psat-quiz-math

PSAT Math Quiz: Equations and Word Problems

Content Review:

Test your PSAT readiness by taking this PSAT Math quiz!

Question 1

−2 (x − 3) = 17. Solve for x.

A. -22/3

B. -10

C. -7

D. -11/2

Answer 1

D: Straightforward math works well on simple equations like this one. Start by carefully distributing the -1 on the left. Then combine like terms and divide by -2 on both sides to isolate x. You should find that = -11/2, which is (D).

Question 2

Jacques Charles was a French scientist who discovered the relationship between the temperature and volume of a gas. Specifically, Charles found that gases expand when heated. This relationship was formalized in Charles’s Law, which illustrates a linear relationship between temperature and volume in gases. The graph here shows the volume of a sample of gas as it is cooled. If T is the temperature of the gas in °C and V is the volume in liters, which of the following equations, when plotted, could produce the graph shown?

psat math

A. V = 0.004T + 100

B. V = 0.004T

C. V = 0.004T + 1

D. V = 0.004T – 0.25

Answer 2

C: Don’t get bogged down by the prose; focus on what you need to answer the question posed. Temperature (T) is the independent variable on the x-axis, and volume (V) is the dependent variable on the y-axis. Therefore, the skeleton of the equation you’re looking for is V = mT + b. Because each answer choice has a different y-intercept, finding this is enough to get you to the right answer; there is no need to determine the slope. Although the graph is not centered like you’re used to, you can still find the y-intercept. In this case, it’s 1. This eliminates every answer choice except (C), which is correct.

Question 3

Ms. Walser’s class had 18 students. She used three equally weighted tests to determine their final grades. The class average for the first test was 92, and the class average for the second test was 77. If the overall class average was 84, what was the average score for the third test?

A. 74.3

B. 77

C. 83

D. 84.3

Answer 3

C: The Kaplan Strategy for Translating English into Math will work well here. Watch out for extra information that may confuse you. Let a be the average of Test One (92); b, the average of Test Two (77); c, the average of Test Three (what you need to find); and d, the overall test average (84). The average is the sum of the terms divided by the number of terms: (a + b + c) / 3 = d. Plugging in the values you know yields (92 + 77 + c) / 3 = 84. Multiply both sides by 3 and then subtract to solve for c, which gives 83. This corresponds to (C).

Question 4

A certain gym sells two membership packages. The first package, the Die-Hard Package, costs $250 for 6 months of unlimited use. The second package, the Personal Package, costs $130 initially plus $4 each day the member visits. How many visits would a person need to use for each package to cost the same amount over a 6-month period?

A. 2

B. 20

C. 96

D. 120

Answer 4

B: Follow the Kaplan Strategy for Translating English into Math. Assemble equations and set them equal to each other. Let = Die-Hard Package, p = Personal Package, and v = number of visits. Using the information about each package, you know that d = 250 and p = 130 + 4v. Now, solve for v:

250 = 130 + 4v

120 + 4v

30 = v

Question 5

A municipality charges two types of local taxes: a per capita tax, which is a flat fee that every person pays, and a local income tax, which is a percentage of the person’s annual income, i. If a taxpayer’s total tax bill is given by the function T = 0.02i + 25, then the value 0.02 best represents which of the following?

A. The per capita tax

B. The taxpayer’s annual income

C. The total tax bill minus the per capita tax

D. The amount of the income tax as a percentage

Answer 5

The total bill consists of a flat tax and a percentage of annual income. The flat per capita tax is a one-time fee that does not depend on the taxpayer’s income and therefore should not be multiplied by i. This means that 25 is the per capita tax. The other expression in the equation, 0.02i, represents the percentage income tax times the annual income (which the question tells you is i). Therefore, 0.02 must represent the amount of the income tax as a percentage, which is (D).

 

Next: PSAT Math Quiz: Systems of Equations