REVIEW: BASIC ALGEBRA AND GRAPHS

Mr. Velazquez

Honors Precalculus

ALGEBRAIC EXPRESSIONS

Example: 37 7 7 7=

EVALUATING ALGEBRAIC EXPRESSIONS

Evaluating an expression is the same as performing a calculation to find the outcome of a particular expression. However, we must take care to follow the order of operations when doing so:

P E M D A S

EVALUATING ALGEBRAIC EXPRESSIONS

22 3( 1) 4 for x =3x+ − −Example: Evaluate

USING MATHEMATICAL FORMULAS

Mathematical Modeling is the process of finding formulas to describe real-world occurrences or phenomena

USING MATHEMATICAL FORMULAS

Example: It takes you 30 minutes to get to your first period class. This includes driving at a rate of .8 miles per minute, and walking from the parking lot to your class at a rate of .07 miles per minute. The total distance of both walking and driving is given by the algebraic expression below. Find the distance if it takes you 5 minutes to walk to class.

0.07 .8(30 )D t t= + −

SETS AND SET NOTATION

A set is a collection of objects, whose elements can be clearly determined.

The Roster Method lists the elements of the set, with commas in between. The three dots (ellipsis) indicate that the listing continues for ever.

{1, 2, 3, 4, 5, … }

If a set has no elements at all, then it is called the null set or

empty set, represented by the symbol ∅.

SETS AND SET NOTATION

With Set Builder Notation, the elements are described, rather than listed.

If a set has no elements at all, then it is called the null set or

empty set, represented by the symbol ∅.

SETS AND SET NOTATION

SETS AND SET NOTATION

SETS AND SET NOTATION

Example: For the following sets of numbers find the Union and the Intersection.

2,4,6,8,10 3,4,5,6,7

2,4,6,8,10 3,4,5,6,7

THE REAL NUMBERS

Every Real Number is either rational or irrational. We refer to these sets as subsets of the real numbers, meaning that all elements in each subset are also elements in the set of real numbers.

| is rational or x is irrationalx x

THE REAL NUMBERS

25 is rational because 25 = 5

Numbers Examples

Natural Numbers 2,3,4,17

Whole Numbers 0,2,3,4,17

Integers -5,-2,0,2,5

1 5 1 2Rational Numbers , ,.4 ,0,.6

2 1 5 3

Irrational Numbers 2, , 3

− = =

−

THE REAL NUMBERS

13, 0, , .95, , 8, 16

2

−

Consider the following set of numbers.

List the numbers in the set that are:

a. Natural Numbers

b. Whole Numbers

c. Integers

d. Rational Numbers

e. Irrational Numbers

f. Real numbers

ORDERING THE REAL NUMBERS

We can use a number line to organize the real numbers.

ABSOLUTE VALUE

Example: Find the distance between -7 and 3

on the number line.

SIMPLIFYING ALGEBRAIC EXPRESSIONS

SIMPLIFYING ALGEBRAIC EXPRESSIONS

An Algebraic Expression is simplified when parentheses have been removed and like terms have been combined. Like terms are terms that have exactly the same variable factors. For example 5x and 7x are like terms.

5 7 12x x x+ =

Example: Simplify this Algebraic Expression

2 22( 3 ) (5 4) 9x x x x+ − + +

PROPERTIES OF NEGATIVES

LESSON REVIEW

( )3

9 2 4 1 for x=-3x− + +

(a) 4

(b) 10

(c) 12

(d) 8

LESSON REVIEW

Find the distance between -8 and 4 on

the number line.

(a) -4

(b) 12

(c) 10

(d) 8

LESSON REVIEW

List the numbers in the set below that belong to

the set of rational numbers.

(a)

(b)

(c)

(d)

15, , .3, .8, 9, , 13

2

− −

15, , .3, .8, 9,

2

− −

15, , .3, .8, 9, 13

2

− −

15, , .3, .8,

2

− −

15, , .8,

2

− −

CLASSWORK & HOMEWORK

Classwork:

1. IN YOUR MATH JOURNAL: Explain the difference between natural, whole, integer, rational and irrational numbers; summarize anything else you learned today.

2. VOCABULARY (DO NOW): Create a list of any six terms that were talked about today. Define these terms on a separate sheet of paper and turn it in to the assignment bin.

Homework:

Complete the EVEN NUMBERED problems posted on the website.