Digital SAT Practice Questions

A data set consists of 15 distinct positive integers. The median of the data set is 25, and the range of the data set is 40. What is the maximum possible sum of...

A line \( L \) is tangent to the parabola \( y = x^2 \) at the point \( (2, 4) \). A circle is tangent to line \( L \) at the point \( (2, 4) \) and is also tan...

The art critic argued that the director's latest film was an unfortunate exercise in _______; rather than inventing a new visual language or exploring novel the...

Text 1 In analyzing the explosion of literary realism in the mid-19th century, scholars often emphasize its moral dimensions. Writers like Charles Dickens and H...

In historical linguistics, the comparative method is actively utilized to reconstruct proto-languages by assuming that phonetic shifts occur uniformly across a ...

In a recent astrophysics study, researchers observed a series of Fast Radio Bursts (FRBs) emitting from a distant magnetar. Traditionally, FRBs are theorized to...

While architectural historian David Watkin argued that the Gothic Revival of the 19th century was fundamentally a conservative movement—a nostalgic retreat into...

In the \( xy \)-plane, the quadratic equation \( y = -2x^2 + bx + c \) intersects the line passing through the origin at exactly one point, \( (3, 5) \). What i...

The polynomial \( p(x) = ax^4 - 3x^3 + bx^2 + 4x - 6 \) is divided by \( (x - 2) \), resulting in a remainder of 10. When \( p(x) \) is divided by \( (x + 1) \)...

Consider the following system of equations: \[ 8^{x} \cdot 4^{y} = 32 \] \[ 9^{x} \cdot 27^{y-1} = 81 \] If \( (x, y) \) is the solution to the system of equati...

In the quadratic equation \( 2x^2 - px + q = 0 \), \( p \) and \( q \) are real constants. If one of the solutions to the equation is \( 3 - 4i \), where \( i =...

In the \( xy \)-plane, a circle has the equation \( x^2 + y^2 - 10x + 6y + c = 0 \), where \( c \) is a constant. If the area of the circle is \( 16\pi \), what...

Researchers theorize that the European robin navigates using a quantum phenomenon known as the radical pair mechanism. Cryptochrome proteins in the bird's retin...

Text 1 Late 19th-century marginalists revolutionized economic theory by discarding the classical labor theory of value, which posited that a good's value is der...

The decipherment of Linear B by Michael Ventris in 1952 revolutionized the study of the ancient Aegean. By demonstrating that the script was an early form of Gr...

To investigate the 'urban heat island' (UHI) effect, meteorologists analyzed temperature disparities between downtown metropolitan areas and their surrounding r...

While a cursory reading of the philosopher's treatise might suggest a rigid adherence to fatalism, a more meticulous analysis reveals a deeply embedded ______: ...

The system of equations is given by: \[ y = x^2 - 6x + k \] \[ y = mx - 4 \] where \( k \) and \( m \) are constants. The equations intersect at exactly one poi...

Let \( P(x) = x^3 + ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are real constants. The polynomial \( P(x) \) has a root at \( x = 3 + 2i \), where \(...

In a circle with center \( O \) and radius \( r \), points \( J \) and \( K \) lie on the circle. The area of sector \( JOK \) is \( \frac{5}{12} \) the area of...

A radioactive isotope decays such that its mass, \( M(t) \), in grams, after \( t \) days is modeled by the function \( M(t) = M_0 (0.5)^{\frac{t}{h}} \), where...

Consider the equation: \[ \frac{2x^2}{x^2 - 9} - \frac{5}{x + 3} = \frac{x}{x - 3} \] What is the sum of all valid solutions to the equation above?...

In her definitive biography of Napoleon, Dr. Aris Thorne argues that the historian’s endeavor is less a process of mere accumulation than one of careful _____, ...

Text 1 The moss P. pyriforme relies entirely on wind for spore dispersal. Because its spores lack any aerodynamic adaptations for sustained high-altitude drift,...