Digital SAT Practice Questions

The population of a certain bacteria colony triples every \( k \) hours. If the population increases by exactly \( 400\% \) in \( 14 \) hours, what is the value...

Let \( p(x) = x^3 + ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants. When \( p(x) \) is divided by \( x - 2 \), the remainder is \( 15 \). W...

A circle with center \( O \) has a radius of \( 5 \). A chord \( AB \) has a length of \( 8 \). What is the area of the largest triangle that can be inscribed i...

How many distinct real solutions does the equation \[ (x^2 - 4x + 3)^2 - 5(x^2 - 4x + 3) - 6 = 0 \] have?...

In his seminal 1935 essay, cultural critic Walter Benjamin argued that the mechanical reproduction of art (such as photography) inherently strips a masterwork o...

Text 1 The recent unearthing of a complex, multi-component stone tool in the Lomekwi basin heavily implies that early hominids possessed a sophisticated form of...

In the chaotic immediate aftermath of the regime change, the new Prime Minister's decision to retain the former administration's widely despised economic minist...

To accurately map the intricate topography of the ocean floor, marine geologists rely heavily on multibeam sonar, a highly sophisticated technology that emits f...

Literary critics often note that in the works of 19th-century poet Silas Waverly, memory is rarely depicted as a comforting sanctuary or a nostalgic refuge. Ins...

In the \(xy\)-plane, a parabola with equation \( y = ax^2 + bx + c \) passes through the points \( (-1, 0) \), \( (0, -6) \), and \( (3, 0) \). A second parabol...

The polynomial \( P(x) = x^3 + cx^2 + dx - 12 \), where \( c \) and \( d \) are constants, is perfectly divisible by \( (x - 2)^2 \). What is the value of \( c ...

The circle with equation \( x^2 + y^2 - 10x + 6y + c = 0 \) has a radius of \( r \). Points \( P \) and \( Q \) lie on the circle such that the length of the mi...

A high-security digital lock requires a 5-digit PIN using the digits 0 through 9. A valid PIN must contain the digit '7' exactly twice, and no other digit in th...

The atmospheric pressure \( P \), in kilopascals (kPa), at an altitude of \( h \) kilometers above Earth's surface can be modeled by the equation \( P(h) = 101 ...

Text 1 Historians have long argued that medieval European merchant and artisan guilds severely hindered technological innovation. By enforcing strict monopolies...

Deep-sea hydrothermal vents emit superheated water rich in toxic minerals, creating environments where photosynthesis is impossible. Conventional marine biology...

While the mayor's rhetoric was frequently celebrated by the press for its soaring, poetic idealism, her actual policy proposals were heavily criticized by veter...

Embedded within the dense, metamorphic rock formations of the remote and inhospitable mountain range ______ the exceptionally well-preserved fossilized remains ...

While researching space observatories, a student has taken the following notes: - The James Webb Space Telescope (JWST) was launched by NASA in 2021. - It is eq...

\[ y = 2x^2 - 4x + 7 \] \[ y = kx - 1 \] In the given system of equations, \( k \) is a constant. If the system has exactly one real solution \( (x, y) \), what...

\[ x^2 + y^2 - 10x + 24y + 153 = 0 \] What is the minimum possible distance from the origin \( (0,0) \) to a point \( (x, y) \) on the graph of the given equati...

\[ f(x) = x^{15} - 2x^{14} + ax^3 + bx - 6 \] In the polynomial function \( f \) defined above, \( a \) and \( b \) are constants. When \( f(x) \) is divided by...

\[ 8^{2x - 1} = 16^{\frac{y}{2}} \] \[ 9^{x + y} = 27^{x + 1} \] If \( (x, y) \) is the solution to the system of equations above, what is the value of \( x + y...

In right triangle \( ABC \), the right angle is at vertex \( B \). Point \( D \) lies on the hypotenuse \( AC \) such that line segment \( BD \) is perpendicula...