Digital SAT Practice Questions

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...

In the standard coordinate plane, a circle has the general equation $x^2 + y^2 - 8x + 10y - 8 = 0$. What is the area of this circle, in square units?...

In the $xy$-plane, the graph of the parabola $y = x^2 - 6x + c$ intersects the line $y = 2x - 1$ at exactly one point. What is the value of the constant $c$?...

In the $xy$-plane, the graph of the parabola $y = x^2 + 4x + c$ intersects the line $y = -2x + 5$ at exactly one point. What is the value of the constant $c$?...

In the $xy$-plane, the graph of the parabola $y = x^2 - 2x + c$ intersects the line $y = 4x - 10$ at exactly one point. What is the value of the constant $c$?...

In the $xy$-plane, the graph of the parabola $y = 2x^2 - 4x + c$ intersects the line $y = 4x - 9$ at exactly one point. What is the value of the constant $c$?...

In the system of equations below, \(k\) is a constant: \(\begin{cases} 4x - 6y = 15 \\ kx - 9y = 28 \end{cases}\) If the system has no solutions, what is the va...

The height \(h(t)\), in feet, of a model rocket launched from a platform is modeled by \(h(t) = -16(t - 3)^2 + 144\), where \(t\) represents time in seconds aft...

For what value of \(c\) does the quadratic equation \(2x^2 - 8x + c = 0\) have exactly one distinct real solution?...

The equation of a circle in the xy-plane is \(x^2 + y^2 - 6x + 8y = 24\). What is the radius of the circle?...

The population of a bacterial colony is modeled by the function \(P(t) = 450(1.24)^{t/3}\), where \(t\) is measured in hours. By what percentage does the popula...

When the polynomial \(P(x) = 2x^3 - 5x^2 + 4x - 7\) is divided by \(x - 2\), what is the remainder?...

What are the vertical asymptotes of the rational function \(f(x) = \frac{x + 4}{x^2 - 9}\)?...

Triangle \(ABC\) is similar to triangle \(DEF\), where vertices \(A, B,\) and \(C\) correspond to \(D, E,\) and \(F\), respectively. If the ratio of side \(AB\)...

If \(\sin(3x - 10^\circ) = \cos(2x + 25^\circ)\), where all angle measures are acute, what is the value of \(x\)?...