Digital SAT Flashcards: Math, Grammar & Words in Context

Карточки в этой колоде

1. Карточка 1

   Вопрос

   Central idea of a passage?

   Ответ

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

2. Карточка 2

   Вопрос

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

   Ответ

   Reduced. The trees made the heat less severe.

3. Карточка 3

   Вопрос

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

   Ответ

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

4. Карточка 4

   Вопрос

   Three standard joins for two independent clauses?

   Ответ

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

5. Карточка 5

   Вопрос

   Best supporting detail?

   Ответ

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

6. Карточка 6

   Вопрос

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

   Ответ

   Confirmed with supporting evidence.

7. Карточка 7

   Вопрос

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

   Ответ

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

8. Карточка 8

   Вопрос

   Introductory dependent clause before a main clause?

   Ответ

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

9. Карточка 9

   Вопрос

   Valid inference?

   Ответ

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

10. Карточка 10

    Вопрос

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

    Ответ

    Provisional or not yet certain.

11. Карточка 11

    Вопрос

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

    Ответ

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

12. Карточка 12

    Вопрос

    Singular subject with an intervening prepositional phrase?

    Ответ

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

13. Карточка 13

    Вопрос

    Strongest textual evidence?

    Ответ

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

14. Карточка 14

    Вопрос

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

    Ответ

    So small that it is not important.

15. Карточка 15

    Вопрос

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

    Ответ

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

16. Карточка 16

    Вопрос

    Opening modifier placement?

    Ответ

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

17. Карточка 17

    Вопрос

    Quantitative evidence for a claim?

    Ответ

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

18. Карточка 18

    Вопрос

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

    Ответ

    Traditional or commonly accepted.

19. Карточка 19

    Вопрос

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

    Ответ

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

20. Карточка 20

    Вопрос

    Singular possessive noun?

    Ответ

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

21. Карточка 21

    Вопрос

    Trend in a table or graph?

    Ответ

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

22. Карточка 22

    Вопрос

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

    Ответ

    New or original in this context.

23. Карточка 23

    Вопрос

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

    Ответ

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

24. Карточка 24

    Вопрос

    Parallel items in a series?

    Ответ

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

25. Карточка 25

    Вопрос

    Claim stronger than the evidence?

    Ответ

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

26. Карточка 26

    Вопрос

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

    Ответ

    Reasonable or believable.

27. Карточка 27

    Вопрос

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

    Ответ

    Addition. The second statement adds a related supporting point.

28. Карточка 28

    Вопрос

    Colon before an explanation or list?

    Ответ

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

29. Карточка 29

    Вопрос

    Claim versus evidence?

    Ответ

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

30. Карточка 30

    Вопрос

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

    Ответ

    Open to more than one interpretation.

31. Карточка 31

    Вопрос

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

    Ответ

    Replacement. The second statement substitutes one action for another.

32. Карточка 32

    Вопрос

    Count nouns versus mass nouns?

    Ответ

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

33. Карточка 33

    Вопрос

    Effect of a counterexample?

    Ответ

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

34. Карточка 34

    Вопрос

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

    Ответ

    Irregular and occasional.

35. Карточка 35

    Вопрос

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

    Ответ

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

36. Карточка 36

    Вопрос

    Essential clause punctuation?

    Ответ

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

37. Карточка 37

    Вопрос

    Correlation alone proves causation?

    Ответ

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

38. Карточка 38

    Вопрос

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

    Ответ

    Coming later in time.

39. Карточка 39

    Вопрос

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

    Ответ

    Restatement for clarity. The second statement rephrases the first.

40. Карточка 40

    Вопрос

    Verb tense across a paragraph?

    Ответ

    Keep the time frame consistent unless the timing actually changes.

41. Карточка 41

    Вопрос

    Missing information in a data claim?

    Ответ

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

42. Карточка 42

    Вопрос

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

    Ответ

    Keep or continue to hold.

43. Карточка 43

    Вопрос

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

    Ответ

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

44. Карточка 44

    Вопрос

    Coordinate adjectives?

    Ответ

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

45. Карточка 45

    Вопрос

    Two sources on the same event?

    Ответ

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

46. Карточка 46

    Вопрос

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

    Ответ

    Draw out or bring forth.

47. Карточка 47

    Вопрос

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

    Ответ

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

48. Карточка 48

    Вопрос

    Sentence fragment?

    Ответ

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

49. Карточка 49

    Вопрос

    Inference from a narrow sample?

    Ответ

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

50. Карточка 50

    Вопрос

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

    Ответ

    A limit or restriction.

51. Карточка 51

    Вопрос

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

    Ответ

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

52. Карточка 52

    Вопрос

    Conjunctive adverb between independent clauses?

    Ответ

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

53. Карточка 53

    Вопрос

    Most accurate summary?

    Ответ

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

54. Карточка 54

    Вопрос

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

    Ответ

    Complete and wide-ranging.

55. Карточка 55

    Вопрос

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

    Ответ

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

56. Карточка 56

    Вопрос

    Who versus whom?

    Ответ

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

57. Карточка 57

    Вопрос

    Evidence that best resolves a disagreement?

    Ответ

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

58. Карточка 58

    Вопрос

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

    Ответ

    Clearly different or separate.

59. Карточка 59

    Вопрос

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

    Ответ

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

60. Карточка 60

    Вопрос

    Comma before an introduced direct quotation?

    Ответ

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

61. Карточка 61

    Вопрос

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

    Ответ

    Limited or modified, rather than stated without conditions.

62. Карточка 62

    Вопрос

    Notes for a synthesis goal?

    Ответ

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

63. Карточка 63

    Вопрос

    Comma splice?

    Ответ

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

64. Карточка 64

    Вопрос

    Comma between subject and verb?

    Ответ

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

65. Карточка 65

    Вопрос

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

    Ответ

    No longer useful or current because something newer replaced it.

66. Карточка 66

    Вопрос

    Source attribution in a synthesis?

    Ответ

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

67. Карточка 67

    Вопрос

    Compound subject joined by “and”?

    Ответ

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

68. Карточка 68

    Вопрос

    Dangling opening modifier?

    Ответ

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

69. Карточка 69

    Вопрос

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

    Ответ

    Obtained from a source or calculation.

70. Карточка 70

    Вопрос

    Chronological synthesis?

    Ответ

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

71. Карточка 71

    Вопрос

    Plural noun ending in s: possessive form?

    Ответ

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

72. Карточка 72

    Вопрос

    Logical comparison?

    Ответ

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

73. Карточка 73

    Вопрос

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

    Ответ

    Publicly supports or argues for.

74. Карточка 74

    Вопрос

    Compare evidence from two studies?

    Ответ

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

75. Карточка 75

    Вопрос

    Colon after an incomplete lead-in?

    Ответ

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

76. Карточка 76

    Вопрос

    Number versus amount?

    Ответ

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

77. Карточка 77

    Вопрос

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

    Ответ

    Present or found almost everywhere.

78. Карточка 78

    Вопрос

    Synthesis that emphasizes a difference?

    Ответ

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

79. Карточка 79

    Вопрос

    Nonessential clause or phrase?

    Ответ

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

80. Карточка 80

    Вопрос

    Earlier of two past actions?

    Ответ

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

81. Карточка 81

    Вопрос

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

    Ответ

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

82. Карточка 82

    Вопрос

    Rhetorical goal: define a term?

    Ответ

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

83. Карточка 83

    Вопрос

    Cumulative adjectives?

    Ответ

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

84. Карточка 84

    Вопрос

    Run-on sentence?

    Ответ

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

85. Карточка 85

    Вопрос

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

    Ответ

    It illustrates the claim with an example.

86. Карточка 86

    Вопрос

    Introduce a quotation in a synthesis?

    Ответ

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

87. Карточка 87

    Вопрос

    Relative pronoun for people?

    Ответ

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

88. Карточка 88

    Вопрос

    Integrated quotation punctuation?

    Ответ

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

89. Карточка 89

    Вопрос

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

    Ответ

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

90. Карточка 90

    Вопрос

    Avoid redundancy in synthesis?

    Ответ

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

91. Карточка 91

    Вопрос

    Semicolon between two independent clauses?

    Ответ

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

92. Карточка 92

    Вопрос

    Comma in a compound predicate?

    Ответ

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

93. Карточка 93

    Вопрос

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

    Ответ

    It defines or clarifies the term.

94. Карточка 94

    Вопрос

    Combine two related sentences?

    Ответ

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

95. Карточка 95

    Вопрос

    Either/or subject agreement?

    Ответ

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

96. Карточка 96

    Вопрос

    Active versus passive voice?

    Ответ

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

97. Карточка 97

    Вопрос

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

    Ответ

    It presents an effect or consequence.

98. Карточка 98

    Вопрос

    Formal academic register?

    Ответ

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

99. Карточка 99

    Вопрос

    Its or it's?

    Ответ

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

100. Карточка 100

     Вопрос

     Adjective versus adverb?

     Ответ

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

101. Карточка 101

     Вопрос

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

     Ответ

     To inform or explain, not necessarily to persuade.

102. Карточка 102

     Вопрос

     Concise synthesis?

     Ответ

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

103. Карточка 103

     Вопрос

     Single dash for emphasis?

     Ответ

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

104. Карточка 104

     Вопрос

     Comma with direct address?

     Ответ

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

105. Карточка 105

     Вопрос

     Why acknowledge a limitation?

     Ответ

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

106. Карточка 106

     Вопрос

     Quantitative comparison in a synthesis?

     Ответ

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

107. Карточка 107

     Вопрос

     Each of the samples: verb number?

     Ответ

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

108. Карточка 108

     Вопрос

     Between versus among?

     Ответ

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

109. Карточка 109

     Вопрос

     Rhetorical question in an argument?

     Ответ

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

110. Карточка 110

     Вопрос

     Claim before or after support?

     Ответ

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

111. Карточка 111

     Вопрос

     Restrictive “that” versus nonrestrictive “which”?

     Ответ

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

112. Карточка 112

     Вопрос

     Present perfect use?

     Ответ

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

113. Карточка 113

     Вопрос

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

     Ответ

     They agree in conclusion but support it through different evidence.

114. Карточка 114

     Вопрос

     Group related ideas in a synthesis?

     Ответ

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

115. Карточка 115

     Вопрос

     Compound modifier before a noun?

     Ответ

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

116. Карточка 116

     Вопрос

     Affect or effect?

     Ответ

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

117. Карточка 117

     Вопрос

     Two texts offer incompatible explanations. Relationship?

     Ответ

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

118. Карточка 118

     Вопрос

     Replace a vague pronoun in synthesis?

     Ответ

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

119. Карточка 119

     Вопрос

     Comma-separated list?

     Ответ

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

120. Карточка 120

     Вопрос

     Main clause before a dependent clause?

     Ответ

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

121. Карточка 121

     Вопрос

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

     Ответ

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Карточка 122

     Вопрос

     Independent clauses joined with a coordinating conjunction?

     Ответ

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

123. Карточка 123

     Вопрос

     Introductory transition?

     Ответ

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

124. Карточка 124

     Вопрос

     Pronoun–antecedent agreement?

     Ответ

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

125. Карточка 125

     Вопрос

     Paired em dashes?

     Ответ

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

126. Карточка 126

     Вопрос

     How does new evidence relate to an earlier claim?

     Ответ

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

127. Карточка 127

     Вопрос

     Their, there, or they're?

     Ответ

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

128. Карточка 128

     Вопрос

     Good or well?

     Ответ

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

129. Карточка 129

     Вопрос

     Appositive naming the same noun?

     Ответ

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

130. Карточка 130

     Вопрос

     Why use an analogy?

     Ответ

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

131. Карточка 131

     Вопрос

     Than or then?

     Ответ

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

132. Карточка 132

     Вопрос

     Hypothetical contrary-to-fact “if” clause?

     Ответ

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

133. Карточка 133

     Вопрос

     Plural noun with no possession?

     Ответ

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

134. Карточка 134

     Вопрос

     Neutral, evidence-led wording indicates what tone?

     Ответ

     Objective. It emphasizes information rather than strong personal judgment.

135. Карточка 135

     Вопрос

     Complex list with internal commas?

     Ответ

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

136. Карточка 136

     Вопрос

     Ambiguous pronoun?

     Ответ

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

137. Карточка 137

     Вопрос

     Parentheses around nonessential information?

     Ответ

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

138. Карточка 138

     Вопрос

     Repeated doubt about the evidence indicates what tone?

     Ответ

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

139. Карточка 139

     Вопрос

     Superlative comparison?

     Ответ

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

140. Карточка 140

     Вопрос

     Pronoun after a preposition?

     Ответ

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

141. Карточка 141

     Вопрос

     Apostrophe in a contraction?

     Ответ

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

142. Карточка 142

     Вопрос

     Coordinate-adjective test?

     Ответ

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

143. Карточка 143

     Вопрос

     Double comparative?

     Ответ

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

144. Карточка 144

     Вопрос

     Lie or lay?

     Ответ

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

145. Карточка 145

     Вопрос

     Who's or whose?

     Ответ

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

146. Карточка 146

     Вопрос

     Standard comparison with “different”?

     Ответ

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

147. Карточка 147

     Вопрос

     Paired construction with two endpoints?

     Ответ

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

148. Карточка 148

     Вопрос

     Verb mood in a coordinated idea?

     Ответ

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

149. Карточка 149

     Вопрос

     Possessive pronoun apostrophe?

     Ответ

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

150. Карточка 150

     Вопрос

     Comma between a preposition and its object?

     Ответ

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

     

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     Digital SAT Flashcards: Math, Grammar & Words in Context

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151. Карточка 151

     Вопрос

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

     Ответ

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

152. Карточка 152

     Вопрос

     Product of powers with the same base?

     Ответ

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

153. Карточка 153

     Вопрос

     Unit rate?

     Ответ

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

154. Карточка 154

     Вопрос

     Rectangle area?

     Ответ

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

155. Карточка 155

     Вопрос

     Slope from two points?

     Ответ

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

156. Карточка 156

     Вопрос

     Quotient of powers with the same base?

     Ответ

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Карточка 157

     Вопрос

     Conversion factor setup?

     Ответ

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

158. Карточка 158

     Вопрос

     Triangle area?

     Ответ

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

159. Карточка 159

     Вопрос

     Slope-intercept form?

     Ответ

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

160. Карточка 160

     Вопрос

     Power raised to a power?

     Ответ

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

161. Карточка 161

     Вопрос

     Dimensional analysis check?

     Ответ

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

162. Карточка 162

     Вопрос

     Trapezoid area?

     Ответ

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

163. Карточка 163

     Вопрос

     Point-slope form?

     Ответ

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

164. Карточка 164

     Вопрос

     Negative exponent?

     Ответ

     $a^{-n}=1/a^n$ for $a≠0$.

165. Карточка 165

     Вопрос

     Constant of proportionality in $y=kx$?

     Ответ

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

166. Карточка 166

     Вопрос

     Circle area?

     Ответ

     $A=πr^2$.

167. Карточка 167

     Вопрос

     Intercepts from $Ax+By=C$?

     Ответ

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

168. Карточка 168

     Вопрос

     Fractional exponent?

     Ответ

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

169. Карточка 169

     Вопрос

     Scale drawing length?

     Ответ

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

170. Карточка 170

     Вопрос

     Circle circumference?

     Ответ

     $C=2πr=πd$.

171. Карточка 171

     Вопрос

     Parallel nonvertical lines: slope relationship?

     Ответ

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

172. Карточка 172

     Вопрос

     Difference of squares?

     Ответ

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

173. Карточка 173

     Вопрос

     Percent change?

     Ответ

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

174. Карточка 174

     Вопрос

     Arc length from central angle $θ$ in degrees?

     Ответ

     $L=(θ/360)(2πr)$.

175. Карточка 175

     Вопрос

     Perpendicular nonvertical lines: slope relationship?

     Ответ

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

176. Карточка 176

     Вопрос

     Perfect-square trinomial pattern?

     Ответ

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

177. Карточка 177

     Вопрос

     Increase by $r$ percent: multiplier?

     Ответ

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

178. Карточка 178

     Вопрос

     Sector area from central angle $θ$ in degrees?

     Ответ

     $A=(θ/360)(πr^2)$.

179. Карточка 179

     Вопрос

     x-intercept of a graph?

     Ответ

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

180. Карточка 180

     Вопрос

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

     Ответ

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

181. Карточка 181

     Вопрос

     Original value after a 20 percent increase to 84?

     Ответ

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

182. Карточка 182

     Вопрос

     Triangle interior-angle sum?

     Ответ

     $180°$.

183. Карточка 183

     Вопрос

     y-intercept of a graph?

     Ответ

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

184. Карточка 184

     Вопрос

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

     Ответ

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

185. Карточка 185

     Вопрос

     Weighted average?

     Ответ

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

186. Карточка 186

     Вопрос

     Exterior angle of a triangle?

     Ответ

     It equals the sum of the two remote interior angles.

187. Карточка 187

     Вопрос

     Line through two points?

     Ответ

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

188. Карточка 188

     Вопрос

     Quadratic formula?

     Ответ

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

189. Карточка 189

     Вопрос

     Arithmetic mean?

     Ответ

     Add all values and divide by the number of values.

190. Карточка 190

     Вопрос

     Parallel lines cut by a transversal: alternate interior angles?

     Ответ

     They are congruent.

191. Карточка 191

     Вопрос

     Slope's units in context?

     Ответ

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

192. Карточка 192

     Вопрос

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

     Ответ

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

193. Карточка 193

     Вопрос

     Median?

     Ответ

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

194. Карточка 194

     Вопрос

     Similar triangles: corresponding sides?

     Ответ

     They are proportional. Match sides opposite equal angles.

195. Карточка 195

     Вопрос

     Direct variation model?

     Ответ

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

196. Карточка 196

     Вопрос

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

     Ответ

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

197. Карточка 197

     Вопрос

     Range of a data set?

     Ответ

     Maximum minus minimum.

198. Карточка 198

     Вопрос

     Scale factor $k$: area factor?

     Ответ

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

199. Карточка 199

     Вопрос

     Solution of a two-line system?

     Ответ

     The intersection point, whose coordinates satisfy both equations.

200. Карточка 200

     Вопрос

     Vertex form of a quadratic?

     Ответ

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

201. Карточка 201

     Вопрос

     Interquartile range?

     Ответ

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

202. Карточка 202

     Вопрос

     Pythagorean theorem?

     Ответ

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

203. Карточка 203

     Вопрос

     Substitution in a system?

     Ответ

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

204. Карточка 204

     Вопрос

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

     Ответ

     $x=h$.

205. Карточка 205

     Вопрос

     Larger standard deviation means what?

     Ответ

     The data are more spread out around the mean.

206. Карточка 206

     Вопрос

     45°-45°-90° side ratio?

     Ответ

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

207. Карточка 207

     Вопрос

     Elimination in a system?

     Ответ

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

208. Карточка 208

     Вопрос

     Completing the square?

     Ответ

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

209. Карточка 209

     Вопрос

     Effect of a high outlier on the mean?

     Ответ

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

210. Карточка 210

     Вопрос

     30°-60°-90° side ratio?

     Ответ

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

211. Карточка 211

     Вопрос

     Parallel lines in a system?

     Ответ

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

212. Карточка 212

     Вопрос

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

     Ответ

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

213. Карточка 213

     Вопрос

     Add the same constant to every data value: effect?

     Ответ

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

214. Карточка 214

     Вопрос

     Right-triangle sine?

     Ответ

     Sine of $θ$ equals opposite over hypotenuse.

215. Карточка 215

     Вопрос

     Same line written two ways in a system?

     Ответ

     Infinitely many solutions. Simplifying either equation produces the other.

216. Карточка 216

     Вопрос

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

     Ответ

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

217. Карточка 217

     Вопрос

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

     Ответ

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

218. Карточка 218

     Вопрос

     Right-triangle cosine?

     Ответ

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Карточка 219

     Вопрос

     Multiply or divide an inequality by a negative number?

     Ответ

     Reverse the inequality sign.

220. Карточка 220

     Вопрос

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

     Ответ

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

221. Карточка 221

     Вопрос

     Joint probability from a two-way table?

     Ответ

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

222. Карточка 222

     Вопрос

     Right-triangle tangent?

     Ответ

     Tangent of $θ$ equals opposite over adjacent.

223. Карточка 223

     Вопрос

     Compound inequality with “and”?

     Ответ

     Use the intersection: values that satisfy both inequalities.

224. Карточка 224

     Вопрос

     Even degree with positive leading coefficient: end behavior?

     Ответ

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

225. Карточка 225

     Вопрос

     Conditional probability $P(A|B)$?

     Ответ

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

226. Карточка 226

     Вопрос

     Complementary acute angles: sine–cosine relationship?

     Ответ

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

227. Карточка 227

     Вопрос

     Compound inequality with “or”?

     Ответ

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

228. Карточка 228

     Вопрос

     Odd degree with positive leading coefficient: end behavior?

     Ответ

     The left end falls and the right end rises.

229. Карточка 229

     Вопрос

     Independent events $A$ and $B$?

     Ответ

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

230. Карточка 230

     Вопрос

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

     Ответ

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Карточка 231

     Вопрос

     Solve $|x-a|=b$ for $b≥0$.

     Ответ

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

232. Карточка 232

     Вопрос

     Exponential growth model?

     Ответ

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

233. Карточка 233

     Вопрос

     Mutually exclusive events?

     Ответ

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

234. Карточка 234

     Вопрос

     Midpoint of two points?

     Ответ

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

235. Карточка 235

     Вопрос

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

     Ответ

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

236. Карточка 236

     Вопрос

     Exponential decay model?

     Ответ

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

237. Карточка 237

     Вопрос

     Complement rule?

     Ответ

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

238. Карточка 238

     Вопрос

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

     Ответ

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

239. Карточка 239

     Вопрос

     Evaluate $f(a)$?

     Ответ

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

240. Карточка 240

     Вопрос

     Growth factor 1.08: percent growth rate?

     Ответ

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

241. Карточка 241

     Вопрос

     Representative random sample permits what conclusion?

     Ответ

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

242. Карточка 242

     Вопрос

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

     Ответ

     $r=√R$, provided $R>0$.

243. Карточка 243

     Вопрос

     Linear table: constant slope check?

     Ответ

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

244. Карточка 244

     Вопрос

     Decay factor 0.73: percent decrease?

     Ответ

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

245. Карточка 245

     Вопрос

     Random assignment permits what causal claim?

     Ответ

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

246. Карточка 246

     Вопрос

     Radius and tangent at the contact point?

     Ответ

     They are perpendicular.

247. Карточка 247

     Вопрос

     Positive slope means what for a linear function?

     Ответ

     The output increases as the input increases.

248. Карточка 248

     Вопрос

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

     Ответ

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

249. Карточка 249

     Вопрос

     Observational study supports causation?

     Ответ

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

250. Карточка 250

     Вопрос

     Rectangular-prism volume?

     Ответ

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

251. Карточка 251

     Вопрос

     Arithmetic sequence common difference?

     Ответ

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

252. Карточка 252

     Вопрос

     Compound interest formula?

     Ответ

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

253. Карточка 253

     Вопрос

     Larger random sample: effect on margin of error?

     Ответ

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

254. Карточка 254

     Вопрос

     Cylinder volume?

     Ответ

     $V=πr^2h$.

255. Карточка 255

     Вопрос

     Arithmetic sequence nth term?

     Ответ

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

256. Карточка 256

     Вопрос

     Rational expression: first domain check?

     Ответ

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

257. Карточка 257

     Вопрос

     Slope of a line of best fit?

     Ответ

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

258. Карточка 258

     Вопрос

     Cone volume?

     Ответ

     $V=(1/3)πr^2h$.

259. Карточка 259

     Вопрос

     Solve a literal equation for one variable?

     Ответ

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

260. Карточка 260

     Вопрос

     Why check rational-equation solutions?

     Ответ

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

261. Карточка 261

     Вопрос

     Residual?

     Ответ

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

262. Карточка 262

     Вопрос

     Sphere volume?

     Ответ

     $V=(4/3)πr^3$.

263. Карточка 263

     Вопрос

     Boundary for a two-variable linear inequality?

     Ответ

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

264. Карточка 264

     Вопрос

     Why check a solution after squaring both sides?

     Ответ

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

265. Карточка 265

     Вопрос

     Positive correlation?

     Ответ

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

266. Карточка 266

     Вопрос

     Rectangular-prism surface area?

     Ответ

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

267. Карточка 267

     Вопрос

     Check a proposed system solution?

     Ответ

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

268. Карточка 268

     Вопрос

     Simplify $√72$.

     Ответ

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

269. Карточка 269

     Вопрос

     Extrapolation risk?

     Ответ

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

270. Карточка 270

     Вопрос

     Area scale factor when lengths double?

     Ответ

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

271. Карточка 271

     Вопрос

     Horizontal line slope?

     Ответ

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

272. Карточка 272

     Вопрос

     Inverse function setup?

     Ответ

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

273. Карточка 273

     Вопрос

     Percentage points versus percent change?

     Ответ

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

274. Карточка 274

     Вопрос

     y-intercept in a context?

     Ответ

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

275. Карточка 275

     Вопрос

     Quadratic maximum or minimum from vertex form?

     Ответ

     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. Карточка 276

     Вопрос

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

     Ответ

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

277. Карточка 277

     Вопрос

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

     Ответ

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

278. Карточка 278

     Вопрос

     Population versus sample?

     Ответ

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

279. Карточка 279

     Вопрос

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

     Ответ

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

280. Карточка 280

     Вопрос

     Function composition $(f∘g)(x)$?

     Ответ

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

281. Карточка 281

     Вопрос

     Density?

     Ответ

     Mass divided by volume. Keep the units consistent.

282. Карточка 282

     Вопрос

     Vertical line slope?

     Ответ

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

283. Карточка 283

     Вопрос

     Nonlinear system with one equation solved for $y$?

     Ответ

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

284. Карточка 284

     Вопрос

     Weighted percentage across unequal groups?

     Ответ

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

285. Карточка 285

     Вопрос

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

     Ответ

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

286. Карточка 286

     Вопрос

     Cancel a common factor in a rational expression?

     Ответ

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

287. Карточка 287

     Вопрос

     Solve a linear equation containing fractions?

     Ответ

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

288. Карточка 288

     Вопрос

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

     Ответ

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

289. Карточка 289

     Вопрос

     Rate units check?

     Ответ

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

290. Карточка 290

     Вопрос

     Strict versus inclusive inequality endpoint?

     Ответ

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

291. Карточка 291

     Вопрос

     Even-multiplicity zero on a graph?

     Ответ

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

292. Карточка 292

     Вопрос

     System word problem: first setup step?

     Ответ

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

293. Карточка 293

     Вопрос

     When does a quadratic have exactly one real solution?

     Ответ

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

294. Карточка 294

     Вопрос

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

     Ответ

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

295. Карточка 295

     Вопрос

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

     Ответ

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

296. Карточка 296

     Вопрос

     Graph of $-f(x)$?

     Ответ

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

297. Карточка 297

     Вопрос

     Three consecutive integers starting with $n$?

     Ответ

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

298. Карточка 298

     Вопрос

     Line–parabola intersections from a substituted quadratic?

     Ответ

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

299. Карточка 299

     Вопрос

     Linear equation with no solution: coefficient pattern?

     Ответ

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

300. Карточка 300

     Вопрос

     Zeros of a function on its graph?

     Ответ

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

300 карточек

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