Because the volume is 36 cubic feet, and the base is 9 square feet, the height must be 4 feet.. The context requires a word synonymous to surrender or yield, so choice b is correct.. Cho
Trang 112 c Let E equal emergency room cost; H equal
hos-pice cost, which is 14E; N equal home nursing
cost, which is 2H, or 2(14)E, or 12E The total bill
is E + H + N, which equals E + 14E + 24E, or
140,000 So 44E + 14E + 24E = 140,000, so 74E =
140,000 Multiplying both sides by 47to solve for
E, we get E = 140,000(47), or 80,000 Therefore
H = 14E, or (14)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 2S, or 32T The
sum of the ages is 55, which is 32T + 3T + T,
which is equal to 32T+ 62T+ 22T, which is equal to
(3T + 62T + 2T)or 112T Now multiply both sides of
55 = 112T 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 32T, 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 12bh = 12 The area of the circle is πr2, which is equal to 9π Therefore, the half-circle’s area is 92π Adding gives 92π+ 12
19 c If the pentagons are similar, then the two
dif-ferent pentagons will have similar proportions
Because A B is similar to FG , and AB = 10, and F
G = 30, the second pentagon is 3 times as large
Therefore, I H is 3 times as large as CD, which is 15
20 d The volume of a sphere is 43π3 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 12bh
= 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
Trang 2splitting 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 222π=
2π and 422π= 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
hour This gives 1.80 104
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;06.705= 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 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 5 days + 20 miles per day 2 days =
= 4.6 gallons Five gallons must
be purchased
35 a The earning rate must be calculated for each
vehicle A car earns 35dollar per minute, a truck earns 47dollar per minute, and a van earns 12 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 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 addiaddi-tion
40 b Use 35 for C; F = (95 35) + 32 Therefore F =
63 + 32, or 95° F
115 miles
25 miles per gallon
6 hours
day 0.50 100 gallons
Trang 341 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
= πr2 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 = 4(3) = 43 = 23 Therefore,
312 = 63
46 b Use the formula beginning with the operation in
parentheses: 98 minus 32 equals 66 Then
mul-tiply 66 by 59, 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 802and 602 The length of the hypotenuse
equals the square root of (802plus 602), 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
Trang 4Choice 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 contraccontrac-tions
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, or d would create
a nonstandard sentence
34 c Part 2 contains a comma splice; the comma should be replaced with a semicolon Choices a,
b, and d 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
Trang 536 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
Trang 6A “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