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.

लेखक Open Study Contributor

इस डेक से मुफ़्त में पढ़ें

पढ़ाई शुरू करने के लिए Flashcards खुलेगा।

डेक का विवरण

कार्ड: 300 कार्ड
संस्करण: 1
प्रकाशित: 1 सितंबर 2026
पिछली बार अपडेट किया गया: 1 सितंबर 2026
लाइसेंस: Common knowledge · CC0 1.0
लक्षित शिक्षार्थियों की भाषाएँ: en
टैग: digital-sat, rw, math

मिलते-जुलते डेक

इस डेक के बारे में

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.

इस डेक के कार्ड

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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