ACT Math Practice Test 14

How many different positive three-digit integers can be formed if the three digits 3, 4, and 5 must be used in each of the integers?

What is the value of log⁴ 64?

For real numbers r and s, when is the equation |r −s| = |r + s| true?

The sides of a triangle are 9, 12, and 15 centimeters long. What is the angle between the 2 shortest sides?

What is the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4)?

What is the smallest possible integer for which 15% of that integer is greater than 2.3?

If x and y are positive integers such that the greatest common factor of x²y² and xy³ is 27, then which of the following could y equal?

For what value of n would the following system of equations have an infinite number of solutions?
3a + b = 12
12a + 4b = 3n

For which of the following functions is f (−5) > f (5)?

Considering all values of a and b for which a + b is at most 9, a is at least 2, and b is at least −2, what is the minimum value of b − a?

If the edges of a cube are tripled in length to produce a new, larger cube, then the larger cube’s surface area is how many times larger than the smaller cube’s surface area?

Let n equal 3a + 2b − 7. What happens to the value of n if the value of a increases by 2 and the value of b decreases by 1?

Kate rode her bicycle to visit her grandmother. The trip to Kate’s grandmother’s house was mostly uphill, and took m minutes. On the way home, Kate rode mostly downhill and was able to travel at an average speed twice that of her trip to her grandmother’s house. Which of the following expresses the total number of minutes that Kate bicycled on her entire trip?

The City Council has approved the construction of a circular pool in front of City Hall. The area available for the pool is a rectangular region 12 feet by 18 feet, surrounded by a brick wall. If the pool is to be as large as possible within the walled area, and edge of the pool must be at least 2 feet from the wall all around, how many feet long should the radius of the pool be?

If cos θ = −³⁄₅ and ^π⁄₂ < θ < π, then tan θ = ?

If each element in a data set is multiplied by 3, and each resulting product is then reduced by 4, which of the following expressions gives the mean of the resulting data set in terms of x?

What is the slope of a line that is perpendicular to the line determined by the equation 7x + 4y = 11?

Which of the following is the set of all real numbers x such that x − 3 < x − 5?