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. In the triangular arrangement of fractions below, the first and last fraction in row \( \frac{1}{n} \) is . Any other entry is the sum of the 2 fractions on either side of that entry in the row directly beneath it. What is the 3rd fraction in the 5th row?
F. \( \frac{1}{4} \)
G. \( \frac{1}{15} \)
H. \( \frac{1}{25} \)
J. \( \frac{1}{30} \)
K. \( \frac{1}{100} \)
2. Of the 300 juniors at Northeast High School, 130 are taking both math and English, 139 are taking both science and English, 119 are taking both math and science, and 98 are taking all 3 courses. Only 18 students are taking none of the 3 courses. The data are shown in the Venn diagram below.
One of the juniors from Northeast High School will be chosen at random. What is the probability that the chosen student is taking exactly 1 of these 3 courses?
A. 0.30
B. 0.33
C. 0.36
D. 0.64
E. 0.67
3. For what positive value of k will the expression 9x² + kx + 25 factor into the form (ax + b) ² for some real number a and some real number b ?
F. 30
G. 16
H. 15
J. 8
K. 2
4. A class of 32 students took a 10-point quiz. The frequency distribution of their scores is given below. What was the median score for the class?
A. 3
B. 5
C. 6
D. 7
E. 8
5. . For certain positive integers a and b, the greatest common divisor of a and b is 1, and 9a = 4b. If it can be determined, which of the following statements must be true for a and b ?
F. 2 is a prime factor of a, and 3 is a prime factor of b.
G. 2 is a prime factor of a, and 3 is not a prime factor of b.
H. 2 is not a prime factor of a, and 3 is a prime factor of b.
J. 2 is not a prime factor of a, and 3 is not a prime factor of b.
K. Cannot be determined from the given information