ALGEBRA REVIEW

The Real Number Line negative numbers are to the left of 0 positive numbers are to the right of 0 a < b is read "a is less than b" and means a is further to the left on the number line than b a > b is read "a is greater than b" and means a is further to the right on the number line than b These are called strict inequalities a  b or a  b are nonstrict inequalities and mean besides being less than or greater than b, a can equal b. a > 0 means a is positivea < 0 means a is negative

[ Because the inequality is "greater than or equal to" the solution can equal the endpoint. A square bracket means it can equal the endpoint. squared end bracket We can graph inequalities on the number line.

Let's look at a different inequality sign ) Since this says "less than" we make the arrow go the other way. Since it doesn't say "or equal to" the solution cannot equal the endpoint. A rounded bracket means it cannot equal the endpoint. rounded end bracket

Absolute value is the distance from zero. It doesn't matter whether we are in the positive direction or the negative direction, we just care about how far away we are units away from 0

If we want to know how far apart points on the number line are, we can take the difference between them and then take the absolute value units apart What is the distance from -5 to 3?

Evaluating Algebraic Expressions If we are given an algebraic expression, we can substitute values for the variables to evaluate it. Be sure to put the values you are substituting in in parenthesis. Evaluate if x = 2 and y = -1.

EXPONENTS BASE exponentAn exponent means to multiply the base together that many times. Anything (except 0) to the 0 power is 1 A negative exponent means the reciporical (move to the bottom of a fraction)

LAWS OF EXPONENTS To multiply, if the bases are the same, keep the base and add the exponents To divide, if the bases are the same, keep the base and take top exponent minus bottom If you have one base raised to an exponent and the whole thing to another exponent, keep the base and multiply the exponents If you have a product to an exponent, apply the exponent to each factor If you have a quotient to an exponent, apply the exponent to the numerator and to the denominator

SQUARE ROOTS This is called a radical sign and denotes the principal square root which is nonnegative. This is asking what squared is 36. Although -6 squared is 36, the radical sign refers to the nonnegative root. The absolute value means we get a nonnegative result.

SCIENTIFIC NOTATION Scientific notation takes a number (particularly a large one with lots of zeros or a small one with lots of zeros between the decimal point and other digits) and uses powers of 10 to express it more easily. The decimal should be after the first nonzero digit ,0 0 0,0 0 0,0 0 0,0 0 0 To keep the number equal we’d need to multiply by a power of 10. Count how many decimal places to get to original decimal point to see what that power of 10 should be x x 10 14

If the number was very small we'd do the same thing, but since we'd be counting in the opposite direction, our power of 10 would be negative. The decimal should be after the first nonzero digit To keep the number equal we’d need to multiply by a negative power of 10. Count how many decimal places to get to original decimal point to see what that power of 10 should be x x 10 -7