Digital SAT Flashcards: Math, Grammar & Words in Context

Cards in this deck

1. Card 1

   Question

   Central idea of a passage?

   Answer

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

2. Card 2

   Question

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

   Answer

   Reduced. The trees made the heat less severe.

3. Card 3

   Question

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

   Answer

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

4. Card 4

   Question

   Three standard joins for two independent clauses?

   Answer

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

5. Card 5

   Question

   Best supporting detail?

   Answer

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

6. Card 6

   Question

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

   Answer

   Confirmed with supporting evidence.

7. Card 7

   Question

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

   Answer

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

8. Card 8

   Question

   Introductory dependent clause before a main clause?

   Answer

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

9. Card 9

   Question

   Valid inference?

   Answer

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

10. Card 10

    Question

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

    Answer

    Provisional or not yet certain.

11. Card 11

    Question

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

    Answer

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

12. Card 12

    Question

    Singular subject with an intervening prepositional phrase?

    Answer

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

13. Card 13

    Question

    Strongest textual evidence?

    Answer

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

14. Card 14

    Question

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

    Answer

    So small that it is not important.

15. Card 15

    Question

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

    Answer

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

16. Card 16

    Question

    Opening modifier placement?

    Answer

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

17. Card 17

    Question

    Quantitative evidence for a claim?

    Answer

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

18. Card 18

    Question

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

    Answer

    Traditional or commonly accepted.

19. Card 19

    Question

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

    Answer

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

20. Card 20

    Question

    Singular possessive noun?

    Answer

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

21. Card 21

    Question

    Trend in a table or graph?

    Answer

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

22. Card 22

    Question

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

    Answer

    New or original in this context.

23. Card 23

    Question

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

    Answer

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

24. Card 24

    Question

    Parallel items in a series?

    Answer

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

25. Card 25

    Question

    Claim stronger than the evidence?

    Answer

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

26. Card 26

    Question

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

    Answer

    Reasonable or believable.

27. Card 27

    Question

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

    Answer

    Addition. The second statement adds a related supporting point.

28. Card 28

    Question

    Colon before an explanation or list?

    Answer

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

29. Card 29

    Question

    Claim versus evidence?

    Answer

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

30. Card 30

    Question

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

    Answer

    Open to more than one interpretation.

31. Card 31

    Question

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

    Answer

    Replacement. The second statement substitutes one action for another.

32. Card 32

    Question

    Count nouns versus mass nouns?

    Answer

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

33. Card 33

    Question

    Effect of a counterexample?

    Answer

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

34. Card 34

    Question

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

    Answer

    Irregular and occasional.

35. Card 35

    Question

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

    Answer

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

36. Card 36

    Question

    Essential clause punctuation?

    Answer

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

37. Card 37

    Question

    Correlation alone proves causation?

    Answer

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

38. Card 38

    Question

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

    Answer

    Coming later in time.

39. Card 39

    Question

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

    Answer

    Restatement for clarity. The second statement rephrases the first.

40. Card 40

    Question

    Verb tense across a paragraph?

    Answer

    Keep the time frame consistent unless the timing actually changes.

41. Card 41

    Question

    Missing information in a data claim?

    Answer

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

42. Card 42

    Question

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

    Answer

    Keep or continue to hold.

43. Card 43

    Question

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

    Answer

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

44. Card 44

    Question

    Coordinate adjectives?

    Answer

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

45. Card 45

    Question

    Two sources on the same event?

    Answer

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

46. Card 46

    Question

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

    Answer

    Draw out or bring forth.

47. Card 47

    Question

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

    Answer

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

48. Card 48

    Question

    Sentence fragment?

    Answer

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

49. Card 49

    Question

    Inference from a narrow sample?

    Answer

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

50. Card 50

    Question

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

    Answer

    A limit or restriction.

51. Card 51

    Question

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

    Answer

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

52. Card 52

    Question

    Conjunctive adverb between independent clauses?

    Answer

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

53. Card 53

    Question

    Most accurate summary?

    Answer

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

54. Card 54

    Question

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

    Answer

    Complete and wide-ranging.

55. Card 55

    Question

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

    Answer

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

56. Card 56

    Question

    Who versus whom?

    Answer

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

57. Card 57

    Question

    Evidence that best resolves a disagreement?

    Answer

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

58. Card 58

    Question

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

    Answer

    Clearly different or separate.

59. Card 59

    Question

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

    Answer

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

60. Card 60

    Question

    Comma before an introduced direct quotation?

    Answer

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

61. Card 61

    Question

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

    Answer

    Limited or modified, rather than stated without conditions.

62. Card 62

    Question

    Notes for a synthesis goal?

    Answer

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

63. Card 63

    Question

    Comma splice?

    Answer

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

64. Card 64

    Question

    Comma between subject and verb?

    Answer

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

65. Card 65

    Question

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

    Answer

    No longer useful or current because something newer replaced it.

66. Card 66

    Question

    Source attribution in a synthesis?

    Answer

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

67. Card 67

    Question

    Compound subject joined by “and”?

    Answer

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

68. Card 68

    Question

    Dangling opening modifier?

    Answer

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

69. Card 69

    Question

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

    Answer

    Obtained from a source or calculation.

70. Card 70

    Question

    Chronological synthesis?

    Answer

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

71. Card 71

    Question

    Plural noun ending in s: possessive form?

    Answer

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

72. Card 72

    Question

    Logical comparison?

    Answer

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

73. Card 73

    Question

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

    Answer

    Publicly supports or argues for.

74. Card 74

    Question

    Compare evidence from two studies?

    Answer

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

75. Card 75

    Question

    Colon after an incomplete lead-in?

    Answer

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

76. Card 76

    Question

    Number versus amount?

    Answer

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

77. Card 77

    Question

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

    Answer

    Present or found almost everywhere.

78. Card 78

    Question

    Synthesis that emphasizes a difference?

    Answer

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

79. Card 79

    Question

    Nonessential clause or phrase?

    Answer

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

80. Card 80

    Question

    Earlier of two past actions?

    Answer

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

81. Card 81

    Question

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

    Answer

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

82. Card 82

    Question

    Rhetorical goal: define a term?

    Answer

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

83. Card 83

    Question

    Cumulative adjectives?

    Answer

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

84. Card 84

    Question

    Run-on sentence?

    Answer

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

85. Card 85

    Question

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

    Answer

    It illustrates the claim with an example.

86. Card 86

    Question

    Introduce a quotation in a synthesis?

    Answer

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

87. Card 87

    Question

    Relative pronoun for people?

    Answer

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

88. Card 88

    Question

    Integrated quotation punctuation?

    Answer

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

89. Card 89

    Question

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

    Answer

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

90. Card 90

    Question

    Avoid redundancy in synthesis?

    Answer

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

91. Card 91

    Question

    Semicolon between two independent clauses?

    Answer

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

92. Card 92

    Question

    Comma in a compound predicate?

    Answer

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

93. Card 93

    Question

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

    Answer

    It defines or clarifies the term.

94. Card 94

    Question

    Combine two related sentences?

    Answer

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

95. Card 95

    Question

    Either/or subject agreement?

    Answer

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

96. Card 96

    Question

    Active versus passive voice?

    Answer

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

97. Card 97

    Question

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

    Answer

    It presents an effect or consequence.

98. Card 98

    Question

    Formal academic register?

    Answer

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

99. Card 99

    Question

    Its or it's?

    Answer

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

100. Card 100

     Question

     Adjective versus adverb?

     Answer

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

101. Card 101

     Question

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

     Answer

     To inform or explain, not necessarily to persuade.

102. Card 102

     Question

     Concise synthesis?

     Answer

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

103. Card 103

     Question

     Single dash for emphasis?

     Answer

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

104. Card 104

     Question

     Comma with direct address?

     Answer

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

105. Card 105

     Question

     Why acknowledge a limitation?

     Answer

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

106. Card 106

     Question

     Quantitative comparison in a synthesis?

     Answer

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

107. Card 107

     Question

     Each of the samples: verb number?

     Answer

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

108. Card 108

     Question

     Between versus among?

     Answer

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

109. Card 109

     Question

     Rhetorical question in an argument?

     Answer

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

110. Card 110

     Question

     Claim before or after support?

     Answer

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

111. Card 111

     Question

     Restrictive “that” versus nonrestrictive “which”?

     Answer

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

112. Card 112

     Question

     Present perfect use?

     Answer

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

113. Card 113

     Question

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

     Answer

     They agree in conclusion but support it through different evidence.

114. Card 114

     Question

     Group related ideas in a synthesis?

     Answer

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

115. Card 115

     Question

     Compound modifier before a noun?

     Answer

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

116. Card 116

     Question

     Affect or effect?

     Answer

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

117. Card 117

     Question

     Two texts offer incompatible explanations. Relationship?

     Answer

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

118. Card 118

     Question

     Replace a vague pronoun in synthesis?

     Answer

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

119. Card 119

     Question

     Comma-separated list?

     Answer

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

120. Card 120

     Question

     Main clause before a dependent clause?

     Answer

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

121. Card 121

     Question

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

     Answer

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Card 122

     Question

     Independent clauses joined with a coordinating conjunction?

     Answer

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

123. Card 123

     Question

     Introductory transition?

     Answer

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

124. Card 124

     Question

     Pronoun–antecedent agreement?

     Answer

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

125. Card 125

     Question

     Paired em dashes?

     Answer

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

126. Card 126

     Question

     How does new evidence relate to an earlier claim?

     Answer

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

127. Card 127

     Question

     Their, there, or they're?

     Answer

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

128. Card 128

     Question

     Good or well?

     Answer

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

129. Card 129

     Question

     Appositive naming the same noun?

     Answer

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

130. Card 130

     Question

     Why use an analogy?

     Answer

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

131. Card 131

     Question

     Than or then?

     Answer

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

132. Card 132

     Question

     Hypothetical contrary-to-fact “if” clause?

     Answer

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

133. Card 133

     Question

     Plural noun with no possession?

     Answer

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

134. Card 134

     Question

     Neutral, evidence-led wording indicates what tone?

     Answer

     Objective. It emphasizes information rather than strong personal judgment.

135. Card 135

     Question

     Complex list with internal commas?

     Answer

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

136. Card 136

     Question

     Ambiguous pronoun?

     Answer

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

137. Card 137

     Question

     Parentheses around nonessential information?

     Answer

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

138. Card 138

     Question

     Repeated doubt about the evidence indicates what tone?

     Answer

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

139. Card 139

     Question

     Superlative comparison?

     Answer

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

140. Card 140

     Question

     Pronoun after a preposition?

     Answer

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

141. Card 141

     Question

     Apostrophe in a contraction?

     Answer

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

142. Card 142

     Question

     Coordinate-adjective test?

     Answer

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

143. Card 143

     Question

     Double comparative?

     Answer

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

144. Card 144

     Question

     Lie or lay?

     Answer

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

145. Card 145

     Question

     Who's or whose?

     Answer

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

146. Card 146

     Question

     Standard comparison with “different”?

     Answer

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

147. Card 147

     Question

     Paired construction with two endpoints?

     Answer

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

148. Card 148

     Question

     Verb mood in a coordinated idea?

     Answer

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

149. Card 149

     Question

     Possessive pronoun apostrophe?

     Answer

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

150. Card 150

     Question

     Comma between a preposition and its object?

     Answer

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

     

     300 cards

     Digital SAT Flashcards: Math, Grammar & Words in Context

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151. Card 151

     Question

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

     Answer

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

152. Card 152

     Question

     Product of powers with the same base?

     Answer

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

153. Card 153

     Question

     Unit rate?

     Answer

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

154. Card 154

     Question

     Rectangle area?

     Answer

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

155. Card 155

     Question

     Slope from two points?

     Answer

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

156. Card 156

     Question

     Quotient of powers with the same base?

     Answer

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Card 157

     Question

     Conversion factor setup?

     Answer

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

158. Card 158

     Question

     Triangle area?

     Answer

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

159. Card 159

     Question

     Slope-intercept form?

     Answer

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

160. Card 160

     Question

     Power raised to a power?

     Answer

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

161. Card 161

     Question

     Dimensional analysis check?

     Answer

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

162. Card 162

     Question

     Trapezoid area?

     Answer

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

163. Card 163

     Question

     Point-slope form?

     Answer

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

164. Card 164

     Question

     Negative exponent?

     Answer

     $a^{-n}=1/a^n$ for $a≠0$.

165. Card 165

     Question

     Constant of proportionality in $y=kx$?

     Answer

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

166. Card 166

     Question

     Circle area?

     Answer

     $A=πr^2$.

167. Card 167

     Question

     Intercepts from $Ax+By=C$?

     Answer

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

168. Card 168

     Question

     Fractional exponent?

     Answer

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

169. Card 169

     Question

     Scale drawing length?

     Answer

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

170. Card 170

     Question

     Circle circumference?

     Answer

     $C=2πr=πd$.

171. Card 171

     Question

     Parallel nonvertical lines: slope relationship?

     Answer

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

172. Card 172

     Question

     Difference of squares?

     Answer

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

173. Card 173

     Question

     Percent change?

     Answer

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

174. Card 174

     Question

     Arc length from central angle $θ$ in degrees?

     Answer

     $L=(θ/360)(2πr)$.

175. Card 175

     Question

     Perpendicular nonvertical lines: slope relationship?

     Answer

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

176. Card 176

     Question

     Perfect-square trinomial pattern?

     Answer

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

177. Card 177

     Question

     Increase by $r$ percent: multiplier?

     Answer

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

178. Card 178

     Question

     Sector area from central angle $θ$ in degrees?

     Answer

     $A=(θ/360)(πr^2)$.

179. Card 179

     Question

     x-intercept of a graph?

     Answer

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

180. Card 180

     Question

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

     Answer

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

181. Card 181

     Question

     Original value after a 20 percent increase to 84?

     Answer

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

182. Card 182

     Question

     Triangle interior-angle sum?

     Answer

     $180°$.

183. Card 183

     Question

     y-intercept of a graph?

     Answer

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

184. Card 184

     Question

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

     Answer

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

185. Card 185

     Question

     Weighted average?

     Answer

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

186. Card 186

     Question

     Exterior angle of a triangle?

     Answer

     It equals the sum of the two remote interior angles.

187. Card 187

     Question

     Line through two points?

     Answer

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

188. Card 188

     Question

     Quadratic formula?

     Answer

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

189. Card 189

     Question

     Arithmetic mean?

     Answer

     Add all values and divide by the number of values.

190. Card 190

     Question

     Parallel lines cut by a transversal: alternate interior angles?

     Answer

     They are congruent.

191. Card 191

     Question

     Slope's units in context?

     Answer

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

192. Card 192

     Question

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

     Answer

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

193. Card 193

     Question

     Median?

     Answer

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

194. Card 194

     Question

     Similar triangles: corresponding sides?

     Answer

     They are proportional. Match sides opposite equal angles.

195. Card 195

     Question

     Direct variation model?

     Answer

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

196. Card 196

     Question

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

     Answer

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

197. Card 197

     Question

     Range of a data set?

     Answer

     Maximum minus minimum.

198. Card 198

     Question

     Scale factor $k$: area factor?

     Answer

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

199. Card 199

     Question

     Solution of a two-line system?

     Answer

     The intersection point, whose coordinates satisfy both equations.

200. Card 200

     Question

     Vertex form of a quadratic?

     Answer

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

201. Card 201

     Question

     Interquartile range?

     Answer

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

202. Card 202

     Question

     Pythagorean theorem?

     Answer

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

203. Card 203

     Question

     Substitution in a system?

     Answer

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

204. Card 204

     Question

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

     Answer

     $x=h$.

205. Card 205

     Question

     Larger standard deviation means what?

     Answer

     The data are more spread out around the mean.

206. Card 206

     Question

     45°-45°-90° side ratio?

     Answer

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

207. Card 207

     Question

     Elimination in a system?

     Answer

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

208. Card 208

     Question

     Completing the square?

     Answer

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

209. Card 209

     Question

     Effect of a high outlier on the mean?

     Answer

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

210. Card 210

     Question

     30°-60°-90° side ratio?

     Answer

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

211. Card 211

     Question

     Parallel lines in a system?

     Answer

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

212. Card 212

     Question

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

     Answer

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

213. Card 213

     Question

     Add the same constant to every data value: effect?

     Answer

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

214. Card 214

     Question

     Right-triangle sine?

     Answer

     Sine of $θ$ equals opposite over hypotenuse.

215. Card 215

     Question

     Same line written two ways in a system?

     Answer

     Infinitely many solutions. Simplifying either equation produces the other.

216. Card 216

     Question

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

     Answer

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

217. Card 217

     Question

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

     Answer

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

218. Card 218

     Question

     Right-triangle cosine?

     Answer

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Card 219

     Question

     Multiply or divide an inequality by a negative number?

     Answer

     Reverse the inequality sign.

220. Card 220

     Question

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

     Answer

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

221. Card 221

     Question

     Joint probability from a two-way table?

     Answer

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

222. Card 222

     Question

     Right-triangle tangent?

     Answer

     Tangent of $θ$ equals opposite over adjacent.

223. Card 223

     Question

     Compound inequality with “and”?

     Answer

     Use the intersection: values that satisfy both inequalities.

224. Card 224

     Question

     Even degree with positive leading coefficient: end behavior?

     Answer

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

225. Card 225

     Question

     Conditional probability $P(A|B)$?

     Answer

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

226. Card 226

     Question

     Complementary acute angles: sine–cosine relationship?

     Answer

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

227. Card 227

     Question

     Compound inequality with “or”?

     Answer

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

228. Card 228

     Question

     Odd degree with positive leading coefficient: end behavior?

     Answer

     The left end falls and the right end rises.

229. Card 229

     Question

     Independent events $A$ and $B$?

     Answer

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

230. Card 230

     Question

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

     Answer

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Card 231

     Question

     Solve $|x-a|=b$ for $b≥0$.

     Answer

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

232. Card 232

     Question

     Exponential growth model?

     Answer

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

233. Card 233

     Question

     Mutually exclusive events?

     Answer

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

234. Card 234

     Question

     Midpoint of two points?

     Answer

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

235. Card 235

     Question

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

     Answer

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

236. Card 236

     Question

     Exponential decay model?

     Answer

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

237. Card 237

     Question

     Complement rule?

     Answer

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

238. Card 238

     Question

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

     Answer

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

239. Card 239

     Question

     Evaluate $f(a)$?

     Answer

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

240. Card 240

     Question

     Growth factor 1.08: percent growth rate?

     Answer

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

241. Card 241

     Question

     Representative random sample permits what conclusion?

     Answer

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

242. Card 242

     Question

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

     Answer

     $r=√R$, provided $R>0$.

243. Card 243

     Question

     Linear table: constant slope check?

     Answer

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

244. Card 244

     Question

     Decay factor 0.73: percent decrease?

     Answer

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

245. Card 245

     Question

     Random assignment permits what causal claim?

     Answer

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

246. Card 246

     Question

     Radius and tangent at the contact point?

     Answer

     They are perpendicular.

247. Card 247

     Question

     Positive slope means what for a linear function?

     Answer

     The output increases as the input increases.

248. Card 248

     Question

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

     Answer

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

249. Card 249

     Question

     Observational study supports causation?

     Answer

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

250. Card 250

     Question

     Rectangular-prism volume?

     Answer

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

251. Card 251

     Question

     Arithmetic sequence common difference?

     Answer

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

252. Card 252

     Question

     Compound interest formula?

     Answer

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

253. Card 253

     Question

     Larger random sample: effect on margin of error?

     Answer

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

254. Card 254

     Question

     Cylinder volume?

     Answer

     $V=πr^2h$.

255. Card 255

     Question

     Arithmetic sequence nth term?

     Answer

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

256. Card 256

     Question

     Rational expression: first domain check?

     Answer

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

257. Card 257

     Question

     Slope of a line of best fit?

     Answer

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

258. Card 258

     Question

     Cone volume?

     Answer

     $V=(1/3)πr^2h$.

259. Card 259

     Question

     Solve a literal equation for one variable?

     Answer

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

260. Card 260

     Question

     Why check rational-equation solutions?

     Answer

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

261. Card 261

     Question

     Residual?

     Answer

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

262. Card 262

     Question

     Sphere volume?

     Answer

     $V=(4/3)πr^3$.

263. Card 263

     Question

     Boundary for a two-variable linear inequality?

     Answer

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

264. Card 264

     Question

     Why check a solution after squaring both sides?

     Answer

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

265. Card 265

     Question

     Positive correlation?

     Answer

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

266. Card 266

     Question

     Rectangular-prism surface area?

     Answer

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

267. Card 267

     Question

     Check a proposed system solution?

     Answer

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

268. Card 268

     Question

     Simplify $√72$.

     Answer

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

269. Card 269

     Question

     Extrapolation risk?

     Answer

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

270. Card 270

     Question

     Area scale factor when lengths double?

     Answer

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

271. Card 271

     Question

     Horizontal line slope?

     Answer

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

272. Card 272

     Question

     Inverse function setup?

     Answer

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

273. Card 273

     Question

     Percentage points versus percent change?

     Answer

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

274. Card 274

     Question

     y-intercept in a context?

     Answer

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

275. Card 275

     Question

     Quadratic maximum or minimum from vertex form?

     Answer

     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. Card 276

     Question

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

     Answer

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

277. Card 277

     Question

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

     Answer

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

278. Card 278

     Question

     Population versus sample?

     Answer

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

279. Card 279

     Question

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

     Answer

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

280. Card 280

     Question

     Function composition $(f∘g)(x)$?

     Answer

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

281. Card 281

     Question

     Density?

     Answer

     Mass divided by volume. Keep the units consistent.

282. Card 282

     Question

     Vertical line slope?

     Answer

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

283. Card 283

     Question

     Nonlinear system with one equation solved for $y$?

     Answer

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

284. Card 284

     Question

     Weighted percentage across unequal groups?

     Answer

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

285. Card 285

     Question

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

     Answer

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

286. Card 286

     Question

     Cancel a common factor in a rational expression?

     Answer

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

287. Card 287

     Question

     Solve a linear equation containing fractions?

     Answer

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

288. Card 288

     Question

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

     Answer

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

289. Card 289

     Question

     Rate units check?

     Answer

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

290. Card 290

     Question

     Strict versus inclusive inequality endpoint?

     Answer

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

291. Card 291

     Question

     Even-multiplicity zero on a graph?

     Answer

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

292. Card 292

     Question

     System word problem: first setup step?

     Answer

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

293. Card 293

     Question

     When does a quadratic have exactly one real solution?

     Answer

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

294. Card 294

     Question

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

     Answer

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

295. Card 295

     Question

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

     Answer

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

296. Card 296

     Question

     Graph of $-f(x)$?

     Answer

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

297. Card 297

     Question

     Three consecutive integers starting with $n$?

     Answer

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

298. Card 298

     Question

     Line–parabola intersections from a substituted quadratic?

     Answer

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

299. Card 299

     Question

     Linear equation with no solution: coefficient pattern?

     Answer

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

300. Card 300

     Question

     Zeros of a function on its graph?

     Answer

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

300 cards

Digital SAT Flashcards: Math, Grammar & Words in Context

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