Digital SAT Flashcards: Math, Grammar & Words in Context

Spjöld í þessum stokki

1. Spjald 1

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   Central idea of a passage?

   Svar

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

2. Spjald 2

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

   Svar

   Reduced. The trees made the heat less severe.

3. Spjald 3

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

   Svar

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

4. Spjald 4

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   Three standard joins for two independent clauses?

   Svar

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

5. Spjald 5

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   Best supporting detail?

   Svar

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

6. Spjald 6

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

   Svar

   Confirmed with supporting evidence.

7. Spjald 7

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

   Svar

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

8. Spjald 8

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   Introductory dependent clause before a main clause?

   Svar

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

9. Spjald 9

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   Valid inference?

   Svar

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

10. Spjald 10

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

    Svar

    Provisional or not yet certain.

11. Spjald 11

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

    Svar

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

12. Spjald 12

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    Singular subject with an intervening prepositional phrase?

    Svar

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

13. Spjald 13

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    Strongest textual evidence?

    Svar

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

14. Spjald 14

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

    Svar

    So small that it is not important.

15. Spjald 15

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

    Svar

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

16. Spjald 16

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    Opening modifier placement?

    Svar

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

17. Spjald 17

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    Quantitative evidence for a claim?

    Svar

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

18. Spjald 18

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

    Svar

    Traditional or commonly accepted.

19. Spjald 19

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

    Svar

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

20. Spjald 20

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    Singular possessive noun?

    Svar

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

21. Spjald 21

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    Trend in a table or graph?

    Svar

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

22. Spjald 22

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

    Svar

    New or original in this context.

23. Spjald 23

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

    Svar

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

24. Spjald 24

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    Parallel items in a series?

    Svar

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

25. Spjald 25

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    Claim stronger than the evidence?

    Svar

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

26. Spjald 26

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

    Svar

    Reasonable or believable.

27. Spjald 27

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

    Svar

    Addition. The second statement adds a related supporting point.

28. Spjald 28

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    Colon before an explanation or list?

    Svar

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

29. Spjald 29

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    Claim versus evidence?

    Svar

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

30. Spjald 30

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

    Svar

    Open to more than one interpretation.

31. Spjald 31

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

    Svar

    Replacement. The second statement substitutes one action for another.

32. Spjald 32

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    Count nouns versus mass nouns?

    Svar

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

33. Spjald 33

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    Effect of a counterexample?

    Svar

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

34. Spjald 34

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

    Svar

    Irregular and occasional.

35. Spjald 35

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

    Svar

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

36. Spjald 36

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    Essential clause punctuation?

    Svar

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

37. Spjald 37

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    Correlation alone proves causation?

    Svar

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

38. Spjald 38

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

    Svar

    Coming later in time.

39. Spjald 39

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

    Svar

    Restatement for clarity. The second statement rephrases the first.

40. Spjald 40

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    Verb tense across a paragraph?

    Svar

    Keep the time frame consistent unless the timing actually changes.

41. Spjald 41

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    Missing information in a data claim?

    Svar

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

42. Spjald 42

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

    Svar

    Keep or continue to hold.

43. Spjald 43

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

    Svar

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

44. Spjald 44

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    Coordinate adjectives?

    Svar

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

45. Spjald 45

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    Two sources on the same event?

    Svar

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

46. Spjald 46

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

    Svar

    Draw out or bring forth.

47. Spjald 47

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

    Svar

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

48. Spjald 48

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    Sentence fragment?

    Svar

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

49. Spjald 49

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    Inference from a narrow sample?

    Svar

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

50. Spjald 50

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

    Svar

    A limit or restriction.

51. Spjald 51

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

    Svar

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

52. Spjald 52

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    Conjunctive adverb between independent clauses?

    Svar

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

53. Spjald 53

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    Most accurate summary?

    Svar

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

54. Spjald 54

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

    Svar

    Complete and wide-ranging.

55. Spjald 55

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

    Svar

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

56. Spjald 56

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    Who versus whom?

    Svar

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

57. Spjald 57

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    Evidence that best resolves a disagreement?

    Svar

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

58. Spjald 58

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

    Svar

    Clearly different or separate.

59. Spjald 59

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

    Svar

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

60. Spjald 60

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    Comma before an introduced direct quotation?

    Svar

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

61. Spjald 61

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

    Svar

    Limited or modified, rather than stated without conditions.

62. Spjald 62

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    Notes for a synthesis goal?

    Svar

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

63. Spjald 63

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    Comma splice?

    Svar

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

64. Spjald 64

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    Comma between subject and verb?

    Svar

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

65. Spjald 65

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

    Svar

    No longer useful or current because something newer replaced it.

66. Spjald 66

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    Source attribution in a synthesis?

    Svar

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

67. Spjald 67

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    Compound subject joined by “and”?

    Svar

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

68. Spjald 68

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    Dangling opening modifier?

    Svar

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

69. Spjald 69

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

    Svar

    Obtained from a source or calculation.

70. Spjald 70

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    Chronological synthesis?

    Svar

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

71. Spjald 71

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    Plural noun ending in s: possessive form?

    Svar

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

72. Spjald 72

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    Logical comparison?

    Svar

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

73. Spjald 73

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

    Svar

    Publicly supports or argues for.

74. Spjald 74

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    Compare evidence from two studies?

    Svar

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

75. Spjald 75

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    Colon after an incomplete lead-in?

    Svar

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

76. Spjald 76

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    Number versus amount?

    Svar

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

77. Spjald 77

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

    Svar

    Present or found almost everywhere.

78. Spjald 78

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    Synthesis that emphasizes a difference?

    Svar

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

79. Spjald 79

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    Nonessential clause or phrase?

    Svar

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

80. Spjald 80

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    Earlier of two past actions?

    Svar

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

81. Spjald 81

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

    Svar

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

82. Spjald 82

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    Rhetorical goal: define a term?

    Svar

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

83. Spjald 83

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    Cumulative adjectives?

    Svar

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

84. Spjald 84

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    Run-on sentence?

    Svar

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

85. Spjald 85

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

    Svar

    It illustrates the claim with an example.

86. Spjald 86

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    Introduce a quotation in a synthesis?

    Svar

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

87. Spjald 87

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    Relative pronoun for people?

    Svar

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

88. Spjald 88

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    Integrated quotation punctuation?

    Svar

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

89. Spjald 89

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

    Svar

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

90. Spjald 90

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    Avoid redundancy in synthesis?

    Svar

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

91. Spjald 91

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    Semicolon between two independent clauses?

    Svar

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

92. Spjald 92

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    Comma in a compound predicate?

    Svar

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

93. Spjald 93

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

    Svar

    It defines or clarifies the term.

94. Spjald 94

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    Combine two related sentences?

    Svar

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

95. Spjald 95

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    Either/or subject agreement?

    Svar

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

96. Spjald 96

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    Active versus passive voice?

    Svar

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

97. Spjald 97

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

    Svar

    It presents an effect or consequence.

98. Spjald 98

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    Formal academic register?

    Svar

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

99. Spjald 99

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    Its or it's?

    Svar

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

100. Spjald 100

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     Adjective versus adverb?

     Svar

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

101. Spjald 101

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

     Svar

     To inform or explain, not necessarily to persuade.

102. Spjald 102

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     Concise synthesis?

     Svar

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

103. Spjald 103

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     Single dash for emphasis?

     Svar

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

104. Spjald 104

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     Comma with direct address?

     Svar

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

105. Spjald 105

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     Why acknowledge a limitation?

     Svar

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

106. Spjald 106

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     Quantitative comparison in a synthesis?

     Svar

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

107. Spjald 107

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     Each of the samples: verb number?

     Svar

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

108. Spjald 108

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     Between versus among?

     Svar

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

109. Spjald 109

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     Rhetorical question in an argument?

     Svar

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

110. Spjald 110

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     Claim before or after support?

     Svar

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

111. Spjald 111

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     Restrictive “that” versus nonrestrictive “which”?

     Svar

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

112. Spjald 112

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     Present perfect use?

     Svar

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

113. Spjald 113

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

     Svar

     They agree in conclusion but support it through different evidence.

114. Spjald 114

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     Group related ideas in a synthesis?

     Svar

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

115. Spjald 115

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     Compound modifier before a noun?

     Svar

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

116. Spjald 116

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     Affect or effect?

     Svar

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

117. Spjald 117

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     Two texts offer incompatible explanations. Relationship?

     Svar

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

118. Spjald 118

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     Replace a vague pronoun in synthesis?

     Svar

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

119. Spjald 119

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     Comma-separated list?

     Svar

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

120. Spjald 120

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     Main clause before a dependent clause?

     Svar

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

121. Spjald 121

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

     Svar

     Their perspectives or interpretive frameworks, not the underlying evidence.

122. Spjald 122

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     Independent clauses joined with a coordinating conjunction?

     Svar

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

123. Spjald 123

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     Introductory transition?

     Svar

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

124. Spjald 124

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     Pronoun–antecedent agreement?

     Svar

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

125. Spjald 125

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     Paired em dashes?

     Svar

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

126. Spjald 126

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     How does new evidence relate to an earlier claim?

     Svar

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

127. Spjald 127

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     Their, there, or they're?

     Svar

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

128. Spjald 128

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     Good or well?

     Svar

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

129. Spjald 129

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     Appositive naming the same noun?

     Svar

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

130. Spjald 130

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     Why use an analogy?

     Svar

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

131. Spjald 131

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     Than or then?

     Svar

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

132. Spjald 132

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     Hypothetical contrary-to-fact “if” clause?

     Svar

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

133. Spjald 133

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     Plural noun with no possession?

     Svar

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

134. Spjald 134

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     Neutral, evidence-led wording indicates what tone?

     Svar

     Objective. It emphasizes information rather than strong personal judgment.

135. Spjald 135

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     Complex list with internal commas?

     Svar

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

136. Spjald 136

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     Ambiguous pronoun?

     Svar

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

137. Spjald 137

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     Parentheses around nonessential information?

     Svar

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

138. Spjald 138

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     Repeated doubt about the evidence indicates what tone?

     Svar

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

139. Spjald 139

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     Superlative comparison?

     Svar

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

140. Spjald 140

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     Pronoun after a preposition?

     Svar

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

141. Spjald 141

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     Apostrophe in a contraction?

     Svar

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

142. Spjald 142

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     Coordinate-adjective test?

     Svar

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

143. Spjald 143

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     Double comparative?

     Svar

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

144. Spjald 144

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     Lie or lay?

     Svar

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

145. Spjald 145

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     Who's or whose?

     Svar

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

146. Spjald 146

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     Standard comparison with “different”?

     Svar

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

147. Spjald 147

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     Paired construction with two endpoints?

     Svar

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

148. Spjald 148

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     Verb mood in a coordinated idea?

     Svar

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

149. Spjald 149

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     Possessive pronoun apostrophe?

     Svar

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

150. Spjald 150

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     Comma between a preposition and its object?

     Svar

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

     

     300 spjöld

     Digital SAT Flashcards: Math, Grammar & Words in Context

     Læra þennan stokk ókeypis

     Nibomo opnast svo þú getir byrjað að læra.

151. Spjald 151

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

     Svar

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

152. Spjald 152

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     Product of powers with the same base?

     Svar

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

153. Spjald 153

     Spurning

     Unit rate?

     Svar

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

154. Spjald 154

     Spurning

     Rectangle area?

     Svar

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

155. Spjald 155

     Spurning

     Slope from two points?

     Svar

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

156. Spjald 156

     Spurning

     Quotient of powers with the same base?

     Svar

     $a^m/a^n=a^{m-n}$ for $a≠0$.

157. Spjald 157

     Spurning

     Conversion factor setup?

     Svar

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

158. Spjald 158

     Spurning

     Triangle area?

     Svar

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

159. Spjald 159

     Spurning

     Slope-intercept form?

     Svar

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

160. Spjald 160

     Spurning

     Power raised to a power?

     Svar

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

161. Spjald 161

     Spurning

     Dimensional analysis check?

     Svar

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

162. Spjald 162

     Spurning

     Trapezoid area?

     Svar

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

163. Spjald 163

     Spurning

     Point-slope form?

     Svar

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

164. Spjald 164

     Spurning

     Negative exponent?

     Svar

     $a^{-n}=1/a^n$ for $a≠0$.

165. Spjald 165

     Spurning

     Constant of proportionality in $y=kx$?

     Svar

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

166. Spjald 166

     Spurning

     Circle area?

     Svar

     $A=πr^2$.

167. Spjald 167

     Spurning

     Intercepts from $Ax+By=C$?

     Svar

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

168. Spjald 168

     Spurning

     Fractional exponent?

     Svar

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

169. Spjald 169

     Spurning

     Scale drawing length?

     Svar

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

170. Spjald 170

     Spurning

     Circle circumference?

     Svar

     $C=2πr=πd$.

171. Spjald 171

     Spurning

     Parallel nonvertical lines: slope relationship?

     Svar

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

172. Spjald 172

     Spurning

     Difference of squares?

     Svar

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

173. Spjald 173

     Spurning

     Percent change?

     Svar

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

174. Spjald 174

     Spurning

     Arc length from central angle $θ$ in degrees?

     Svar

     $L=(θ/360)(2πr)$.

175. Spjald 175

     Spurning

     Perpendicular nonvertical lines: slope relationship?

     Svar

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

176. Spjald 176

     Spurning

     Perfect-square trinomial pattern?

     Svar

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

177. Spjald 177

     Spurning

     Increase by $r$ percent: multiplier?

     Svar

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

178. Spjald 178

     Spurning

     Sector area from central angle $θ$ in degrees?

     Svar

     $A=(θ/360)(πr^2)$.

179. Spjald 179

     Spurning

     x-intercept of a graph?

     Svar

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

180. Spjald 180

     Spurning

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

     Svar

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

181. Spjald 181

     Spurning

     Original value after a 20 percent increase to 84?

     Svar

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

182. Spjald 182

     Spurning

     Triangle interior-angle sum?

     Svar

     $180°$.

183. Spjald 183

     Spurning

     y-intercept of a graph?

     Svar

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

184. Spjald 184

     Spurning

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

     Svar

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

185. Spjald 185

     Spurning

     Weighted average?

     Svar

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

186. Spjald 186

     Spurning

     Exterior angle of a triangle?

     Svar

     It equals the sum of the two remote interior angles.

187. Spjald 187

     Spurning

     Line through two points?

     Svar

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

188. Spjald 188

     Spurning

     Quadratic formula?

     Svar

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

189. Spjald 189

     Spurning

     Arithmetic mean?

     Svar

     Add all values and divide by the number of values.

190. Spjald 190

     Spurning

     Parallel lines cut by a transversal: alternate interior angles?

     Svar

     They are congruent.

191. Spjald 191

     Spurning

     Slope's units in context?

     Svar

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

192. Spjald 192

     Spurning

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

     Svar

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

193. Spjald 193

     Spurning

     Median?

     Svar

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

194. Spjald 194

     Spurning

     Similar triangles: corresponding sides?

     Svar

     They are proportional. Match sides opposite equal angles.

195. Spjald 195

     Spurning

     Direct variation model?

     Svar

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

196. Spjald 196

     Spurning

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

     Svar

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

197. Spjald 197

     Spurning

     Range of a data set?

     Svar

     Maximum minus minimum.

198. Spjald 198

     Spurning

     Scale factor $k$: area factor?

     Svar

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

199. Spjald 199

     Spurning

     Solution of a two-line system?

     Svar

     The intersection point, whose coordinates satisfy both equations.

200. Spjald 200

     Spurning

     Vertex form of a quadratic?

     Svar

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

201. Spjald 201

     Spurning

     Interquartile range?

     Svar

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

202. Spjald 202

     Spurning

     Pythagorean theorem?

     Svar

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

203. Spjald 203

     Spurning

     Substitution in a system?

     Svar

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

204. Spjald 204

     Spurning

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

     Svar

     $x=h$.

205. Spjald 205

     Spurning

     Larger standard deviation means what?

     Svar

     The data are more spread out around the mean.

206. Spjald 206

     Spurning

     45°-45°-90° side ratio?

     Svar

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

207. Spjald 207

     Spurning

     Elimination in a system?

     Svar

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

208. Spjald 208

     Spurning

     Completing the square?

     Svar

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

209. Spjald 209

     Spurning

     Effect of a high outlier on the mean?

     Svar

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

210. Spjald 210

     Spurning

     30°-60°-90° side ratio?

     Svar

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

211. Spjald 211

     Spurning

     Parallel lines in a system?

     Svar

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

212. Spjald 212

     Spurning

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

     Svar

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

213. Spjald 213

     Spurning

     Add the same constant to every data value: effect?

     Svar

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

214. Spjald 214

     Spurning

     Right-triangle sine?

     Svar

     Sine of $θ$ equals opposite over hypotenuse.

215. Spjald 215

     Spurning

     Same line written two ways in a system?

     Svar

     Infinitely many solutions. Simplifying either equation produces the other.

216. Spjald 216

     Spurning

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

     Svar

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

217. Spjald 217

     Spurning

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

     Svar

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

218. Spjald 218

     Spurning

     Right-triangle cosine?

     Svar

     Cosine of $θ$ equals adjacent over hypotenuse.

219. Spjald 219

     Spurning

     Multiply or divide an inequality by a negative number?

     Svar

     Reverse the inequality sign.

220. Spjald 220

     Spurning

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

     Svar

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

221. Spjald 221

     Spurning

     Joint probability from a two-way table?

     Svar

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

222. Spjald 222

     Spurning

     Right-triangle tangent?

     Svar

     Tangent of $θ$ equals opposite over adjacent.

223. Spjald 223

     Spurning

     Compound inequality with “and”?

     Svar

     Use the intersection: values that satisfy both inequalities.

224. Spjald 224

     Spurning

     Even degree with positive leading coefficient: end behavior?

     Svar

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

225. Spjald 225

     Spurning

     Conditional probability $P(A|B)$?

     Svar

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

226. Spjald 226

     Spurning

     Complementary acute angles: sine–cosine relationship?

     Svar

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

227. Spjald 227

     Spurning

     Compound inequality with “or”?

     Svar

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

228. Spjald 228

     Spurning

     Odd degree with positive leading coefficient: end behavior?

     Svar

     The left end falls and the right end rises.

229. Spjald 229

     Spurning

     Independent events $A$ and $B$?

     Svar

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

230. Spjald 230

     Spurning

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

     Svar

     $√((x_2-x_1)^2+(y_2-y_1)^2)$.

231. Spjald 231

     Spurning

     Solve $|x-a|=b$ for $b≥0$.

     Svar

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

232. Spjald 232

     Spurning

     Exponential growth model?

     Svar

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

233. Spjald 233

     Spurning

     Mutually exclusive events?

     Svar

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

234. Spjald 234

     Spurning

     Midpoint of two points?

     Svar

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

235. Spjald 235

     Spurning

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

     Svar

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

236. Spjald 236

     Spurning

     Exponential decay model?

     Svar

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

237. Spjald 237

     Spurning

     Complement rule?

     Svar

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

238. Spjald 238

     Spurning

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

     Svar

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

239. Spjald 239

     Spurning

     Evaluate $f(a)$?

     Svar

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

240. Spjald 240

     Spurning

     Growth factor 1.08: percent growth rate?

     Svar

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

241. Spjald 241

     Spurning

     Representative random sample permits what conclusion?

     Svar

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

242. Spjald 242

     Spurning

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

     Svar

     $r=√R$, provided $R>0$.

243. Spjald 243

     Spurning

     Linear table: constant slope check?

     Svar

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

244. Spjald 244

     Spurning

     Decay factor 0.73: percent decrease?

     Svar

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

245. Spjald 245

     Spurning

     Random assignment permits what causal claim?

     Svar

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

246. Spjald 246

     Spurning

     Radius and tangent at the contact point?

     Svar

     They are perpendicular.

247. Spjald 247

     Spurning

     Positive slope means what for a linear function?

     Svar

     The output increases as the input increases.

248. Spjald 248

     Spurning

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

     Svar

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

249. Spjald 249

     Spurning

     Observational study supports causation?

     Svar

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

250. Spjald 250

     Spurning

     Rectangular-prism volume?

     Svar

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

251. Spjald 251

     Spurning

     Arithmetic sequence common difference?

     Svar

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

252. Spjald 252

     Spurning

     Compound interest formula?

     Svar

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

253. Spjald 253

     Spurning

     Larger random sample: effect on margin of error?

     Svar

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

254. Spjald 254

     Spurning

     Cylinder volume?

     Svar

     $V=πr^2h$.

255. Spjald 255

     Spurning

     Arithmetic sequence nth term?

     Svar

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

256. Spjald 256

     Spurning

     Rational expression: first domain check?

     Svar

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

257. Spjald 257

     Spurning

     Slope of a line of best fit?

     Svar

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

258. Spjald 258

     Spurning

     Cone volume?

     Svar

     $V=(1/3)πr^2h$.

259. Spjald 259

     Spurning

     Solve a literal equation for one variable?

     Svar

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

260. Spjald 260

     Spurning

     Why check rational-equation solutions?

     Svar

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

261. Spjald 261

     Spurning

     Residual?

     Svar

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

262. Spjald 262

     Spurning

     Sphere volume?

     Svar

     $V=(4/3)πr^3$.

263. Spjald 263

     Spurning

     Boundary for a two-variable linear inequality?

     Svar

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

264. Spjald 264

     Spurning

     Why check a solution after squaring both sides?

     Svar

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

265. Spjald 265

     Spurning

     Positive correlation?

     Svar

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

266. Spjald 266

     Spurning

     Rectangular-prism surface area?

     Svar

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

267. Spjald 267

     Spurning

     Check a proposed system solution?

     Svar

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

268. Spjald 268

     Spurning

     Simplify $√72$.

     Svar

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

269. Spjald 269

     Spurning

     Extrapolation risk?

     Svar

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

270. Spjald 270

     Spurning

     Area scale factor when lengths double?

     Svar

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

271. Spjald 271

     Spurning

     Horizontal line slope?

     Svar

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

272. Spjald 272

     Spurning

     Inverse function setup?

     Svar

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

273. Spjald 273

     Spurning

     Percentage points versus percent change?

     Svar

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

274. Spjald 274

     Spurning

     y-intercept in a context?

     Svar

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

275. Spjald 275

     Spurning

     Quadratic maximum or minimum from vertex form?

     Svar

     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. Spjald 276

     Spurning

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

     Svar

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

277. Spjald 277

     Spurning

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

     Svar

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

278. Spjald 278

     Spurning

     Population versus sample?

     Svar

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

279. Spjald 279

     Spurning

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

     Svar

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

280. Spjald 280

     Spurning

     Function composition $(f∘g)(x)$?

     Svar

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

281. Spjald 281

     Spurning

     Density?

     Svar

     Mass divided by volume. Keep the units consistent.

282. Spjald 282

     Spurning

     Vertical line slope?

     Svar

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

283. Spjald 283

     Spurning

     Nonlinear system with one equation solved for $y$?

     Svar

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

284. Spjald 284

     Spurning

     Weighted percentage across unequal groups?

     Svar

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

285. Spjald 285

     Spurning

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

     Svar

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

286. Spjald 286

     Spurning

     Cancel a common factor in a rational expression?

     Svar

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

287. Spjald 287

     Spurning

     Solve a linear equation containing fractions?

     Svar

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

288. Spjald 288

     Spurning

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

     Svar

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

289. Spjald 289

     Spurning

     Rate units check?

     Svar

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

290. Spjald 290

     Spurning

     Strict versus inclusive inequality endpoint?

     Svar

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

291. Spjald 291

     Spurning

     Even-multiplicity zero on a graph?

     Svar

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

292. Spjald 292

     Spurning

     System word problem: first setup step?

     Svar

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

293. Spjald 293

     Spurning

     When does a quadratic have exactly one real solution?

     Svar

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

294. Spjald 294

     Spurning

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

     Svar

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

295. Spjald 295

     Spurning

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

     Svar

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

296. Spjald 296

     Spurning

     Graph of $-f(x)$?

     Svar

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

297. Spjald 297

     Spurning

     Three consecutive integers starting with $n$?

     Svar

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

298. Spjald 298

     Spurning

     Line–parabola intersections from a substituted quadratic?

     Svar

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

299. Spjald 299

     Spurning

     Linear equation with no solution: coefficient pattern?

     Svar

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

300. Spjald 300

     Spurning

     Zeros of a function on its graph?

     Svar

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

300 spjöld

Digital SAT Flashcards: Math, Grammar & Words in Context

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