Digital SAT Practice Questions

While researching marine biology, a student took the following notes: - The mantis shrimp is a marine crustacean known for its highly specialized, spring-loaded...

The system of equations is given by: \[ y = ax^2 + 4x - 5 \] \[ y = -2x + b \] where \( a \) and \( b \) are constants, and \( a > 0 \). If the system of equati...

What is the sum of all valid solutions to the given equation? \[ \frac{x^2 - 3x}{x + 2} = \frac{10}{x + 2} + 2 \]...

A circle in the \( xy \)-plane has the equation \( x^2 + y^2 - 12x + ky = 13 \), where \( k \) is a positive constant. If the area of the circle is \( 85\pi \),...

The population of a specific bacterial culture decreases by \( p\% \) every \( h \) hours, where \( p \) and \( h \) are positive constants. If the initial popu...

The function \( f \) is defined by \( f(x) = c \cdot 3^{kx} \), where \( c \) and \( k \) are positive constants. If \( f(x + 2) = 16 \cdot f(x) \) for all real...

In forest ecosystems, mycorrhizal networks allow trees to share resources such as carbon. Ecologist Suzanne Simard and her colleagues conducted an experiment us...

Literary critics frequently mistake the conversational tone of Jane Austen's prose for mere simplicity, assuming her style was a natural, effortless byproduct o...

In 1856, amateur scientist Eunice Newton Foote conducted a groundbreaking experiment demonstrating that carbon dioxide absorbs solar heat, concluding that an at...

A team of urban economists evaluated the impact of a state-level tax subsidy designed to encourage the purchase of electric vehicles (EVs). The subsidy was unif...

Text 1 Art critics have long celebrated Jackson Pollock's "drip paintings" as the pinnacle of Abstract Expressionism, arguing that his technique was entirely sp...

The system of equations below consists of a parabola and a line: \[ y = x^2 - 6x + k \] \[ y = 2x - 5 \] For what value of the constant \( k \) does the system ...

Let \( P(x) = ax^3 + bx^2 - 14x + 8 \), where \( a \) and \( b \) are constants. If \( P(x) \) is divisible by both \( (x - 2) \) and \( (x + 1) \), what is the...

The equation \( 2x^2 + 2y^2 - 12x + 16y = 10 \) represents a circle in the \( xy \)-plane. If points \( A \) and \( B \) lie on the circle such that the line se...

A radioactive isotope decays such that its mass decreases by \( 18\% \) every 4 hours. If the initial mass of the isotope is \( M_0 \) grams, which of the follo...

What is the sum of all valid solutions to the following equation? \[ \frac{x}{x - 3} - \frac{2}{x + 3} = \frac{18}{x^2 - 9} \]...

Paleoclimatologists routinely use pollen preserved in ancient sediment cores to reconstruct historical ecosystems. However, pollen preservation and dispersal ar...

Text 1 Many technological determinists argue that the introduction of Johannes Gutenberg's printing press in 15th-century Europe was the singular catalyst for t...

Despite his public reputation as a ruthless corporate raider who would dismantle companies without a second thought, billionaire investor Richard Vance was know...

The sprawling underground city of Derinkuyu in modern-day Turkey is an architectural marvel extending hundreds of feet beneath the earth's surface. With its int...

In 2022, astronomers utilizing the James Webb Space Telescope announced the detection of carbon dioxide in the atmosphere of WASP-39b, a "hot Jupiter" exoplanet...

The system of equations below is given by: \[ y = a x^2 + b x + c \] \[ y = m x + k \] where \( a \), \( b \), \( c \), \( m \), and \( k \) are constants, and ...

The rational expression \( \frac{3x^3 + 4x^2 + x - 15}{x + 2} \) is equivalent to the expression \( A x^2 + B x + C + \frac{D}{x + 2} \) for all \( x eq -2 \), ...

If \( x \) and \( y \) are the solutions to the system of equations below, what is the value of the product \( xy \)? \[ 8^x \cdot 16^y = 2^{24} \] \[ \frac{9^x...