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.

מאת Open Study Contributor

על החפיסה הזו

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.

הכרטיסים בחפיסה הזו

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

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