Digital SAT Flashcards: Math, Grammar & Words in Context

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1. Κάρτα 1

   Ερώτηση

   Central idea of a passage?

   Απάντηση

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

2. Κάρτα 2

   Ερώτηση

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

   Απάντηση

   Reduced. The trees made the heat less severe.

3. Κάρτα 3

   Ερώτηση

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

   Απάντηση

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

4. Κάρτα 4

   Ερώτηση

   Three standard joins for two independent clauses?

   Απάντηση

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

5. Κάρτα 5

   Ερώτηση

   Best supporting detail?

   Απάντηση

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

6. Κάρτα 6

   Ερώτηση

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

   Απάντηση

   Confirmed with supporting evidence.

7. Κάρτα 7

   Ερώτηση

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

   Απάντηση

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

8. Κάρτα 8

   Ερώτηση

   Introductory dependent clause before a main clause?

   Απάντηση

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

9. Κάρτα 9

   Ερώτηση

   Valid inference?

   Απάντηση

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

10. Κάρτα 10

    Ερώτηση

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

    Απάντηση

    Provisional or not yet certain.

11. Κάρτα 11

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

    Απάντηση

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

12. Κάρτα 12

    Ερώτηση

    Singular subject with an intervening prepositional phrase?

    Απάντηση

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

13. Κάρτα 13

    Ερώτηση

    Strongest textual evidence?

    Απάντηση

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

14. Κάρτα 14

    Ερώτηση

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

    Απάντηση

    So small that it is not important.

15. Κάρτα 15

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

    Απάντηση

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

16. Κάρτα 16

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    Opening modifier placement?

    Απάντηση

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

17. Κάρτα 17

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    Quantitative evidence for a claim?

    Απάντηση

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

18. Κάρτα 18

    Ερώτηση

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

    Απάντηση

    Traditional or commonly accepted.

19. Κάρτα 19

    Ερώτηση

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

    Απάντηση

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

20. Κάρτα 20

    Ερώτηση

    Singular possessive noun?

    Απάντηση

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

21. Κάρτα 21

    Ερώτηση

    Trend in a table or graph?

    Απάντηση

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

22. Κάρτα 22

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

    Απάντηση

    New or original in this context.

23. Κάρτα 23

    Ερώτηση

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

    Απάντηση

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

24. Κάρτα 24

    Ερώτηση

    Parallel items in a series?

    Απάντηση

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

25. Κάρτα 25

    Ερώτηση

    Claim stronger than the evidence?

    Απάντηση

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

26. Κάρτα 26

    Ερώτηση

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

    Απάντηση

    Reasonable or believable.

27. Κάρτα 27

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

    Απάντηση

    Addition. The second statement adds a related supporting point.

28. Κάρτα 28

    Ερώτηση

    Colon before an explanation or list?

    Απάντηση

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

29. Κάρτα 29

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    Claim versus evidence?

    Απάντηση

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

30. Κάρτα 30

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

    Απάντηση

    Open to more than one interpretation.

31. Κάρτα 31

    Ερώτηση

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

    Απάντηση

    Replacement. The second statement substitutes one action for another.

32. Κάρτα 32

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    Count nouns versus mass nouns?

    Απάντηση

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

33. Κάρτα 33

    Ερώτηση

    Effect of a counterexample?

    Απάντηση

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

34. Κάρτα 34

    Ερώτηση

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

    Απάντηση

    Irregular and occasional.

35. Κάρτα 35

    Ερώτηση

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

    Απάντηση

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

36. Κάρτα 36

    Ερώτηση

    Essential clause punctuation?

    Απάντηση

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

37. Κάρτα 37

    Ερώτηση

    Correlation alone proves causation?

    Απάντηση

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

38. Κάρτα 38

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

    Απάντηση

    Coming later in time.

39. Κάρτα 39

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

    Απάντηση

    Restatement for clarity. The second statement rephrases the first.

40. Κάρτα 40

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    Verb tense across a paragraph?

    Απάντηση

    Keep the time frame consistent unless the timing actually changes.

41. Κάρτα 41

    Ερώτηση

    Missing information in a data claim?

    Απάντηση

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

42. Κάρτα 42

    Ερώτηση

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

    Απάντηση

    Keep or continue to hold.

43. Κάρτα 43

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

    Απάντηση

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

44. Κάρτα 44

    Ερώτηση

    Coordinate adjectives?

    Απάντηση

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

45. Κάρτα 45

    Ερώτηση

    Two sources on the same event?

    Απάντηση

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

46. Κάρτα 46

    Ερώτηση

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

    Απάντηση

    Draw out or bring forth.

47. Κάρτα 47

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

    Απάντηση

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

48. Κάρτα 48

    Ερώτηση

    Sentence fragment?

    Απάντηση

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

49. Κάρτα 49

    Ερώτηση

    Inference from a narrow sample?

    Απάντηση

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

50. Κάρτα 50

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

    Απάντηση

    A limit or restriction.

51. Κάρτα 51

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

    Απάντηση

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

52. Κάρτα 52

    Ερώτηση

    Conjunctive adverb between independent clauses?

    Απάντηση

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

53. Κάρτα 53

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    Most accurate summary?

    Απάντηση

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

54. Κάρτα 54

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

    Απάντηση

    Complete and wide-ranging.

55. Κάρτα 55

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

    Απάντηση

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

56. Κάρτα 56

    Ερώτηση

    Who versus whom?

    Απάντηση

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

57. Κάρτα 57

    Ερώτηση

    Evidence that best resolves a disagreement?

    Απάντηση

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

58. Κάρτα 58

    Ερώτηση

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

    Απάντηση

    Clearly different or separate.

59. Κάρτα 59

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

    Απάντηση

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

60. Κάρτα 60

    Ερώτηση

    Comma before an introduced direct quotation?

    Απάντηση

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

61. Κάρτα 61

    Ερώτηση

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

    Απάντηση

    Limited or modified, rather than stated without conditions.

62. Κάρτα 62

    Ερώτηση

    Notes for a synthesis goal?

    Απάντηση

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

63. Κάρτα 63

    Ερώτηση

    Comma splice?

    Απάντηση

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

64. Κάρτα 64

    Ερώτηση

    Comma between subject and verb?

    Απάντηση

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

65. Κάρτα 65

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

    Απάντηση

    No longer useful or current because something newer replaced it.

66. Κάρτα 66

    Ερώτηση

    Source attribution in a synthesis?

    Απάντηση

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

67. Κάρτα 67

    Ερώτηση

    Compound subject joined by “and”?

    Απάντηση

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

68. Κάρτα 68

    Ερώτηση

    Dangling opening modifier?

    Απάντηση

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

69. Κάρτα 69

    Ερώτηση

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

    Απάντηση

    Obtained from a source or calculation.

70. Κάρτα 70

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    Chronological synthesis?

    Απάντηση

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

71. Κάρτα 71

    Ερώτηση

    Plural noun ending in s: possessive form?

    Απάντηση

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

72. Κάρτα 72

    Ερώτηση

    Logical comparison?

    Απάντηση

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

73. Κάρτα 73

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

    Απάντηση

    Publicly supports or argues for.

74. Κάρτα 74

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    Compare evidence from two studies?

    Απάντηση

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

75. Κάρτα 75

    Ερώτηση

    Colon after an incomplete lead-in?

    Απάντηση

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

76. Κάρτα 76

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    Number versus amount?

    Απάντηση

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

77. Κάρτα 77

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

    Απάντηση

    Present or found almost everywhere.

78. Κάρτα 78

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    Synthesis that emphasizes a difference?

    Απάντηση

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

79. Κάρτα 79

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    Nonessential clause or phrase?

    Απάντηση

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

80. Κάρτα 80

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    Earlier of two past actions?

    Απάντηση

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

81. Κάρτα 81

    Ερώτηση

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

    Απάντηση

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

82. Κάρτα 82

    Ερώτηση

    Rhetorical goal: define a term?

    Απάντηση

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

83. Κάρτα 83

    Ερώτηση

    Cumulative adjectives?

    Απάντηση

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

84. Κάρτα 84

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    Run-on sentence?

    Απάντηση

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

85. Κάρτα 85

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

    Απάντηση

    It illustrates the claim with an example.

86. Κάρτα 86

    Ερώτηση

    Introduce a quotation in a synthesis?

    Απάντηση

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

87. Κάρτα 87

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    Relative pronoun for people?

    Απάντηση

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

88. Κάρτα 88

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    Integrated quotation punctuation?

    Απάντηση

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

89. Κάρτα 89

    Ερώτηση

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

    Απάντηση

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

90. Κάρτα 90

    Ερώτηση

    Avoid redundancy in synthesis?

    Απάντηση

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

91. Κάρτα 91

    Ερώτηση

    Semicolon between two independent clauses?

    Απάντηση

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

92. Κάρτα 92

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    Comma in a compound predicate?

    Απάντηση

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

93. Κάρτα 93

    Ερώτηση

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

    Απάντηση

    It defines or clarifies the term.

94. Κάρτα 94

    Ερώτηση

    Combine two related sentences?

    Απάντηση

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

95. Κάρτα 95

    Ερώτηση

    Either/or subject agreement?

    Απάντηση

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

96. Κάρτα 96

    Ερώτηση

    Active versus passive voice?

    Απάντηση

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

97. Κάρτα 97

    Ερώτηση

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

    Απάντηση

    It presents an effect or consequence.

98. Κάρτα 98

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    Formal academic register?

    Απάντηση

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

99. Κάρτα 99

    Ερώτηση

    Its or it's?

    Απάντηση

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

100. Κάρτα 100

     Ερώτηση

     Adjective versus adverb?

     Απάντηση

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

101. Κάρτα 101

     Ερώτηση

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

     Απάντηση

     To inform or explain, not necessarily to persuade.

102. Κάρτα 102

     Ερώτηση

     Concise synthesis?

     Απάντηση

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

103. Κάρτα 103

     Ερώτηση

     Single dash for emphasis?

     Απάντηση

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

104. Κάρτα 104

     Ερώτηση

     Comma with direct address?

     Απάντηση

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

105. Κάρτα 105

     Ερώτηση

     Why acknowledge a limitation?

     Απάντηση

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

106. Κάρτα 106

     Ερώτηση

     Quantitative comparison in a synthesis?

     Απάντηση

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

107. Κάρτα 107

     Ερώτηση

     Each of the samples: verb number?

     Απάντηση

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

108. Κάρτα 108

     Ερώτηση

     Between versus among?

     Απάντηση

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

109. Κάρτα 109

     Ερώτηση

     Rhetorical question in an argument?

     Απάντηση

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

110. Κάρτα 110

     Ερώτηση

     Claim before or after support?

     Απάντηση

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

111. Κάρτα 111

     Ερώτηση

     Restrictive “that” versus nonrestrictive “which”?

     Απάντηση

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

112. Κάρτα 112

     Ερώτηση

     Present perfect use?

     Απάντηση

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

113. Κάρτα 113

     Ερώτηση

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

     Απάντηση

     They agree in conclusion but support it through different evidence.

114. Κάρτα 114

     Ερώτηση

     Group related ideas in a synthesis?

     Απάντηση

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

115. Κάρτα 115

     Ερώτηση

     Compound modifier before a noun?

     Απάντηση

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

116. Κάρτα 116

     Ερώτηση

     Affect or effect?

     Απάντηση

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

117. Κάρτα 117

     Ερώτηση

     Two texts offer incompatible explanations. Relationship?

     Απάντηση

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

118. Κάρτα 118

     Ερώτηση

     Replace a vague pronoun in synthesis?

     Απάντηση

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

119. Κάρτα 119

     Ερώτηση

     Comma-separated list?

     Απάντηση

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

120. Κάρτα 120

     Ερώτηση

     Main clause before a dependent clause?

     Απάντηση

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

121. Κάρτα 121

     Ερώτηση

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

     Απάντηση

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Κάρτα 122

     Ερώτηση

     Independent clauses joined with a coordinating conjunction?

     Απάντηση

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

123. Κάρτα 123

     Ερώτηση

     Introductory transition?

     Απάντηση

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

124. Κάρτα 124

     Ερώτηση

     Pronoun–antecedent agreement?

     Απάντηση

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

125. Κάρτα 125

     Ερώτηση

     Paired em dashes?

     Απάντηση

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

126. Κάρτα 126

     Ερώτηση

     How does new evidence relate to an earlier claim?

     Απάντηση

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

127. Κάρτα 127

     Ερώτηση

     Their, there, or they're?

     Απάντηση

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

128. Κάρτα 128

     Ερώτηση

     Good or well?

     Απάντηση

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

129. Κάρτα 129

     Ερώτηση

     Appositive naming the same noun?

     Απάντηση

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

130. Κάρτα 130

     Ερώτηση

     Why use an analogy?

     Απάντηση

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

131. Κάρτα 131

     Ερώτηση

     Than or then?

     Απάντηση

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

132. Κάρτα 132

     Ερώτηση

     Hypothetical contrary-to-fact “if” clause?

     Απάντηση

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

133. Κάρτα 133

     Ερώτηση

     Plural noun with no possession?

     Απάντηση

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

134. Κάρτα 134

     Ερώτηση

     Neutral, evidence-led wording indicates what tone?

     Απάντηση

     Objective. It emphasizes information rather than strong personal judgment.

135. Κάρτα 135

     Ερώτηση

     Complex list with internal commas?

     Απάντηση

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

136. Κάρτα 136

     Ερώτηση

     Ambiguous pronoun?

     Απάντηση

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

137. Κάρτα 137

     Ερώτηση

     Parentheses around nonessential information?

     Απάντηση

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

138. Κάρτα 138

     Ερώτηση

     Repeated doubt about the evidence indicates what tone?

     Απάντηση

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

139. Κάρτα 139

     Ερώτηση

     Superlative comparison?

     Απάντηση

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

140. Κάρτα 140

     Ερώτηση

     Pronoun after a preposition?

     Απάντηση

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

141. Κάρτα 141

     Ερώτηση

     Apostrophe in a contraction?

     Απάντηση

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

142. Κάρτα 142

     Ερώτηση

     Coordinate-adjective test?

     Απάντηση

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

143. Κάρτα 143

     Ερώτηση

     Double comparative?

     Απάντηση

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

144. Κάρτα 144

     Ερώτηση

     Lie or lay?

     Απάντηση

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

145. Κάρτα 145

     Ερώτηση

     Who's or whose?

     Απάντηση

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

146. Κάρτα 146

     Ερώτηση

     Standard comparison with “different”?

     Απάντηση

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

147. Κάρτα 147

     Ερώτηση

     Paired construction with two endpoints?

     Απάντηση

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

148. Κάρτα 148

     Ερώτηση

     Verb mood in a coordinated idea?

     Απάντηση

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

149. Κάρτα 149

     Ερώτηση

     Possessive pronoun apostrophe?

     Απάντηση

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

150. Κάρτα 150

     Ερώτηση

     Comma between a preposition and its object?

     Απάντηση

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

     

     300 κάρτες

     Digital SAT Flashcards: Math, Grammar & Words in Context

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151. Κάρτα 151

     Ερώτηση

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

     Απάντηση

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

152. Κάρτα 152

     Ερώτηση

     Product of powers with the same base?

     Απάντηση

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

153. Κάρτα 153

     Ερώτηση

     Unit rate?

     Απάντηση

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

154. Κάρτα 154

     Ερώτηση

     Rectangle area?

     Απάντηση

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

155. Κάρτα 155

     Ερώτηση

     Slope from two points?

     Απάντηση

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

156. Κάρτα 156

     Ερώτηση

     Quotient of powers with the same base?

     Απάντηση

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Κάρτα 157

     Ερώτηση

     Conversion factor setup?

     Απάντηση

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

158. Κάρτα 158

     Ερώτηση

     Triangle area?

     Απάντηση

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

159. Κάρτα 159

     Ερώτηση

     Slope-intercept form?

     Απάντηση

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

160. Κάρτα 160

     Ερώτηση

     Power raised to a power?

     Απάντηση

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

161. Κάρτα 161

     Ερώτηση

     Dimensional analysis check?

     Απάντηση

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

162. Κάρτα 162

     Ερώτηση

     Trapezoid area?

     Απάντηση

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

163. Κάρτα 163

     Ερώτηση

     Point-slope form?

     Απάντηση

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

164. Κάρτα 164

     Ερώτηση

     Negative exponent?

     Απάντηση

     $a^{-n}=1/a^n$ for $a≠0$.

165. Κάρτα 165

     Ερώτηση

     Constant of proportionality in $y=kx$?

     Απάντηση

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

166. Κάρτα 166

     Ερώτηση

     Circle area?

     Απάντηση

     $A=πr^2$.

167. Κάρτα 167

     Ερώτηση

     Intercepts from $Ax+By=C$?

     Απάντηση

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

168. Κάρτα 168

     Ερώτηση

     Fractional exponent?

     Απάντηση

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

169. Κάρτα 169

     Ερώτηση

     Scale drawing length?

     Απάντηση

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

170. Κάρτα 170

     Ερώτηση

     Circle circumference?

     Απάντηση

     $C=2πr=πd$.

171. Κάρτα 171

     Ερώτηση

     Parallel nonvertical lines: slope relationship?

     Απάντηση

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

172. Κάρτα 172

     Ερώτηση

     Difference of squares?

     Απάντηση

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

173. Κάρτα 173

     Ερώτηση

     Percent change?

     Απάντηση

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

174. Κάρτα 174

     Ερώτηση

     Arc length from central angle $θ$ in degrees?

     Απάντηση

     $L=(θ/360)(2πr)$.

175. Κάρτα 175

     Ερώτηση

     Perpendicular nonvertical lines: slope relationship?

     Απάντηση

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

176. Κάρτα 176

     Ερώτηση

     Perfect-square trinomial pattern?

     Απάντηση

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

177. Κάρτα 177

     Ερώτηση

     Increase by $r$ percent: multiplier?

     Απάντηση

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

178. Κάρτα 178

     Ερώτηση

     Sector area from central angle $θ$ in degrees?

     Απάντηση

     $A=(θ/360)(πr^2)$.

179. Κάρτα 179

     Ερώτηση

     x-intercept of a graph?

     Απάντηση

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

180. Κάρτα 180

     Ερώτηση

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

     Απάντηση

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

181. Κάρτα 181

     Ερώτηση

     Original value after a 20 percent increase to 84?

     Απάντηση

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

182. Κάρτα 182

     Ερώτηση

     Triangle interior-angle sum?

     Απάντηση

     $180°$.

183. Κάρτα 183

     Ερώτηση

     y-intercept of a graph?

     Απάντηση

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

184. Κάρτα 184

     Ερώτηση

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

     Απάντηση

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

185. Κάρτα 185

     Ερώτηση

     Weighted average?

     Απάντηση

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

186. Κάρτα 186

     Ερώτηση

     Exterior angle of a triangle?

     Απάντηση

     It equals the sum of the two remote interior angles.

187. Κάρτα 187

     Ερώτηση

     Line through two points?

     Απάντηση

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

188. Κάρτα 188

     Ερώτηση

     Quadratic formula?

     Απάντηση

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

189. Κάρτα 189

     Ερώτηση

     Arithmetic mean?

     Απάντηση

     Add all values and divide by the number of values.

190. Κάρτα 190

     Ερώτηση

     Parallel lines cut by a transversal: alternate interior angles?

     Απάντηση

     They are congruent.

191. Κάρτα 191

     Ερώτηση

     Slope's units in context?

     Απάντηση

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

192. Κάρτα 192

     Ερώτηση

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

     Απάντηση

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

193. Κάρτα 193

     Ερώτηση

     Median?

     Απάντηση

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

194. Κάρτα 194

     Ερώτηση

     Similar triangles: corresponding sides?

     Απάντηση

     They are proportional. Match sides opposite equal angles.

195. Κάρτα 195

     Ερώτηση

     Direct variation model?

     Απάντηση

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

196. Κάρτα 196

     Ερώτηση

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

     Απάντηση

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

197. Κάρτα 197

     Ερώτηση

     Range of a data set?

     Απάντηση

     Maximum minus minimum.

198. Κάρτα 198

     Ερώτηση

     Scale factor $k$: area factor?

     Απάντηση

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

199. Κάρτα 199

     Ερώτηση

     Solution of a two-line system?

     Απάντηση

     The intersection point, whose coordinates satisfy both equations.

200. Κάρτα 200

     Ερώτηση

     Vertex form of a quadratic?

     Απάντηση

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

201. Κάρτα 201

     Ερώτηση

     Interquartile range?

     Απάντηση

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

202. Κάρτα 202

     Ερώτηση

     Pythagorean theorem?

     Απάντηση

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

203. Κάρτα 203

     Ερώτηση

     Substitution in a system?

     Απάντηση

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

204. Κάρτα 204

     Ερώτηση

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

     Απάντηση

     $x=h$.

205. Κάρτα 205

     Ερώτηση

     Larger standard deviation means what?

     Απάντηση

     The data are more spread out around the mean.

206. Κάρτα 206

     Ερώτηση

     45°-45°-90° side ratio?

     Απάντηση

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

207. Κάρτα 207

     Ερώτηση

     Elimination in a system?

     Απάντηση

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

208. Κάρτα 208

     Ερώτηση

     Completing the square?

     Απάντηση

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

209. Κάρτα 209

     Ερώτηση

     Effect of a high outlier on the mean?

     Απάντηση

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

210. Κάρτα 210

     Ερώτηση

     30°-60°-90° side ratio?

     Απάντηση

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

211. Κάρτα 211

     Ερώτηση

     Parallel lines in a system?

     Απάντηση

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

212. Κάρτα 212

     Ερώτηση

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

     Απάντηση

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

213. Κάρτα 213

     Ερώτηση

     Add the same constant to every data value: effect?

     Απάντηση

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

214. Κάρτα 214

     Ερώτηση

     Right-triangle sine?

     Απάντηση

     Sine of $θ$ equals opposite over hypotenuse.

215. Κάρτα 215

     Ερώτηση

     Same line written two ways in a system?

     Απάντηση

     Infinitely many solutions. Simplifying either equation produces the other.

216. Κάρτα 216

     Ερώτηση

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

     Απάντηση

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

217. Κάρτα 217

     Ερώτηση

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

     Απάντηση

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

218. Κάρτα 218

     Ερώτηση

     Right-triangle cosine?

     Απάντηση

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Κάρτα 219

     Ερώτηση

     Multiply or divide an inequality by a negative number?

     Απάντηση

     Reverse the inequality sign.

220. Κάρτα 220

     Ερώτηση

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

     Απάντηση

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

221. Κάρτα 221

     Ερώτηση

     Joint probability from a two-way table?

     Απάντηση

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

222. Κάρτα 222

     Ερώτηση

     Right-triangle tangent?

     Απάντηση

     Tangent of $θ$ equals opposite over adjacent.

223. Κάρτα 223

     Ερώτηση

     Compound inequality with “and”?

     Απάντηση

     Use the intersection: values that satisfy both inequalities.

224. Κάρτα 224

     Ερώτηση

     Even degree with positive leading coefficient: end behavior?

     Απάντηση

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

225. Κάρτα 225

     Ερώτηση

     Conditional probability $P(A|B)$?

     Απάντηση

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

226. Κάρτα 226

     Ερώτηση

     Complementary acute angles: sine–cosine relationship?

     Απάντηση

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

227. Κάρτα 227

     Ερώτηση

     Compound inequality with “or”?

     Απάντηση

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

228. Κάρτα 228

     Ερώτηση

     Odd degree with positive leading coefficient: end behavior?

     Απάντηση

     The left end falls and the right end rises.

229. Κάρτα 229

     Ερώτηση

     Independent events $A$ and $B$?

     Απάντηση

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

230. Κάρτα 230

     Ερώτηση

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

     Απάντηση

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Κάρτα 231

     Ερώτηση

     Solve $|x-a|=b$ for $b≥0$.

     Απάντηση

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

232. Κάρτα 232

     Ερώτηση

     Exponential growth model?

     Απάντηση

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

233. Κάρτα 233

     Ερώτηση

     Mutually exclusive events?

     Απάντηση

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

234. Κάρτα 234

     Ερώτηση

     Midpoint of two points?

     Απάντηση

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

235. Κάρτα 235

     Ερώτηση

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

     Απάντηση

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

236. Κάρτα 236

     Ερώτηση

     Exponential decay model?

     Απάντηση

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

237. Κάρτα 237

     Ερώτηση

     Complement rule?

     Απάντηση

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

238. Κάρτα 238

     Ερώτηση

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

     Απάντηση

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

239. Κάρτα 239

     Ερώτηση

     Evaluate $f(a)$?

     Απάντηση

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

240. Κάρτα 240

     Ερώτηση

     Growth factor 1.08: percent growth rate?

     Απάντηση

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

241. Κάρτα 241

     Ερώτηση

     Representative random sample permits what conclusion?

     Απάντηση

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

242. Κάρτα 242

     Ερώτηση

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

     Απάντηση

     $r=√R$, provided $R>0$.

243. Κάρτα 243

     Ερώτηση

     Linear table: constant slope check?

     Απάντηση

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

244. Κάρτα 244

     Ερώτηση

     Decay factor 0.73: percent decrease?

     Απάντηση

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

245. Κάρτα 245

     Ερώτηση

     Random assignment permits what causal claim?

     Απάντηση

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

246. Κάρτα 246

     Ερώτηση

     Radius and tangent at the contact point?

     Απάντηση

     They are perpendicular.

247. Κάρτα 247

     Ερώτηση

     Positive slope means what for a linear function?

     Απάντηση

     The output increases as the input increases.

248. Κάρτα 248

     Ερώτηση

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

     Απάντηση

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

249. Κάρτα 249

     Ερώτηση

     Observational study supports causation?

     Απάντηση

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

250. Κάρτα 250

     Ερώτηση

     Rectangular-prism volume?

     Απάντηση

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

251. Κάρτα 251

     Ερώτηση

     Arithmetic sequence common difference?

     Απάντηση

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

252. Κάρτα 252

     Ερώτηση

     Compound interest formula?

     Απάντηση

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

253. Κάρτα 253

     Ερώτηση

     Larger random sample: effect on margin of error?

     Απάντηση

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

254. Κάρτα 254

     Ερώτηση

     Cylinder volume?

     Απάντηση

     $V=πr^2h$.

255. Κάρτα 255

     Ερώτηση

     Arithmetic sequence nth term?

     Απάντηση

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

256. Κάρτα 256

     Ερώτηση

     Rational expression: first domain check?

     Απάντηση

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

257. Κάρτα 257

     Ερώτηση

     Slope of a line of best fit?

     Απάντηση

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

258. Κάρτα 258

     Ερώτηση

     Cone volume?

     Απάντηση

     $V=(1/3)πr^2h$.

259. Κάρτα 259

     Ερώτηση

     Solve a literal equation for one variable?

     Απάντηση

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

260. Κάρτα 260

     Ερώτηση

     Why check rational-equation solutions?

     Απάντηση

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

261. Κάρτα 261

     Ερώτηση

     Residual?

     Απάντηση

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

262. Κάρτα 262

     Ερώτηση

     Sphere volume?

     Απάντηση

     $V=(4/3)πr^3$.

263. Κάρτα 263

     Ερώτηση

     Boundary for a two-variable linear inequality?

     Απάντηση

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

264. Κάρτα 264

     Ερώτηση

     Why check a solution after squaring both sides?

     Απάντηση

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

265. Κάρτα 265

     Ερώτηση

     Positive correlation?

     Απάντηση

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

266. Κάρτα 266

     Ερώτηση

     Rectangular-prism surface area?

     Απάντηση

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

267. Κάρτα 267

     Ερώτηση

     Check a proposed system solution?

     Απάντηση

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

268. Κάρτα 268

     Ερώτηση

     Simplify $√72$.

     Απάντηση

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

269. Κάρτα 269

     Ερώτηση

     Extrapolation risk?

     Απάντηση

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

270. Κάρτα 270

     Ερώτηση

     Area scale factor when lengths double?

     Απάντηση

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

271. Κάρτα 271

     Ερώτηση

     Horizontal line slope?

     Απάντηση

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

272. Κάρτα 272

     Ερώτηση

     Inverse function setup?

     Απάντηση

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

273. Κάρτα 273

     Ερώτηση

     Percentage points versus percent change?

     Απάντηση

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

274. Κάρτα 274

     Ερώτηση

     y-intercept in a context?

     Απάντηση

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

275. Κάρτα 275

     Ερώτηση

     Quadratic maximum or minimum from vertex form?

     Απάντηση

     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. Κάρτα 276

     Ερώτηση

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

     Απάντηση

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

277. Κάρτα 277

     Ερώτηση

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

     Απάντηση

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

278. Κάρτα 278

     Ερώτηση

     Population versus sample?

     Απάντηση

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

279. Κάρτα 279

     Ερώτηση

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

     Απάντηση

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

280. Κάρτα 280

     Ερώτηση

     Function composition $(f∘g)(x)$?

     Απάντηση

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

281. Κάρτα 281

     Ερώτηση

     Density?

     Απάντηση

     Mass divided by volume. Keep the units consistent.

282. Κάρτα 282

     Ερώτηση

     Vertical line slope?

     Απάντηση

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

283. Κάρτα 283

     Ερώτηση

     Nonlinear system with one equation solved for $y$?

     Απάντηση

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

284. Κάρτα 284

     Ερώτηση

     Weighted percentage across unequal groups?

     Απάντηση

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

285. Κάρτα 285

     Ερώτηση

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

     Απάντηση

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

286. Κάρτα 286

     Ερώτηση

     Cancel a common factor in a rational expression?

     Απάντηση

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

287. Κάρτα 287

     Ερώτηση

     Solve a linear equation containing fractions?

     Απάντηση

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

288. Κάρτα 288

     Ερώτηση

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

     Απάντηση

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

289. Κάρτα 289

     Ερώτηση

     Rate units check?

     Απάντηση

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

290. Κάρτα 290

     Ερώτηση

     Strict versus inclusive inequality endpoint?

     Απάντηση

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

291. Κάρτα 291

     Ερώτηση

     Even-multiplicity zero on a graph?

     Απάντηση

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

292. Κάρτα 292

     Ερώτηση

     System word problem: first setup step?

     Απάντηση

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

293. Κάρτα 293

     Ερώτηση

     When does a quadratic have exactly one real solution?

     Απάντηση

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

294. Κάρτα 294

     Ερώτηση

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

     Απάντηση

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

295. Κάρτα 295

     Ερώτηση

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

     Απάντηση

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

296. Κάρτα 296

     Ερώτηση

     Graph of $-f(x)$?

     Απάντηση

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

297. Κάρτα 297

     Ερώτηση

     Three consecutive integers starting with $n$?

     Απάντηση

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

298. Κάρτα 298

     Ερώτηση

     Line–parabola intersections from a substituted quadratic?

     Απάντηση

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

299. Κάρτα 299

     Ερώτηση

     Linear equation with no solution: coefficient pattern?

     Απάντηση

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

300. Κάρτα 300

     Ερώτηση

     Zeros of a function on its graph?

     Απάντηση

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

300 κάρτες

Digital SAT Flashcards: Math, Grammar & Words in Context

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