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Real NumbersAlgebra 5
Casa Grande Union High School
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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.
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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
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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.
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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
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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
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MATHO Clues
Less than symbol
8 is the square _____ of 64
2 and 3 are ____ of 6…another word for divisor
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Real Numbers
What is a real number?
What is a rational number?
What is an irrational number?
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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|
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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.
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Evaluate.
|10||-5||5 – 8|-|5|-|-15||0||4 - |
-3|4|2|33||-1| - |-2|-5/|-5||-1/2|-|-7|-(-6)
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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?
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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
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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
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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
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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
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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
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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
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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
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Assignment
Pg. 10-12: 19-25(odd) 42-66 (x3),84, 85, 97-100