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.

De autorul Open Study Contributor

Despre acest pachet

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.

Fișele din acest pachet

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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