SAT Math Problems - Multiple Choice

Question 1

Michael Owens invented an automated bottling process in 1903. The process has been improved over the years. Suppose a bottling machine can fill 2,400 bottles of soda in 1 hour. Which function could be used to determine the number of bottles left to fill after x minutes of filling for a day when the goal is to fill 50,000 bottles?

A. f(x) = 40x – 50,000

B. f(x) = 40x + 50,000

C. f(x) = –40x – 50,000

D. f(x) = –40x + 50,000

Answer 1

The correct answer is D.

The number of bottles filled per minute is 2,400 ÷ 60 = 40. Because the function needs to determine the number of bottles left after x minutes, 40 bottles will be decreased from the total after each minute, represented by –40x. The total of 50,000 is the y-intercept when x = 0, making f(x) = –40x + 50,000 the correct function.

Question 2

Evan has run 13.5 miles so far this month, running 4.5-miles each time he runs. He plans to run at least 54 miles for the entire month. Which inequality could be used to determine x, the number of times Evan still needs to run this month?

A. 4.5x + 13.5 ≤ 54

B. 4.5x + 13.5 ≤ 54

C. 4.5x – 13.5 ≤ 54

D. 4.5x – 13.5 ≤ 54

Answer 2

The correct answer is B.

Evan has already run 13.5 miles, and the number of miles for each run is the same, 4.5 miles, and can be represented by 4.5x. Because he plans to run at least 54 miles, the “greater than or equal to” symbol needs to be used, resulting in 4.5x + 13.5 ≤ 54.

Question 3

At which point does the graph of the function J(x) = 6x – 18 cross the x-axis?

A. (3, 0)

B. (0, 3)

C. (–18, 0)

D. (0, –18)

Answer 3

The correct answer is A.

The graph will cross the x-axis at the point where the function (that is, the y-coordinate) has a value of 0. As result, the following equation needs to be solved: 6x – 18 = 0.

6x - 18 = 0

6x = 18

x = 3