Digital SAT Practice Questions

Embedded within the fossilized resin of the mid-Cretaceous period ________ fragments of a nearly perfectly preserved theropod tail, providing unprecedented insi...

The system of equations consists of a parabola \( y = px^2 - 4x + 5 \) and a line \( y = 2x + r \), where \( p \) and \( r \) are non-zero real constants. If th...

An isosceles trapezoid has bases of length \( 18 \) and \( 32 \). A circle is inscribed within the trapezoid such that it is tangent to all four of its sides. W...

The polynomial \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) has real roots at \( x = 1 \), \( x = -2 \), and a double root at \( x = k \). If the \( y \)-intercept o...

The equation \( 2^{2x+3} - 17(2^x) + 2 = 0 \) has two real solutions, \( x_1 \) and \( x_2 \). What is the value of \( x_1 + x_2 \)?...

In the \( xy \)-plane, the graph of the equation \( x^2 + y^2 - 10x + 6y + c = 0 \) is a circle, where \( c \) is a constant. If the line \( y = x - 1 \) is tan...

Physicist Elena Rostova posits that macroscopic systems do not exhibit observable quantum entanglement because interaction with the surrounding environment caus...

Text 1 The swift adoption of the heavy plow in Northern Europe during the 11th century was fundamentally an economic phenomenon. Lords mandated its use to maxim...

Historian Carter G. Woodson’s magnum opus, *The Mis-Education of the Negro*, revolutionized the study of African American history by arguing that the educationa...

In evolutionary biology, the "Red Queen Hypothesis" posits that species must constantly adapt and evolve not merely to gain a reproductive advantage, but simply...

In American jurisprudence, the doctrine of *stare decisis* dictates that courts must generally adhere to prior precedent when adjudicating contemporary cases wi...

In the \( xy \)-plane, the graph of \( y = x^4 - 2x^3 + kx^2 + mx - 8 \) intersects the \( x \)-axis at \( (2, 0) \). If the remainder when the polynomial is di...

In the \( xy \)-plane, a circle with center \( O \) is given by the equation \[ x^2 + y^2 - 10x + 6y + 9 = 0 \] Line \( L \) is tangent to the circle at point \...

In the \( xy \)-plane, the parabola \( y = ax^2 + bx + c \) has its vertex at \( (2, 1) \) and passes through the point \( (4, 9) \). A line with the equation \...

A farmer wants to construct a rectangular enclosure adjacent to a straight river. The side along the river requires no fencing. The enclosure is divided into 4 ...

In the complex plane, a sequence of complex numbers is defined by \( z_1 = 1 + i \) and \( z_{n+1} = (1 - i)z_n \) for all integers \( n \geq 1 \). What is the ...

English economist William Stanley Jevons argued in the 19th century that technological improvements that increase the efficiency of resource use tend to increas...

Many contemporary historians view the drafting of the Magna Carta not as a soaring triumph of ideological liberty, but rather as a profoundly ______ compromise....

The discovery of the Burgess Shale fossils in the Canadian Rockies radically altered our understanding of the Cambrian explosion. The pristine shale preserves t...

Text 1 Some translation theorists suggest that the translation of ancient texts should prioritize strict literal fidelity. To smooth over the idiosyncratic synt...

A biologist hypothesizes that the reintroduction of apex predators regulates the population of large herbivores, which in turn relieves overgrazing pressure on ...

The polynomial \( P(x) = x^4 - 2x^3 + kx^2 - 4x + 8 \), where \( k \) is a constant, is perfectly divisible by the polynomial \( x^2 + 2 \). What is the value o...

A rhombus is drawn in the \( xy \)-plane. The lengths of its two diagonals are 10 and 24. A circle is inscribed perfectly within the rhombus, such that it is ta...

How many distinct real solutions does the following equation have? \[ \frac{x}{x-4} - \frac{4}{x+4} = \frac{32}{x^2-16} \]...