Digital SAT Flashcards: Math, Grammar & Words in Context

Karty w tej talii

1. Karta 1

   Pytanie

   Central idea of a passage?

   Odpowiedź

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

2. Karta 2

   Pytanie

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

   Odpowiedź

   Reduced. The trees made the heat less severe.

3. Karta 3

   Pytanie

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

   Odpowiedź

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

4. Karta 4

   Pytanie

   Three standard joins for two independent clauses?

   Odpowiedź

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

5. Karta 5

   Pytanie

   Best supporting detail?

   Odpowiedź

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

6. Karta 6

   Pytanie

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

   Odpowiedź

   Confirmed with supporting evidence.

7. Karta 7

   Pytanie

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

   Odpowiedź

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

8. Karta 8

   Pytanie

   Introductory dependent clause before a main clause?

   Odpowiedź

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

9. Karta 9

   Pytanie

   Valid inference?

   Odpowiedź

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

10. Karta 10

    Pytanie

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

    Odpowiedź

    Provisional or not yet certain.

11. Karta 11

    Pytanie

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

    Odpowiedź

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

12. Karta 12

    Pytanie

    Singular subject with an intervening prepositional phrase?

    Odpowiedź

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

13. Karta 13

    Pytanie

    Strongest textual evidence?

    Odpowiedź

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

14. Karta 14

    Pytanie

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

    Odpowiedź

    So small that it is not important.

15. Karta 15

    Pytanie

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

    Odpowiedź

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

16. Karta 16

    Pytanie

    Opening modifier placement?

    Odpowiedź

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

17. Karta 17

    Pytanie

    Quantitative evidence for a claim?

    Odpowiedź

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

18. Karta 18

    Pytanie

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

    Odpowiedź

    Traditional or commonly accepted.

19. Karta 19

    Pytanie

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

    Odpowiedź

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

20. Karta 20

    Pytanie

    Singular possessive noun?

    Odpowiedź

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

21. Karta 21

    Pytanie

    Trend in a table or graph?

    Odpowiedź

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

22. Karta 22

    Pytanie

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

    Odpowiedź

    New or original in this context.

23. Karta 23

    Pytanie

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

    Odpowiedź

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

24. Karta 24

    Pytanie

    Parallel items in a series?

    Odpowiedź

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

25. Karta 25

    Pytanie

    Claim stronger than the evidence?

    Odpowiedź

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

26. Karta 26

    Pytanie

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

    Odpowiedź

    Reasonable or believable.

27. Karta 27

    Pytanie

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

    Odpowiedź

    Addition. The second statement adds a related supporting point.

28. Karta 28

    Pytanie

    Colon before an explanation or list?

    Odpowiedź

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

29. Karta 29

    Pytanie

    Claim versus evidence?

    Odpowiedź

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

30. Karta 30

    Pytanie

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

    Odpowiedź

    Open to more than one interpretation.

31. Karta 31

    Pytanie

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

    Odpowiedź

    Replacement. The second statement substitutes one action for another.

32. Karta 32

    Pytanie

    Count nouns versus mass nouns?

    Odpowiedź

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

33. Karta 33

    Pytanie

    Effect of a counterexample?

    Odpowiedź

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

34. Karta 34

    Pytanie

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

    Odpowiedź

    Irregular and occasional.

35. Karta 35

    Pytanie

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

    Odpowiedź

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

36. Karta 36

    Pytanie

    Essential clause punctuation?

    Odpowiedź

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

37. Karta 37

    Pytanie

    Correlation alone proves causation?

    Odpowiedź

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

38. Karta 38

    Pytanie

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

    Odpowiedź

    Coming later in time.

39. Karta 39

    Pytanie

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

    Odpowiedź

    Restatement for clarity. The second statement rephrases the first.

40. Karta 40

    Pytanie

    Verb tense across a paragraph?

    Odpowiedź

    Keep the time frame consistent unless the timing actually changes.

41. Karta 41

    Pytanie

    Missing information in a data claim?

    Odpowiedź

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

42. Karta 42

    Pytanie

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

    Odpowiedź

    Keep or continue to hold.

43. Karta 43

    Pytanie

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

    Odpowiedź

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

44. Karta 44

    Pytanie

    Coordinate adjectives?

    Odpowiedź

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

45. Karta 45

    Pytanie

    Two sources on the same event?

    Odpowiedź

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

46. Karta 46

    Pytanie

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

    Odpowiedź

    Draw out or bring forth.

47. Karta 47

    Pytanie

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

    Odpowiedź

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

48. Karta 48

    Pytanie

    Sentence fragment?

    Odpowiedź

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

49. Karta 49

    Pytanie

    Inference from a narrow sample?

    Odpowiedź

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

50. Karta 50

    Pytanie

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

    Odpowiedź

    A limit or restriction.

51. Karta 51

    Pytanie

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

    Odpowiedź

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

52. Karta 52

    Pytanie

    Conjunctive adverb between independent clauses?

    Odpowiedź

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

53. Karta 53

    Pytanie

    Most accurate summary?

    Odpowiedź

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

54. Karta 54

    Pytanie

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

    Odpowiedź

    Complete and wide-ranging.

55. Karta 55

    Pytanie

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

    Odpowiedź

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

56. Karta 56

    Pytanie

    Who versus whom?

    Odpowiedź

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

57. Karta 57

    Pytanie

    Evidence that best resolves a disagreement?

    Odpowiedź

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

58. Karta 58

    Pytanie

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

    Odpowiedź

    Clearly different or separate.

59. Karta 59

    Pytanie

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

    Odpowiedź

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

60. Karta 60

    Pytanie

    Comma before an introduced direct quotation?

    Odpowiedź

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

61. Karta 61

    Pytanie

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

    Odpowiedź

    Limited or modified, rather than stated without conditions.

62. Karta 62

    Pytanie

    Notes for a synthesis goal?

    Odpowiedź

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

63. Karta 63

    Pytanie

    Comma splice?

    Odpowiedź

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

64. Karta 64

    Pytanie

    Comma between subject and verb?

    Odpowiedź

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

65. Karta 65

    Pytanie

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

    Odpowiedź

    No longer useful or current because something newer replaced it.

66. Karta 66

    Pytanie

    Source attribution in a synthesis?

    Odpowiedź

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

67. Karta 67

    Pytanie

    Compound subject joined by “and”?

    Odpowiedź

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

68. Karta 68

    Pytanie

    Dangling opening modifier?

    Odpowiedź

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

69. Karta 69

    Pytanie

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

    Odpowiedź

    Obtained from a source or calculation.

70. Karta 70

    Pytanie

    Chronological synthesis?

    Odpowiedź

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

71. Karta 71

    Pytanie

    Plural noun ending in s: possessive form?

    Odpowiedź

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

72. Karta 72

    Pytanie

    Logical comparison?

    Odpowiedź

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

73. Karta 73

    Pytanie

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

    Odpowiedź

    Publicly supports or argues for.

74. Karta 74

    Pytanie

    Compare evidence from two studies?

    Odpowiedź

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

75. Karta 75

    Pytanie

    Colon after an incomplete lead-in?

    Odpowiedź

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

76. Karta 76

    Pytanie

    Number versus amount?

    Odpowiedź

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

77. Karta 77

    Pytanie

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

    Odpowiedź

    Present or found almost everywhere.

78. Karta 78

    Pytanie

    Synthesis that emphasizes a difference?

    Odpowiedź

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

79. Karta 79

    Pytanie

    Nonessential clause or phrase?

    Odpowiedź

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

80. Karta 80

    Pytanie

    Earlier of two past actions?

    Odpowiedź

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

81. Karta 81

    Pytanie

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

    Odpowiedź

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

82. Karta 82

    Pytanie

    Rhetorical goal: define a term?

    Odpowiedź

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

83. Karta 83

    Pytanie

    Cumulative adjectives?

    Odpowiedź

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

84. Karta 84

    Pytanie

    Run-on sentence?

    Odpowiedź

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

85. Karta 85

    Pytanie

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

    Odpowiedź

    It illustrates the claim with an example.

86. Karta 86

    Pytanie

    Introduce a quotation in a synthesis?

    Odpowiedź

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

87. Karta 87

    Pytanie

    Relative pronoun for people?

    Odpowiedź

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

88. Karta 88

    Pytanie

    Integrated quotation punctuation?

    Odpowiedź

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

89. Karta 89

    Pytanie

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

    Odpowiedź

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

90. Karta 90

    Pytanie

    Avoid redundancy in synthesis?

    Odpowiedź

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

91. Karta 91

    Pytanie

    Semicolon between two independent clauses?

    Odpowiedź

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

92. Karta 92

    Pytanie

    Comma in a compound predicate?

    Odpowiedź

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

93. Karta 93

    Pytanie

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

    Odpowiedź

    It defines or clarifies the term.

94. Karta 94

    Pytanie

    Combine two related sentences?

    Odpowiedź

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

95. Karta 95

    Pytanie

    Either/or subject agreement?

    Odpowiedź

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

96. Karta 96

    Pytanie

    Active versus passive voice?

    Odpowiedź

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

97. Karta 97

    Pytanie

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

    Odpowiedź

    It presents an effect or consequence.

98. Karta 98

    Pytanie

    Formal academic register?

    Odpowiedź

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

99. Karta 99

    Pytanie

    Its or it's?

    Odpowiedź

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

100. Karta 100

     Pytanie

     Adjective versus adverb?

     Odpowiedź

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

101. Karta 101

     Pytanie

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

     Odpowiedź

     To inform or explain, not necessarily to persuade.

102. Karta 102

     Pytanie

     Concise synthesis?

     Odpowiedź

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

103. Karta 103

     Pytanie

     Single dash for emphasis?

     Odpowiedź

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

104. Karta 104

     Pytanie

     Comma with direct address?

     Odpowiedź

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

105. Karta 105

     Pytanie

     Why acknowledge a limitation?

     Odpowiedź

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

106. Karta 106

     Pytanie

     Quantitative comparison in a synthesis?

     Odpowiedź

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

107. Karta 107

     Pytanie

     Each of the samples: verb number?

     Odpowiedź

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

108. Karta 108

     Pytanie

     Between versus among?

     Odpowiedź

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

109. Karta 109

     Pytanie

     Rhetorical question in an argument?

     Odpowiedź

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

110. Karta 110

     Pytanie

     Claim before or after support?

     Odpowiedź

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

111. Karta 111

     Pytanie

     Restrictive “that” versus nonrestrictive “which”?

     Odpowiedź

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

112. Karta 112

     Pytanie

     Present perfect use?

     Odpowiedź

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

113. Karta 113

     Pytanie

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

     Odpowiedź

     They agree in conclusion but support it through different evidence.

114. Karta 114

     Pytanie

     Group related ideas in a synthesis?

     Odpowiedź

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

115. Karta 115

     Pytanie

     Compound modifier before a noun?

     Odpowiedź

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

116. Karta 116

     Pytanie

     Affect or effect?

     Odpowiedź

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

117. Karta 117

     Pytanie

     Two texts offer incompatible explanations. Relationship?

     Odpowiedź

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

118. Karta 118

     Pytanie

     Replace a vague pronoun in synthesis?

     Odpowiedź

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

119. Karta 119

     Pytanie

     Comma-separated list?

     Odpowiedź

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

120. Karta 120

     Pytanie

     Main clause before a dependent clause?

     Odpowiedź

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

121. Karta 121

     Pytanie

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

     Odpowiedź

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Karta 122

     Pytanie

     Independent clauses joined with a coordinating conjunction?

     Odpowiedź

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

123. Karta 123

     Pytanie

     Introductory transition?

     Odpowiedź

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

124. Karta 124

     Pytanie

     Pronoun–antecedent agreement?

     Odpowiedź

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

125. Karta 125

     Pytanie

     Paired em dashes?

     Odpowiedź

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

126. Karta 126

     Pytanie

     How does new evidence relate to an earlier claim?

     Odpowiedź

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

127. Karta 127

     Pytanie

     Their, there, or they're?

     Odpowiedź

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

128. Karta 128

     Pytanie

     Good or well?

     Odpowiedź

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

129. Karta 129

     Pytanie

     Appositive naming the same noun?

     Odpowiedź

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

130. Karta 130

     Pytanie

     Why use an analogy?

     Odpowiedź

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

131. Karta 131

     Pytanie

     Than or then?

     Odpowiedź

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

132. Karta 132

     Pytanie

     Hypothetical contrary-to-fact “if” clause?

     Odpowiedź

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

133. Karta 133

     Pytanie

     Plural noun with no possession?

     Odpowiedź

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

134. Karta 134

     Pytanie

     Neutral, evidence-led wording indicates what tone?

     Odpowiedź

     Objective. It emphasizes information rather than strong personal judgment.

135. Karta 135

     Pytanie

     Complex list with internal commas?

     Odpowiedź

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

136. Karta 136

     Pytanie

     Ambiguous pronoun?

     Odpowiedź

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

137. Karta 137

     Pytanie

     Parentheses around nonessential information?

     Odpowiedź

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

138. Karta 138

     Pytanie

     Repeated doubt about the evidence indicates what tone?

     Odpowiedź

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

139. Karta 139

     Pytanie

     Superlative comparison?

     Odpowiedź

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

140. Karta 140

     Pytanie

     Pronoun after a preposition?

     Odpowiedź

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

141. Karta 141

     Pytanie

     Apostrophe in a contraction?

     Odpowiedź

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

142. Karta 142

     Pytanie

     Coordinate-adjective test?

     Odpowiedź

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

143. Karta 143

     Pytanie

     Double comparative?

     Odpowiedź

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

144. Karta 144

     Pytanie

     Lie or lay?

     Odpowiedź

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

145. Karta 145

     Pytanie

     Who's or whose?

     Odpowiedź

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

146. Karta 146

     Pytanie

     Standard comparison with “different”?

     Odpowiedź

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

147. Karta 147

     Pytanie

     Paired construction with two endpoints?

     Odpowiedź

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

148. Karta 148

     Pytanie

     Verb mood in a coordinated idea?

     Odpowiedź

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

149. Karta 149

     Pytanie

     Possessive pronoun apostrophe?

     Odpowiedź

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

150. Karta 150

     Pytanie

     Comma between a preposition and its object?

     Odpowiedź

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

     

     300 kart

     Digital SAT Flashcards: Math, Grammar & Words in Context

     Ucz się z tej talii za darmo

     Otworzy się Nibomo, żeby od razu zacząć naukę.

151. Karta 151

     Pytanie

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

     Odpowiedź

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

152. Karta 152

     Pytanie

     Product of powers with the same base?

     Odpowiedź

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

153. Karta 153

     Pytanie

     Unit rate?

     Odpowiedź

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

154. Karta 154

     Pytanie

     Rectangle area?

     Odpowiedź

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

155. Karta 155

     Pytanie

     Slope from two points?

     Odpowiedź

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

156. Karta 156

     Pytanie

     Quotient of powers with the same base?

     Odpowiedź

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Karta 157

     Pytanie

     Conversion factor setup?

     Odpowiedź

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

158. Karta 158

     Pytanie

     Triangle area?

     Odpowiedź

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

159. Karta 159

     Pytanie

     Slope-intercept form?

     Odpowiedź

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

160. Karta 160

     Pytanie

     Power raised to a power?

     Odpowiedź

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

161. Karta 161

     Pytanie

     Dimensional analysis check?

     Odpowiedź

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

162. Karta 162

     Pytanie

     Trapezoid area?

     Odpowiedź

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

163. Karta 163

     Pytanie

     Point-slope form?

     Odpowiedź

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

164. Karta 164

     Pytanie

     Negative exponent?

     Odpowiedź

     $a^{-n}=1/a^n$ for $a≠0$.

165. Karta 165

     Pytanie

     Constant of proportionality in $y=kx$?

     Odpowiedź

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

166. Karta 166

     Pytanie

     Circle area?

     Odpowiedź

     $A=πr^2$.

167. Karta 167

     Pytanie

     Intercepts from $Ax+By=C$?

     Odpowiedź

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

168. Karta 168

     Pytanie

     Fractional exponent?

     Odpowiedź

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

169. Karta 169

     Pytanie

     Scale drawing length?

     Odpowiedź

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

170. Karta 170

     Pytanie

     Circle circumference?

     Odpowiedź

     $C=2πr=πd$.

171. Karta 171

     Pytanie

     Parallel nonvertical lines: slope relationship?

     Odpowiedź

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

172. Karta 172

     Pytanie

     Difference of squares?

     Odpowiedź

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

173. Karta 173

     Pytanie

     Percent change?

     Odpowiedź

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

174. Karta 174

     Pytanie

     Arc length from central angle $θ$ in degrees?

     Odpowiedź

     $L=(θ/360)(2πr)$.

175. Karta 175

     Pytanie

     Perpendicular nonvertical lines: slope relationship?

     Odpowiedź

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

176. Karta 176

     Pytanie

     Perfect-square trinomial pattern?

     Odpowiedź

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

177. Karta 177

     Pytanie

     Increase by $r$ percent: multiplier?

     Odpowiedź

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

178. Karta 178

     Pytanie

     Sector area from central angle $θ$ in degrees?

     Odpowiedź

     $A=(θ/360)(πr^2)$.

179. Karta 179

     Pytanie

     x-intercept of a graph?

     Odpowiedź

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

180. Karta 180

     Pytanie

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

     Odpowiedź

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

181. Karta 181

     Pytanie

     Original value after a 20 percent increase to 84?

     Odpowiedź

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

182. Karta 182

     Pytanie

     Triangle interior-angle sum?

     Odpowiedź

     $180°$.

183. Karta 183

     Pytanie

     y-intercept of a graph?

     Odpowiedź

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

184. Karta 184

     Pytanie

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

     Odpowiedź

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

185. Karta 185

     Pytanie

     Weighted average?

     Odpowiedź

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

186. Karta 186

     Pytanie

     Exterior angle of a triangle?

     Odpowiedź

     It equals the sum of the two remote interior angles.

187. Karta 187

     Pytanie

     Line through two points?

     Odpowiedź

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

188. Karta 188

     Pytanie

     Quadratic formula?

     Odpowiedź

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

189. Karta 189

     Pytanie

     Arithmetic mean?

     Odpowiedź

     Add all values and divide by the number of values.

190. Karta 190

     Pytanie

     Parallel lines cut by a transversal: alternate interior angles?

     Odpowiedź

     They are congruent.

191. Karta 191

     Pytanie

     Slope's units in context?

     Odpowiedź

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

192. Karta 192

     Pytanie

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

     Odpowiedź

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

193. Karta 193

     Pytanie

     Median?

     Odpowiedź

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

194. Karta 194

     Pytanie

     Similar triangles: corresponding sides?

     Odpowiedź

     They are proportional. Match sides opposite equal angles.

195. Karta 195

     Pytanie

     Direct variation model?

     Odpowiedź

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

196. Karta 196

     Pytanie

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

     Odpowiedź

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

197. Karta 197

     Pytanie

     Range of a data set?

     Odpowiedź

     Maximum minus minimum.

198. Karta 198

     Pytanie

     Scale factor $k$: area factor?

     Odpowiedź

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

199. Karta 199

     Pytanie

     Solution of a two-line system?

     Odpowiedź

     The intersection point, whose coordinates satisfy both equations.

200. Karta 200

     Pytanie

     Vertex form of a quadratic?

     Odpowiedź

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

201. Karta 201

     Pytanie

     Interquartile range?

     Odpowiedź

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

202. Karta 202

     Pytanie

     Pythagorean theorem?

     Odpowiedź

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

203. Karta 203

     Pytanie

     Substitution in a system?

     Odpowiedź

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

204. Karta 204

     Pytanie

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

     Odpowiedź

     $x=h$.

205. Karta 205

     Pytanie

     Larger standard deviation means what?

     Odpowiedź

     The data are more spread out around the mean.

206. Karta 206

     Pytanie

     45°-45°-90° side ratio?

     Odpowiedź

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

207. Karta 207

     Pytanie

     Elimination in a system?

     Odpowiedź

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

208. Karta 208

     Pytanie

     Completing the square?

     Odpowiedź

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

209. Karta 209

     Pytanie

     Effect of a high outlier on the mean?

     Odpowiedź

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

210. Karta 210

     Pytanie

     30°-60°-90° side ratio?

     Odpowiedź

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

211. Karta 211

     Pytanie

     Parallel lines in a system?

     Odpowiedź

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

212. Karta 212

     Pytanie

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

     Odpowiedź

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

213. Karta 213

     Pytanie

     Add the same constant to every data value: effect?

     Odpowiedź

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

214. Karta 214

     Pytanie

     Right-triangle sine?

     Odpowiedź

     Sine of $θ$ equals opposite over hypotenuse.

215. Karta 215

     Pytanie

     Same line written two ways in a system?

     Odpowiedź

     Infinitely many solutions. Simplifying either equation produces the other.

216. Karta 216

     Pytanie

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

     Odpowiedź

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

217. Karta 217

     Pytanie

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

     Odpowiedź

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

218. Karta 218

     Pytanie

     Right-triangle cosine?

     Odpowiedź

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Karta 219

     Pytanie

     Multiply or divide an inequality by a negative number?

     Odpowiedź

     Reverse the inequality sign.

220. Karta 220

     Pytanie

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

     Odpowiedź

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

221. Karta 221

     Pytanie

     Joint probability from a two-way table?

     Odpowiedź

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

222. Karta 222

     Pytanie

     Right-triangle tangent?

     Odpowiedź

     Tangent of $θ$ equals opposite over adjacent.

223. Karta 223

     Pytanie

     Compound inequality with “and”?

     Odpowiedź

     Use the intersection: values that satisfy both inequalities.

224. Karta 224

     Pytanie

     Even degree with positive leading coefficient: end behavior?

     Odpowiedź

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

225. Karta 225

     Pytanie

     Conditional probability $P(A|B)$?

     Odpowiedź

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

226. Karta 226

     Pytanie

     Complementary acute angles: sine–cosine relationship?

     Odpowiedź

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

227. Karta 227

     Pytanie

     Compound inequality with “or”?

     Odpowiedź

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

228. Karta 228

     Pytanie

     Odd degree with positive leading coefficient: end behavior?

     Odpowiedź

     The left end falls and the right end rises.

229. Karta 229

     Pytanie

     Independent events $A$ and $B$?

     Odpowiedź

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

230. Karta 230

     Pytanie

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

     Odpowiedź

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Karta 231

     Pytanie

     Solve $|x-a|=b$ for $b≥0$.

     Odpowiedź

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

232. Karta 232

     Pytanie

     Exponential growth model?

     Odpowiedź

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

233. Karta 233

     Pytanie

     Mutually exclusive events?

     Odpowiedź

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

234. Karta 234

     Pytanie

     Midpoint of two points?

     Odpowiedź

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

235. Karta 235

     Pytanie

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

     Odpowiedź

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

236. Karta 236

     Pytanie

     Exponential decay model?

     Odpowiedź

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

237. Karta 237

     Pytanie

     Complement rule?

     Odpowiedź

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

238. Karta 238

     Pytanie

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

     Odpowiedź

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

239. Karta 239

     Pytanie

     Evaluate $f(a)$?

     Odpowiedź

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

240. Karta 240

     Pytanie

     Growth factor 1.08: percent growth rate?

     Odpowiedź

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

241. Karta 241

     Pytanie

     Representative random sample permits what conclusion?

     Odpowiedź

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

242. Karta 242

     Pytanie

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

     Odpowiedź

     $r=√R$, provided $R>0$.

243. Karta 243

     Pytanie

     Linear table: constant slope check?

     Odpowiedź

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

244. Karta 244

     Pytanie

     Decay factor 0.73: percent decrease?

     Odpowiedź

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

245. Karta 245

     Pytanie

     Random assignment permits what causal claim?

     Odpowiedź

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

246. Karta 246

     Pytanie

     Radius and tangent at the contact point?

     Odpowiedź

     They are perpendicular.

247. Karta 247

     Pytanie

     Positive slope means what for a linear function?

     Odpowiedź

     The output increases as the input increases.

248. Karta 248

     Pytanie

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

     Odpowiedź

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

249. Karta 249

     Pytanie

     Observational study supports causation?

     Odpowiedź

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

250. Karta 250

     Pytanie

     Rectangular-prism volume?

     Odpowiedź

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

251. Karta 251

     Pytanie

     Arithmetic sequence common difference?

     Odpowiedź

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

252. Karta 252

     Pytanie

     Compound interest formula?

     Odpowiedź

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

253. Karta 253

     Pytanie

     Larger random sample: effect on margin of error?

     Odpowiedź

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

254. Karta 254

     Pytanie

     Cylinder volume?

     Odpowiedź

     $V=πr^2h$.

255. Karta 255

     Pytanie

     Arithmetic sequence nth term?

     Odpowiedź

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

256. Karta 256

     Pytanie

     Rational expression: first domain check?

     Odpowiedź

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

257. Karta 257

     Pytanie

     Slope of a line of best fit?

     Odpowiedź

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

258. Karta 258

     Pytanie

     Cone volume?

     Odpowiedź

     $V=(1/3)πr^2h$.

259. Karta 259

     Pytanie

     Solve a literal equation for one variable?

     Odpowiedź

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

260. Karta 260

     Pytanie

     Why check rational-equation solutions?

     Odpowiedź

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

261. Karta 261

     Pytanie

     Residual?

     Odpowiedź

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

262. Karta 262

     Pytanie

     Sphere volume?

     Odpowiedź

     $V=(4/3)πr^3$.

263. Karta 263

     Pytanie

     Boundary for a two-variable linear inequality?

     Odpowiedź

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

264. Karta 264

     Pytanie

     Why check a solution after squaring both sides?

     Odpowiedź

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

265. Karta 265

     Pytanie

     Positive correlation?

     Odpowiedź

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

266. Karta 266

     Pytanie

     Rectangular-prism surface area?

     Odpowiedź

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

267. Karta 267

     Pytanie

     Check a proposed system solution?

     Odpowiedź

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

268. Karta 268

     Pytanie

     Simplify $√72$.

     Odpowiedź

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

269. Karta 269

     Pytanie

     Extrapolation risk?

     Odpowiedź

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

270. Karta 270

     Pytanie

     Area scale factor when lengths double?

     Odpowiedź

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

271. Karta 271

     Pytanie

     Horizontal line slope?

     Odpowiedź

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

272. Karta 272

     Pytanie

     Inverse function setup?

     Odpowiedź

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

273. Karta 273

     Pytanie

     Percentage points versus percent change?

     Odpowiedź

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

274. Karta 274

     Pytanie

     y-intercept in a context?

     Odpowiedź

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

275. Karta 275

     Pytanie

     Quadratic maximum or minimum from vertex form?

     Odpowiedź

     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. Karta 276

     Pytanie

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

     Odpowiedź

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

277. Karta 277

     Pytanie

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

     Odpowiedź

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

278. Karta 278

     Pytanie

     Population versus sample?

     Odpowiedź

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

279. Karta 279

     Pytanie

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

     Odpowiedź

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

280. Karta 280

     Pytanie

     Function composition $(f∘g)(x)$?

     Odpowiedź

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

281. Karta 281

     Pytanie

     Density?

     Odpowiedź

     Mass divided by volume. Keep the units consistent.

282. Karta 282

     Pytanie

     Vertical line slope?

     Odpowiedź

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

283. Karta 283

     Pytanie

     Nonlinear system with one equation solved for $y$?

     Odpowiedź

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

284. Karta 284

     Pytanie

     Weighted percentage across unequal groups?

     Odpowiedź

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

285. Karta 285

     Pytanie

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

     Odpowiedź

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

286. Karta 286

     Pytanie

     Cancel a common factor in a rational expression?

     Odpowiedź

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

287. Karta 287

     Pytanie

     Solve a linear equation containing fractions?

     Odpowiedź

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

288. Karta 288

     Pytanie

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

     Odpowiedź

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

289. Karta 289

     Pytanie

     Rate units check?

     Odpowiedź

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

290. Karta 290

     Pytanie

     Strict versus inclusive inequality endpoint?

     Odpowiedź

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

291. Karta 291

     Pytanie

     Even-multiplicity zero on a graph?

     Odpowiedź

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

292. Karta 292

     Pytanie

     System word problem: first setup step?

     Odpowiedź

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

293. Karta 293

     Pytanie

     When does a quadratic have exactly one real solution?

     Odpowiedź

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

294. Karta 294

     Pytanie

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

     Odpowiedź

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

295. Karta 295

     Pytanie

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

     Odpowiedź

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

296. Karta 296

     Pytanie

     Graph of $-f(x)$?

     Odpowiedź

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

297. Karta 297

     Pytanie

     Three consecutive integers starting with $n$?

     Odpowiedź

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

298. Karta 298

     Pytanie

     Line–parabola intersections from a substituted quadratic?

     Odpowiedź

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

299. Karta 299

     Pytanie

     Linear equation with no solution: coefficient pattern?

     Odpowiedź

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

300. Karta 300

     Pytanie

     Zeros of a function on its graph?

     Odpowiedź

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

300 kart

Digital SAT Flashcards: Math, Grammar & Words in Context

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