670 McGRAW-HILL’S SAT 6 6 666 6 31. Which of the following is the best way to com- bine sentences 3, 4, and 5? (A) The name of the phenomenon comes from the legend of Archimedes, who had been thinking for days about how to determine whether King Hieron II’s crown was pure gold without destroying it. (B) Archimedes had been thinking for days about how to determine whether King Hieron II’s crown was pure gold without destroying it, and this is where the name of the phenomenon comes from. (C) The legend of Archimedes thinking about how to determine whether King Hieron II’s crown was pure gold without destroying it is the origin of the name of the phenomenon. (D) The phenomenon is named for Archimedes and his thinking for days about how to determine whether King Hieron II’s crown was pure gold without destroying it. (E) The name of the phenomenon was from Archimedes, and his thinking for days about how to determine without destroy- ing it whether King Hieron II’s crown was pure gold. 32. Which of the following revisions of sentence 7 most clearly and logically introduces the sec- ond paragraph? (A) This historical episode is something that all students should learn about in school. (B) Understanding this phenomenon may help students to improve their studies. (C) Nevertheless, this episode is something that all students should know. (D) Understanding this episode requires a more thorough understanding of its historical setting. (E) Many have tried to understand this phenomenon, but few have succeeded. 33. Which of the following is the best revision of the underlined portion of sentence 8 (repro- duced below)? You have probably had the experience of think- ing about a paper or a math problem for so long that it’s like one’s brain gets frozen . (A) it seems that your brain gets frozen (B) one’s brain gets frozen (C) your brain seems to freeze (D) your brains seem to freeze (E) one’s brain seems to freeze 34. Where is the best place to insert the following sentence? Perhaps if students could work such little excur- sions into their busy study schedules, they would have similar “eureka” experiences. (A) after sentence 7 (B) after sentence 8 (C) after sentence 9 (D) after sentence 10 (E) after sentence 11 (as the last sentence of the second paragraph) 35. In context, which of the following revisions of the underlined portion of sentence 12 (repro- duced below) is most effective at making it clearer and more specific? Unfortunately, many students today don’t have time for that. (A) today have hardly even 1 hour for such things (B) today, unlike those in Archimedes’ time, don’t have time to go to the movies (C) today don’t have time for such excursions (D) of modern times lack sufficient time for the kinds of things explained above (E) today lack sufficient time for things like this STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. CHAPTER 16 / PRACTICE TEST 2 671 7 7 777 7 GO ON TO THE NEXT PAGE 1. If four apples cost 20 cents, then, at this rate, how much would ten apples cost? (A) $.40 (B) $.50 (C) $.60 (D) $.70 (E) $.80 2. If 2 b = 8, then 3 b = (A) 6 (B) 9 (C) 27 (D) 64 (E) 81 3. How much greater is the average (arithmetic mean) of a, b, and 18 than the average of a, b, and 12? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 SECTION 7 Time—20 minutes 16 questions Turn to Section 7 of your answer sheet to answer the questions in this section. Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. 1. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solv- ing the problems. They are drawn as accurately as possible EXCEPT when it is stated in a spe- cific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real num- bers x for which f(x) is a real number. The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180. NotesReference Information r A = πr 2 C=2πr ᐉ w A = ᐉw V = ᐉwh V = πr 2 h Special right triangles c 2 = a 2 + b 2 A = 1 / 2 bh h b ᐉ w h r h b c a 2x x x s s s 3 2 30° 60° 45° 45° 672 McGRAW-HILL’S SAT 7 7 777 7 GO ON TO THE NEXT PAGE 4. The first day of a particular month is a Tuesday. What day of the week will it be on the 31st day of the month? (A) Wednesday (B) Thursday (C) Friday (D) Saturday (E) Sunday 5. How many integer pairs (m, n) satisfy the statements 0 < m + n < 50 and ? (A) 5 (B) 6 (C) 7 (D) 8 (E) more than 8 6. If y% of 50 is 32, then what is 200% of y? (A) 16 (B) 32 (C) 64 (D) 128 (E) 256 7. For x > 0, the function g(x) is defined by the equation g(x) = x + x 1/2 . What is the value of g(16)? (A) 16 (B) 20 (C) 24 (D) 64 (E) 272 m n = 8 Note: Figure not drawn to scale. 8. In the figure above, if the slope of AB — is − 3 ⁄ 4 , what is the area of ΔABO? (A) 54 (B) 72 (C) 96 (D) 108 (E) 192 –1, 1, 2, −1, 1, 2, −1, 1, 2, . . . 9. The sequence above continues according to the pattern shown. What is the sum of the first 25 terms of this sequence? (A) 15 (B) 16 (C) 18 (D) 19 (E) 21 10. A jar contains only white and blue marbles of identical size and weight. The ratio of the number of white marbles to the number of blue marbles is 4 to b. If the probability of choosing a white marble from the jar at ran- dom is 1 ⁄ 4 , then what is the value of b? (A) 1 (B) 2 (C) 6 (D) 12 (E) 16 O x y A 12 B CHAPTER 16 / PRACTICE TEST 2 673 7 7 777 7 11. The area of a right triangle is 10 square centimeters. If the length of each leg, in cen- timeters, is a positive integer, then what is the least possible length, in centimeters, of the hypotenuse? (A) (B) (C) (D) (E) 12. If y is a number less than 0 but greater than −1, which of the following expressions has the greatest value? (A) 100y (B) y 2 (C) y 3 (D) y 4 (E) y 5 13. If at least one wuzzle is grumpy, then some fuzzles are lumpy. If the statement above is true, then which of the following must also be true? (A) If all wuzzles are grumpy, then all fuzzles are lumpy. (B) If no wuzzle is grumpy, then all fuzzles are lumpy. (C) If all fuzzles are lumpy, then all wuzzles are grumpy. (D) If no wuzzle is grumpy, then no fuzzle is lumpy. (E) If no fuzzle is lumpy, then no wuzzle is grumpy. 401 104 101 41 29 14. Six buses are to carry 200 students on a field trip. If each bus must have no more than 40 students and no fewer than 30 students, then what is the greatest number of buses that can have 40 students? (A) 6 (B) 5 (C) 4 (D) 3 (E) 2 15. The volume of right cylinder A is twice the vol- ume of right cylinder B. If the height of cylin- der B is twice the height of cylinder A, then what is the ratio of the radius of cylinder A to the radius of cylinder B? (A) 1 to 2 (B) 1 to 1 (C) (D) 2 to 1 (E) 4 to 1 16. In a garden that is divided into x rows of x squares each, w of the squares lie along the boundary of the garden. Which of the follow- ing is a possible value for w? (A) 29 (B) 34 (C) 40 (D) 46 (E) 55 21to STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. 674 McGRAW-HILL’S SAT 8 8 888 8 GO ON TO THE NEXT PAGE 2. The concept that the Earth is round was once theory, but is now accepted as an inarguable truth. (A) an incontrovertible (B) a mellifluous (C) an admirable (D) a dubious (E) an accurate 3. The controversy within the party produced a that broke it into several factions even before the matter could be fully discussed among the members. (A) unanimity (B) schism (C) caucus (D) commemoration (E) prognostication 4. Horace Mann, widely acknowledged as the fa- ther of American public schooling, the Massachusetts legislature to institute a system for universal access to education. (A) petitioned . . restricting (B) established . . denying (C) persuaded . . ensuring (D) tolerated . . requiring (E) discouraged . . vouchsafing 1. The evidence for ESP is at best, so very few reputable scientists are willing to even that the phenomenon exists. (A) meager . . regret (B) unconvincing . . suggest (C) plentiful . . admit (D) paltry . . deny (E) strong . . assume SECTION 8 Time—20 minutes 19 questions Turn to Section 8 of your answer sheet to answer the questions in this section. Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. EXAMPLE: Rather than accepting the theory unquestion- ingly, Deborah regarded it with . (A) mirth (B) sadness (C) responsibility (D) ignorance (E) skepticism A C D B B CHAPTER 16 / PRACTICE TEST 2 675 8 8 888 8 Questions 7–19 are based on the following passages. The following two passages concern the use of “reinforcers,” which are rewards or punish- ments used to encourage desired behaviors, and “contingencies,” which are the arrangements of those reinforcers to shape behavior. PASSAGE 1 “Avoid compulsion,” said Plato in The Republic, “and let your children’s lessons take the form of play.” Horace, among others, recom- mended rewarding a child with cakes. Eras- mus tells of an English gentleman who tried to teach his son Greek and Latin without pun- ishment. He taught the boy to use a bow and arrow and set up targets in the shape of Greek and Latin letters, rewarding each hit with a cherry. He also fed the boy letters cut from GO ON TO THE NEXT PAGE 5. The light from most stars takes millions of years to reach us, so not only is the present existence of these stars , but so are the very concepts of “the present” and “existence.” (A) debatable (B) methodical (C) indecorous (D) imperious (E) profuse 6. Although many parents prefer to be when their children broach sensitive personal sub- jects, others resort instead to so as to make any potentially offensive matters seem less ob- jectionable. (A) honest . . anachronism (B) intolerant . . laudation (C) clandestine . . obligation (D) candid . . euphemism (E) forthright . . coercion delicious biscuits. Privileges and favors are often suggested, and the teacher may be personally reinforcing as friend or entertainer. In indus- trial education students are paid for learning. Certain explicit contrived reinforcers, such as marks, grades, and diplomas, are characteris- tic of education as an institution. (These sug- gest progress, but like progress they must be made reinforcing for other reasons.) Prizes are intrinsically reinforcing. Honors and medals derive their power from prestige or esteem. This varies between cultures and epochs. In 1876 Oscar Wilde, then 22 years old and halfway toward his B.A. at Oxford, got a “first in Mods.” He wrote to a friend: “. . . I did not know what I had got till the next morning at 12 o’clock, breakfasting at the Mitre, I read it in the Times. Altogether I swaggered horribly but am really pleased with myself. My poor mother is in great delight, and I was overwhelmed with telegrams on Thursday from everyone I knew.” The con- temporary student graduating summa cum laude is less widely acclaimed. Although free of some of the by-products of aversive control, positive reinforcers of this sort are not without their problems. Many are effective only in certain states of deprivation which are not always easily arranged. Making a student hungry in order to reinforce him with food would raise personal issues which are not entirely avoided with other kinds of reinforcers. We cannot all get prizes, and if some students get high grades, others must get low. But the main problem again is the contin- gencies. Much of what the child is to do in school does not have the form of play, with its naturally reinforcing consequences, nor is there any natural connection with food or a passing grade or a medal. Such contingencies must be arranged by the teacher, and the arrangement is often defective. The boy men- tioned by Erasmus may have salivated slightly First passage: B. F. Skinner, The Technology of Teaching, © 1968 Prentice-Hall. Second passage: © 2004 Christopher Black. All rights reserved. Reprinted by permission of the author. Line 5 10 15 20 25 30 35 40 45 50 The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is stated or implied in the passage and in any introductory material that may be provided. 676 McGRAW-HILL’S SAT 8 8 888 8 GO ON TO THE NEXT PAGE upon seeing a Greek or Latin text, and he was probably a better archer, but his knowledge of Greek and Latin could not have been appre- ciably improved. Grades are almost always given long after the student has stopped be- having as a student. We must know that such contingencies are weak because we would never use them to shape skilled behavior. In industrial education pay is usually by the hour—in other words, contingent mainly on being present. Scholarships are contingent on a general level of performance. All these con- tingencies could no doubt be improved, but there is probably good reason why they re- main defective. PASSAGE 2 Even if they don’t study it as a philosophi- cal matter, all teachers must at some point confront the issue of whether, when, and how to punish or reward student behavior. Unless a teacher is blessed with a class full of highly motivated adult-pleasers, it is nearly impossi- ble to avoid the need to nudge students in one direction or another. Simple suggestion works occasionally, but not frequently enough. Rea- soning sometimes works, too, but explaining the logical nuances of behavioral standards is often time-consuming and too often falls on deaf ears. So the practical question becomes: the carrot or the stick? Most educators and psychologists agree that reward is always better than punishment, but a small yet vocal group of psychologists have maintained since the 1960s that reward is often just as harmful as punishment, if not more so. Their arguments are subtle but very persuasive. Educators like Alfie Kohn and psy- chologists like Edward Deci claim that careful study has shown that the introduction of a re- ward system, like gold stars on an attendance sheet or extra recess time for good behavior, changes the nature of the desired behavior completely, and not for the better. For in- stance, Deci conducted a study in which peo- ple were given a puzzle to solve. Some were given money as a “reward” for solving the puzzle and others were simply asked to solve the puzzle. Afterwards, both groups were left alone but watched carefully. Those who had been paid stopped playing, but those who had not been paid continued. Deci concluded that the subjects who were paid probably con- strued the task as being manipulative: the ex- perimenter was trying to get them to do something through bribery. The unpaid sub- jects, however, were more likely to see the task as fun and worth doing for its own sake. This study and many like it have profound implications for the classroom. Several exper- iments have demonstrated that “pay-to-read” programs, where students are given money or certificates to read books, have surprisingly negative effects on literacy. Such programs usually get kids to “read” a lot more books, but their reading skills and, far more impor- tantly, their love of reading decline. Such pro- grams, research suggests, turn reading into a performance rather than a fulfilling personal experience. They encourage students to read books only superficially and only to get the reward. What is worse, like Deci’s puzzle- solvers, the students don’t want to continue reading after the payments stop. Books have become only enrichment for the pocket, not enrichment for the mind. Of course, the human mind is an enor- mously complex machine, and it would be a mistake to use these few experiments to gen- eralize that all rewards are bad. Certainly, honest and mindful praise from a respected teacher can do a great deal to encourage not only good behavior but rigorous intellectual curiosity. Parents and teachers, however, need to be very aware of children’s need to feel in control of themselves. 7. It can be inferred that the “English gentleman” (line 5) believed that good teaching utilized (A) punishment (B) well-written books (C) reward (D) humor (E) careful grading 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 CHAPTER 16 / PRACTICE TEST 2 677 8 8 888 8 GO ON TO THE NEXT PAGE 8. The parenthetical remark in lines 17–19 is intended to caution educators against (A) failing to make grades and diplomas meaningful to students (B) punishing students unnecessarily (C) employing dull lessons (D) emphasizing entertainment over rigor (E) using rewards as reinforcers 9. Passage 1 indicates that “cultures and epochs” (lines 22–23) vary in the ways that (A) universities choose from among their ap- plicants (B) academic awards are effective as motivators (C) universities teach literature (D) students are paid money for learning (E) the media portray educational crises 10. The Wilde story in lines 23–32, “In 1876 . . . everyone I knew,’ ” is intended to illustrate (A) how the modern cultural perception of academic honors differs from that of a previous era (B) a particularly effective teaching strategy (C) how a famous author used rewards to teach his students (D) the dangerous effects of using academic rewards (E) the point that Plato makes in the first sentence 11. Passage 1 mentions which of the following as “problems” (line 37) inherent in the use of positive reinforcers in education? I. difficulties in scheduling the rein- forcers II. limitations in the supply of rein- forcers III. the fact that rewards encourage only superficial learning (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 12. In the final paragraph of Passage 1, the author suggests that grades are problematic as re- inforcers because they (A) cannot be given to every student (B) do not provide sensual gratification, as food does (C) are not publicized enough (D) are not given immediately after the de- sired behavior is exhibited (E) are not as useful to the student as money 13. The sentence that begins on line 78, “Reason- ing sometimes works . . . on deaf ears” is in- tended to describe the interaction between (A) those who promote the use of punish- ments and those who oppose it (B) educators and philosophers (C) parents and teachers (D) teachers and administrators (E) teachers and students 14. In Passage 2, Alfie Kohn and Edward Deci (lines 90–91) are mentioned as examples of (A) teachers who use rewards as reinforcers (B) experts who question the effectiveness of rewards as reinforcers (C) scientists on opposite sides of a debate (D) educators who prefer negative re- inforcers to positive reinforcers (E) educators who advocate a careful sched- ule of contingencies for students 678 McGRAW-HILL’S SAT 8 8 888 8 15. In saying that “the introduction of a reward system . . . changes the nature of the desired behavior” (lines 92–95), the author of Passage 2 indicates that (A) many people object to the use of punish- ments in school (B) teachers find it difficult to find the right kinds of rewards for student performance (C) experts disagree about the effects of rewards on human behavior (D) such systems tend to decrease student in- terest in the activity for its own sake (E) not enough study has been done on the effectiveness of rewards in education 16. Deci’s conclusion about the experiment de- scribed in Passage 2 (lines 96–110) assumes that the subjects in the study (A) are well educated (B) are highly proficient at solving puzzles (C) have not participated in reward systems before (D) can make inferences about the motives of the experimenter (E) have some teaching experience 17. The author of Passage 2 mentions that “the human mind is an enormously complex ma- chine” (lines 129–130) in order to suggest that (A) a simplistic theory about the effective- ness of rewards is unwise (B) people cannot be easily fooled (C) many learning disabilities require special attention (D) teachers often find it hard to teach certain subjects (E) Deci’s experiment was poorly constructed 18. The description of the “problems” (line 37) with positive reinforcers in Passage 1 would most likely be regarded by Edward Deci as (A) thorough and fair (B) presumptuous and incomplete (C) unfair to educators (D) erroneous in concluding that the methods of the “gentleman” were ineffective (E) likely correct, but worthy of further study 19. Which of the following assumptions is shared by the authors of both passages? (A) Rewards are ineffective as reinforcers of behavior. (B) Honors and grades are necessary ele- ments of institutional education. (C) Good teaching is always focused on play. (D) Negative feedback is not an effective teaching tool. (E) If prizes are to be used in a classroom, there must be enough for all students. STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test. CHAPTER 16 / PRACTICE TEST 2 679 9 9 999 9 GO ON TO THE NEXT PAGE 1. Choreographer Alvin Ailey’s works, whose style is rooted in the techniques of modern dance, jazz dance and ballet, draw upon African American themes. (A) Choreographer Alvin Ailey’s works, whose style is rooted in the techniques of modern dance, jazz dance and ballet, draw upon African American themes. (B) Alvin Ailey has a style of a choreographer that is rooted in the techniques of modern dance, jazz dance and ballet of which also draws upon African American themes. (C) The works of choreographer Alvin Ailey, which draw upon African American themes, have a style that is rooted in the techniques of modern dance, jazz dance, and ballet. (D) Choreographer Alvin Ailey’s works, which have a style that is rooted in the techniques of modern dance, jazz dance, and ballet, drawing upon African American themes. (E) Alvin Ailey’s style, a choreographer, is rooted in the techniques of modern dance and jazz dance and ballet which also draws upon African American themes. SECTION 9 Time—10 minutes 14 questions Turn to Section 9 of your answer sheet to answer the questions in this section. Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. The following sentences test correctness and effectiveness of expression. Part of each sen- tence or the entire sentence is underlined; beneath each sentence are five ways of phras- ing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making your selection, follow the require- ments of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence— clear and precise, without awkwardness or ambiguity. EXAMPLE: The children couldn’t hardly believe their eyes . (A) couldn’t hardly believe their eyes (B) could hardly believe their eyes (C) would not hardly believe their eyes (D) couldn’t nearly believe their eyes (E) couldn’t hardly believe his or her eyes A C D E B . educators who prefer negative re- inforcers to positive reinforcers (E) educators who advocate a careful sched- ule of contingencies for students 678 McGRAW-HILL’S SAT 8 8 888 8 15. In saying that. 1 / 2 bh h b ᐉ w h r h b c a 2x x x s s s 3 2 30° 60° 45° 45° 672 McGRAW-HILL’S SAT 7 7 777 7 GO ON TO THE NEXT PAGE 4. The first day of a particular month is a Tuesday. What day of the week will it. provided. 676 McGRAW-HILL’S SAT 8 8 888 8 GO ON TO THE NEXT PAGE upon seeing a Greek or Latin text, and he was probably a better archer, but his knowledge of Greek and Latin could not have been appre- ciably