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.

Umbhali Open Study Contributor

Mayelana naleli qoqo

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.

Amakhadi akuleli qoqo

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

amakhadi angu-300

Digital SAT Flashcards: Math, Grammar & Words in Context

Funda leli qoqo mahhala

I-Nibomo iyavuleka ukuze uqale ukufunda.

Mayelana naleli qoqo

Digital SAT Flashcards: Math, Grammar & Words in Context

What the cards practice

What is deliberately left out

Coverage and learning order

Scope, provenance, and reuse

Amakhadi akuleli qoqo

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