Review ChapterWhat you Should Learn

REALLY WHAT YOU SHOULD HAVE ALREADY LEARNED

If not, then you might be in too high of a course level decide soon!!!

Henry David Thoreau - authorIt affords me no satisfaction to commence to spring an arch before I have got a solid foundation.

ObjectiveUnderstand the structure of algebra including language and symbols.

ObjectiveUnderstand the structure of algebra including language and symbols.

DefinitonExpression a collection of constants, variables, and arithmetic symbols

DefinitionInequality two expression separated by , -2>-34 < 54 < 4

DefinitionEquation two expression set equal to each other4x + 2 = 3x - 5

Def: evaluateWhen we evaluate a numerical expression, we determine the value of the expression by performing the indicated operations.

DefinitionSet is a collection of objectsUse capitol letters to representElement is one of the items of the collectionNormally use lower case letters to describe

Procedure to describe setsListing: Write the members of a set within bracesUse commas betweenUse to mean so on and so forthUse a sentenceUse a picture

Julia Ward Howe - PoetThe strokes of the pen need deliberation as much as the sword needs swiftness.

Examples of Sets{1, 2, 3}{1, 2, 3, , 9, 10}{1, 2, 3, } = N = Natural numbers

Set Builder Notation{x|description}Example {x|x is a living United States President}

Def: Empty Set or Null set is the set that contains no elementsSymbolism

Symbolism element is an element of

Def: Subset: A is a subset of B if and only if ever element of A is an element of BSymbolism

Examples of subset{1, 2} {1, 2, 3}{1, 2} {1, 2}{ } {1, 2, 3, }

Def: Union symbolism: A BA union B is the set of all elements of A or all elements of B.

Example of Union of setsA = {1, 2, 3}B = {3, 4, 5}A B = {1, 2, 3, 4, 5}

Real NumbersClassify Real NumbersNaturals = NWholes = WIntegers = JRationals = QIrrationals = HReals = R

Def: Sets of NumbersNatural numbersN = {1,2,3, }Whole numbersW = {0,1,2,3, }

IntegersJ = { , -3, -2, -1, 0, 1, 2, 3, }

NaturalsIntegersWholes

Def: Rational numberAny number that can be expressed in the form p/q where p and q are integers and q is not equal to 0.Use Q to represent

Def (2): Rational numberAny number that can be represented by a terminating or repeating decimal expansion.

Examples of rational numbersExamples: 1/5, -2/3, 0.5, 0.33333Write repeating decimals with a bar above.12121212 =

Def: Irrational NumberH represents the setA non-repeating infinite decimal expansion

Def: Set of Real Numbers = RR = the union of the set of rational and irrational numbers

Def: Set of Real Numbers = RR = the union of the set of rational and irrational numbers

Def: Number lineA number line is a set of points with each point associated with a real number called the coordinate of the point.

Def: originThe point whose coordinate is 0 is the origin.

Definition of Opposite of oppositeFor any real number a, the opposite of the opposite of a number is -(-a) = a

Definition: For All

Def: There exists

Bill Wheeler - artistGood writing is clear thinking made visible.

Def: intuitiveabsolute valueThe absolute value of any real number a is the distance between a and 0 on the number line

Def: algebraic absolute value

Calculator notesTI-84 APPSALG1PRT1Useful overview

George PattonAccept challenges, so that you may feel the exhilaration of victory.

Properties of Real NumbersClosureCommutativeAssociativeDistributiveIdentitiesInverses

Commutative for Additiona + b = b + a2+3=3+2

Commutative for Multiplicationab = ba2 x 3 = 3 x 32 * 3 = 3 * 2

Associative for Additiona + (b + c) = (a + b) + c2 + (3 + 4) = (2 + 3) + 4

Associative for Multiplication(ab)c = a(bc)(2 x 3) x 4 = 2 x (3 x 4)

Distributivemultiplication over additiona(b + c) = ab + ac2(3 + 4) = 2 x 3 + 2 x 4X(Y + Z) = XY +XZ

Additive Identitya + 0 = a3 + 0 = 3X + 0 = X

Multiplicative Identitya x 1 = a5 x 1 = 51 x 5 = 5Y * 1 = Y

Additive Inversea(1/a) = 1 where a not equal to 03(1/3) = 1

George Simmel - SociologistHe is educated who knows how to find out what he doesnt know.

Order to Real NumbersSymbols for inequalityBounded Interval notation*** Definition of Absolute ValueAbsolute Value PropertiesDistance between points on # line

George Simmel - SociologistHe is educated who knows how to find out what he doesnt know.

The order of operationsPerform within grouping symbols work innermost group first and then outward.Evaluate exponents and roots.Perform multiplication and division left to right.Perform addition and subtraction left to right.

Grouping SymbolsParenthesesBracketsBracesRadical symbolsFraction symbols fraction barAbsolute value

Algebraic ExpressionAny combination of numbers, variables, grouping symbols, and operation symbols.

To evaluate an algebraic expression, replace each variable with a specific value and then perform all indicated operations.

Evaluate Expression byCalculatorPlug inUse store featureUse Alpha key for formulasTableProgram - evaluate

The Pythagorean TheoremIn a right triangle, the sum of the square of the legs is equal to the square of the hypotenuse.

Operations on FractionsFundamental PropertyAdd or SubtractMultiplyDivide

Properties of ExponentsMultiplyDivideOpposite exponentProduct to powerPower to powerQuotient to powerScientific Notation

COLLEGE ALGEBRA REVIEWInteger Exponents

Integer ExponentsFor any real number b and any natural number n, the nth power of b o if found by multiplying b as a factor n times.

N times

Exponential Expression an expression that involves exponentsBase the number being multipliedExponent the number of factors of the base.

Exponential Expression an expression that involves exponentsBase the number being multipliedExponent the number of factors of the base.

Quotient Rule

Integer Exponent

Zero as an exponent

Calculator KeyExponent Key

Sample problem

more exponentsPower to a Power

Product to a Power

Quotient to a Power

Sample problem

Scientific NotationA number is in scientific notation if it is written as a product of a number between 1 and 10 times 10 to some power.

Calculator KeyEEMode - SCI

Sydney Harris:When I hear somebody sigh,Life is hard, I am always tempted to ask, Compared to what?

RadicalsPrincipal nth rootTerminology IndexRadicand

Properties of RadicalsProduct of radicalsQuotient of RadicalsIndex is even or odd and radicand of any Real number

Rational ExponentsDefinitionEvaluationEvaluation with calculator

Operations on RadicalsAdd or subtractMultiply Divide**** Rationalize

PolynomialsMultiply FOILEvaluateProduct of polynomialsSpecial ProductsSum and DifferenceSquaring

FactoringCommon FactorBy GroupingDifference of Two SquaresPerfect Square TrinomialsGeneral TrinomialsDifference of CubesSum of Cubes

Rational ExpressionsFind DomainSimplifyMultiply and DivideAdd and SubtractComplex Fractions

Cartesian PlanePlot Points**** Distance Formula** Midpoint FormulaGeneral Equation of Circle

Chapter SummaryText Chapter Summary and Review end of chapterWhat You Should Learn beginning of each sectionReview Exercises broken down by sections Chapter Test Good Practice

The END.Or The Beginning of possibly one of the most challenging courses you will take that will require the following:CommitmentTimeDedicationPerseveranceMore Work than you Think if you want to be successful!

Good Luck

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