Download Practice Test 2 - Calvin College

PRE Practice Test #2
Calvin College Education Program http://www.calvin.edu/academic/education/
Answer key found at the end of the test.
Sample mathematical definitions and formulas to help you are given on the next two pages,
just as they are on the actual test. However, you should try to answer questions by referring to
these definitions and formula as little as possible. Constant page turning back and forth will
slow you down and can actually over-tax your working memory.
1.
Which of the following expressions best exemplifies the identity operation of
multiplication?
A. 4 x 0 = 0
B. 4 x 1 = 4
C. 4 x
D.
1
=1
4
0
=0
4
F(x)
2.
3#
2#
Which of the following could be the
equation of the graph shown here?
1#
x
0#
!1#
!2#
!3#
!4#
!5#
!6#
!7#
A.
(x - 2)2 - 2
B.
-(x - 2)2 - 2
C.
2(x - 2)2 + 2
D.
-2(x - 2)2 + 2
0#
1#
2#
3#
4#
5#
3.
For the triangle shown here, when is the cosine of
angle a equal to the sine of angle a?
H
A. Whenever H = X = Y
Y
B. Whenever H2 = X2 + Y2
C. Whenever a = 45°
D. Whenever a = 90°
a
X
4.
When the lengths of the sides of a cube are doubled, how does the volume of
the cube change?
A. The volume increases by a factor of 2.
B. The volume increases by a factor of 4.
C. The volume increases by a factor of 8.
D. The volume increases by a factor of 16.
5.
Which of the following is equal to 3-5 ⋅ 4-32 +1 ?
A. 0
B. -9
C. -11
D. 16
6.
What is log464 – log39 ?
A. 1
B. 5
C. 54
D. 55
7.
Which of the following is not contained in the set of real numbers?
A. 3 x 0
B.
0
3
C.
3
D.
-9
8.
A coat that was for sale for $100 was reduced in price by 50%. Later, the sale
price of the coat was increased by 50%. What was the final price of the coat?
A. $50
B. $75
C. $100
D. $150
9.
For what value of n (where n = 0, 1, 2, …) does the series a n =
undefined term?
A. n = 0
B. n = 2
C. n = 5
D. The series is defined for all n.
2n-4
have an
2
(n-5)
10.
If a student scores in the 69th percentile on a standardized test, then this means
that the student
A. answered 69% of the questions.
B. answered 69% of the questions correctly.
C. answered 69% of the questions incorrectly.
D. scored better that 69% of the students taking the test.
11.
If a measurement is stated as being equal to 100 ± 5%, this means that the
measurement is
A. accurate 5% of the time.
B. accurate 95% of the time.
C. probably somewhere between 95 and 105.
D. definitely somewhere between 95 and 105.
12.
What is (3 – 2i) subtracted from (1 + 3i) ?
A. 2 – 5i
B. 2 + i
C. -2 + 5i
D. -2 - 5i
13.
If it is true that the number of pollutants in a local pond always increases when it
rains, then it is also true that
A. the pollutants in the pond are caused by the rain.
B. the number of pollutants in the pond will not increase unless it rains.
C. when the number of pollutants in the pond increases, it must have rained.
D. when the number of pollutants in the pond decreases, it must not have
rained.
14.
Ayoke is twice as old as Bill. Comfort is four years older than Bill, but 6 years
younger than Ayoke. How old is Bill?
A. 5
B. 10
C. 15
D. 20
15.
p=
If n=3, then what is p?
A. 9
B. 15
C. 18
D. 27
n 3 2n-4
(
( 3)
1
)
n2
16.
The height of a cylinder is equal to its radius r. What is the surface area of the
cylinder equal to?
A.
1 2
πr
2
B. πr2
C. 2πr2
D. 4πr2
17.
What polynomial do you get when you subtract 2x3 + 3x – 3 from 2x2 – x + 6?
A. x3 - 2x2 - 4x + 12
B. x3 + 2x2 + 5x - 3
C. -x3 + 2x2 - 5x + 3
D. -2x3 + 2x2 - 4x + 9
18.
F(x)
5#
4#
For what values of x is F(x) positive?
3#
2#
1#
x
!4#
!3#
!2#
!1#
0#
!1#
!2#
A. x ≥ 1
B. x < 0
C. x > 0
D. All x
x
0#
1#
2#
19.
Consider these values for x and f(x):
x
1
10
100
1000
10000
f(x)
0
1
2
3
4
The relationship of f(x) to x is
A. Linear
B. Quadratic
C. Cubic
D. Logarithmic
20.
The half-life of a certain radioactive material is 10 hours. How much of the
original material would be left after 20 hours?
A. one fourth
B. one eighth
C. one sixteenth
D. none of it
21.
Equation #1 is given by y = -4 x + 1.
Equation #2 is given by y = - x + 7.
Where do these two lines intersect?
A. (-2, 9)
B. (-4, 7)
C. (-1, 1)
D. (-4, 7)
22.
A hollow plastic cube without a top
is just large enough that a metal
sphere will fit snugly inside of it.
If the plastic cube is completely
filled with water, and then the
!
sphere is slowly and carefully lowered into the cube, about how much water
will be left in the cube? The radius of the sphere is given by R.
A.
3R
π2
3 4
R
- πR 3
B.
3
π
C. R 3 (1- )
6
π
D. 8R 3 (1- )
6
!
23.
A very large gumball machine is completely filled with equal numbers of red,
white, blue, and green gumballs. If two gumballs are randomly removed from
the gumball machine, what is the probability that both of the gumballs are the
same color?
A. 1/2
B. 1/4
C. 1/8
D. 1/16
24.
What is the midpoint between the two points (2, -3) and (4, 5) ?
A.
(6, 2)
B. (2, 8)
C. (3, 1)
D.
(-2, -8)
25.
If a standardized test with a normal distribution of scores has a mean of 65
and a standard deviation of 7, then what percentage of the scores lie between
the values of 58 and 72?
A. about 34% of them
B. about 50% of them
C. about 68% of them
D. 100% of them
26.
What is the mode for this data set?
4, 4, 4, 6, 8, 10, 13
A. 4
B. 6
C. 10
D. 25
27.
A bag contains 5 red balls, 3 blue balls, 2 yellow balls, and 1 green ball. If you
want to find out what the probability is of randomly selecting a blue ball when
you close your eyes and remove one of the balls, then one way of finding this
out would be to
A. randomly remove one ball and check to see if it is blue.
B. randomly remove balls, one by one, until you remove a blue one.
C. randomly remove a ball, check to see if it is blue, replace it, and then do it
all over again many times.
D. count out how many different ways you can remove a blue ball, and then
subtract one from that number.
28.
F(x)
5#
4#
3#
What is the polynomial graphed
here?
2#
1#
x
0#
!3#
!2#
!1#
!1#
!2#
!3#
!4#
!5#
A. f(x) = x(x+1)(x-2)
B. f(x) = (x-1)(x+2)(x+1)
C. f(x) = (x+2)(x-1)(x-2)
D. f(x) = (x-3)(x+2)(x-1)
0#
1#
2#
3#
29.
1m
What is the area of the wedge shown here?
A. 2π
B. π
C.
1
π
2
D.
1
π
8
45°
30.
b
a
If triangle a is similar to triangle b, then
A. the two triangles must be congruent.
B. the sides of the triangles must be equal.
C. the areas of the two triangles must be the same.
D. triangle a would map onto triangle b with a dilation and rotation.
31.
Which of the following functions is periodic in x?
A. f(x) = 3x2 + 3
B. f(x) = 3sin(x) + 3
C. f(x) = 3log3(x)
D. f(x) = 3x
32.
Which graph below could represent a function that is exponential in x?
f(x)
f(x)
x
x
A
B
f(x)
f(x)
x
C
x
D
33.
What is
A. 2
B. 4
C. 12
D. 60
(8 - 4)!
?
3!
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
B
D
C
C
A
A
D
B
C
D
C
C
D
B
C
D
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
D
D
D
A
A
D
B
C
C
A
C
B
D
D
B
B
33. B