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SAT Study Guides
2.1 SAT Math - Pretty Easy Math Used to Trick You
As you just learned, the actual math used on the SAT is not that hard; it's the way the questions are asked. There is a lot of very, very 'easy' math - we're talking stuff you learned in fifth grade - that regular, smart juniors and seniors in high school get wrong because of not reading carefully, careless mistakes, and just plain forgetfulness.
Remember: the easier questions (roughly 1-6 or 8 on the 25 and 20 minute sections without grid-ins, roughly the first three multiple choice and the first three grid-ins on the grid-in section) are supposed to be easy. Don't overthink them. You should be able to pinpoint what they're asking fairly quickly, answer it and move on. If it seems difficult, stop, consider what skills they might be testing here, and see if you can remember what to do. If it still seems difficult, skip it. Once your brain has locked into 'panic' mode on any question, but especially the easier ones, you're better off coming back with a fresh eye. You don't want to waste time on the easy ones. Circle the question number in your answer booklet so you don't forget to come back to it (and be sure to skip the line on your bubble sheet! You would be horrified at the number of students that bubble wrong if they've skipped a question.) and move on.
That being said, don't get cocky and speed through. Watch those overly obvious answers and simply "playing with" numbers. What's the absolutely Number One problem students make? Yup. Careless mistakes.
So let's review some of the Math Vocab you may have forgotten, and some of the arithmetic you may encounter on the SAT exam.
SAT Math Vocabulary Review
Know What These Words Mean (and Know the Difference between concepts that are similar!):
-Whole Numbers: Your basic counting numbers: 0, 1, 2, 100, 4215... Whole numbers are:
-zero and above up to positive infinity
-positive (well, except for zero. Zero isn't positive, but is a whole number. Zero has some special rules that will be covered in a moment)
-no fractions
-no decimals
-Integers: Just like whole numbers, but also includes negatives. Some examples are -4, -3, -416, and also 0, 1, 2, etc. Integers are:
-positive or negative up to infinity
-"counting numbers" only
-no fractions
-no decimals
-Hint: The word 'Integer' in a pretty easy math question tends to be a Classic SAT Trick - with a classic easy strategy to answer it. If the question asks "What integer...blah blah blah" get rid of any answer choices with fractions or decimals - and there will usually be at least two or three. This is a nice and easy way to quickly narrow down your choices. (By the way, it should go without saying, but since so many people make careless mistakes: If the question is asking for an integer, you should NEVER choose an answer containing a fraction or decimal! Got that? Good.)
-Odd Numbers: 1, 3, 5, 7, etc. Also, -1, -3, -5, etc. (all the way to infinity on either side)
-positive or negative
-integers only (no fractions, no decimals)
-not evenly divisible by 2
-Even Numbers: 0, 2, 4, 6, etc. Also, -2, -4, -6...(up to infinity on either side)
-positive or negative
-integers only (no fractions, no decimals)
-evenly divisible by 2
-Consecutive: means 'in a row.' A question might say "Three consecutive numbers" where the answer could be 3, 4, 5. A question could also say "Three consecutive even numbers" where the answer could be 6, 8, 10. Consecutive numbers can be negative, and they can also cross the 'zero' line - that is, "three consecutive numbers" could be -1, 0, 1, so don't rule out any possibilities except fractions and decimals. Consecutive numbers will be integers.
-Trick to Watch Out For: Keep in mind that while "consecutive numbers" will be integers, it IS possible that the question will put those integers somewhere weird which would make the real numbers you're dealing with fractions. For example, a question might say:
The sum of three fractions with the same denominator and numerators that are consecutive integers whose sum is less than the denominator will always be:
(A) less than 1
(B) 1
(C) greater than 1
(D) 3
(E) greater than 3
In this example, the consecutive numbers are the numerators of a set of fractions, which means the actual numbers you're working with are in fact fractions, even though the word "consecutive" showed up in the question.
(By the way, do you know the answer to the question above? Don't try to reason out the wording - make up your own numbers that fit the criteria presented to see what works in real life. It's a technique that will be covered in more detail later. The answer is (A) less than 1.)
-Hint: Consecutive Numbers with Variables. If given a question that says "three consecutive numbers" and it's a question you will need algebra to solve (that is, you'll need to use variables like x, y, or the like), set up your equation using x for the smallest number. The next number will be x + 1, then x + 2 and so forth for each consecutive number. If it's consecutive odds or consecutive evens, set up x for the smallest number, but use xfor the second number, x + 4 for the third number, etc. Even for consecutive odd numbers, you still use x + 2, x + 4, etc! (If this doesn't make sense to you, think about it for a moment. Pick an odd number. Let's say 11. What's the next consecutive odd number? 13, right? Which is also 11+2. If you do the rest of your math right in that problem, you'll get an odd number for x, and everything else will then work itself out.)
-Real Numbers: All numbers except imaginary numbers.
Yeah, this one's pretty obvious, but people get thrown by the term sometimes because it seems SO obvious that they worry it must mean something else. It doesn't. If you haven't seen imaginary numbers in math class yet, don't worry, they're not on this test. If you have, you won't see them here either, so don't worry about it.
-Rational Numbers: Now this one means something. The technical definition of a rational number is "any number that can be written as
where x and y are integers," but what that means is basically this:
x
---------
y
-a rational number should be a repeating decimal such as .77, a terminating decimal such as .316, or a regular-looking fraction like
| 4 |
| --------- |
| 9 |
| 23 |
| --------- |
| 7 |
-Keep in mind that in an algebra problem, if they specify the variable is an integer, something like 4/x will be a rational number.
-Examples of non-rational numbers (or Irrational as they're called) are things like π or √2 --numbers that don't end and cannot be written as fractions.
-Positive Numbers: Numbers greater than zero
-Negative Numbers: Numbers less than zero
-Digits: Digits consist of the numbers 0 through 9 regardless of place value. Think of digits like a telephone keypad (hence the phrase, "getting someone's digits"). A question might say "When a three-digit number is added to a two-digit number the result is always..." Your job will be to try various numbers 0 through 9 in each of the separate place values to determine the answer. Digit-specific questions will be covered in more detail in Algebra Oddities.
-Distinct: means 'different' or 'separate.' The word 'distinct' most often shows up as a way to limit the possible numbers you should try. For example, "In a fraction in which x and y are distinct integers, what is the result when...blah blah blah." This means, for you, don't try the number 3 or both x and y; pick separate numbers for each.
-Hint: If the word 'distinct' does NOT appear in a question when it would make a difference in your answer (like in the brief example above), then you should definitely see what happens if you choose the same number for both variables. This will most often happen on Must/Always questions, covered in detail in Algebra Oddities.
-Divisible: able to be evenly divided by. Ex: "24 is divisible by 8"
-Divisor: The number that is going into the other number. In the equation "32 ÷ 4" the divisor is the number 4. Also known as the number "outside the bridge" if you're doing long division. The dividend is the number "under the bridge." See?
(Yeah, fifth grade math here, folks. But you probably didn't remember which was which, did you?)
-Sum/Difference/Product/Quotient: The answers when you do math. Sum is addition, Difference is subtraction, Product is multiplication, Quotient is division.
-Hint: Know these. The question WON'T usually say "If you multiply 4 and x + 2 the answer will be..." It will usually say "The product of 4 and x + 2 will be..." If you don't know what these four words mean, you won't know what to do. Likewise, the word 'and' doesn't usually mean to add on the SAT test, it means "do the mathematical operation here."
Special Rules for Zero:
-Zero is NEITHER positive nor negative
-Zero is even
-Zero is real, rational, an integer, a whole number, and a digit
-Zero is a multiple of every number
-Anything times zero equals zero (and that means anything! 0 times 
equals? Zero.
Please Excuse My Dear Aunt Sally, or PEMDAS
Order of operations will be tested directly, and also is important to know in order to solve most other problems correctly. The correct order of operations is:
Parentheses
Exponents
Multiply
Divide
Add
Subtract
Keep in mind that Multiplication and Division are the same "level," as are addition and subtraction. That means you don't do multiplication before division when you get to that step, you simply go left to right. So really PEMDAS should look like:
Parentheses
Exponents
Multiply/Divide
Add/Subtract
-Hint: Your calculator has PEMDAS programmed, so if you simply enter a numerical problem into it, it will do it correctly…sort of. Your calculator will follow the rules very strictly, which means if you enter -2 squared as +22 your calculator will first do the exponent, then multiply the result by -1, giving you -4 as an answer. Same with fractions: if you want to find the answer to
| 2 |
| --------- |
| 3 |
| 2 |
| --------- |
| 9 |
| 4 |
| --------- |
| 9 |
-Calculator Rule #1: ALWAYS use parentheses around fractions and negatives when typing them into your calculator. Even if you don't think you need them, it is far better to be in the habit of having them then to get something wrong for a silly reason.
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