More Math Vocabulary

A few months ago we sent you some key math vocabulary words. Understanding math terms is essential for acing the math sections of the ACT and SAT. Please e-mail us if you missed the first math vocabulary newsletter and would like us to send it to you. Here are some more important terms:

CONSTANT

A constant means an unchanging number, like 3, as opposed to a variable, like x.

Warning! The SAT will often use a letter to stand for a constant. For example:

“The population of hummingbirds t years after 1980 can be given by the equation 5000t + k, where k is a constant.”

However, notice the difference between t (a variable) and k (a constant). t stands for the number of years after 1980, so you could plug in different numbers for t depending on what year you were interested in.

k, on the other hand, is always the same number. This would be a perfect opportunity to use Picking Numbers: replace k with a number of your choice to make the question more straightforward.

INTEGER

A whole number, such as -5 or 18.

Yes, integers may be positive or negative. And don’t forget zero, especially on hard questions!

RATIONAL NUMBER

This one’s confusing. There are several correct definitions. Just remember that ALL of the following are rational numbers:

(a) Any fraction (that includes integers – remember, 3 is the same as 3/1)

(b) Any repeating decimal (such as 0.4545454545…)

(c) Any terminating decimal (i.e. any decimal that stops at some point)

You may ask, “What’s left?” The only non-rational (irrational) numbers are decimals that go on forever with no apparent pattern, such as π = 3.141592653… or √2 = 1.4142135…

nth TERM

Once in a while, the SAT will ask about a sequence of numbers, such as the following:

4, 7, 10, 13, 16, . . .

“The first term of the above sequence is 4, and each term after the first is three more than the preceding term. Which of the following expressions represents the nth term of the sequence?”

The letter n refers to a number’s place in the sequence. For example, 16 is the 5th term, so n = 5.

Whenever you’re working with sequences and the “nth term” is mentioned, it’s a good idea to write a row for n on top, like this:

n: 1 , 2 , 3 , 4 , 5 , 6 , 7 , etc

S: 4, 7, 10, 13, 16, 19, 22, etc.

UNITS DIGIT

For its own nefarious reasons, the SAT prefers to say “units digit,” even though every student learns this concept as “the ones place.”

In the number 452, the “units digit” is 2.

BONUS: Even vs. Positive

I know you know what an even number is, and I know you know what a positive number is.

However, time after time, SAT students at every level get the two mixed up. This is probably because even numbers and positive numbers are both “nice” kinds of numbers. Just be aware of this phenomenon and be extra alert whenever you see one of these key words mentioned.

Don’t Be Bored When Reading

If I had a nickel for every time a student has complained during a tutoring session that, “Ugh….these readings are SO BORING…,” I would be a very rich woman.

Believe me; I get it. Who wants to read about black holes or Mark Twain at 8 am on a Saturday morning? I know the passages are “boring,” and I know students can’t help but tune out, get confused, and begin to re-read over and over again, losing precious time and absorbing nothing.

But, if you are thinking that the passages are boring, you are addressing the reading passages all wrong! Yes, they are reading passages, but I don’t want you to read!

Think of the readings as a DETECTIVE GAME. Games are fun! Your job is to WIN, and you win by being the first person to solve the mystery. How do you solve the mystery? Find the clues. By thinking of the readings as a game you will not get bogged down in the details, and it is the details that make a reading “boring.” Thinking like a detective ACTIVELY engages you in the reading process. You need to look for clues like thought-reversers (but, however, yet…), italics, rhetorical questions…anything that will help you get the main idea and tone of a passage. Literally imagine yourself holding a magnifying glass. Skim the passage super focused on finding the clues. Once you find the clues, put the clues together to get the main point of the passage. Then, and only then, do you go to the questions and look back to the passage, focusing now on the details in order to answer specific questions.

Whenever you ACTIVELY look for something (think “detective”), things tend to not be so boring, and it is a whole lot harder to zone out.

So…how to turn a BORING reading into an ENGAGING one? Make reading an active process by becoming a detective, thinking of the SAT as a game – you are out to win. Can you beat the clock by finding the main idea and tone of the passage in 2 minutes? Can you get the questions correct by going back to the readings and specifically focusing on the lines/paragraph that the question is asking about?

Yes, I too used to find the readings “boring,” but now I truly enjoy hunting for the clues and solving the mystery.

So, I end asking you, “Do you want to read/play to win or do you just want to be bored?”

Don’t Goof Up the Grid-Ins

Sitting on the train this week, I overheard a group of mothers discussing the recent SAT. Of course I couldn’t help but eavesdrop! One mother was complaining that her daughter ran out of time because her daughter was confused about how to answer the math grid-ins. (One math section has 10 questions that are not multiple choice.) Being the pushy woman that I am, I asked the mom for her email address so that she could show this week’s newsletter to her daughter.

Math Grid-In Tips

Always start from the left.
The grid cannot accommodate: negative answers, answers with variables, answers greater than 9999, or answers with mixed numbers.
Always use the most accurate number that fits. 1.4 is not a substitute for 1.43.
Grid only the first three digits of long or repeating decimals.
It is not necessary to round repeating decimals.
Always guess if you have time- you don’t lose any points for a wrong answer.
Unless the problem indicates otherwise, an answer can be entered on the grid either as a decimal or as a fraction.
You don’t have to reduce fractions to their lowest terms.
Convert all mixed numbers to improper fractions before gridding the answer.
Some questions will have more than one right answer.

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