Real NumbersAlgebra 5

Casa Grande Union High School

MATHO TERMS

<>Absolute valueAddAssociativeBinomialCoefficientCommutativeComposite NumberConstant

DegreeDenominatorDistanceDistributiveExponentFactorsMultiplyNegativeNonterminatingNumeratorPolynomial

PositivePrimeRationalRootScientific SubtractTerminatingTermsTrinomialVariable

On the MATHO card from the center table, fill in each blank (in pen) with one of the terms below. Do not use the terms more than once. Fill in all blanks.

MATHO Clues

Parts of an algebraic expression. 3x2 + 5x + 2 has 3 of these

The number in front of a variableThe value that changes, usually

represented by a letterInfinity SymbolThe value indicating the number of times

a base is multiplied. In 35, 5 is the ___.Greater Than Symbol

MATHO Clues

Radical symbolThe top number in a fractionThe bottom number in a fractionA number that can be written as a

fraction or ratioA polynomial with 3 termsTo simplify (a5)6, you ___ 5 and 6.

MATHO Clues

The distance a number is from 0The magnitude or difference in valuesProperty shown: 3 + a = a + 3Property shown: (a + b) + c = a + (b + c)8 x 105 is called ____ notationProperty shown: a(b + c) = ab + acTo simplify , you ____ the exponents.Absolute value is always what type of

number?

3

8

a

a

MATHO Clues

An integer that has exactly 2 positive factors: itself and 1.

An integer that has more than 2 positive factors.A polynomial with 2 terms.To simplify a5 * a6, you ___ 5 and 6.What type of exponent (positive or negative) is x to turn 5x into

? A decimal that ends, such as 3.571The greatest exponent is the ___ of the polynomial.A decimal that continues to infinity, such as 5.333…A polynomial with many terms

5

1

MATHO Clues

Less than symbol

8 is the square _____ of 64

2 and 3 are ____ of 6…another word for divisor

Real Numbers

What is a real number?

What is a rational number?

What is an irrational number?

Rational, Irrational or Neither?

5-½¾0.17Square root of

153i|7.3|

Square of 15|-4.25|Square root of 73.25Square root of

16-i|85|*|32|

Absolute Value

You’re at the Florence Boulevard exit off I-10 and travel to the Pinal exit. How far did you travel?

Define absolute value.

Evaluate.

|10||-5||5 – 8|-|5|-|-15||0||4 - |

-3|4|2|33||-1| - |-2|-5/|-5||-1/2|-|-7|-(-6)

Interval Notation

You go to the store. What is the amount of money (interval) that you must have to purchase a $15 gift for your teacher?

You have a checking account. What is the amount of money (interval) possible for your current balance for an account in good standing?

Bounded Intervals

Notation Interval Type Inequality Graph[a,b] closed a < x < b [

]

(a,b) open a x b ( )

[a,b) half-open a x b

(a,b] half-open a x b

Unbounded Intervals from here to infinity…

Notation Interval Type Inequality Graph

[a,) half-open x > a

(a, ) open x > a

(- , b] half-open x b

(- , b) half-open x b

(- , ) entire real line

Words to Symbols

c is at most 2You have to be at least 18 to vote.F is between 3 and 7I need at least $5 to buy lunch.I’m leaving at 6 and can’t stay out

past 12 midnight.m is nonnegativeThe legal driving age is Arizona

Algebraic Expressions

An algebraic expression is a collection of letters (called ____________) and real numbers (called __________) combined using the operations of __________, __________, _______, __________, and ____________.

3x + 5 versus 3x + 5 = 187Identify:terms coefficients constant

variable

Evaluate Algebraic Expressions

4x – 6 for x = -19 – 7x for x = 26x + x2 for x = ½f(2) given f(x) = 3xg(-1) given g(m) = m2 + 2m – 5 m(0) given m(t) = 5t2 + 3t + 7

Exercises

Describe the subset of real numbers represented by the inequality and sketch on a number line.

1. x < 5 6. -5 < h < -32. -3 < m < 7 7. 4 < y < 53. 0 < p < 17 8. x is negative4. All real numbers 9. y is no more than

55. x > -2 10. z is at least -6

Evaluate the expression.

11. |-15| 17. f + 9 for f = 15

12. |3 - | 18. 2(u – 7) for u = 5

13. 2|33| 19. n (-3) for n = 12

14. -5|- 9|15. |-3| - |-5| 20.16. -|16.25| + 20

2)13(

1

mform

m

Assignment

Pg. 10-12: 19-25(odd) 42-66 (x3),84, 85, 97-100