Cerro - For the Love of ACT Math - Chapter 7 - Classified

44π/3 + 16√3

In the figure below, a band is wrapped tightly around two pulleys. The center of the pulleys are 16 inches apart. The band wraps two-thirds around the larger pulley, which has a radius of 10 inches, and one-third of the way around the smaller pulley, which has a radius of 2 inches. What is the length of the band, in inches?

(-½,(√3)/2)

In the standard (x,y) coordinate plane below, D is on the positive x-axis, the measure of ∠COD is 120°, and the length of CO is 1 coordinate unit. What are the coordinates of C? ½(√3)/2

√73

What is the distance in coordinate units between 3 + 5i and -5 + 2i in the complex plane?

5

What is the minimum degree of possible for the polynomial function whose graph is shown in the standard (x,y) coordinate plane below?

1

What is the tangent of the angle formed by AB and AC in the graph shown below?

E. (x + 12π)² + (y - 3)² = 9

A circle with center (0, 3) is graphed in the standard (x,y) coordinate plane below. Suppose the circle rolls along the positive x-axis for 2 rotations and then stops. Which of the following is an equation of the circle in its new position? A. (x + 3)² + (y - 3)² = 9 B. (x + 6π)² + (y - 3)² = 3 C. (x + 6π)² + (y - 3)² = 9 D. (x + 12π)² + (y - 3)² = 3 E. (x + 12π)² + (y - 3)² = 9

0 (zero)

A parabola and circle are graphed on the standard (x,y) coordinate plane. The parabola has a vertex at (0,-3) and crosses the x-axis at +-4. The circle has a center at (0,5) with a radius of 4. How many points of intersection are there between the parabola and circle?

192

A plane contains 17 horizontal lines and 13 vertical lines. These lines divide the plane into disjoint regions. How many of these disjoint regions have a finite nonzero area?

rs

A polynomial in x has r nonzero terms. Another polynomial in x has s nonzero terms, where r < s. These polynomials are multiplied and all like terms are combined. The resulting polynomial in x has a maximum of how many nonzero terms?

B

A right circular cylinder is intersected by a plane that is not parallel to the base and does not intersect the base, as shown in the figure below.

12

A teacher assigns each of her 14 students a different integer from 1 through 14. The teacher forms pairs of study partners by using rule that the sum of the pair of numbers is a perfect square. Assuming the 7 pairs of students follow this rule, the student assigned which number must be paired with the student assigned the number 4?

(0,-√2,1)

As shown in the (x,y,z) coordinate space below, cube P with vertices A through H has edges that are 0.5 coordinate units long. The coordinates of F are (0,0,0) and H is on the positive y-axis. P', not shown below, is P reflected over the z-axis and multiplied by a factor of 2. What are the coordinates of D'?

(-2/3,0)

Points O(0,0) and A(2,0) lie on the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from A as from O forms a circle. The point (0,(2√3)/3) is one point on the circle. What are the coordinates of the center of the circle?

6√3

Right ∆ABC shown below will be rotated about the x-axis to form a right circular cone. If BC = 6 and ∠BCA = 60°, how long, in coordinate units, is the diameter of the base of the cone?

B. ns - s

Suppose that equally spaced dots are marked one each side of a regular polygon, with a dot at each vertex, and the distance between consecutive dots is the same of all sides. The figure below shows 4 equally spaced dots per side, including a dot at each vertex, for a regular pentagon. Which of the following expressions represents the number of dots for a regular polygon with n equally spaced dots, including one at each vertex, marked on each of its s sides? A. ns B. ns - s C. ns - 1 D. ns + s E. ns - n

B

The force due to gravity, F, between two masses, m₁ and m₂, varies directly with the product of the two masses and the gravitational constant, and varies indirectly with the square of the distance between them, r. On a certain celestial body the gravitational constant is 13 m/s². Which of the following graphs shows the force due to gravity, F, on this celestial body between two objects with masses m₁ and m₂ for all values of r in the (r, F) coordinate plane?

A. 2, 2, 2, 2, 12, 12, 12, 12

Which of the following data sets has the greatest standard deviation? A. 2, 2, 2, 2, 12, 12, 12, 12 B. 2, 2, 7, 7, 11, 11, 12 C. 2, 3, 4, 5, 6, 7 D. 6, 6, 6, 6, 6, 6, 6 E. 6, 7, 8, 9, 10, 11, 12

B. 4, 6, 9

Which of the following lists of numbers could be the sides lengths, in inches, of a triangle? A. 1, 2, 4 B. 4, 6, 9 C. 5, 7, 13 D. 8, 9, 18 E. 10, 10, 20

B. Commutative: x + y = y + x

Which of the following number properties is illustrated in the statement below? 7 + (2 + 3) = (2 + 3) + 7 A. Associative: x + (y + z) = (x + y) + z B. Commutative: x + y = y + x C. Distributive: x(y + z) = xy + xz D. Identity: x + 0 = x E. Inverse: x + (-x) = 0

(5, 15π/4)

Which of the following polar coordinates represents the same location as (5, π/4)? A. (5, 15π/4) B. (5, 3π/4) C. (5, π/4) D. (5, -3π/4) E. (5, -15π/4)

A. x² - 2xy⁴ + 4y⁸

Which one of the following expressions could be a factor of the expression below? x^3 + 8y^12 A. x² - 2xy⁴ + 4y⁸ B. x² + 2xy⁴ + 4y⁸ C. x² - 2x²y⁴ + 4y⁸ D. x² + 2x²y⁴ - 4y⁸ E. x² - 2xy⁴ - 4y⁸