Digital ACT Practice Questions
Access 107 official-caliber practice questions. Filter by subject or difficulty to pinpoint your cognitive blind spots.
In $\triangle ABC$, the length of side $a$ is $8$ cm, the length of side $b$ is $11$ cm, and the measure of angle $C$ between them is $60^\circ$. What is the ex...
An ellipse centered at the origin in the standard $(x,y)$-coordinate plane has a major horizontal axis of length $14$ and a minor vertical axis of length $8$. W...
If $\log_2(x) + \log_2(x - 6) = 4$, what is the real solution for $x$?...
Vectors $\mathbf{u} = \langle 3, -4 \rangle$ and $\mathbf{v} = \langle k, 6 \rangle$ are perpendicular in the standard coordinate plane. What is the value of th...
How many distinct real solutions does the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ have?...
If $f(x) = 2x^2 - 3x + 1$ and $g(x) = x + 4$, what is the value of $(f \circ g)(-2)$?...
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?...
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?...
What is the minimum value of the quadratic function $g(x) = 3x^2 - 12x + 19$?...
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?...
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...
A sample of Radon-222, commonly utilized as a subterranean geological tracer, exhibits an initial radioactivity of $1600\text{ megabecquerels (MBq)}$. The half-...
What is the domain of the real-valued function $f(x) = \frac{\sqrt{4x - 12}}{x - 7}$?...
A circle in the standard $(x,y)$-coordinate plane has the equation $x^2 + y^2 - 6x + 8y - 11 = 0$. What is the length of the radius of this circle?...
If $\log_{10}(x) = 2$ and $\log_{10}(y) = -3$, what is the value of $\log_{10}\left(\frac{100x^3}{\sqrt{y}}\right)$?...
A fair six-sided die is rolled three times. What is the probability that the numbers rolled strictly increase (that is, the second roll is greater than the firs...
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