PSAT Math Multiple-Choice Practice Test 40: Passport to Advanced Math: Quadratics

1.

The figure above shows the partial trajectory of a cannonball shot into the air. Assuming that the cannonball lands at a point where the height is 0, approximately how many feet farther did the cannonball travel horizontally than vertically upward? (1 yard = 3 feet)

2.

If (x, y) is a solution to the system of equations shown here, what is the value of x² ?

3. One of the x-coordinates of the solutions to a system of equations is -8. Which of the following could be the system?

A.

B.

C.

D.

4. Which system of equations has only one solution?

A.

B.

C.

D.

5. Will the graph of intersect the graph of ?

6.

The functions f(x) = 2x² - 5 and g(x) = 6x² - 7 are graphed in the xy-plane above. The points where the two functions intersect are (z, -4) and (-z, -4). What is the value of z?

A.

B.

7.

A car's fuel economy generally increases as its speed increases, but past a certain speed, it starts to drop, as depicted for a particular car in the graph above. What is the best estimate of this car's fuel economy, in miles per gallon, at 100 miles per hour?

8. Shawna throws a baseball into the air. The equation h = -5(t² - 4t + 4) + 22 represents the height of the ball in meters t seconds after it is thrown. Which of the following equations could represent the height of a second ball that was thrown by Meagan, if Meagan's ball did not go as high as Shawna's ball?

9. Which of the following equations could represent a parabola that has a minimum value of -3 and whose axis of symmetry is the line x = 2?

10. Which of the following is a solution to the equation x² + 24 = 14x - x² ?

B.

11. Which of the following is an equivalent form of 4x² - 8x + 64 = 0?

12. Which of the following is equivalent to 64x² - 81y²?

13. Which of the following quadratics has only one real solution?

14. Which of the following coordinates is the vertex of the parabola y = x² - 14x + 3?