
Advanced Algebra NotesUpdated Notes can be found on the Advanced Algebra Notes link:SPRING SEMESTER S2Conic SectionsChapter 8 Rationals
Rational ExpressionsFind common denominators, combine like terms, factor is possible and reduce.Adding and Subtracting Compound Rationals (nested fractions) and negative exponents:
Chapter 7 Polynomials
Graphing Polynomials in Factored Form: (Polynomial Graphs KEY)FALL SEMESTER S1Changes to FER#2:Change the right hand side of the equation toln(6225x) and it should workProblem XVII should have a starting amount of 100 bacteria instead of just 1.
Chapter 6 Logarithms
Chapter 3 SystemsOctober 15, 2013Linear Inequalities Quiz Review and More Mixture ProblemsOctober 14, 2013Chapter 2 FunctionsChapter 2 Review answers:Transformations answer key:
Chapter 1 Foundations ReviewSeptember 9, 2013Nine zulu queens rule China but the king awakes and surveys hisDomain (horizon from left to right, xvalues) and imagines theRange (vertical up and down yvalues) of possibilities. "Sky's the limit." y goes with sky.Exponents are defined as repeated multiplication.5^2 means multiply 5 by itself twice, 5*5 = 25.2^3 means multiply 2 by itself three times, 2*2*2 = 8.This also means add exponents when multiplying identical bases:x^2 * x^3 = x*x*x*x*x = x^5 = x^(2+3).Likewise, subtract exponents when dividing identical bases:a^4 / a^3 = a*a*a*a / (a*a*a) = a (a*a*a) /(a*a*a) = a ^ 1 = a ^ (43) = a.Since a negative is the opposite of a positive, a negative exponent meansdo the opposite of multiplying. So divide. For example,5^(1) means do the opposite of multiplying by 5 once. So instead of 1*5,do 1/5. So 5^(1) = 0.2.5^(2) means divide by 5 twice. 1/5/5 = 1/5^2 = 1/25.What about fractional exponents?If 2*2*2 = 8, then8^(1/3) = 2 (one third of the product) and8^(2/3) = 2*2 = 4 (two thirds of the product.)Therefore, 8^(1/3) is the cube root of 8, or 2.Square that to get 8^(2/3), or 2^2 = 4.Unit 2Nine Zulu Queens Rule China:N = Natural "counting" numbersZ = Integers, 0 with positive and negative natural numbersQ = Rational numbers, ratios of two integers, Q meaning quotient.(Proper and improper fractions, mixed numbers, repeating and terminating decimals.)R = Real numbers, which is the set of Q along with irrational numbers(nonrepeating nonterminating decimals, e.g. Φ = 1.618033..., √2, 0.12345678910111213..., 0.101001000100001...)Closure is the property by which the resulting answer is a member of the same set as the two operands.For example, adding or multiplying two natural numbers results in another natural number.So the Natural number set is closed under addition and multiplication. But not subtraction because 25 = 3.However, the set Z of integers is closed under addition, multiplication, AND subtraction as sums, products, and differences of integers are still integers. But not quotients. Sometimes dividing two integers yields a fraction or a decimal, in other words, a rational number.Therefore, the set of rationals Q is closed under all four operations (+, , *, /) and integral powers. However, inverting powers, i.e. taking roots, often results in an irrational number. √2, √3, √5, etc. all result in nonterminating nonrepeating decimals. This development was once so controversial it cost a mathematician his life as Hipparchus showed his Pythagoreans colleagues that √2 was not a fraction, and therefore all was not number as they had previously believed every number could be written as a fraction. They were none too happy with him about this discovery.Quite often, a new number set was discovered and developed by inverting an operation on a simpler set(subtracting Naturals, dividing Integers, rooting Rationals.) Indeed, square rooting a negative number is not closed in the set of Reals, which leads to another larger number set denoted by C. We will learn these imaginary complex numbers in a later chapter.Review Unit 1Unit 1 Lesson 1 Notesheet 1.1 (Slope Triangles and x and yintercepts)Notesheet 1.2 (Linear Equations and Solving Systems of Equations)Unit 1 Lesson 8/22/2013 (Factoring Trinomials, Parallel Lines)Perpendicular Lines, Graphing ParabolasSolving absolute value EQuations and Quadratic EQuations
Last Modified on September 11, 2017