Digital SAT Practice Questions

\[ x^2 + y^2 - 10x + 24y + 153 = 0 \] 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...

Researchers theorize that the *Ranitomeya imitator* frog evolved its vibrant visual patterns and acoustic calls to mimic the highly toxic *Ranitomeya variabilis...

Text 1 The Efficient Market Hypothesis (EMH) posits that financial markets are profoundly rational entities. According to strict interpretations of this theory,...

Though the exact mechanisms of quantum entanglement remain heavily debated among theoretical physicists, the phenomenon's fundamental premise—that two particles...

In his landmark 1848 treatise on political economy, philosopher John Stuart Mill argued that an overabundance of capital within a wealthy nation inevitably lead...

The English Romantic poet John Keats frequently used his work to explore the profound tension between the fleeting, fragile nature of mortal human existence and...

Let the quadratic function \( f(x) = ax^2 + bx + c \) have a vertex at the coordinate \( (4, -2) \) and intersect the x-axis at \( x = 2 \) and \( x = 6 \). The...

What is the sum of all real values of \( x \) that satisfy the rational equation below? \[ \frac{x}{x-4} + \frac{4}{x+4} = \frac{32}{x^2 - 16} \]...

In a circle with center \( O \), points \( P \), \( Q \), and \( R \) lie on the circumference such that the inscribed angle \( \angle PQR = \frac{\pi}{4} \) ra...

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a, b, c, \) and \( d \) are real constants. When \( P(x) \) is divided by \( x - 2 \), the remainder is 5....

The exponential equation \( 2^{2x+1} - 17(2^x) + 8 = 0 \) has two real solutions, \( m \) and \( n \). What is the value of \( m + n \)?...

Isotopic analysis of marine microfossils, specifically the ratio of oxygen-18 to oxygen-16, is a cornerstone of paleoclimatology. Traditionally, an increase in ...

For decades, the standard narrative in the history of science portrayed the transition from alchemy to modern chemistry as a sudden, rationalist awakening. Howe...

Recognizing the rapidly escalating threat of orbital debris, commonly known as space junk, the international aerospace coalition issued a sweeping emergency dir...

Text 1: Behavioral economist Daniel Kahneman posits that human decision-making is driven by two distinct systems: System 1, which is fast, intuitive, and highly...

Philosopher Karl Popper famously asserted that for any theory to be considered empirically valid and scientifically rigorous, it must possess the inherent capac...

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a, b, c, \) and \( d \) are constants. When \( P(x) \) is divided by \( x^2 - 1 \), the remainder is \( 3x...

A circle in the \( xy \)-plane has the equation \( x^2 - 4x + y^2 + 6y = k \), where \( k \) is a constant. A line with the equation \( y = 2x - 3 \) intersects...

The rational function \( f(x) = \frac{ax^2 + bx + c}{3x^2 + dx - 6} \), where \( a, b, c, \) and \( d \) are constants, has a horizontal asymptote at \( y = 4 \...

A plane parallel to the circular base of a right circular cone intersects the cone, separating it into a smaller cone and a frustum. The volume of the smaller c...

A dataset consists of 100 positive integers. The mean of the dataset is 54, and the median is 60. The sum of the 25 largest integers in the dataset is exactly 2...