Unit 48: Constants

Many students find constants on the SAT to be intimidating. The most important thing to remember, is a constant is just some number we don’t know yet.

The number of hours in a day is a constant. It is always 24. No matter what day it is, what week of the year, always 24. We know this, but young children haven’t learned this yet. If you ask a young child how many hours there are in a day, they might guess wildly or just say “I have no idea”.

When we first get to a constant problem on the SAT, we’re like that little kid, we have no idea what the number is. By the time we’re done with the problem, though, we’ll be like the smart teenager you are now, knowing exactly what that number is.

Constants can be represented in two ways.

  1. As a number, like x + 3 = 10. In this example, 3 and 10 are constants. They will always be that number, and this is exactly like we’re used to.
  2. As a letter, like a (x + 2) = 2x + 4. In this example, a is a constant. It’s a number that will never change, unlike x in this example, which could be literally any number.

How do we know whether a letter in an equation is a variable or a constant? They tell us! There is verbiage like “In the equation above, a is a constant”. If they don’t tell us a letter is a constant, you can assume it is a variable.

These problems are often challenging because they ask us to combine constants along with other knowledge, such as slope-intercept rules or how quadratic zeros and factors work.

Strategy for constants:

  1. Remember that a constant is just a number we don’t know yet.
  2. Identify they type of equation. Is it linear or quadratic?
  3. Solve for the constant using the rules you know about that type of equation. Some common rules you might use:
    • Parallel lines have the same slope (and no common solutions)
    • The discriminant of a quadratic tells you how many solutions it has.
    • How the equation for the vertex form of a parabola works

Let’s look at some examples.