PSAT Math Multiple-Choice Practice Test 45: Heart of Algebra Drill

1. What is the value of x in the following equation?

D.

2. What is the value of a in the following equation?

A.

C.

D.

3. What is the solution with the least possible y-value that satisfies both of the following inequalities?

y ≥ 2x + 5
and
4 - y ≤ x

A.

B.

C.

D.

4. If |3x - 1| = 4, what are all of the possible value(s) of x?

I. -1

II.

III. 1

5. What is the value of x?

A.

B.

C.

D.

6. The graph of each equation in the system below is a line in the xy-plane.

y = 6x -2
-6 = 12x -2y

What must be true about these two lines?

C. The lines intersect at .

7. Towns A and B are 200 miles apart. Caitlin starts driving from Town A to Town B at 3 P.M. at a rate of 30 miles per hour. Hannah starts driving from Town B to Town A at 4 P.M. on the same day at a rate of 40 miles per hour. At what time will they meet (to the nearest minute)?

8. A person can ride a roller coaster at an amusement park if he or she is between 36 and 72 inches tall. Which of the following inequalities models all possible values of permitted heights in inches for the ride?

9. A line in the xy-plane has a slope of and passes through the origin. Which of the following is a point on the line?

C.

10. A salesperson earns a commission (C) on the number of phone plans sold (x) if the value of C is positive. (There is no penalty or cost to the salesperson for a negative value of C; simply no commission is paid.) The amount of commission in dollars is modeled by this equation:

C = 50x + 25(x - 100) - 2,000

What is the least number of phone plans that the salesperson must sell in order to earn a commission?