Digital SAT Practice Questions

If \( \frac{x^{a^2}}{x^{b^2}} = x^{16} \), where \( x > 1 \), and \( a + b = 2 \), what is the value of \( a - b \)?...

The equation \( y = -2x^2 + 12x - 10 \) is graphed in the \( xy \)-plane. What is the \( y \)-coordinate of the vertex of the parabola?...

In right triangle \( ABC \), the measure of angle \( C \) is \( 90^\circ \). If \( \sin(A) = \frac{3}{5} \), what is the value of \( \cos(B) \)?...

A list of 5 numbers has a mean (average) of 12. If a 6th number, \( n \), is added to the list, the new mean of the 6 numbers becomes 15. What is the value of \...

While studying the intricate root systems of old-growth forests, ecologist Dr. Suzanne Simard discovered that trees do not merely compete for resources; rather,...

Though she was largely celebrated for her groundbreaking work in theoretical physics, Dr. Vance’s peers were careful to ______ their praise, noting that her mat...

During the mid-twentieth century, the widespread adoption of synthetic pesticides drastically increased agricultural crop yields by decimating insect population...

The integration of artificial intelligence into weather forecasting models has vastly improved the accuracy of short-term predictions. Meteorologists are now ab...

Biologist Jane Goodall famously observed chimpanzees modifying twigs to extract termites from their mounds, proving that humans were not the only species capabl...

A system of two linear equations is given below: \[ 3x + 4y = 18 \] \[ 2x - y = 1 \] If the ordered pair \( (x, y) \) is the solution to the system of equations...

The quadratic equation \( 2x^2 - 4x + c = 0 \) has exactly one real solution. What is the value of the constant \( c \)?...

A boutique clothing store increases the price of a winter coat by \( 20\% \) at the start of the season. At the end of the season, the store decreases the new p...

If \( 8^x = 2^{y+1} \), which of the following expressions correctly represents \( y \) in terms of \( x \)?...

The equation of a circle in the \( xy \)-plane is given by \( x^2 + 6x + y^2 - 8y = 11 \). What is the radius of the circle?...

In the system of equations below, \(k\) is a constant: \(\begin{cases} 4x - 6y = 15 \\ kx - 9y = 28 \end{cases}\) If the system has no solutions, what is the va...

For what value of \(c\) does the quadratic equation \(2x^2 - 8x + c = 0\) have exactly one distinct real solution?...

The equation of a circle in the xy-plane is \(x^2 + y^2 - 6x + 8y = 24\). What is the radius of the circle?...

The population of a bacterial colony is modeled by the function \(P(t) = 450(1.24)^{t/3}\), where \(t\) is measured in hours. By what percentage does the popula...

When the polynomial \(P(x) = 2x^3 - 5x^2 + 4x - 7\) is divided by \(x - 2\), what is the remainder?...

What are the vertical asymptotes of the rational function \(f(x) = \frac{x + 4}{x^2 - 9}\)?...

Triangle \(ABC\) is similar to triangle \(DEF\), where vertices \(A, B,\) and \(C\) correspond to \(D, E,\) and \(F\), respectively. If the ratio of side \(AB\)...

A polling institute surveyed a random sample of 400 voters in a city and found a 95% confidence interval with a margin of error of 4.9%. If the institute wishes...

What is the x-coordinate of the single point of intersection between the line \(y = 2x - 2\) and the parabola \(y = x^2 - 4x + 7\)?...

What is the positive solution to the equation \(|3x - 5| = 2x + 10\)?...