Algebra Review india

7/27/2019 Algebra Review india

1/20

Intermediate Algebraby Gustafson and Frisk

Chapter 1

A Review of Basic Algebra


2/20

Section 1.1: The Real Number System

SETS: collections of objects.

Natural NumbersWhole NumbersRational NumbersIrrational NumbersReal Numbers

IntegersPositive NumbersNegative NumbersEven NumbersOdd Numbers

Use { } {x | x > 5}is read the set of all x such thatx is greater than 5


3/20


GRAPHS: plot on the number line.

-1 0 31 42-2-3

Individual numbers are dots


4/20

-1 0 31 42-2-3



-1 0 31 42-2-3

Intervals including end points

[

[ ]


5/20

-1 0 31 42-2-3



-1 0 31 42-2-3

Intervals not including end points

(

( )


6/20

Section 1.2: Arithmetic & Properties of Real Numbers

OPERATIONS: AdditionSubtraction (the same as adding anumber with the opposite sign)

MultiplicationDivision (the same as multiplying bythe reciprocal)


7/20


ADDITION:

Addends that have opposite signs

Subtract absolute valuesKeep the sign of the addend with the

largest absolute value

Addends that have the same signs Add absolute valuesKeep the sign of the addends


8/20


MULTIPLICATION:

Multiply absolute values

If the factors have the same signs,the product is positiveIf the factors have opposite signs,

the product is negative


9/20


STATISTICS: measures of central tendency

Mean

MedianMode


10/20


Properties: Associative addition, multiplicationCommutative addition, multiplication

Distributive multiplication isdistributed over additiona (b + c) = ab + ac


11/20


Identities: Addition zeroMultiplication one

Inverses:

Addition oppositesMultiplication reciprocals


12/20

Section 1.3: Definition of Exponents

EXPONENTS: repeated multiplication

In the expression: a n

a is the base and n is the exponentExponents are NOT factorsMeans to multiply a n times


13/20

Section 1.3: Definition of Exponents

ORDER OF OPERATIONS:If an algebraic expression has more than one

operation, the following order applies:

1. Clear up any grouping.2. Evaluate exponents.3. Do multiplication and division from left to

right.4. Do addition and subtraction from left to

right.


14/20

Section 1.5: Solving Equations

Algebraic Expression vs. Equation

Expressions: a combination of

numbers and operationsEquation: a statement that twoexpressions are equal


15/20


EXPRESSIONS:

Terms

Like termsWhen multiplying, the terms do notneed to be alike

Can only add like terms!


16/20


TO SOLVE AN EQUATION IN ONE VARIABLE:

If you see fractions, multiply both sides by the LCD .This will eliminate the fractions.Simplify the algebraic expressions on each side of theequal sign (eliminate parentheses and combine liketerms).Use the addition property of equality to isolate thevariable terms from the constant terms on opposite

sides of the equal sign.Use the multiplication property to make the coefficientof the variable equal to one.Check your results by evaluating.


17/20


TYPES OF EQUATIONS: CONDITIONAL: if x equals this, then yequals that.

IDENTITY: always true no matter whatnumbers you use.CONTRADICTION: never true no matterwhat numbers you use.FORMULAS: conditional equations thatmodel a relationship between the variables.


18/20

Section 1.6 & 1.7: Solving Problems, Applications

TYPES OF PROBLEMS: GeometryPercentPhysics (forces)Uniform motionMixturesGood ole common sense analysis


19/20

Chapter 1: Basic Algebra Review

SUMMARY: KNOW YOUR VOCABULARY! You can t followdirections if you don t know what the wordsin the instructions mean.Memorize the processes and the properties.I will provide formulas for your reference.

Ask questions if you are unsure. Always check your work to make sure thatyou answered the question, and that youranswer is reasonable.


20/20

This powerpoint was kindly donated to

www.worldofteaching.com

http://www.worldofteaching.com Is home to well over a thousand powerpointssubmitted by teachers. This a free site. Please visit

and I hope it will help in your teaching
http://www.worldofteaching.com/http://www.worldofteaching.com/http://www.worldofteaching.com/http://www.worldofteaching.com/

Algebra Review india

Documents

Transcript of Algebra Review india