# PSAT Math Quiz: Equations and Word Problems

Content Review:

- PSAT Math: Math Strategies and Linear Equations
- PSAT Math: Linear Equations Practice Questions
- PSAT Math: Linear Word Problems
- PSAT Math: Linear Graphs

Test your PSAT readiness by taking this PSAT Math quiz!

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 *x *= -11/2, which is (D).

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.

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).

Answer 4

**B: **Follow the Kaplan Strategy for Translating English into Math. Assemble equations and set them equal to each other. Let *d *= 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 + 4*v. *Now, solve for *v*:

250 = 130 + 4v

120 + 4v

30 = v

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, 0.02*i,* 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).