820 Six Model SAT Tests GO ON TO THE NEXT PAGE 7. What is the area of the quadrilateral whose vertices are at (1, 1), (5, 1), (5, 5) and (3, 5)? (A) 8 (B) 12 (C) 16 (D) 24 (E) 10 + 2 8. In the figure above, the graph on the top is the graph of y = f(x). Which of the following is the equation of the graph on the bottom? (A) y = f(x + 2) (B) y = f(x – 2) (C) y = f(x + 2) + 2 (D) y = f(x – 2) + 2 (E) y = f(x + 2) – 2 x y x y 2 7 Test 6 821 7 9. What is the value of ? 10. If ab = 20 and a = –5, what is the value of a 2 – b 2 ? 1 5 2 10 3 15 4 20 5 25 ++++ Directions for Student-Produced Response Questions (Grid-ins) In questions 9–18, first solve the problem, and then enter your answer on the grid pro- vided on the answer sheet. The instructions for entering your answers are as follows: • First, write your answer in the boxes at the top of the grid. • Second, grid your answer in the columns below the boxes. • Use the fraction bar in the first row or the decimal point in the second row to enter fractions and decimal answers. • All decimals must be entered as accu- rately as possible. Here are the three acceptable ways of gridding 3 11 = 0.272727 3/11 .272 .273 1 2 3 4 5 6 9 0 1 2 3 4 5 6 8 9 0 2 3 4 5 6 7 8 9 0 1 3 4 6 7 8 9 7 7 2 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 8 9 0 1 2 3 4 6 7 8 9 0 1 2 3 4 5 6 7 8 9 1 2 3 4 0 2 3 4 1 2 3 4 1 2 3 4 2 3 4 1 2 3 4 1 2 3 0 1 2 3 1 2 4 5 6 0 1 2 3 4 5 6 0 2 3 4 5 6 0 2 3 4 5 6 1 2 3 4 5 6 0 1 3 4 5 6 7 0 1 2 3 4 5 6 0 1 3 4 5 6 1 2 3 4 5 6 0 1 3 4 5 6 7 0 1 2 3 4 5 6 0 1 2 4 5 6 ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ GO ON TO THE NEXT PAGE • Note that rounding to .273 is acceptable, because you are using the full grid, but you would receive no credit for .3 or .27, because these answers are less accurate. Answer: Answer: 1.75 Answer: 100 Write your → answer in the boxes. Grid in → your answer. • Grid only one space in each column. • Entering the answer in the boxes is recom- mended as an aid in gridding, but is not required. • The machine scoring your exam can read only what you grid, so you must grid in your answers correctly to get credit. • If a question has more than one correct answer, grid in only one of these answers. • The grid does not have a minus sign, so no answer can be negative. • A mixed number must be converted to an improper fraction or a decimal before it is gridded. Enter 1 as 5/4 or 1.25; the machine will interpret 1 1/4 as and mark it wrong. Either position is acceptable 8 15 11 4 1 4 822 Six Model SAT Tests 11. If of x equals of x, what is of x? 12. A clock chimes every hour to indicate the time, and also chimes once every 15 minutes on the quarter-hour and half-hour. For example, it chimes 3 times at 3:00, once at 3:15, once at 3:30, once at 3:45, and 4 times at 4:00. What is the smallest number of times the clock can chime in an interval of 2 hours? Note: Figure not drawn to scale 13. For the figure above, what is the largest value of x that will fit in the grid? 14. The average (arithmetic mean) amount of savings of 10 students is $60. If 3 of the students have no savings at all, and each of the others has at least $25, including John, who has exactly $130, what is the largest amount, in dollars, that any one student can have? 15. In the stair unit in the figure above, all the angles are right angles. The left side is 5 feet 4 inches, and the bottom is 9 feet 2 inches. Each vertical riser is 8 inches. The top step is 10.25 inches, and each step below it is 1 inch longer than the preceding step. What is the perimeter, in inches, of the figure? 16. In the figure above, what is the value of h? 17. Let a and b be positive numbers such that a% of a% of b equals c. If a 2 % of b equals kc, what is the value of k? 18. For how many positive three-digit numbers is the average of the three digits equal to 2? 10 1 4 11 8" 8" 9'2" 5'4" 1 4 " " 17 1 4 " 1 2 4 5 3 4 2 3 YOU MAY GO BACK AND REVIEW THIS SECTION IN THE REMAINING TIME, BUT DO NOT WORK IN ANY OTHER SECTION UNTIL TOLD TO DO SO. S T O P 7 3 h 4 Test 6 823 8 888888888 8 SECTION 8 Time—20 Minutes 19 Questions Select the best answer to each of the following questions; then blacken the appropriate space on your answer sheet. Each of the following sentences contains one or two blanks; each blank indicates that a word or set of words has been left out. Below the sentence are five words or phrases, lettered A through E. Select the word or set of words that best completes the sentence. Example: Fame is ; today’s rising star is all too soon tomorrow’s washed-up has-been. (A) rewarding (B) gradual (C) essential (D) spontaneous (E) transitory 1. Given the nature of wood, the oldest totem poles of the Northwest Coast Indians eventually fell to decay; only a few still stand today. (A) resilient (B) combustible (C) malleable (D) perishable (E) solid 2. Lee, who refrained from excesses in his personal life, differed markedly from Grant, who notori- ous drinking bouts with his cronies. (A) deprecated (B) minimized (C) indulged in (D) shunned (E) compensated for 3. By nature Toshiro was , given to striking up casual conversations with strangers he encountered at bus stops or check-out stands. (A) diffident (B) observant (C) reticent (D) gregarious (E) laconic 4. In the absence of native predators to stop their spread, imported deer to such an inordinate degree that they overgrazed the countryside and the native vegetation. (A) thrived threatened (B) propagated cultivated (C) suffered abandoned (D) flourished scrutinized (E) dwindled eliminated 5. The contract negotiations were often surprisingly , deteriorating at times into a welter of accusa- tions and counteraccusations. (A) perspicacious (B) phlegmatic (C) sedate (D) acrimonious (E) propitious 6. Black religion was in part a protest movement—a protest against a system and a society that was designed to the dignity of a segment of God’s creation. (A) unintentionally reflect (B) explicitly foster (C) inevitably assess (D) deliberately demean (E) provocatively enhance Ꭽ Ꭾ Ꭿ ൳ ൴ GO ON TO THE NEXT PAGE 824 Six Model SAT Tests Questions 7–19 are based on the following passages. The following passages deal with the importance of money to Americans. The first is taken from a commencement address made by American philosopher George Santayana in 1904. The second is taken from an essay written by British poet W. H. Auden in 1963. Passage 1 American life, everyone has heard, has extra- ordinary intensity; it goes at a great rate. This is not due, I should say, to any particular urgency in the object pursued. Other nations have more pressing motives to bestir themselves than America has: and it is observable that not all the new nations, in either hemisphere, are energetic. This energy can hardly spring either from unusu- ally intolerable conditions which people wish to overcome, nor from unusually important objects which they wish to attain. It springs, I should ven- ture to say, from the harmony which subsists between the task and the spirit, between the mind’s vitality and the forms which, in America, political and industrial tradition has taken on. It is sometimes said that the ruling passion in America is the love of money. This seems to me a com- plete mistake. The ruling passion is the love of business, which is something quite different. The lover of money would be jealous of it; he would spend it carefully; he would study to get out of it the most he could. But the lover of business, when he is successful, does not much change his way of living; he does not think out what further advantages he can get out of his success. His joy is in that business itself and in its further opera- tion, in making it greater and better organized and a mightier engine in the general life. The adventi- tious personal profit in it is the last thing he thinks of, the last thing he is skillful in bringing about; and the same zeal and intensity is applied in managing a college, or a public office, or a naval establishment, as is lavished on private business, for it is not a motive of personal gain that stimulates to such exertions. It is the absorb- ing, satisfying character of the activities them- selves; it is the art, the happiness, the greatness of them. So that in beginning life in such a society, which has developed a native and vital tradition out of its practice, you have good reason to feel that your spirit will be freed, that you will begin to realize a part of what you are living for. Passage 2 Political and technological developments are rapidly obliterating all cultural differences and it is possible that, in a not remote future, it will be impossible to distinguish human beings living on one area of the earth’s surface from those living on any other, but our different pasts have not yet been completely erased and cultural differences are still perceptible. The most striking difference between an American and a European is the dif- ference in their attitudes towards money. Every European knows, as a matter of historical fact, that, in Europe, wealth could only be acquired at the expense of other human beings, either by con- quering them or by exploiting their labor in facto- ries. Further, even after the Industrial Revolution began, the number of persons who could rise from poverty to wealth was small; the vast major- ity took it for granted that they would not be much richer nor poorer than their fathers. In con- sequence, no European associates wealth with personal merit or poverty with personal failure. To a European, money means power, the free- dom to do as he likes, which also means that, consciously or unconsciously, he says: “I want to have as much money as possible myself and oth- ers to have as little money as possible.” In the United States, wealth was also acquired by stealing, but the real exploited victim was not a human being but poor Mother Earth and her creatures who were ruthlessly plundered. It is true that the Indians were expropriated or exterminat- ed, but this was not, as it had always been in Europe, a matter of the conqueror seizing the wealth of the conquered, for the Indian had never realized the potential riches of his country. It is also true that, in the Southern states, men lived on the labor of slaves, but slave labor did not make them fortunes; what made slavery in the South all the more inexcusable was that, in addition to being morally wicked, it didn’t even pay off handsomely. Thanks to the natural resources of the country, every American, until quite recently, could rea- sonably look forward to making more money than his father, so that, if he made less, the fault must GO ON TO THE NEXT PAGE The questions that follow the next two passages relate to the content of both, and to their relationship. The correct response may be stated outright in the passage or merely suggested. 8 888888888 8 Line (5) (10) (15) (20) (25) (30) (35) (40) (45) (50) (55) (60) (65) (70) (75) (80) (85) Test 6 825 8 888888888 8 be his; he was either lazy or inefficient. What an American values, therefore, is not the possession of money as such, but his power to make it as a proof of his manhood; once he has proved himself by making it, it has served its function and can be lost or given away. In no society in history have rich men given away so large a part of their for- tunes. A poor American feels guilty at being poor, but less guilt than an American rentier * who has inherited wealth but is doing nothing to increase it; what can the latter do but take to drink and psychoanalysis? *A rentier lives on a fixed income from rents and investments. 7. In Passage 1, the word “spring” in line 8 means (A) leap (B) arise (C) extend (D) break (E) blossom 8. The lover of business (lines 22–38) can be described as all of the following EXCEPT (A) enthusiastic (B) engrossed (C) enterprising (D) industrious (E) mercenary 9. The author of Passage 1 maintains that Americans find the prospect of improving business organiza- tions (A) pleasurable (B) problematic (C) implausible (D) wearing (E) unanticipated 10. In line 28, “engine” most nearly means (A) artifice (B) locomotive (C) mechanical contrivance (D) financial windfall (E) driving force 11. The author of Passage 1 contends that those who grow up in American society will be influenced by its native traditions to (A) fight the intolerable conditions afflicting their country (B) achieve spiritual harmony through meditation (C) find self-fulfillment through their business activities (D) acknowledge the importance of financial accountability (E) conserve the country’s natural resources 12. In lines 43–48 the author of Passage 2 asserts that technological advances (A) are likely to promote greater divisions between the rich and the poor (B) may eventually lead to worldwide cultural uniformity (C) can enable us to tolerate any cultural differ- ences between us (D) may make the distinctions between people increasingly easy to discern (E) destroy the cultural differences they are intended to foster 13. The word “striking” in line 50 means (A) attractive (B) marked (C) shocking (D) protesting (E) commanding 14. In taking it for granted that they will not be much richer or poorer than their fathers (lines 59–61), Europeans do which of the following? (A) They express a preference. (B) They refute an argument. (C) They qualify an assertion. (D) They correct a misapprehension. (E) They make an assumption. GO ON TO THE NEXT PAGE (90) (95) 15. Until quite recently, according to lines 84–88, to Americans the failure to surpass one’s father in income indicated (A) a dislike of inherited wealth (B) a lack of proper application on one’s part (C) a fear of the burdens inherent in success (D) the height of fiscal irresponsibility (E) the effects of a guilty conscience 16. The author’s description of the likely fate of the American rentier living on inherited wealth is (A) astonished (B) indulgent (C) sorrowful (D) sympathetic (E) ironic 17. In Passage 2 the author does all of the following EXCEPT (A) make a categorical statement (B) correct a misapprehension (C) draw a contrast (D) pose a question (E) cite an authority 18. The authors of both passages most likely would agree that Americans engage in business (A) on wholly altruistic grounds (B) as a test of their earning capacity (C) only out of economic necessity (D) regardless of the example set by their parents (E) for psychological rather than financial reasons 19. Compared to the attitude toward Americans expressed in Passage 1, the attitude toward them expressed in Passage 2 is (A) more admiring (B) less disapproving (C) more cynical (D) less patronizing (E) more chauvinistic 826 Six Model SAT Tests YOU MAY GO BACK AND REVIEW THIS SECTION IN THE REMAINING TIME, BUT DO NOT WORK IN ANY OTHER SECTION UNTIL TOLD TO DO SO. S T O P 8 888888888 8 Test 6 827 9 99999 9 1. If a = –2, what is the value of a 4 – a 3 + a 2 – a? (A) –30 (B) –10 (C) 0 (D) 10 (E) 30 2. If a mixture of nuts consists of 3 pounds of peanuts, 1 pound of walnuts, and 5 pounds of cashews, by weight, what fraction of the mixture is peanuts? (A) (B) (C) (D) (E) 3. When a digital clock reads 3:47, the sum of the digits is 14. How many minutes after 3:47 will the sum of the digits be 20 for the first time? (A) 42 (B) 132 (C) 192 (D) 251 (E) 301 4. Gilda drove 650 miles at an average speed of 50 miles per hour. How many miles per hour faster would she have had to drive in order for the trip to have taken 1 hour less? (A) 6 (B) 4 (C) 4 (D) 4 (E) 3 AC — and BD — are diameters. Note : Figure not drawn to scale 5. In the figure above, if w = 40, what is the ratio of the total length of arcs and to the circumference? (A) (B) (C) (D) (E) 1 2 2 5 1 4 2 9 1 9 CD  AB  1 3 1 6 1 3 2 3 2 3 1 2 3 8 1 3 1 5 1 9 GO ON TO THE NEXT PAGE For each problem in this section determine which of the five choices Time—20 Minutes is correct and blacken the corresponding choice on your answer 16 Questions sheet. You may use any blank space on the page for your work. Notes: • You may use a calculator whenever you think it will be helpful. • Use the diagrams provided to help you solve the problems. Unless you see the words “Note: Figure not drawn to scale” under a diagram, it has been drawn as accurately as possible. Unless it is stated that a figure is three-dimensional, you may assume it lies in a plane. SECTION 9 Area Facts Volume Facts Triangle Facts Angle Facts Reference Information A = w h b A = bh 1 2 A = πr 2 C = 2πr h h V = wh w V = π r 2 h a a 45° 45° a a 2a 60° 30° c b a 2 + b 2 = c 2 360° x° y° z° x + y + z = 180 r r 3 a 2 a w w° A D C B 6. Phil’s Phone Shop sells three models of cellular phones, priced at $100, $125, and $225. In January, Phil sold exactly the same number of each model. What percent of the total income from the sales of cellular phones was attributable to sales of the cheapest model? (A) 22 % (B) 28 % (C) 33 % (D) 44 % (E) It cannot be determined from the information given. 7. In the figure above, a circle is inscribed in a square. If a point is chosen at random inside the square, which of the following is closest to the probability that the point is in the shaded region? (A) 0.1 (B) 0.15 (C) 0.2 (D) 0.25 (E) 0.3 8. Let f(x) = . What is the smallest integer for which f(x) is defined? (A) 0 (B) 1 (C) 3 (D) 4 (E) 5 9. The chart above shows the percent of students at Central High School taking each of the four science courses offered. If every student takes exactly one science course, and if 20% of the students taking chemistry switch to physics, what percent of the students will be taking physics? (A) 7% (B) 17% (C) 20% (D) 25% (E) 30% 10. If a team played g games and won w of them, what fraction of the games played did the team lose? (A) (B) (C) (D) (E) 11. In 1980, the cost of p pounds of potatoes was d dollars. In 1990, the cost of 2p pounds of potatoes was d dollars. By what percent did the price of potatoes decrease from 1980 to 1990? (A) 25% (B) 50% (C) 75% (D) 100% (E) 400% 1 2 gw w − g gw− gw g − wg g − wg w − Biology 25% Earth Science 30% Chemistry 35% Physics x x − − π 4 4 9 1 3 4 7 2 9 828 Six Model SAT Tests GO ON TO THE NEXT PAGE 9 999999 Test 6 829 9 99999 9 12. If a square and an equilateral triangle have equal perimeters, what is the ratio of the area of the triangle to the area of the square? (A) (B) (C) (D) (E) It cannot be determined from the information given. 13. If A is at (3, –1) and B is at (5, 6), what is the slope of the perpendicular bisector of segment AB — ? (A) (B) (C) (D) (E) 14. In the sequence 1, 2, 3, –4, 1, 2, 3, –4, …, the numbers 1, 2, 3, –4 repeat indefinitely. What is the sum of the first 150 terms? (A) 0 (B) 3 (C) 37 (D) 77 (E) 300 15. In the figure above, AB — is a diameter of circle O. If AC = 6 and the radius of the circle is 5, what is the perimeter of the shaded region? (A) 14 + 5π (B) 17 + 5π (C) 14 + 10π (D) 17 + 10π (E) 24 + 5π 16. If the sum of all the positive even integers less than 1000 is A, what is the sum of all the positive odd integers less than 1000? (A) A – 998 (B) A – 499 (C) A + 1 (D) A + 500 (E) + 999 A 2 C B A O 2 5 2 7 − 2 7 − 2 5 − 7 2 4 3 1 1 3 4 43 9 YOU MAY GO BACK AND REVIEW THIS SECTION IN THE REMAINING TIME, BUT DO NOT WORK IN ANY OTHER SECTION UNTIL TOLD TO DO SO. S T O P [...]... by the passage 14 D The tapestries are known as The Lady with the Unicorn In the central tapestry, the lion and the unicorn kneel before the lady, who gently, irresistibly, subdues the forces of nature 15 D To draw carts of stones up the hill for the building of Chartres Cathedral” is to haul the stones used to construct the cathedral In doing such hard manual labor, the noble knights and ladies showed... 12 6 = (5)h ⇒ 5h = 12 ⇒ h = or 2.4 2 5 **There are several other ways to get this answer if you know more than the basic geometry required for the SAT For example, the little triangle on the left in the figure is similar to the large one, and the ratio of the 848 Six Model SAT Tests hypotenuse of the small triangle to the hypotenuse of the large triangle is 3:5 Then, 3:5 = h: 4 ⇒ h = 2.4 a a × ×b = 100... radii of the semicircle If r is the radius, then the area of the semi1 circle is πr 2 Since r is the diameter of the 2 1 circle, the circle’s radius is r and its area 2 2 1 ⎛1 ⎞ is π ⎜ r ⎟ = π r 2 Then the area of the ⎝2 ⎠ 4 shaded region is 1 2 1 2 1 2 πr − πr = πr 2 4 4 The area of the shaded region and the area of the unshaded region are equal Therefore, the probability that the point is in the shaded... the least possible), then the tenth student will have $600 – $130 – $125 = $345 15 (348) You don’t need to add up the lengths of the steps Together, all the horizontal steps are equal to the bottom, and all the vertical risers are equal to the left side The sum of the left side, 5 feet 4 inches, or 64 inches, and the bottom, 9 feet 2 inches, or 110 inches, is half the perimeter The perimeter is 2(64... Add the numbers together and divide by 6 to determine your total score The higher your total score, the better you are likely to do on the essay section of the SAT Note that on the actual SAT two readers will rate your essay; your essay score will be the sum of their two ratings and could range from 12 (highest) to 2 (lowest) Also, they will grade your essay holistically, rating it on the basis of their... a value for a side of the square, say 2 Then the area of the square is 4 Since the diameter of the circle is also 2, the radius is 1, and the area of the circle is π Then the area of the unshaded region is 4 – π, and the probability that the chosen part is in the shaded region 4−π ഠ 0.214 Of the choices, 0.2 is the 4 closest is 8 E The expression x − π is defined only if x – π ≥ 0, so x ≥ π The smallest... is to list them If there are only a few, list them all; if it seems that there will be too many to list, look for a pattern The list starts this way: 105, 114, 123, 132, 141, 150, so there are 6 positive three-digit numbers in the 100’s Continue: 204, 213, 222, 231, 240; there are 5 in the 200’s You can conclude, correctly, that there are 4 in the 300’s, 3 in the 400’s, 2 in the 500’s, and 1 in the. .. NOT WORK IN ANY OTHER SECTION UNTIL TOLD TO DO SO STOP Test 6/Answer Key 833 Answer Key Note: The letters in brackets following the Mathematical Reasoning answers refer to the sections of Chapter 12 in which you can find the information you need to answer the questions For example, 1 C [E] means that the answer to question 1 is C, and that the solution requires information found in Section 12-E: Averages... moving object) 18 B To part the flesh is to split or separate the skin 19 E The “strange flowers” with their looped handles are the hemostats, forceps, and other surgical tools attached to the opening 20 D To write of one object by using a term that normally indicates a different object, suggesting a likeness between them, is to make an implicit comparison, that is, to be metaphorical 21 B The simile “like... Note how the “either or” structure sets up a contrast between the two clauses (Contrast Signal) 2 B The librarian has the committee’s acquiescence or agreement; they assent but do not go so far as to encourage or spur on the librarian Their support is of a lesser degree Note how the “with the if not the structure signals that the missing word and the noun encouragement must differ in meaning to some . ANY OTHER SECTION UNTIL TOLD TO DO SO. S T O P 10 10 10 10 10 10 10 Test 6/Answer Key 833 Answer Key Note: The letters in brackets following the Mathematical Reasoning answers refer to the. thinks the entire universe revolves around him or her. (E) An egotistical person thinks the entire universe revolves around himself or herself. 830 Six Model SAT Tests 10 10 10 10 10 10 10 GO ON TO. alternative to mastering an instrument. (A) genre, not a (B) genre, it is not a (C) genre; not a (D) genre, but is not a (E) genre; and it is not a 10 10 10 10 10 10 10 GO ON TO THE NEXT PAGE