Digital SAT Practice Questions

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...

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 ...