Digital ACT Practice Questions

A circle has equation $(x + 3)^2 + (y - 5)^2 = 36$. Which of the following represents the circumference of this circle?...

How many distinct real solutions does the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ have?...

What is the sum of the infinite geometric series $18 - 12 + 8 - \frac{16}{3} + \cdots$?...

If $f(x) = 2x^2 - 3x + 1$ and $g(x) = x + 4$, what is the value of $(f \circ g)(-2)$?...

The volume of a sphere is $288\pi$ cubic units. What is the surface area, in square units, of this sphere?...

What is the degree measure of the smaller angle between the hour hand and the minute hand of a standard 12-hour analog clock at precisely 3:40?...

In the standard $(x,y)$-coordinate plane, the line $3x - 4y = 12$ is perpendicular to the line passing through points $(2, -1)$ and $(5, k)$. What is the value ...

How many distinct four-letter arrangements can be formed using the letters in the word 'KIDNEY' if each letter may be used at most once in each arrangement?...

If $\log_b(3) = x$ and $\log_b(5) = y$, what is the value of $\log_b(45\sqrt{b})$ expressed in terms of $x$ and $y$?...

A right circular cone and a right circular cylinder have equal heights and equal base radii. If the volume of the cylinder is $54\pi$ cubic centimeters, what is...

What is the minimum value of the quadratic function $g(x) = 3x^2 - 12x + 19$?...

For what value of $\theta$, where $0 \le \theta \le \pi$, does $\sin(2\theta) = \cos(\theta)$ have the greatest number of solutions?...

A rectangular garden has an area of $180$ square feet. If the length is $3$ feet more than three times the width, what is the perimeter, in feet, of the garden?...

If $x$ and $y$ are positive integers such that $x^2 - y^2 = 31$, what is the value of $x$?...

What is the matrix product $\begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 \\ -2 \end{bmatrix}$?...

In a triangular municipal park, surveyors map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $7\text{ meters}$, the distance from $B$ t...

In a cellular communications tower array, technicians map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $5\text{ kilometers}$, the dis...

In a navigational shipping lane, navigators map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $9\text{ nautical miles}$, the distance ...

In a triangular suspension bridge truss, structural engineers map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $6\text{ feet}$, the d...

In a flight path between two regional waypoints, air traffic controllers map three survey markers $A$, $B$, and $C$. The distance from $A$ to $C$ is $8\text{ mi...

A sample of Iodine-131, commonly utilized as a medical imaging radiotracer, exhibits an initial radioactivity of $640\text{ megabecquerels (MBq)}$. The half-lif...

A sample of Phosphorus-32, commonly utilized as a molecular biology genetic probe, exhibits an initial radioactivity of $960\text{ megabecquerels (MBq)}$. The h...

A sample of Sodium-24, commonly utilized as a industrial pipeline leak detector, exhibits an initial radioactivity of $800\text{ megabecquerels (MBq)}$. The hal...

A sample of Bismuth-212, commonly utilized as a alpha-radiation targeted therapy, exhibits an initial radioactivity of $1280\text{ megabecquerels (MBq)}$. The h...