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.

من إعداد Open Study Contributor

حول هذه الرزمة

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.

بطاقات هذه الرزمة

البطاقة ١
السؤال
Central idea of a passage?
الإجابة
The passage's main claim or controlling point. It should cover the whole passage, not one striking detail.
البطاقة ٢
السؤال
The shade trees mitigated the midday heat. Meaning of “mitigated”?
الإجابة
Reduced. The trees made the heat less severe.
البطاقة ٣
السؤال
The first plan was affordable. However, it took twice as long. What relationship does “However” signal?
الإجابة
Contrast. The second statement differs from or qualifies the first.
البطاقة ٤
السؤال
Three standard joins for two independent clauses?
الإجابة
A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence.
البطاقة ٥
السؤال
Best supporting detail?
الإجابة
The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is.
البطاقة ٦
السؤال
A second archive corroborated the diary's date. Meaning of “corroborated”?
الإجابة
Confirmed with supporting evidence.
البطاقة ٧
السؤال
Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal?
الإجابة
Conclusion from a reason. The final statement follows logically from the stated premises.
البطاقة ٨
السؤال
Introductory dependent clause before a main clause?
الإجابة
Use a comma after the dependent clause. Example: “Although rain fell, the match continued.”
البطاقة ٩
السؤال
Valid inference?
الإجابة
A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports.
البطاقة ١٠
السؤال
The team called its result tentative until replication. Meaning of “tentative”?
الإجابة
Provisional or not yet certain.
البطاقة ١١
السؤال
Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal?
الإجابة
Illustration. The second statement gives a specific case of the broader point.
البطاقة ١٢
السؤال
Singular subject with an intervening prepositional phrase?
الإجابة
Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject.
البطاقة ١٣
السؤال
Strongest textual evidence?
الإجابة
The quotation or detail that most directly supports the target claim, with the fewest extra assumptions.
البطاقة ١٤
السؤال
The error had a negligible effect on the total. Meaning of “negligible”?
الإجابة
So small that it is not important.
البطاقة ١٥
السؤال
The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal?
الإجابة
Similarity. The second statement matches the first in a relevant way.
البطاقة ١٦
السؤال
Opening modifier placement?
الإجابة
Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.”
البطاقة ١٧
السؤال
Quantitative evidence for a claim?
الإجابة
Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline.
البطاقة ١٨
السؤال
The lab used a conventional method before testing a new one. Meaning of “conventional”?
الإجابة
Traditional or commonly accepted.
البطاقة ١٩
السؤال
Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal?
الإجابة
Simultaneous events. The second event happens at the same time as the first.
البطاقة ٢٠
السؤال
Singular possessive noun?
الإجابة
Usually add apostrophe + s. Example: “the scientist's notebook.”
البطاقة ٢١
السؤال
Trend in a table or graph?
الإجابة
State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence.
البطاقة ٢٢
السؤال
The essay offered a novel explanation for the pattern. Meaning of “novel”?
الإجابة
New or original in this context.
البطاقة ٢٣
السؤال
The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal?
الإجابة
Concession. The second statement remains true despite the limitation in the first.
البطاقة ٢٤
السؤال
Parallel items in a series?
الإجابة
Use the same grammatical form for each item. Example: “to collect, analyze, and report data.”
البطاقة ٢٥
السؤال
Claim stronger than the evidence?
الإجابة
Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion.
البطاقة ٢٦
السؤال
Her account is plausible because it matches the records. Meaning of “plausible”?
الإجابة
Reasonable or believable.
البطاقة ٢٧
السؤال
The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal?
الإجابة
Addition. The second statement adds a related supporting point.
البطاقة ٢٨
السؤال
Colon before an explanation or list?
الإجابة
Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.”
البطاقة ٢٩
السؤال
Claim versus evidence?
الإجابة
A claim is the point being argued; evidence is the information used to support it.
البطاقة ٣٠
السؤال
The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”?
الإجابة
Open to more than one interpretation.
البطاقة ٣١
السؤال
The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal?
الإجابة
Replacement. The second statement substitutes one action for another.
البطاقة ٣٢
السؤال
Count nouns versus mass nouns?
الإجابة
Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise.
البطاقة ٣٣
السؤال
Effect of a counterexample?
الإجابة
It weakens a universal claim by showing at least one case where the claim fails.
البطاقة ٣٤
السؤال
Rainfall was sporadic: brief showers interrupted long dry periods. Meaning of “sporadic”?
الإجابة
Irregular and occasional.
البطاقة ٣٥
السؤال
The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal?
الإجابة
Later step in a sequence. The second event occurs after the first.
البطاقة ٣٦
السؤال
Essential clause punctuation?
الإجابة
Do not surround an essential clause with commas. It identifies which person or thing the sentence means.
البطاقة ٣٧
السؤال
Correlation alone proves causation?
الإجابة
No. A relationship between variables does not by itself show that one caused the other.
البطاقة ٣٨
السؤال
Subsequent trials produced the same result. Meaning of “subsequent”?
الإجابة
Coming later in time.
البطاقة ٣٩
السؤال
The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal?
الإجابة
Restatement for clarity. The second statement rephrases the first.
البطاقة ٤٠
السؤال
Verb tense across a paragraph?
الإجابة
Keep the time frame consistent unless the timing actually changes.
البطاقة ٤١
السؤال
Missing information in a data claim?
الإجابة
Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim.
البطاقة ٤٢
السؤال
The coating helps the fabric retain heat. Meaning of “retain”?
الإجابة
Keep or continue to hold.
البطاقة ٤٣
السؤال
The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal?
الإجابة
General-to-specific detail. The second statement narrows the broad first statement.
البطاقة ٤٤
السؤال
Coordinate adjectives?
الإجابة
Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.”
البطاقة ٤٥
السؤال
Two sources on the same event?
الإجابة
Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement.
البطاقة ٤٦
السؤال
The survey was designed to elicit candid responses. Meaning of “elicit”?
الإجابة
Draw out or bring forth.
البطاقة ٤٧
السؤال
Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal?
الإجابة
Cause and effect. The second statement is an outcome of the first.
البطاقة ٤٨
السؤال
Sentence fragment?
الإجابة
A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb.
البطاقة ٤٩
السؤال
Inference from a narrow sample?
الإجابة
Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence.
البطاقة ٥٠
السؤال
Cost was the main constraint on the project. Meaning of “constraint”?
الإجابة
A limit or restriction.
البطاقة ٥١
السؤال
Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal?
الإجابة
Overall conclusion. The second statement gives the final judgment after earlier considerations.
البطاقة ٥٢
السؤال
Conjunctive adverb between independent clauses?
الإجابة
Use a semicolon before it and a comma after it. Example: “The route was longer; however, it was safer.”
البطاقة ٥٣
السؤال
Most accurate summary?
الإجابة
State the central idea and its essential support without adding opinions or minor details.
البطاقة ٥٤
السؤال
The review was comprehensive, covering every recorded case. Meaning of “comprehensive”?
الإجابة
Complete and wide-ranging.
البطاقة ٥٥
السؤال
The method is efficient. Indeed, it cuts processing time in half. What relationship does “Indeed” signal?
الإجابة
Emphasis and confirmation. The second statement reinforces the first with a stronger detail.
البطاقة ٥٦
السؤال
Who versus whom?
الإجابة
Use “who” as a subject and “whom” as an object. Test with he/him: “whom” matches “him.”
البطاقة ٥٧
السؤال
Evidence that best resolves a disagreement?
الإجابة
Choose evidence that tests the specific point on which the sources differ, not a fact both already accept.
البطاقة ٥٨
السؤال
The two materials have distinct properties. Meaning of “distinct”?
الإجابة
Clearly different or separate.
البطاقة ٥٩
السؤال
The forecast warned of rain. Still, the outdoor concert began on time. What relationship does “Still” signal?
الإجابة
Concession. The second statement remains true despite the obstacle in the first.
البطاقة ٦٠
السؤال
Comma before an introduced direct quotation?
الإجابة
Use a comma after a speech tag. Example: “Mina wrote, ‘The sample is ready.’”
البطاقة ٦١
السؤال
The conclusion was qualified by two important exceptions. Meaning of “qualified”?
الإجابة
Limited or modified, rather than stated without conditions.
البطاقة ٦٢
السؤال
Notes for a synthesis goal?
الإجابة
Use only facts that directly serve the stated goal. Relevant notes can be omitted if they do not help that purpose.
البطاقة ٦٣
السؤال
Comma splice?
الإجابة
Two independent clauses joined only by a comma. Replace it with a period or semicolon, or add a coordinating conjunction.
البطاقة ٦٤
السؤال
Comma between subject and verb?
الإجابة
Do not use one unless an interrupting phrase requires paired commas. “The results of the trial were clear” takes no comma after “trial.”
البطاقة ٦٥
السؤال
The new sensor made the older model obsolete. Meaning of “obsolete”?
الإجابة
No longer useful or current because something newer replaced it.
البطاقة ٦٦
السؤال
Source attribution in a synthesis?
الإجابة
Name the source when its identity, authority, or perspective matters to the rhetorical goal.
البطاقة ٦٧
السؤال
Compound subject joined by “and”?
الإجابة
Use a plural verb in the usual case. Example: “The map and the notes are useful.”
البطاقة ٦٨
السؤال
Dangling opening modifier?
الإجابة
It lacks the intended doer immediately after the modifier. Rewrite so the doer becomes the subject.
البطاقة ٦٩
السؤال
Researchers derived the estimate from three measurements. Meaning of “derived”?
الإجابة
Obtained from a source or calculation.
البطاقة ٧٠
السؤال
Chronological synthesis?
الإجابة
Order events by time and use dates or sequence words only when they help the reader follow the progression.
البطاقة ٧١
السؤال
Plural noun ending in s: possessive form?
الإجابة
Add an apostrophe after the existing s. Example: “the researchers' notes.”
البطاقة ٧٢
السؤال
Logical comparison?
الإجابة
Compare like with like. Example: compare one city's rainfall with another city's rainfall, not with the city itself.
البطاقة ٧٣
السؤال
The article advocates preserving the wetland. Meaning of “advocates”?
الإجابة
Publicly supports or argues for.
البطاقة ٧٤
السؤال
Compare evidence from two studies?
الإجابة
State the shared measure first, then the relevant difference in result, method, or population.
البطاقة ٧٥
السؤال
Colon after an incomplete lead-in?
الإجابة
Do not use one. A colon must follow a complete clause, so “The reasons include:” is incorrect.
البطاقة ٧٦
السؤال
Number versus amount?
الإجابة
Use “number” for countable items and “amount” for uncountable quantities. Example: number of files, amount of water.
البطاقة ٧٧
السؤال
Portable chargers are now ubiquitous on long trips. Meaning of “ubiquitous”?
الإجابة
Present or found almost everywhere.
البطاقة ٧٨
السؤال
Synthesis that emphasizes a difference?
الإجابة
Use the same comparison point for both subjects, then state the contrast directly.
البطاقة ٧٩
السؤال
Nonessential clause or phrase?
الإجابة
Set it off with paired commas. The sentence should keep its core identity and meaning when the phrase is removed.
البطاقة ٨٠
السؤال
Earlier of two past actions?
الإجابة
Use past perfect when the sequence needs clarification. Example: “The team had left before the storm began.”
البطاقة ٨١
السؤال
Sentence 2 presents an exception to sentence 1. Its function?
الإجابة
It qualifies the first claim by limiting when or how broadly it applies.
البطاقة ٨٢
السؤال
Rhetorical goal: define a term?
الإجابة
Give the term's relevant meaning before using details or examples that depend on it.
البطاقة ٨٣
السؤال
Cumulative adjectives?
الإجابة
Do not separate them with a comma when each adjective builds on the next. Example: “three small glass jars.”
البطاقة ٨٤
السؤال
Run-on sentence?
الإجابة
Independent clauses joined without valid punctuation or a conjunction. Add a period, semicolon, or comma plus coordinating conjunction.
البطاقة ٨٥
السؤال
Sentence 2 gives a specific case after a general claim. Its function?
الإجابة
It illustrates the claim with an example.
البطاقة ٨٦
السؤال
Introduce a quotation in a synthesis?
الإجابة
Give enough source and context to show why the quotation matters; do not leave it unattached.
البطاقة ٨٧
السؤال
Relative pronoun for people?
الإجابة
Use “who” or “whom,” depending on case. Example: “the engineer who designed the bridge.”
البطاقة ٨٨
السؤال
Integrated quotation punctuation?
الإجابة
Do not add a comma when the quotation completes the grammar of the sentence. Example: The report calls the result “unexpected.”
البطاقة ٨٩
السؤال
Sentence 2 admits a limitation before defending the claim. Its function?
الإجابة
It makes a concession, showing that the writer recognizes a complication.
البطاقة ٩٠
السؤال
Avoid redundancy in synthesis?
الإجابة
State each needed idea once. Prefer the version that preserves meaning with fewer repeated words.
البطاقة ٩١
السؤال
Semicolon between two independent clauses?
الإجابة
Use it without a coordinating conjunction when the ideas are closely related. Example: “The trial ended; the analysis began.”
البطاقة ٩٢
السؤال
Comma in a compound predicate?
الإجابة
Usually omit it when one subject performs both actions. Example: “The team collected the samples and recorded the temperature.”
البطاقة ٩٣
السؤال
Sentence 2 explains what a technical term means. Its function?
الإجابة
It defines or clarifies the term.
البطاقة ٩٤
السؤال
Combine two related sentences?
الإجابة
Make the logical relationship explicit and remove repeated material without changing the facts.
البطاقة ٩٥
السؤال
Either/or subject agreement?
الإجابة
Make the verb agree with the nearer subject. Example: “Either the notes or the map is missing.”
البطاقة ٩٦
السؤال
Active versus passive voice?
الإجابة
Choose the voice that fits the focus. Active highlights the doer; passive can highlight the action or receiver.
البطاقة ٩٧
السؤال
Sentence 2 describes the outcome of sentence 1. Its function?
الإجابة
It presents an effect or consequence.
البطاقة ٩٨
السؤال
Formal academic register?
الإجابة
Use precise, neutral wording and avoid slang, vague intensifiers, and chatty asides unless the goal calls for them.
البطاقة ٩٩
السؤال
Its or it's?
الإجابة
“Its” is possessive; “it's” means “it is” or “it has.”
البطاقة ١٠٠
السؤال
Adjective versus adverb?
الإجابة
An adjective modifies a noun; an adverb usually modifies a verb, adjective, or adverb. Example: a careful test; test carefully.
البطاقة ١٠١
السؤال
A study reports a result without arguing for a policy. Author's purpose?
الإجابة
To inform or explain, not necessarily to persuade.
البطاقة ١٠٢
السؤال
Concise synthesis?
الإجابة
Keep every fact needed for the rhetorical goal and remove details that repeat or distract from it.
البطاقة ١٠٣
السؤال
Single dash for emphasis?
الإجابة
Use it after a complete thought to spotlight a final explanation or turn. Example: “One result stood out—the oldest sample.”
البطاقة ١٠٤
السؤال
Comma with direct address?
الإجابة
Set off the person being addressed. Example: “Rina, please check the units.”
البطاقة ١٠٥
السؤال
Why acknowledge a limitation?
الإجابة
To define the claim's boundary and show how the evidence should be interpreted.
البطاقة ١٠٦
السؤال
Quantitative comparison in a synthesis?
الإجابة
Name both values, the shared unit, and the direction or size of the difference.
البطاقة ١٠٧
السؤال
Each of the samples: verb number?
الإجابة
Singular. “Each of the samples was labeled.” The subject is “each.”
البطاقة ١٠٨
السؤال
Between versus among?
الإجابة
Use “between” for distinct individual relationships and “among” for a group without separate pairings.
البطاقة ١٠٩
السؤال
Rhetorical question in an argument?
الإجابة
It can frame the issue or prompt the reader to consider an implied answer; it is not evidence by itself.
البطاقة ١١٠
السؤال
Claim before or after support?
الإجابة
Place it where the rhetorical goal is clearest: before evidence for a direct point, or after evidence for an evidence-led conclusion.
البطاقة ١١١
السؤال
Restrictive “that” versus nonrestrictive “which”?
الإجابة
Use “that” without commas for essential information; use “which” with commas for removable information.
البطاقة ١١٢
السؤال
Present perfect use?
الإجابة
Use it for an action connected to the present or continuing to now. Example: “The team has tracked rainfall since May.”
البطاقة ١١٣
السؤال
Two texts reach the same conclusion with different evidence. Relationship?
الإجابة
They agree in conclusion but support it through different evidence.
البطاقة ١١٤
السؤال
Group related ideas in a synthesis?
الإجابة
Keep facts serving the same point together, then signal the move to a new point.
البطاقة ١١٥
السؤال
Compound modifier before a noun?
الإجابة
Hyphenate it when needed for clarity. Example: “a well-designed study.”
البطاقة ١١٦
السؤال
Affect or effect?
الإجابة
“Affect” is usually a verb meaning influence; “effect” is usually a noun meaning result.
البطاقة ١١٧
السؤال
Two texts offer incompatible explanations. Relationship?
الإجابة
They disagree about the cause or interpretation, even if they share the same observations.
البطاقة ١١٨
السؤال
Replace a vague pronoun in synthesis?
الإجابة
Use the precise noun when two or more possible antecedents could confuse the reader.
البطاقة ١١٩
السؤال
Comma-separated list?
الإجابة
Use commas between three or more parallel items. A final serial comma can prevent ambiguity.
البطاقة ١٢٠
السؤال
Main clause before a dependent clause?
الإجابة
Usually no comma when the dependent clause is essential. Example: “The match continued although rain fell.”
البطاقة ١٢١
السؤال
Two authors use the same evidence but different assumptions. Key difference?
الإجابة
Their perspectives or interpretive frameworks, not the underlying evidence.
البطاقة ١٢٢
السؤال
Independent clauses joined with a coordinating conjunction?
الإجابة
Place a comma before the conjunction. Example: “The sensor failed, so the team repeated the trial.”
البطاقة ١٢٣
السؤال
Introductory transition?
الإجابة
Follow it with a comma when it modifies the whole sentence. Example: “However, the second trial succeeded.”
البطاقة ١٢٤
السؤال
Pronoun–antecedent agreement?
الإجابة
Match number and make the reference clear. Singular “they” is standard when a person's gender is unknown or irrelevant.
البطاقة ١٢٥
السؤال
Paired em dashes?
الإجابة
Use them to set off an emphatic interruption. Both dashes are needed when the sentence continues after it.
البطاقة ١٢٦
السؤال
How does new evidence relate to an earlier claim?
الإجابة
It may support, weaken, qualify, or leave the claim unchanged. Match the evidence to the exact claim.
البطاقة ١٢٧
السؤال
Their, there, or they're?
الإجابة
“Their” is possessive, “there” refers to place or existence, and “they're” means “they are.”
البطاقة ١٢٨
السؤال
Good or well?
الإجابة
“Good” is usually an adjective; “well” is usually an adverb. A person can feel good and perform well.
البطاقة ١٢٩
السؤال
Appositive naming the same noun?
الإجابة
Set a nonessential appositive off with commas. Example: “Dr. Rao, the lead author, presented the findings.”
البطاقة ١٣٠
السؤال
Why use an analogy?
الإجابة
To clarify an unfamiliar idea through a relevant similarity to something more familiar.
البطاقة ١٣١
السؤال
Than or then?
الإجابة
“Than” makes a comparison; “then” refers to time or consequence.
البطاقة ١٣٢
السؤال
Hypothetical contrary-to-fact “if” clause?
الإجابة
Use subjunctive “were.” Example: “If the sample were larger, the estimate would be steadier.”
البطاقة ١٣٣
السؤال
Plural noun with no possession?
الإجابة
Do not add an apostrophe. Write “three sensors,” not “three sensor's.”
البطاقة ١٣٤
السؤال
Neutral, evidence-led wording indicates what tone?
الإجابة
Objective. It emphasizes information rather than strong personal judgment.
البطاقة ١٣٥
السؤال
Complex list with internal commas?
الإجابة
Use semicolons between the main items. Example: “Lima, Peru; Accra, Ghana; and Hanoi, Vietnam.”
البطاقة ١٣٦
السؤال
Ambiguous pronoun?
الإجابة
A pronoun with more than one plausible antecedent. Replace it with the intended noun.
البطاقة ١٣٧
السؤال
Parentheses around nonessential information?
الإجابة
Use them for an aside that is less central than the main sentence. The sentence must remain grammatical without it.
البطاقة ١٣٨
السؤال
Repeated doubt about the evidence indicates what tone?
الإجابة
Skeptical. The writer questions whether a claim is adequately supported.
البطاقة ١٣٩
السؤال
Superlative comparison?
الإجابة
Use it for one member against a group of three or more. Example: “the fastest of the four methods.”
البطاقة ١٤٠
السؤال
Pronoun after a preposition?
الإجابة
Use the object form. Write “between you and me,” not “between you and I.”
البطاقة ١٤١
السؤال
Apostrophe in a contraction?
الإجابة
It marks omitted letters. Example: “can't” contracts “cannot,” and “they're” contracts “they are.”
البطاقة ١٤٢
السؤال
Coordinate-adjective test?
الإجابة
If “and” works between the adjectives and their order can reverse, use a comma between them.
البطاقة ١٤٣
السؤال
Double comparative?
الإجابة
Use only one comparative marker. Write “more efficient” or “faster,” not “more faster.”
البطاقة ١٤٤
السؤال
Lie or lay?
الإجابة
“Lie” means recline and takes no object; “lay” means place and takes an object. Present: lie/lay; past: lay/laid.
البطاقة ١٤٥
السؤال
Who's or whose?
الإجابة
“Who's” means “who is” or “who has”; “whose” is possessive.
البطاقة ١٤٦
السؤال
Standard comparison with “different”?
الإجابة
Use “different from.” Example: “This result is different from the earlier estimate.”
البطاقة ١٤٧
السؤال
Paired construction with two endpoints?
الإجابة
Use “between” with “and”: “between 10 and 15,” not “between 10 to 15.”
البطاقة ١٤٨
السؤال
Verb mood in a coordinated idea?
الإجابة
Keep the mood consistent unless the meaning changes. Do not shift from a command to a statement without reason.
البطاقة ١٤٩
السؤال
Possessive pronoun apostrophe?
الإجابة
Do not use one. Write “hers,” “ours,” “yours,” and “theirs.”
البطاقة ١٥٠
السؤال
Comma between a preposition and its object?
الإجابة
Do not use one. Keep the prepositional phrase intact: “in the final report,” not “in, the final report.”
٣٠٠ بطاقة
Digital SAT Flashcards: Math, Grammar & Words in Context
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البطاقة ١٥١
السؤال
Solve $ax+b=c$ for $x$ , where $a≠0$ .
الإجابة
$x=(c-b)/a$ . Subtract $b$ first, then divide by $a$ .
البطاقة ١٥٢
السؤال
Product of powers with the same base?
الإجابة
$a^m a^n=a^{m+n}$ . Keep the base and add the exponents.
البطاقة ١٥٣
السؤال
Unit rate?
الإجابة
The amount per 1 unit. Divide both quantities by the same value so the denominator becomes 1.
البطاقة ١٥٤
السؤال
Rectangle area?
الإجابة
$A=lw$ , where $l$ is length and $w$ is width.
البطاقة ١٥٥
السؤال
Slope from two points?
الإجابة
$m=(y_2-y_1)/(x_2-x_1)$ . Subtract coordinates in the same order.
البطاقة ١٥٦
السؤال
Quotient of powers with the same base?
الإجابة
$a^m/a^n=a^{m-n}$ for $a≠0$ .
البطاقة ١٥٧
السؤال
Conversion factor setup?
الإجابة
Multiply by a ratio equal to 1, with the unwanted unit placed to cancel.
البطاقة ١٥٨
السؤال
Triangle area?
الإجابة
$A=(1/2)bh$ . The height must be perpendicular to the chosen base.
البطاقة ١٥٩
السؤال
Slope-intercept form?
الإجابة
$y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.
البطاقة ١٦٠
السؤال
Power raised to a power?
الإجابة
$(a^m)^n=a^{mn}$ . Multiply the exponents.
البطاقة ١٦١
السؤال
Dimensional analysis check?
الإجابة
Cancel units algebraically. The units left at the end should match the quantity requested.
البطاقة ١٦٢
السؤال
Trapezoid area?
الإجابة
$A=(1/2)(b_1+b_2)h$ . The height is perpendicular to the parallel bases.
البطاقة ١٦٣
السؤال
Point-slope form?
الإجابة
$y-y_1=m(x-x_1)$ . Use a known point $(x_1,y_1)$ and the slope $m$ .
البطاقة ١٦٤
السؤال
Negative exponent?
الإجابة
$a^{-n}=1/a^n$ for $a≠0$ .
البطاقة ١٦٥
السؤال
Constant of proportionality in $y=kx$ ?
الإجابة
$k=y/x$ for $x≠0$ . It is also the unit rate and slope.
البطاقة ١٦٦
السؤال
Circle area?
الإجابة
$A=πr^2$ .
البطاقة ١٦٧
السؤال
Intercepts from $Ax+By=C$ ?
الإجابة
Set $y=0$ for the x-intercept and set $x=0$ for the y-intercept.
البطاقة ١٦٨
السؤال
Fractional exponent?
الإجابة
$a^{m/n}$ means the nth root of $a^m$ . For example, $a^{1/2}=√a$ .
البطاقة ١٦٩
السؤال
Scale drawing length?
الإجابة
Use a proportion with corresponding lengths in the same order, then apply the stated scale factor.
البطاقة ١٧٠
السؤال
Circle circumference?
الإجابة
$C=2πr=πd$ .
البطاقة ١٧١
السؤال
Parallel nonvertical lines: slope relationship?
الإجابة
They have equal slopes. Distinct parallel lines have different intercepts.
البطاقة ١٧٢
السؤال
Difference of squares?
الإجابة
$a^2-b^2=(a-b)(a+b)$ .
البطاقة ١٧٣
السؤال
Percent change?
الإجابة
New minus original, divided by the original, then multiplied by 100 percent. The original value is the denominator.
البطاقة ١٧٤
السؤال
Arc length from central angle $θ$ in degrees?
الإجابة
$L=(θ/360)(2πr)$ .
البطاقة ١٧٥
السؤال
Perpendicular nonvertical lines: slope relationship?
الإجابة
Their slopes are negative reciprocals, so $m_1m_2=-1$ .
البطاقة ١٧٦
السؤال
Perfect-square trinomial pattern?
الإجابة
$a^2+2ab+b^2=(a+b)^2$ and $a^2-2ab+b^2=(a-b)^2$ .
البطاقة ١٧٧
السؤال
Increase by $r$ percent: multiplier?
الإجابة
$1+r/100$ . Multiply the original value by this factor.
البطاقة ١٧٨
السؤال
Sector area from central angle $θ$ in degrees?
الإجابة
$A=(θ/360)(πr^2)$ .
البطاقة ١٧٩
السؤال
x-intercept of a graph?
الإجابة
A point where $y=0$ and the graph meets the x-axis.
البطاقة ١٨٠
السؤال
First step in factoring $ax^2+bx+c$ ?
الإجابة
Look for common factors and two binomials whose product reproduces the middle and constant terms.
البطاقة ١٨١
السؤال
Original value after a 20 percent increase to 84?
الإجابة
Divide the final value by the multiplier: $84/1.20=70$.
البطاقة ١٨٢
السؤال
Triangle interior-angle sum?
الإجابة
$180°$ .
البطاقة ١٨٣
السؤال
y-intercept of a graph?
الإجابة
A point where $x=0$ and the graph meets the y-axis.
البطاقة ١٨٤
السؤال
Roots from $(x-p)(x-q)=0$ ?
الإجابة
$x=p$ or $x=q$ , by the zero-product property.
البطاقة ١٨٥
السؤال
Weighted average?
الإجابة
Sum of each value times its weight, divided by the sum of the weights. Do not take a simple average of unequal groups.
البطاقة ١٨٦
السؤال
Exterior angle of a triangle?
الإجابة
It equals the sum of the two remote interior angles.
البطاقة ١٨٧
السؤال
Line through two points?
الإجابة
Find the slope, then substitute either point into point-slope or slope-intercept form.
البطاقة ١٨٨
السؤال
Quadratic formula?
الإجابة
$x=(-b±√(b^2-4ac))/(2a)$ for $ax^2+bx+c=0$ .
البطاقة ١٨٩
السؤال
Arithmetic mean?
الإجابة
Add all values and divide by the number of values.
البطاقة ١٩٠
السؤال
Parallel lines cut by a transversal: alternate interior angles?
الإجابة
They are congruent.
البطاقة ١٩١
السؤال
Slope's units in context?
الإجابة
Output units per input unit. In $y$ versus $x$ , slope units are y-units divided by x-units.
البطاقة ١٩٢
السؤال
What does $b^2-4ac$ tell you?
الإجابة
The number of real solutions: positive gives two, zero gives one, and negative gives none.
البطاقة ١٩٣
السؤال
Median?
الإجابة
The middle value after ordering the data; for an even count, average the two middle values.
البطاقة ١٩٤
السؤال
Similar triangles: corresponding sides?
الإجابة
They are proportional. Match sides opposite equal angles.
البطاقة ١٩٥
السؤال
Direct variation model?
الإجابة
$y=kx$ . It is linear and passes through the origin.
البطاقة ١٩٦
السؤال
Vertex x-coordinate of $ax^2+bx+c$ ?
الإجابة
$x=-b/(2a)$ .
البطاقة ١٩٧
السؤال
Range of a data set?
الإجابة
Maximum minus minimum.
البطاقة ١٩٨
السؤال
Scale factor $k$ : area factor?
الإجابة
$k^2$ . Lengths scale by $k$ , while areas scale by the square of $k$ .
البطاقة ١٩٩
السؤال
Solution of a two-line system?
الإجابة
The intersection point, whose coordinates satisfy both equations.
البطاقة ٢٠٠
السؤال
Vertex form of a quadratic?
الإجابة
$y=a(x-h)^2+k$ , with vertex $(h,k)$ .
البطاقة ٢٠١
السؤال
Interquartile range?
الإجابة
$IQR=Q_3-Q_1$ . It measures the spread of the middle half of the data.
البطاقة ٢٠٢
السؤال
Pythagorean theorem?
الإجابة
$a^2+b^2=c^2$ for a right triangle, where $c$ is the hypotenuse.
البطاقة ٢٠٣
السؤال
Substitution in a system?
الإجابة
Solve one equation for a variable and replace that variable in the other equation.
البطاقة ٢٠٤
السؤال
Axis of symmetry of $y=a(x-h)^2+k$ ?
الإجابة
$x=h$ .
البطاقة ٢٠٥
السؤال
Larger standard deviation means what?
الإجابة
The data are more spread out around the mean.
البطاقة ٢٠٦
السؤال
45°-45°-90° side ratio?
الإجابة
$1:1:√2$ . The hypotenuse is a leg times $√2$ .
البطاقة ٢٠٧
السؤال
Elimination in a system?
الإجابة
Add or subtract equations so one variable cancels, then solve for the other.
البطاقة ٢٠٨
السؤال
Completing the square?
الإجابة
For $x^2+bx$ , add $(b/2)^2$ to form $(x+b/2)^2$ .
البطاقة ٢٠٩
السؤال
Effect of a high outlier on the mean?
الإجابة
It usually pulls the mean upward. The median is often less affected.
البطاقة ٢١٠
السؤال
30°-60°-90° side ratio?
الإجابة
$1:√3:2$ , opposite $30°$ , $60°$ , and $90°$ respectively.
البطاقة ٢١١
السؤال
Parallel lines in a system?
الإجابة
No solution when they are distinct: equal slopes and different intercepts.
البطاقة ٢١٢
السؤال
Sum and product of roots of $ax^2+bx+c=0$ ?
الإجابة
Sum $=-b/a$ and product $=c/a$ .
البطاقة ٢١٣
السؤال
Add the same constant to every data value: effect?
الإجابة
The mean and median increase by that constant; measures of spread stay unchanged.
البطاقة ٢١٤
السؤال
Right-triangle sine?
الإجابة
Sine of $θ$ equals opposite over hypotenuse.
البطاقة ٢١٥
السؤال
Same line written two ways in a system?
الإجابة
Infinitely many solutions. Simplifying either equation produces the other.
البطاقة ٢١٦
السؤال
Remainder when $P(x)$ is divided by $x-a$ ?
الإجابة
$P(a)$ , by the Remainder Theorem.
البطاقة ٢١٧
السؤال
Multiply every data value by positive $k$ : effect?
الإجابة
The mean, median, range, IQR, and standard deviation are all multiplied by $k$ .
البطاقة ٢١٨
السؤال
Right-triangle cosine?
الإجابة
Cosine of $θ$ equals adjacent over hypotenuse.
البطاقة ٢١٩
السؤال
Multiply or divide an inequality by a negative number?
الإجابة
Reverse the inequality sign.
البطاقة ٢٢٠
السؤال
When is $x-a$ a factor of $P(x)$ ?
الإجابة
When $P(a)=0$ , by the Factor Theorem.
البطاقة ٢٢١
السؤال
Joint probability from a two-way table?
الإجابة
Divide the count in the intersection cell by the grand total.
البطاقة ٢٢٢
السؤال
Right-triangle tangent?
الإجابة
Tangent of $θ$ equals opposite over adjacent.
البطاقة ٢٢٣
السؤال
Compound inequality with “and”?
الإجابة
Use the intersection: values that satisfy both inequalities.
البطاقة ٢٢٤
السؤال
Even degree with positive leading coefficient: end behavior?
الإجابة
Both ends rise: $P(x)→∞$ as $x→±∞$ .
البطاقة ٢٢٥
السؤال
Conditional probability $P(A|B)$ ?
الإجابة
$P(A∩B)/P(B)$ . Restrict the denominator to outcomes in $B$ .
البطاقة ٢٢٦
السؤال
Complementary acute angles: sine–cosine relationship?
الإجابة
The sine of $θ$ equals the cosine of $90°-θ$ .
البطاقة ٢٢٧
السؤال
Compound inequality with “or”?
الإجابة
Use the union: values that satisfy at least one inequality.
البطاقة ٢٢٨
السؤال
Odd degree with positive leading coefficient: end behavior?
الإجابة
The left end falls and the right end rises.
البطاقة ٢٢٩
السؤال
Independent events $A$ and $B$ ?
الإجابة
$P(A∩B)=P(A)P(B)$ . Knowing one occurred does not change the probability of the other.
البطاقة ٢٣٠
السؤال
Distance between $(x_1,y_1)$ and $(x_2,y_2)$ ?
الإجابة
$√((x_2-x_1)^2+(y_2-y_1)^2)$ .
البطاقة ٢٣١
السؤال
Solve $|x-a|=b$ for $b≥0$ .
الإجابة
$x-a=b$ or $x-a=-b$ . Absolute value represents distance from $a$ .
البطاقة ٢٣٢
السؤال
Exponential growth model?
الإجابة
$y=a(1+r)^t$ , where $a$ is the initial value and $r$ is the growth rate per period.
البطاقة ٢٣٣
السؤال
Mutually exclusive events?
الإجابة
They cannot occur together, so $P(A∪B)=P(A)+P(B)$ .
البطاقة ٢٣٤
السؤال
Midpoint of two points?
الإجابة
$((x_1+x_2)/2,(y_1+y_2)/2)$ .
البطاقة ٢٣٥
السؤال
Solve $|x-a|<b$ for $b>0$ .
الإجابة
$a-b<x<a+b$ . The solution lies within distance $b$ of $a$ .
البطاقة ٢٣٦
السؤال
Exponential decay model?
الإجابة
$y=a(1-r)^t$ , where $0<r<1$ is the decay rate per period.
البطاقة ٢٣٧
السؤال
Complement rule?
الإجابة
The probability that $A$ does not occur is $1-P(A)$ .
البطاقة ٢٣٨
السؤال
Circle with center $(h,k)$ and radius $r$ ?
الإجابة
$(x-h)^2+(y-k)^2=r^2$ .
البطاقة ٢٣٩
السؤال
Evaluate $f(a)$ ?
الإجابة
Substitute $a$ for every input variable in the function rule, then simplify.
البطاقة ٢٤٠
السؤال
Growth factor 1.08: percent growth rate?
الإجابة
8 percent. Subtract 1 and convert the decimal to a percent.
البطاقة ٢٤١
السؤال
Representative random sample permits what conclusion?
الإجابة
A cautious generalization from the sample to the population it represents.
البطاقة ٢٤٢
السؤال
Radius from $(x-h)^2+(y-k)^2=R$ ?
الإجابة
$r=√R$ , provided $R>0$ .
البطاقة ٢٤٣
السؤال
Linear table: constant slope check?
الإجابة
Equal changes in $x$ must produce equal changes in $y$ ; compare $Δy/Δx$ across intervals.
البطاقة ٢٤٤
السؤال
Decay factor 0.73: percent decrease?
الإجابة
27 percent. Compute $1-0.73=0.27$ .
البطاقة ٢٤٥
السؤال
Random assignment permits what causal claim?
الإجابة
If the experiment is well controlled, differences between treatment groups can support a causal conclusion.
البطاقة ٢٤٦
السؤال
Radius and tangent at the contact point?
الإجابة
They are perpendicular.
البطاقة ٢٤٧
السؤال
Positive slope means what for a linear function?
الإجابة
The output increases as the input increases.
البطاقة ٢٤٨
السؤال
Solve $3^{2x}=3^{10}$ .
الإجابة
$x=5$ . Equal positive bases other than 1 have equal exponents.
البطاقة ٢٤٩
السؤال
Observational study supports causation?
الإجابة
No. It can show association, but uncontrolled confounding variables may explain the pattern.
البطاقة ٢٥٠
السؤال
Rectangular-prism volume?
الإجابة
$V=lwh$ , or base area times height.
البطاقة ٢٥١
السؤال
Arithmetic sequence common difference?
الإجابة
Subtract consecutive terms: $d=a_n-a_{n-1}$ .
البطاقة ٢٥٢
السؤال
Compound interest formula?
الإجابة
$A=P(1+r/n)^{nt}$ , where $n$ is the number of compounding periods per year.
البطاقة ٢٥٣
السؤال
Larger random sample: effect on margin of error?
الإجابة
It generally decreases the margin of error when the sampling method stays sound.
البطاقة ٢٥٤
السؤال
Cylinder volume?
الإجابة
$V=πr^2h$ .
البطاقة ٢٥٥
السؤال
Arithmetic sequence nth term?
الإجابة
$a_n=a_1+(n-1)d$ .
البطاقة ٢٥٦
السؤال
Rational expression: first domain check?
الإجابة
Exclude values that make any original denominator zero, even if a factor later cancels.
البطاقة ٢٥٧
السؤال
Slope of a line of best fit?
الإجابة
The predicted change in the response variable for each 1-unit increase in the explanatory variable.
البطاقة ٢٥٨
السؤال
Cone volume?
الإجابة
$V=(1/3)πr^2h$ .
البطاقة ٢٥٩
السؤال
Solve a literal equation for one variable?
الإجابة
Treat the other symbols as constants and use inverse operations to isolate the target variable.
البطاقة ٢٦٠
السؤال
Why check rational-equation solutions?
الإجابة
Clearing denominators can produce a value excluded from the original equation. Reject any value that makes an original denominator zero.
البطاقة ٢٦١
السؤال
Residual?
الإجابة
Actual value minus predicted value. A positive residual means the point lies above the model.
البطاقة ٢٦٢
السؤال
Sphere volume?
الإجابة
$V=(4/3)πr^3$ .
البطاقة ٢٦٣
السؤال
Boundary for a two-variable linear inequality?
الإجابة
Replace the inequality with equality to draw the boundary line, then test a point for the shaded side.
البطاقة ٢٦٤
السؤال
Why check a solution after squaring both sides?
الإجابة
Squaring can introduce an extraneous solution. Substitute each candidate into the original radical equation.
البطاقة ٢٦٥
السؤال
Positive correlation?
الإجابة
Larger values of one variable tend to occur with larger values of the other. It does not prove causation.
البطاقة ٢٦٦
السؤال
Rectangular-prism surface area?
الإجابة
$SA=2(lw+lh+wh)$ .
البطاقة ٢٦٧
السؤال
Check a proposed system solution?
الإجابة
Substitute the ordered pair into both original equations. It must make both true.
البطاقة ٢٦٨
السؤال
Simplify $√72$ .
الإجابة
$6√2$ . Factor $72=36×2$ and take $√36$ outside the radical.
البطاقة ٢٦٩
السؤال
Extrapolation risk?
الإجابة
A model may not keep the same pattern outside the observed data range.
البطاقة ٢٧٠
السؤال
Area scale factor when lengths double?
الإجابة
Area scales with the square of the length factor: $2^2=4$.
البطاقة ٢٧١
السؤال
Horizontal line slope?
الإجابة
Its y-value does not change as x changes.
البطاقة ٢٧٢
السؤال
Inverse function setup?
الإجابة
Write $y=f(x)$ , swap $x$ and $y$ , then solve for $y$ . Restrict the domain when needed to make the inverse a function.
البطاقة ٢٧٣
السؤال
Percentage points versus percent change?
الإجابة
A rate moving from 40 percent to 50 percent rises 10 percentage points but 25 percent relative to 40.
البطاقة ٢٧٤
السؤال
y-intercept in a context?
الإجابة
The predicted or initial output when the input is zero; check whether zero is meaningful in the situation.
البطاقة ٢٧٥
السؤال
Quadratic maximum or minimum from vertex form?
الإجابة
The vertex value is $k$ in $a(x-h)^2+k$ ; it is a minimum if $a>0$ and a maximum if $a<0$ .
البطاقة ٢٧٦
السؤال
Line parallel to $y=mx+b$ through $(p,q)$ ?
الإجابة
$y-q=m(x-p)$ . Parallel lines keep the same slope.
البطاقة ٢٧٧
السؤال
Graph of $f(x-h)+k$ ?
الإجابة
Shift the graph of $f$ right $h$ units and up $k$ units.
البطاقة ٢٧٨
السؤال
Population versus sample?
الإجابة
The population is the full group of interest; a sample is the subset actually observed.
البطاقة ٢٧٩
السؤال
Linear model from initial value $b$ and rate $m$ ?
الإجابة
$y=mx+b$ . The initial value is the output at input zero.
البطاقة ٢٨٠
السؤال
Function composition $(f∘g)(x)$ ?
الإجابة
$f(g(x))$ . Evaluate the inner function $g$ first.
البطاقة ٢٨١
السؤال
Density?
الإجابة
Mass divided by volume. Keep the units consistent.
البطاقة ٢٨٢
السؤال
Vertical line slope?
الإجابة
Undefined because $Δx=0$ , which would require division by zero.
البطاقة ٢٨٣
السؤال
Nonlinear system with one equation solved for $y$ ?
الإجابة
Substitute that expression for $y$ into the other equation, solve for $x$ , then find each matching $y$ .
البطاقة ٢٨٤
السؤال
Weighted percentage across unequal groups?
الإجابة
Convert each percentage to a count or weight, add the successes, then divide by the combined total.
البطاقة ٢٨٥
السؤال
Line perpendicular to a nonzero finite slope $m$ through $(p,q)$ ?
الإجابة
Use slope $-1/m$ in $y-q=(-1/m)(x-p)$ , when $m$ is nonzero and finite.
البطاقة ٢٨٦
السؤال
Cancel a common factor in a rational expression?
الإجابة
Cancel factors, not terms, and keep every restriction from the original denominator.
البطاقة ٢٨٧
السؤال
Solve a linear equation containing fractions?
الإجابة
Multiply every term by the least common denominator first, then solve the resulting linear equation.
البطاقة ٢٨٨
السؤال
Rewrite $a^{2x}$ using base $a^x$ .
الإجابة
$(a^x)^2$ . This can turn an exponential expression into a quadratic form.
البطاقة ٢٨٩
السؤال
Rate units check?
الإجابة
Write the numerator and denominator units explicitly, such as kilometers per hour, then convert only if the requested units differ.
البطاقة ٢٩٠
السؤال
Strict versus inclusive inequality endpoint?
الإجابة
Use an open point for $<$ or $>$ and a closed point for $≤$ or $≥$ .
البطاقة ٢٩١
السؤال
Even-multiplicity zero on a graph?
الإجابة
The graph touches the x-axis and turns around; it does not cross there.
البطاقة ٢٩٢
السؤال
System word problem: first setup step?
الإجابة
Define the variables with units, then translate two independent relationships into equations.
البطاقة ٢٩٣
السؤال
When does a quadratic have exactly one real solution?
الإجابة
When $b^2-4ac=0$ . The repeated root is the vertex's x-coordinate.
البطاقة ٢٩٤
السؤال
Two-way table: denominator for “among group B”?
الإجابة
Use the total for group B, not the grand total. The wording makes B the condition.
البطاقة ٢٩٥
السؤال
Find an input when $f(x)=k$ .
الإجابة
Set the function rule equal to $k$ and solve for $x$ ; there may be zero, one, or several inputs.
البطاقة ٢٩٦
السؤال
Graph of $-f(x)$ ?
الإجابة
Reflect the graph of $f(x)$ across the x-axis.
البطاقة ٢٩٧
السؤال
Three consecutive integers starting with $n$ ?
الإجابة
$n$ , $n+1$ , and $n+2$ .
البطاقة ٢٩٨
السؤال
Line–parabola intersections from a substituted quadratic?
الإجابة
Use its discriminant: positive means two intersections, zero one tangent intersection, and negative none.
البطاقة ٢٩٩
السؤال
Linear equation with no solution: coefficient pattern?
الإجابة
After simplification, the variable terms cancel and leave a false statement, such as $0=5$ .
البطاقة ٣٠٠
السؤال
Zeros of a function on its graph?
الإجابة
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.

٣٠٠ بطاقة

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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