Algebra Basics

What will be covered: Order of Operations Variables vs. Constants The Quadratic Formula Common Algebra Mistakes What will be tested: Any basics that have been covered heavily in math courses up to and including Algebra I, all of which are prerequisites for this course.

Solve this:

Order of Operations Please Excuse My Dear Aunt Sally Parentheses - {[(a + b)]} Exponents - a b Multiplication - a x b, a b Division - a/b, a ÷ b Addition - a + b Subtraction - a - b

Order of Operations Parenthesis – First proceed through PEMDAS through the parenthesis ( ) – Next, follow PEMDAS through any brackets [ ] – Then, do PEDMAS through braces { } – Finally, do PEDMAS through chevrons – Don’t forget that parenthesis are implied around the dividend and the divisor:

Order of Operations Exponents – Exponents are concise ways of displaying that the base is multiplied by itself: 6 4 = 6 x 6 x 6 x 6 – A negative exponent means that you should invert the base and then multiply = ½ x ½ x ½ = 1/(2 3 ) – An exponent applies ONLY to the base it is immediately attached to: 5y 2 = 5(y 2 )... NOT (5y) 2

Order of Operations Exponents (con’t) – A fraction exponent means that you should take the denominator root of the base: 6 1/2 = 625 1/4 = – When negatives and fractions are both present, you treat them separately. 2 -1/4 = 2 -1 x ¼ =

Order of Operations Exponents (continued) – Product of Powers a m * a n = a m+n – Power of a Power (a m ) n = a mn – Power of a Product (ab) m = a m * b m – Zero Exponent a 0 = 1; unless a = 0, at which point a 0 = 0 – Quotient of Powers a m / a n = a m-n ; a can not equal 0 – Powers of a Quotient (a / b) m = a m / b m ; b can not equal 0

Order of Operations Simplify these: – 1. (x 4 ) 2 – 2. x 3 + y 3 – * 3 4 – 4. z 8 / z 11 – 5. (5x 2 y 2 ) 7 – 6. (x 8 / xy) 2 – 7. x -3/2 Product of Powers a m * a n = a m+n Power of a Power (a m ) n = a mn Power of a Product (ab) m = a m * b m Zero Exponent a 0 = 1; unless a = 0, at which point a 0 = 0 Quotient of Powers a m / a n = a m-n ; a can not equal 0 Powers of a Quotient (a / b) m = a m / b m ; b can not equal 0

Order of Operations Multiplication and Division – Since division is really just inverted multiplication, we can do both steps at the same time, from left to right.

Order of Operations Addition and Subtraction – Since Subtraction is really just adding a negative value, we can do both in the same step, from left to right = = 6 + 4

NOW, Solve this:

Here we go: We can work on each term separately. What did I do? Now what did I do? (Science text will always skip steps, it’s up to you to figure out what they did!

Here we go:

Variables vs. Constants Variables are numbers that are dynamic and will change as the other variables in the equation change to keep the statements true. For the very beginning of this class, variables will typically be indicated in italic font as x and y Constants are numbers in an equation that do not change. They are typically coefficients and, for the beginning of this class, will be indicated by normal, lowercase letters from the beginning of the alphabet like a, b and c, or the first letter of the word they represent, like g for gravity.

The Quadratic Formula A Quadratic Equation is any equation that can be manipulated into the form: y = ax 2 + bx + c Solutions to quadratic equations can be found using the formula: *** Get the program QUADFORM on your calculator NOW!!!***

Common Algebra Mistakes: Combining factors: – Find the mistake: – Correct: Solving Linear equations: – Find the mistake: – Correct:

Common Algebra Mistakes: Exponents: – Find the mistake: – Correct: Exponents: – Find the mistake: – Correct:

Common Algebra Mistakes: Parenthesis: – Find the mistake: – Correct: Simplifying Fractions: – Find the mistake: – Correct:

Common Algebra Mistakes: Simplifying Fractions: – Find the mistake: – Correct: Simplifying Radicals: – Find the mistake: – Correct:

Common Algebra Mistakes: Solving Linear Expressions: – Find the mistake: – Correct: Simplifying Radicals: – Find the mistake: – Correct:

Common Algebra Mistakes: Solving Linear Expressions: – Find the mistake: – Correct: Solving Quadratic Functions: – Find the mistake: