12. c. Let E equal emergency room cost; H equal hos- pice cost, which is ᎏ 1 4 ᎏ E; N equal home nursing cost, which is 2H, or 2( ᎏ 1 4 ᎏ )E,or ᎏ 1 2 ᎏ E. The total bill is E + H + N, which equals E + ᎏ 1 4 ᎏ E + ᎏ 2 4 ᎏ E,or 140,000. So ᎏ 4 4 ᎏ E + ᎏ 1 4 ᎏ E + ᎏ 2 4 ᎏ E = 140,000, so ᎏ 7 4 ᎏ E = 140,000. Multiplying both sides by ᎏ 4 7 ᎏ to solve for E,we get E = 140,000( ᎏ 4 7 ᎏ ), or 80,000. Therefore H = ᎏ 1 4 ᎏ E,or ( ᎏ 1 4 ᎏ )80,000, which equals 20,000, and N = 2H, or 2(20,000), or 40,000. 13. b. M = 3N and 3N + N = 24, which implies that N = 6 and M = 3N = 18. If Nick catches up to Mike’s typing speed, then both M and N will equal 18, and then the combined rate will be 18 plus 18 or 36 pages per hour. 14. c. Let T equal Ted’s age; S equal Sam’s age, which is 3T; R equal Ron’s age, which is ᎏ 2 S ᎏ ,or ᎏ 3 2 T ᎏ .The sum of the ages is 55, which is ᎏ 3 2 T ᎏ + 3T + T, which is equal to ᎏ 3 2 T ᎏ + ᎏ 6 2 T ᎏ + ᎏ 2 2 T ᎏ , which is equal to ᎏ (3T +6 2 T +2T) ᎏ or ᎏ 11 2 T ᎏ . Now multiply both sides of 55 = ᎏ 11 2 T ᎏ by 2 to get 110 = 11T. Divide through by 11 to get 10 = T. That is Ted’s age, so Sam is 3T, or 3(10), or 30 years old, and Ron is ᎏ 3 2 T ᎏ ,or 15 years old. 15. a. In order to find the perimeter, the hypotenuse of the triangle must be found. This comes from recognizing that the triangle is a 5-12-13 trian- gle, or by using the Pythagorean theorem. Therefore, 5 + 12 + 13 = 30. 16. a. This uses the Pythagorean theorem. The longest object would fit on a diagonal from an upper corner to a lower corner. Since the square base is 9 feet squared, the length and width is 3 feet. Because the volume is 36 cubic feet, and the base is 9 square feet, the height must be 4 feet. First, the diagonal in the rectangular wall of the box is 5, because the other sides are 3 and 4 feet. (It is a 3-4-5 triangle.) The longest diagonal can then be found by using the Pythagorean theorem, with a width of 5 and a height of 3 feet. This leaves 5.8 feet as the only reasonable answer. 17. d. If angle 1 is 30°, angle 3 must be 60° by right tri- angle geometry. Because the two lines are par- allel, angles 3 and 4 must be congruent. Therefore, to find angle 5, angle 4 must be sub- tracted from 180 degrees. This is 120°. 18. d. Because the radius of the hemisphere is 3, and it is the same as the half the base of the triangle, the base must be 6. Therefore, the area of the tri- angle is ᎏ 1 2 ᎏ bh = 12. The area of the circle is πr 2 , which is equal to 9π. Therefore, the half-circle’s area is ᎏ 9 2 π ᎏ . Adding gives ᎏ 9 2 π ᎏ + 12. 19. c. If the pentagons are similar, then the two dif- ferent pentagons will have similar proportions. Because A ෆ B ෆ is similar to F ෆ G ෆ , and A ෆ B ෆ = 10, and F ෆ G ෆ = 30, the second pentagon is 3 times as large. Therefore, I ෆ H ෆ is 3 times as large as C ෆ D ෆ , which is 15. 20. d. The volume of a sphere is ᎏ 4 3 ᎏ π 3 . Therefore, the volume of the hemisphere is 18π. This is about 56.5. The water in the cylinder is the total water minus the water in the hemisphere, which leaves 113.5 cubic feet. Volume of a cylinder is area times height. The area of the base is 9π, or about 28.3. Divide the volume of 113.5 by the area of 28.3 to find the height, 4 feet. 21. b. The surface area of the walls is found by multi- plying: 4 walls times 120 square feet = 480 square feet. The area of the door and window to be subtracted is 12 + 21 square feet = 33 square feet; 480 – 33 = 447, so 447 square feet are needed. Louise must buy 5 rolls of wallpaper. 22. d. The total area is equal to the area of the circle minus the area of the triangle. The area of the circle is 16π, and the area of the triangle is ᎏ 1 2 ᎏ bh = 8 square feet. Therefore, the area is 16π – 8. 23. a. The area of the parallelogram can be found in one of two ways. The first would be using a for- mula, which is not provided. The second is by – THEA PRACTICE EXAM 2– 230 splitting the parallelogram into two triangles and a rectangle. The rectangle would have an area of (12 – 3)4 = 36 square feet. The area of the triangles is 3(4). This gives a total area of 48. 24. d. This can be divided into a rectangle and two half-circles. The area of the rectangle is 4(8) = 32 square feet. The diameter of the half-circles cor- responds with the height and width of the rec- tangle. Therefore, the area of the circles is ᎏ 2 2 2π ᎏ = 2π and ᎏ 4 2 2π ᎏ = 8π. Therefore, the answer is 32 + 10π. 25. d. This series actually has two alternating sets of numbers. The first number is doubled, giving the third number. The second number has 4 subtracted from it, giving the fourth number. Therefore, the blank space will be 12 doubled, or 24. 26. b. The amount of water would be equal to ϫϫ60 minutes per hour. This gives 1.80 ϫ 10 4 . 27. d. Since the price per copy is $0.75, divide 60 by 0.75 to find the total number that can be pur- chased with $60; ᎏ 0 6 .7 0 5 ᎏ = 80. 28. c. The speed of the train is 60 miles per hour, obtained from the table. Therefore, the distance from Chicago would be equal to 60t.However, as the train moves on, the distance decreases from Los Angeles, so there must be a function of –60t in the equation. At time t = 0, the distance is 2,000 miles, so the function is 2,000 – 60t. 29. d. First, examine the table to determine that there are 40 minutes in each class period and 4 min- utes of passing time between each class. To determine the starting time of period 3, add 4 minutes to the ending time of period 2. Thus, the starting time of period 3 is 9:23. To calcu- late the ending time of period 8, add 40 min- utes to the starting time. The ending time is 1:43. The answer choice with both of these times is choice d. 30. a. The amount of water held in each container must be found. The rectangular box starts with 16 square inches ϫ 9 inches = 144 cubic inches of water. The cylindrical container can hold 44π cubic inches of water, which is approximately 138 cubic inches. Therefore, the cylinder will overflow. 31. d. This problem can be solved using only state- ments I and III. Since the cousin who fishes is female, either Lucia or Samantha likes to fish. Statement III eliminates Samantha, which leaves Lucia. 32. c. An algebraic equation must be used to solve this problem. The shortest side can be denoted by s. Therefore, s + (s + 2) + (s + 4) = 24; 3s + 6 = 24, and s = 6. 33. d. The letter in the sequence is decreasing by two letters, and the number is decreasing by three. This gives r14. 34. c. The total number of miles driven is 15 miles per day ϫ 5 days + 20 miles per day ϫ 2 days = = 4.6 gallons. Five gallons must be purchased. 35. a. The earning rate must be calculated for each vehicle. A car earns ᎏ 3 5 ᎏ dollar per minute, a truck earns ᎏ 4 7 ᎏ dollar per minute, and a van earns ᎏ 1 2 ᎏ dol- lar per minute. The cars earn the most money. 36. b. This must be solved with an algebraic equation; L = 2W + 4; 3L + 2W = 28. Therefore, 6W + 12 + 2W = 28; 8W = 16; W = 2; L = 8; 2 ϫ 8 = 16 square inches. 37. c. The answer is arrived at by dividing 175 by 45. Since the answer is 3.89, not a whole number, the gardener needs 4 sections of hose. Three sections of hose would be too short. 38. c. The farther to the right the digits go, the smaller the number. 39. a. The expression 5n means 5 times n. The addi- tion sign before the 7 indicates addition. 40. b. Use 35 for C; F = ( ᎏ 9 5 ᎏ ϫ 35) + 32. Therefore F = 63 + 32, or 95° F. 115 miles ᎏᎏ 25 miles per gallon 6 hours ᎏ day 0.50 ϫ 100 gallons ᎏᎏ minute – THEA PRACTICE EXAM 2– 231 41. d. Substitute 3 for x in the expression 5 + 4x to determine that y equals 17. 42. b. The formula for finding the area of a circle is A = πr 2 . First, square the radius: 13 times 13 equals 169. Then multiply by the approximate value of π, 3.14, to get 530.66. 43. c. 5 times 3 times 8 is 120; 120 divided by 3 is 40. 44. c. This is the only choice that includes a 90-degree angle. 45. b. ͙12 ෆ = ͙4(3) ෆ = ͙4 ෆ ͙3 ෆ = 2͙3 ෆ . Therefore, 3͙12 ෆ = 6͙3 ෆ . 46. b. Use the formula beginning with the operation in parentheses: 98 minus 32 equals 66. Then mul- tiply 66 by ᎏ 5 9 ᎏ , first multiplying 66 by 5 to get 330; 330 divided by 9 is 36.66667, which is rounded up to 36.7. 47. a. The distance between Plattville and Quincy is the hypotenuse of a right triangle with sides of length 80 2 and 60 2 . The length of the hypotenuse equals the square root of (80 2 plus 60 2 ), which equals the square root of (6,400 plus 3,600), which equals the square root of 10,000, which equals 100 miles. 48. d. Multiply 16 times 5 to find out how many gal- lons all five sprinklers will release in one minute. Then multiply the result (80 gallons per minute) by the number of minutes (10) to get 800 gallons. Section 3: Writing (Part A— Multiple-Choice) 1. b. Part 3 requires a comma before the coordinate conjunction so. 2. a. This answer is in the simple past tense, which is the tense used throughout the paragraph. 3. b. The context requires that the noun renown be replaced by the adjective renowned. 4. b. The semicolon in Part 2 is used incorrectly to introduce a list; it needs to be replaced with a colon. Choices a, c, and d are incorrect because, in each, the semicolon correctly separates two independent clauses. 5. c. The expressions year-round and in all seasons repeat the same idea. Choices a, b, and d are incorrect because none of these sentences con- tains unnecessary repetition. Part 4 may seem to, at first; however, the words hot and humid are expanded on the rest of the sentence and made more interesting and specific. 6. d. The subject of Part 3 is climate and therefore requires the third-person singular form of the verb to be—is. 7. c. Part 3 provides information about the Surgeon General’s findings that are off the topic of the announcement about the FDA’s ruling about the labeling of milk. All of the other sentences add information about the FDA ruling, its rea- sons, and its effects. 8. a. The word imply, meaning to express or indi- cate indirectly, is misused in the context of Part 4; the word infer, to surmise, makes sense in the context. 9. d. In Part 1, the adjective good is misused as an adverb; it needs to be replaced by the adverb well. 10. a. In Part 4, the verb assures, to make certain, is nonsensical in the context; it should be replaced by the verb assumes, to suppose or take for granted. 11. d. The paragraph consistently uses the pronoun you; therefore, the inconsistent use of our should be replaced by your. 12. c. The word Greek in Part 2 is a proper noun and should be capitalized. 13. c. Part 1 contains a run-on sentence. It requires a semicolon after the parentheses and before we. 14. b. The context requires a word synonymous to surrender or yield, so choice b is correct. 15. d. To make the pair of verbs in the sentence paral- lel, overlooking should be changed to overlooks to match the form of the verb towers. 16. d. A comma is required after an introductory dependent clause. Choice a would introduce a comma fault, separating a verb from its object. – THEA PRACTICE EXAM 2– 232 Choice b is incorrect because the semicolon would have to be followed by a complete sen- tence, which is not the case. Choice c is incorrect because removing the colon would create a run- on sentence. 17. c. Choices a and b would cause an unwarranted shift in tense from past (in which most of the passage is written) to present. Choice d would change the correctly written noun, effect, to an incorrect verb form. (Affect is a verb, except when used as a noun to denote a person’s emo- tional expression, or lack thereof, as in He has a joyless affect.) 18. b. The adjective shallow in Part 5 actually modifies the verb set; therefore, the adjective should be revised to be the adverb shallowly. 19. c. The proper noun Lake must be made possessive because it is followed by the gerund arriving. 20. c. This paragraph is about how to handle busi- ness phone calls. Reversing the order of Parts 9 and 13 would cause the paragraph to follow the natural order of the beginning to the end of a phone conversation. 21. b. This sentence requires the adverb then in this context. 22. d. The verb depend is, idiomatically, followed by the preposition on; in Part 10 it is wrongly fol- lowed by in. 23. b. The antecedent of the pronoun they in this sen- tence is someone. Since someone is singular, the subject pronoun should be he or she. 24. c. The sentence requires the contraction we’re, short for we are. It is all right to use a contrac- tion because the writer uses contractions else- where in the passage. 25. a. This passage’s tone is the impersonal, objective style of an official announcement. Choice a is correct because it retains the same objective tone as the rest of the paragraph. Choice b is incorrect because the phrase the guys, referring here to sanitation workers, is too casual in tone for the rest of the paragraph. Choice c is incor- rect because the adjective filthy is too pejorative in tone for the objective style of the paragraph. Choice d is incorrect because the phrase spruce up is too colloquial for the tone of the paragraph. 26. d. Part 3 contains a run-on sentence; it requires a semicolon rather than a comma after varies. 27. a. Another sentence is needed to add the infor- mation that the program is only for passengers leaving the bus, not those boarding it. This information is implied in the paragraph but not directly stated; without the direct statement, the paragraph is confusing and the reader must read between the lines to get the information. 28. c. The subjective pronoun who is incorrectly used to refer to the Stop Here Program; the pronoun which would be a better choice. 29. b. Part 5 contains two sentences linked only by a comma; a semicolon is required. 30. d. In Part 4, a semicolon is used incorrectly to introduce a list; it should be replaced by a colon. 31. a. Part 5 is the only sentence fragment in this pas- sage. It needs a subject in order to express a complete thought. 32. d. The word Recently is the best contrast to Finally though in Part 2. Choices a, b, and c indicate time lapses that would not necessarily take place in the context of the passage. 33. a. The comma is needed to set off the introductory clause from the independent clause. Making the changes stated in choices b, c,ord would create a nonstandard sentence. 34. c. Part 2 contains a comma splice; the comma should be replaced with a semicolon. Choices a, b,andd are incorrect because they contain stan- dard sentences. 35. d. Even though it may look like a question, Part 6 is not an interrogatory sentence. It should not be punctuated with a question mark. – THEA PRACTICE EXAM 2– 233 36. a. Choice a corrects the lack of grammatical par- allelism in the list in Part 5. The other choices all fail to correct the error in parallelism. 37. d. The sentence is written in past tense, and the verb needs to be singular to agree with the sin- gular subject of the sentence, percent. The other choices introduce a shift in tense. 38. a. The subject of this paragraph is the appearance and observation of cuttlefish. Choice a is about observing cuttlefish in the wild and the labora- tory. Choices b and c are off the topic of the paragraph. Choice d, while having something to do with the appearance of cuttlefish, is written in jargon that is too technical to match the tone of the rest of the passage. 39. c. The double mention in Part 6 of the humanlike eyes of the cuttlefish is unnecessarily repeti- tious. 40. d. The correct choice is hover. Section 3: Writing (Part B— Writing Sample) Following are the criteria for scoring THEA essays. A “4” essay is a well-formed writing sample that addresses the assigned topic and conveys a unified mes- sage to its audience. Additionally, it has the following characteristics: ■ a clear purpose and focus ■ controlled development of a main idea ■ clear, concrete, and effective details supporting the main idea ■ effective, error-free sentence structure ■ precise and careful word choice ■ mastery of mechanics such as punctuation and spelling A “3” essay is an adequate writing sample that addresses the assigned topic and clearly attempts to convey a message to its audience. Generally, it has the following additional characteristics: ■ a clear focus and purpose ■ organization of ideas that may be vague, incom- plete, or only partially effective ■ an attempt at development of supporting details, which is only partly realized ■ word choice and language usage that are ade- quate; but with minor errors in sentence struc- ture, usage, and word choice ■ mechanical mistakes such as errors in spelling and punctuation A “2” essay is an incompletely formed writing sample that lacks clear focus. It has the following addi- tional characteristics: ■ main topic announced, but focus on it is not maintained ■ unclear purpose ■ use of some supporting detail but development and organization unclear ■ sentences and paragraphs poorly structured ■ distracting errors in sentence structure ■ imprecise word usage ■ distracting mechanical mistakes such as errors in spelling and punctuation A “1” essay is an incompletely formed writing sample that fails to convey a unified message. It has the following additional characteristics: ■ attempt at addressing the topic, which fails ■ no clear main idea ■ language and style that are inappropriate to the audience and purpose ■ attempt to present supporting detail which is muddled and unclear ■ attempt at organization but failure to present a clear sequence of ideas ■ ineffective sentences, very few of which are free of error ■ imprecise word usage ■ many distracting mechanical mistakes, such as errors in spelling and punctuation – THEA PRACTICE EXAM 2– 234 A “U” essay is a writing sample that fails because of one or more of the following: ■ failure to address the assigned topic ■ illegibility ■ written primarily in a language other than English ■ length insufficient to score A “B” essay is a writing sample left completely blank (that is, the test-taker did not respond at all). Following are examples of scored writing sam- ples. (Note: There are some deliberate errors in all the essays.) Sample “4” essay Courage and cowardice seem like absolutes. We are often quick to label other people, or ourselves, either “brave” or “timid,” “courageous,” or “cowardly.” However, one bright afternoon on a river deep in the wilds of the Ozark mountains, I learned that these qualities are as changeable as mercury. During a cross-country drive, my friend Nina and I decided to stop at a campsite in Missouri and spend the afternoon on a float trip down Big Piney River, 14 miles through the wilderness. We rented a canoe and paddled happily off. Things went fine—for the first seven or eight miles. We gazed at the overhanging bluffs, com- mented on the wonderful variety of trees (it was spring, and the dogwood was in bloom), and mar- veled at the clarity of the water. Then, in approach- ing a bend in the river (which we later learned was called “Devil’s Elbow”) the current suddenly swept us in toward the bank, underneath the low-hanging branches of a weeping willow. The canoe tipped over and I was pulled under, my foot caught for just a few seconds on the submerged roots of the willow. Just as I surfaced, taking my first frantic gulp of air, I saw the canoe sweeping out, upright again, but empty, and Nina frantically swimming after it. I knew I should help but I was petrified and hung my head in shame as I let my friend brave the treacherous rapids and haul the canoe back onto the gravel bar, while I stood by cravenly. Then came the scream. Startled, I glanced up to see Nina, both hands over her eyes, dash off the gravel bar and back into the water. I gazed down into the canoe to see, coiled in the bottom of it, the unmistakable, black-and-brown, checkerboard-pat- tered form of a copperhead snake. It had evidently been sunning itself peacefully on the weeping willow branch when we passed by underneath. I don’t know exactly why. but the supposedly inborn terror of snakes is something that has passed me by completely. I actually find them rather charm- ing in a scaly sort of way. Nina was still screaming, near hysterics: “Kill it!” But I was calm in a way that must have seemed smug. “We’re in its home, it’s not in ours,” I informed her. And gently I prodded it with the oar until it reared up, slithered over the side of the canoe, and raced away—terrified, itself—into the underbrush. Later that night, in our cozy, safe motel room, we agreed that we each had cold chills thinking about what might have happened. Still, I learned something important from the ordeal. I know that, had we encountered only the rapids, I might have come away ashamed, labeling myself a coward, and had we encountered only the snake, Nina might have done the same. And I also know that neither of us will ever again be quite so apt to brand another person as lacking courage. Because we will always know that, just around the corner, may be the snake or the bend in the river or the figure in the shadows or something else as yet unanticipated, that will cause our own blood to freeze. – THEA PRACTICE EXAM 2– 235 . 12. The area of the circle is πr 2 , which is equal to 9 . Therefore, the half-circle’s area is ᎏ 9 2 π ᎏ . Adding gives ᎏ 9 2 π ᎏ + 12. 19. c. If the pentagons are similar, then the two dif- ferent. addition. 40. b. Use 35 for C; F = ( ᎏ 9 5 ᎏ ϫ 35) + 32. Therefore F = 63 + 32, or 95 ° F. 115 miles ᎏᎏ 25 miles per gallon 6 hours ᎏ day 0.50 ϫ 100 gallons ᎏᎏ minute – THEA PRACTICE EXAM 2– 231 41. d beginning with the operation in parentheses: 98 minus 32 equals 66. Then mul- tiply 66 by ᎏ 5 9 ᎏ , first multiplying 66 by 5 to get 330; 330 divided by 9 is 36.66667, which is rounded up to 36.7. 47.