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. Numbered below are the 14 angles formed by parallel lines l and m and transversals p and q. Lines l, p, and q intersect at a single point. Which of the following congruence statements must be true?
A. ∠1 ≅ ∠5
B. ∠2 ≅ ∠1
C. ∠3 ≅ ∠10
D. ∠4 ≅ ∠2
E. ∠5 ≅ ∠8
2. A section of highway is represented by a line segment with endpoints (30,50) and (90,100) in the standard (x,y) coordinate plane. Exactly halfway along this highway section is a road sign. What are the coordinates of the road sign?
F. (30,25)
G. (60,50)
H. (60,75)
J. (70,65)
K. (75,60)
3. The Student Council is preparing a budget for an upcoming fund-raising dance. They have decided to spend $150 for a light and sound show, $400 for refreshments, and $50 for decorations. These are the only expenses. Given that the Student Council estimates 500 students will attend the dance, what should be the price, per student, for admission to the dance if the Student Council wants to raise as close as possible to $300 after paying expenses?
A. $0.60
B. $1.20
C. $1.67
D. $1.80
E. $3.33
4. The following shapes are a circle and some regular polygons that have their centers marked. All units are given in feet. Which of these shapes has the greatest area?
5. Last semester, each of the 4 students listed below took 6 classes worth 1 credit each. In the 1st matrix, the row corresponding to each student gives the counts of the letter grades earned by that student. The second matrix gives the point value of each letter grade.
The grade point average of each student is the total number of grade points earned by that student divided by that student’s total number of class credits. To the nearest 0.01, what is Ann’s grade point average?
A. 1.92
B. 2.00
C. 3.00
D. 3.83
E. 4.00