The surface area of the square face is equal to nine square units, so surface area of one face of the cube is nine square units.. You just need to figure out which of the provided answer
Trang 1The radius of the circle is equal to 6, half its
diameter The area of a circle is equal to πr2,
so the area of the circle is equal to 36π square
units
12 d The sides of a square and the diagonal of a
square form an isosceles right triangle The
length of the diagonal is 2 times the
length of a side The diagonal of the square
is 16 2 cm, therefore, one side of the
square measures 16 cm The area of a square
is equal to the length of one side squared:
(16 cm)2 256 cm2
13 a If both sides of the inequality m2> n2are
mul-tiplied by 2, the result is the original
inequal-ity, m > n m2is not greater than n2when m is
a positive number such as 1 and n is a
nega-tive number such as –2 mn is not greater than
zero when m is positive and n is negative The
absolute value of m is not greater than the
absolute value of n when m is 1 and n is –2.
The product mn is not greater than the
prod-uct –mn when m is positive and n is negative.
14 c. There are 60 minutes in an hour and 120
minutes in two hours If 4 liters are poured
every 3 minutes, then 4 liters are poured 40
times (120 3); 40 4 160 The tank,
which holds 2,000 liters of water, is filled with
160 liters;21,060001800 8% of the tank is full
15 d The curved portion of the shape is 14πd,
which is 4π The linear portions are both the
radius, so the solution is simply 4π 16
17 35 Angles OBC and OCB are congruent, so both
are equal to 55 degrees The third angle in the
triangle, angle O, is equal to 180 – (55 55)
180 – 110 70 degrees Angle O is a cen-tral angle; therefore, arc BC is also equal to 70 degrees Angle A is an inscribed angle The
measure of an inscribed angle is equal to half the measure of its intercepted arc The
meas-ure of angle A 70 2 35 degrees
18 4 The function f(a) (4a2(a2 –
12 1
a
6
) 9)
is undefined
when its denominator is equal to zero; a2– 16
is equal to zero when a 4 and when a –4.
The only positive value for which the func-tion is undefined is 4
19 46 Over 12 hours, Kiki climbs (1,452 – 900)
552 feet On average, Kiki climbs (552 12)
46 feet per hour
20 55 The total weight of the first three dogs is
equal to 75 3 225 pounds The weight of
the fourth dog, d, plus 225, divided by 4, is
equal to the average weight of the four dogs,
70 pounds:
d4225 70
d 225 280
d 55 pounds
21 260 The weight Kerry can lift now, 312 pounds, is
20% more, or 1.2 times more, than the
weight, w, he could lift in January:
1.2w 312
w 260 pounds
22 485 2,200(0.07) equals $154; 1,400(0.04) equals
– M AT H P R E T E S T –
Trang 224. 8 3 1 2 Each term is equal to the previous term
mul-tiplied by 32 The fifth term in the sequence is
98232176, and the sixth term is 2176328312
25 –1 4 The question is asking you to find the
y-inter-cept of the equation 2x3–y3 4 Multiply both
sides by 3y and divide by 12: y16x – 14 The
graph of the equation crosses the y-axis at
(0,–14)
26 100 Set the measures of the angles equal to 1x, 3x,
and 5x The sum of the angle measures of a
triangle is equal to 180 degrees:
1x 3x 5x 180
9x 180
x 20
The angles of the triangle measure 20 degrees,
60 degrees, and 100 degrees
27 54 One face of the prism has a surface area of
nine square units and another face has a
sur-face area of 21 square units These sur-faces share
a common edge Three is the only factor
common to 9 and 21 (other than one), which
means that one face measures three units by
three units and the other measures three units
by seven units The face of the prism that is
identical to the face of the cube is in the shape
of a square, since every face of a cube is in the
shape of a square The surface area of the
square face is equal to nine square units, so
surface area of one face of the cube is nine square units A cube has six faces, so the sur-face area of the cube is 9 6 54 square units
28. 1 1 1 Seven cards are removed from the deck of
40, leaving 33 cards There are three cards remaining that are both a multiple of 4 and
a factor of 40: 4, 20, and 40 The probability
of selecting one of those cards is 333or 111
29 4 We are seeking D number of feet away
from the microwave where the amount of radiation is 116the initial amount We are given: radiation varies inversely as the square
of the distance or: R 1 D2 When D 1,
R 1, so we are looking for D when R 116 Substituting:116 1 D2 Cross multiplying:
(1)(D2) (1)(16) Simplifying: D2 16, or
D 4 feet
30 4 The factors of a number that is whole and
prime are 1 and itself For this we are given x and y, x > y > 1 and x and y are both prime Therefore, the factors of x are 1 and x, and the factors of y are 1 and y The factors of the product xy are 1, x, y, and xy For a given x and y under these conditions, there are four factors for xy, the product of the girls’ favorite
numbers
– M AT H P R E T E S T –
2 5
Trang 4A l l Te s t s A r e N o t A l i k e
The SAT is not like the tests you are used to taking in school It may test the same skills and concepts that your teachers have tested you on, but it tests them in different ways Therefore, you need to know how to approach the questions on the SAT so that they don’t surprise you with their tricks
C H A P T E R
Techniques and Strategies
The next four chapters will help you review all the mathematics you need to know for the SAT However, before you jump ahead, make sure you first read and understand this chapter thoroughly It includes tech-niques and strategies that you can apply to all SAT math questions
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Trang 5T h e Tr u t h a b o u t M u l t i p l e
-C h o i c e Q u e s t i o n s
Many students think multiple-choice questions are
easier than other types of questions because, unlike
other types of questions, they provide you with the
correct answer You just need to figure out which of the
provided answer choices is the correct one Seems
sim-ple, right? Not necessarily
There are two types of multiple-choice questions
The first is the easy one It asks a question and provides
several answer choices One of the answer choices is
correct and the rest are obviously wrong Here is an
example:
Who was the fourteenth president of the United
States?
a Walt Disney
b Tom Cruise
c Oprah Winfrey
d Franklin Pierce
e Homer Simpson
Even if you don’t know who was the fourteenth
president, you can still answer the question correctly
because the wrong answers are obviously wrong Walt
Disney founded the Walt Disney Company, Tom Cruise
is an actor, Oprah Winfrey is a talk show host, and
Homer Simpson is a cartoon character Answer choice
c, Franklin Pierce, is therefore correct.
Unfortunately, the SAT does not include this type
Who was the fourteenth president of the United States?
a George Washington
b James Buchanan
c Millard Fillmore
d Franklin Pierce
e Abraham Lincoln
This question is much more difficult than the previous question, isn’t it? Let’s examine what makes it more complicated
First, all the answer choices are actual presidents None of the answer choices is obviously wrong Unless you know exactly which president was the fourteenth, the answer choices don’t give you any hints As a result, you may pick George Washington or Abraham Lincoln because they are two of the best-known presidents This is exactly what the test writers would want you to do! They included George Washington and Abraham Lincoln because they want you to see a familiar name and assume it’s the correct answer
But what if you know that George Washington was the first president and Abraham Lincoln was the sixteenth president? The question gets even trickier because the other two incorrect answer choices are James Buchanan, the thirteenth president, and Mil-lard Fillmore, the fifteenth president In other words, unless you happen to know that Franklin Pierce was the fourteenth president, it would be very difficult to fig-ure out he is the correct answer based solely on the answer choices
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Trang 6F i n d i n g F o u r I n c o r r e c t A n s w e r
C h o i c e s I s t h e S a m e a s
F i n d i n g O n e C o r r e c t A n s w e r
C h o i c e
Think about it: A multiple-choice question on the SAT
has five answer choices Only one answer choice is
cor-rect, which means the other four must be incorrect You
can use this fact to your advantage Sometimes it’s
eas-ier to figure out which answer choices are incorrect
than to figure out which answer choice is correct
Here’s an exaggerated example:
What is 9,424 2,962?
a 0
b 10
c 20
d 100
e 27,913,888
Even without doing any calculations, you still
know that answer choice e is correct because answer
choices a, b, c, and d are obviously incorrect Of course,
questions on the SAT will not be this easy, but you can
still apply this idea to every multiple-choice question on
the SAT Let’s see how
C h o i c e s a n d I n c r e a s e
Yo u r L u c k
Remember that multiple-choice questions on the SAT
contain distracters: incorrect answer choices designed
to distract you from the correct answer choice Your job
is to get rid of as many of those distracters as you can
when answering a question Even if you can get rid of
only one of the five answer choices in a question, you have still increased your chances of answering the ques-tion correctly
Think of it this way: Each SAT question provides five answer choices If you guess blindly from the five choices, your chances of choosing the correct answer are 1 in 5, or 20% If you get rid of one answer choice before guessing because you determine that it is incor-rect, your chances of choosing the correct answer are 1
in 4, or 25%, because you are choosing from only the four remaining answer choices If you get rid of two incorrect answer choices before guessing, your chances
of choosing the correct answer are 1 in 3, or 33% Get rid of three incorrect answer choices, and your chances are 1 in 2, or 50% If you get rid of all four incorrect answer choices, your chances of guessing the correct answer choice are 1 in 1, or 100%! As you can see, each answer choice you eliminate increases your chances of guessing the correct answer
ODDS YOU CAN
0 1 in 5, or 20%
1 1 in 4, or 25%
2 1 in 3, or 33%
3 1 in 2, or 50%
4 1 in 1, or 100%
Of course, on most SAT questions, you won’t be guessing blindly—you’ll ideally be able to use your math skills to choose the correct answer—so your chances of picking the correct answer choice are even greater than those listed above after eliminating distracters
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