ACT Math Practice Test 8

After polling a class of 24 students by a show of hands, you find that 9 students play soccer and 21 students play basketball. Given that information, what is the number of students in the class who must play both soccer and basketball?

Using the complex number i, where i² = −1, $\frac{2}{(1 − i)}\times \frac{(1 + i)}{(1 + i)}$ =?

A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?

The ratio of the radii of two circles is 9:16. What is the ratio of their circumferences?

What is the distance in the standard (x, y) coordinate plane between the points (2,3) and (5,5)?

Let x ◙ y = (x − 2y)² for all integers x and y. Which of the following is the value of 5 ◙ (−3)?

If 125% of a number is 425, what is 65% of the number?

Of the 517 graduating seniors at Brighton High School, approximately ⁴⁄₅ will be attending college, and approximately ¹⁄₂ of those going to college will be attending a state college. Which of the following is the closest estimate of the number of graduating seniors who will be attending a state college?

If x = 3r − 4 and y = 3r + 2, which of the following expresses y in terms of x?

A triangle, ΔABD, is reflected across the y-axis to have the image ΔA’B’D’ in the standard (x, y) coordinate plane: thus A reflects to A’ . The coordinates of point A are (m, n). What are the coordinates of point A’ ?

Which of the following is the graph, in the standard (x, y) coordinate plane, of y = $\frac{x^{2}+3x}{x}$ ?

If f (x) = 2x² + 3, then f (x + h) = ?

If sin θ = ⁴⁄₅ and ^π⁄₂ < θ < π, then tan θ = ?

John wants to draw a circle graph showing his friends’ favorite ice cream flavors. When he polled his friends asking each their favorite flavor of ice cream, 35% of his friends said chocolate, 20% of his friends said vanilla, 15% of his friends said strawberry, 25% of his friends said mint chocolate chip, and 5% of his friends said flavors other than those previously listed. What will be the degree measure of the vanilla sector of the circle graph?

Which of the following is the set of all real numbers x such that x + 2 > x + 5 ?