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. The table below gives the lengths, widths, and heights, in feet, of 3 right rectangular prisms. The difference between the volume of Prism A and the volume of Prism B is how many times the volume of Prism C ?
F. 0
G. 1
H. 5
J. 8
K. 12
2. Which of the following is the complex conjugate of 2 + 7i ?
3. Given functions f(x) = 3x + 4 and g(x) = x² − 2, what is the value of f (g(−3))?
F. −29
G. −27
H. −20
J. 23
K. 25
4. . Which of the following is equivalent to for all nonzero real numbers A and B ?
A. 9AB
B. 9A²B²
C. 7A + 6AB²
D. 7A + 6B
E. 7A + 2B
5. Which of the following lists gives the numbers below arranged in order from least to greatest?
\[ 0.6, 0.08, \frac{5}{8} \]
6. A 2-digit number will be formed by randomly selecting each digit from the set {2, 3, 9}. What is the probability that the number formed will be 99 ?
7. Which of the following expressions is equivalent to (y + 8)³ ?
F. y³ + 24y² + 192y + 512
G. y³ + 16y + 512
H. y³ + 16y + 64
J. y³ + 512
K. y³ + 24
8. The average of a list of 4 numbers is 88.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 50, and the fourth number in the new list is 70. What is the average of this new list of numbers?
A. 83.5
B. 88.0
C. 93.0
D. 95.0
E. 96.8
9. Which of the following number line graphs is that of the solution set to the inequality −2x + 7 ≥ 19 ?
10. A circle with radius 4 centimeters is inscribed in a square, as shown below. Which of the following represents the area, in square centimeters, of the shaded region?
A. 32 − 8π
B. 32 − 16π
C. 32 + 16π
D. 64 − 16π
E. 64 + 16π