Digital SAT Practice Questions

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 + 6x - 8y - 75 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(-3, 1...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 12x - 16y = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(6, 18) \...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 + 4x + 10y - 35 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(-2, ...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 14x + 2y - 14 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(7, 7...

A marine bacterial culture has an initial population of 250 and grows according to the model: \[ P(t) = 250 \cdot (1.44)^{\frac{t}{4}} \] where \( t \) is the t...

While researching exoplanetary atmospheres, a student took the following notes: • Exoplanet WASP-121b is an ultra-hot Jupiter orbiting an F-type star every 1.27...

Although the poet’s later anthologies were praised for their lyricism, several prominent critics condemned his prose essays as unduly [____], lamenting that his...

Early twentieth-century dialectologists assumed that regional accents across North America would inexorably homogenize under the pervasive influence of nationwi...

While researching a topic, a student has taken the following notes: • Archaeologists excavated a 3,200-year-old bronze cauldron from the Tel Hazor site in north...

A marine bacterial culture has an initial population of 500 and grows according to the model: \[ P(t) = 500 \cdot (1.69)^{\frac{t}{6}} \] where \( t \) is the t...

A marine bacterial culture has an initial population of 100 and grows according to the model: \[ P(t) = 100 \cdot (1.96)^{\frac{t}{8}} \] where \( t \) is the t...

A marine bacterial culture has an initial population of 800 and grows according to the model: \[ P(t) = 800 \cdot (2.25)^{\frac{t}{10}} \] where \( t \) is the ...

A marine bacterial culture has an initial population of 1200 and grows according to the model: \[ P(t) = 1200 \cdot (2.56)^{\frac{t}{12}} \] where \( t \) is th...

A marine bacterial culture has an initial population of 400 and grows according to the model: \[ P(t) = 400 \cdot (1.21)^{\frac{t}{2}} \] where \( t \) is the t...

In comparative physiological analyses of deep-diving mammals, researchers observed that Weddell seals exhibit severe peripheral vasoconstriction during extended...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-4, 2) \) and \( B(6, 8) \). The perpendicular bisector of segment \( AB \) can be written in the for...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-2, -3) \) and \( B(4, 9) \). The perpendicular bisector of segment \( AB \) can be written in the fo...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-6, 4) \) and \( B(2, -2) \). The perpendicular bisector of segment \( AB \) can be written in the fo...

In the \( xy \)-plane, segment \( AB \) has endpoints \( A(-4, 0) \) and \( B(4, 6) \). The perpendicular bisector of segment \( AB \) can be written in the for...

The rational function \( f \) is defined by: \[ f(x) = \frac{2x^2 + ax - 12}{x^2 - 9} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{3x^2 + bx - 10}{x^2 - 4} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{x^2 + cx - 20}{x^2 - 16} \] where the coefficient in the numerator is a constant. If \( f \) has a ...

The rational function \( f \) is defined by: \[ f(x) = \frac{2x^2 + kx - 15}{x^2 - 25} \] where the coefficient in the numerator is a constant. If \( f \) has a...

The polynomial function \( P \) is defined by: \[ P(x) = 2x^3 - kx^2 + 4x - 8 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \( ...