The population
of an ant-farm that starts at 80
and triples every 9 years can be
expressed as 
.
How big will the ant population be
after 27 years?
(A) 4320
(B) 2880
(C) 2160
(D) 480
(E) 80
Answer: C
EXPLANATION:
For exponential growth and decay
problems, fill in the missing information
and solve. In this case the missing
information is the number of years. t =
27. 
simplified
becomes 
,
or 2160. The answer is C.
Set A {1, 3,
7, 13, 17}
Set B {1, 4, 7, 10, 15, 17}
What set
of numbers represents the intersection
of sets A and B?
(A) {1, 3}
(B) {1, 7, 10}
(C) {1,
7, 17}
(D) {1,
3, 7, 13, 17}
(E) {1, 3, 4, 7, 10 13, 15,
17}
ANSWER: C
EXPLANATION:
Intersection means the numbers that
are in both sets. Only 1, 7, and
17 are in both Set A and Set B. The
answer is C.
Which of
the following describes all values
of x for which |x +
5| > 7?
(A) ?2 < x < 2
(B) ? < x < 12
(C) x > 2
(D) x < ?2
(E) x < ?2
or x > 2
ANSWER: E
EXPLANATION:
Set up your two equations (one for
if the stuff within the absolute
value is positive, the other if it
's negative): x + 5 > 7
and ?(x + 5) > 7. Now
solve for both. The first one simplifies
to x > 2. Eliminate A and
D. For the next one, multiply both
sides by ? and you get x +
5 < ?, which simplified is x < ?2.
The answer is E.
For all 
or 7, 
(A) 
(B) 
(C) x2 ?12x ?14
(D) x +
2
(E) 
ANSWER: A
EXPLANATION:
Factor the top and bottom of the
fraction. The top becomes (x ?7)(x +
4) and the bottom becomes (x ?7)(x ?2).
Cancel the (x ?7) and you're
left with 
. The answer is A.
If 
, what is one possible value of x?
(A) 1
(B) 2
(C) 4
(D) 16
(E) 32
ANSWER: D
EXPLANATION:
Solve for x. Use bite-sized
pieces. First add 12 to both sides: 
.
Now divide both sides by 32 and you
get 
.
Finally square both sides: x =
16. The answer is D.
(A) 5z3
(B) 
(C) 
(D) ?z3
(E) ?z5
ANSWER: C
EXPLANATION:
Use the rules of exponents. If you
have a fraction exponent, the numerator
is the exponent and the denominator
is the root. In this case, the exponent
is 3 and the root is 5. So the answer
is . You can also plug in and use
your calculator to eliminate. The
answer is C.
If f(x)
= 3x2 ?6x,
then f(2) =
(A) ?4
(B) ?2
(C) 0
(D) 8
(E) 10
ANSWER: A
EXPLANATION:
Since x = 2 in this question,
put in a 2 everywhere you see an x in
the equation:
3(2)2 ?62. Now
simplify: 3(4) ?36, or 12 ?36, which
is ?4. The answer is A.
If a varies
directly as b2 and a =
36 when b = 3 what is the
value of a when b is
7?
(A) 4
(B) 7
(C) 28
(D) 98
(E) 196
ANSWER: E
EXPLANATION:
Since this is direct variation, set
up a proportion. Make sure you use b2. 
. Simplified this becomes 
, so a = 196. The answer
is E.
Which of
the following describes the domain
of 
?
(A) 
(B) 
(C) 
(D) all positive numbers
(E) all
real numbers
ANSWER: E
EXPLANATION:
This is a tricky one. We know that
the domain (what numbers we can plug
in for x) is limited to what
will give us something greater than
or equal to zero under the square
root sign. Since we are squaring x,
then no matter what we plug in, it
will always be greater than or equal
to 0. The answer is E.
What is
the y–intercept for the equation
2x + 5y = 10?
(A) (?0,
0)
(B) (2,
0)
(C) 
(D) (0, 2)
(E) (0, 10)
ANSWER: D
EXPLANATION:
Change the equation to be in y = mx + b form.
5y = ?x + 10 and 
. Remember that the b represents
the y–coordinate of the y–intercept.
The answer is D.
Which of
the following is the solution set
of the equation x2 =
3x + 10?
(A) {?, ?}
(B) {?,
5}
(C) {?,
3}
(D) {?,
5}
(E) {3,
5}
ANSWER: B
EXPLANATION:
Set the equation equal to zero so
that you can factor. So x2 ?3x ?10
= 0. Now ask yourself what multiplies
to ?0: 1 and ?0, ? and 10, 2 and ?,
and ? and 5. You also want the pair
to add to ?. So the equation factors
to (x ?5)(x + 2) =
0. If that is true, then either x ?5
= 0 or
x + 2 = 0. So x = 5 or ?.
The answer is B.
If 
above is an equilateral triangle,
and the height of the figure is 6,
what is the length of side DE?
(A) 
(B) 
(C) 
(D) 
(E) 
ANSWER:
D
EXPLANATION:
The figure is broken into two identical
right triangles, which are each 30?0?0.
Use the rule of 30?0?0. DE =
2x, since it is the hypotenuse.
Since the height is the longer leg,
we know that 
. So 
and 
. Since ETS doesn't have answers
with roots in the denominator, either
put the answers in your calculator,
or multiply the answer by 
(to get the radical out of the
denominator) and you get 
or 
. The answer is D.
If 
is 5 and 
is 12, what is the value of 
(not shown)?
(A) 
(B) 
(C) 12
(D) 13
(E) 
ANSWER: D
EXPLANATION:
Since is tangent to the circle, it is
perpendicular to . So the two create a right angle.
If you draw in , you have a right triangle with
legs measuring 5 and 12. So either
use special right triangles or Pythagorean
Theorem to figure out that must be 13. The answer is D.
What is
the distance between the points (2,
4) and (3, 12)?
(A) 
(B) 9
(C) 
(D) 10
(E) 13
ANSWER:
A
EXPLANATION:
Draw the line. Now create a right
triangle with vertices of (2, 4),
(3, 12) and (3, 12). The lengths
of the two sides are 1 (3 ?2) and
8 (12 ?4). Use Pythagorean Theorem:
12 + 82 = z2.
Simplify 65 = z2,
and 
. The answer is A.
A bakery
sells fresh bread on Fridays, and
whatever is not sold Friday is marked
down and sold on Saturday. What is
the total amount of money the bakery
made on the two days described below?
(Note: Ignore dollar sign when filling
in your answer)
Number
of loaves sold |
|
Rye |
Sourdough |
French |
Pumpernickel |
Friday |
25 |
30 |
15 |
20 |
Saturday |
10 |
15 |
20 |
10 |
|
Price
of bread |
|
regular |
reduced |
Rye |
$2.00 |
$1.25 |
Sourdough |
$1.75 |
$1.00 |
French |
$2.50 |
$1.25 |
Pumpernickel |
$2.25 |
$1.25 |
|
Answer: 250
Explanation:
Get a total for Friday by multiplying
the number of loaves of each type
of bread sold on Friday by the regular
price for each type. $185 of bread
was sold on Friday. Get a total for
Saturday by multiplying the number
of loaves of each type of bread sold
on Saturday by the reduced price
for each type. $65 of bread was sold
on Saturday. The total for the two
days is $250.
