Digital SAT Flashcards: Math, Grammar & Words in Context

Kort i denne kortstokken

1. Kort 1

   Spørsmål

   Central idea of a passage?

   Svar

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

2. Kort 2

   Spørsmål

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

   Svar

   Reduced. The trees made the heat less severe.

3. Kort 3

   Spørsmål

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

   Svar

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

4. Kort 4

   Spørsmål

   Three standard joins for two independent clauses?

   Svar

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

5. Kort 5

   Spørsmål

   Best supporting detail?

   Svar

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

6. Kort 6

   Spørsmål

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

   Svar

   Confirmed with supporting evidence.

7. Kort 7

   Spørsmål

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

   Svar

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

8. Kort 8

   Spørsmål

   Introductory dependent clause before a main clause?

   Svar

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

9. Kort 9

   Spørsmål

   Valid inference?

   Svar

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

10. Kort 10

    Spørsmål

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

    Svar

    Provisional or not yet certain.

11. Kort 11

    Spørsmål

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

    Svar

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

12. Kort 12

    Spørsmål

    Singular subject with an intervening prepositional phrase?

    Svar

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

13. Kort 13

    Spørsmål

    Strongest textual evidence?

    Svar

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

14. Kort 14

    Spørsmål

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

    Svar

    So small that it is not important.

15. Kort 15

    Spørsmål

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

    Svar

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

16. Kort 16

    Spørsmål

    Opening modifier placement?

    Svar

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

17. Kort 17

    Spørsmål

    Quantitative evidence for a claim?

    Svar

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

18. Kort 18

    Spørsmål

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

    Svar

    Traditional or commonly accepted.

19. Kort 19

    Spørsmål

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

    Svar

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

20. Kort 20

    Spørsmål

    Singular possessive noun?

    Svar

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

21. Kort 21

    Spørsmål

    Trend in a table or graph?

    Svar

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

22. Kort 22

    Spørsmål

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

    Svar

    New or original in this context.

23. Kort 23

    Spørsmål

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

    Svar

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

24. Kort 24

    Spørsmål

    Parallel items in a series?

    Svar

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

25. Kort 25

    Spørsmål

    Claim stronger than the evidence?

    Svar

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

26. Kort 26

    Spørsmål

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

    Svar

    Reasonable or believable.

27. Kort 27

    Spørsmål

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

    Svar

    Addition. The second statement adds a related supporting point.

28. Kort 28

    Spørsmål

    Colon before an explanation or list?

    Svar

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

29. Kort 29

    Spørsmål

    Claim versus evidence?

    Svar

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

30. Kort 30

    Spørsmål

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

    Svar

    Open to more than one interpretation.

31. Kort 31

    Spørsmål

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

    Svar

    Replacement. The second statement substitutes one action for another.

32. Kort 32

    Spørsmål

    Count nouns versus mass nouns?

    Svar

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

33. Kort 33

    Spørsmål

    Effect of a counterexample?

    Svar

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

34. Kort 34

    Spørsmål

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

    Svar

    Irregular and occasional.

35. Kort 35

    Spørsmål

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

    Svar

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

36. Kort 36

    Spørsmål

    Essential clause punctuation?

    Svar

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

37. Kort 37

    Spørsmål

    Correlation alone proves causation?

    Svar

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

38. Kort 38

    Spørsmål

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

    Svar

    Coming later in time.

39. Kort 39

    Spørsmål

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

    Svar

    Restatement for clarity. The second statement rephrases the first.

40. Kort 40

    Spørsmål

    Verb tense across a paragraph?

    Svar

    Keep the time frame consistent unless the timing actually changes.

41. Kort 41

    Spørsmål

    Missing information in a data claim?

    Svar

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

42. Kort 42

    Spørsmål

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

    Svar

    Keep or continue to hold.

43. Kort 43

    Spørsmål

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

    Svar

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

44. Kort 44

    Spørsmål

    Coordinate adjectives?

    Svar

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

45. Kort 45

    Spørsmål

    Two sources on the same event?

    Svar

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

46. Kort 46

    Spørsmål

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

    Svar

    Draw out or bring forth.

47. Kort 47

    Spørsmål

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

    Svar

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

48. Kort 48

    Spørsmål

    Sentence fragment?

    Svar

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

49. Kort 49

    Spørsmål

    Inference from a narrow sample?

    Svar

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

50. Kort 50

    Spørsmål

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

    Svar

    A limit or restriction.

51. Kort 51

    Spørsmål

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

    Svar

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

52. Kort 52

    Spørsmål

    Conjunctive adverb between independent clauses?

    Svar

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

53. Kort 53

    Spørsmål

    Most accurate summary?

    Svar

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

54. Kort 54

    Spørsmål

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

    Svar

    Complete and wide-ranging.

55. Kort 55

    Spørsmål

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

    Svar

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

56. Kort 56

    Spørsmål

    Who versus whom?

    Svar

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

57. Kort 57

    Spørsmål

    Evidence that best resolves a disagreement?

    Svar

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

58. Kort 58

    Spørsmål

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

    Svar

    Clearly different or separate.

59. Kort 59

    Spørsmål

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

    Svar

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

60. Kort 60

    Spørsmål

    Comma before an introduced direct quotation?

    Svar

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

61. Kort 61

    Spørsmål

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

    Svar

    Limited or modified, rather than stated without conditions.

62. Kort 62

    Spørsmål

    Notes for a synthesis goal?

    Svar

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

63. Kort 63

    Spørsmål

    Comma splice?

    Svar

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

64. Kort 64

    Spørsmål

    Comma between subject and verb?

    Svar

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

65. Kort 65

    Spørsmål

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

    Svar

    No longer useful or current because something newer replaced it.

66. Kort 66

    Spørsmål

    Source attribution in a synthesis?

    Svar

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

67. Kort 67

    Spørsmål

    Compound subject joined by “and”?

    Svar

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

68. Kort 68

    Spørsmål

    Dangling opening modifier?

    Svar

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

69. Kort 69

    Spørsmål

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

    Svar

    Obtained from a source or calculation.

70. Kort 70

    Spørsmål

    Chronological synthesis?

    Svar

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

71. Kort 71

    Spørsmål

    Plural noun ending in s: possessive form?

    Svar

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

72. Kort 72

    Spørsmål

    Logical comparison?

    Svar

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

73. Kort 73

    Spørsmål

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

    Svar

    Publicly supports or argues for.

74. Kort 74

    Spørsmål

    Compare evidence from two studies?

    Svar

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

75. Kort 75

    Spørsmål

    Colon after an incomplete lead-in?

    Svar

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

76. Kort 76

    Spørsmål

    Number versus amount?

    Svar

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

77. Kort 77

    Spørsmål

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

    Svar

    Present or found almost everywhere.

78. Kort 78

    Spørsmål

    Synthesis that emphasizes a difference?

    Svar

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

79. Kort 79

    Spørsmål

    Nonessential clause or phrase?

    Svar

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

80. Kort 80

    Spørsmål

    Earlier of two past actions?

    Svar

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

81. Kort 81

    Spørsmål

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

    Svar

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

82. Kort 82

    Spørsmål

    Rhetorical goal: define a term?

    Svar

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

83. Kort 83

    Spørsmål

    Cumulative adjectives?

    Svar

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

84. Kort 84

    Spørsmål

    Run-on sentence?

    Svar

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

85. Kort 85

    Spørsmål

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

    Svar

    It illustrates the claim with an example.

86. Kort 86

    Spørsmål

    Introduce a quotation in a synthesis?

    Svar

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

87. Kort 87

    Spørsmål

    Relative pronoun for people?

    Svar

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

88. Kort 88

    Spørsmål

    Integrated quotation punctuation?

    Svar

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

89. Kort 89

    Spørsmål

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

    Svar

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

90. Kort 90

    Spørsmål

    Avoid redundancy in synthesis?

    Svar

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

91. Kort 91

    Spørsmål

    Semicolon between two independent clauses?

    Svar

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

92. Kort 92

    Spørsmål

    Comma in a compound predicate?

    Svar

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

93. Kort 93

    Spørsmål

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

    Svar

    It defines or clarifies the term.

94. Kort 94

    Spørsmål

    Combine two related sentences?

    Svar

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

95. Kort 95

    Spørsmål

    Either/or subject agreement?

    Svar

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

96. Kort 96

    Spørsmål

    Active versus passive voice?

    Svar

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

97. Kort 97

    Spørsmål

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

    Svar

    It presents an effect or consequence.

98. Kort 98

    Spørsmål

    Formal academic register?

    Svar

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

99. Kort 99

    Spørsmål

    Its or it's?

    Svar

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

100. Kort 100

     Spørsmål

     Adjective versus adverb?

     Svar

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

101. Kort 101

     Spørsmål

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

     Svar

     To inform or explain, not necessarily to persuade.

102. Kort 102

     Spørsmål

     Concise synthesis?

     Svar

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

103. Kort 103

     Spørsmål

     Single dash for emphasis?

     Svar

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

104. Kort 104

     Spørsmål

     Comma with direct address?

     Svar

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

105. Kort 105

     Spørsmål

     Why acknowledge a limitation?

     Svar

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

106. Kort 106

     Spørsmål

     Quantitative comparison in a synthesis?

     Svar

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

107. Kort 107

     Spørsmål

     Each of the samples: verb number?

     Svar

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

108. Kort 108

     Spørsmål

     Between versus among?

     Svar

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

109. Kort 109

     Spørsmål

     Rhetorical question in an argument?

     Svar

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

110. Kort 110

     Spørsmål

     Claim before or after support?

     Svar

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

111. Kort 111

     Spørsmål

     Restrictive “that” versus nonrestrictive “which”?

     Svar

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

112. Kort 112

     Spørsmål

     Present perfect use?

     Svar

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

113. Kort 113

     Spørsmål

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

     Svar

     They agree in conclusion but support it through different evidence.

114. Kort 114

     Spørsmål

     Group related ideas in a synthesis?

     Svar

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

115. Kort 115

     Spørsmål

     Compound modifier before a noun?

     Svar

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

116. Kort 116

     Spørsmål

     Affect or effect?

     Svar

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

117. Kort 117

     Spørsmål

     Two texts offer incompatible explanations. Relationship?

     Svar

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

118. Kort 118

     Spørsmål

     Replace a vague pronoun in synthesis?

     Svar

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

119. Kort 119

     Spørsmål

     Comma-separated list?

     Svar

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

120. Kort 120

     Spørsmål

     Main clause before a dependent clause?

     Svar

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

121. Kort 121

     Spørsmål

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

     Svar

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Kort 122

     Spørsmål

     Independent clauses joined with a coordinating conjunction?

     Svar

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

123. Kort 123

     Spørsmål

     Introductory transition?

     Svar

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

124. Kort 124

     Spørsmål

     Pronoun–antecedent agreement?

     Svar

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

125. Kort 125

     Spørsmål

     Paired em dashes?

     Svar

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

126. Kort 126

     Spørsmål

     How does new evidence relate to an earlier claim?

     Svar

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

127. Kort 127

     Spørsmål

     Their, there, or they're?

     Svar

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

128. Kort 128

     Spørsmål

     Good or well?

     Svar

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

129. Kort 129

     Spørsmål

     Appositive naming the same noun?

     Svar

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

130. Kort 130

     Spørsmål

     Why use an analogy?

     Svar

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

131. Kort 131

     Spørsmål

     Than or then?

     Svar

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

132. Kort 132

     Spørsmål

     Hypothetical contrary-to-fact “if” clause?

     Svar

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

133. Kort 133

     Spørsmål

     Plural noun with no possession?

     Svar

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

134. Kort 134

     Spørsmål

     Neutral, evidence-led wording indicates what tone?

     Svar

     Objective. It emphasizes information rather than strong personal judgment.

135. Kort 135

     Spørsmål

     Complex list with internal commas?

     Svar

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

136. Kort 136

     Spørsmål

     Ambiguous pronoun?

     Svar

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

137. Kort 137

     Spørsmål

     Parentheses around nonessential information?

     Svar

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

138. Kort 138

     Spørsmål

     Repeated doubt about the evidence indicates what tone?

     Svar

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

139. Kort 139

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     Superlative comparison?

     Svar

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

140. Kort 140

     Spørsmål

     Pronoun after a preposition?

     Svar

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

141. Kort 141

     Spørsmål

     Apostrophe in a contraction?

     Svar

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

142. Kort 142

     Spørsmål

     Coordinate-adjective test?

     Svar

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

143. Kort 143

     Spørsmål

     Double comparative?

     Svar

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

144. Kort 144

     Spørsmål

     Lie or lay?

     Svar

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

145. Kort 145

     Spørsmål

     Who's or whose?

     Svar

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

146. Kort 146

     Spørsmål

     Standard comparison with “different”?

     Svar

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

147. Kort 147

     Spørsmål

     Paired construction with two endpoints?

     Svar

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

148. Kort 148

     Spørsmål

     Verb mood in a coordinated idea?

     Svar

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

149. Kort 149

     Spørsmål

     Possessive pronoun apostrophe?

     Svar

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

150. Kort 150

     Spørsmål

     Comma between a preposition and its object?

     Svar

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

     

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151. Kort 151

     Spørsmål

     Solve $ax+b=c$ for $x$, where $a≠0$.

     Svar

     $x=(c-b)/a$. Subtract $b$ first, then divide by $a$.

152. Kort 152

     Spørsmål

     Product of powers with the same base?

     Svar

     $a^m a^n=a^{m+n}$. Keep the base and add the exponents.

153. Kort 153

     Spørsmål

     Unit rate?

     Svar

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

154. Kort 154

     Spørsmål

     Rectangle area?

     Svar

     $A=lw$, where $l$ is length and $w$ is width.

155. Kort 155

     Spørsmål

     Slope from two points?

     Svar

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

156. Kort 156

     Spørsmål

     Quotient of powers with the same base?

     Svar

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Kort 157

     Spørsmål

     Conversion factor setup?

     Svar

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

158. Kort 158

     Spørsmål

     Triangle area?

     Svar

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

159. Kort 159

     Spørsmål

     Slope-intercept form?

     Svar

     $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

160. Kort 160

     Spørsmål

     Power raised to a power?

     Svar

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

161. Kort 161

     Spørsmål

     Dimensional analysis check?

     Svar

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

162. Kort 162

     Spørsmål

     Trapezoid area?

     Svar

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

163. Kort 163

     Spørsmål

     Point-slope form?

     Svar

     $y-y_1=m(x-x_1)$. Use a known point $(x_1,y_1)$ and the slope $m$.

164. Kort 164

     Spørsmål

     Negative exponent?

     Svar

     $a^{-n}=1/a^n$ for $a≠0$.

165. Kort 165

     Spørsmål

     Constant of proportionality in $y=kx$?

     Svar

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

166. Kort 166

     Spørsmål

     Circle area?

     Svar

     $A=πr^2$.

167. Kort 167

     Spørsmål

     Intercepts from $Ax+By=C$?

     Svar

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

168. Kort 168

     Spørsmål

     Fractional exponent?

     Svar

     $a^{m/n}$ means the nth root of $a^m$. For example, $a^{1/2}=√a$.

169. Kort 169

     Spørsmål

     Scale drawing length?

     Svar

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

170. Kort 170

     Spørsmål

     Circle circumference?

     Svar

     $C=2πr=πd$.

171. Kort 171

     Spørsmål

     Parallel nonvertical lines: slope relationship?

     Svar

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

172. Kort 172

     Spørsmål

     Difference of squares?

     Svar

     $a^2-b^2=(a-b)(a+b)$.

173. Kort 173

     Spørsmål

     Percent change?

     Svar

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

174. Kort 174

     Spørsmål

     Arc length from central angle $θ$ in degrees?

     Svar

     $L=(θ/360)(2πr)$.

175. Kort 175

     Spørsmål

     Perpendicular nonvertical lines: slope relationship?

     Svar

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

176. Kort 176

     Spørsmål

     Perfect-square trinomial pattern?

     Svar

     $a^2+2ab+b^2=(a+b)^2$ and $a^2-2ab+b^2=(a-b)^2$.

177. Kort 177

     Spørsmål

     Increase by $r$ percent: multiplier?

     Svar

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

178. Kort 178

     Spørsmål

     Sector area from central angle $θ$ in degrees?

     Svar

     $A=(θ/360)(πr^2)$.

179. Kort 179

     Spørsmål

     x-intercept of a graph?

     Svar

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

180. Kort 180

     Spørsmål

     First step in factoring $ax^2+bx+c$?

     Svar

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

181. Kort 181

     Spørsmål

     Original value after a 20 percent increase to 84?

     Svar

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

182. Kort 182

     Spørsmål

     Triangle interior-angle sum?

     Svar

     $180°$.

183. Kort 183

     Spørsmål

     y-intercept of a graph?

     Svar

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

184. Kort 184

     Spørsmål

     Roots from $(x-p)(x-q)=0$?

     Svar

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

185. Kort 185

     Spørsmål

     Weighted average?

     Svar

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

186. Kort 186

     Spørsmål

     Exterior angle of a triangle?

     Svar

     It equals the sum of the two remote interior angles.

187. Kort 187

     Spørsmål

     Line through two points?

     Svar

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

188. Kort 188

     Spørsmål

     Quadratic formula?

     Svar

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

189. Kort 189

     Spørsmål

     Arithmetic mean?

     Svar

     Add all values and divide by the number of values.

190. Kort 190

     Spørsmål

     Parallel lines cut by a transversal: alternate interior angles?

     Svar

     They are congruent.

191. Kort 191

     Spørsmål

     Slope's units in context?

     Svar

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

192. Kort 192

     Spørsmål

     What does $b^2-4ac$ tell you?

     Svar

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

193. Kort 193

     Spørsmål

     Median?

     Svar

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

194. Kort 194

     Spørsmål

     Similar triangles: corresponding sides?

     Svar

     They are proportional. Match sides opposite equal angles.

195. Kort 195

     Spørsmål

     Direct variation model?

     Svar

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

196. Kort 196

     Spørsmål

     Vertex x-coordinate of $ax^2+bx+c$?

     Svar

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

197. Kort 197

     Spørsmål

     Range of a data set?

     Svar

     Maximum minus minimum.

198. Kort 198

     Spørsmål

     Scale factor $k$: area factor?

     Svar

     $k^2$. Lengths scale by $k$, while areas scale by the square of $k$.

199. Kort 199

     Spørsmål

     Solution of a two-line system?

     Svar

     The intersection point, whose coordinates satisfy both equations.

200. Kort 200

     Spørsmål

     Vertex form of a quadratic?

     Svar

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

201. Kort 201

     Spørsmål

     Interquartile range?

     Svar

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

202. Kort 202

     Spørsmål

     Pythagorean theorem?

     Svar

     $a^2+b^2=c^2$ for a right triangle, where $c$ is the hypotenuse.

203. Kort 203

     Spørsmål

     Substitution in a system?

     Svar

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

204. Kort 204

     Spørsmål

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

     Svar

     $x=h$.

205. Kort 205

     Spørsmål

     Larger standard deviation means what?

     Svar

     The data are more spread out around the mean.

206. Kort 206

     Spørsmål

     45°-45°-90° side ratio?

     Svar

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

207. Kort 207

     Spørsmål

     Elimination in a system?

     Svar

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

208. Kort 208

     Spørsmål

     Completing the square?

     Svar

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

209. Kort 209

     Spørsmål

     Effect of a high outlier on the mean?

     Svar

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

210. Kort 210

     Spørsmål

     30°-60°-90° side ratio?

     Svar

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

211. Kort 211

     Spørsmål

     Parallel lines in a system?

     Svar

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

212. Kort 212

     Spørsmål

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

     Svar

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

213. Kort 213

     Spørsmål

     Add the same constant to every data value: effect?

     Svar

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

214. Kort 214

     Spørsmål

     Right-triangle sine?

     Svar

     Sine of $θ$ equals opposite over hypotenuse.

215. Kort 215

     Spørsmål

     Same line written two ways in a system?

     Svar

     Infinitely many solutions. Simplifying either equation produces the other.

216. Kort 216

     Spørsmål

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

     Svar

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

217. Kort 217

     Spørsmål

     Multiply every data value by positive $k$: effect?

     Svar

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

218. Kort 218

     Spørsmål

     Right-triangle cosine?

     Svar

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Kort 219

     Spørsmål

     Multiply or divide an inequality by a negative number?

     Svar

     Reverse the inequality sign.

220. Kort 220

     Spørsmål

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

     Svar

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

221. Kort 221

     Spørsmål

     Joint probability from a two-way table?

     Svar

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

222. Kort 222

     Spørsmål

     Right-triangle tangent?

     Svar

     Tangent of $θ$ equals opposite over adjacent.

223. Kort 223

     Spørsmål

     Compound inequality with “and”?

     Svar

     Use the intersection: values that satisfy both inequalities.

224. Kort 224

     Spørsmål

     Even degree with positive leading coefficient: end behavior?

     Svar

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

225. Kort 225

     Spørsmål

     Conditional probability $P(A|B)$?

     Svar

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

226. Kort 226

     Spørsmål

     Complementary acute angles: sine–cosine relationship?

     Svar

     The sine of $θ$ equals the cosine of $90°-θ$.

227. Kort 227

     Spørsmål

     Compound inequality with “or”?

     Svar

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

228. Kort 228

     Spørsmål

     Odd degree with positive leading coefficient: end behavior?

     Svar

     The left end falls and the right end rises.

229. Kort 229

     Spørsmål

     Independent events $A$ and $B$?

     Svar

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

230. Kort 230

     Spørsmål

     Distance between $(x_1,y_1)$ and $(x_2,y_2)$?

     Svar

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Kort 231

     Spørsmål

     Solve $|x-a|=b$ for $b≥0$.

     Svar

     $x-a=b$ or $x-a=-b$. Absolute value represents distance from $a$.

232. Kort 232

     Spørsmål

     Exponential growth model?

     Svar

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

233. Kort 233

     Spørsmål

     Mutually exclusive events?

     Svar

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

234. Kort 234

     Spørsmål

     Midpoint of two points?

     Svar

     $((x_1+x_2)/2,(y_1+y_2)/2)$.

235. Kort 235

     Spørsmål

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

     Svar

     $a-b<x<a+b$. The solution lies within distance $b$ of $a$.

236. Kort 236

     Spørsmål

     Exponential decay model?

     Svar

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

237. Kort 237

     Spørsmål

     Complement rule?

     Svar

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

238. Kort 238

     Spørsmål

     Circle with center $(h,k)$ and radius $r$?

     Svar

     $(x-h)^2+(y-k)^2=r^2$.

239. Kort 239

     Spørsmål

     Evaluate $f(a)$?

     Svar

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

240. Kort 240

     Spørsmål

     Growth factor 1.08: percent growth rate?

     Svar

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

241. Kort 241

     Spørsmål

     Representative random sample permits what conclusion?

     Svar

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

242. Kort 242

     Spørsmål

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

     Svar

     $r=√R$, provided $R>0$.

243. Kort 243

     Spørsmål

     Linear table: constant slope check?

     Svar

     Equal changes in $x$ must produce equal changes in $y$; compare $Δy/Δx$ across intervals.

244. Kort 244

     Spørsmål

     Decay factor 0.73: percent decrease?

     Svar

     27 percent. Compute $1-0.73=0.27$.

245. Kort 245

     Spørsmål

     Random assignment permits what causal claim?

     Svar

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

246. Kort 246

     Spørsmål

     Radius and tangent at the contact point?

     Svar

     They are perpendicular.

247. Kort 247

     Spørsmål

     Positive slope means what for a linear function?

     Svar

     The output increases as the input increases.

248. Kort 248

     Spørsmål

     Solve $3^{2x}=3^{10}$.

     Svar

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

249. Kort 249

     Spørsmål

     Observational study supports causation?

     Svar

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

250. Kort 250

     Spørsmål

     Rectangular-prism volume?

     Svar

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

251. Kort 251

     Spørsmål

     Arithmetic sequence common difference?

     Svar

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

252. Kort 252

     Spørsmål

     Compound interest formula?

     Svar

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

253. Kort 253

     Spørsmål

     Larger random sample: effect on margin of error?

     Svar

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

254. Kort 254

     Spørsmål

     Cylinder volume?

     Svar

     $V=πr^2h$.

255. Kort 255

     Spørsmål

     Arithmetic sequence nth term?

     Svar

     $a_n=a_1+(n-1)d$.

256. Kort 256

     Spørsmål

     Rational expression: first domain check?

     Svar

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

257. Kort 257

     Spørsmål

     Slope of a line of best fit?

     Svar

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

258. Kort 258

     Spørsmål

     Cone volume?

     Svar

     $V=(1/3)πr^2h$.

259. Kort 259

     Spørsmål

     Solve a literal equation for one variable?

     Svar

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

260. Kort 260

     Spørsmål

     Why check rational-equation solutions?

     Svar

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

261. Kort 261

     Spørsmål

     Residual?

     Svar

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

262. Kort 262

     Spørsmål

     Sphere volume?

     Svar

     $V=(4/3)πr^3$.

263. Kort 263

     Spørsmål

     Boundary for a two-variable linear inequality?

     Svar

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

264. Kort 264

     Spørsmål

     Why check a solution after squaring both sides?

     Svar

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

265. Kort 265

     Spørsmål

     Positive correlation?

     Svar

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

266. Kort 266

     Spørsmål

     Rectangular-prism surface area?

     Svar

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

267. Kort 267

     Spørsmål

     Check a proposed system solution?

     Svar

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

268. Kort 268

     Spørsmål

     Simplify $√72$.

     Svar

     $6√2$. Factor $72=36×2$ and take $√36$ outside the radical.

269. Kort 269

     Spørsmål

     Extrapolation risk?

     Svar

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

270. Kort 270

     Spørsmål

     Area scale factor when lengths double?

     Svar

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

271. Kort 271

     Spørsmål

     Horizontal line slope?

     Svar

     0. Its y-value does not change as x changes.

272. Kort 272

     Spørsmål

     Inverse function setup?

     Svar

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

273. Kort 273

     Spørsmål

     Percentage points versus percent change?

     Svar

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

274. Kort 274

     Spørsmål

     y-intercept in a context?

     Svar

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

275. Kort 275

     Spørsmål

     Quadratic maximum or minimum from vertex form?

     Svar

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

276. Kort 276

     Spørsmål

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

     Svar

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

277. Kort 277

     Spørsmål

     Graph of $f(x-h)+k$?

     Svar

     Shift the graph of $f$ right $h$ units and up $k$ units.

278. Kort 278

     Spørsmål

     Population versus sample?

     Svar

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

279. Kort 279

     Spørsmål

     Linear model from initial value $b$ and rate $m$?

     Svar

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

280. Kort 280

     Spørsmål

     Function composition $(f∘g)(x)$?

     Svar

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

281. Kort 281

     Spørsmål

     Density?

     Svar

     Mass divided by volume. Keep the units consistent.

282. Kort 282

     Spørsmål

     Vertical line slope?

     Svar

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

283. Kort 283

     Spørsmål

     Nonlinear system with one equation solved for $y$?

     Svar

     Substitute that expression for $y$ into the other equation, solve for $x$, then find each matching $y$.

284. Kort 284

     Spørsmål

     Weighted percentage across unequal groups?

     Svar

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

285. Kort 285

     Spørsmål

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

     Svar

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

286. Kort 286

     Spørsmål

     Cancel a common factor in a rational expression?

     Svar

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

287. Kort 287

     Spørsmål

     Solve a linear equation containing fractions?

     Svar

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

288. Kort 288

     Spørsmål

     Rewrite $a^{2x}$ using base $a^x$.

     Svar

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

289. Kort 289

     Spørsmål

     Rate units check?

     Svar

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

290. Kort 290

     Spørsmål

     Strict versus inclusive inequality endpoint?

     Svar

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

291. Kort 291

     Spørsmål

     Even-multiplicity zero on a graph?

     Svar

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

292. Kort 292

     Spørsmål

     System word problem: first setup step?

     Svar

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

293. Kort 293

     Spørsmål

     When does a quadratic have exactly one real solution?

     Svar

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

294. Kort 294

     Spørsmål

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

     Svar

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

295. Kort 295

     Spørsmål

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

     Svar

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

296. Kort 296

     Spørsmål

     Graph of $-f(x)$?

     Svar

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

297. Kort 297

     Spørsmål

     Three consecutive integers starting with $n$?

     Svar

     $n$, $n+1$, and $n+2$.

298. Kort 298

     Spørsmål

     Line–parabola intersections from a substituted quadratic?

     Svar

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

299. Kort 299

     Spørsmål

     Linear equation with no solution: coefficient pattern?

     Svar

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

300. Kort 300

     Spørsmål

     Zeros of a function on its graph?

     Svar

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

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