A function is defined for x and y such that f(x, y) = -2xy + y + x - 4. So, for x = 2 and y = 3, f(2, 3) = -2 × 2 × 3 + 3 + 2 - 4 = -12 + 1 = -11. If x and y are to be chosen such that f(x,y) = f(y,x), then which of the following restrictions must be placed on x and y?
(F) x > 0 and y > 0
(G) x < 0 and y < 0
(H) x = y
(J) xy < 0
(K) No restrictions are needed.
Greg is making a triangular sail for a boat, shaped like a right triangle and shown below.
To determine how much trim to buy for the sail, Greg calculated the sail's perimeter. What is the sail's perimeter, in feet?
(A) 275 (B) 300 (C) 290 (D) 220 (E) 170
Correct Answer: B
Admission to the martial arts tournament is $30, but participants must purchase separate tickets for each event they wish to participate in once inside. Each event is the same price as any other event. The graph below shows the total cost for a person, for admission and events, as a function of the number of events paid for. One of the following is the price of a single event. Which one is it?
| 0 | $30 |
| 1 | $42 |
| 2 | $54 |
| 3 | $66 |
| 4 | $78 |
| 5 | $90 |
(F) $11 (G) $12 (H) $13 (J) $14 (K) $15
Correct Answer: G
What values of x are solutions in the equation x2 + 4x = 12?
（A）8 and 12 （B） 0 and 4 （C） -2 and 6 （D） -4 and 0 （E） -6 and 2
Correct Answer: E
More ACT Math Exam Questions
- 1Dave leaves his house and bikes directly east for 3 miles. He then turns and bikes directly south for 4 miles. How many miles is Dave from his house?
- 2
A rectangle is 5 times as wide as it is long. The area of the rectangle is 320 square feet. What is the perimeter of the rectangle, in feet?
- 3
A two-digit number from 10 to 99, inclusive, is chosen at random. What is the probability that this number is divisible by 5?
- 4
The Crestview High School student body is made up only of freshmen, sophomores, juniors, and seniors. 25% of the students are freshmen, 35% are sophomores, and 20% are juniors. If no student can be considered to be in two classes, and there are 150 seniors, how many students make up the Crestview High School student body?
- 5
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?