Interpreting Values in Equations on the SAT
One of the most commonly tested concepts on the SAT Math is your algebraic understanding. You’ll have to take real-world scenarios and identify how those relate to the coefficients and constants of an equation. Let’s brush up on those basic definitions:
- Coefficient: The number in front of the variable, which represents a rate of change. (In other words, how much the product increases or decreases for each unit of the variable). In addition, you might also want to pay attention to the units used in that rate.
- Constant: The number that remains the same regardless of a change to the variable.
Consider the following:
Karen opens a bank account with an initial deposit and then makes a fixed deposit into the account once per week. The equation B = 40x + 200 models the amount of money in Karen’s bank account x weeks after she opens it.
In this case, the coefficient is 40, which means that Karen deposits an additional $40 to her bank account each week. The 200 represents the initial deposit, which is the value when x is 0.
Similarly, the equation B = 200 – 40x could be used to model how much money is left in her account after x weeks if she removes $40 each week.
Here’s a sample question:
Mike is reading a book. The number of pages that he has left to read, P, is given by the equation P = 530 – 57t, where t represents the number of days since he started reading the book. What are the meanings of 530 and 57 in this equation?
A. It will take Mike 530 days to read the book at a rate of 57 pages per day.
B. The book has 530 pages, and Mike reads 57 pages per day.
C. Mike reads the book, which has 530 pages, at a rate of 57 pages per hour.
D. After 57 days, Mike has read 530 pages of the book.
Let’s look at this one part at a time:
The coefficient 57 represents a rate, not a number of days, so eliminate (D).
Also be wary of your units; the question specifies t is the number of days, so you can eliminate (C).
Lastly, when t = 0, Mike should have 530 pages left to read since that means he has been reading the book for 0 days. Therefore, the book must have 530 pages. The correct answer is (B).
A lot of the math on the SAT will require you to interpret and manipulate equations. You’ll also have to work with fractions, exponents, roots, quadratics and polynomials. Don’t be caught off guard by anything on the test. Instead, study up beforehand with our books Cracking the SAT and Crash Course for the SAT. You should also take practice tests to ensure you know how to apply these practices when you actually sit down on test day.