Digital SAT Flashcards: Math, Grammar & Words in Context

Bu destedeki kartlar

1. Kart 1

   Soru

   Central idea of a passage?

   Cevap

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

2. Kart 2

   Soru

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

   Cevap

   Reduced. The trees made the heat less severe.

3. Kart 3

   Soru

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

   Cevap

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

4. Kart 4

   Soru

   Three standard joins for two independent clauses?

   Cevap

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

5. Kart 5

   Soru

   Best supporting detail?

   Cevap

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

6. Kart 6

   Soru

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

   Cevap

   Confirmed with supporting evidence.

7. Kart 7

   Soru

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

   Cevap

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

8. Kart 8

   Soru

   Introductory dependent clause before a main clause?

   Cevap

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

9. Kart 9

   Soru

   Valid inference?

   Cevap

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

10. Kart 10

    Soru

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

    Cevap

    Provisional or not yet certain.

11. Kart 11

    Soru

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

    Cevap

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

12. Kart 12

    Soru

    Singular subject with an intervening prepositional phrase?

    Cevap

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

13. Kart 13

    Soru

    Strongest textual evidence?

    Cevap

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

14. Kart 14

    Soru

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

    Cevap

    So small that it is not important.

15. Kart 15

    Soru

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

    Cevap

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

16. Kart 16

    Soru

    Opening modifier placement?

    Cevap

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

17. Kart 17

    Soru

    Quantitative evidence for a claim?

    Cevap

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

18. Kart 18

    Soru

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

    Cevap

    Traditional or commonly accepted.

19. Kart 19

    Soru

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

    Cevap

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

20. Kart 20

    Soru

    Singular possessive noun?

    Cevap

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

21. Kart 21

    Soru

    Trend in a table or graph?

    Cevap

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

22. Kart 22

    Soru

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

    Cevap

    New or original in this context.

23. Kart 23

    Soru

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

    Cevap

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

24. Kart 24

    Soru

    Parallel items in a series?

    Cevap

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

25. Kart 25

    Soru

    Claim stronger than the evidence?

    Cevap

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

26. Kart 26

    Soru

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

    Cevap

    Reasonable or believable.

27. Kart 27

    Soru

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

    Cevap

    Addition. The second statement adds a related supporting point.

28. Kart 28

    Soru

    Colon before an explanation or list?

    Cevap

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

29. Kart 29

    Soru

    Claim versus evidence?

    Cevap

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

30. Kart 30

    Soru

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

    Cevap

    Open to more than one interpretation.

31. Kart 31

    Soru

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

    Cevap

    Replacement. The second statement substitutes one action for another.

32. Kart 32

    Soru

    Count nouns versus mass nouns?

    Cevap

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

33. Kart 33

    Soru

    Effect of a counterexample?

    Cevap

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

34. Kart 34

    Soru

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

    Cevap

    Irregular and occasional.

35. Kart 35

    Soru

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

    Cevap

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

36. Kart 36

    Soru

    Essential clause punctuation?

    Cevap

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

37. Kart 37

    Soru

    Correlation alone proves causation?

    Cevap

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

38. Kart 38

    Soru

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

    Cevap

    Coming later in time.

39. Kart 39

    Soru

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

    Cevap

    Restatement for clarity. The second statement rephrases the first.

40. Kart 40

    Soru

    Verb tense across a paragraph?

    Cevap

    Keep the time frame consistent unless the timing actually changes.

41. Kart 41

    Soru

    Missing information in a data claim?

    Cevap

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

42. Kart 42

    Soru

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

    Cevap

    Keep or continue to hold.

43. Kart 43

    Soru

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

    Cevap

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

44. Kart 44

    Soru

    Coordinate adjectives?

    Cevap

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

45. Kart 45

    Soru

    Two sources on the same event?

    Cevap

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

46. Kart 46

    Soru

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

    Cevap

    Draw out or bring forth.

47. Kart 47

    Soru

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

    Cevap

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

48. Kart 48

    Soru

    Sentence fragment?

    Cevap

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

49. Kart 49

    Soru

    Inference from a narrow sample?

    Cevap

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

50. Kart 50

    Soru

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

    Cevap

    A limit or restriction.

51. Kart 51

    Soru

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

    Cevap

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

52. Kart 52

    Soru

    Conjunctive adverb between independent clauses?

    Cevap

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

53. Kart 53

    Soru

    Most accurate summary?

    Cevap

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

54. Kart 54

    Soru

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

    Cevap

    Complete and wide-ranging.

55. Kart 55

    Soru

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

    Cevap

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

56. Kart 56

    Soru

    Who versus whom?

    Cevap

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

57. Kart 57

    Soru

    Evidence that best resolves a disagreement?

    Cevap

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

58. Kart 58

    Soru

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

    Cevap

    Clearly different or separate.

59. Kart 59

    Soru

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

    Cevap

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

60. Kart 60

    Soru

    Comma before an introduced direct quotation?

    Cevap

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

61. Kart 61

    Soru

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

    Cevap

    Limited or modified, rather than stated without conditions.

62. Kart 62

    Soru

    Notes for a synthesis goal?

    Cevap

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

63. Kart 63

    Soru

    Comma splice?

    Cevap

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

64. Kart 64

    Soru

    Comma between subject and verb?

    Cevap

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

65. Kart 65

    Soru

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

    Cevap

    No longer useful or current because something newer replaced it.

66. Kart 66

    Soru

    Source attribution in a synthesis?

    Cevap

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

67. Kart 67

    Soru

    Compound subject joined by “and”?

    Cevap

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

68. Kart 68

    Soru

    Dangling opening modifier?

    Cevap

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

69. Kart 69

    Soru

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

    Cevap

    Obtained from a source or calculation.

70. Kart 70

    Soru

    Chronological synthesis?

    Cevap

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

71. Kart 71

    Soru

    Plural noun ending in s: possessive form?

    Cevap

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

72. Kart 72

    Soru

    Logical comparison?

    Cevap

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

73. Kart 73

    Soru

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

    Cevap

    Publicly supports or argues for.

74. Kart 74

    Soru

    Compare evidence from two studies?

    Cevap

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

75. Kart 75

    Soru

    Colon after an incomplete lead-in?

    Cevap

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

76. Kart 76

    Soru

    Number versus amount?

    Cevap

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

77. Kart 77

    Soru

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

    Cevap

    Present or found almost everywhere.

78. Kart 78

    Soru

    Synthesis that emphasizes a difference?

    Cevap

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

79. Kart 79

    Soru

    Nonessential clause or phrase?

    Cevap

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

80. Kart 80

    Soru

    Earlier of two past actions?

    Cevap

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

81. Kart 81

    Soru

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

    Cevap

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

82. Kart 82

    Soru

    Rhetorical goal: define a term?

    Cevap

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

83. Kart 83

    Soru

    Cumulative adjectives?

    Cevap

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

84. Kart 84

    Soru

    Run-on sentence?

    Cevap

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

85. Kart 85

    Soru

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

    Cevap

    It illustrates the claim with an example.

86. Kart 86

    Soru

    Introduce a quotation in a synthesis?

    Cevap

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

87. Kart 87

    Soru

    Relative pronoun for people?

    Cevap

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

88. Kart 88

    Soru

    Integrated quotation punctuation?

    Cevap

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

89. Kart 89

    Soru

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

    Cevap

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

90. Kart 90

    Soru

    Avoid redundancy in synthesis?

    Cevap

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

91. Kart 91

    Soru

    Semicolon between two independent clauses?

    Cevap

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

92. Kart 92

    Soru

    Comma in a compound predicate?

    Cevap

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

93. Kart 93

    Soru

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

    Cevap

    It defines or clarifies the term.

94. Kart 94

    Soru

    Combine two related sentences?

    Cevap

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

95. Kart 95

    Soru

    Either/or subject agreement?

    Cevap

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

96. Kart 96

    Soru

    Active versus passive voice?

    Cevap

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

97. Kart 97

    Soru

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

    Cevap

    It presents an effect or consequence.

98. Kart 98

    Soru

    Formal academic register?

    Cevap

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

99. Kart 99

    Soru

    Its or it's?

    Cevap

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

100. Kart 100

     Soru

     Adjective versus adverb?

     Cevap

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

101. Kart 101

     Soru

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

     Cevap

     To inform or explain, not necessarily to persuade.

102. Kart 102

     Soru

     Concise synthesis?

     Cevap

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

103. Kart 103

     Soru

     Single dash for emphasis?

     Cevap

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

104. Kart 104

     Soru

     Comma with direct address?

     Cevap

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

105. Kart 105

     Soru

     Why acknowledge a limitation?

     Cevap

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

106. Kart 106

     Soru

     Quantitative comparison in a synthesis?

     Cevap

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

107. Kart 107

     Soru

     Each of the samples: verb number?

     Cevap

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

108. Kart 108

     Soru

     Between versus among?

     Cevap

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

109. Kart 109

     Soru

     Rhetorical question in an argument?

     Cevap

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

110. Kart 110

     Soru

     Claim before or after support?

     Cevap

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

111. Kart 111

     Soru

     Restrictive “that” versus nonrestrictive “which”?

     Cevap

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

112. Kart 112

     Soru

     Present perfect use?

     Cevap

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

113. Kart 113

     Soru

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

     Cevap

     They agree in conclusion but support it through different evidence.

114. Kart 114

     Soru

     Group related ideas in a synthesis?

     Cevap

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

115. Kart 115

     Soru

     Compound modifier before a noun?

     Cevap

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

116. Kart 116

     Soru

     Affect or effect?

     Cevap

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

117. Kart 117

     Soru

     Two texts offer incompatible explanations. Relationship?

     Cevap

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

118. Kart 118

     Soru

     Replace a vague pronoun in synthesis?

     Cevap

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

119. Kart 119

     Soru

     Comma-separated list?

     Cevap

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

120. Kart 120

     Soru

     Main clause before a dependent clause?

     Cevap

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

121. Kart 121

     Soru

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

     Cevap

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Kart 122

     Soru

     Independent clauses joined with a coordinating conjunction?

     Cevap

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

123. Kart 123

     Soru

     Introductory transition?

     Cevap

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

124. Kart 124

     Soru

     Pronoun–antecedent agreement?

     Cevap

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

125. Kart 125

     Soru

     Paired em dashes?

     Cevap

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

126. Kart 126

     Soru

     How does new evidence relate to an earlier claim?

     Cevap

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

127. Kart 127

     Soru

     Their, there, or they're?

     Cevap

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

128. Kart 128

     Soru

     Good or well?

     Cevap

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

129. Kart 129

     Soru

     Appositive naming the same noun?

     Cevap

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

130. Kart 130

     Soru

     Why use an analogy?

     Cevap

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

131. Kart 131

     Soru

     Than or then?

     Cevap

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

132. Kart 132

     Soru

     Hypothetical contrary-to-fact “if” clause?

     Cevap

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

133. Kart 133

     Soru

     Plural noun with no possession?

     Cevap

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

134. Kart 134

     Soru

     Neutral, evidence-led wording indicates what tone?

     Cevap

     Objective. It emphasizes information rather than strong personal judgment.

135. Kart 135

     Soru

     Complex list with internal commas?

     Cevap

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

136. Kart 136

     Soru

     Ambiguous pronoun?

     Cevap

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

137. Kart 137

     Soru

     Parentheses around nonessential information?

     Cevap

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

138. Kart 138

     Soru

     Repeated doubt about the evidence indicates what tone?

     Cevap

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

139. Kart 139

     Soru

     Superlative comparison?

     Cevap

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

140. Kart 140

     Soru

     Pronoun after a preposition?

     Cevap

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

141. Kart 141

     Soru

     Apostrophe in a contraction?

     Cevap

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

142. Kart 142

     Soru

     Coordinate-adjective test?

     Cevap

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

143. Kart 143

     Soru

     Double comparative?

     Cevap

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

144. Kart 144

     Soru

     Lie or lay?

     Cevap

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

145. Kart 145

     Soru

     Who's or whose?

     Cevap

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

146. Kart 146

     Soru

     Standard comparison with “different”?

     Cevap

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

147. Kart 147

     Soru

     Paired construction with two endpoints?

     Cevap

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

148. Kart 148

     Soru

     Verb mood in a coordinated idea?

     Cevap

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

149. Kart 149

     Soru

     Possessive pronoun apostrophe?

     Cevap

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

150. Kart 150

     Soru

     Comma between a preposition and its object?

     Cevap

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

     

     300 kart

     Digital SAT Flashcards: Math, Grammar & Words in Context

     Bu desteyle ücretsiz çalış

     Nibomo açılır ve hemen çalışmaya başlayabilirsiniz.

151. Kart 151

     Soru

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

     Cevap

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

152. Kart 152

     Soru

     Product of powers with the same base?

     Cevap

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

153. Kart 153

     Soru

     Unit rate?

     Cevap

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

154. Kart 154

     Soru

     Rectangle area?

     Cevap

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

155. Kart 155

     Soru

     Slope from two points?

     Cevap

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

156. Kart 156

     Soru

     Quotient of powers with the same base?

     Cevap

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Kart 157

     Soru

     Conversion factor setup?

     Cevap

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

158. Kart 158

     Soru

     Triangle area?

     Cevap

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

159. Kart 159

     Soru

     Slope-intercept form?

     Cevap

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

160. Kart 160

     Soru

     Power raised to a power?

     Cevap

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

161. Kart 161

     Soru

     Dimensional analysis check?

     Cevap

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

162. Kart 162

     Soru

     Trapezoid area?

     Cevap

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

163. Kart 163

     Soru

     Point-slope form?

     Cevap

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

164. Kart 164

     Soru

     Negative exponent?

     Cevap

     $a^{-n}=1/a^n$ for $a≠0$.

165. Kart 165

     Soru

     Constant of proportionality in $y=kx$?

     Cevap

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

166. Kart 166

     Soru

     Circle area?

     Cevap

     $A=πr^2$.

167. Kart 167

     Soru

     Intercepts from $Ax+By=C$?

     Cevap

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

168. Kart 168

     Soru

     Fractional exponent?

     Cevap

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

169. Kart 169

     Soru

     Scale drawing length?

     Cevap

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

170. Kart 170

     Soru

     Circle circumference?

     Cevap

     $C=2πr=πd$.

171. Kart 171

     Soru

     Parallel nonvertical lines: slope relationship?

     Cevap

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

172. Kart 172

     Soru

     Difference of squares?

     Cevap

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

173. Kart 173

     Soru

     Percent change?

     Cevap

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

174. Kart 174

     Soru

     Arc length from central angle $θ$ in degrees?

     Cevap

     $L=(θ/360)(2πr)$.

175. Kart 175

     Soru

     Perpendicular nonvertical lines: slope relationship?

     Cevap

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

176. Kart 176

     Soru

     Perfect-square trinomial pattern?

     Cevap

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

177. Kart 177

     Soru

     Increase by $r$ percent: multiplier?

     Cevap

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

178. Kart 178

     Soru

     Sector area from central angle $θ$ in degrees?

     Cevap

     $A=(θ/360)(πr^2)$.

179. Kart 179

     Soru

     x-intercept of a graph?

     Cevap

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

180. Kart 180

     Soru

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

     Cevap

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

181. Kart 181

     Soru

     Original value after a 20 percent increase to 84?

     Cevap

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

182. Kart 182

     Soru

     Triangle interior-angle sum?

     Cevap

     $180°$.

183. Kart 183

     Soru

     y-intercept of a graph?

     Cevap

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

184. Kart 184

     Soru

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

     Cevap

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

185. Kart 185

     Soru

     Weighted average?

     Cevap

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

186. Kart 186

     Soru

     Exterior angle of a triangle?

     Cevap

     It equals the sum of the two remote interior angles.

187. Kart 187

     Soru

     Line through two points?

     Cevap

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

188. Kart 188

     Soru

     Quadratic formula?

     Cevap

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

189. Kart 189

     Soru

     Arithmetic mean?

     Cevap

     Add all values and divide by the number of values.

190. Kart 190

     Soru

     Parallel lines cut by a transversal: alternate interior angles?

     Cevap

     They are congruent.

191. Kart 191

     Soru

     Slope's units in context?

     Cevap

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

192. Kart 192

     Soru

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

     Cevap

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

193. Kart 193

     Soru

     Median?

     Cevap

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

194. Kart 194

     Soru

     Similar triangles: corresponding sides?

     Cevap

     They are proportional. Match sides opposite equal angles.

195. Kart 195

     Soru

     Direct variation model?

     Cevap

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

196. Kart 196

     Soru

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

     Cevap

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

197. Kart 197

     Soru

     Range of a data set?

     Cevap

     Maximum minus minimum.

198. Kart 198

     Soru

     Scale factor $k$: area factor?

     Cevap

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

199. Kart 199

     Soru

     Solution of a two-line system?

     Cevap

     The intersection point, whose coordinates satisfy both equations.

200. Kart 200

     Soru

     Vertex form of a quadratic?

     Cevap

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

201. Kart 201

     Soru

     Interquartile range?

     Cevap

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

202. Kart 202

     Soru

     Pythagorean theorem?

     Cevap

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

203. Kart 203

     Soru

     Substitution in a system?

     Cevap

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

204. Kart 204

     Soru

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

     Cevap

     $x=h$.

205. Kart 205

     Soru

     Larger standard deviation means what?

     Cevap

     The data are more spread out around the mean.

206. Kart 206

     Soru

     45°-45°-90° side ratio?

     Cevap

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

207. Kart 207

     Soru

     Elimination in a system?

     Cevap

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

208. Kart 208

     Soru

     Completing the square?

     Cevap

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

209. Kart 209

     Soru

     Effect of a high outlier on the mean?

     Cevap

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

210. Kart 210

     Soru

     30°-60°-90° side ratio?

     Cevap

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

211. Kart 211

     Soru

     Parallel lines in a system?

     Cevap

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

212. Kart 212

     Soru

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

     Cevap

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

213. Kart 213

     Soru

     Add the same constant to every data value: effect?

     Cevap

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

214. Kart 214

     Soru

     Right-triangle sine?

     Cevap

     Sine of $θ$ equals opposite over hypotenuse.

215. Kart 215

     Soru

     Same line written two ways in a system?

     Cevap

     Infinitely many solutions. Simplifying either equation produces the other.

216. Kart 216

     Soru

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

     Cevap

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

217. Kart 217

     Soru

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

     Cevap

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

218. Kart 218

     Soru

     Right-triangle cosine?

     Cevap

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Kart 219

     Soru

     Multiply or divide an inequality by a negative number?

     Cevap

     Reverse the inequality sign.

220. Kart 220

     Soru

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

     Cevap

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

221. Kart 221

     Soru

     Joint probability from a two-way table?

     Cevap

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

222. Kart 222

     Soru

     Right-triangle tangent?

     Cevap

     Tangent of $θ$ equals opposite over adjacent.

223. Kart 223

     Soru

     Compound inequality with “and”?

     Cevap

     Use the intersection: values that satisfy both inequalities.

224. Kart 224

     Soru

     Even degree with positive leading coefficient: end behavior?

     Cevap

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

225. Kart 225

     Soru

     Conditional probability $P(A|B)$?

     Cevap

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

226. Kart 226

     Soru

     Complementary acute angles: sine–cosine relationship?

     Cevap

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

227. Kart 227

     Soru

     Compound inequality with “or”?

     Cevap

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

228. Kart 228

     Soru

     Odd degree with positive leading coefficient: end behavior?

     Cevap

     The left end falls and the right end rises.

229. Kart 229

     Soru

     Independent events $A$ and $B$?

     Cevap

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

230. Kart 230

     Soru

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

     Cevap

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Kart 231

     Soru

     Solve $|x-a|=b$ for $b≥0$.

     Cevap

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

232. Kart 232

     Soru

     Exponential growth model?

     Cevap

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

233. Kart 233

     Soru

     Mutually exclusive events?

     Cevap

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

234. Kart 234

     Soru

     Midpoint of two points?

     Cevap

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

235. Kart 235

     Soru

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

     Cevap

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

236. Kart 236

     Soru

     Exponential decay model?

     Cevap

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

237. Kart 237

     Soru

     Complement rule?

     Cevap

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

238. Kart 238

     Soru

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

     Cevap

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

239. Kart 239

     Soru

     Evaluate $f(a)$?

     Cevap

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

240. Kart 240

     Soru

     Growth factor 1.08: percent growth rate?

     Cevap

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

241. Kart 241

     Soru

     Representative random sample permits what conclusion?

     Cevap

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

242. Kart 242

     Soru

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

     Cevap

     $r=√R$, provided $R>0$.

243. Kart 243

     Soru

     Linear table: constant slope check?

     Cevap

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

244. Kart 244

     Soru

     Decay factor 0.73: percent decrease?

     Cevap

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

245. Kart 245

     Soru

     Random assignment permits what causal claim?

     Cevap

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

246. Kart 246

     Soru

     Radius and tangent at the contact point?

     Cevap

     They are perpendicular.

247. Kart 247

     Soru

     Positive slope means what for a linear function?

     Cevap

     The output increases as the input increases.

248. Kart 248

     Soru

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

     Cevap

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

249. Kart 249

     Soru

     Observational study supports causation?

     Cevap

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

250. Kart 250

     Soru

     Rectangular-prism volume?

     Cevap

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

251. Kart 251

     Soru

     Arithmetic sequence common difference?

     Cevap

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

252. Kart 252

     Soru

     Compound interest formula?

     Cevap

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

253. Kart 253

     Soru

     Larger random sample: effect on margin of error?

     Cevap

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

254. Kart 254

     Soru

     Cylinder volume?

     Cevap

     $V=πr^2h$.

255. Kart 255

     Soru

     Arithmetic sequence nth term?

     Cevap

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

256. Kart 256

     Soru

     Rational expression: first domain check?

     Cevap

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

257. Kart 257

     Soru

     Slope of a line of best fit?

     Cevap

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

258. Kart 258

     Soru

     Cone volume?

     Cevap

     $V=(1/3)πr^2h$.

259. Kart 259

     Soru

     Solve a literal equation for one variable?

     Cevap

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

260. Kart 260

     Soru

     Why check rational-equation solutions?

     Cevap

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

261. Kart 261

     Soru

     Residual?

     Cevap

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

262. Kart 262

     Soru

     Sphere volume?

     Cevap

     $V=(4/3)πr^3$.

263. Kart 263

     Soru

     Boundary for a two-variable linear inequality?

     Cevap

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

264. Kart 264

     Soru

     Why check a solution after squaring both sides?

     Cevap

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

265. Kart 265

     Soru

     Positive correlation?

     Cevap

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

266. Kart 266

     Soru

     Rectangular-prism surface area?

     Cevap

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

267. Kart 267

     Soru

     Check a proposed system solution?

     Cevap

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

268. Kart 268

     Soru

     Simplify $√72$.

     Cevap

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

269. Kart 269

     Soru

     Extrapolation risk?

     Cevap

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

270. Kart 270

     Soru

     Area scale factor when lengths double?

     Cevap

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

271. Kart 271

     Soru

     Horizontal line slope?

     Cevap

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

272. Kart 272

     Soru

     Inverse function setup?

     Cevap

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

273. Kart 273

     Soru

     Percentage points versus percent change?

     Cevap

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

274. Kart 274

     Soru

     y-intercept in a context?

     Cevap

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

275. Kart 275

     Soru

     Quadratic maximum or minimum from vertex form?

     Cevap

     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. Kart 276

     Soru

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

     Cevap

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

277. Kart 277

     Soru

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

     Cevap

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

278. Kart 278

     Soru

     Population versus sample?

     Cevap

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

279. Kart 279

     Soru

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

     Cevap

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

280. Kart 280

     Soru

     Function composition $(f∘g)(x)$?

     Cevap

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

281. Kart 281

     Soru

     Density?

     Cevap

     Mass divided by volume. Keep the units consistent.

282. Kart 282

     Soru

     Vertical line slope?

     Cevap

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

283. Kart 283

     Soru

     Nonlinear system with one equation solved for $y$?

     Cevap

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

284. Kart 284

     Soru

     Weighted percentage across unequal groups?

     Cevap

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

285. Kart 285

     Soru

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

     Cevap

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

286. Kart 286

     Soru

     Cancel a common factor in a rational expression?

     Cevap

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

287. Kart 287

     Soru

     Solve a linear equation containing fractions?

     Cevap

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

288. Kart 288

     Soru

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

     Cevap

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

289. Kart 289

     Soru

     Rate units check?

     Cevap

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

290. Kart 290

     Soru

     Strict versus inclusive inequality endpoint?

     Cevap

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

291. Kart 291

     Soru

     Even-multiplicity zero on a graph?

     Cevap

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

292. Kart 292

     Soru

     System word problem: first setup step?

     Cevap

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

293. Kart 293

     Soru

     When does a quadratic have exactly one real solution?

     Cevap

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

294. Kart 294

     Soru

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

     Cevap

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

295. Kart 295

     Soru

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

     Cevap

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

296. Kart 296

     Soru

     Graph of $-f(x)$?

     Cevap

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

297. Kart 297

     Soru

     Three consecutive integers starting with $n$?

     Cevap

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

298. Kart 298

     Soru

     Line–parabola intersections from a substituted quadratic?

     Cevap

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

299. Kart 299

     Soru

     Linear equation with no solution: coefficient pattern?

     Cevap

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

300. Kart 300

     Soru

     Zeros of a function on its graph?

     Cevap

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

300 kart

Digital SAT Flashcards: Math, Grammar & Words in Context

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