ACT math practice test 41

1. Josh pounded a stake into the ground. When he attached a leash to both the stake and his dog's collar, the dog could walk 12 feet from the stake in any direction. Using 3.14 for π, what is the approximate area of the lawn, in square feet, that the dog could roam while tied to the stake?

A. 38
B. 75
C. 151
D. 377
E. 452

2. Television screen sizes are determined by the diagonal length of the rectangular screen. Chad recently changed from watching a television with a 19-inch screen to a television with a similarly shaped 32-inch screen. If a car on the 19-inch screen appeared 12 inches long, how long, to the nearest inch, would the same car appear on the 32-inch screen?

F. 16
G. 18
H. 20
J. 22
K. 24

3. In the figure below, ABCD is a square. Points are connected on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below. Each of these triangles has one leg that is twice as long as the other leg. If the area of the shaded region is 25 square feet, what is the area of square ABCD in square feet?

image

A. 225
B. 112.5
C. 56.25
D. 45
E. 27

4. A surveyor took and recorded the measurements shown in the figure below. If the surveyor wants to use these 3 measurements to calculate the length of the pond, which of the following would he find to be the most useful?

image

F. The Pythagorean Theorem
G. The ratios for the side lengths of 30°-60°-90° triangles
H. The ratios for the side lengths of 45°-45°-90° triangles
J. The law of cosines, which states that for any ΔABC, where a is the length of the side opposite imagea, b is the length of the side opposite imageb, and c is the length of the side opposite imagec, a2 = b2 + c2 - 2BC[cos
K. The law of sines, which states that the ratio between the length of the side opposite an angle and the sine of that angle is the same for all of the interior angles in the same triangle.

5. Which of the following is the graph of the equation image in the standard (x, y) coordinate plane?

A. image
B. image
C. image
D. image
E. image

6. A line in a plane separates the plane into how many sets of points that do not contain the line?

F. 0
G. 1
H. 2
J. 3
K. Cannot be determined

7. What is the maximum number of distinct diagonals that can be drawn in the hexagon shown below?

image

A. 12
B. 9
C. 6
D. 5
E. 4

8. In the standard (x, y) coordinate plane, the center of a circle lies in quadrant III. If the circle is tangent to the x-axis and the y-axis, which of the following is an equation for the circle?

F. (x + 4)2 + (y + 4)2 = 4
G. (x - 4)2 + (y - 4)2 = 4
H. x2 + (y - 4)2 = 16
J. (x + 4)2 + (y + 4)2 = 16
K. (x + 4)2 + (y - 4)2 = 16

9. How must - image, - image, - image, and - image be arranged so that they are listed in increasing order?

A. - image - image - image - image
B. - image - image - image - image
C. - image - image - image - image
D. - image - image - image - image
E. - image - image - image - image

10. The perimeter of an elliptical billiard table is to be covered with red velvet. The perimeter of an ellipse is given by the formula image, where l is the length and w is the width, as shown in the diagram below. If the length is 4 feet and the width is 3 feet, what is the outside perimeter of the ellipse in feet?

image

F. imageπ image
G. image (4 image + 3)
H. imageπ image
J. (4π + 3) image
K. 5π image

11. If image and a, b, and x are integers greater than 1, what must x equal?

A. 11
B. 154
C. 252
D. 1,134
E. 3,528

12. Which one of the following expresses the number of meters that a contestant must travel in a 5-lap race around a circular track with a radius of R meters?

F. 5R
G. 5πR
H. 5πR2
J. 6R
K. 10πR

13. In ΔABC, shown below, the measure of imageb is 40°, the measure of imagec is 35°, and image is 27 units long. Which one of the following is an expression of the length, in units, of image?

(Note: The law of sines states that for any triangle, the ratio between the sine of an angle and the length of the side opposite that angle is the same for all of the interior angles in the triangle.)

image

A. image
B. image
C. image
D. image
E. image

14. Kaylee is planning to purchase a car. She will need to borrow some of the money and has a chart, shown below, that will help her to approximate her monthly payment. The chart gives the approximate monthly payment per $1,000 borrowed.

image

Kaylee found a used car that she is thinking about purchasing. The list price is $8,785. She calculates that she will need to borrow $6,500. Approximately what would her monthly payment be if she borrowed the money for 36 months at an annual interest rate of 10%?

F. $164.84
G. $171.21
H. $209.76
J. $234.72
K. $283.81

15. Kaylee is planning to purchase a car. She will need to borrow some of the money and has a chart, shown below, that will help her to approximate her monthly payment. The chart gives the approximate monthly payment per $1,000 borrowed.

image

A local dealership is having an end-of-the-modelyear clearance sale and is offering 5% annual interest on new-car loans for 36, 48, or 60 months. The maximum amount that Kaylee can budget for her monthly car payment is $300. Of the following loan amounts, which one represents the maximum amount that Kaylee can borrow at 5% annual interest while staying within her budget?

A. $10,000
B. $13,000
C. $14,000
D. $15,000
E. $20,000