Central idea of a passage?

The passage's main claim or controlling point. It should cover the whole passage, not one striking detail.

The shade trees mitigated the midday heat. Meaning of “mitigated”?

Reduced. The trees made the heat less severe.

The first plan was affordable. However, it took twice as long. What relationship does “However” signal?

Contrast. The second statement differs from or qualifies the first.

Three standard joins for two independent clauses?

A period, a semicolon, or a comma plus a coordinating conjunction. Each side must be a complete sentence.

Best supporting detail?

The detail that most directly proves the claim. Relevance matters more than how vivid or surprising it is.

A second archive corroborated the diary's date. Meaning of “corroborated”?

Confirmed with supporting evidence.

Every member of set A is even. Nine is odd; therefore, nine is not in set A. What relationship does “therefore” signal?

Conclusion from a reason. The final statement follows logically from the stated premises.

Introductory dependent clause before a main clause?

Use a comma after the dependent clause. Example: “Although rain fell, the match continued.”

A conclusion that must follow, or that most reasonably follows, from the stated evidence. Avoid assumptions the text never supports.

The team called its result tentative until replication. Meaning of “tentative”?

Provisional or not yet certain.

Several materials block sound. For example, thick felt absorbs echoes. What relationship does “For example” signal?

Illustration. The second statement gives a specific case of the broader point.

Singular subject with an intervening prepositional phrase?

Use a singular verb. Example: “The box of samples is sealed.” The phrase “of samples” does not change the subject.

Strongest textual evidence?

The quotation or detail that most directly supports the target claim, with the fewest extra assumptions.

The error had a negligible effect on the total. Meaning of “negligible”?

So small that it is not important.

The first route avoids steep hills. Similarly, the second stays nearly level. What relationship does “Similarly” signal?

Similarity. The second statement matches the first in a relevant way.

Opening modifier placement?

Place the noun being modified immediately after the opening phrase. Example: “Walking home, Lena noticed the mural.”

Quantitative evidence for a claim?

Use the value, comparison, or trend that directly tests the claim, including the correct units and baseline.

The lab used a conventional method before testing a new one. Meaning of “conventional”?

Traditional or commonly accepted.

Mira checked the figures. Meanwhile, Omar revised the caption. What relationship does “Meanwhile” signal?

Simultaneous events. The second event happens at the same time as the first.

Singular possessive noun?

Usually add apostrophe + s. Example: “the scientist's notebook.”

Trend in a table or graph?

State what changes, in which direction, and across which interval. Do not turn a pattern into a cause without evidence.

The essay offered a novel explanation for the pattern. Meaning of “novel”?

New or original in this context.

The device was old. Nevertheless, it performed reliably. What relationship does “Nevertheless” signal?

Concession. The second statement remains true despite the limitation in the first.

Parallel items in a series?

Use the same grammatical form for each item. Example: “to collect, analyze, and report data.”

Claim stronger than the evidence?

Qualify the claim. Limited evidence can support “may” or “suggests,” not an absolute conclusion.

The plan cuts costs. Moreover, it shortens delivery time. What relationship does “Moreover” signal?

Addition. The second statement adds a related supporting point.

Colon before an explanation or list?

Use it only after a complete independent clause. Example: “The kit needs three items: tape, gloves, and labels.”

Claim versus evidence?

A claim is the point being argued; evidence is the information used to support it.

The memo's ambiguous wording allowed two readings. Meaning of “ambiguous”?

Open to more than one interpretation.

The team didn't replace the sensor. Instead, it recalibrated the existing one. What relationship does “Instead” signal?

Replacement. The second statement substitutes one action for another.

Count nouns versus mass nouns?

Use “fewer” with countable items and “less” with amounts. Example: fewer errors, less noise.

Effect of a counterexample?

It weakens a universal claim by showing at least one case where the claim fails.

The seedlings grew indoors. Subsequently, workers moved them outside. What relationship does “Subsequently” signal?

Later step in a sequence. The second event occurs after the first.

Essential clause punctuation?

Do not surround an essential clause with commas. It identifies which person or thing the sentence means.

Correlation alone proves causation?

No. A relationship between variables does not by itself show that one caused the other.

The coating is hydrophobic. In other words, it repels water. What relationship does “In other words” signal?

Restatement for clarity. The second statement rephrases the first.

Verb tense across a paragraph?

Keep the time frame consistent unless the timing actually changes.

Missing information in a data claim?

Look for the baseline, sample size, units, comparison group, or time interval needed to judge the claim.

The repair requires specialized tools. Specifically, it needs a torque wrench. What relationship does “Specifically” signal?

General-to-specific detail. The second statement narrows the broad first statement.

Coordinate adjectives?

Separate them with a comma when their order can switch and “and” can fit between them. Example: “a clear, concise note.”

Two sources on the same event?

Compare the exact claims, evidence, scope, and perspective. Shared topic does not guarantee agreement.

Heavy rain loosened the soil. Consequently, the trail closed. What relationship does “Consequently” signal?

Cause and effect. The second statement is an outcome of the first.

A group of words missing an independent clause. Attach it to a complete sentence or supply the missing subject and verb.

Inference from a narrow sample?

Limit the conclusion to the population the sample can represent. Do not generalize beyond the evidence.

Early results conflicted. Ultimately, the team accepted the model. What relationship does “Ultimately” signal?

Overall conclusion. The second statement gives the final judgment after earlier considerations.

Digital SAT Flashcards: Math, Grammar & Words in Context

Practice Digital SAT math formulas, grammar rules, transitions, and words in context with original, installable flashcards built for active recall.

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Tietoja tästä pakasta

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.

Tämän pakan kortit

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

Digital SAT Flashcards: Math, Grammar & Words in Context

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Digital SAT Flashcards: Math, Grammar & Words in Context

What the cards practice

What is deliberately left out

Coverage and learning order

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