What's on the SHSAT: Math

There’s a lot of math out there. Someday you may need or may choose to immerse yourself in the intricacies of number theory or multivariable calculus. However, for the purposes of the SHSAT Math section, you need to know a relatively small subset of all of the math out there. You are not permitted to use a calculator, but the most commonly tested math concepts fall within the areas of arithmetic, algebra, and geometry. It is also not uncommon to see simple probability and statistics. You will see some math with which you are unfamiliar because the Department of Education deliberately tests unfamiliar math.
 

There are 57 SHSAT Math questions; 5 are grid-in and 52 are multiple-choice questions.

The beginning of the SHSAT Math section will look like this:



The directions are pretty straightforward on the SHSAT Math section. Essentially, they tell you to answer the questions and mark the answers on your answer sheet. However, the directions do include a few notes that can help with your preparation and save you time on Test Day. Here are a few things you should know:
Math formulas and definitions are NOT provided.
What this means: The Department of Education is not going to provide the shortcuts, so memorize those math formulas. Of course, you don’t have to know very many, but make certain you know the basics.
Diagrams other than graphs are NOT drawn to scale unless otherwise noted. 
What this means: You cannot take much for granted about diagrams unless you are specifically told that they are drawn to scale. For example, lines that look parallel may, in fact, not be parallel. Figures that look like squares may not be square. Lines that look like the diameter of a circle may not be the diameter. You get the picture.
Diagrams are in one plane, unless otherwise stated.
What this means: One thing that you can assume is that diagrams are in one plane. In other words, assume that figures are flat unless you are told otherwise.
Graphs are drawn to scale, unless otherwise stated.
What this means: You can eyeball graphs and take what you see for granted. For example, if lines look parallel, you can assume that they are. You can also estimate and label coordinates of points on graphs.
Fractions should be reduced to their lowest terms.
What this means: If you solve a problem that has a fraction for its answer and you do not reduce the fraction to its lowest terms, you will not find your answer among the answer choices.
 

Do Not Waste Time Reading Directions!

Know what to expect on Test Day. The directions are not going to change, so learn them now and save yourself time later.

You’ve done math before. You’ve most likely been exposed to the majority of the math concepts you’ll see on the SHSAT Math section. This raises the question as to why you would need to approach SHSAT Math differently than you would approach any other math.
The answer to this question is that it’s not that you necessarily have to do the math differently, it’s just that you have to do it very deliberately. What this means is that you’ll be under a lot of time pressure when you take the test, so you’ll want to use your time well. You may not want to answer every SHSAT Math problem the way that you would approach the same problem in math class.
 

The SHSAT is Not Math Class

No one is going to check your work. Choose the fastest method to solve the problem, even if your math teacher would not approve.

Ultimately, the best way to take control of your testing experience is to approach every SHSAT math problem the same way. This doesn’t mean that you will solve every problem the same way. Rather, it means that you’ll use the same process to decide how to solve—or whether to solve—each problem.

Okay, this may seem a little too obvious. Of course you’re going to read the question. How else can you solve the problem? In reality, this is not quite as obvious as it seems. The point here is that you need to read the entire question carefully before you start solving the problem. When you do not read the question carefully, it’s incredibly easy to make careless mistakes.
There are other reasons to read the whole question before you start solving the problem. One is that you may save yourself some work. If you start to answer too quickly, you may assume that a problem is more difficult than it actually is. Similarly, you might assume that the problem is less difficult than it actually is and skip a necessary step or two.
Another reason to read carefully before answering is that you probably shouldn’t solve every problem on your first pass. A big part of taking control of your SHSAT experience is deciding which problems to answer and which to save for later.

Every time you approach a new math problem, you have the option of whether or not to answer the question. Therefore, you have to make a decision each time about how to best use your time. You have three options.

1. If you can solve the problem relatively quickly and efficiently, do it. This is the best option.
2. If you think you can solve it but it will take you a long time, circle the number in your test booklet and go back to it later.
3. If you have no idea what to do, skip the problem and circle it. Save your time for the problems you can do.

Remember that when you go back to the problems you skip, you want to fill in an answer even if it’s a random guess. You’ll see more about this later, but do not underestimate your ability to eliminate wrong answers even when you do not know how to solve a problem. Every time you eliminate a wrong answer, you increase your chances of guessing correctly.

Don’t leave any answers blank on the SHSAT. Since there’s no penalty for wrong answers, there is no harm in guessing when you don’t know the answer.
 

Do Not Underestimate the Value of Guessing

Remember, there’s no penalty for wrong answers. Even if you guess randomly, you have a 1 in 4 chance of guessing correctly.