The SAT will frequently trip you up with what may seem the most simple numbers of all—0, 1 and 2.  In the context of Arithmetic Questions on the SAT, these numbers are deceptively simple, but all have specific special properties.  Memorize these few facts about 0, 1 and 2 and be prepared for their tricks.

Facts About 0

1. Any number multiplied by 0 equals 0.

example –>  6 x 0 = 0

2. You may NOT divide a number by 0.

example –> 6/0 is undefined

*Similarly, 1/(x-3) is undefined when x=3.  Therefore, x=3 could not be a solution to a question containing this expression.

3. 0 to any power is 0.

example –> 0^2 = 0,  0^1.5 = 0, 0^78 = 0, etc.

4. Any number to the power of 0 is 1.

example –> 1^0 = 1,  147^0 = 1,  1,000,000^0 = 1, etc.

Facts About 1

1. Any number multiplied by 1 is that number.

example –> 147 x 1 =147,  132.667 x 1 = 132.667, (a/b) x 1 = 0

*Be on the lookout for ones in disguise, usually in fraction form, i.e. 3/3, (x-2)/(x-2) or b/b.

2. One to any power is still 1.

example –> 1^3 = 1, 1^2.3 = 1, 1^-3 = 1, etc.

3. Any number to the power of 1 is that number.

example –> 147^1 = 147, 0^1 = 0, (x-b)^1 = x-b

4. 1 is NOT a prime number.

A prime must have only two distinct factors.  While 1 has only two factors (1 and 1), they are not distinct (different) from each other; therefore, 1 is NOT prime.

Facts About 2

1. Any integer multiplied by 2 will be even.

example –> 3×2=6, 1×2=2, 0×2=0 (0 is even)

2. 2 is a prime number.

It is the lowest prime number and the only even prime number.

Sometimes remembering the definitions of math terms is all you need to answer a question on the Arithmetic portions of the SAT Math sections.

Here’s a quick review of basic (but important!) math terms:

WHOLE NUMBERS: a whole number can’t be a fraction of a number, a percentage, or have a decimal. Whole numbers are always positive, and are all also called the “counting numbers,” because they include the first numbers we ever learn to count as children (1, 2, 3… 147… a million…). 0 is a whole number.

INTEGERS: all whole numbers and their negatives, from negative infinity to positive infinity (-3, -2, -1, 0, 1, 2…).

RATIONAL NUMBERS: includes all integers, as well as terminating or repeating decimals, such as 1.125, or 2.7777777… These numbers could all be expressed as a fraction.

IRRATIONAL NUMBERS: decimals that never end and never repeat, such as pi or e.  These numbers cannot be written as fractions or integers.

REAL NUMBERS: includes all rational numbers as well as irrational numbers.  Excludes i.

QUICK TIP for SAT Math Arithmetic: In a Venn diagram, whole numbers are the smallest group, completely inside integers.  Integers and fractions are inside rational numbers.  Rational and irrational numbers are inside real numbers. Imaginary numbers are separate from everything.

Remember these definitions and you’ll be ready to learn more strategies for approaching Arithmetic questions on the SAT Math sections.