PSAT Math Multiple-Choice Practice Test 47: Heart of Algebra Drill

1. If , what is the range of x?

B.

2. Susan is given a piggybank for her birthday that can hold a maximum of 500 quarters. The piggy­bank initially has 120 quarters. Each day after she receives the bank, 4 quarters are added. No coins or other objects are added to the piggybank. Which equation could be used to solve for the number of days (D) after Susan's birthday that it will take to fill the bank?

3. In basketball, 1 point is awarded for a free throw, 2 points for a shot within the three-point line, and 3 points for shots outside the three-point line. If the number of points from x two-point shots is at least as great as the number of points from y three-point shots and z free throws, which expression would represent this relationship?

4. What is the value of x in this pair of equations?

B.

C.

D.

5. If -2| -3| < -3|x + 5|, what are all possible values of x?

6. Machine 1 can manufacture one box in A hours, and Machine 2 can manufacture an identical box in B hours. When working simultaneously, Machines A and B can produce 1 box in T hours. This relationship is given by the following formula:

What is the value of B in terms of the other two variables?

A.

B.

C.

D.

7. If the manufacturer of the XYZ machine develops new technology that makes creating the machine less expensive, in which zone(s) of the graph would the new supply curve most likely be?

8. Line A has points (1, -2) and (-1, 0). Line B has point (3, 4). What would the y-value of the y-intercept of line B need to be in order for line A and line B to intersect at a 90° angle?

9. A library fines a patron who fails to return a book on time the replacement cost of the book plus an additional 10 cents each day that the fine is not paid in full. On December 1, Jane borrowed a book with a replacement cost of $30. The book was due to be returned on December 14. Which function models the total amount of dollars (A ) that Jane will need to pay x days after December 14?

10. What is the value of a in this system of equations?

A.

B.

C.

D.