ACT Math Practice
What is the minimum value of 2x - 3y given that x and y satisfy the system of inequalities below? x > -2 y < 3 x - y < 5
-13
What is the solution of the equation 8(x + 2) = 4x - 2(x - 3)?
-5/3
In the standard (x,y) coordinate plane, points A(2,3), B(4,0), and C(7,b) lie on the same line. What is b?
-9/2
A board 1 5/8inches by 3 5/8 inches is 6 1/2 feet long. You want to cut as many pieces as possible from the board so that each piece is 1 5/8 inches by 3 5/8 inches and 6 inches long. Each saw cut wastes 1/8 inch of the board. How many 6-inch long pieces will you be able to cut?
12
Triangle ACD is a right triangle. Which of the following expressions represents the length, in centimeters, of line AC?
12 sin 35°
What is the measure, in degrees, of an angle with a measure of 7π/9 radians?
140°
The diagram below shows the location of Manuel's boat, which is on a lake and anchored to a stationary buoy at point B. On the shore, Manuel's house is at point H and his nearest neighbor's house is at point N, which is 150 meters from H. The measures of 2 angels are given. Which of the following expressions represents the straight-line distance, in meters, from B to N?
150 sin 50° sin 70°
For her mathematics class, Ms. Wilkerson is preparing a probability experiment using only dried kidney beans, dried pinto beans, and an empty jar. First, she puts 4 kidney beans into the empty jar. How many pinto beans must be added to the jar in order to make the probability of drawing a kidney bean exactly 1/5 when randomly drawing 1 bean from the jar?
16
Let a, b, and c be respective side lengths, in feet, of a triangle. Given that a is 5 and b is 7, which of the following inequalities gives all and only the possible values of c?
2 < c < 12
What is the measure of major arc ACE?
240°
Packmore Box Company manufactures a standard rectangular box a feet by b feet by c feet. A customer ordered a new box with double the volume of the standard box. Which of the following expressions represents the volume, in cubic feet, of the new box?
2abc
The ratio of a to b is 5 to 1, and the ratio of b to c is 9 to 1. What is the value of 2a + 3b ? 4b + 3c
3
When a ≠ 0, which of the following is equivalent to 1/a + 2/3?
3 + 2a 3a
The probability that Event A will occur is 1/8. The probability that Event B will occur is 1/4. Given that Events A and B are mutually exclusive, what is the probability that Event A or Event B will occur?
3/8
What is the least positive number that has a remainder of 5 when divided by 7 and a remainder of 3 when divided by 5?
33
When Professor Soto began his trip to a mathematics conference, he noticed that the two digits of the recorded temperature, in degrees Fahrenheit, had a sum of 8. Later, he noticed that the two digits were reversed and that the temperature had warmed 18 °F. What was the temperature, in degrees Fahrenheit, at the beginning of his trip?
35 °F
For all positive values of x, which of the following expressions is equivalent to 2(3√(2x)) • 3√(x)?
3√(16x^2)
The function f(x) = x^3 is defined for all real numbers x. Which of the following expressions represents f^-1(x)?
3√(x)
Petsnacks is going to test its catnip ball on 200 domestic cats. Which of the following values is equal to the number of cats that will NOT have a reaction to the catnip in the toy?
40
Chou flies directly from New York City to San Francisco. New York City's time is 3 hours later than San Francisco's time. Chou left New York City at 7:30 a.m. local time and landed in San Francisco at 11:12 a.m. local time. How long was the trip?
6 hours 42 minutes
A tree farmer has exactly 3 kinds of trees on his farm: apple, cherry, and evergreen. Of these trees, 1/2 are apple, 1/3 are cherry, and 120 trees are evergreen. The farmer has how many trees on his farm?
720
Let a and b be positive real numbers such that log(a) = 3 and log(b) = 2. What is the value of log(a^2b)?
8
What is the median of the list of 10 numbers below? 87, 85, 78, 94, 67, 97, 55, 81, 87, 99
86
A 2-liter bottle of Fizzo contains approximately 67.6 ounces of soda. An 8-ounce serving of Fizzo has 110 calories. Which of the following is closest to the number of calories in a 2-liter bottle of Fizzo?
930
As shown below, D is on side line CE of rectangle ABCE such that the measure of angle ADB is 90°. Which of the following angles must be congruent to angle 1?
Angle 3 and angle 6
If t is any real number, which of the following statements must be true? A. -t < 0 B. -t < t C. -t = t D. -t < | -t | E. (-t)^2 = -t^2
D. -t < | -t |
At an end-of-school-year party for juniors and seniors only, there are 20 more juniors than seniors. Of the 52 students at the party, 25% have summer jobs. Which of the following is closest to the maximum possible percent of seniors at the party who have summer jobs? A. 25% B. 36% C. 44% D. 81% E. 97%
D. 81%
If all points on the circle remain fixed in their current positions except E, which moves along the circle counterclockwise until it reaches A, the length of line CE during this movement will: A. Remain unchanged B. Decrease, then increase C. Decrease only D. Increase only E. Increase, then decrease
E. Increase, then decrease
On her algebra exam, Hannah had to solve the equation x^2 + 3x - 8 = 0 for x. Confident that the quadratic formula was the correct method to solve this equation, she started her solution with the equation below. What error, if any, did Hannah make in setting up the equation?
Hannah should have used -8 instead of 8 in the term -4(1)(8) under the radical.
A portion of a regular polygon (all sides of equal length and all interior angles of equal measure) with n sides is shown below. The midpoint of line BC is M. The distance, in centimeters, from the polygon's center, R, to the midpoint of a side is the same for all sides. Which of the following is an expression for the area, in square centimeters, of the polygon?
n (BC)(MR) 2
For the complex number i, which of the following expressions is equivalent to (x + i)(x - i)?
x^2 + 1
Two side lengths of the right triangle shown below are given in inches. How many inches long is the hypotenuse?
√73