Welcome to our “Daily Math Practice Challenge: Preparing for the ACT Exam”! This challenge is designed to help you engage in targeted math practice every day, gearing up for the ACT exam. Through daily exercises, you will enhance your problem-solving speed, deepen your understanding of mathematical concepts, and strengthen your ability to tackle a variety of math problems.
1. Rafael wrapped a gift box l inches long, w inches wide, and h inches high. He tied a decorative rope around it and used an extra 6 inches for a tie at the top, as shown below. On both the top and the bottom, he formed right angles where the rope crossed. About how many inches of decorative rope did Rafael use?
F. 2l + 2w + 2h
G. 2l + 2w + 2h + 6
H. 2l + 2w + 4h + 6
J. 2l + 4w + 2h + 6
K. 4l + 2w + 2h + 6
2. A piece of chocolate candy enclosing an almond in the center is made in a rectangular mold that has inside dimensions 4 cm, 3 cm, and 2 cm. If the volume of the almond is 2 cubic centimeters, what is the maximum volume, in cubic centimeters, of the chocolate in the piece of candy?
A. 7
B. 12
C. 16
D. 22
E. 24
3. An automobile gasoline tank is \( \frac{3}{8} \)full. After 6 gallons of gasoline are added to the tank, it is \( \frac{3}{4} \)full. Gasoline sells for $1.50 per gallon. If the tank is empty, what would be the cost to fill it \( \frac{3}{4} \)full?
F. $6.00
G. $9.00
H. $15.00
J. $18.00
K. $24.00
4. In a certain triangle that has an area of 12 square inches, the length of one altitude is the length of its corresponding base. What is the length of that base, in inches?
A. 2
B. 3
C. 6
D. 9
E. \( \sqrt[]{18} \)
5. A circle is tangent to the x-axis and to the y-axis. The coordinates of its center are both positive. The area of the circle is 64π. What are the coordinates of the point of tangency on the y-axis?
F. (0,04)
G. (0,08)
H. (0,16)
J. (0,32)
K. (0,64)