ACT math practice test 31

1. A restaurant decides on the following production model, where N is the number of ounces of flour the restaurant purchases each month, based on the number of ounces, x, the restaurant uses during the preceding month. N = x2 - 600x - 160,000. According to this model, what is the greatest quantity of flour, in number of ounces, that the restaurant can use during a month, without having to purchase any new flour the next month?

A. 800
B. 550
C. 400
D. 350
E. 200

A poor, frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately shows the cost and revenue of his plan. The linear cost function, C(x), represents the total money spent to make and market the art, while the linear revenue function, R(x), shows the amount of money he has made in sculpture sales.

2.

Fresco initially spent money promoting the project in the media. He also had to pay the celebrities to participate. After 6 months, Fresco had created and sold x number of trash sculptures and finally broke even: he hadn't made or lost any money. How many sculptures did Fresco sell in his first 6 months of the project?

F. 3
G. 5
H. 7
J. 10
K. 15

A poor, frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately shows the cost and revenue of his plan. The linear cost function, C(x), represents the total money spent to make and market the art, while the linear revenue function, R(x), shows the amount of money he has made in sculpture sales.

3.

The cost function in the chart is determined by a constant production cost per sculpture—in this case the amount Fresco pays each celebrity to participate—as well as a fixed cost, or the initial cost of promoting the project. What is the fixed cost of Fresco's trash sculpture project?

A. $1,000
B. $5,000
C. $10,000
D. $15,000
E. $50,000

A poor, frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately shows the cost and revenue of his plan. The linear cost function, C(x), represents the total money spent to make and market the art, while the linear revenue function, R(x), shows the amount of money he has made in sculpture sales.

4.

The selling price of each trash sculpture is an integer number of dollars. According to the revenue function, what is the selling price of one trash sculpture?

F. $1,000
G. $1,667
H. $2,000
J. $3,000
K. Cannot be determined from the chart

5. Which of the following is a complete factorization of the expression 12b2c + 6bc + 3b?

A. 4bc + 2c + 1
B. 3b (9bc + 2c + 1)
C. 3b (4bc + 2c + 1)
D. 3b (4bc + 2c)
E. 6bc (2b + 6) + 3b

6. Which of the following could be the equation of a line that passes through the points (-2,-7) and (2,17) in the standard (x,y) coordinate plane?

F. 3x - 2y = 8
G. 6x - y = -5
H. 5x - 2y = 7
J. 9x - 2y = -16
K. x + y = 6

7. A circle has a radius that is the same length as the sides of a square. If the square has a perimeter of 64 square inches, what is the area, in square inches, of the circle?

A. 16
B. 16π
C. 32π
D. 64π
E. 256π

8. What is the y-coordinate of the solution of the following system, presuming the system has a solution?

8x + y = 30
8x + 4y = 96

F. 1
G. 8
H. 19
J. 22
K. The system has no solution.

In the figure below, M is on and Q is on The measurements are given in feet. Both NPQM and MQRL are trapezoids. The area, A, of a trapezoid is given by A = h(b1 + b2), where h is the height and b1 and b2 are the lengths of the 2 parallel sides.

9.

What is the area of MQRL, in square feet?

A. 3,200
B. 1,750
C. 1,600
D. 600
E. 500

In the figure below, M is on and Q is on The measurements are given in feet. Both NPQM and MQRL are trapezoids. The area, A, of a trapezoid is given by A = h(b1 + b2), where h is the height and b1 and b2 are the lengths of the 2 parallel sides.

10.

What is the length of in feet?

F.
G.
H.
J. 50
K. 45

In the figure below, M is on and Q is on The measurements are given in feet. Both NPQM and MQRL are trapezoids. The area, A, of a trapezoid is given by A = h(b1 + b2), where h is the height and b1 and b2 are the lengths of the 2 parallel sides.

11.

What is the diameter, in feet, of the largest circle that can be drawn inside MNPQ?

A. 20
B. 40
C. 50
D. 60
E. 70

12. The figure below shows a ramp for skateboarders. The base of the ramp is 25 feet long, and it rises at a 10° angle.

Given the trigonometric calculations in the table below, how high off the ground will a skateboarder be at the top of the ramp, rounded to the nearest 0.1 foot?

F. 2.3
G. 2.5
H. 4.3
J. 4.4
K. 24.6

13. The 12 numbers on a circular clock are equally spaced around the edges of the clock. Belinda chooses an integer, n, that is greater than 1. Beginning at a randomly chosen number, Belinda goes around the circle counterclockwise and paints in every nth number. She continues going around and around the clock, painting in every nth number, until all twelve numbers on the clock are painted. Which of the following could have been Belinda's integer n?

A. 2
B. 3
C. 6
D. 7
E. 9

14. Consider the exponential equation y = , where K and p are positive real constants and x is a positive real number. The value of y decreases as the value of x increases if and only if which of the following statements about p is true?

F. 0 < p < 1
G. 1 < p < 2
H. p > -1
J. p > 0
K. p > 1

15. What is the distance, in coordinate units, between the points M (1,-3) and N (-5,5) in the standard (x,y) coordinate plane?

A.
B.
C. 8
D. 10
E. 20