Digital SAT Practice Questions

A circle in the \( xy \)-plane has the equation \( x^2 + y^2 - 12x + 8y + 27 = 0 \). Points \( A \) and \( B \) lie on the circle such that the length of minor ...

A data set consists of 9 strictly distinct positive integers. The median of the data set is 20, and the range is 17. What is the maximum possible arithmetic mea...

In evolutionary biology, the standard neo-Darwinian synthesis posits that genetic mutations occur randomly, and natural selection subsequently acts upon these r...

Text 1 The sudden, catastrophic collapse of the Bronze Age civilizations across the Eastern Mediterranean around 1177 BCE has long baffled historians. Tradition...

In deep-sea hydrothermal vent ecosystems, the complete absence of sunlight inherently precludes the process of photosynthesis, which for centuries was considere...

The sheer structural complexity of the newly mapped biochemical pathways—which govern everything from resilient cellular respiration in highly acidic environmen...

The massive excavation of the ancient Mesopotamian city of Uruk yielded tens of thousands of clay tablets meticulously inscribed with cuneiform script. These ub...

The polynomial \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a \), \( b \), \( c \), and \( d \) are constants, has roots at \( x = 1 \), \( x = -2 \), and ...

In the \( xy \)-plane, the circle defined by the equation \( x^2 + y^2 - 6x + 8y = c \) has an area of \( 16\pi \). A line defined by the equation \( y = mx + b...

The rational equation \[ \frac{kx^2 - 18}{2x^2 - mx + n} = 4 \] has infinitely many solutions for \( x \), where \( k \), \( m \), and \( n \) are constants. Wh...

A specific radioactive isotope decays such that its mass decreases by 19% every 45 years. The mass \( M(t) \), in grams, of the isotope \( t \) decades after an...

In the \( xy \)-plane, a circle with radius \( r \) is completely inscribed within a rhombus. The lengths of the diagonals of the rhombus are 10 and 24. What is...

Text 1 For decades, paleontologists hypothesized that *Spinosaurus aegyptiacus* was primarily a high-speed pursuit predator. Proponents of this view cited its e...

I look into my glass, And view my wasting skin, And say, "Would God it came to pass My heart had shrunk as thin!" For then, I, undistrest By hearts grown cold t...

During the mid-20th century, a controversial geoengineering proposal suggested that mechanically altering the Earth's orbit could permanently resolve the proble...

The population collapse of the Rapa Nui people on Easter Island prior to European contact has traditionally been attributed to 'ecocide,' a theory positing that...

The sheer scale of the ocean’s abyssal zone makes it one of the most difficult environments on Earth to explore. Not only ______ the physiological mechanisms of...

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) be a polynomial, where \( a \), \( b \), \( c \), and \( d \) are constants. The polynomial \( P(x) \) is perfectly ...

In triangle \( PQR \), the measure of angle \( Q \) is \( 90^\circ \). The length of the hypotenuse \( PR \) is \( \sqrt{104} \). If \( \sin(P) + \cos(P) = \fra...

The equation \( \frac{x^2 - cx + 12}{x - 4} = 2 \) has exactly one real solution for \( x \). If \( c \) is an integer, what is the value of \( c \)?...

A data set consists of 15 distinct positive integers. The median of the data set is 25, and the range of the data set is 40. What is the maximum possible sum of...

A line \( L \) is tangent to the parabola \( y = x^2 \) at the point \( (2, 4) \). A circle is tangent to line \( L \) at the point \( (2, 4) \) and is also tan...

The art critic argued that the director's latest film was an unfortunate exercise in _______; rather than inventing a new visual language or exploring novel the...

Text 1 In analyzing the explosion of literary realism in the mid-19th century, scholars often emphasize its moral dimensions. Writers like Charles Dickens and H...