SAT key math facts

A10

-Every integer has a finite set of factors (or divisors) an an infinite set of multiples

A28

-For any number a: 1 x a=a and a/1 =a. -For any integer n: 1^n=1. -1 is a divisor of every integer. -1 is the smallest positive integer. -1 is an odd integer. -1 is the only integer with only one divisor. It is not a prime.

A15

-For any number b: b^1=b -For any number b and integer n>1: b^n = bxbx...x b, where b is used as a factor n times.

A16

-For any numbers b and c and positive integers m and n: b^mb^n=b^m+n -b^m/b^n=b^mn -b^mc^m=(bc)^m -b^m/c^m=(b/c)^m

A18

-For any positive number a, there is a positive number b that satisfies the equation b^2=a. -That number is called the square root of a, and we write b=the square of a -Therefore for any positive number a: the square of a times the square of a = (the square of a)^2=a

A22

-For any real numbers a, b and c -a(b+c)=ab+ac -a(b-c)=ab-ac -if b plus c divided by a =b/a plus c/a, b-c/a = b/a - c/a

A6

-The reciprocal of any nonzero number is 1/a -The product of any number and its reciprocal is 1: a(1/a)=1

A8

-The sum of any number and its opposite is 0 i.e. -a+a=0

A7

-The sum of two positive numbers is positive -The sum of two negative numbers is negative -To find the sum of a positive and negative number, find the difference of their absolute values and use the sign of the number with the larger absolute value

A9

-To subtract signed numbers, change the problem to an addition problem y changing the sign of what is being subtracted

A2

-for any number a and positive number b -|a| = b = a is equal to b or a is equal to negative b -|a|< b = -b<a<b -|a|>b = a<-b or a>b

A1

-for any number a, a is negative, a is positive, a=0 -the absolute value of a number a, denoted as |a| is the distance between a and 0

A23

-for any numbers a and b: a>b means that a-b is positive -for any numbers a and b, a<b means that a-b is negative

A19

-for any positive numbers a and b: the square of a and b = the square of a times the square of b -the square of a/b equals the square of a over the square of b

A20

-for any real nonzero number a, a^0=1 -for any real nonzero number a, a^-n=1/a^n -For any positive number a and positive integer n: a^1/n=n in the square of a, for example 8^1/3 =3 in the square of 8 = 2

A26

-if 0<x<1, and a is positive, then xa<a -if 0<x<1, and m and n are integers with m>n>1, then x^m < x^n < x. -if 0<x<1, then the square of x > x. -if 0<x<1, then 1/x > x. In fact, 1/x > x.

A14

-if two integers are both even or both odd, their sum and difference are even -if one integer is even and the other odd, their sum and difference are odd. -the product of two integers is even unless both of them are odd

A5

-the product of an even number of negative factors is positive -the product of an odd number of negative factors is negative

A11

Every integer greater than 1 that is not a prime can be written as a product of primes

A24

For any numbers a and b, exactly one of the following is true: a>b, or a=b, or a<b

A17

For any positive integer n: -0^n=0 -if a is positive, a^n is positive -if a is negative, a^n is positive if n is even, and -negative if n is odd.

A25

INEQUALITIES -adding a number to an inequality or subtracting a number from the inequality preserves the inequality: if a<b, then a+c<b+c and a-c<b-c -Adding inequalities in the same direction preserves them a<b and c<d, then a+c<b+d -Multiplying or dividing an inequality by a positive number preserves the inequality. if a<b, and c is positive, then ac<bc and a/c < b/c -Multiplying or dividing an inequality by a negative number reverses the inequality. if a<b, and c is negative, then ac>bc and a/c > b/c -Taking negatives reverses an inequality. If a<b, then -a>-b and if a>b, then -a>-b. -If two numbers are each positive or each negative, taking reciprocals reverses an inequality. If a and b are both positive or both negative and a<b, then 1/a>1/b

A27

Properties of zero -0 is neither positive nor negative -0 is smaller than every positive number and greater than any negative number -0 is an even integer. -0 is a multiple of every integer. -For every number a: a+0=a and a-0=a. -For every number a: a x 0=0 -for every integer n: 0^n=0. -For every number a (including 0) a/0 is a meaningless expression. They are undefined. -For every number a other than 0: 0/a=0/ -Zero is the only number equal to its opposite -If the product of two or more numbers is 0, at least one of the numbers is 0.

A21

The laws of positive exponents also apply to negative exponents

A4

The product and the quotient of two positive numbers or two negative numbers are positive; the product and the quotient of a positive number and negative number are negative.

A12

The product of the GCF and LCM of two numbers is equal to the product of the two numbers.

A13

To find the GCF or LCM of two or more integers, first get their prime factorization.

A3

for any number a, ax0=0. if the product of two numbers are 0, one of them must be 0.