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. One of the following equations is an equation of the circle graphed in the standard (x,y) coordinate plane below. Which one is it?
2. Aman left his bicycle at his friend’s house last night. Today, he decided to walk from home to his friend’s house, visit, and then ride the bicycle back home along the same route he walked. Aman walked at 3 mph, visited for 1.5 hours, and then rode the bicycle at 8 mph. Aman arrived home 3 hours after he started walking. Which of the following values is closest to the number of miles Aman walked?
A. 2.3
B. 3.3
C. 4.1
D. 4.5
E. 8.3
3. Points A(8,5) and C(−4,11) lie in the standard (x,y) coordinate plane. Point B lies on AC such that AB:BC = 1:2. What are the coordinates of B ?
F. (−8,13)
G. ( 0,9)
H. ( 2,8)
J. ( 3,6)
K. ( 4,7)
4. The ratio of a to b is 3 to 1, and the ratio of b to c is 6 to 1. What is the value of \( \frac{2a+3b}{4b+3c} \)?
5. In the 3 equations below, A, B, and C are positive real numbers. Each equation will be graphed in the standard (x,y) coordinate plane. Which of the following equations will result in lines that have a negative slope?
I. Ax + By = C
II. Ax − By = C
III. −Ax − By = C
F. I only
G. II only
H. III only
J. I and II only
K. I and III only