ACT math practice test 49

1. If ? is defined for all real numbers x and y by x ? y = (x + y)(x - y), then 1 ? (2 ? 2) = ?

A. 0
B. 1
C. 3
D. 4
E. 5

2. Sophie has played 6 games of soccer scoring 0, 1, 3, 2, 4, and 1 goals respectively in those games. For game 7, which of the following values will NOT yield a median of 2 goals scored?

F. 1 goal
G. 2 goals
H. 3 goals
J. 4 goals
K. 5 goals

3. What is the center of the circle with equation (x + 7)2 + (y - 5)2 = 121?

A. (-7, -5)
B. (-7, 5)
C. (7, -5)
D. (7, 5)
E. (5, 11)

4. Given the equation 3x - 7y = 21, what is the equation in slope-intercept form?

F. image
G. image
H. image
J. image
K. image

5. In the graph below, line m is parallel to line n. Find the value of a.

image

A. 17°
B. 68°
C. 85°
D. 95°
E. 112°

6. Which of the following is the set of solutions to the inequality image?

F. x < 6
G. x > -6
H. x > 6
J. There is no solution.
K. The set of all real numbers

7. Given the equation - imagex + 6y = 18, which of the following equations is perpendicular to the given equation?

A. image
B. image
C. image
D. y = -10x + 1
E. y = 10x + 18

8. Dustin is in a 40-foot air traffic control tower at the local airport. He spots a plane that has just landed and using his protractor measures the angle of depression from the top of the tower to the landed plane to be 12°. How far from the base of the control tower is the plane?

F. image
G. image
H. image
J. image
K. image

9. For what values of x is the function image undefined in the real number system?

A. x = 0
B. x = 5
C. x = -5
D. x < 5
E. x > 5

10. In the standard (x, y) coordinate plane, what are the coordinates of point a after the graph is reflected over the line x = 7?

image

F. (3, m)
G. (-3, -m)
H. (10, m)
J. (15, m)
K. (17, m)

11. Given line segment AB with a(-3, 2) and b(5, 8), which of the following is the length of AB?

A. image
B. 2 image
C. 10
D. 9 image
E. image

12. Given similar rectangles QUAD and RECT, the ratio of sides QU to RE is 1:4. If the area of QUAD is 12, what is the area of RECT?

F. 0.75
G. 3
H. 12
J. 48
K. 192

13. Forty students were asked to name their favorite pet. The following table lists the results.

image

Erick wants to make a circle graph from the given information. What would be the central angle for the dog piece of the graph?

A. 16°
B. 135°
C. 144°
D. 154°
E. 180°

14. Forty students were asked to name their favorite pet. The following table lists the results.

image

When Erick recounted the votes later, he realized 3 of the votes that had actually been cast for cats got recorded as votes for dogs. What is the difference between the original percent of votes cast for cats and the corrected percent of votes for cats?

F. 2.50%
G. 7.50%
H. 15%
J. 37.50%
K. 45%

15. Forty students were asked to name their favorite pet. The following table lists the results.

image

A parking lot downtown charges x dollars for the first hour and y dollars for each hour after the first. If Daniel parks in the lot for h hours where h > 6, which of the following equations represents P, the amount Daniel has to pay to park in the lot?

A. P = h(x + y)
B. P = x + yh
C. P = y + x(h - 1)
D. P = xh + y(h - 1)
E. P = x + y(h - 1)