Digital SAT Practice Questions

The population of City A grows by \( 50\% \) every 5 years, and the population of City B grows by \( q\% \) every 10 years, where \( q \) is a positive constant...

The rational function \( f \) is defined by \( f(x) = \frac{ax + b}{cx + d} \), where \( a, b, c, \) and \( d \) are constants. In the \( xy \)-plane, the graph...

In her 2004 monograph, historian Elena Rostova evaluates the economic policies of the Late Byzantine Empire. Traditionally, scholars have cited the debasement o...

Text 1 Ecologists have long observed that anthropogenic environments, such as heavily polluted urban centers, can drive rapid evolutionary changes in local wild...

The architectural movement known as Brutalism is frequently criticized for its imposing, monolithic concrete structures. However, its pioneers intended these de...

Despite the prevailing belief among early 20th-century astronomers that the universe's expansion was driven by a uniform cosmological constant, astrophysicist D...

Literary critic Arthur Pendelton argues that modernist author Virginia Woolf’s use of fluid, non-linear time in her novel *Mrs. Dalloway* serves primarily to al...

In the \( xy \)-plane, the circle with equation \( x^2 + y^2 - 10x + 6y + c = 0 \) is tangent to the line \( y = \frac{3}{4}x + 2 \). What is the value of the c...

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 system of linear equations below: \[ 3x - 4y = 12 \] \[ ax + by = c \] If the system has infinitely many solutions, and \( a, b, \) and \( c \) are...

The polynomial \( P(x) = x^3 + ax^2 + bx + c \) has roots at \( x = 2 \) and \( x = -3 \). When \( P(x) \) is divided by \( (x - 1) \), the remainder is \( -12 ...

In the \( xy \)-plane, the parabola given by the equation \( y = cx^2 - 4x + c \) intersects the line \( y = 2x - 5 \) at exactly one point. If \( c > 0 \), wha...

In 19th-century geology, uniformitarianism posited that the Earth's features were shaped by continuous, gradual processes operating over vast expanses of time. ...

Entomologists studying the foraging behavior of the Cataglyphis desert ant noted that the ants use path integration to return directly to their nest after a win...

Text 1: Historian A argues that the rapid industrialization of the late 19th century was primarily driven by relaxed government regulations. These laissez-faire...

A linguist analyzed the frequency of archaic syntactical structures (such as inverted word order) in published British literature from 1800 to 1900. The linguis...

The sheer diversity of extremophiles—organisms capable of surviving in environments previously deemed completely inhospitable, such as hydrothermal vents, highl...

The graph of the equation \( y = ax^2 + bx + c \) in the \( xy \)-plane, where \( a \), \( b \), and \( c \) are constants and \( a > 0 \), has its vertex at \(...

The polynomial \( P(x) = x^4 - 5x^3 + cx^2 - 15x + d \), where \( c \) and \( d \) are constants, is perfectly divisible by \( (x - 3)^2 \). What is the value o...

In the \( xy \)-plane, a circle is given by the equation \[ x^2 + y^2 - 10x + 8y + 16 = 0 \] A line passing through the origin with equation \( y = mx \), where...

If \( (\sqrt{3})^{x} \cdot 9^{y} = 27\sqrt{3} \) and \( 4^{x} \cdot \left(\frac{1}{2}\right)^{y} = 32 \), what is the value of \( x - y \)?...

In right triangle \( \triangle ABC \), the right angle is at \( B \). The lengths of sides \( AB \) and \( AC \) are \( 3 \) and \( 5 \), respectively. Point \(...

Biologist Dr. Aris studies a population of *Anolis* lizards that were relocated to a significantly cooler island a decade ago. Over this 10-year period, the liz...

Text 1 Literary critic Arthur P. Mudge argues that poet Eliza Harwood’s final collection, *The Weeping Sun*, represents a dramatic, unheralded stylistic rupture...