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# College Algebra, Week One MATH 1100.140

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This 7 page Class Notes was uploaded by Kait Brown on Monday September 5, 2016. The Class Notes belongs to MATH 1100.140 at University of North Texas taught by Mary Ann Barber in Fall 2016. Since its upload, it has received 25 views. For similar materials see College Algebra in Math at University of North Texas.

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Date Created: 09/05/16

W eekly Notes Math 1100.140,84 0 Week one Chapters p.1 The Real numbers and their properties p.2 Integer exponents and scientific notation Solve vs. Simplify o Solve Obtaining a value or a set of values, sometimes a graph or number line. An algebraic solution will include >, <, =, ≥, or ≤. o Simplify Obtain an equivalent expression in a simpler form Zero Product Property of Multiplication o If A•B=0, then A=0 and/or B=0 The Distributive Property of Multiplication Over Addition o A(B+C)=AB+AC DO NOT distribute multiplication over multiplication Importance of Notation/Hidden Meaning o => Implies o Є Element of o ⊂ Subset of o [ ] Includes endpoints o ( ) Does not include endpoints Types of Real Numbers and Their Importance o Natural N Counting numbers, starting at 1 {1, 2, 3…} o Whole W Counting numbers, starting with 0 {0, 1, 2…} o Integer Z Whole numbers, including negatives {…-1, 0, 1…} o Rational Q Any number that can be written as a ratio .872, ½, .3 o Irrational Q Any number that cannot be written as a ration, i.e., not a rational number √2, π P.1.1. 1. An integer that is not whole 2. An irrational number 3. Rational, but not an integer -3 π 1132/11 P.1.2. 5 1/7 -5 Z, Q, R Q, R R, Q, Z √4 √5 √-5 N, W, Z, Q, R Q, R Complex .123 . 123 .11235813… Q, R Q, R Q, R Set Notation o Set Collection of Objects o Roster Method A list of the elements {1, 2, 3, 4, 5, 6} o Set Builder Notation Describe the elements of the set {x x Є ℕ, x ≤6} OR {x x Є ℕ, x <7} o Number line How to show a set {x -1≤x<3} -2 -1 0 1 2 3 4 5 6 7 P.1.3. Write the set of natural numbers less than 10 with each set notation Roster Set Builder Number Line {1, 2, 3, 4, 5, 6, 7, 8, 9} {x x Є ℕ, x ≤9} <10} 1 2 3 4 5 6 7 8 9 10 11 12 13 Union and Intersection o Union ⋃ Represents the elements that are in one or both sets o Intersection ∩ Represents elements only in both sets P.1.4. If S={2, 3, 5, 7}, T={2, 4, 6, 8}, and V={1, 3, 5, 7}, find S ⋃ T and T ⋃ V S ⋃ T = {2, 3, 4, 5, 6, 7, 8} T ⋃ V = { } P.1.5. If A={x -1≤x<2} and B={x x>1}. Find A ⋃ B and A ∩ B. A={-1, 0, 1} -2 -1 0 1 2 A ⋃ B = {x -1≤x} B={ } 0 1 2 3 4 5 6 A ∩ B = {x 1<x<2} P.1.6. Use the number line below to write the set in interval notation. -5 -4 -3 -2 -1 0 1 2 3 4 5 [-4,1) ⋃ (2, 3] P.1.7. Rewrite │√17-5│without absolute value bars. 5-√17Because √17 is less than 5 P.1.9. Simplify 5(x-4)-10 1. Multiply 5 into (x-4) 5x-20 5 a. 5(x-4) 5x-20 2. Divide numerator by denominator, 5 a. 5x-20-10 (5x/5)-(20/5)-(10/5)x-4-2 3. Simplify a. -4-2 -6 b. x-6 Integer Exponents and Scientific Notation For a real number a, called the base, and a natural number n, called the exponent, aⁿ=a•a•a…a•a n number of times Exponential Rules to Know Product Rule o If a is a real number and m and n are integers, then a •a =a+n o Keep base, add exponents Quotient Rule o If a is a nonzero, real number, and m and n are integers, then m n m-n a /a =a . o To divide exponents (with the same base), keep the base and subtract exponents. Power-of-a-Power Rule m n mn o If a is a real number and m and n are integers, (a ) =a o Keep base, multiply exponents Power-of-a-Product Rule n n n o If a and b are real numbers and n is an integer, (a*b) =a *b Power-of-a-Quotient Rule n n n o (a/b) =-n/b n n n o (a/b) =(b/a) =b /a P.2.4 Suppose x *x =1. What is t? When we multiply the same base with exponents, we add the exponents. So x •x =1. t=1/7 -2 P.2.5 Simplify 5 . To rid our equations of negative exponents we use the reciprocal of the 1 base, so the answer is 5 2 P.2.8 3 -4 Simplify ( -2x y -4 3(-4) 1 -12 1. Apply -4 to the numerator: -2 x - 16 x And the -4 denominator: y y 2. To get rid of the negative exponents we flip the numerator and the denominator: 1 -12 4 - 16 x y y -4 16x 12 P.2.10. Write the following in scientific notation: 00.00365 3.65*10 -3 36500 3.65*10 4

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