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.

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การ์ด: 300 การ์ด
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อัปเดตล่าสุด: 10 กันยายน 2569
สัญญาอนุญาต: Common knowledge · CC0 1.0
ภาษาของผู้เรียน: en
วิชา: General aptitude
ระดับ: Digital SAT
แท็ก: digital-sat, rw, math

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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.

การ์ดในเด็คนี้

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

What the cards practice

What is deliberately left out

Coverage and learning order

Scope, provenance, and reuse

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