Digital SAT Flashcards: Math, Grammar & Words in Context

Карти в това тесте

1. Карта 1

   Въпрос

   Central idea of a passage?

   Отговор

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

2. Карта 2

   Въпрос

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

   Отговор

   Reduced. The trees made the heat less severe.

3. Карта 3

   Въпрос

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

   Отговор

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

4. Карта 4

   Въпрос

   Three standard joins for two independent clauses?

   Отговор

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

5. Карта 5

   Въпрос

   Best supporting detail?

   Отговор

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

6. Карта 6

   Въпрос

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

   Отговор

   Confirmed with supporting evidence.

7. Карта 7

   Въпрос

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

   Отговор

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

8. Карта 8

   Въпрос

   Introductory dependent clause before a main clause?

   Отговор

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

9. Карта 9

   Въпрос

   Valid inference?

   Отговор

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

10. Карта 10

    Въпрос

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

    Отговор

    Provisional or not yet certain.

11. Карта 11

    Въпрос

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

    Отговор

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

12. Карта 12

    Въпрос

    Singular subject with an intervening prepositional phrase?

    Отговор

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

13. Карта 13

    Въпрос

    Strongest textual evidence?

    Отговор

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

14. Карта 14

    Въпрос

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

    Отговор

    So small that it is not important.

15. Карта 15

    Въпрос

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

    Отговор

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

16. Карта 16

    Въпрос

    Opening modifier placement?

    Отговор

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

17. Карта 17

    Въпрос

    Quantitative evidence for a claim?

    Отговор

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

18. Карта 18

    Въпрос

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

    Отговор

    Traditional or commonly accepted.

19. Карта 19

    Въпрос

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

    Отговор

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

20. Карта 20

    Въпрос

    Singular possessive noun?

    Отговор

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

21. Карта 21

    Въпрос

    Trend in a table or graph?

    Отговор

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

22. Карта 22

    Въпрос

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

    Отговор

    New or original in this context.

23. Карта 23

    Въпрос

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

    Отговор

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

24. Карта 24

    Въпрос

    Parallel items in a series?

    Отговор

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

25. Карта 25

    Въпрос

    Claim stronger than the evidence?

    Отговор

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

26. Карта 26

    Въпрос

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

    Отговор

    Reasonable or believable.

27. Карта 27

    Въпрос

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

    Отговор

    Addition. The second statement adds a related supporting point.

28. Карта 28

    Въпрос

    Colon before an explanation or list?

    Отговор

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

29. Карта 29

    Въпрос

    Claim versus evidence?

    Отговор

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

30. Карта 30

    Въпрос

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

    Отговор

    Open to more than one interpretation.

31. Карта 31

    Въпрос

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

    Отговор

    Replacement. The second statement substitutes one action for another.

32. Карта 32

    Въпрос

    Count nouns versus mass nouns?

    Отговор

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

33. Карта 33

    Въпрос

    Effect of a counterexample?

    Отговор

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

34. Карта 34

    Въпрос

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

    Отговор

    Irregular and occasional.

35. Карта 35

    Въпрос

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

    Отговор

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

36. Карта 36

    Въпрос

    Essential clause punctuation?

    Отговор

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

37. Карта 37

    Въпрос

    Correlation alone proves causation?

    Отговор

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

38. Карта 38

    Въпрос

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

    Отговор

    Coming later in time.

39. Карта 39

    Въпрос

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

    Отговор

    Restatement for clarity. The second statement rephrases the first.

40. Карта 40

    Въпрос

    Verb tense across a paragraph?

    Отговор

    Keep the time frame consistent unless the timing actually changes.

41. Карта 41

    Въпрос

    Missing information in a data claim?

    Отговор

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

42. Карта 42

    Въпрос

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

    Отговор

    Keep or continue to hold.

43. Карта 43

    Въпрос

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

    Отговор

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

44. Карта 44

    Въпрос

    Coordinate adjectives?

    Отговор

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

45. Карта 45

    Въпрос

    Two sources on the same event?

    Отговор

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

46. Карта 46

    Въпрос

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

    Отговор

    Draw out or bring forth.

47. Карта 47

    Въпрос

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

    Отговор

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

48. Карта 48

    Въпрос

    Sentence fragment?

    Отговор

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

49. Карта 49

    Въпрос

    Inference from a narrow sample?

    Отговор

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

50. Карта 50

    Въпрос

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

    Отговор

    A limit or restriction.

51. Карта 51

    Въпрос

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

    Отговор

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

52. Карта 52

    Въпрос

    Conjunctive adverb between independent clauses?

    Отговор

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

53. Карта 53

    Въпрос

    Most accurate summary?

    Отговор

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

54. Карта 54

    Въпрос

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

    Отговор

    Complete and wide-ranging.

55. Карта 55

    Въпрос

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

    Отговор

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

56. Карта 56

    Въпрос

    Who versus whom?

    Отговор

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

57. Карта 57

    Въпрос

    Evidence that best resolves a disagreement?

    Отговор

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

58. Карта 58

    Въпрос

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

    Отговор

    Clearly different or separate.

59. Карта 59

    Въпрос

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

    Отговор

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

60. Карта 60

    Въпрос

    Comma before an introduced direct quotation?

    Отговор

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

61. Карта 61

    Въпрос

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

    Отговор

    Limited or modified, rather than stated without conditions.

62. Карта 62

    Въпрос

    Notes for a synthesis goal?

    Отговор

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

63. Карта 63

    Въпрос

    Comma splice?

    Отговор

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

64. Карта 64

    Въпрос

    Comma between subject and verb?

    Отговор

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

65. Карта 65

    Въпрос

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

    Отговор

    No longer useful or current because something newer replaced it.

66. Карта 66

    Въпрос

    Source attribution in a synthesis?

    Отговор

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

67. Карта 67

    Въпрос

    Compound subject joined by “and”?

    Отговор

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

68. Карта 68

    Въпрос

    Dangling opening modifier?

    Отговор

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

69. Карта 69

    Въпрос

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

    Отговор

    Obtained from a source or calculation.

70. Карта 70

    Въпрос

    Chronological synthesis?

    Отговор

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

71. Карта 71

    Въпрос

    Plural noun ending in s: possessive form?

    Отговор

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

72. Карта 72

    Въпрос

    Logical comparison?

    Отговор

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

73. Карта 73

    Въпрос

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

    Отговор

    Publicly supports or argues for.

74. Карта 74

    Въпрос

    Compare evidence from two studies?

    Отговор

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

75. Карта 75

    Въпрос

    Colon after an incomplete lead-in?

    Отговор

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

76. Карта 76

    Въпрос

    Number versus amount?

    Отговор

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

77. Карта 77

    Въпрос

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

    Отговор

    Present or found almost everywhere.

78. Карта 78

    Въпрос

    Synthesis that emphasizes a difference?

    Отговор

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

79. Карта 79

    Въпрос

    Nonessential clause or phrase?

    Отговор

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

80. Карта 80

    Въпрос

    Earlier of two past actions?

    Отговор

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

81. Карта 81

    Въпрос

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

    Отговор

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

82. Карта 82

    Въпрос

    Rhetorical goal: define a term?

    Отговор

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

83. Карта 83

    Въпрос

    Cumulative adjectives?

    Отговор

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

84. Карта 84

    Въпрос

    Run-on sentence?

    Отговор

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

85. Карта 85

    Въпрос

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

    Отговор

    It illustrates the claim with an example.

86. Карта 86

    Въпрос

    Introduce a quotation in a synthesis?

    Отговор

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

87. Карта 87

    Въпрос

    Relative pronoun for people?

    Отговор

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

88. Карта 88

    Въпрос

    Integrated quotation punctuation?

    Отговор

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

89. Карта 89

    Въпрос

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

    Отговор

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

90. Карта 90

    Въпрос

    Avoid redundancy in synthesis?

    Отговор

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

91. Карта 91

    Въпрос

    Semicolon between two independent clauses?

    Отговор

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

92. Карта 92

    Въпрос

    Comma in a compound predicate?

    Отговор

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

93. Карта 93

    Въпрос

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

    Отговор

    It defines or clarifies the term.

94. Карта 94

    Въпрос

    Combine two related sentences?

    Отговор

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

95. Карта 95

    Въпрос

    Either/or subject agreement?

    Отговор

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

96. Карта 96

    Въпрос

    Active versus passive voice?

    Отговор

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

97. Карта 97

    Въпрос

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

    Отговор

    It presents an effect or consequence.

98. Карта 98

    Въпрос

    Formal academic register?

    Отговор

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

99. Карта 99

    Въпрос

    Its or it's?

    Отговор

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

100. Карта 100

     Въпрос

     Adjective versus adverb?

     Отговор

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

101. Карта 101

     Въпрос

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

     Отговор

     To inform or explain, not necessarily to persuade.

102. Карта 102

     Въпрос

     Concise synthesis?

     Отговор

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

103. Карта 103

     Въпрос

     Single dash for emphasis?

     Отговор

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

104. Карта 104

     Въпрос

     Comma with direct address?

     Отговор

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

105. Карта 105

     Въпрос

     Why acknowledge a limitation?

     Отговор

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

106. Карта 106

     Въпрос

     Quantitative comparison in a synthesis?

     Отговор

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

107. Карта 107

     Въпрос

     Each of the samples: verb number?

     Отговор

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

108. Карта 108

     Въпрос

     Between versus among?

     Отговор

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

109. Карта 109

     Въпрос

     Rhetorical question in an argument?

     Отговор

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

110. Карта 110

     Въпрос

     Claim before or after support?

     Отговор

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

111. Карта 111

     Въпрос

     Restrictive “that” versus nonrestrictive “which”?

     Отговор

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

112. Карта 112

     Въпрос

     Present perfect use?

     Отговор

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

113. Карта 113

     Въпрос

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

     Отговор

     They agree in conclusion but support it through different evidence.

114. Карта 114

     Въпрос

     Group related ideas in a synthesis?

     Отговор

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

115. Карта 115

     Въпрос

     Compound modifier before a noun?

     Отговор

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

116. Карта 116

     Въпрос

     Affect or effect?

     Отговор

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

117. Карта 117

     Въпрос

     Two texts offer incompatible explanations. Relationship?

     Отговор

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

118. Карта 118

     Въпрос

     Replace a vague pronoun in synthesis?

     Отговор

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

119. Карта 119

     Въпрос

     Comma-separated list?

     Отговор

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

120. Карта 120

     Въпрос

     Main clause before a dependent clause?

     Отговор

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

121. Карта 121

     Въпрос

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

     Отговор

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Карта 122

     Въпрос

     Independent clauses joined with a coordinating conjunction?

     Отговор

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

123. Карта 123

     Въпрос

     Introductory transition?

     Отговор

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

124. Карта 124

     Въпрос

     Pronoun–antecedent agreement?

     Отговор

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

125. Карта 125

     Въпрос

     Paired em dashes?

     Отговор

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

126. Карта 126

     Въпрос

     How does new evidence relate to an earlier claim?

     Отговор

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

127. Карта 127

     Въпрос

     Their, there, or they're?

     Отговор

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

128. Карта 128

     Въпрос

     Good or well?

     Отговор

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

129. Карта 129

     Въпрос

     Appositive naming the same noun?

     Отговор

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

130. Карта 130

     Въпрос

     Why use an analogy?

     Отговор

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

131. Карта 131

     Въпрос

     Than or then?

     Отговор

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

132. Карта 132

     Въпрос

     Hypothetical contrary-to-fact “if” clause?

     Отговор

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

133. Карта 133

     Въпрос

     Plural noun with no possession?

     Отговор

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

134. Карта 134

     Въпрос

     Neutral, evidence-led wording indicates what tone?

     Отговор

     Objective. It emphasizes information rather than strong personal judgment.

135. Карта 135

     Въпрос

     Complex list with internal commas?

     Отговор

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

136. Карта 136

     Въпрос

     Ambiguous pronoun?

     Отговор

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

137. Карта 137

     Въпрос

     Parentheses around nonessential information?

     Отговор

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

138. Карта 138

     Въпрос

     Repeated doubt about the evidence indicates what tone?

     Отговор

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

139. Карта 139

     Въпрос

     Superlative comparison?

     Отговор

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

140. Карта 140

     Въпрос

     Pronoun after a preposition?

     Отговор

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

141. Карта 141

     Въпрос

     Apostrophe in a contraction?

     Отговор

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

142. Карта 142

     Въпрос

     Coordinate-adjective test?

     Отговор

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

143. Карта 143

     Въпрос

     Double comparative?

     Отговор

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

144. Карта 144

     Въпрос

     Lie or lay?

     Отговор

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

145. Карта 145

     Въпрос

     Who's or whose?

     Отговор

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

146. Карта 146

     Въпрос

     Standard comparison with “different”?

     Отговор

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

147. Карта 147

     Въпрос

     Paired construction with two endpoints?

     Отговор

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

148. Карта 148

     Въпрос

     Verb mood in a coordinated idea?

     Отговор

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

149. Карта 149

     Въпрос

     Possessive pronoun apostrophe?

     Отговор

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

150. Карта 150

     Въпрос

     Comma between a preposition and its object?

     Отговор

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

     

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151. Карта 151

     Въпрос

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

     Отговор

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

152. Карта 152

     Въпрос

     Product of powers with the same base?

     Отговор

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

153. Карта 153

     Въпрос

     Unit rate?

     Отговор

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

154. Карта 154

     Въпрос

     Rectangle area?

     Отговор

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

155. Карта 155

     Въпрос

     Slope from two points?

     Отговор

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

156. Карта 156

     Въпрос

     Quotient of powers with the same base?

     Отговор

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Карта 157

     Въпрос

     Conversion factor setup?

     Отговор

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

158. Карта 158

     Въпрос

     Triangle area?

     Отговор

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

159. Карта 159

     Въпрос

     Slope-intercept form?

     Отговор

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

160. Карта 160

     Въпрос

     Power raised to a power?

     Отговор

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

161. Карта 161

     Въпрос

     Dimensional analysis check?

     Отговор

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

162. Карта 162

     Въпрос

     Trapezoid area?

     Отговор

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

163. Карта 163

     Въпрос

     Point-slope form?

     Отговор

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

164. Карта 164

     Въпрос

     Negative exponent?

     Отговор

     $a^{-n}=1/a^n$ for $a≠0$.

165. Карта 165

     Въпрос

     Constant of proportionality in $y=kx$?

     Отговор

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

166. Карта 166

     Въпрос

     Circle area?

     Отговор

     $A=πr^2$.

167. Карта 167

     Въпрос

     Intercepts from $Ax+By=C$?

     Отговор

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

168. Карта 168

     Въпрос

     Fractional exponent?

     Отговор

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

169. Карта 169

     Въпрос

     Scale drawing length?

     Отговор

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

170. Карта 170

     Въпрос

     Circle circumference?

     Отговор

     $C=2πr=πd$.

171. Карта 171

     Въпрос

     Parallel nonvertical lines: slope relationship?

     Отговор

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

172. Карта 172

     Въпрос

     Difference of squares?

     Отговор

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

173. Карта 173

     Въпрос

     Percent change?

     Отговор

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

174. Карта 174

     Въпрос

     Arc length from central angle $θ$ in degrees?

     Отговор

     $L=(θ/360)(2πr)$.

175. Карта 175

     Въпрос

     Perpendicular nonvertical lines: slope relationship?

     Отговор

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

176. Карта 176

     Въпрос

     Perfect-square trinomial pattern?

     Отговор

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

177. Карта 177

     Въпрос

     Increase by $r$ percent: multiplier?

     Отговор

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

178. Карта 178

     Въпрос

     Sector area from central angle $θ$ in degrees?

     Отговор

     $A=(θ/360)(πr^2)$.

179. Карта 179

     Въпрос

     x-intercept of a graph?

     Отговор

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

180. Карта 180

     Въпрос

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

     Отговор

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

181. Карта 181

     Въпрос

     Original value after a 20 percent increase to 84?

     Отговор

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

182. Карта 182

     Въпрос

     Triangle interior-angle sum?

     Отговор

     $180°$.

183. Карта 183

     Въпрос

     y-intercept of a graph?

     Отговор

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

184. Карта 184

     Въпрос

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

     Отговор

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

185. Карта 185

     Въпрос

     Weighted average?

     Отговор

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

186. Карта 186

     Въпрос

     Exterior angle of a triangle?

     Отговор

     It equals the sum of the two remote interior angles.

187. Карта 187

     Въпрос

     Line through two points?

     Отговор

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

188. Карта 188

     Въпрос

     Quadratic formula?

     Отговор

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

189. Карта 189

     Въпрос

     Arithmetic mean?

     Отговор

     Add all values and divide by the number of values.

190. Карта 190

     Въпрос

     Parallel lines cut by a transversal: alternate interior angles?

     Отговор

     They are congruent.

191. Карта 191

     Въпрос

     Slope's units in context?

     Отговор

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

192. Карта 192

     Въпрос

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

     Отговор

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

193. Карта 193

     Въпрос

     Median?

     Отговор

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

194. Карта 194

     Въпрос

     Similar triangles: corresponding sides?

     Отговор

     They are proportional. Match sides opposite equal angles.

195. Карта 195

     Въпрос

     Direct variation model?

     Отговор

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

196. Карта 196

     Въпрос

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

     Отговор

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

197. Карта 197

     Въпрос

     Range of a data set?

     Отговор

     Maximum minus minimum.

198. Карта 198

     Въпрос

     Scale factor $k$: area factor?

     Отговор

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

199. Карта 199

     Въпрос

     Solution of a two-line system?

     Отговор

     The intersection point, whose coordinates satisfy both equations.

200. Карта 200

     Въпрос

     Vertex form of a quadratic?

     Отговор

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

201. Карта 201

     Въпрос

     Interquartile range?

     Отговор

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

202. Карта 202

     Въпрос

     Pythagorean theorem?

     Отговор

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

203. Карта 203

     Въпрос

     Substitution in a system?

     Отговор

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

204. Карта 204

     Въпрос

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

     Отговор

     $x=h$.

205. Карта 205

     Въпрос

     Larger standard deviation means what?

     Отговор

     The data are more spread out around the mean.

206. Карта 206

     Въпрос

     45°-45°-90° side ratio?

     Отговор

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

207. Карта 207

     Въпрос

     Elimination in a system?

     Отговор

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

208. Карта 208

     Въпрос

     Completing the square?

     Отговор

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

209. Карта 209

     Въпрос

     Effect of a high outlier on the mean?

     Отговор

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

210. Карта 210

     Въпрос

     30°-60°-90° side ratio?

     Отговор

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

211. Карта 211

     Въпрос

     Parallel lines in a system?

     Отговор

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

212. Карта 212

     Въпрос

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

     Отговор

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

213. Карта 213

     Въпрос

     Add the same constant to every data value: effect?

     Отговор

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

214. Карта 214

     Въпрос

     Right-triangle sine?

     Отговор

     Sine of $θ$ equals opposite over hypotenuse.

215. Карта 215

     Въпрос

     Same line written two ways in a system?

     Отговор

     Infinitely many solutions. Simplifying either equation produces the other.

216. Карта 216

     Въпрос

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

     Отговор

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

217. Карта 217

     Въпрос

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

     Отговор

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

218. Карта 218

     Въпрос

     Right-triangle cosine?

     Отговор

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Карта 219

     Въпрос

     Multiply or divide an inequality by a negative number?

     Отговор

     Reverse the inequality sign.

220. Карта 220

     Въпрос

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

     Отговор

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

221. Карта 221

     Въпрос

     Joint probability from a two-way table?

     Отговор

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

222. Карта 222

     Въпрос

     Right-triangle tangent?

     Отговор

     Tangent of $θ$ equals opposite over adjacent.

223. Карта 223

     Въпрос

     Compound inequality with “and”?

     Отговор

     Use the intersection: values that satisfy both inequalities.

224. Карта 224

     Въпрос

     Even degree with positive leading coefficient: end behavior?

     Отговор

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

225. Карта 225

     Въпрос

     Conditional probability $P(A|B)$?

     Отговор

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

226. Карта 226

     Въпрос

     Complementary acute angles: sine–cosine relationship?

     Отговор

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

227. Карта 227

     Въпрос

     Compound inequality with “or”?

     Отговор

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

228. Карта 228

     Въпрос

     Odd degree with positive leading coefficient: end behavior?

     Отговор

     The left end falls and the right end rises.

229. Карта 229

     Въпрос

     Independent events $A$ and $B$?

     Отговор

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

230. Карта 230

     Въпрос

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

     Отговор

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Карта 231

     Въпрос

     Solve $|x-a|=b$ for $b≥0$.

     Отговор

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

232. Карта 232

     Въпрос

     Exponential growth model?

     Отговор

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

233. Карта 233

     Въпрос

     Mutually exclusive events?

     Отговор

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

234. Карта 234

     Въпрос

     Midpoint of two points?

     Отговор

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

235. Карта 235

     Въпрос

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

     Отговор

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

236. Карта 236

     Въпрос

     Exponential decay model?

     Отговор

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

237. Карта 237

     Въпрос

     Complement rule?

     Отговор

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

238. Карта 238

     Въпрос

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

     Отговор

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

239. Карта 239

     Въпрос

     Evaluate $f(a)$?

     Отговор

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

240. Карта 240

     Въпрос

     Growth factor 1.08: percent growth rate?

     Отговор

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

241. Карта 241

     Въпрос

     Representative random sample permits what conclusion?

     Отговор

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

242. Карта 242

     Въпрос

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

     Отговор

     $r=√R$, provided $R>0$.

243. Карта 243

     Въпрос

     Linear table: constant slope check?

     Отговор

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

244. Карта 244

     Въпрос

     Decay factor 0.73: percent decrease?

     Отговор

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

245. Карта 245

     Въпрос

     Random assignment permits what causal claim?

     Отговор

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

246. Карта 246

     Въпрос

     Radius and tangent at the contact point?

     Отговор

     They are perpendicular.

247. Карта 247

     Въпрос

     Positive slope means what for a linear function?

     Отговор

     The output increases as the input increases.

248. Карта 248

     Въпрос

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

     Отговор

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

249. Карта 249

     Въпрос

     Observational study supports causation?

     Отговор

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

250. Карта 250

     Въпрос

     Rectangular-prism volume?

     Отговор

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

251. Карта 251

     Въпрос

     Arithmetic sequence common difference?

     Отговор

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

252. Карта 252

     Въпрос

     Compound interest formula?

     Отговор

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

253. Карта 253

     Въпрос

     Larger random sample: effect on margin of error?

     Отговор

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

254. Карта 254

     Въпрос

     Cylinder volume?

     Отговор

     $V=πr^2h$.

255. Карта 255

     Въпрос

     Arithmetic sequence nth term?

     Отговор

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

256. Карта 256

     Въпрос

     Rational expression: first domain check?

     Отговор

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

257. Карта 257

     Въпрос

     Slope of a line of best fit?

     Отговор

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

258. Карта 258

     Въпрос

     Cone volume?

     Отговор

     $V=(1/3)πr^2h$.

259. Карта 259

     Въпрос

     Solve a literal equation for one variable?

     Отговор

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

260. Карта 260

     Въпрос

     Why check rational-equation solutions?

     Отговор

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

261. Карта 261

     Въпрос

     Residual?

     Отговор

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

262. Карта 262

     Въпрос

     Sphere volume?

     Отговор

     $V=(4/3)πr^3$.

263. Карта 263

     Въпрос

     Boundary for a two-variable linear inequality?

     Отговор

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

264. Карта 264

     Въпрос

     Why check a solution after squaring both sides?

     Отговор

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

265. Карта 265

     Въпрос

     Positive correlation?

     Отговор

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

266. Карта 266

     Въпрос

     Rectangular-prism surface area?

     Отговор

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

267. Карта 267

     Въпрос

     Check a proposed system solution?

     Отговор

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

268. Карта 268

     Въпрос

     Simplify $√72$.

     Отговор

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

269. Карта 269

     Въпрос

     Extrapolation risk?

     Отговор

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

270. Карта 270

     Въпрос

     Area scale factor when lengths double?

     Отговор

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

271. Карта 271

     Въпрос

     Horizontal line slope?

     Отговор

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

272. Карта 272

     Въпрос

     Inverse function setup?

     Отговор

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

273. Карта 273

     Въпрос

     Percentage points versus percent change?

     Отговор

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

274. Карта 274

     Въпрос

     y-intercept in a context?

     Отговор

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

275. Карта 275

     Въпрос

     Quadratic maximum or minimum from vertex form?

     Отговор

     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. Карта 276

     Въпрос

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

     Отговор

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

277. Карта 277

     Въпрос

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

     Отговор

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

278. Карта 278

     Въпрос

     Population versus sample?

     Отговор

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

279. Карта 279

     Въпрос

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

     Отговор

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

280. Карта 280

     Въпрос

     Function composition $(f∘g)(x)$?

     Отговор

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

281. Карта 281

     Въпрос

     Density?

     Отговор

     Mass divided by volume. Keep the units consistent.

282. Карта 282

     Въпрос

     Vertical line slope?

     Отговор

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

283. Карта 283

     Въпрос

     Nonlinear system with one equation solved for $y$?

     Отговор

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

284. Карта 284

     Въпрос

     Weighted percentage across unequal groups?

     Отговор

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

285. Карта 285

     Въпрос

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

     Отговор

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

286. Карта 286

     Въпрос

     Cancel a common factor in a rational expression?

     Отговор

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

287. Карта 287

     Въпрос

     Solve a linear equation containing fractions?

     Отговор

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

288. Карта 288

     Въпрос

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

     Отговор

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

289. Карта 289

     Въпрос

     Rate units check?

     Отговор

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

290. Карта 290

     Въпрос

     Strict versus inclusive inequality endpoint?

     Отговор

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

291. Карта 291

     Въпрос

     Even-multiplicity zero on a graph?

     Отговор

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

292. Карта 292

     Въпрос

     System word problem: first setup step?

     Отговор

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

293. Карта 293

     Въпрос

     When does a quadratic have exactly one real solution?

     Отговор

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

294. Карта 294

     Въпрос

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

     Отговор

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

295. Карта 295

     Въпрос

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

     Отговор

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

296. Карта 296

     Въпрос

     Graph of $-f(x)$?

     Отговор

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

297. Карта 297

     Въпрос

     Three consecutive integers starting with $n$?

     Отговор

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

298. Карта 298

     Въпрос

     Line–parabola intersections from a substituted quadratic?

     Отговор

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

299. Карта 299

     Въпрос

     Linear equation with no solution: coefficient pattern?

     Отговор

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

300. Карта 300

     Въпрос

     Zeros of a function on its graph?

     Отговор

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

300 карти

Digital SAT Flashcards: Math, Grammar & Words in Context

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