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Glossary of SAT - 200 Math Formulas, Concepts, and Practice Questions

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How do you know if an integer is a multiple of 3 or 9?
An integer is divisible by 3 if the sum of its digits is divisible by 3.

An integer is divisble by 9 if the sum of its digits is divisible by 9.

For example, the sum of the digits in 957 is 21, which is divisible by 3 but not 9. Therefore, 957 is divisible by 3 but not 9.
What is the definition of an integer?
Integers are whole numbers and their opposites; they include the negatives of whole numbers and zero.

For example, -15, -4, 0, 1, and 457 are all integers.
What is the definition of a rational number?
A rational number is a number that can be expressed as a ratio of two integers or as a terminating or repeating decimal.

For example, -87, 1/2, 4.33333 (4 1/3), 59, and 100.5 (100 1/2) are all rational numbers.
What is the definiton of an irrational number?
Irrational numbers are real numbers--they have locations on the number line--but they can't be expressed precisely as a fraction or decimal. They are non-repeating non-terminating decimals.

For the purposes of teh SAT, the most important irrational numbers are square root of 2, square root of 3, and pi. (Note that 3.14 is only an approximation of pi. Pi is a non-repeating, non-terminating decimal.)
How do you add a positive number to a negative number?
To add a positive and a negative, first ignore the signs and find the positive difference between the numbers. Then attach the sign of the original number with the larger absolute value.

For example, to add 23 and -34, first ignore the negative sign and find the positive difference between 23 and 34--that's 11. Then attach the sign of the number with the larger absolute valule--in this case it's the negative from the -34. So, 23 + (-34) = -11.
How do you multiply and divide positive and negative numbers?
To multiply and/or divide positive and negatives, treat the number parts as usual, and attach a negative sign if there is an odd number of negatives.

For example, to multiply -2, -3, and -5, first multiply the number parts: 2 x 3 x 5 = 30. Then go back and note that there were three--an odd number--negatives, so the product is negative: (-2) x (-3) x (-5) = -30.
Explain the memory device "PEMDAS."
When performing multiple operations, you must remember to perform them in the correct order: PEMDAS, Parenthesis first, the Exponents, then Multiplication and Division (left to right), and then Addition and Subtraction (left to right).
How do you count consecutive integers?
To count consecutive integers, subtract the smallest from the largest and add 1.

For example, to count the integers from 13 through 31, subtract: 31 - 13 = 18. Then add 1: 18 + 1 = 19.
How do you express the union and intersection of sets?
The union of Set A and B, sometimes expressed as A U B, is the set of elements that are in either or both Set A and set B.

For example, if Set A = {1,2,3} and Set B = {3,4}, then A U B = {1,2,3,4}.

The intersection of Set A and Set B, sometimes expressed as A n B, is the set of elements common to both Set A and Set B.

For example, if Set A = {1,2,3} and Set B = {3,4,5}, then A n B = {3}.
What is the difference between a factor and a multiple?
The factors of integer n are the positive integers that divide into n with no remainder. The multiples of n are the positie integers that n divides into with no remainder.

For example, 6 is a factor of 12, and 24 is a multiple of 12.

12 is both a factor and a multiple of itself, since 12 x 1 = 12 and 12/1 = 12.
What is the prime factorization of a number?
To find the prime factorization of an integer, just keep breaking it up into factors until all of th factors are prime numbers.
What are numbers that are "relatively prime?"
Two relatively prime numbers are integers that have no common factor other than 1. To determine whether two integers are relatively prime, break them both down to their prime factorizations.

For example: 35 = 5 x 7, and 54 = 2 x 3 x 3 x 3. They have no prime factors in common, so 35 and 54 are relatively prime.
How do you find the least common multiple (LCM) of two or more numbers?
You can get a common multiple of two integers by multiplying them, but unless the two numbers are relative primes, the product will not be the least common multiple.

To find the least common multiple, check out the multiples of the larger integer until you find one that's also a multiple of the smaller.
How do you find the greatest common factor (GCF) of two or more numbers?
To find the greatest common factor, break down the integers into their prime factorizations, and multiply all the prime factors they have in common.