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.

Über dieses Lernkartenset

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.

Karten in diesem Lernkartenset

  1. Karte 1

    Frage

    Central idea of a passage?

    Antwort

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

  2. Karte 2

    Frage

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

    Antwort

    Reduced. The trees made the heat less severe.

  3. Karte 3

    Frage

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

    Antwort

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

  4. Karte 4

    Frage

    Three standard joins for two independent clauses?

    Antwort

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

  5. Karte 5

    Frage

    Best supporting detail?

    Antwort

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

  6. Karte 6

    Frage

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

    Antwort

    Confirmed with supporting evidence.

  7. Karte 7

    Frage

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

    Antwort

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

  8. Karte 8

    Frage

    Introductory dependent clause before a main clause?

    Antwort

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

  9. Karte 9

    Frage

    Valid inference?

    Antwort

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

  10. Karte 10

    Frage

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

    Antwort

    Provisional or not yet certain.

  11. Karte 11

    Frage

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

    Antwort

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

  12. Karte 12

    Frage

    Singular subject with an intervening prepositional phrase?

    Antwort

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

  13. Karte 13

    Frage

    Strongest textual evidence?

    Antwort

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

  14. Karte 14

    Frage

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

    Antwort

    So small that it is not important.

  15. Karte 15

    Frage

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

    Antwort

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

  16. Karte 16

    Frage

    Opening modifier placement?

    Antwort

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

  17. Karte 17

    Frage

    Quantitative evidence for a claim?

    Antwort

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

  18. Karte 18

    Frage

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

    Antwort

    Traditional or commonly accepted.

  19. Karte 19

    Frage

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

    Antwort

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

  20. Karte 20

    Frage

    Singular possessive noun?

    Antwort

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

  21. Karte 21

    Frage

    Trend in a table or graph?

    Antwort

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

  22. Karte 22

    Frage

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

    Antwort

    New or original in this context.

  23. Karte 23

    Frage

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

    Antwort

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

  24. Karte 24

    Frage

    Parallel items in a series?

    Antwort

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

  25. Karte 25

    Frage

    Claim stronger than the evidence?

    Antwort

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

  26. Karte 26

    Frage

    Her account is plausible because it matches the records. Meaning of “plausible”?

    Antwort

    Reasonable or believable.

  27. Karte 27

    Frage

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

    Antwort

    Addition. The second statement adds a related supporting point.

  28. Karte 28

    Frage

    Colon before an explanation or list?

    Antwort

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

  29. Karte 29

    Frage

    Claim versus evidence?

    Antwort

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

  30. Karte 30

    Frage

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

    Antwort

    Open to more than one interpretation.

  31. Karte 31

    Frage

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

    Antwort

    Replacement. The second statement substitutes one action for another.

  32. Karte 32

    Frage

    Count nouns versus mass nouns?

    Antwort

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

  33. Karte 33

    Frage

    Effect of a counterexample?

    Antwort

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

  34. Karte 34

    Frage

    Rainfall was sporadic: brief showers interrupted long dry periods. Meaning of “sporadic”?

    Antwort

    Irregular and occasional.

  35. Karte 35

    Frage

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

    Antwort

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

  36. Karte 36

    Frage

    Essential clause punctuation?

    Antwort

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

  37. Karte 37

    Frage

    Correlation alone proves causation?

    Antwort

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

  38. Karte 38

    Frage

    Subsequent trials produced the same result. Meaning of “subsequent”?

    Antwort

    Coming later in time.

  39. Karte 39

    Frage

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

    Antwort

    Restatement for clarity. The second statement rephrases the first.

  40. Karte 40

    Frage

    Verb tense across a paragraph?

    Antwort

    Keep the time frame consistent unless the timing actually changes.

  41. Karte 41

    Frage

    Missing information in a data claim?

    Antwort

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

  42. Karte 42

    Frage

    The coating helps the fabric retain heat. Meaning of “retain”?

    Antwort

    Keep or continue to hold.

  43. Karte 43

    Frage

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

    Antwort

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

  44. Karte 44

    Frage

    Coordinate adjectives?

    Antwort

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

  45. Karte 45

    Frage

    Two sources on the same event?

    Antwort

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

  46. Karte 46

    Frage

    The survey was designed to elicit candid responses. Meaning of “elicit”?

    Antwort

    Draw out or bring forth.

  47. Karte 47

    Frage

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

    Antwort

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

  48. Karte 48

    Frage

    Sentence fragment?

    Antwort

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

  49. Karte 49

    Frage

    Inference from a narrow sample?

    Antwort

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

  50. Karte 50

    Frage

    Cost was the main constraint on the project. Meaning of “constraint”?

    Antwort

    A limit or restriction.

  51. Karte 51

    Frage

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

    Antwort

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

  52. Karte 52

    Frage

    Conjunctive adverb between independent clauses?

    Antwort

    Use a semicolon before it and a comma after it. Example: “The route was longer; however, it was safer.”

  53. Karte 53

    Frage

    Most accurate summary?

    Antwort

    State the central idea and its essential support without adding opinions or minor details.

  54. Karte 54

    Frage

    The review was comprehensive, covering every recorded case. Meaning of “comprehensive”?

    Antwort

    Complete and wide-ranging.

  55. Karte 55

    Frage

    The method is efficient. Indeed, it cuts processing time in half. What relationship does “Indeed” signal?

    Antwort

    Emphasis and confirmation. The second statement reinforces the first with a stronger detail.

  56. Karte 56

    Frage

    Who versus whom?

    Antwort

    Use “who” as a subject and “whom” as an object. Test with he/him: “whom” matches “him.”

  57. Karte 57

    Frage

    Evidence that best resolves a disagreement?

    Antwort

    Choose evidence that tests the specific point on which the sources differ, not a fact both already accept.

  58. Karte 58

    Frage

    The two materials have distinct properties. Meaning of “distinct”?

    Antwort

    Clearly different or separate.

  59. Karte 59

    Frage

    The forecast warned of rain. Still, the outdoor concert began on time. What relationship does “Still” signal?

    Antwort

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

  60. Karte 60

    Frage

    Comma before an introduced direct quotation?

    Antwort

    Use a comma after a speech tag. Example: “Mina wrote, ‘The sample is ready.’”

  61. Karte 61

    Frage

    The conclusion was qualified by two important exceptions. Meaning of “qualified”?

    Antwort

    Limited or modified, rather than stated without conditions.

  62. Karte 62

    Frage

    Notes for a synthesis goal?

    Antwort

    Use only facts that directly serve the stated goal. Relevant notes can be omitted if they do not help that purpose.

  63. Karte 63

    Frage

    Comma splice?

    Antwort

    Two independent clauses joined only by a comma. Replace it with a period or semicolon, or add a coordinating conjunction.

  64. Karte 64

    Frage

    Comma between subject and verb?

    Antwort

    Do not use one unless an interrupting phrase requires paired commas. “The results of the trial were clear” takes no comma after “trial.”

  65. Karte 65

    Frage

    The new sensor made the older model obsolete. Meaning of “obsolete”?

    Antwort

    No longer useful or current because something newer replaced it.

  66. Karte 66

    Frage

    Source attribution in a synthesis?

    Antwort

    Name the source when its identity, authority, or perspective matters to the rhetorical goal.

  67. Karte 67

    Frage

    Compound subject joined by “and”?

    Antwort

    Use a plural verb in the usual case. Example: “The map and the notes are useful.”

  68. Karte 68

    Frage

    Dangling opening modifier?

    Antwort

    It lacks the intended doer immediately after the modifier. Rewrite so the doer becomes the subject.

  69. Karte 69

    Frage

    Researchers derived the estimate from three measurements. Meaning of “derived”?

    Antwort

    Obtained from a source or calculation.

  70. Karte 70

    Frage

    Chronological synthesis?

    Antwort

    Order events by time and use dates or sequence words only when they help the reader follow the progression.

  71. Karte 71

    Frage

    Plural noun ending in s: possessive form?

    Antwort

    Add an apostrophe after the existing s. Example: “the researchers' notes.”

  72. Karte 72

    Frage

    Logical comparison?

    Antwort

    Compare like with like. Example: compare one city's rainfall with another city's rainfall, not with the city itself.

  73. Karte 73

    Frage

    The article advocates preserving the wetland. Meaning of “advocates”?

    Antwort

    Publicly supports or argues for.

  74. Karte 74

    Frage

    Compare evidence from two studies?

    Antwort

    State the shared measure first, then the relevant difference in result, method, or population.

  75. Karte 75

    Frage

    Colon after an incomplete lead-in?

    Antwort

    Do not use one. A colon must follow a complete clause, so “The reasons include:” is incorrect.

  76. Karte 76

    Frage

    Number versus amount?

    Antwort

    Use “number” for countable items and “amount” for uncountable quantities. Example: number of files, amount of water.

  77. Karte 77

    Frage

    Portable chargers are now ubiquitous on long trips. Meaning of “ubiquitous”?

    Antwort

    Present or found almost everywhere.

  78. Karte 78

    Frage

    Synthesis that emphasizes a difference?

    Antwort

    Use the same comparison point for both subjects, then state the contrast directly.

  79. Karte 79

    Frage

    Nonessential clause or phrase?

    Antwort

    Set it off with paired commas. The sentence should keep its core identity and meaning when the phrase is removed.

  80. Karte 80

    Frage

    Earlier of two past actions?

    Antwort

    Use past perfect when the sequence needs clarification. Example: “The team had left before the storm began.”

  81. Karte 81

    Frage

    Sentence 2 presents an exception to sentence 1. Its function?

    Antwort

    It qualifies the first claim by limiting when or how broadly it applies.

  82. Karte 82

    Frage

    Rhetorical goal: define a term?

    Antwort

    Give the term's relevant meaning before using details or examples that depend on it.

  83. Karte 83

    Frage

    Cumulative adjectives?

    Antwort

    Do not separate them with a comma when each adjective builds on the next. Example: “three small glass jars.”

  84. Karte 84

    Frage

    Run-on sentence?

    Antwort

    Independent clauses joined without valid punctuation or a conjunction. Add a period, semicolon, or comma plus coordinating conjunction.

  85. Karte 85

    Frage

    Sentence 2 gives a specific case after a general claim. Its function?

    Antwort

    It illustrates the claim with an example.

  86. Karte 86

    Frage

    Introduce a quotation in a synthesis?

    Antwort

    Give enough source and context to show why the quotation matters; do not leave it unattached.

  87. Karte 87

    Frage

    Relative pronoun for people?

    Antwort

    Use “who” or “whom,” depending on case. Example: “the engineer who designed the bridge.”

  88. Karte 88

    Frage

    Integrated quotation punctuation?

    Antwort

    Do not add a comma when the quotation completes the grammar of the sentence. Example: The report calls the result “unexpected.”

  89. Karte 89

    Frage

    Sentence 2 admits a limitation before defending the claim. Its function?

    Antwort

    It makes a concession, showing that the writer recognizes a complication.

  90. Karte 90

    Frage

    Avoid redundancy in synthesis?

    Antwort

    State each needed idea once. Prefer the version that preserves meaning with fewer repeated words.

  91. Karte 91

    Frage

    Semicolon between two independent clauses?

    Antwort

    Use it without a coordinating conjunction when the ideas are closely related. Example: “The trial ended; the analysis began.”

  92. Karte 92

    Frage

    Comma in a compound predicate?

    Antwort

    Usually omit it when one subject performs both actions. Example: “The team collected the samples and recorded the temperature.”

  93. Karte 93

    Frage

    Sentence 2 explains what a technical term means. Its function?

    Antwort

    It defines or clarifies the term.

  94. Karte 94

    Frage

    Combine two related sentences?

    Antwort

    Make the logical relationship explicit and remove repeated material without changing the facts.

  95. Karte 95

    Frage

    Either/or subject agreement?

    Antwort

    Make the verb agree with the nearer subject. Example: “Either the notes or the map is missing.”

  96. Karte 96

    Frage

    Active versus passive voice?

    Antwort

    Choose the voice that fits the focus. Active highlights the doer; passive can highlight the action or receiver.

  97. Karte 97

    Frage

    Sentence 2 describes the outcome of sentence 1. Its function?

    Antwort

    It presents an effect or consequence.

  98. Karte 98

    Frage

    Formal academic register?

    Antwort

    Use precise, neutral wording and avoid slang, vague intensifiers, and chatty asides unless the goal calls for them.

  99. Karte 99

    Frage

    Its or it's?

    Antwort

    “Its” is possessive; “it's” means “it is” or “it has.”

  100. Karte 100

    Frage

    Adjective versus adverb?

    Antwort

    An adjective modifies a noun; an adverb usually modifies a verb, adjective, or adverb. Example: a careful test; test carefully.

  101. Karte 101

    Frage

    A study reports a result without arguing for a policy. Author's purpose?

    Antwort

    To inform or explain, not necessarily to persuade.

  102. Karte 102

    Frage

    Concise synthesis?

    Antwort

    Keep every fact needed for the rhetorical goal and remove details that repeat or distract from it.

  103. Karte 103

    Frage

    Single dash for emphasis?

    Antwort

    Use it after a complete thought to spotlight a final explanation or turn. Example: “One result stood out—the oldest sample.”

  104. Karte 104

    Frage

    Comma with direct address?

    Antwort

    Set off the person being addressed. Example: “Rina, please check the units.”

  105. Karte 105

    Frage

    Why acknowledge a limitation?

    Antwort

    To define the claim's boundary and show how the evidence should be interpreted.

  106. Karte 106

    Frage

    Quantitative comparison in a synthesis?

    Antwort

    Name both values, the shared unit, and the direction or size of the difference.

  107. Karte 107

    Frage

    Each of the samples: verb number?

    Antwort

    Singular. “Each of the samples was labeled.” The subject is “each.”

  108. Karte 108

    Frage

    Between versus among?

    Antwort

    Use “between” for distinct individual relationships and “among” for a group without separate pairings.

  109. Karte 109

    Frage

    Rhetorical question in an argument?

    Antwort

    It can frame the issue or prompt the reader to consider an implied answer; it is not evidence by itself.

  110. Karte 110

    Frage

    Claim before or after support?

    Antwort

    Place it where the rhetorical goal is clearest: before evidence for a direct point, or after evidence for an evidence-led conclusion.

  111. Karte 111

    Frage

    Restrictive “that” versus nonrestrictive “which”?

    Antwort

    Use “that” without commas for essential information; use “which” with commas for removable information.

  112. Karte 112

    Frage

    Present perfect use?

    Antwort

    Use it for an action connected to the present or continuing to now. Example: “The team has tracked rainfall since May.”

  113. Karte 113

    Frage

    Two texts reach the same conclusion with different evidence. Relationship?

    Antwort

    They agree in conclusion but support it through different evidence.

  114. Karte 114

    Frage

    Group related ideas in a synthesis?

    Antwort

    Keep facts serving the same point together, then signal the move to a new point.

  115. Karte 115

    Frage

    Compound modifier before a noun?

    Antwort

    Hyphenate it when needed for clarity. Example: “a well-designed study.”

  116. Karte 116

    Frage

    Affect or effect?

    Antwort

    “Affect” is usually a verb meaning influence; “effect” is usually a noun meaning result.

  117. Karte 117

    Frage

    Two texts offer incompatible explanations. Relationship?

    Antwort

    They disagree about the cause or interpretation, even if they share the same observations.

  118. Karte 118

    Frage

    Replace a vague pronoun in synthesis?

    Antwort

    Use the precise noun when two or more possible antecedents could confuse the reader.

  119. Karte 119

    Frage

    Comma-separated list?

    Antwort

    Use commas between three or more parallel items. A final serial comma can prevent ambiguity.

  120. Karte 120

    Frage

    Main clause before a dependent clause?

    Antwort

    Usually no comma when the dependent clause is essential. Example: “The match continued although rain fell.”

  121. Karte 121

    Frage

    Two authors use the same evidence but different assumptions. Key difference?

    Antwort

    Their perspectives or interpretive frameworks, not the underlying evidence.

  122. Karte 122

    Frage

    Independent clauses joined with a coordinating conjunction?

    Antwort

    Place a comma before the conjunction. Example: “The sensor failed, so the team repeated the trial.”

  123. Karte 123

    Frage

    Introductory transition?

    Antwort

    Follow it with a comma when it modifies the whole sentence. Example: “However, the second trial succeeded.”

  124. Karte 124

    Frage

    Pronoun–antecedent agreement?

    Antwort

    Match number and make the reference clear. Singular “they” is standard when a person's gender is unknown or irrelevant.

  125. Karte 125

    Frage

    Paired em dashes?

    Antwort

    Use them to set off an emphatic interruption. Both dashes are needed when the sentence continues after it.

  126. Karte 126

    Frage

    How does new evidence relate to an earlier claim?

    Antwort

    It may support, weaken, qualify, or leave the claim unchanged. Match the evidence to the exact claim.

  127. Karte 127

    Frage

    Their, there, or they're?

    Antwort

    “Their” is possessive, “there” refers to place or existence, and “they're” means “they are.”

  128. Karte 128

    Frage

    Good or well?

    Antwort

    “Good” is usually an adjective; “well” is usually an adverb. A person can feel good and perform well.

  129. Karte 129

    Frage

    Appositive naming the same noun?

    Antwort

    Set a nonessential appositive off with commas. Example: “Dr. Rao, the lead author, presented the findings.”

  130. Karte 130

    Frage

    Why use an analogy?

    Antwort

    To clarify an unfamiliar idea through a relevant similarity to something more familiar.

  131. Karte 131

    Frage

    Than or then?

    Antwort

    “Than” makes a comparison; “then” refers to time or consequence.

  132. Karte 132

    Frage

    Hypothetical contrary-to-fact “if” clause?

    Antwort

    Use subjunctive “were.” Example: “If the sample were larger, the estimate would be steadier.”

  133. Karte 133

    Frage

    Plural noun with no possession?

    Antwort

    Do not add an apostrophe. Write “three sensors,” not “three sensor's.”

  134. Karte 134

    Frage

    Neutral, evidence-led wording indicates what tone?

    Antwort

    Objective. It emphasizes information rather than strong personal judgment.

  135. Karte 135

    Frage

    Complex list with internal commas?

    Antwort

    Use semicolons between the main items. Example: “Lima, Peru; Accra, Ghana; and Hanoi, Vietnam.”

  136. Karte 136

    Frage

    Ambiguous pronoun?

    Antwort

    A pronoun with more than one plausible antecedent. Replace it with the intended noun.

  137. Karte 137

    Frage

    Parentheses around nonessential information?

    Antwort

    Use them for an aside that is less central than the main sentence. The sentence must remain grammatical without it.

  138. Karte 138

    Frage

    Repeated doubt about the evidence indicates what tone?

    Antwort

    Skeptical. The writer questions whether a claim is adequately supported.

  139. Karte 139

    Frage

    Superlative comparison?

    Antwort

    Use it for one member against a group of three or more. Example: “the fastest of the four methods.”

  140. Karte 140

    Frage

    Pronoun after a preposition?

    Antwort

    Use the object form. Write “between you and me,” not “between you and I.”

  141. Karte 141

    Frage

    Apostrophe in a contraction?

    Antwort

    It marks omitted letters. Example: “can't” contracts “cannot,” and “they're” contracts “they are.”

  142. Karte 142

    Frage

    Coordinate-adjective test?

    Antwort

    If “and” works between the adjectives and their order can reverse, use a comma between them.

  143. Karte 143

    Frage

    Double comparative?

    Antwort

    Use only one comparative marker. Write “more efficient” or “faster,” not “more faster.”

  144. Karte 144

    Frage

    Lie or lay?

    Antwort

    “Lie” means recline and takes no object; “lay” means place and takes an object. Present: lie/lay; past: lay/laid.

  145. Karte 145

    Frage

    Who's or whose?

    Antwort

    “Who's” means “who is” or “who has”; “whose” is possessive.

  146. Karte 146

    Frage

    Standard comparison with “different”?

    Antwort

    Use “different from.” Example: “This result is different from the earlier estimate.”

  147. Karte 147

    Frage

    Paired construction with two endpoints?

    Antwort

    Use “between” with “and”: “between 10 and 15,” not “between 10 to 15.”

  148. Karte 148

    Frage

    Verb mood in a coordinated idea?

    Antwort

    Keep the mood consistent unless the meaning changes. Do not shift from a command to a statement without reason.

  149. Karte 149

    Frage

    Possessive pronoun apostrophe?

    Antwort

    Do not use one. Write “hers,” “ours,” “yours,” and “theirs.”

  150. Karte 150

    Frage

    Comma between a preposition and its object?

    Antwort

    Do not use one. Keep the prepositional phrase intact: “in the final report,” not “in, the final report.”

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  151. Karte 151

    Frage

    Solve ax+b=cax+b=c for xx, where a0a≠0.

    Antwort

    x=(cb)/ax=(c-b)/a. Subtract bb first, then divide by aa.

  152. Karte 152

    Frage

    Product of powers with the same base?

    Antwort

    aman=am+na^m a^n=a^{m+n}. Keep the base and add the exponents.

  153. Karte 153

    Frage

    Unit rate?

    Antwort

    The amount per 1 unit. Divide both quantities by the same value so the denominator becomes 1.

  154. Karte 154

    Frage

    Rectangle area?

    Antwort

    A=lwA=lw, where ll is length and ww is width.

  155. Karte 155

    Frage

    Slope from two points?

    Antwort

    m=(y2y1)/(x2x1)m=(y_2-y_1)/(x_2-x_1). Subtract coordinates in the same order.

  156. Karte 156

    Frage

    Quotient of powers with the same base?

    Antwort

    am/an=amna^m/a^n=a^{m-n} for a0a≠0.

  157. Karte 157

    Frage

    Conversion factor setup?

    Antwort

    Multiply by a ratio equal to 1, with the unwanted unit placed to cancel.

  158. Karte 158

    Frage

    Triangle area?

    Antwort

    A=(1/2)bhA=(1/2)bh. The height must be perpendicular to the chosen base.

  159. Karte 159

    Frage

    Slope-intercept form?

    Antwort

    y=mx+by=mx+b, where mm is the slope and bb is the y-intercept.

  160. Karte 160

    Frage

    Power raised to a power?

    Antwort

    (am)n=amn(a^m)^n=a^{mn}. Multiply the exponents.

  161. Karte 161

    Frage

    Dimensional analysis check?

    Antwort

    Cancel units algebraically. The units left at the end should match the quantity requested.

  162. Karte 162

    Frage

    Trapezoid area?

    Antwort

    A=(1/2)(b1+b2)hA=(1/2)(b_1+b_2)h. The height is perpendicular to the parallel bases.

  163. Karte 163

    Frage

    Point-slope form?

    Antwort

    yy1=m(xx1)y-y_1=m(x-x_1). Use a known point (x1,y1)(x_1,y_1) and the slope mm.

  164. Karte 164

    Frage

    Negative exponent?

    Antwort

    an=1/ana^{-n}=1/a^n for a0a≠0.

  165. Karte 165

    Frage

    Constant of proportionality in y=kxy=kx?

    Antwort

    k=y/xk=y/x for x0x≠0. It is also the unit rate and slope.

  166. Karte 166

    Frage

    Circle area?

    Antwort

    A=πr2A=πr^2.

  167. Karte 167

    Frage

    Intercepts from Ax+By=CAx+By=C?

    Antwort

    Set y=0y=0 for the x-intercept and set x=0x=0 for the y-intercept.

  168. Karte 168

    Frage

    Fractional exponent?

    Antwort

    am/na^{m/n} means the nth root of ama^m. For example, a1/2=aa^{1/2}=√a.

  169. Karte 169

    Frage

    Scale drawing length?

    Antwort

    Use a proportion with corresponding lengths in the same order, then apply the stated scale factor.

  170. Karte 170

    Frage

    Circle circumference?

    Antwort

    C=2πr=πdC=2πr=πd.

  171. Karte 171

    Frage

    Parallel nonvertical lines: slope relationship?

    Antwort

    They have equal slopes. Distinct parallel lines have different intercepts.

  172. Karte 172

    Frage

    Difference of squares?

    Antwort

    a2b2=(ab)(a+b)a^2-b^2=(a-b)(a+b).

  173. Karte 173

    Frage

    Percent change?

    Antwort

    New minus original, divided by the original, then multiplied by 100 percent. The original value is the denominator.

  174. Karte 174

    Frage

    Arc length from central angle θθ in degrees?

    Antwort

    L=(θ/360)(2πr)L=(θ/360)(2πr).

  175. Karte 175

    Frage

    Perpendicular nonvertical lines: slope relationship?

    Antwort

    Their slopes are negative reciprocals, so m1m2=1m_1m_2=-1.

  176. Karte 176

    Frage

    Perfect-square trinomial pattern?

    Antwort

    a2+2ab+b2=(a+b)2a^2+2ab+b^2=(a+b)^2 and a22ab+b2=(ab)2a^2-2ab+b^2=(a-b)^2.

  177. Karte 177

    Frage

    Increase by rr percent: multiplier?

    Antwort

    1+r/1001+r/100. Multiply the original value by this factor.

  178. Karte 178

    Frage

    Sector area from central angle θθ in degrees?

    Antwort

    A=(θ/360)(πr2)A=(θ/360)(πr^2).

  179. Karte 179

    Frage

    x-intercept of a graph?

    Antwort

    A point where y=0y=0 and the graph meets the x-axis.

  180. Karte 180

    Frage

    First step in factoring ax2+bx+cax^2+bx+c?

    Antwort

    Look for common factors and two binomials whose product reproduces the middle and constant terms.

  181. Karte 181

    Frage

    Original value after a 20 percent increase to 84?

    Antwort

    1. Divide the final value by the multiplier: $84/1.20=70$.
  182. Karte 182

    Frage

    Triangle interior-angle sum?

    Antwort

    180°180°.

  183. Karte 183

    Frage

    y-intercept of a graph?

    Antwort

    A point where x=0x=0 and the graph meets the y-axis.

  184. Karte 184

    Frage

    Roots from (xp)(xq)=0(x-p)(x-q)=0?

    Antwort

    x=px=p or x=qx=q, by the zero-product property.

  185. Karte 185

    Frage

    Weighted average?

    Antwort

    Sum of each value times its weight, divided by the sum of the weights. Do not take a simple average of unequal groups.

  186. Karte 186

    Frage

    Exterior angle of a triangle?

    Antwort

    It equals the sum of the two remote interior angles.

  187. Karte 187

    Frage

    Line through two points?

    Antwort

    Find the slope, then substitute either point into point-slope or slope-intercept form.

  188. Karte 188

    Frage

    Quadratic formula?

    Antwort

    x=(b±(b24ac))/(2a)x=(-b±√(b^2-4ac))/(2a) for ax2+bx+c=0ax^2+bx+c=0.

  189. Karte 189

    Frage

    Arithmetic mean?

    Antwort

    Add all values and divide by the number of values.

  190. Karte 190

    Frage

    Parallel lines cut by a transversal: alternate interior angles?

    Antwort

    They are congruent.

  191. Karte 191

    Frage

    Slope's units in context?

    Antwort

    Output units per input unit. In yy versus xx, slope units are y-units divided by x-units.

  192. Karte 192

    Frage

    What does b24acb^2-4ac tell you?

    Antwort

    The number of real solutions: positive gives two, zero gives one, and negative gives none.

  193. Karte 193

    Frage

    Median?

    Antwort

    The middle value after ordering the data; for an even count, average the two middle values.

  194. Karte 194

    Frage

    Similar triangles: corresponding sides?

    Antwort

    They are proportional. Match sides opposite equal angles.

  195. Karte 195

    Frage

    Direct variation model?

    Antwort

    y=kxy=kx. It is linear and passes through the origin.

  196. Karte 196

    Frage

    Vertex x-coordinate of ax2+bx+cax^2+bx+c?

    Antwort

    x=b/(2a)x=-b/(2a).

  197. Karte 197

    Frage

    Range of a data set?

    Antwort

    Maximum minus minimum.

  198. Karte 198

    Frage

    Scale factor kk: area factor?

    Antwort

    k2k^2. Lengths scale by kk, while areas scale by the square of kk.

  199. Karte 199

    Frage

    Solution of a two-line system?

    Antwort

    The intersection point, whose coordinates satisfy both equations.

  200. Karte 200

    Frage

    Vertex form of a quadratic?

    Antwort

    y=a(xh)2+ky=a(x-h)^2+k, with vertex (h,k)(h,k).

  201. Karte 201

    Frage

    Interquartile range?

    Antwort

    IQR=Q3Q1IQR=Q_3-Q_1. It measures the spread of the middle half of the data.

  202. Karte 202

    Frage

    Pythagorean theorem?

    Antwort

    a2+b2=c2a^2+b^2=c^2 for a right triangle, where cc is the hypotenuse.

  203. Karte 203

    Frage

    Substitution in a system?

    Antwort

    Solve one equation for a variable and replace that variable in the other equation.

  204. Karte 204

    Frage

    Axis of symmetry of y=a(xh)2+ky=a(x-h)^2+k?

    Antwort

    x=hx=h.

  205. Karte 205

    Frage

    Larger standard deviation means what?

    Antwort

    The data are more spread out around the mean.

  206. Karte 206

    Frage

    45°-45°-90° side ratio?

    Antwort

    1:1:21:1:√2. The hypotenuse is a leg times 2√2.

  207. Karte 207

    Frage

    Elimination in a system?

    Antwort

    Add or subtract equations so one variable cancels, then solve for the other.

  208. Karte 208

    Frage

    Completing the square?

    Antwort

    For x2+bxx^2+bx, add (b/2)2(b/2)^2 to form (x+b/2)2(x+b/2)^2.

  209. Karte 209

    Frage

    Effect of a high outlier on the mean?

    Antwort

    It usually pulls the mean upward. The median is often less affected.

  210. Karte 210

    Frage

    30°-60°-90° side ratio?

    Antwort

    1:3:21:√3:2, opposite 30°30°, 60°60°, and 90°90° respectively.

  211. Karte 211

    Frage

    Parallel lines in a system?

    Antwort

    No solution when they are distinct: equal slopes and different intercepts.

  212. Karte 212

    Frage

    Sum and product of roots of ax2+bx+c=0ax^2+bx+c=0?

    Antwort

    Sum =b/a=-b/a and product =c/a=c/a.

  213. Karte 213

    Frage

    Add the same constant to every data value: effect?

    Antwort

    The mean and median increase by that constant; measures of spread stay unchanged.

  214. Karte 214

    Frage

    Right-triangle sine?

    Antwort

    Sine of θθ equals opposite over hypotenuse.

  215. Karte 215

    Frage

    Same line written two ways in a system?

    Antwort

    Infinitely many solutions. Simplifying either equation produces the other.

  216. Karte 216

    Frage

    Remainder when P(x)P(x) is divided by xax-a?

    Antwort

    P(a)P(a), by the Remainder Theorem.

  217. Karte 217

    Frage

    Multiply every data value by positive kk: effect?

    Antwort

    The mean, median, range, IQR, and standard deviation are all multiplied by kk.

  218. Karte 218

    Frage

    Right-triangle cosine?

    Antwort

    Cosine of θθ equals adjacent over hypotenuse.

  219. Karte 219

    Frage

    Multiply or divide an inequality by a negative number?

    Antwort

    Reverse the inequality sign.

  220. Karte 220

    Frage

    When is xax-a a factor of P(x)P(x)?

    Antwort

    When P(a)=0P(a)=0, by the Factor Theorem.

  221. Karte 221

    Frage

    Joint probability from a two-way table?

    Antwort

    Divide the count in the intersection cell by the grand total.

  222. Karte 222

    Frage

    Right-triangle tangent?

    Antwort

    Tangent of θθ equals opposite over adjacent.

  223. Karte 223

    Frage

    Compound inequality with “and”?

    Antwort

    Use the intersection: values that satisfy both inequalities.

  224. Karte 224

    Frage

    Even degree with positive leading coefficient: end behavior?

    Antwort

    Both ends rise: P(x)P(x)→∞ as x±x→±∞.

  225. Karte 225

    Frage

    Conditional probability P(AB)P(A|B)?

    Antwort

    P(AB)/P(B)P(A∩B)/P(B). Restrict the denominator to outcomes in BB.

  226. Karte 226

    Frage

    Complementary acute angles: sine–cosine relationship?

    Antwort

    The sine of θθ equals the cosine of 90°θ90°-θ.

  227. Karte 227

    Frage

    Compound inequality with “or”?

    Antwort

    Use the union: values that satisfy at least one inequality.

  228. Karte 228

    Frage

    Odd degree with positive leading coefficient: end behavior?

    Antwort

    The left end falls and the right end rises.

  229. Karte 229

    Frage

    Independent events AA and BB?

    Antwort

    P(AB)=P(A)P(B)P(A∩B)=P(A)P(B). Knowing one occurred does not change the probability of the other.

  230. Karte 230

    Frage

    Distance between (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)?

    Antwort

    ((x2x1)2+(y2y1)2)√((x_2-x_1)^2+(y_2-y_1)^2).

  231. Karte 231

    Frage

    Solve xa=b|x-a|=b for b0b≥0.

    Antwort

    xa=bx-a=b or xa=bx-a=-b. Absolute value represents distance from aa.

  232. Karte 232

    Frage

    Exponential growth model?

    Antwort

    y=a(1+r)ty=a(1+r)^t, where aa is the initial value and rr is the growth rate per period.

  233. Karte 233

    Frage

    Mutually exclusive events?

    Antwort

    They cannot occur together, so P(AB)=P(A)+P(B)P(A∪B)=P(A)+P(B).

  234. Karte 234

    Frage

    Midpoint of two points?

    Antwort

    ((x1+x2)/2,(y1+y2)/2)((x_1+x_2)/2,(y_1+y_2)/2).

  235. Karte 235

    Frage

    Solve xa<b|x-a|<b for b>0b>0.

    Antwort

    ab<x<a+ba-b<x<a+b. The solution lies within distance bb of aa.

  236. Karte 236

    Frage

    Exponential decay model?

    Antwort

    y=a(1r)ty=a(1-r)^t, where 0<r<10<r<1 is the decay rate per period.

  237. Karte 237

    Frage

    Complement rule?

    Antwort

    The probability that AA does not occur is 1P(A)1-P(A).

  238. Karte 238

    Frage

    Circle with center (h,k)(h,k) and radius rr?

    Antwort

    (xh)2+(yk)2=r2(x-h)^2+(y-k)^2=r^2.

  239. Karte 239

    Frage

    Evaluate f(a)f(a)?

    Antwort

    Substitute aa for every input variable in the function rule, then simplify.

  240. Karte 240

    Frage

    Growth factor 1.08: percent growth rate?

    Antwort

    8 percent. Subtract 1 and convert the decimal to a percent.

  241. Karte 241

    Frage

    Representative random sample permits what conclusion?

    Antwort

    A cautious generalization from the sample to the population it represents.

  242. Karte 242

    Frage

    Radius from (xh)2+(yk)2=R(x-h)^2+(y-k)^2=R?

    Antwort

    r=Rr=√R, provided R>0R>0.

  243. Karte 243

    Frage

    Linear table: constant slope check?

    Antwort

    Equal changes in xx must produce equal changes in yy; compare Δy/ΔxΔy/Δx across intervals.

  244. Karte 244

    Frage

    Decay factor 0.73: percent decrease?

    Antwort

    27 percent. Compute 10.73=0.271-0.73=0.27.

  245. Karte 245

    Frage

    Random assignment permits what causal claim?

    Antwort

    If the experiment is well controlled, differences between treatment groups can support a causal conclusion.

  246. Karte 246

    Frage

    Radius and tangent at the contact point?

    Antwort

    They are perpendicular.

  247. Karte 247

    Frage

    Positive slope means what for a linear function?

    Antwort

    The output increases as the input increases.

  248. Karte 248

    Frage

    Solve 32x=3103^{2x}=3^{10}.

    Antwort

    x=5x=5. Equal positive bases other than 1 have equal exponents.

  249. Karte 249

    Frage

    Observational study supports causation?

    Antwort

    No. It can show association, but uncontrolled confounding variables may explain the pattern.

  250. Karte 250

    Frage

    Rectangular-prism volume?

    Antwort

    V=lwhV=lwh, or base area times height.

  251. Karte 251

    Frage

    Arithmetic sequence common difference?

    Antwort

    Subtract consecutive terms: d=anan1d=a_n-a_{n-1}.

  252. Karte 252

    Frage

    Compound interest formula?

    Antwort

    A=P(1+r/n)ntA=P(1+r/n)^{nt}, where nn is the number of compounding periods per year.

  253. Karte 253

    Frage

    Larger random sample: effect on margin of error?

    Antwort

    It generally decreases the margin of error when the sampling method stays sound.

  254. Karte 254

    Frage

    Cylinder volume?

    Antwort

    V=πr2hV=πr^2h.

  255. Karte 255

    Frage

    Arithmetic sequence nth term?

    Antwort

    an=a1+(n1)da_n=a_1+(n-1)d.

  256. Karte 256

    Frage

    Rational expression: first domain check?

    Antwort

    Exclude values that make any original denominator zero, even if a factor later cancels.

  257. Karte 257

    Frage

    Slope of a line of best fit?

    Antwort

    The predicted change in the response variable for each 1-unit increase in the explanatory variable.

  258. Karte 258

    Frage

    Cone volume?

    Antwort

    V=(1/3)πr2hV=(1/3)πr^2h.

  259. Karte 259

    Frage

    Solve a literal equation for one variable?

    Antwort

    Treat the other symbols as constants and use inverse operations to isolate the target variable.

  260. Karte 260

    Frage

    Why check rational-equation solutions?

    Antwort

    Clearing denominators can produce a value excluded from the original equation. Reject any value that makes an original denominator zero.

  261. Karte 261

    Frage

    Residual?

    Antwort

    Actual value minus predicted value. A positive residual means the point lies above the model.

  262. Karte 262

    Frage

    Sphere volume?

    Antwort

    V=(4/3)πr3V=(4/3)πr^3.

  263. Karte 263

    Frage

    Boundary for a two-variable linear inequality?

    Antwort

    Replace the inequality with equality to draw the boundary line, then test a point for the shaded side.

  264. Karte 264

    Frage

    Why check a solution after squaring both sides?

    Antwort

    Squaring can introduce an extraneous solution. Substitute each candidate into the original radical equation.

  265. Karte 265

    Frage

    Positive correlation?

    Antwort

    Larger values of one variable tend to occur with larger values of the other. It does not prove causation.

  266. Karte 266

    Frage

    Rectangular-prism surface area?

    Antwort

    SA=2(lw+lh+wh)SA=2(lw+lh+wh).

  267. Karte 267

    Frage

    Check a proposed system solution?

    Antwort

    Substitute the ordered pair into both original equations. It must make both true.

  268. Karte 268

    Frage

    Simplify 72√72.

    Antwort

    626√2. Factor 72=36×272=36×2 and take 36√36 outside the radical.

  269. Karte 269

    Frage

    Extrapolation risk?

    Antwort

    A model may not keep the same pattern outside the observed data range.

  270. Karte 270

    Frage

    Area scale factor when lengths double?

    Antwort

    1. Area scales with the square of the length factor: $2^2=4$.
  271. Karte 271

    Frage

    Horizontal line slope?

    Antwort

    1. Its y-value does not change as x changes.
  272. Karte 272

    Frage

    Inverse function setup?

    Antwort

    Write y=f(x)y=f(x), swap xx and yy, then solve for yy. Restrict the domain when needed to make the inverse a function.

  273. Karte 273

    Frage

    Percentage points versus percent change?

    Antwort

    A rate moving from 40 percent to 50 percent rises 10 percentage points but 25 percent relative to 40.

  274. Karte 274

    Frage

    y-intercept in a context?

    Antwort

    The predicted or initial output when the input is zero; check whether zero is meaningful in the situation.

  275. Karte 275

    Frage

    Quadratic maximum or minimum from vertex form?

    Antwort

    The vertex value is kk in a(xh)2+ka(x-h)^2+k; it is a minimum if a>0a>0 and a maximum if a<0a<0.

  276. Karte 276

    Frage

    Line parallel to y=mx+by=mx+b through (p,q)(p,q)?

    Antwort

    yq=m(xp)y-q=m(x-p). Parallel lines keep the same slope.

  277. Karte 277

    Frage

    Graph of f(xh)+kf(x-h)+k?

    Antwort

    Shift the graph of ff right hh units and up kk units.

  278. Karte 278

    Frage

    Population versus sample?

    Antwort

    The population is the full group of interest; a sample is the subset actually observed.

  279. Karte 279

    Frage

    Linear model from initial value bb and rate mm?

    Antwort

    y=mx+by=mx+b. The initial value is the output at input zero.

  280. Karte 280

    Frage

    Function composition (fg)(x)(f∘g)(x)?

    Antwort

    f(g(x))f(g(x)). Evaluate the inner function gg first.

  281. Karte 281

    Frage

    Density?

    Antwort

    Mass divided by volume. Keep the units consistent.

  282. Karte 282

    Frage

    Vertical line slope?

    Antwort

    Undefined because Δx=0Δx=0, which would require division by zero.

  283. Karte 283

    Frage

    Nonlinear system with one equation solved for yy?

    Antwort

    Substitute that expression for yy into the other equation, solve for xx, then find each matching yy.

  284. Karte 284

    Frage

    Weighted percentage across unequal groups?

    Antwort

    Convert each percentage to a count or weight, add the successes, then divide by the combined total.

  285. Karte 285

    Frage

    Line perpendicular to a nonzero finite slope mm through (p,q)(p,q)?

    Antwort

    Use slope 1/m-1/m in yq=(1/m)(xp)y-q=(-1/m)(x-p), when mm is nonzero and finite.

  286. Karte 286

    Frage

    Cancel a common factor in a rational expression?

    Antwort

    Cancel factors, not terms, and keep every restriction from the original denominator.

  287. Karte 287

    Frage

    Solve a linear equation containing fractions?

    Antwort

    Multiply every term by the least common denominator first, then solve the resulting linear equation.

  288. Karte 288

    Frage

    Rewrite a2xa^{2x} using base axa^x.

    Antwort

    (ax)2(a^x)^2. This can turn an exponential expression into a quadratic form.

  289. Karte 289

    Frage

    Rate units check?

    Antwort

    Write the numerator and denominator units explicitly, such as kilometers per hour, then convert only if the requested units differ.

  290. Karte 290

    Frage

    Strict versus inclusive inequality endpoint?

    Antwort

    Use an open point for << or >> and a closed point for or .

  291. Karte 291

    Frage

    Even-multiplicity zero on a graph?

    Antwort

    The graph touches the x-axis and turns around; it does not cross there.

  292. Karte 292

    Frage

    System word problem: first setup step?

    Antwort

    Define the variables with units, then translate two independent relationships into equations.

  293. Karte 293

    Frage

    When does a quadratic have exactly one real solution?

    Antwort

    When b24ac=0b^2-4ac=0. The repeated root is the vertex's x-coordinate.

  294. Karte 294

    Frage

    Two-way table: denominator for “among group B”?

    Antwort

    Use the total for group B, not the grand total. The wording makes B the condition.

  295. Karte 295

    Frage

    Find an input when f(x)=kf(x)=k.

    Antwort

    Set the function rule equal to kk and solve for xx; there may be zero, one, or several inputs.

  296. Karte 296

    Frage

    Graph of f(x)-f(x)?

    Antwort

    Reflect the graph of f(x)f(x) across the x-axis.

  297. Karte 297

    Frage

    Three consecutive integers starting with nn?

    Antwort

    nn, n+1n+1, and n+2n+2.

  298. Karte 298

    Frage

    Line–parabola intersections from a substituted quadratic?

    Antwort

    Use its discriminant: positive means two intersections, zero one tangent intersection, and negative none.

  299. Karte 299

    Frage

    Linear equation with no solution: coefficient pattern?

    Antwort

    After simplification, the variable terms cancel and leave a false statement, such as 0=50=5.

  300. Karte 300

    Frage

    Zeros of a function on its graph?

    Antwort

    The x-coordinates where the graph meets the x-axis, so f(x)=0f(x)=0.

An open study book surrounded by punctuation marks, a coordinate graph, a right triangle, a circle, and a data chart.

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