Digital SAT Practice Questions

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 1x^2 + (-10)x + 15 \] \[ y = 2x - k \] where \( k \) is ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 4x^2 + (-16)x + 7 \] \[ y = 8x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 2x^2 + (-4)x + 9 \] \[ y = 8x - k \] where \( k \) is a ...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 1x^2 + (-6)x + 12 \] \[ y = 4x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 2x^2 + (-10)x + 3 \] \[ y = 2x - k \] where \( k \) is a...

In the \( xy \)-plane, the system of equations below has exactly one real solution \( (x, y) \): \[ y = 3x^2 + (-12)x + 4 \] \[ y = 6x - k \] where \( k \) is a...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 8x + 6y - 11 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(4, 3)...

The equation of a circle in the \( xy \)-plane is given by: \[ x^2 + y^2 - 10x + 4y - 20 = 0 \] Line \( \ell \) is tangent to this circle at the point \( P(5, 5...

The graph of the quadratic function \( f(x) = ax^2 + bx + c \) in the \( xy \)-plane passes through the point \( (0, 18) \) and has a vertex at \( (3, 0) \). If...

A circle in the \( xy \)-plane is defined by the equation \( x^2 + y^2 - 8x + 14y - 35 = 0 \). A line passing through the center of this circle has an equation ...

For a certain exponential growth model \( P(t) = C \cdot (1.25)^{\frac{t}{6}} \), where \( t \) represents the number of hours elapsed, by what percent does \( ...

>P >Q >R >S >12 >x >x+7 Note: Figure not drawn to scale. In the right triangle \( riangle PQR\), shown above, \(\angle PQR\) is a right angle. Altitude \(QS\) i...

>A >B >C >D >BD=x >DC=15 Note: Figure not drawn to scale. In right triangle ABC, with the right angle at vertex A, an altitude is drawn from A to hypotenuse BC,...

.label { font-family: serif; font-style: italic; font-size: 14px; } >O >A >B >C >θ Note: Figure not drawn to scale. In the \(xy\)-plane, a circle has the equati...

>r >h Note: Figure not drawn to scale. A company plans to paint the exterior of a grain silo, which is shaped like a cylinder topped with a hemisphere, as shown...

>L >H >W >r Note: Figure not drawn to scale. A solid rectangular block of wood has dimensions: length \(L = 10\) cm, width \(W = 6\) cm, and height \(H = 8\) cm...

Note: Figure not drawn to scale. In the \( xy \)-plane, a parabola is defined by the equation \( y = x^2 - 4x + 7 \). A line is defined by the equation \( y = 2...

Note: Figure not drawn to scale. In the \( xy \)-plane, a circle is centered at the origin and has a radius of 5. A line with the equation \( y = x + 1 \) inter...

>M Note: Figure not drawn to scale. In the \( xy \)-plane, a parabola is given by the equation \( y = x^2 - 6x + 10 \). A line with the equation \( y = mx + c \...

A civil engineer is modeling the flow rate of water through a pipe system using the equation: \[ \frac{x^2+1}{x-1} = \frac{2x}{x-1} + 2 \] where \( x \) represe...

In a sophisticated data analysis model, a variable expression \( E(x) \) is defined as: \[ E(x) = \frac{x^3-x^2-6x}{x^3-9x} \] Which of the following expression...

In a study of chemical reaction rates, the concentration of a certain reactant is modeled by the equation: \[ \frac{2x}{x^2-1} + \frac{1}{x+1} = \frac{1}{x-1} \...

The concentration of a certain drug in a patient's bloodstream, in milligrams per liter, \( t \) hours after administration, can be modeled by the polynomial fu...

Engineers designing a new audio processing unit are modeling signal responses using polynomial functions. The behavior of these functions, particularly their ro...