Digital SAT Practice Questions

In the \( xy \)-plane, a circle has the equation \( x^2 + y^2 - 2ax - 2by + c = 0 \). The circle intersects the \( x \)-axis at points \( A \) and \( B \), wher...

The function \( f(x) = c \cdot d^x \) is defined such that \( c \) and \( d \) are positive constants. If \( f(x+3) = 64 \cdot f(x) \) for all real values of \(...

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a, b, c, \) and \( d \) are real constants. If two of the roots of the equation \( P(x) = 0 \) are \( 3 - ...

The function \( g(x) = \frac{ax^2 + bx + c}{2x^2 - 8} \), where \( a, b, \) and \( c \) are constants, has a horizontal asymptote at \( y = 3 \) and vertical as...

Researchers have long hypothesized that the abrupt onset of the Younger Dryas cooling period roughly 12,900 years ago was triggered by a massive influx of fresh...

Text 1 Historians have frequently attributed the unprecedented success of the Industrial Revolution in Great Britain to geographical determinism. Specifically, ...

For decades, cosmologists believed that the gravitational pull of matter would eventually slow down the expansion of the universe. However, observations made in...

The senator’s latest speech was widely condemned by political analysts for its highly ______ nature; rather than addressing the substantive economic policy issu...

While researching human evolution, a student took the following notes: - Paleontologists study fossilized footprints to understand the locomotion of ancient hom...

In the \( xy \)-plane, the equations for a parabola and a line are given by the system below: \[ y = x^2 - 4x + c \] \[ y = mx + 2 \] The system of equations ab...

In right triangle \( XYZ \) with the right angle at \( Y \), \( \sin(X) = a \) and \( \cos(X) = b \). If \( a - b = \frac{1}{5} \), what is the value of \( a \t...

For all \( x > 0 \), the expression \( \sqrt[3]{x^a \cdot \sqrt{x^b}} \) is mathematically equivalent to \( x^{\frac{11}{6}} \). If \( a \) and \( b \) are posi...

The graph of \( y = f(x) \) in the \( xy \)-plane is a parabola with vertex \( (-3, 5) \). The function \( g \) is defined by \( g(x) = a \cdot f(x - h) + k \),...

A data set consists of 15 distinct positive integers. The median of the data set is 40, and the range of the data set is 74. What is the maximum possible value ...

Biologists have historically operated under the premise that extreme cellular longevity requires high baseline levels of telomerase, an enzyme that replenishes ...

Text 1 Economic historians often celebrate the widespread adoption of the gold standard in the late 19th century for its role in globalizing trade. By tying dom...

The philosopher’s new treatise argues that human consciousness is not a singular, unified entity but rather a fluctuating amalgamation of three distinct tempora...

While prolonged droughts undoubtedly stressed the Classic Maya civilization during the 9th century, the prevailing theory that climate change alone precipitated...

Evolutionary biologist Dr. Aris Lin hypothesized that a specific species of island-dwelling lizard evolved a darker scale pigmentation primarily to absorb more ...

In the \( xy \)-plane, the graph of the equation \( x^2 + y^2 - 6x + 8y = 0 \) intersects the graph of the linear equation \( y = 2x - 10 \) at points \( A \) a...

The polynomial \( p(x) = 3x^3 - kx^2 + 17x - 10 \), where \( k \) is a constant, has a factor of \( (x - 2) \). If \( p(x) \) can be rewritten in the factored f...

A local coffee shop sells two coffee blends: Blend A and Blend B. Blend A consists of 20% Arabica beans and 80% Robusta beans by weight. Blend B consists of 60%...

If \( \frac{9^{2x-1}}{\sqrt{27^{x+2}}} = 3^{x-4} \), what is the value of \( x \)?...

In the \( xy \)-plane, a circle with center \( O \) passes through the origin \( (0, 0) \) and has a radius of \( 4\sqrt{2} \). A line \( \ell \) is tangent to ...