Digital SAT Flashcards: Math, Grammar & Words in Context

Cartes de ce paquet

1. Carte 1

   Question

   Central idea of a passage?

   Réponse

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

2. Carte 2

   Question

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

   Réponse

   Reduced. The trees made the heat less severe.

3. Carte 3

   Question

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

   Réponse

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

4. Carte 4

   Question

   Three standard joins for two independent clauses?

   Réponse

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

5. Carte 5

   Question

   Best supporting detail?

   Réponse

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

6. Carte 6

   Question

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

   Réponse

   Confirmed with supporting evidence.

7. Carte 7

   Question

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

   Réponse

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

8. Carte 8

   Question

   Introductory dependent clause before a main clause?

   Réponse

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

9. Carte 9

   Question

   Valid inference?

   Réponse

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

10. Carte 10

    Question

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

    Réponse

    Provisional or not yet certain.

11. Carte 11

    Question

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

    Réponse

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

12. Carte 12

    Question

    Singular subject with an intervening prepositional phrase?

    Réponse

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

13. Carte 13

    Question

    Strongest textual evidence?

    Réponse

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

14. Carte 14

    Question

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

    Réponse

    So small that it is not important.

15. Carte 15

    Question

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

    Réponse

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

16. Carte 16

    Question

    Opening modifier placement?

    Réponse

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

17. Carte 17

    Question

    Quantitative evidence for a claim?

    Réponse

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

18. Carte 18

    Question

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

    Réponse

    Traditional or commonly accepted.

19. Carte 19

    Question

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

    Réponse

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

20. Carte 20

    Question

    Singular possessive noun?

    Réponse

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

21. Carte 21

    Question

    Trend in a table or graph?

    Réponse

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

22. Carte 22

    Question

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

    Réponse

    New or original in this context.

23. Carte 23

    Question

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

    Réponse

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

24. Carte 24

    Question

    Parallel items in a series?

    Réponse

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

25. Carte 25

    Question

    Claim stronger than the evidence?

    Réponse

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

26. Carte 26

    Question

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

    Réponse

    Reasonable or believable.

27. Carte 27

    Question

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

    Réponse

    Addition. The second statement adds a related supporting point.

28. Carte 28

    Question

    Colon before an explanation or list?

    Réponse

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

29. Carte 29

    Question

    Claim versus evidence?

    Réponse

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

30. Carte 30

    Question

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

    Réponse

    Open to more than one interpretation.

31. Carte 31

    Question

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

    Réponse

    Replacement. The second statement substitutes one action for another.

32. Carte 32

    Question

    Count nouns versus mass nouns?

    Réponse

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

33. Carte 33

    Question

    Effect of a counterexample?

    Réponse

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

34. Carte 34

    Question

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

    Réponse

    Irregular and occasional.

35. Carte 35

    Question

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

    Réponse

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

36. Carte 36

    Question

    Essential clause punctuation?

    Réponse

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

37. Carte 37

    Question

    Correlation alone proves causation?

    Réponse

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

38. Carte 38

    Question

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

    Réponse

    Coming later in time.

39. Carte 39

    Question

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

    Réponse

    Restatement for clarity. The second statement rephrases the first.

40. Carte 40

    Question

    Verb tense across a paragraph?

    Réponse

    Keep the time frame consistent unless the timing actually changes.

41. Carte 41

    Question

    Missing information in a data claim?

    Réponse

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

42. Carte 42

    Question

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

    Réponse

    Keep or continue to hold.

43. Carte 43

    Question

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

    Réponse

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

44. Carte 44

    Question

    Coordinate adjectives?

    Réponse

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

45. Carte 45

    Question

    Two sources on the same event?

    Réponse

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

46. Carte 46

    Question

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

    Réponse

    Draw out or bring forth.

47. Carte 47

    Question

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

    Réponse

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

48. Carte 48

    Question

    Sentence fragment?

    Réponse

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

49. Carte 49

    Question

    Inference from a narrow sample?

    Réponse

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

50. Carte 50

    Question

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

    Réponse

    A limit or restriction.

51. Carte 51

    Question

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

    Réponse

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

52. Carte 52

    Question

    Conjunctive adverb between independent clauses?

    Réponse

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

53. Carte 53

    Question

    Most accurate summary?

    Réponse

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

54. Carte 54

    Question

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

    Réponse

    Complete and wide-ranging.

55. Carte 55

    Question

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

    Réponse

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

56. Carte 56

    Question

    Who versus whom?

    Réponse

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

57. Carte 57

    Question

    Evidence that best resolves a disagreement?

    Réponse

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

58. Carte 58

    Question

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

    Réponse

    Clearly different or separate.

59. Carte 59

    Question

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

    Réponse

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

60. Carte 60

    Question

    Comma before an introduced direct quotation?

    Réponse

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

61. Carte 61

    Question

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

    Réponse

    Limited or modified, rather than stated without conditions.

62. Carte 62

    Question

    Notes for a synthesis goal?

    Réponse

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

63. Carte 63

    Question

    Comma splice?

    Réponse

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

64. Carte 64

    Question

    Comma between subject and verb?

    Réponse

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

65. Carte 65

    Question

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

    Réponse

    No longer useful or current because something newer replaced it.

66. Carte 66

    Question

    Source attribution in a synthesis?

    Réponse

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

67. Carte 67

    Question

    Compound subject joined by “and”?

    Réponse

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

68. Carte 68

    Question

    Dangling opening modifier?

    Réponse

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

69. Carte 69

    Question

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

    Réponse

    Obtained from a source or calculation.

70. Carte 70

    Question

    Chronological synthesis?

    Réponse

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

71. Carte 71

    Question

    Plural noun ending in s: possessive form?

    Réponse

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

72. Carte 72

    Question

    Logical comparison?

    Réponse

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

73. Carte 73

    Question

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

    Réponse

    Publicly supports or argues for.

74. Carte 74

    Question

    Compare evidence from two studies?

    Réponse

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

75. Carte 75

    Question

    Colon after an incomplete lead-in?

    Réponse

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

76. Carte 76

    Question

    Number versus amount?

    Réponse

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

77. Carte 77

    Question

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

    Réponse

    Present or found almost everywhere.

78. Carte 78

    Question

    Synthesis that emphasizes a difference?

    Réponse

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

79. Carte 79

    Question

    Nonessential clause or phrase?

    Réponse

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

80. Carte 80

    Question

    Earlier of two past actions?

    Réponse

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

81. Carte 81

    Question

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

    Réponse

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

82. Carte 82

    Question

    Rhetorical goal: define a term?

    Réponse

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

83. Carte 83

    Question

    Cumulative adjectives?

    Réponse

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

84. Carte 84

    Question

    Run-on sentence?

    Réponse

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

85. Carte 85

    Question

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

    Réponse

    It illustrates the claim with an example.

86. Carte 86

    Question

    Introduce a quotation in a synthesis?

    Réponse

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

87. Carte 87

    Question

    Relative pronoun for people?

    Réponse

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

88. Carte 88

    Question

    Integrated quotation punctuation?

    Réponse

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

89. Carte 89

    Question

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

    Réponse

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

90. Carte 90

    Question

    Avoid redundancy in synthesis?

    Réponse

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

91. Carte 91

    Question

    Semicolon between two independent clauses?

    Réponse

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

92. Carte 92

    Question

    Comma in a compound predicate?

    Réponse

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

93. Carte 93

    Question

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

    Réponse

    It defines or clarifies the term.

94. Carte 94

    Question

    Combine two related sentences?

    Réponse

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

95. Carte 95

    Question

    Either/or subject agreement?

    Réponse

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

96. Carte 96

    Question

    Active versus passive voice?

    Réponse

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

97. Carte 97

    Question

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

    Réponse

    It presents an effect or consequence.

98. Carte 98

    Question

    Formal academic register?

    Réponse

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

99. Carte 99

    Question

    Its or it's?

    Réponse

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

100. Carte 100

     Question

     Adjective versus adverb?

     Réponse

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

101. Carte 101

     Question

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

     Réponse

     To inform or explain, not necessarily to persuade.

102. Carte 102

     Question

     Concise synthesis?

     Réponse

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

103. Carte 103

     Question

     Single dash for emphasis?

     Réponse

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

104. Carte 104

     Question

     Comma with direct address?

     Réponse

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

105. Carte 105

     Question

     Why acknowledge a limitation?

     Réponse

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

106. Carte 106

     Question

     Quantitative comparison in a synthesis?

     Réponse

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

107. Carte 107

     Question

     Each of the samples: verb number?

     Réponse

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

108. Carte 108

     Question

     Between versus among?

     Réponse

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

109. Carte 109

     Question

     Rhetorical question in an argument?

     Réponse

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

110. Carte 110

     Question

     Claim before or after support?

     Réponse

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

111. Carte 111

     Question

     Restrictive “that” versus nonrestrictive “which”?

     Réponse

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

112. Carte 112

     Question

     Present perfect use?

     Réponse

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

113. Carte 113

     Question

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

     Réponse

     They agree in conclusion but support it through different evidence.

114. Carte 114

     Question

     Group related ideas in a synthesis?

     Réponse

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

115. Carte 115

     Question

     Compound modifier before a noun?

     Réponse

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

116. Carte 116

     Question

     Affect or effect?

     Réponse

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

117. Carte 117

     Question

     Two texts offer incompatible explanations. Relationship?

     Réponse

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

118. Carte 118

     Question

     Replace a vague pronoun in synthesis?

     Réponse

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

119. Carte 119

     Question

     Comma-separated list?

     Réponse

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

120. Carte 120

     Question

     Main clause before a dependent clause?

     Réponse

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

121. Carte 121

     Question

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

     Réponse

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Carte 122

     Question

     Independent clauses joined with a coordinating conjunction?

     Réponse

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

123. Carte 123

     Question

     Introductory transition?

     Réponse

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

124. Carte 124

     Question

     Pronoun–antecedent agreement?

     Réponse

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

125. Carte 125

     Question

     Paired em dashes?

     Réponse

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

126. Carte 126

     Question

     How does new evidence relate to an earlier claim?

     Réponse

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

127. Carte 127

     Question

     Their, there, or they're?

     Réponse

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

128. Carte 128

     Question

     Good or well?

     Réponse

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

129. Carte 129

     Question

     Appositive naming the same noun?

     Réponse

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

130. Carte 130

     Question

     Why use an analogy?

     Réponse

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

131. Carte 131

     Question

     Than or then?

     Réponse

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

132. Carte 132

     Question

     Hypothetical contrary-to-fact “if” clause?

     Réponse

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

133. Carte 133

     Question

     Plural noun with no possession?

     Réponse

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

134. Carte 134

     Question

     Neutral, evidence-led wording indicates what tone?

     Réponse

     Objective. It emphasizes information rather than strong personal judgment.

135. Carte 135

     Question

     Complex list with internal commas?

     Réponse

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

136. Carte 136

     Question

     Ambiguous pronoun?

     Réponse

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

137. Carte 137

     Question

     Parentheses around nonessential information?

     Réponse

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

138. Carte 138

     Question

     Repeated doubt about the evidence indicates what tone?

     Réponse

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

139. Carte 139

     Question

     Superlative comparison?

     Réponse

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

140. Carte 140

     Question

     Pronoun after a preposition?

     Réponse

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

141. Carte 141

     Question

     Apostrophe in a contraction?

     Réponse

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

142. Carte 142

     Question

     Coordinate-adjective test?

     Réponse

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

143. Carte 143

     Question

     Double comparative?

     Réponse

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

144. Carte 144

     Question

     Lie or lay?

     Réponse

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

145. Carte 145

     Question

     Who's or whose?

     Réponse

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

146. Carte 146

     Question

     Standard comparison with “different”?

     Réponse

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

147. Carte 147

     Question

     Paired construction with two endpoints?

     Réponse

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

148. Carte 148

     Question

     Verb mood in a coordinated idea?

     Réponse

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

149. Carte 149

     Question

     Possessive pronoun apostrophe?

     Réponse

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

150. Carte 150

     Question

     Comma between a preposition and its object?

     Réponse

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

     

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     Digital SAT Flashcards: Math, Grammar & Words in Context

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151. Carte 151

     Question

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

     Réponse

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

152. Carte 152

     Question

     Product of powers with the same base?

     Réponse

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

153. Carte 153

     Question

     Unit rate?

     Réponse

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

154. Carte 154

     Question

     Rectangle area?

     Réponse

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

155. Carte 155

     Question

     Slope from two points?

     Réponse

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

156. Carte 156

     Question

     Quotient of powers with the same base?

     Réponse

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Carte 157

     Question

     Conversion factor setup?

     Réponse

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

158. Carte 158

     Question

     Triangle area?

     Réponse

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

159. Carte 159

     Question

     Slope-intercept form?

     Réponse

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

160. Carte 160

     Question

     Power raised to a power?

     Réponse

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

161. Carte 161

     Question

     Dimensional analysis check?

     Réponse

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

162. Carte 162

     Question

     Trapezoid area?

     Réponse

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

163. Carte 163

     Question

     Point-slope form?

     Réponse

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

164. Carte 164

     Question

     Negative exponent?

     Réponse

     $a^{-n}=1/a^n$ for $a≠0$.

165. Carte 165

     Question

     Constant of proportionality in $y=kx$?

     Réponse

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

166. Carte 166

     Question

     Circle area?

     Réponse

     $A=πr^2$.

167. Carte 167

     Question

     Intercepts from $Ax+By=C$?

     Réponse

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

168. Carte 168

     Question

     Fractional exponent?

     Réponse

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

169. Carte 169

     Question

     Scale drawing length?

     Réponse

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

170. Carte 170

     Question

     Circle circumference?

     Réponse

     $C=2πr=πd$.

171. Carte 171

     Question

     Parallel nonvertical lines: slope relationship?

     Réponse

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

172. Carte 172

     Question

     Difference of squares?

     Réponse

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

173. Carte 173

     Question

     Percent change?

     Réponse

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

174. Carte 174

     Question

     Arc length from central angle $θ$ in degrees?

     Réponse

     $L=(θ/360)(2πr)$.

175. Carte 175

     Question

     Perpendicular nonvertical lines: slope relationship?

     Réponse

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

176. Carte 176

     Question

     Perfect-square trinomial pattern?

     Réponse

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

177. Carte 177

     Question

     Increase by $r$ percent: multiplier?

     Réponse

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

178. Carte 178

     Question

     Sector area from central angle $θ$ in degrees?

     Réponse

     $A=(θ/360)(πr^2)$.

179. Carte 179

     Question

     x-intercept of a graph?

     Réponse

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

180. Carte 180

     Question

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

     Réponse

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

181. Carte 181

     Question

     Original value after a 20 percent increase to 84?

     Réponse

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

182. Carte 182

     Question

     Triangle interior-angle sum?

     Réponse

     $180°$.

183. Carte 183

     Question

     y-intercept of a graph?

     Réponse

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

184. Carte 184

     Question

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

     Réponse

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

185. Carte 185

     Question

     Weighted average?

     Réponse

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

186. Carte 186

     Question

     Exterior angle of a triangle?

     Réponse

     It equals the sum of the two remote interior angles.

187. Carte 187

     Question

     Line through two points?

     Réponse

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

188. Carte 188

     Question

     Quadratic formula?

     Réponse

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

189. Carte 189

     Question

     Arithmetic mean?

     Réponse

     Add all values and divide by the number of values.

190. Carte 190

     Question

     Parallel lines cut by a transversal: alternate interior angles?

     Réponse

     They are congruent.

191. Carte 191

     Question

     Slope's units in context?

     Réponse

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

192. Carte 192

     Question

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

     Réponse

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

193. Carte 193

     Question

     Median?

     Réponse

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

194. Carte 194

     Question

     Similar triangles: corresponding sides?

     Réponse

     They are proportional. Match sides opposite equal angles.

195. Carte 195

     Question

     Direct variation model?

     Réponse

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

196. Carte 196

     Question

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

     Réponse

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

197. Carte 197

     Question

     Range of a data set?

     Réponse

     Maximum minus minimum.

198. Carte 198

     Question

     Scale factor $k$: area factor?

     Réponse

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

199. Carte 199

     Question

     Solution of a two-line system?

     Réponse

     The intersection point, whose coordinates satisfy both equations.

200. Carte 200

     Question

     Vertex form of a quadratic?

     Réponse

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

201. Carte 201

     Question

     Interquartile range?

     Réponse

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

202. Carte 202

     Question

     Pythagorean theorem?

     Réponse

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

203. Carte 203

     Question

     Substitution in a system?

     Réponse

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

204. Carte 204

     Question

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

     Réponse

     $x=h$.

205. Carte 205

     Question

     Larger standard deviation means what?

     Réponse

     The data are more spread out around the mean.

206. Carte 206

     Question

     45°-45°-90° side ratio?

     Réponse

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

207. Carte 207

     Question

     Elimination in a system?

     Réponse

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

208. Carte 208

     Question

     Completing the square?

     Réponse

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

209. Carte 209

     Question

     Effect of a high outlier on the mean?

     Réponse

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

210. Carte 210

     Question

     30°-60°-90° side ratio?

     Réponse

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

211. Carte 211

     Question

     Parallel lines in a system?

     Réponse

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

212. Carte 212

     Question

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

     Réponse

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

213. Carte 213

     Question

     Add the same constant to every data value: effect?

     Réponse

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

214. Carte 214

     Question

     Right-triangle sine?

     Réponse

     Sine of $θ$ equals opposite over hypotenuse.

215. Carte 215

     Question

     Same line written two ways in a system?

     Réponse

     Infinitely many solutions. Simplifying either equation produces the other.

216. Carte 216

     Question

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

     Réponse

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

217. Carte 217

     Question

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

     Réponse

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

218. Carte 218

     Question

     Right-triangle cosine?

     Réponse

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Carte 219

     Question

     Multiply or divide an inequality by a negative number?

     Réponse

     Reverse the inequality sign.

220. Carte 220

     Question

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

     Réponse

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

221. Carte 221

     Question

     Joint probability from a two-way table?

     Réponse

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

222. Carte 222

     Question

     Right-triangle tangent?

     Réponse

     Tangent of $θ$ equals opposite over adjacent.

223. Carte 223

     Question

     Compound inequality with “and”?

     Réponse

     Use the intersection: values that satisfy both inequalities.

224. Carte 224

     Question

     Even degree with positive leading coefficient: end behavior?

     Réponse

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

225. Carte 225

     Question

     Conditional probability $P(A|B)$?

     Réponse

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

226. Carte 226

     Question

     Complementary acute angles: sine–cosine relationship?

     Réponse

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

227. Carte 227

     Question

     Compound inequality with “or”?

     Réponse

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

228. Carte 228

     Question

     Odd degree with positive leading coefficient: end behavior?

     Réponse

     The left end falls and the right end rises.

229. Carte 229

     Question

     Independent events $A$ and $B$?

     Réponse

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

230. Carte 230

     Question

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

     Réponse

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Carte 231

     Question

     Solve $|x-a|=b$ for $b≥0$.

     Réponse

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

232. Carte 232

     Question

     Exponential growth model?

     Réponse

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

233. Carte 233

     Question

     Mutually exclusive events?

     Réponse

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

234. Carte 234

     Question

     Midpoint of two points?

     Réponse

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

235. Carte 235

     Question

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

     Réponse

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

236. Carte 236

     Question

     Exponential decay model?

     Réponse

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

237. Carte 237

     Question

     Complement rule?

     Réponse

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

238. Carte 238

     Question

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

     Réponse

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

239. Carte 239

     Question

     Evaluate $f(a)$?

     Réponse

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

240. Carte 240

     Question

     Growth factor 1.08: percent growth rate?

     Réponse

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

241. Carte 241

     Question

     Representative random sample permits what conclusion?

     Réponse

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

242. Carte 242

     Question

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

     Réponse

     $r=√R$, provided $R>0$.

243. Carte 243

     Question

     Linear table: constant slope check?

     Réponse

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

244. Carte 244

     Question

     Decay factor 0.73: percent decrease?

     Réponse

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

245. Carte 245

     Question

     Random assignment permits what causal claim?

     Réponse

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

246. Carte 246

     Question

     Radius and tangent at the contact point?

     Réponse

     They are perpendicular.

247. Carte 247

     Question

     Positive slope means what for a linear function?

     Réponse

     The output increases as the input increases.

248. Carte 248

     Question

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

     Réponse

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

249. Carte 249

     Question

     Observational study supports causation?

     Réponse

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

250. Carte 250

     Question

     Rectangular-prism volume?

     Réponse

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

251. Carte 251

     Question

     Arithmetic sequence common difference?

     Réponse

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

252. Carte 252

     Question

     Compound interest formula?

     Réponse

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

253. Carte 253

     Question

     Larger random sample: effect on margin of error?

     Réponse

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

254. Carte 254

     Question

     Cylinder volume?

     Réponse

     $V=πr^2h$.

255. Carte 255

     Question

     Arithmetic sequence nth term?

     Réponse

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

256. Carte 256

     Question

     Rational expression: first domain check?

     Réponse

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

257. Carte 257

     Question

     Slope of a line of best fit?

     Réponse

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

258. Carte 258

     Question

     Cone volume?

     Réponse

     $V=(1/3)πr^2h$.

259. Carte 259

     Question

     Solve a literal equation for one variable?

     Réponse

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

260. Carte 260

     Question

     Why check rational-equation solutions?

     Réponse

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

261. Carte 261

     Question

     Residual?

     Réponse

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

262. Carte 262

     Question

     Sphere volume?

     Réponse

     $V=(4/3)πr^3$.

263. Carte 263

     Question

     Boundary for a two-variable linear inequality?

     Réponse

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

264. Carte 264

     Question

     Why check a solution after squaring both sides?

     Réponse

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

265. Carte 265

     Question

     Positive correlation?

     Réponse

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

266. Carte 266

     Question

     Rectangular-prism surface area?

     Réponse

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

267. Carte 267

     Question

     Check a proposed system solution?

     Réponse

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

268. Carte 268

     Question

     Simplify $√72$.

     Réponse

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

269. Carte 269

     Question

     Extrapolation risk?

     Réponse

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

270. Carte 270

     Question

     Area scale factor when lengths double?

     Réponse

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

271. Carte 271

     Question

     Horizontal line slope?

     Réponse

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

272. Carte 272

     Question

     Inverse function setup?

     Réponse

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

273. Carte 273

     Question

     Percentage points versus percent change?

     Réponse

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

274. Carte 274

     Question

     y-intercept in a context?

     Réponse

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

275. Carte 275

     Question

     Quadratic maximum or minimum from vertex form?

     Réponse

     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. Carte 276

     Question

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

     Réponse

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

277. Carte 277

     Question

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

     Réponse

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

278. Carte 278

     Question

     Population versus sample?

     Réponse

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

279. Carte 279

     Question

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

     Réponse

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

280. Carte 280

     Question

     Function composition $(f∘g)(x)$?

     Réponse

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

281. Carte 281

     Question

     Density?

     Réponse

     Mass divided by volume. Keep the units consistent.

282. Carte 282

     Question

     Vertical line slope?

     Réponse

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

283. Carte 283

     Question

     Nonlinear system with one equation solved for $y$?

     Réponse

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

284. Carte 284

     Question

     Weighted percentage across unequal groups?

     Réponse

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

285. Carte 285

     Question

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

     Réponse

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

286. Carte 286

     Question

     Cancel a common factor in a rational expression?

     Réponse

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

287. Carte 287

     Question

     Solve a linear equation containing fractions?

     Réponse

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

288. Carte 288

     Question

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

     Réponse

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

289. Carte 289

     Question

     Rate units check?

     Réponse

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

290. Carte 290

     Question

     Strict versus inclusive inequality endpoint?

     Réponse

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

291. Carte 291

     Question

     Even-multiplicity zero on a graph?

     Réponse

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

292. Carte 292

     Question

     System word problem: first setup step?

     Réponse

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

293. Carte 293

     Question

     When does a quadratic have exactly one real solution?

     Réponse

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

294. Carte 294

     Question

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

     Réponse

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

295. Carte 295

     Question

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

     Réponse

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

296. Carte 296

     Question

     Graph of $-f(x)$?

     Réponse

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

297. Carte 297

     Question

     Three consecutive integers starting with $n$?

     Réponse

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

298. Carte 298

     Question

     Line–parabola intersections from a substituted quadratic?

     Réponse

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

299. Carte 299

     Question

     Linear equation with no solution: coefficient pattern?

     Réponse

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

300. Carte 300

     Question

     Zeros of a function on its graph?

     Réponse

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

300 cartes

Digital SAT Flashcards: Math, Grammar & Words in Context

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