Digital ACT Practice Questions

An ellipse in the standard xy-coordinate plane has the equation (x - 2)^2 / 25 + (y + 1)^2 / 9 = 1. What is the distance between the two foci of this ellipse?...

For all values of theta where the expression is defined, which of the following is equivalent to (1 - sin^2(theta)) / (cos(theta) * sin(theta))?...

A carnival game charges $5 to play. A player draws one marble from a bag containing 3 gold marbles, 7 silver marbles, and 10 black marbles. Drawing a gold marbl...

What are the equations of the asymptotes of the hyperbola with equation x^2 / 16 - y^2 / 25 = 1?...

In triangle PQR, the measure of angle P is 45°, the measure of angle Q is 30°, and the side opposite angle Q has length 12. What is the length of side p, which ...

In three-dimensional space, what is the distance between the points A(2, -1, 5) and B(5, 3, -7)?...

What is the exact value of tan(5pi/3)?...

What is the real solution to the equation sqrt(2x + 15) - x = 0?...

A circle in the standard xy-coordinate plane is given by the equation x^2 + y^2 - 8x + 6y - 11 = 0. What is the radius of this circle?...

If matrix A = [[2, -1], [0, 3]] and matrix B = [[4, 1], [-2, 5]], what is the entry in row 1, column 2 of the product matrix AB?...

Which of the following complex numbers is equivalent to the expression (3 + 4i) / (1 - 2i)?...

When the polynomial P(x) = 2x^3 - 5x^2 + 4x - 9 is divided by (x - 3), what is the remainder?...

What is the value of the expression log_2(64) - log_5(125) + log_3(sqrt(27))?...

How many distinct 6-letter permutations can be formed using the letters in the word BANANA?...

In a high school senior class of 200 students, 120 take AP Calculus, 90 take AP Physics, and 50 take both. If a student is selected at random from the students ...

If f(x) = 3x - 5 and g(x) = x^2 + 2x, what is the value of g(f(3))?...

What is the period of the trigonometric function y = -3*sin(4x - pi/2) + 7?...

For what value of k will the quadratic equation 3x^2 - 12x + k = 0 have exactly one real solution?...

At what xy-coordinates do the parabola y = x^2 - 4x + 3 and the line y = 2x - 6 intersect?...

Suppose y varies directly as the square of x and inversely as z. If y = 18 when x = 3 and z = 4, what is the value of y when x = 5 and z = 10?...

Two similar solid cones have surface areas of 36pi square centimeters and 81pi square centimeters, respectively. If the volume of the smaller cone is 48 cubic c...

Which of the following describes the set of all real numbers x that satisfy |3x - 7| >= 14?...

A dataset of 9 exam scores has a mean of 76. If a tenth student's score of 96 is added to the dataset, what is the new mean of the 10 scores?...

A circle has a radius of 12 inches. What is the area, in square inches, of a sector of this circle with a central angle of 75°?...