ACT Math Practice Test

If the function \(f(x) = \frac{3x - 7}{2x + 5}\) is defined for all real numbers except \(x = -\frac{5}{2}\), what is \(f\left(\frac{1}{f(-3)}\right)\)?

If \(g(x) = x^3 - 4x^2 + x + 6\) and \(g(k) = 0\), which of the following could be a possible value of \(k\)?

The equation \(\frac{1}{x-1} + \frac{1}{x+1} = \frac{2}{x}\) is valid for all \(x\) except:

What is the minimum value of the function \(h(t) = t^4 - 4t^3 + 6t^2 - 4t + 5\)?

A cube has a volume of \(8x^3\) cubic units. If each side of the cube is multiplied by 3, what is the new volume?

The function \(f(x) = a^x\) passes through the point (2,9). What is the value of \(a\)?

If the inequality \(|x - 5| > 7\) is true, which of the following represents all possible values of \(x\)?

What are the roots of the equation \(x^3 - 2x^2 - 5x + 6 = 0\)?

Given the sequence defined by the recursive formula \(a_{n+1} = 3a_n + 1\) with \(a_1 = 1\), what is \(a_4\)?

If the set \(S\) contains all solutions \(x\) to the inequality \(x^2 - 3x - 18 \leq 0\), what are the interval bounds of \(S\)?

If \(z\) and \(w\) are complex numbers such that \(z = 3 + 4i\) and \(w = 1 - 2i\), what is \(z \cdot w\)?

The sides of a triangle are given by \(x\), \(x+1\), and \(x+2\). If \(x+2\) is the longest side, what is the range of possible values for \(x\)?

What is the solution set to the equation \(\sqrt{9x^2 - 54x + 81} = 3x - 9\)?

What is the sum of the solutions to the equation \(\sin^2 x - \sin x - 6 = 0\) over the interval \([0, 2\pi]\)?

The function \(f(x) = \frac{2x}{x^2 + 1}\) reaches its maximum on the interval \([-1, 2]\) at \(x =\):

A geometric series has a first term of 5 and a common ratio of \(\frac{1}{2}\). What is the sum of the first 6 terms?

If \( \log_2 (8x) = 6 \), what is \(x\)?

The roots of the equation \(x^2 - 8x + 15 = 0\) are:

If the points (1,1), (4,y), and (9,9) lie on the graph of a quadratic function \(y = ax^2 + bx + c\), what is the value of \(y\) when \(x = 4\)?

For the circle with equation \((x - 4)^2 + (y + 3)^2 = 16\), what are the coordinates of its center and the length of its radius?

What is the area of a triangle with vertices at \((0,0)\), \((4,0)\), and \((0,3)\)?

Solve for \(x\) in the equation \(4^{x+1} = 16^x\).

If the function \( f(x) = \frac{x^2 - 1}{x - 1} \) is evaluated for \( x \neq 1 \), which expression is equivalent to \( f(x) \)?

What is the sum of the solutions to the equation \( 2x^2 - 8x + 8 = 0 \)?

A circle has equation \( x^2 + y^2 + 6x - 4y + 9 = 0 \). What is the radius of this circle?

If \( \log_b(3) = a \) and \( \log_b(5) = c \), what is \( \log_b(45) \) in terms of \( a \) and \( c \)?

For \( f(x) = \sqrt{2x + 3} \), what is the domain of \( f \)?

If \( i \) is the imaginary unit, what is the product \( (3 - 4i)(3 + 4i) \)?

How many integer solutions satisfy the inequality \( |x - 3| > 2 \)?

The equation \( e^{2x} - 7e^x + 10 = 0 \) can be rewritten as a quadratic equation. What are the roots?

A cubic function \( f(x) = x^3 - 6x^2 + 9x \) has a factor \( x \). What are the other factors?

Given the function \( f(x) = \frac{x^2 - 4x + 4}{x - 2} \), what is the value of \( f(2) \)?

What is the vertex of the parabola represented by the equation \( y = 3(x - 2)^2 - 5 \)?

If \( f(x) = \frac{1}{x-1} \) and \( g(x) = \frac{1}{x+1} \), what is \( f(g(1)) \)?

What is the remainder when the polynomial \( x^3 - 4x^2 + x + 6 \) is divided by \( x - 2 \)?

For the equation \( \sqrt{3x+15} = x + 3 \), what is the value of \( x \)?

If the perimeter of a rectangular garden is 60 feet and the length is twice the width, what is the area of the garden?

A rectangle is three times as long as it is wide. If the length and width are both increased by 5 feet, the area becomes 100 square feet. What were the original dimensions?

A circular park with a radius of 30 feet is surrounded by a walkway of uniform width. If the total area of the park and walkway is four times the area of the park alone, what is the width of the walkway?

If \(f(x) = 2x^2 - 3x + 5\) and \(g(x) = x - 2\), what is \(f(g(3))\)?

A cylindrical tank has a radius of 5 feet and is filled with water to a height of 12 feet. If the water is drained until the height of the water is 4 feet, what is the volume of water remaining in the tank?

A square and a rectangle have the same perimeter. The rectangle's length is twice its width. If the side of the square is 10 units, what is the area of the rectangle?

A train travels from Station A to Station B at 60 mph and returns at 40 mph. What is the average speed for the round trip if both segments are the same distance?

Two angles are supplementary. If one angle is 30 degrees less than four times the other, what is the measure of the larger angle?

If 8 workers can complete 6 tasks in 3 hours, how many hours would it take 4 workers to complete 9 tasks?

A clock shows the time as 3:15. What is the angle between the hour and the minute hands?

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the base of the wall, how high on the wall does the ladder reach?

A rectangular field is three times as long as it is wide. If decreasing the width by 10 meters and increasing the length by 30 meters doubles the area, what was the original width?

A train leaves from City A to City B at a speed of 80 km/h. Two hours later, another train leaves from City B to City A on a parallel track at a speed of 100 km/h. If the distance between City A and City B is 720 km, how far from City A do the trains meet?

If \(5^x \times 5^{x+2} = 5^{11}\), what is the value of \(x\)?

A sequence is defined as \(a_n = n^2 + n - 1\). What is the fifth term of the sequence?

A train leaves from City A to City B at a speed of 80 km/h. Two hours later, another train leaves from City B to City A on a parallel track at a speed of 100 km/h. If the distance between City A and City B is 720 km, how far from City A do the trains meet?

A square and a circle have the same perimeter. If the side of the square is 10 units, what is the area of the circle?

Three numbers are in the ratio 3:4:5 and their sum is 60. What is the largest number?

If \(x\) and \(y\) are numbers such that \(x + y = 10\) and \(xy = 16\), what is \(x^2 + y^2\)?

A square and a rectangle have the same area. The rectangle's length is twice its width. If the side of the square is 12 units, what is the perimeter of the rectangle?

A cube has a volume of 64 cubic units. What is the surface area of the cube?

In a right triangle, the lengths of the legs are 7 units and 24 units. What is the length of the hypotenuse?

A container initially holds 10 gallons of water. Water is added at a rate of 2 gallons per minute, and at the same time, water leaks out at a rate of 0.5 gallons per minute. After 10 minutes, how many gallons of water are in the container?

A rectangle's length is decreased by 4 units and its width is increased by 3 units, resulting in no change to the area. If the original dimensions of the rectangle were 12 units by 5 units, what is the new length and width?