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Algebra 2 - Block G


Solutions to Practice Test Posted below

Topics Covered on Second Semester Algebra 2 Final

 

Chapter 6 – Exponential and Logarithmic Function

Section 6.6 – Scientific Notation

Section 6.7 – Exponential Functions Solved by Brute Force

Section 6.8 – Exponential Functions Solved by Logarithms

Section 6.9 – Logarithms with Other Bases

Section 6.10 – Properties of Logarithms

Section 6.11 – Proofs of Properties of Logarithms

Section 6.12 – Inverses of Functions – The Logarithmic Function

Section 6.14 – Exponential Functions and Other Functions as Mathematical Models

 

Chapter 7 – Rational Algebraic Functions

Section 7.1 – Introduction to Rational Algebraic Functions

Section 7.2 – Rational Function Graphs – Discontinuities and Asymptotes

Section 7.3 – Special Products and Factoring

Section 7.4 – More Factoring and Graphing

Section 7.5 – Long Division of Polynomials

Section 7.7 - Products and Quotients of Rational Expressions

Section 7.8 – Sums and Differences of Rational Expressions

Section 7.10 – Fractional Equations and Extraneous Solutions

 

Chapter 8 – Irrational Algebraic Functions

Section 8.1 – Introduction to Rational Algebraic Functions

Section 8.2 – Graphs of Irrational Functions

Section 8.3 – Radicals and Simple Radical Form

Section 8.4 – Radical Equations

 

Chapter 9 – Quadratic Relations and Systems

Section 9.1 – Introduction to Quadratic Relations

Section 9.2 – Circles

Section 9.3 - Ellipses

Section 9.4 - Hyperbolas

Section 9.5 - Parabolas

Section 9.6 – Equations from Geometric Definitions

 

Chapter 12 – Probability

Section 12.1 – Introduction to Probability

Section 12.2 – Words Associated with Probability

Section 12.3 – Two Counting Principles

Section 12.4 – Probabilities of Various Permutations

Section 12.5 – Probabilities of Various Combination

Section 12.6 – Properties of Probabilities

 

Chapter 7 & 8 Test - Tuesday March 27, 2012

Practice Test and Solutions posted below
 

Topics Covered on Chapter 7 & 8 Test 

Each Colored Item is a link to a video - the same color links go to the same video. 

Chapter 7 - Rational Algebraic Functions

Section 7.1 – Introduction to Rational Algebraic Functions

-      Definition of a rational algebraic function(def. # 74)

-      Objective: pointwise plotting of the graph of a rational function


Section 7.2 – Rational Function Graphs – Discontinuities andAsymptotes

-      Objective: simplify a rational algebraicfunction, find the discontinuities, and graph it.

 

Section 7.3 – Special Products and Factoring

-      Product of Conjugate Binomials (def. # 75)

-       Products of any polynomials (p.329)

-      Completely Factored Form (def. #76)

-      Objectives: be able to

o  Multiply conjugate binomials

o   Factor a difference of two squares

o  Multiply polynomials with more than two terms

o  Factor quadratic trinomials

 

Section 7.4 – More Factoring and Graphing

                -       Factoring a sum or difference of two cubes (p. 336, def. # 77)   


-      Discriminant test for prime quadratics (p. 337,def. # 79)

-      Objectives: be able to factor a sum ordifference of two cubes, determine whether a quadratic trinomial is prime – ifit is not prime, be able to factor it by inspection or splitting the middleterm.

 

Section 7.5 – Long Division of Polynomials

                - Objective: be able to perform long division on a polynomial, and use the results to factor and graph the polynomial.

 

Section 7.7 – Products and Quotients of Rational Expressions

-      Objective: be able to multiply or divide severalrational expressions and simplify the result.

-      Definition of a simplified rational expression(def. # 80)

-      Definition of canceling (def. # 81)

 

Section 7.8 – Addition and Subtration of RationalExpressions

-      Objective: be able to add or subtract severalrational expressions and simplify the result.

 

Section 7.10 – Fractional Equations and Extraneous Solutions

-      Objective: be able to solve fractionalequations.

-      Technique summary (p.379)

 

  

Chapter 8 - Irrational Algebraic Functions

Section 8.1 - Introduction to Irrational Algebraic Functions

            -        Objective: Learn things about an irrational algebraic functions by piecewise plotting and other techniques


Section 8.2 - Graphs of Irrational Functions

            -        Objective: Given the graph of an irrational algebraic function, find f(x) when x is given and find x when f(x) is given, and plot the graph.


Section 8.3 - Radicals and Simple Radical Form

            -        Objective: Given an expression containing radicals, be able to write it in as simple a form as possible without actually evaluating it.

            -        An expression is in simplified radical form if

                       1)  the radicand of an nth root contains no nth powers as factors

                       2)  the root index is as low as possible

                       3)  there are no radicals in the denominator


Section 8.4 - Radical Equations

            -        Objective:  Given a radical equation, be able to find its solution set, discarding any extraneous solutions.

            -        Radical equation definition (p.425)

            -        Flow Chart for solving radical equations (p.427)


You can have one 4 x 6 notecard and you may use your calculator. You MUST show your work for 

full credit especially on problems where you used a calculator.


Note – read and review sections 7.1 - 7.5 and 7.7 , 7.8, 7.10, & 8.1 - 8.4 in your textbook especially any sections you are unsure about.  Look over all your homework, notes, and warm-up problems. Work the practice test posted below.  Solutions are posted also Another great resource is MathXL.  Select "STUDY PLAN" and then look at the problems from rational and irrational algebraic functions.  Please see me if you have any questions about this material.


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