# 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.*)

### Test Information

- 8 questions
- 12 minutes
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