Mar. 17, 2010
Read the following SAT test question, then click on a button to select your answer. ƒ(2n) = 2ƒ(n) for all integers n ƒ(4)= 4 If ƒ is a function defined for all positive integers n, and ƒ satisfies the two conditions above, which of the following could be the definition of ƒ?
It is easy to check whether ƒ(4) = 4 for the functions given. First, eliminate those functions for which ƒ(4) 4. Then evaluate the functions for some values, such as n = 1 or n = 2, to see whether ƒ(2n) = 2ƒ(n) for those values. <Correct Answer> 2 <Here's Why> If ƒ(n) = n – 2, then ƒ(4) = 4 – 2 = 2 4, so the second condition fails. If ƒ(n) = 2n, then ƒ(4) = 8 4, so the second condition fails for this function also. The other three options satisfy ƒ(4) = 4, so it remains to check whether they satisfy the first condition. If n = 1, and ƒ(n) = 4, then ƒ(2n) = ƒ(2) = 4 and 2ƒ(1) = 2(4) = 8, so it is not true that ƒ(2n) = 2ƒ(n) for all integers n. This means that the function ƒ(n) = 4 does not satisfy the first condition. If n = 1, and ƒ(n) = 2n – 4, then ƒ(2n) = ƒ(2) = 2(2)– 4 = 0 and 2ƒ(n) = 2ƒ(1) = 2(–2) = –4, so it is not true that ƒ(2n) = 2ƒ(n) for all integers n. This means that the function ƒ(n) = 2n – 4 does not satisfy the first condition. However, if ƒ(n) = n, then ƒ(2n) = 2n = 2ƒ(n), for all integers n. Also, ƒ(4) = 4. Therefore, the function ƒ(n) = n is the only option that satisfies both conditions. <Difficulty> Hard <Question Type> Standard Multiple Choice Mar. 12, 2010 Read the following SAT test question, then click on a button to select your answer. If the graph of the function ƒ in the xy-plane contains the points (0, –9), (1, –4), and (3, 0), which of the following CANNOT be true?
If three points in the xy-plane lie on a line, the slope of the segment connecting any pair of the points must be the same as the slope of the segment connecting any other pair of the points. <Correct Answer> D <Here's Why> If the graph of the function ƒ, which contains the points (0, –9), (1, –4), and (3, 0), were a line, then the slope of the segment connecting the points (0, –9) and (1, –4) would be the same as the slope of the segment connecting the points (1, –4) and (3, 0). However, the slope of the segment connecting the points (0, –9) and (1, –4) is 5, and the slope of the segment connecting the points (1, –4) and (3, 0) is 2. Therefore, the graph of ƒ cannot be a line. The statements in the other four options could be true. For example, if the equation of ƒ were y = –(x – 3)2, then the graph of ƒ would contain the points (0, –9), (1, –4), and (3, 0). The graph of ƒ would be a parabola symmetric with respect to the line with equation x = 3. The maximum value of ƒ would occur at the point (3, 0), and y 0 would be true for all points (x, y) on the graph of ƒ. <Difficulty> Hard <Question Type> Standard Multiple Choice Mar. 9, 2010 What is the equation of the line parallel to the x-axis and four units above the x-axis? 1. x = –4 2. x = 4 3. y = –4 4. y = 0 5. y = 4 <Hint> Any line that is parallel to the x-axis is a horizontal line. <Correct Answer> 5
A line that is parallel to the x-axis and four units above the x-axis is the vertical translation of the x-axis four units upward. Since the x-axis is a horizontal line and has equation y = 0, it follows that the line parallel to the x-axis and four units above the x-axis has equation y = 4. <Difficulty> Easy <Question Type> Standard Multiple Choice Mar. 4, 2010If 0.036 = 3.6 × 10t, what is the value of t?
If t is a nonzero integer, multiplying a number in decimal form by 10t moves the decimal point to the right or to the left, depending on whether t is positive or negative, respectively. <Correct Answer> B
Feb. 26, 2010 A florist buys roses at $0.50 apiece and sells them for $1.00 apiece. If there are no other expenses, how many roses must be sold in order to make a profit of $300?
<Correct Answer> E
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Mar. 18, 2010
The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. Most ships move (A) through the Suez Canal with (B) their own power, but large ships must (D) be assisted by a tugboat. 1. (A) 2. (B) 3. (C) 4. (D) 5. (E) <Hint> Pay attention to prepositions and what they mean in context. <Correct Answer> B <Here's Why> The error in this sentence occurs at (B), where there is an improper idiom. The idiom is “under their own power,” not “with their own power.” <Question Type> Identifying Sentence Errors Mar. 15 Part of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A. The well-preserved, 121-million-year-old fossilized bird embryo on display at the museum has several features that suggest that its young could move about and feed themselves very soon after they hatched.
<Correct Answer> 4 <Here's Why> Choice (D) is correct. It avoids the pronoun reference error of the original by using “the species” to indicate the kind of birds (birds of the same species) whose “young could move about … hatched.” <Question Type> Improving Sentences Mar. 10, 2010 The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. It weaves (A) across a strip of tropical land where (B) the Isthmus of Panama narrows (C) in the shape of a long flattened letter S, the Panama Canal links the Atlantic(D) and Pacific Oceans. 1. (A) 2. (B) 3. (C) 4. (D) 5. (E) <Hint> Remember that two complete thoughts should never be joined by a comma. <Correct Answer> A
<Question Type> Identifying Sentence Errors Mar. 5, 2010 Part of the following sentence is underlined; beneath the sentence are five ways of phrasing the underlined material. Select the option that produces the best sentence. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A. Its fossil record virtually unchanged over 100 million years, the Gingko tree is one of the oldest living species of tree. 1. Its fossil record 2. Its fossil record was 3. Its fossil record, which is 4. Its fossil record exists 5. Its fossil record, because <Hint> Try placing the adjectival phrase “Its fossil record … years” after the noun it modifies, “the Gingko tree.” <Correct Answer> A
<Question Type> Improving Sentences Mar. 1, 2010 The following sentence contains either a single error or no error at all. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence contains no error, select choice E. Except for (A) the phonograph, the performances of great musicians (B) and the voices of famous people would have been (C) lost to history (D). 1. (A) 2. (B) 3. (C) 4. (D) 5. (E) (no error) <Hint> When choosing prepositions, pay attention to their meaning. <Correct Answer> A
Mar. 19
Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. Rod monochromasy, a type of colorblindness that renders a person’s vision strongest when light is weakest, is so rarely ------- that it is often ------- .
Your best bet in answering this question may be to plug each set of answers into the sentence to see which combination makes the most sense. <Correct Answer> A <Here's Why> Physicians are less likely to be familiar with the symptoms of an illness that is rarely “encountered,” or seen. Therefore, it makes sense to claim that a rare condition is more likely to be “misdiagnosed,” or incorrectly identified. <Difficulty> Medium <Question Type> Sentence Completions Mar. 16 Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. While a “ rock” is usually defined as ------- , or a combination, of one or more minerals, geologists often ------- the definition to include such materials as clay, loose sand, and certain limestones.
The information after the first comma defines the word in the first blank. <Correct Answer> 2 <Here's Why> Choice (B) is correct. If these terms were inserted into the sentence, the sentence would read, “ While a 'rock' is usually defined as an aggregate, or combination, of one or more minerals, geologists often extend the definition to include such materials as clay, loose sand, and certain limestones.” An “ aggregate” is the sum total of a combination of things, so a “ rock” is an aggregate of one or more minerals. In addition to minerals, geologists feel confident including other materials such as “ clay, loose sand, and certain, limestones” in their definition of a rock; they “ extend,” or broaden, the definition. <Difficulty>Medium> <Question>Type: Sentence Completions Mar. 11 Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. Numerous illnesses that were once difficult to ------- may now be diagnosed through ------- blood tests.
The words “once” and “now” suggest that certain illnesses are no longer “difficult” to diagnose. <Correct Answer> A <Here's Why> It makes sense to say that certain diseases are no longer difficult to “detect,” or discover, now that doctors can diagnose them through routine, or “perfunctory,” tests. Difficulty: Medium Question Type: Sentence Completions Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. Mar. 8 Because he was ------- in the face of danger, the explorer won the government’s highest award for conspicuous bravery.
<Correct Answer> C
Choice (C) is correct. Someone who was “dauntless,” or fearless, when faced with danger might very well earn an award for bravery. <Question Type>Sentence Completions Mar. 2 The notoriously temperamental American actor Edwin Forrest was known for his ------- both on stage and off. 1. apologies 2. musings 3. inequities 4. histrionics 5. philosophies <Hint> The structure of the sentence suggests that the word in the blank will pertain to Forrest’s “notorious” behavior.<Correct Answer> D
<Difficulty> Medium <Question Type> Sentence Completions One major component of university application is the SAT score. It is the most common used standardized test that all American universities accept in determining a candidate's readiness for college. For the past 10 years, the test structure hasn't changed. That is about to change in 2016. Below are common questions that may give you a better understanding of what to expect in 2016.
Why is College Board changing the SAT? College Board is changing the SAT to better mirror college classwork. They claim that the new SAT will focus more on essential things that research shows has the most impact on college readiness. Who does the 2016 SAT affect? It will impact students who are enrolling to college in fall 2017. How many sections will there be in the new 2016 SAT? There will be three sections: Evidence-based Reading and Writing, Math, and Essay. However, the Essay section will be made optional. How long will the 2016 SAT take? It will take approximately 3 hours, with an optional 50 minutes for the Essay section. How will the test scoring change? The 2016 SAT scoring will be on a 400 to 1600 scale (200 - 800 points possible for the Evidence-based Reading and Writing, and Math). Scores for the Essay section will be reported separately from the 400 to 1600 scale and has a score range of 2-8. Furthermore, there will no longer be any penalty for any wrong or unanswered items. How will the 2016 SAT affect a non-native student? The section that will be heavily influenced in the 2016 SAT is the English section. Students are expected to engage in close reading, careful analysis and clear writing with supporting evidences. They need to interpret meaning based on context as well as be aware of possible multiple meanings of a word. There will be significantly more information/text for students to understand, dissect and analyze. Therefore, it is that much more vital for students to possess strong English skills. If you have any questions, please feel free to contact us at 886-2-7718-7660. |