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. . Which of the following points is NOT on the graph of the function y = ⎪2x⎪ − 4 in the standard (x,y) coordinate plane?
F. (−2, 0)
G. (−1, 2)
H. ( 1,−2)
J. ( 2, 0)
K. ( 4, 4)
2. Let K and J be independent events. Given that P(K) = 0.40 and P(J) = 0.20, what is the probability that K and J will both occur?
(Note: P(A) is the probability that Event A will occur.)
F. 0.08
G. 0.20
H. 0.40
J. 0.52
K. 0.60
3. Let a and b be unknown nonzero constants such that the equation below is true for all values of θ.
\[ a sin^2θ+ a cos^2θ=b \]
What is the value of \( \frac{b}{a} \)?
F. −1
G. 0
H. \( \frac{1}{2} \)
J. 1
K. 2
4. What is the area, in square millimeters, of a triangle whose side lengths are 5 millimeters, 5 millimeters, and 6 millimeters?
A. 6
B. 12
C. 15
D. 25
E. 30
5. Matrix A has dimensions 3 × 2, and matrix B has dimensions 2 × 3. One of the following matrices is the matrix product AB. Which one?
