Free ACT Math Quiz 4

Question 1: What is the length of the transverse diameter of the following ellipse?
x²/49 + y²/19 = 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 with 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 - sin²x)/cos(x) + (1 - cos²x)/sin(x) is equivalent to:

sin(x)
cos(x)
sin(x) - cos(x)
sin(x) + cos(x)
2sin(x)

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