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.

Tác giả Open Study Contributor

Về bộ thẻ này

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.

Thẻ trong bộ này

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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