ACT math practice test 53

1. The formula for converting Celsius temperature to Fahrenheit temperature is f = img + 32. If the current temperature is 122° Fahrenheit, what is the temperature in Celsius?

A. 50°
B. 59.7°
C. 65.5°
D. 162°
E. 277.2°

2. If a ratio is selected at random from the set img what is the probability that the ratio is greater than img

F. img
G. img
H. img
J. img
K. img

3. Gertrude's Diner offers three different types of salads, two soups, four vegetable sides, five main dishes, and three desserts. If a customer can choose a salad or a soup along with one main dish, one vegetable side, and one dessert, how many different meal combinations are possible?

A. 17
B. 19
C. 300
D. 360
E. 21,600

4. As shown below, imgABC has vertices at points a (1, 1), b (7, 2), and c (3, 4). If imgABC was reflected about the origin to form a new triangle, imgA′Bc′, which of the following correctly lists the coordinates of points a′, b′, and c′, respectively?

img

F. (1, 1); (2, 7); (4, 3)
G. (-1, 1); (-7, 2); (-4, 3)
H. (-1, -1);(-7, -2);(-3, -4)
J. (-1, -1); (-2, -7);(-3, -4)
K. (1, -1); (7, -2); (3, -4)

5. A military tank is 228 meters due north of its target. The commander's jeep is due west of the tank and 247 meters north/northwest of its target. Which of the following gives the distance, in meters, between the tank and the jeep?

img

A. 19
B. 95
C. 190
D. 475
E. 9,025

6. What is the matrix product of [x 2x 3x] · img

F. [6x 0 -6x]
G. [-6x 0 6x]
H. img
J. [ 0 ]
K. img

7. Which of the following expresses the number of meters an athlete must travel in a 6-lap race around a circular track with a diameter of x meters?

A. 6 π x2
B. 3 π x2
C. img π x2
D. 6 π x
E. 3 π x

8. For all real numbers m and n such that the product of m and 4 is n, which of the following expressions represents the sum of m and 4 in terms of n ?

F. n + 4
G. 4n + 4
H. 4 (n + 4)
J. img
K. img+ 4

9. As shown below, rectangle KLMN is divided into 3 large squares (each labeled R) that measure x centimeters on a side, 12 small squares (each labeled S) that measure y centimeters on a side, and 12 rectangles (each labeled P). What is the total area, in square centimeters, of rectangle KLMN?

img

A. 3x + 4xy + 9yx + 12y
B. 12x + 4xy + 9yx + 3y
C. 3x2 + 13xy + 12y2
D. 12x2 + 13xy + 3y2
E. 3x3 + 13xy + 12y12

10. For some real number D, the graph of the line y = (D - 3)x + 7 in the standard (x, y) coordinate plane passes through the point (-5, 2). What is the slope of this line?

F. -3
G. -2
H. 0
J. 1
K. 4

11. When graphed in the standard (x, y) coordinate plane, the lines x = -6 and y = 2x - 4 intersect at what point?

A. (-16, -6)
B. (-6, -16)
C. (-6, 8)
D. (-6, 16)
E. (8, -6)

12. In imgLMP, shown below, image is the perpendicular bisector of image, cos imageLMP = 0.4, and image = 24 inches. How many inches long is image?

img

F. 9.6
G. 30
H. 40
J. 48
K. 60

13. A music instructor charges $30 per lesson, plus an additional fee for violin rental. The charge for the violin varies directly with the square root of the time the violin is used. If a lesson plus 25 minutes of violin rental costs $65, how much would it cost for a lesson plus 81 minutes of violin rental?

A. $93
B. $105
C. $111
D. $141
E. $146

14. The figure below shows a small square inside of a larger square. The smaller square has sides 3 inches long, and the area of the shaded region is 16 square inches. What is the length, in inches, of one side of the larger square?

img

F. 4
G. img
H. 5
J. img
K. 25

15. The quadrants of the standard (x, y) coordinate plane are labeled in the figure below. For each value of θ, let x = cos θ and y = sin θ. Whenever (sin θ) img < 0, the points (x, y) on the unit circle can lie in which of the following quadrants?

img

A. III only
B. IV only
C. I and III only
D. II and III only
E. II and IV only