Digital SAT Practice Questions

Consider the equation \[ \frac{2x^2 + kx - 15}{x - 3} = 2x + 7 \] where \( k \) is a constant. What is the sum of all possible values of \( k \) for which the e...

In the \( xy \)-plane, a circle with center \( O \) has a radius of \( 6\sqrt{2} \). Triangle \( ABC \) is inscribed in the circle such that the length of arc \...

A biologist models the growth of a bacteria colony. The colony's population doubles every 15 hours. The function \( P(m) \) represents the population \( m \) mi...

The quadratic function \( f \) is defined by \( f(x) = -2x^2 + 12x - 14 \). The function \( g \) is defined by \( g(x) = f(x - c) + d \), where \( c \) and \( d...

Researchers comparing two divergent lineages of blind cavefish—*species A* found in hydrothermal deep-sea vents and *species B* found in isolated freshwater lim...

Text 1 Some contemporary art critics argue that the widespread adoption of artificial intelligence in artistic generation will inevitably lead to a "flattening"...

The film critic noted that the director’s latest three-hour epic was severely marred by its ________ pacing; the narrative progressed in jarring fits and starts...

To map the ocean floor, scientists often utilize multibeam sonar, which emits sound waves in a broad fan shape directly beneath a ship's hull. This technique pr...

The researchers hypothesized that the sudden localized drop in temperature was caused by a highly unusual fluctuation in the region’s magnetic ________ an expla...

Let \( f(x) = ax^7 + bx^5 + cx^3 + dx + 5 \), where \( a \), \( b \), \( c \), and \( d \) are constants. If \( f(-3) = 12 \), what is the value of \( f(3) \)?...

In the xy-plane, the parabola \( y = -2x^2 + bx + c \) has its vertex at \( (h, k) \) and intersects the x-axis at \( x = -1 \) and \( x = 5 \). A line with equ...

The equation \( x^2 + y^2 - 2ax + 4by + c = 0 \) represents a circle in the xy-plane, where \( a \), \( b \), and \( c \) are positive constants. The circle is ...

In the xy-plane, the line \( y = mx + d \) intersects the parabola \( y = 3x^2 + bx + c \) at exactly one point. If this unique point of intersection is exactly...

Set A consists of 15 integers with a mean of 40 and a standard deviation of 4. Set B consists of 25 integers with a mean of 60 and a standard deviation of 6. Se...

Traditional ecological models posit that ecosystems with high native biodiversity are intrinsically more resistant to invasive species, a concept known as 'biot...

Text 1 Historian Jonathan Israel characterizes Maximilien Robespierre as a man driven fundamentally by a rigid, uncompromising ideological purity. According to ...

The art historian argued that the acclaimed painter's sudden transition from avant-garde abstraction to highly conventional, widely appealing landscapes was not...

The architectural style known as Brutalism is often criticized for its imposing, monolithic concrete structures. However, its mid-century proponents viewed it a...

For decades, the prevailing historical narrative asserted that the abrupt collapse of Eastern Mediterranean Bronze Age civilizations was primarily caused by the...

The equation \( x^2 - kx + p = 0 \) has roots \( r_1 \) and \( r_2 \). The equation \( x^2 - px + k = 0 \) has roots \( r_1 + 2 \) and \( r_2 + 2 \). If \( k \)...

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...