# PSAT Math Multiple-Choice Practice Test 4: Math Techniques

**1.** David acquired a data plan for his smart phone. Every month he pays a flat rate of $25 and an additional $0.05 for every megabyte he goes over his monthly limit. Which of the following represents David's monthly data bill when he goes over his limit by *m* megabytes?

*m*

*m*

*m*)

*m*)

**2.** If and *c* ≠ 0, what is the value of ?

*ac*

^{2}

*a*

^{2}

*c*

^{4}

**3.** Luciano measured the amount of water that evaporated over a period of time from a container holding *w* ounces of water, where *w* is greater than 12. By the end of the first day, the cup had lost 2 ounces of water. By the end of the 7th day, the cup had lost an additional 8 ounces of water. By the end of the 11th day, the cup had lost half of the water that remained after the 7th day. Which of the following represents the remaining amount of water, in ounces, in Luciano's container at the end of the 11th day?

*w*- 10

**4.** If *p* ≠ 0, what is the value of ?

*p*

**5.** A certain standardized test has 50 questions. A student receives 1 point for each correct answer and loses of a point for each incorrect answer. Which of the following equations best models the net score, *S,* in points, for a student who completes all 50 questions and answers *c* of the questions correctly?

*S*= 50 - 0.25

*c*

*S*= 50 - 0.75

*c*

*S*=

*c*- 0.25(50 -

*c*)

*S*=

*c*- 0.75(50 -

*c*)

**6.** Jodi has *x* dollars in her bank account. She withdraws of the money in her account to pay her rent and another of the money in her account to make her car payment. Jodi then deposits her paycheck of *y* dollars into her account. A week later, she withdraws of the money in her account to spend on a new set of knives. In terms of *x*, how many dollars are left in Jodi's account?

**7.** 2 < 24

What is the sum of all the integer solutions to the inequality above?

**8.** 2(*n* + 5) = 3(*n* - 2) + 8

In the equation above, what is the value of *n*?

**9.** If 3^{x + 2} = 243, what is the value of *x*?

**10.** 2*x* - *y* > -3

4*x* + *y* < 5

*y* > -6

Which of the following points is in the solution set of the system of inequalities above?

### Test Information

- 10 questions
- 15 minutes
- See All test questions

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