Real Numbers Algebra 5 Casa Grande Union High School

MATHO TERMS  < > Absolute value Add Associative Binomial Coefficient Commutative Composite Number Constant Degree Denominator Distance Distributive Exponent Factors Multiply Negative Nonterminating Numerator Polynomial Positive Prime Rational Root Scientific Subtract Terminating Terms Trinomial Variable 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. 3x 2 + 5x + 2 has 3 of these The number in front of a variable The value that changes, usually represented by a letter Infinity Symbol The value indicating the number of times a base is multiplied. In 3 5, 5 is the ___. Greater Than Symbol

MATHO Clues Radical symbol The top number in a fraction The bottom number in a fraction A number that can be written as a fraction or ratio A polynomial with 3 terms To simplify (a 5 ) 6, you ___ 5 and 6.

MATHO Clues The distance a number is from 0 The magnitude or difference in values Property shown: 3 + a = a + 3 Property shown: (a + b) + c = a + (b + c) 8 x 10 5 is called ____ notation Property shown: a(b + c) = ab + ac To simplify, you ____ the exponents. Absolute value is always what type of number?

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 a 5 * a 6, you ___ 5 and 6. What type of exponent (positive or negative) is x to turn 5 x into ? A decimal that ends, such as The greatest exponent is the ___ of the polynomial. A decimal that continues to infinity, such as 5.333… A polynomial with many terms

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 -½ ¾ 0.17 Square root of 15 3i |7.3| Square of 15 |-4.25| Square root of Square 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 NotationInterval TypeInequality Graph [a,b]closeda < x < b [ ] (a,b)opena x b ( ) [a,b)half-opena x b (a,b] half-open a x b

Unbounded Intervals from here to infinity… NotationInterval TypeInequality Graph [a,  )half-openx > a (a,  )openx > a (- , b]half-openx b (- , b) half-open x b (- ,  )entire real line

Words to Symbols c is at most 2 You have to be at least 18 to vote. F is between 3 and 7 I need at least $5 to buy lunch. I’m leaving at 6 and can’t stay out past 12 midnight. m is nonnegative The 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 = 187 Identify: terms coefficients constant variable

Evaluate Algebraic Expressions 4x – 6 for x = -1 9 – 7x for x = 2 6x + x 2 for x = ½ f(2) given f(x) = 3x g(-1) given g(m) = m 2 + 2m – 5 m(0) given m(t) = 5t 2 + 3t + 7

Exercises Describe the subset of real numbers represented by the inequality and sketch on a number line. 1. x < < h < < m < < y < < p < x is negative 4. All real numbers 9. y is no more than 5 5. x > z is at least -6

Evaluate the expression. 11.|-15|17.f + 9 for f = |3 -  |18.2(u – 7) for u = |33|19.n  (-3) for n = |- 9| 15.|-3| - |-5| |16.25| + 20

Assignment Pg : 19-25(odd) (x3),84, 85,