# PSAT Math Multiple-Choice Practice Test 8: Advanced Math

**1.** Delphine is studying the growth of bacteria in a petri dish. She grows 100 colonies of bacteria in dishes at varying temperatures to find the optimal temperature for bacteria growth. The temperature of the 10 colonies with the most rapid growth is used to determine the optimal temperature range, which Delphine finds to be from 30° to 37°C, inclusive. Which of the following inequalities represents the optimal temperature range, *t,* for bacteria growth?

*t*+ 7|≤ 37

*t*- 3.5| ≤ 33.5

*t*- 30|≤ 7

*t*- 33.5| ≤ 3.5

**2.** The sum, *S,* of a set of *n* consecutive integers is given by the equation *S* = . What does *a* + *k* represent?

**3.** If interest deposits are made monthly into an account with a beginning balance of $250, supposing no withdrawals are made from the account, the balance *B* of an account with an annual interest rate of 5% after *t* years can be computed using the equation below.

Which of the following describes what the quantity represents in the equation?

*B*during a given month

*B*after a monthly interest deposit is made

*B*added during a monthly interest deposit

**4.**

If *ABCD* is a square, what is the area of the square?

**5.**

In the figure above, lines *a* and *b* are parallel. Which of the following pairs of angles must have equal degree measures?

I. 1 and 5

II. 2 and 7

III. 3 and 9

**6.**

In the figure above, *BC* || *AD*. What is the measure of ∠*ACD*?

**7.**

Note: Figure not drawn to scale.

In the figure above, if triangle *ABC* is isosceles, what is the perimeter of the triangle?

**8.**

The owner of a barn needs to paint the front of the barn's roof. As shown in the figure above, the roof measures 8 m along the bottom, and the sides of the roof meet the bottom at a 30° angle. If one bucket of paint can cover 5 m^{2}, what is the minimum number of buckets the owner needs to purchase?

**9.**

Note: Figure not drawn to scale.

In the figure above, if *AB* = 5, *AC* = 13, and *DE* = 24, what is the value of *BD*?

**10.**

In the triangle above, *AB* = *BC.* Which of the following accurately expresses the perimeter of the triangle?

### Test Information

- 10 questions
- 15 minutes
- See All test questions

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