PSAT Math Multiple-Choice Practice Test 46: Heart of Algebra Drill

1. If the volume of a pyramid is given by the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height, what is the width of the pyramid in terms of the other variables?

A.

B.

C.

D.

2. What is the negative solution to the following equation, rounded to one decimal place?

3. An employee at a company has the following rules for days off from work:

-Employees are granted 30 flex days paid time off in a year for non-weekend and holiday days.

-Sick days with a doctor's note count as half a flex day.

-Personal days count as a full flex day.

If an employee wants to use at least half of the flex days but less than of them, what inequality would express the total number of sick days, S, and personal days, P, he or she could take in a year?

A.

B.

4. If g(x) = 9x + 2, what does g(-4x) equal?

5. A carpenter charges a $40 initial fee for an in-home visit and $60 for each half hour worked. Which inequality models the total fee, F, for H hours worked where H > 0?

6. What are the values of x and y in the following equations?

0.75x - 0.1y = 1.2
2.6x + 3.4y = 15.4

7. If , what does equal?

B.

C.

8. If Equation A is defined by and if Equation B is defined by 3y = 2x + 3, what must be done to Equation B so that the system of both Equation A and Equation B will have infinitely many solutions?

9. At 1:00 P.M., a blimp and a hot-air balloon are above the cities of Springfield and Washington, respectively. The two cities are 300 miles apart horizontally. The blimp is moving from Springfield to Washington at a horizontal speed of 10 miles per hour; the balloon is moving from Washington to Springfield at a horizontal speed of 200 miles per hour. The blimp starts at an altitude of 5,000 feet and is descending at a rate of 5 feet per minute; the balloon starts at an altitude of 500 feet and is ascending at a rate of 4 feet per minute. At what time will the blimp and balloon be at the same altitude, to the nearest minute?

10. Rosa's metabolism is 65 calories per hour when resting and 300 calories per hour when exercising. If Rosa wants to burn more than 2,000 calories per day, what is the range of hours, H, she should spend exercising, ­calculated to the nearest tenth, assuming that she is either resting or exercising at any time in a given day?