# Avoiding Silly Mistakes

The most common SAT Math Test mistakes students to make are “silly” mistakes. In this section, we’re going to focus on these kinds of mistakes and how to avoid them. Remember that if you make silly mistakes on the test, it doesn’t matter how “good” you are at math.

Whether you’re a math whiz, or you totally hate math, one thing’s guaranteed: you have lost a lot of points on math tests due to “silly mistakes.” These seemingly small mistakes add up in a big, big way, and they can be extremely pernicious factors that impact your overall SAT Math Test performance.

You should not brush off silly mistakes such as “forgetting to add 5 at the end” or picking “radius” rather than “diameter” just because you know how to solve a problem correctly. The reason you got a problem wrong does not change the fact you got it wrong.

Sure, you “could have” gotten the problem right “if you didn’t make that silly mistake,” but then again, a panda bear could have invented the first car if he went back in time, turned himself into a human, and beat Henry Ford to the chase. Could haves are stupid.

Instead, focus on the reality of the situation and become aware. If you’re making silly mistakes during practice tests, you’re even more likely to make them during the real test. So, let’s fix that ASAP.

The tricks in this chapter should eradicate most, if not all, of your silly mistakes. These are not math tricks, but they’re probably more important than any math trick you’ll ever learn.

So, what exactly are silly mistakes? The primary source of these kinds of errors is students confusing questions with prompts. On the SAT, the question and the prompt are two entirely different things.

PROMPT: THE ENTIRE SET OF WORDS, NUMBERS, AND PHRASES THAT MAKE UP A MATH PROBLEM. HERE IS AN EXAMPLE OF A PROMPT:

If the radius of a certain circle is three times the radius of another circle, and if the radius of the larger circle is equal to the area of a square with a side length as long in inches as the square root of 169, then what is the area of the smaller circle?

QUESTION: THE PRECISE QUESTION YOU’D BE ABLE TO ANSWER IF YOU ALREADY HAD ALL THE INFO THAT THE PROMPT PROVIDED. HERE IS AN EXAMPLE OF THE QUESTION:

What is the area of the smaller circle?

When taken alone, the question is almost much simpler and shorter than the prompt. Most students are so focused on the prompt that they forget to answer the question.

Students often find really difficult elements of the prompt and then choose those elements as answers rather than double-checking to narrow in on the actual question.

Here’s what we mean. In the above prompt, you would take some time to figure out the radius of the smaller circle. Once you find it (169/3), you might be very tempted to say, “Yes! I found the radius! 169/3! Boom!”

Not so fast. Read the question again. You’re looking for the area of the smaller circle, not the radius.

But here’s the thing: The SAT will always include solutions to the difficult elements of the prompt alongside the actual answer in answer choices.

So, if your first answer is 169/3 and you see it as an option, you may be tempted to pick it. If you did, you’re cooked!

Hopefully, you see the difference between the prompt elements and the actual answer. Like all AP Guru students, you’ve experienced this scenario many times before: you’ve found the “hard part” of the problem and then selected it as an answer, forgetting to answer the actual question!

Fortunately, there’s a very, very simple method you can use to prevent this mistake from happening in the future. From now on, try the following when tackling math problems:

• Do all the hard work to find your answer the same way you normally would, using all the strategies you normally use.
• Read the prompt again and identify the question.
• Make sure that you’ve answered the question, and not just figured out the most difficult element of the prompt.
• Once you’re sure you’ve actually answered the question, pick your pencil back up and circle the right answer.
• If you have more work to do, solve the actual question, which is usually very simple and only takes 5-10 seconds.

## THE CROSS-OUT METHOD

Now you have the tools you need to avoid any silly mistakes related to questions and prompts. The other kind of silly mistake we see regularly is caused when students miss essential information or read the information incorrectly. Enter the cross-out method, a good technique to ensure you understand the important information you need to solve the problem. Using the method is simple, but a little bit arduous at first. Here’s how it works:

• Cross out every single piece of information in the prompt as you use it, but do not cross
it out until you actively process it!
• Do not answer the question until the entire prompt is crossed out - every single word
and number - from start to finish.

At first, this may sound extremely time-consuming, and maybe it sounds unnecessary. In reality, it makes you move faster (and much more accurately) through a problem because it forces you to actively process information.

EXAMPLE: If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

First, you may draw a circle and a triangle next to each other. Go ahead and cross out those details, so the prompt now looks like this:

If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

Next, you indicate that they have the same area. So, you write this down: πr2 = 1⁄2BH indicating that the area of the circle is the same as the area of the triangle.

Now the prompt looks like this:

If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

Next, the prompt says that the height and base of the triangle are the same, so you can change the equation to this: πr2 = 1⁄2HH. You can also simplify: πr2 = 1⁄2H2

Now the prompt looks like this:

If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

Now you see you can plug 3 in for the height!πr2 = 1⁄2(3)2

Crossing out that information revises the prompt again:
If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

All that’s left is to solve for the radius! r = √(4.5/π).

Now the prompt looks like:

If a certain triangle and a certain circle have the same area, and if the height and the base of the triangle are the same, and if the height of the triangle is 3, then what is the radius of the circle?

And you’re done! That’s all there is to it.

Until you try this for yourself, you might not realize how effective it truly is. When you use the cross-out method, you realize you:

• Cannot possibly miss information. It’ll never happen again. You’re not allowed to cross out a word unless you use it, and you’re not allowed to answer a question until all the words are crossed out.
• Will be much more proactive in solving your problems. The simple act of visually processing and actively using every word in your problem will be enormously helpful.

Math is a visual art, and by actively processing problems and forcing yourself to rewrite all the information you receive, you’ll create more useful, visual models of every single problem you have to solve.

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