PSAT Math Grid-Ins Practice Test 3: Advanced Math

1. The profit that a donut shop makes can be expressed by the equation P = -4(x - 3)² + 2,000, where x is the price per donut sold (in dollars). What price, in dollars, should the donut shop charge its customers in order to maximize its profit?

2.

The diagonal of rectangle ABCD is 13 inches long. What is the area of rectangle ABCD?

3.

In the triangle above, . What is the value of x?

4.

Note: Figure not drawn to scale.

In triangle ABC above, if AB = BC, what is the value of x? (Disregard the degree symbol when gridding your answer.)

5.

What is the area of the circle above with center O?

6.

What is its circumference?

7.

Note: Figure not drawn to scale.

Major arc PSR is the length of minor arc PQR. The length of major arc PSR is 6π units. What is the radius of the circle?

8. A rectangular box is half as long as it is wide and one-third as wide as it is tall. If the volume of the box is 96, then what is its surface area? (Note: The formula for the volume of a rectangular solid is V= lwh.)