
Resposta
$y=a(1+r)^t$ , where $a$ is the initial value and $r$ is the growth rate per period.
Cartão 233
Pergunta
Mutually exclusive events?
Resposta
They cannot occur together, so $P(A∪B)=P(A)+P(B)$ .
Cartão 234
Pergunta
Midpoint of two points?
Resposta
$((x_1+x_2)/2,(y_1+y_2)/2)$ .
Cartão 235
Pergunta
Solve $|x-a|<b$ for $b>0$ .
Resposta
$a-b<x<a+b$ . The solution lies within distance $b$ of $a$ .
Cartão 236
Pergunta
Exponential decay model?
Resposta
$y=a(1-r)^t$ , where $0<r<1$ is the decay rate per period.
Cartão 237
Pergunta
Complement rule?
Resposta
The probability that $A$ does not occur is $1-P(A)$ .
Cartão 238
Pergunta
Circle with center $(h,k)$ and radius $r$ ?
Resposta
$(x-h)^2+(y-k)^2=r^2$ .
Cartão 239
Pergunta
Evaluate $f(a)$ ?
Resposta
Substitute $a$ for every input variable in the function rule, then simplify.
Cartão 240
Pergunta
Growth factor 1.08: percent growth rate?
Resposta
8 percent. Subtract 1 and convert the decimal to a percent.
Cartão 241
Pergunta
Representative random sample permits what conclusion?
Resposta
A cautious generalization from the sample to the population it represents.
Cartão 242
Pergunta
Radius from $(x-h)^2+(y-k)^2=R$ ?
Resposta
$r=√R$ , provided $R>0$ .
Cartão 243
Pergunta
Linear table: constant slope check?
Resposta
Equal changes in $x$ must produce equal changes in $y$ ; compare $Δy/Δx$ across intervals.
Cartão 244
Pergunta
Decay factor 0.73: percent decrease?
Resposta
27 percent. Compute $1-0.73=0.27$ .
Cartão 245
Pergunta
Random assignment permits what causal claim?
Resposta
If the experiment is well controlled, differences between treatment groups can support a causal conclusion.
Cartão 246
Pergunta
Radius and tangent at the contact point?
Resposta
They are perpendicular.
Cartão 247
Pergunta
Positive slope means what for a linear function?
Resposta
The output increases as the input increases.
Cartão 248
Pergunta
Solve $3^{2x}=3^{10}$ .
Resposta
$x=5$ . Equal positive bases other than 1 have equal exponents.
Cartão 249
Pergunta
Observational study supports causation?
Resposta
No. It can show association, but uncontrolled confounding variables may explain the pattern.
Cartão 250
Pergunta
Rectangular-prism volume?
Resposta
$V=lwh$ , or base area times height.
Cartão 251
Pergunta
Arithmetic sequence common difference?
Resposta
Subtract consecutive terms: $d=a_n-a_{n-1}$ .
Cartão 252
Pergunta
Compound interest formula?
Resposta
$A=P(1+r/n)^{nt}$ , where $n$ is the number of compounding periods per year.
Cartão 253
Pergunta
Larger random sample: effect on margin of error?
Resposta
It generally decreases the margin of error when the sampling method stays sound.
Cartão 254
Pergunta
Cylinder volume?
Resposta
$V=πr^2h$ .
Cartão 255
Pergunta
Arithmetic sequence nth term?
Resposta
$a_n=a_1+(n-1)d$ .
Cartão 256
Pergunta
Rational expression: first domain check?
Resposta
Exclude values that make any original denominator zero, even if a factor later cancels.
Cartão 257
Pergunta
Slope of a line of best fit?
Resposta
The predicted change in the response variable for each 1-unit increase in the explanatory variable.
Cartão 258
Pergunta
Cone volume?
Resposta
$V=(1/3)πr^2h$ .
Cartão 259
Pergunta
Solve a literal equation for one variable?
Resposta
Treat the other symbols as constants and use inverse operations to isolate the target variable.
Cartão 260
Pergunta
Why check rational-equation solutions?
Resposta
Clearing denominators can produce a value excluded from the original equation. Reject any value that makes an original denominator zero.
Cartão 261
Pergunta
Residual?
Resposta
Actual value minus predicted value. A positive residual means the point lies above the model.
Cartão 262
Pergunta
Sphere volume?
Resposta
$V=(4/3)πr^3$ .
Cartão 263
Pergunta
Boundary for a two-variable linear inequality?
Resposta
Replace the inequality with equality to draw the boundary line, then test a point for the shaded side.
Cartão 264
Pergunta
Why check a solution after squaring both sides?
Resposta
Squaring can introduce an extraneous solution. Substitute each candidate into the original radical equation.
Cartão 265
Pergunta
Positive correlation?
Resposta
Larger values of one variable tend to occur with larger values of the other. It does not prove causation.
Cartão 266
Pergunta
Rectangular-prism surface area?
Resposta
$SA=2(lw+lh+wh)$ .
Cartão 267
Pergunta
Check a proposed system solution?
Resposta
Substitute the ordered pair into both original equations. It must make both true.
Cartão 268
Pergunta
Simplify $√72$ .
Resposta
$6√2$ . Factor $72=36×2$ and take $√36$ outside the radical.
Cartão 269
Pergunta
Extrapolation risk?
Resposta
A model may not keep the same pattern outside the observed data range.
Cartão 270
Pergunta
Area scale factor when lengths double?
Resposta
Area scales with the square of the length factor: $2^2=4$.
Cartão 271
Pergunta
Horizontal line slope?
Resposta
Its y-value does not change as x changes.
Cartão 272
Pergunta
Inverse function setup?
Resposta
Write $y=f(x)$ , swap $x$ and $y$ , then solve for $y$ . Restrict the domain when needed to make the inverse a function.
Cartão 273
Pergunta
Percentage points versus percent change?
Resposta
A rate moving from 40 percent to 50 percent rises 10 percentage points but 25 percent relative to 40.
Cartão 274
Pergunta
y-intercept in a context?
Resposta
The predicted or initial output when the input is zero; check whether zero is meaningful in the situation.
Cartão 275
Pergunta
Quadratic maximum or minimum from vertex form?
Resposta
The vertex value is $k$ in $a(x-h)^2+k$ ; it is a minimum if $a>0$ and a maximum if $a<0$ .
Cartão 276
Pergunta
Line parallel to $y=mx+b$ through $(p,q)$ ?
Resposta
$y-q=m(x-p)$ . Parallel lines keep the same slope.
Cartão 277
Pergunta
Graph of $f(x-h)+k$ ?
Resposta
Shift the graph of $f$ right $h$ units and up $k$ units.
Cartão 278
Pergunta
Population versus sample?
Resposta
The population is the full group of interest; a sample is the subset actually observed.
Cartão 279
Pergunta
Linear model from initial value $b$ and rate $m$ ?
Resposta
$y=mx+b$ . The initial value is the output at input zero.
Cartão 280
Pergunta
Function composition $(f∘g)(x)$ ?
Resposta
$f(g(x))$ . Evaluate the inner function $g$ first.
Cartão 281
Pergunta
Density?
Resposta
Mass divided by volume. Keep the units consistent.
Cartão 282
Pergunta
Vertical line slope?
Resposta
Undefined because $Δx=0$ , which would require division by zero.
Cartão 283
Pergunta
Nonlinear system with one equation solved for $y$ ?
Resposta
Substitute that expression for $y$ into the other equation, solve for $x$ , then find each matching $y$ .
Cartão 284
Pergunta
Weighted percentage across unequal groups?
Resposta
Convert each percentage to a count or weight, add the successes, then divide by the combined total.
Cartão 285
Pergunta
Line perpendicular to a nonzero finite slope $m$ through $(p,q)$ ?
Resposta
Use slope $-1/m$ in $y-q=(-1/m)(x-p)$ , when $m$ is nonzero and finite.
Cartão 286
Pergunta
Cancel a common factor in a rational expression?
Resposta
Cancel factors, not terms, and keep every restriction from the original denominator.
Cartão 287
Pergunta
Solve a linear equation containing fractions?
Resposta
Multiply every term by the least common denominator first, then solve the resulting linear equation.
Cartão 288
Pergunta
Rewrite $a^{2x}$ using base $a^x$ .
Resposta
$(a^x)^2$ . This can turn an exponential expression into a quadratic form.
Cartão 289
Pergunta
Rate units check?
Resposta
Write the numerator and denominator units explicitly, such as kilometers per hour, then convert only if the requested units differ.
Cartão 290
Pergunta
Strict versus inclusive inequality endpoint?
Resposta
Use an open point for $<$ or $>$ and a closed point for $≤$ or $≥$ .
Cartão 291
Pergunta
Even-multiplicity zero on a graph?
Resposta
The graph touches the x-axis and turns around; it does not cross there.
Cartão 292
Pergunta
System word problem: first setup step?
Resposta
Define the variables with units, then translate two independent relationships into equations.
Cartão 293
Pergunta
When does a quadratic have exactly one real solution?
Resposta
When $b^2-4ac=0$ . The repeated root is the vertex's x-coordinate.
Cartão 294
Pergunta
Two-way table: denominator for “among group B”?
Resposta
Use the total for group B, not the grand total. The wording makes B the condition.
Cartão 295
Pergunta
Find an input when $f(x)=k$ .
Resposta
Set the function rule equal to $k$ and solve for $x$ ; there may be zero, one, or several inputs.
Cartão 296
Pergunta
Graph of $-f(x)$ ?
Resposta
Reflect the graph of $f(x)$ across the x-axis.
Cartão 297
Pergunta
Three consecutive integers starting with $n$ ?
Resposta
$n$ , $n+1$ , and $n+2$ .
Cartão 298
Pergunta
Line–parabola intersections from a substituted quadratic?
Resposta
Use its discriminant: positive means two intersections, zero one tangent intersection, and negative none.
Cartão 299
Pergunta
Linear equation with no solution: coefficient pattern?
Resposta
After simplification, the variable terms cancel and leave a false statement, such as $0=5$ .
Cartão 300
Pergunta
Zeros of a function on its graph?
Resposta
The x-coordinates where the graph meets the x-axis, so $f(x)=0$ .

An open study book surrounded by punctuation marks, a coordinate graph, a right triangle, a circle, and a data chart.

300 cartões

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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