Digital SAT Practice Questions

An archway follows the equation $y = -0.5x(x - 8)$, where $x$ and $y$ are in meters. What is the maximum height of the arch?...

A rectangular garden has a perimeter of 40 meters. What is the maximum possible area, in square meters, of the garden?...

If $f(x) = x^2 - 6x + c$ and the minimum value of $f(x)$ is $-4$, what is the value of $c$?...

The revenue of a product is given by $R(p) = -10p^2 + 300p$. What price $p$ maximizes revenue?...

The equation $h(t) = -16t^2 + 48t$ models a tennis ball's height. After how many seconds does it return to the ground?...

If $(x - a)(x - b) = x^2 - 9x + 20$ for all $x$, what is the value of $a + b$?...

If $x^2 + kx + 36$ is a perfect square trinomial and $k < 0$, what is $k$?...

How many intersection points do the graphs of $y = x^2 - 4x + 3$ and $y = 2x - 6$ have?...

In the $xy$-plane, what is the intersection of $y = x^2$ and $y = 4$?...

For what value of $c$ does the line $y = c$ intersect $y = x^2 - 6x + 5$ at exactly one point?...

If $x^2 - y^2 = 24$ and $x - y = 3$, what is the value of $x + y$?...

Which of the following is equivalent to $3x^2 + 18x + 24$?...

What are the coordinates of the vertex of $f(x) = 2x^2 - 8x + 11$?...

If $(x + k)^2 = x^2 + 14x + c$, what is the value of $c$?...

What is the sum of the solutions to $(2x - 5)(x + 3) = 0$?...

If $f(x) = (x - 2)(x - 8)$, what value of $x$ minimizes $f(x)$?...

Find all real solutions to $x^4 - 5x^2 + 4 = 0$....

If $x > 0$ and $x^2 + 10x = 24$, what is the value of $x$?...

What is the discriminant of $x^2 + 6x + 9 = 0$, and what does it tell you about the roots?...

A population of bacteria satisfies $P(t) = 500(1.08)^t$, where $t$ is hours. By what percent does the population grow each hour?...

An investment value is modeled by $V(t) = 1200(0.85)^t$. What does the value 0.85 represent?...

If a radioactive isotope decays according to $M(t) = 80(0.5)^{t/14}$, what is the half-life of the isotope in days?...

A car's value depreciates by 12% each year. If its initial purchase price was $24,000, which expression represents its value after $t$ years?...

The function $N(d) = 250(2)^{d/3}$ models fruit fly population growth. How many days does it take for the population to double?...