Digital SAT Practice Questions

A regular hexagon is inscribed in a circle whose equation in the \( xy \)-plane is \( x^2 + 2\sqrt{3}x + y^2 - 6y = 26 \). What is the area of the hexagon?...

If \( \frac{3x^3 - kx^2 + 13x - 4}{x - 4} = ax^2 + bx + c \) is true for all values of \( x eq 4 \), what is the value of \( a - b + c \)?...

The population of a certain species of fish in a lake is modeled by the function \( P(t) = 800(1.69)^{\frac{t}{a}} \), where \( t \) is the time in months. It i...

In the \( xy \)-plane, the terminal ray of an angle in standard position with measure \( \alpha \) radians intersects the circle with equation \( x^2 + y^2 = 36...

Paleontologists long posited that the extraordinary accumulation of undecomposed Lepidodendron plant matter during the Carboniferous period was due to an "evolu...

Text 1 Algorithmic trading (AT) has fundamentally stabilized modern financial markets. By executing millions of trades per second, AT firms act as perpetual mar...

In linguistics, the "poverty of the stimulus" argument asserts that children learn language far too quickly and accurately given the fragmented, frequently gram...

The diplomat’s highly anticipated memoirs are ultimately characterized by a frustrating _________; he seemingly goes to great lengths to meticulously strip his ...

Because the intense pressure and freezing temperatures create an incredibly hostile environment, the deep biosphere was long thought to be entirely devoid of li...

In the \( xy \)-plane, the graph of the exponential function \( f(x) = a(b)^x \), where \( a \) and \( b \) are positive constants, passes through the points \(...

The equation \( 2x^2 + 2y^2 - kx + 16y + 14 = 0 \), where \( k \) is a positive constant, represents a circle in the \( xy \)-plane. If the circle is tangent to...

A system of two linear equations is shown below: \[ \frac{3}{2}x - \frac{k}{4}y = 12 \] \[ cx - 5y = 2k \] In the system above, \( c \) and \( k \) are positive...

The function \( g \) is defined by \( g(x) = x^2 - 6x + 13 \). For all real numbers \( x \), what is the minimum value of \( g(g(x)) \)?...

Solution A contains \( p\% \) of a chemical acid by volume, and Solution B contains \( 3p\% \) of the same acid by volume. When \( x \) liters of Solution A are...

In her seminal critique of the nineteenth-century novelist Elias Thorne, Dr. Arisawa posits that Thorne’s predilection for fragmented narratives was not, as his...

Text 1 Proponents of the classical gold standard often point to the period between 1870 and 1914 as a golden age of international economic stability. By pegging...

A team of agronomists hypothesized that introducing Mycorrhizal Fungi Strain Z to a mixed-crop environment would heavily favor the invasive weed *Amaranthus ret...

Following the unprecedented collapse of the global supply chain, analysts eagerly awaited the central bank’s response. Scarcely ________ the new fiscal policy w...

In quantum chromodynamics, the concept of "asymptotic freedom" dictates that quarks behave almost as free particles when at extremely high energies. As energy d...

Let \( P(x) = x^3 + ax^2 + bx + c \) be a polynomial where \( a \), \( b \), and \( c \) are rational numbers. It is given that \( x = 3 + \sqrt{2} \) is a root...

In the \( xy \)-plane, the circle with equation \( x^2 + y^2 - 10x + 6y + c = 0 \) is exactly tangent to the line \( y = 2x - 1 \). What is the value of the con...

A specific financial asset routinely loses \( 87.5\% \) of its current value every 12 years. The value of the asset, in dollars, \( t \) years after its initial...

In triangle \( ABC \), point \( D \) lies on side \( AB \) and point \( E \) lies on side \( AC \) such that the line segment \( DE \) is parallel to side \( BC...

The system of equations below has exactly two distinct real solutions for \( (x,y) \). \[ y = -x^2 + 8x - 12 \] \[ y = k \] If the distance between the two poin...