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ACT Quiz #4
Question 1: What is the length of the transverse diameter of the following ellipse?
x
^{2}
/49 + y
^{2}
/19 = 1
7
14
49
2
19
Question 2: Mr Jones plans to drive 660 miles at an average speed of 60 miles/hour. How many miles per hour faster needs he to average, while driving, to reduce his total time by 1 hour?
5
6
7
8
9
Question 3: If
AC
and
BD
are the diagonals of the
ABCD
rectangle, what is the ratio between the area of triangle
EDC
and the area of triangle
EBC
?
.5
.8
1
1.2
1.5
Question 4: If
a
is an integer chosen randomly from {3, 4, 5, 9} and
b
is an integer chosen randomly from {3, 8, 12, 15}, what is the probability that
a/b
is an integer?
.125
.25
.1
1
.5
Question 5:
2·m - n = 4
m + 2·n = 12
Column A
Column B
(m + n)
^{2}
61
The quantity in Column A is greater then the quantity in Column B.
The quantity in Column B is greater then the quantity in Column A.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question 6: The edges of a cube are each 4 inches long. What is the surface area, in square inches, of this cube?
66
60
76
96
65
Question #7: In triangle
ABC
,
MN
is parallel to
BC
and
AM/AB
=
2/3
. What is the ratio between the area of triangle
AMN
and the area of triangle
ABC
?
2/3
2/9
4/5
4/9
5/9
Question 8: In the standard
(x, y)
plane, the line described by the equation
y = mx + n
intersects the y axis at a higher point than the line
y = ax + b
. Which of the following must be true?
n > b
m > a
n + m > b + a
n < b
m < a
Question #9: If
a
,
b
and
c
are the sides of any triangle, which of the following inequalities is not true?
a·b > 0
a + b > c
a + c/2 >b
b + c > a
(a + b)·(b + c) > a·c
Question 10: For any
x
such that
0 < x < ¶/2
, the expression
(1 - sin
^{2}
x)/cos(x) + (1 - cos
^{2}
x)/sin(x)
is equivalent to:
sin(x)
cos(x)
sin(x) - cos(x)
sin(x) + cos(x)
2sin(x)
Review the correct answers here.