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 el autor Open Study Contributor

Sobre este mazo

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.

Tarjetas de este mazo

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

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Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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