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. Given that f(x) = x² − 5x + 6 and g(x) = x² − 7x − 10, what is g(f(−1)) ?

F. −55

G. −24

H. 20

J. 21

K. 50

2. In a 73-member choir of only altos and sopranos, there are 19 more altos than sopranos. What is the ratio of altos to sopranos?

F. 27:46

G. 27:73

H. 46:27

J. 46:73

K. 54:19

3. A drum contains 40 liters of a 6% potassium bromide solution. This solution is mixed with 80 liters of pure water to produce a new potassium bromide solution. What percent of the new solution is potassium bromide?

A. 2%

B. 3%

C. 6%

D. 8%

E. 12%

4. Given that \( sinθ =\frac{2}{3} \) , which of the following values is a possible value of cos θ ?

5. A certain rectangle in the standard (x,y) coordinate plane has a length of 7 coordinate units and a width of 5 coordinate units. The point (0,0) is in the interior of this rectangle. Two vertices of this rectangle are at (3,2) and (3,−3). What is the x-coordinate of the other 2 vertices?

A. −4

B. −3

C. −2

D. 8

E. 10