In a recent post, we took a look at a classic SAT algebraic word problem and explained how to solve it with an algebraic equation—the approach that all of your math teachers encouraged in class. But on the SAT, working a problem out algebraically isn't always the best strategy. Maybe the equation presents some concept that you’re not comfortable with. Or maybe your mind is just blanking. When you find yourself in this situation, it's time to try plugging in.
If you've spent even a little bit of time prepping for The Test, you're probably familiar with the “plug in” approach. Basically, you take the given answers and stick them into the problem to see which one works. But with a little method, you can use plugging in to shave some time off your test. The key is to always start with C. Let’s work through an example:
If you’ve taken the SAT or even taken a practice test, then you probably know that at the beginning of each math section those friendly SAT folks include a Reference Information box with some handy formulas for your use.
Your initial reaction to this box might be, “Great! Less formulas for me to study! I can just look here if I need to use any of these formulas.” Ah, but don’t be fooled. It might not be in your best interest to rely on the presence of these formulas and forget about studying them. You might be pressed for time when taking the math section. Constantly flipping back and forth between the questions and the formula section will cost you precious time.
Today we’re going to look at absolute values, a concept that pops up often on the SAT. Luckily, you pretty much have to remember one rule in order to work out these questions.
These questions often appear on the student-produced response section, so that’s what our examples will look like. No multiple choice! Let’s get started:
In our last post, we looked at some questions involving functions, specifically functions involving money. Today, we’re going to continue our discussion with a look at how functions can be manipulated.
First of all, remember that evaluating functions involves simply plugging information in. For example, if f(x) = x + 1, then f(2) = 2 + 1 = 3.
The rules of function math are pretty simple: Treat the function like you would any other variable. Let’s jump in with a question:
Let me guess: Ever since you woke up this morning, all you've been able to think about is algebraic equation solving involving money. Am I right? Well, you're in luck! That's exactly what we're going to look at today.
Here's a question:
The cost of renting a car from company A is $850 for up to and including 86 miles and $0.50 per mile thereafter. The cost of renting a car from company B is $3.50 per mile for any amount of miles. For a trip that lasts h miles, the cost of renting from company A is the same as the cost of renting from company B. If h is a positive integer greater than 86, what is the value of h?
A little while back, we introduced some money problems that involved variables in the question and answer. We’re going to continue on the theme of money problems with some questions about percent changes in price. We've all had practice figuring out the sale price on things we buy, but these questions have the potential to be tricky. The benefit is that there is a formula we can use:
Do you have any suggestions for the ACT math? I swear they do not give you enough time to answer the questions, unless you guess on most, like I did. I took the PSAT and the math wasn't easier per se but I did have more time. Is the SAT really that similar?
The SAT makers love writing math questions that involve money. This isn't so surprising: We all buy things and know how money works. But sometimes things can get a little complicated. For example, you might come across a question that asks you to calculate someone’s salary or how much someone has to pay for a gift, and multiple parts of these questions will be in terms of variables. We'll call these questions variable money problems.
The key to solving variable money problems is to not freak out about the variables. Most of the questions use fairly simple concepts; the test makers are just trying to throw you off by using two, three, or even more variables. Here's an example:
In our last post, we went over some examples of the kinds of pattern questions that pop up on the SAT. But pattern questions come in all shapes and sizes, and in this post we’re going to look at a couple of more tricky ones.
The first type that we’re going to look at is a question that asks about nth terms of the sequence, where n is extremely high (these are also known as annoying sequences). Remember that if the SAT asks you about the 75th or the 103rd term of a sequence, there is no way they expect you to calculate all of the terms up to this term. There will always be some kind of shortcut.
