ACT Math Practice Test 23

In the standard (x,y) coordinate plane, what is the distance between the points (4,−7) and (−1,5)?

Rebecca is trying to schedule volunteers to help at a school carnival. There are 5 one-hour shifts to be filled by 5 different volunteers. If each shift must have one and only one volunteer, how many different arrangements can the schedule have?

When entering information about the budget of her charity ball, Laura records an expense of $20.00. However, Laura accidentally enters the $20.00 as income instead of an expense. The balance of the charity ball budget now shows:

If |x| = x + 12, then x = ?

What fraction lies exactly halfway between ¹⁄₃ and ¹⁄₂?

The formula for the area of a trapezoid is A = ¹⁄₂h (b₁ + b₂), where b₁ and b₂ are the lengths of the two parallel sides and h is the height. Which of the following is an expression for b₁?

For positive real numbers x, y, and z, which of the following expressions is equivalent to x^1⁄₂y^3⁄₄z^5⁄₈?

What is the slope of a line that is perpendicular to the line determined by the equation 5x + 8y = 17?

If the volume of a cube is 64, what is the shortest distance from the center of the cube to the base of the cube?

For which of the following values of c will there be 2 distinct real solutions to the equation 5x²+16x+ c = 0?

If a is inversely proportional to b and a = 36 when b = 12, what is the value of a when b = 48?

For values of x where sin x , cos x, and tan x are all defined, $\frac{(cos x)}{(tan x)(sin x)}$ =?

Which of the following is (are) equivalent to the mathematical operation a(b − c) for all real numbers a, b, and c?
I. ca − ba
II. ab − ac
III. (b − c)a

If x² − 45b² = 4xb, what are the 2 solutions for x in terms of b?

It is estimated that, from the beginning of 1993 to the end of 1997, the average number of CDs bought by teenagers increased from 7 per year to 15 per year. During the same time period, the average number of video games purchased by teenagers increased from 6 per year to 18 per year. Assuming that in each case the rates or purchase are the same, in what year did teenagers buy the same average number of CDs and video games?

The figure below is a regular hexagon. What is the measure of one of the interior angles of the hexagon?