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.

Mwandishi Open Study Contributor

Kuhusu fungu hili

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.

Kadi za fungu hili

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

kadi 300

Digital SAT Flashcards: Math, Grammar & Words in Context

Soma fungu hili bila malipo

Nibomo itafunguka ili uanze kusoma.

Kuhusu fungu hili

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

Kadi za fungu hili

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