UCHS Advanced Algebra Honors

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#1:  No Put Downs!

#2:  No Sleeping!

#3:  Technology is a TOOL, not a TOY!

 

 

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Grade Weighting:

** Quizzes:  25%
** Tests:  50%
** Midterm & Final Exam:  25%

** Students may make corrections  for 1/2 credit back.

** Corrections may be made during flex or by appointment during Mrs. Nichols’ planning period (4th Block).  Corrections MAY NOT be made during regular class time.

 

 

 

 

 

Tool+Time+Logo

 

Supplies Needed:

Essential:  Paper & Pencil – whatever kind works best for you.

Helpful (but will have access to some in classroom):  TI-30XS Multiview Calculator

 

 

 

 

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GSE Advanced Algebra (Standards)

Cheat Sheets

Algebra Cheat Sheet

 

 

Unit 1: Polynomial and function operations

math_polynomials

CCGPS Advanced Algebra Standards:

MCC9-12.A.SSE.1, MCC9-12.A.SSE.1a, MCC9-12.A.SSE.1b, MCC9-12.A.SSE.2, MCC9-12.A.APR.1, MCC9-12.A.APR.5

 

 

Content Vocabulary: (Be able to define)

Advanced Algebra Unit 1 Quizlet Flashcards

Coefficient – a number multiplied by a variable

Degree – the greatest exponent of its variable

Binomial – an algebraic expression of the sum or the difference of two terms

Trinomial – an algebraic expression of the sum or the difference of three terms

Expression – A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Function – a special relationship where each input has a single output

Composite function  – a function obtained from two given functions, where the range of one function is contained in the domain of the second function, by assigning to an element in the domain of the first function that element in the range of the second function whose inverse image is the image of the element.

Pascal’s Triangle – an arrangement of the values of n  are in a triangular pattern where each row corresponds to a value of n

Polynomial – a mathematical expression involving a sum of nonnegative integer powers in one or more variables multiplied by coefficients.

Inverse – a function that “reverses” another function

 

 

Essential Questions: (Be able to answer)

What is a polynomial?

What characteristics are used to describe polynomials?

How do you add polynomials?

How do you subtract polynomials?

How do you multiply polynomials?

What is Pascal’s Triangle and how does it apply to polynomials?

How is composition of functions done?

What is an inverse?

How do you prove two functions are inverses of each other?

 

 

Objectives: (Be able to do)

Use the definition of a polynomial to identify polynomials

Interpret the structure and parts of a polynomial expression including terms, factors, and coefficients

Simplify polynomial expressions by performing operations, applying the distributive property, and combining like terms

Perform arithmetic operations on polynomials and understand how closure applies under addition, subtraction, and multiplication

Use Pascal’s Triangle to determine coefficients of binomial expansion:

FOCUS – determine volume of cube with binomial sides.

Find compositions of functions

Determine the inverse of a function

Determine if two functions are inverses of each other

 

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Adding Polynomials Video

Subtracting Polynomials Video

Multiplying Monomials Video

Multiplying Binomials Video

Multiplying Trinomials Video

Binomial Expansion Video

Writing Polynomials in Standard Form Video Tutorials and Examples

Adding and Subtracting Polynomials Video Tutorials and Examples

Multiplying Polynomials Video Tutorials and Examples

Raising a Binomial to a Power Video Tutorials and Examples

How Do You Find f(x) When the Value for x Contains Other Variables? Video

How Do You Find the Sum of Two Functions? Video

Operations on Functions & Composition of Functions Video

Composition of Functions Video

What’s the Inverse of a Relation? Video

Inverse Functions – The Basics! Video

Using Composition to Prove that Two Functions are Inverses Video

 

Print

 

Adding Polynomials Online Practice

Subtracting Polynomials Online Practice

Multiplying by a Monomial Online Practice

Multiplying Binomials Online Practice

Multiplying Mixed Polynomials Online Practice

Applications of Polynomial Operations Online Practice

 

 

Unit 2: Radicals 

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CCGPS Advanced Algebra Standards:

MCC9-12.A.CED.2, MCC9-12.A.REI.2, MCC9-12.A.REI.11, MCC9-12.F.IF.5, MCC9-12.F.IF.7, MCC9-12.F.IF.1b, MCC9-12.F.IF.9, MCC9-12.N.CN.8

 

 

Content Vocabulary:  (Be able to define)

Advanced Algebra Units 2 & 3 Quizlet Flashcards

Domain – The set of values of the independent variable(s) for which a function or relation is defined

Range – The set of y-values (or output values) of a function or relation:  the dependent variable(s)

Extraneous Solution – A solution of the simplified form of the equation that does not satisfy the original equation

Radical expression – any expression containing a radical

Radical equation – any equation containing a radical expression

Square root – a number that produces a specified quantity when multiplied by itself

Cube root – the number that produces a given number when cubed

 

Essential Questions:  (Be able to answer)

What is the difference between exact value and approximate value when referring to radical expressions?

When does a radical expression lead to a complex number?

How do polynomial operations apply to radical expressions?

How do you determine whether a solution is an extraneous solution?

What is a conjugate?

How do you graph radical function?

How does the domain of a radical function impact its graph?

 

 

Objectives: (Be able to do)

Simplify radical expressions

Solve equations involving radicals:  FOCUS – radicals on both sides / square once

Understand that not all solutions generated algebraically are actually solutions to the equations and extraneous solutions will be explored

Graph radical functions:  FOCUS on domain and range

Use the definition complex numbers to distinguish between real and complex numbers

Perform operations with complex numbers

 

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Simplifying Radicals Video #1

Simplifying Radicals Video #2

Multiplying Radicals Video

How to Rationalize a Denominator Video

Adding Radicals Video

Subtracting Radicals Video #1

Subtracting Radicals Video #2

Simplifying Radicals Tutorials and Examples

Simplifying Radicals Tutorials and Examples Part 2

Adding and Subtracting Radicals Tutorials and Examples

Multiplying and Dividing Radicals Tutorials and Examples

 

Print

Simplifying Radicals Online Practice

Mixed Radical Operations Online Practice

Simplifying Square Roots Involving Negatives Online Practice

 

 

 

Unit 3:  Complex Numbers

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Content Vocabulary:  (Be able to define)

Complex number – a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation x² = −1, that is, i² = −1.

Real part – for a complex number a + bi, the real part is a

Imaginary part – The coefficient of i in a complex number. For a complex number a + bi, the imaginary part is b.

Modulus of a Complex Number (aka Absolute Value) – The distance between a complex number and the origin on the complex plane.

 

Essential Questions:  (Be able to answer)

When does a radical expression lead to a complex number?

How do polynomial operations apply to complex numbers?

What is a complex conjugate?

 

Objectives: (Be able to do)

Use the definition complex numbers to distinguish between real and complex numbers

Perform operations with complex numbers

Find the modulus or absolute value of a complex number

 

Print

 

Adding and Subtracting Complex Numbers Online Practice

Complex Numbers Online Practice

Powers of i Online Practice

Multiplying and Dividing Complex Numbers Online Practice

Unit 4: Factoring and Solving Quadratics

GCF

CCGPS Advanced Algebra Standards:

MCC9-12.A.CED.1, MCC9-12.A.REI.11, MCC9-12.F.IF.4, MCC9-12.F.IF.7, MCC9-12.F.IF.9, MCC9-12.A.SSE.1a, MCC9-12.A.SSE.2

 

 

Content Vocabulary:  (Be able to define)

Advanced Algebra Unit 4 Quizlet Flashcards

Factora number or quantity that when multiplied with another produces a given number or expression

Factor of a polynomial (P(x)) – any polynomial which divides evenly into P(x)

Perfect square – the product of a rational number multiplied by itself

Perfect cube – the product of a rational number multiplied by itself three times

Quadratic –  An equation, graph, or data that can be modeled by a degree 2 polynomial.

Quadratic Formula – A formula for the roots of a quadratic equation.

Completing the Square – A technique used to solve quadratic equations by creating a perfect square.

 

 

Essential Questions:(Be able to answer)

What methods can be used for factoring polynomials?

How do you determine which method of factoring to use?

How can factoring methods be used to simplify rational expressions?

How can factoring methods be used to solve rational equations?

What is the difference between rational expressions and rational equations?

How do you determine whether a solution is an extraneous solution?

 

 

Objectives: (Be able to do)

Classify polynomials to determine factoring stategies

Interpret the structure and parts of a polynomial expression including terms, factors, and coefficients

Factor using greatest common factor

Factor using grouping

Factor trinomials

Factor difference of squares

Factor difference and sum of cubes

Identify Rational Functions

Apply factoring techniques to rational expressions and equations

Determine rational numbers extend the arithmetic of integers by allowing division by all numbers except zero

Rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial

Notice the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers

Solve equations involving rational functions

Understand that not all solutions generated algebraically are actually solutions to the equations and extraneous solutions will be explored

Graph rational functions:  FOCUS – vertical asymptotes

 

 

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What’s the Zero Product Property? Video

How Do You Solve a Quadratic Equation by Factoring? Video

Square Root Method Video

Square Root Method Video #2

Completing the Square Video

Discriminant Video

Quadratic Formula Video

Deriving the Quadratic Formula Video

Factoring Video Tutorials and Examples

 

Print

 

Factoring Trinomials with Leading Coefficient of 1 Online Practice

Factoring out GCF Online Practice

Factoring Difference of Squares Online Practice

Mixed Factoring Online Practice

Solving Quadratics by Factoring Online Practice

Solving Quadratics Online Practice

Solving Quadratics Online Practice 2

Quadratic Formula Online Practice

 

 

 

Unit 5: Rational Expressions and Equations

Don't+Argue+with+Irrational+Numbers

 

 

CCGPS Advanced Algebra Standards:

MCC9-12.A.CED.1, MCC9-12.A.REI.11, MCC9-12.F.IF.4, MCC9-12.F.IF.7, MCC9-12.F.IF.9, MCC9-12.A.SSE.1a, MCC9-12.A.SSE.2

 

 

Content Vocabulary:  (Be able to define)

Rational expression – a fraction in which the numerator and/or the denominator are polynomials

Common denominator – a shared multiple of the denominators of several fractions

Simplify – To use the rules of arithmetic and algebra to rewrite an expression as simply as possible (with no common factors)

Reciprocal – a fraction flipped upside down:  multiplicative inverse means the same thing as reciprocal.

Rational equation – an equation in which one or more of its term is a fraction

Extraneous solution – a solution of the simplified form of the equation that does not satisfy the original equation

 

 

Essential Questions:(Be able to answer)

How can factoring methods be used to simplify rational expressions?

When is it necessary to find common denominators for rational expressions and/or equations?

How do you find common denominators for rational expressions and/or equations?

How can factoring methods be used to solve rational equations?

What is the difference between rational expressions and rational equations?

How do you determine whether a solution is an extraneous solution?

 

 

Objectives: (Be able to do)

Identify Rational Functions

Apply factoring techniques to rational expressions and equations

Determine rational numbers extend the arithmetic of integers by allowing division by all numbers except zero

Rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial

Notice the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers

Solve equations involving rational functions

Understand that not all solutions generated algebraically are actually solutions to the equations and extraneous solutions will be explored

Find common denominators when adding and subtracting rational expressions.
Find common denominators when solving rational equations.

 

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Simplifying Rational Expressions Video #1

Simplifying Rational Expressions Video #2

Multiplying Rational Expressions Video #1

Multiplying Rational Expressions Video #2

Dividing Rational Expressions Video #1

Dividing Rational Expressions Video #2

 Finding LCD of a Rational Expression Video

Adding Rational Expressions Video

Subtracting Rational Expressions Video

Complex Expression Video #1

Complex Expression Video #2

 

Print

 

Simplifying Rational Expressions Online Practice

Multiplying Rational Expressions Online Practice

Dividing Rational Expressions Online Practice

Adding and Subtracting Rational Expressions Online Practice

Complex Fractions Online Practice

 

 

Unit 6: Solving  Polynomials

&

Systems of Equations

poly1

CCGPS Advanced Algebra Standards:

MCC9-12.N.CN.9, MCC9-12.A.APR.2, MCC9-12.A.APR.3, MCC9-12.A.REI.11, MCC9-12.F.IF.7, MCC9-12.F.IF.7c

Content Vocabulary:  (Be able to define)

Advanced Algebra Unit 4 Quizlet Flashcards

Zero of a polynomial – a number that, when plugged in for the variable, makes the function equal to zero

Root of a polynomial –  a number that, when plugged in for the variable, makes the function equal to zero

Complex roots – a root of a polynomial function that contains a complex number

Complex Conjugate – each of two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign.

Synthetic division – a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case

Remainder – the part left over after long division or synthetic division

Even function – a  function with a graph that is symmetric with respect to the y-axis.  A function is even if and only if  f(–x) = f(x).

Odd function – a  function with a graph that is symmetric with respect to the origin.  A function is odd if and only if  f(–x) = –f(x).

Essential Questions: (Be able to answer)

What is the difference between synthetic division and long division?

What is the significance of a zero remainder in polynomial division?

What is the relationship between the solutions to polynomial equations and the intersection of their graphs?

What is the relationship between the degree of a polynomial and the number of possible zeros?

What is the difference between a real root and complex root of a polynomial function?

How can a polynomial be written if the real and complex roots are known?

What is the significance of the solution to a system of equations (algebraically & graphically)?

 

Objectives:  (Be able to do)

Determine whether a polynomial is even, odd or neither.

Use the remainder in polynomial division to determine whether a binomial is a factor of the polynomial.

Use the degree of a polynomial to determine the possible number of zeros.

Write the polynomial function given its real and complex roots.

Find the solution to systems of equations algebraically and graphically.

FOCUS:  Using graph and/or equations of linear and quadratic to find solutions.

 

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Synthetic Division Video

What’s the Zero Product Property? Video

How Do You Find All the Rational Zeros of a Polynomial Function? Video

What is the Factor Theorem? Video

What is the Fundamental Theorem of Algebra? Video

Print

 

Solving Polymomials Online Practice

Solving Systems of Equations Online Practice

 

 

 

 

Unit 7: Graphing Polynomials

polynomial-and-thier-graphs-1-728

CCGPS Advanced Algebra Standards:

MCC9-12.A.CED.1, MCC9-12.A.REI.11, MCC9-12.F.IF.4, MCC9-12.F.IF.7, MCC9-12.F.IF.9, MCC9-12.A.SSE.1a, MCC9-12.A.SSE.2

Content Vocabulary:  (Be able to define)

Relative maximum – the highest point in a particular section of a graph

Relative minimum – the lowest point in a particular section of a graph

Asymptote – a line or curve that the graph of a relation approaches more and more closely the further the graph is followed.

Essential Questions:(Be able to answer)

 

Objectives: (Be able to do)

 

Graph rational functions:  FOCUS – vertical asymptotes

Unit 8: Exponentials and Logarithms

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CCGPS Advanced Algebra Standards:

MCC9-12.A.SSE.3, MCC9-12.A.SSE.3c, MCC9-12.F.IF.7, MCC9-12.F.IF.7e, MCC9-12.F.IF., MCC9-12.F.IF.8b, MCC9-12.F.BF.5, MCC9-12.F.LE.4

Content Vocabulary:   (Be able to define)

Advanced Algebra Unit 5 Quizlet Flashcards

Exponential expression – a mathematical expression consisting of a constant raised to some power

Exponential equations – an equation involving exponential functions of a variable

Logarithmic expression – the power to which a base, such as 10, must be raised to produce a given number.

Logarithmic equation – an equation involving logarithmic functions of a variable

Exponential base – the number that is raised to various powers to generate the principal counting units of a number system.

Logarithmic base – the number raised to the logarithm of a designated number in order to produce that designated number

Exponential growth – growth whose rate becomes ever more rapid in proportion to the growing total number or size.

Exponential decay – decay in which the total value decreases but the proportion that leaves remains constant over time

Common logarithm – a logarithm to the base 10

Natural logarithm – a logarithm to the base e (2.71828…)

Essential Questions: (Be able to answer)

What is a logarithm?

What is an exponential?

How are logarithms and exponentials related algebraically and graphically? (emphasize inverse relationship)

What determines whether an exponential function will demonstrate growth or decay?

How can exponential equations be rewritten as logarithmic equations?

How can logarithmic equations be rewritten as exponential equations?

How can logarithmic expressions be expanded and condensed?

How can exponential equations be solved?

How can logarithmic equations be solved?

What are the domain restrictions for logarithmic equations?

Objectives:  (Be able to do)

Review exponential functions and their graphs

Explore exponential growth and decay

Develop the concept of a logarithm as an exponent along with the inverse relationship with exponents:

FOCUS – converting between logarithmic & exponential form

Define the difference between common logarithms and natural logarithms

Define and apply properties of logarithms:  FOCUS – expand and condense

Develop the change of base formula

 

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Print

Writing in Exponent Form Online Practice

Algebraic Exponents Online Practice

Applied Exponents Online Practice

Exponential and Logarithm Online Practice

Logarithms Regents Online Practice

Logarithms Online Practice

Logarithmic Equations Online Practice

 

 

 

 

Unit 9: Statistical Inferences

deviation

CCGPS Advanced Algebra Standards:

Pacing: 1 day

Content Vocabulary:

Essential Questions:

Objectives:

Compare the standard deviations of two data sets

 

 

 

Below is a curve fitting simulation.  It requires Java.

Least-Squares Regression

Click to Run

 

 

 

Below is a curve fitting simulation.  It requires Java.

Curve Fitting

Click to Run