Digital SAT Practice Questions

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...

A computer scientist is analyzing the performance of an algorithm where the number of operations, \( N(k) \), depends on the input size \( k \). The efficiency ...

x y y = x A(0,0) B(6,0) P(6,6) Note: Figure not drawn to scale. In the \(xy\)-plane, a circle passes through the origin \(A(0,0)\) and the point \(B(6,0)\). The...

x y C(1,2) O Q R P(4,6) Note: Figure not drawn to scale. A circle in the \(xy\)-plane has the equation \((x-1)^2 + (y-2)^2 = 25\). Point \(P(4,6)\) lies on this...

x y O(0,0) A(8,0) B(0,6) P(8,6) Note: Figure not drawn to scale. In the \(xy\)-plane, a circle passes through the origin \(O(0,0)\), point \(A(8,0)\), and point...

In the $xy$-plane, a circle with center $(4, -2)$ is tangent to the line $y = 3$. Which of the following equations represents this circle?...

A pollster surveyed a random sample of $1,200$ registered voters in a metropolitan area and found that $64\%$ supported a municipal green energy bond initiative...

In the $xy$-plane, the graphs of $y = 2x^2 - 8x + c$ and $y = 4x - 11$ intersect at exactly one point. What is the value of the constant $c$?...

What are all real values of $x$ that satisfy the rational equation $\frac{x^2 - 9}{x - 3} = 2x - 1$?...

In the $xy$-plane, the line $y = 3x - 5$ intersects the parabola $y = x^2 - 2x + 1$ at points $(x_1, y_1)$ and $(x_2, y_2)$. What is the value of $x_1 + x_2$?...

A cylinder has a radius of $4$ inches and a height of $9$ inches. If the radius is increased by $50\%$ and the height is decreased by $50\%$, how does the volum...