Algebra II Syllabus

Angel Website:  http://pcps.myelearning.org/frameIndex.htm
Angela Schmit's Website:  http://manila.esu4.org/angelaschmit/

Algebra II Quizaroo's:  http://www.geocities.com/ojjk/indexaq.html

Course Syllabus

Description of Course

Prerequisites

• Algebra I (one full academic year)

The Objectives of the Course

• Understand and realize the value of the symbolism of algebra language.
• Use the language of algebra as a natural way of expressing mathematical ideas.
• Help students become independent thinking using various learning strategies.
• Learn through "trial and error" and realize that real learning takes place through asking questions, trying guesses, starting down false paths, and trying new methods of approach to algebraic problems.
• Learn problem solving strategies that can help with algebra, as well as other academic courses.
• Appreciate the power of mathematics and see the connections mathematics has with other subject areas, as well as everyday and career applications.
• Improve students' thinking skills, use them more effectively, and acquire additional skills.

Texts

Explanation of Instruction

• Lecture and discussion every day.
• Quizzes every two or three lessons.
• Tests after every unit.
• Spelling/Writing assignments as needed.
• Angel Website--On-Line Learning
  

Visual Aids, Utilized Films, Film Strips, Etc.

• Marker board
• Calculators (Texas Instruments--TI 83, TI 85, and TI 92) provided by the school district
• Computer Software/Technology
• Supplementary Workbooks

Units and Contents

Chapter 1:  Basic Concepts of Algebra

• Real Numbers and Their Graphs
  To graph real numbers on a number line, to compare numbers, and to find their absolute values
  
• Simplifying Expressions
  To review the methods used to simplify numerical expressions and to evaluate algebraic expressions
  
• Basic Properties of Real Numbers
  To review properties of equality of real numbers and properties for adding and multiplying real numbers
  
• Sums and Differences
  To review the rules for adding and subtracting real numbers
  
• Products
  To review rules for multiplying real numbers
  
• Quotients
  To review rules for dividing real numbers
  
• Solving Equations in One Variable
  To solve certain equations in one variable
  
• Words into Symbols
  To translate word phrases into algebraic expressions and word sentences into equations
  
• Problem Solving with Equations
  To solve word problems by using equations in one variable
  

Chapter 2:  Inequalities and Proof

• Solving Inequalities in One Variable
  To solve simple inequalities in one variable
  
• Solving Combined Inequalities
  To solve conjunctions and disjunctions
  
• Problem Solving Using Inequalities
  To solve word problems by using inequalities in one variable
  
• Absolute Value in Open Sentences
  To solve open sentences involving absolute value
  
• Solving Absolute Value Sentences Graphically
  To use number lines to obtain quick solutions to certain equations and inequalities involving absolute value
  
• Theorems and Proof
  To use axioms, definitions, and theorems to prove some properties of real numbers
  
• Theorems about Order and Absolute Value
  To prove theorems about inequalities and absolute value
  

Chapter 3:  Linear Equations and Functions

• Open Sentences in Two Variables
  To find solutions of open sentences in two variables and to solve problems involving open sentences in two variables
  
• Graphs of Linear Equations in Two Variables
  To graph a linear equation in two variables
  
• The Slope of a Line
  To find the slope of a line and to graph a line given its slope and a point on it
  
• Finding an Equation of a Line
  To find an equation of a line given its slope and a point on the line, or two points, or its slope and the y-intercept
  
• Systems of Linear Equations in Two Variables
  To solve systems of linear equations in two variables
  
• Problem Solving:  Using Systems
  To use systems of equations to solve problems
  
• Linear Inequalities in Two Variables
  To graph linear inequalities in two variables and systems of such inequalities
• Functions
  To find values of functions and to graph functions
• Linear Functions
  To find equations of linear functions and to apply properties of linear functions
• Relations
  To graph relations and to determine when ralations are also functions
  

Chapter 4:  Products and Factors of Polynomials

• Polynomials
  To simplify, add, and subtract polynomials
  
• Using Laws of Exponents
  To use laws of exponents to multiply a polynomial by a monomial
  
• Multiplying Polynomials
  To multiply polynomials
  
• Using Prime Factorization
  To find the GCF and LCM of integers and monomials
  
• Factoring Polynomials
  To factor polynomials by using the GCF, by recognizing special products, and by grouping terms
  
• Factoring Quadratic Polynomials
  To factor quadratic polynomials
  
• Solving Polynomial Equations
  To solve polynomial equations
  
• Problem Solving Using Polynomial Equations
  To solve problems using polynomial equations
  
• Solving Polynomial Inequalities
  To solve polynomial inequalities
  

Chapter 5:  Rational Expressions

• Quotients of Monomials
  To simplify quotients using the laws of exponents
  
• Zero and Negative Exponents
  To simplify expressions involving the exponent zero and negative integral exponents
  
• Scientific Notation and Significant Digits
  To sue scientific notation and significant digits
  
• Rational Algebraic Functions
  To simplify rational algebraic expressions
  
• Products and Quotients of Rational Expressions
  To multiply and divide rational expressions
  
• Sums and Differences of Rational Expressions
  To add and subtract rational expressions
  
• Complex Fractions
  To simplify complex fractions
  
• Fractional Coefficients
  To solve equations and inequalities having fractional coefficients
  
• Fractional Equations
  To solve and use fractional equations
  

Chapter 6:  Irrational and Complex Numbers

• Roots of Real Numbers
  To find the roots or real numbers
  
• Properties of Radicals
  To simplify expressions involving radicals
  
• Sums of Radicals
  To simplify expressions involving sums of radicals
  
• Binomials Containing Radicals
  To simplify products and quotients of binomials that contain radicals
  
• Equations Containing Radicals
  To solve equations containing radicals
  
• Rational and Irrational Numbers
  To find and use decimal representations of real numbers
  
• The Imaginary Number i
  To use the number i to simplify square roots of negative numbers
  
• The Complex Numbers
  To add, subtract, multiply, and divide complex numbers
  

Chapter 7:  Quadratic Equations and Functions

• Completing the Square
  To solve quadratic equations by completing the square
  
• The Quadratic Formula
  To solve quadratic equations by using the quadratic formula
  
• The Discriminant
  To determine the nature of the roots of a quadratic equation by using the discriminant
  
• Equations in Quadratic Form
  To recognize and solve equations in quadratic form
  
• Graphing y - k = a (x - h)^2
  To graph parabolas whose equations have the form y-k = a (x-h)^2 and to find the vertices and axes of symmetry
  
• Quadratic Functions
  To analyze a quadratic function, draw its graph, and find its minimum or maximum value
  
• Writing Quadratic Equations and Functions
  to learn the relationship between the roots and coefficents of a quadratic equation and to write a quadratic equation or function using information about the roots of the graph
  

Chapter 8:  Variation and Polynomial Equations

• Direct Variation and Proportion
  To solve problems involving direct variation
  
• Inverse and Joint Variation
  To solve problems involving inverse and joint variation
  
• Dividing Polynomials
  To divide one polynomial by another polynomial
  
• Synthetic Division
  To use synthetic division to divide a polynomial by a first-degree binomial
  
• The Remainder and Factor Theorems
  To use the remainder and factor theorems to find factors of polynomials and to solve polynomial equations
  
• Some Useful Theorems
  To find or solve a polynomial equation with real coefficients and positive degree n by using these facts:  1)  There are exactly n roots; 2)  The imaginary roots occur in conjugate pairs; 3)  Descartes' rule of signs gives information about the number of positive and negative real roots
  
• Finding Rational Roots
  To find rational roots of polynomial equations with integral coefficients
  
• Approximating Irrational Roots
  To apporximate the real roots of a polynomial equation P(X) = 0 by using the graph of y= P(X)
  
• Linear Interpolation
  To use linear interpolation to find values not listed in a given table of data
  

Chapter 9:  Analytic Geometry

• Distance and Midpoint Formulas
  To find the distance between any two points and the midpoint of the line segment joining them
  
• Circles
  To lean the relationship between the center and radius of a circle and the equation of the circle
  
• Parabolas
  To learn the relationship between the focus, directrix, vertex, and axis of a parabola and the equation of the parabola
  
• Ellipses
  To learn the relationship between the center, foci, and intercepts of an ellipse and the equation of the ellipse
  
• Hyperbolas
  To learn the relationship between the foci, intercepts, and asymptotes of a hyperbola and the equation of the hyperbola
  
• More on Central Conics
  To find an equation of a conic section with center not at the origin and to identify a conic as a circle, ellipse, or hyperbola
  
• The Geometry of Quadratic Systems
  To use graphs to determine the number of real solutions of a quadratic system and to estimate the solutions
  
• Solving Quadratic Systems
  To use algebraic methods to find exact solutions of quadratic systems
  
• Systems of Linear Equations in Three Variables
  To solve systems of linear equations in three variables
  

Chapter 10:  Exponential and Logarithmic Functions

• Rational Exponents
  To extend the meaning of exponents to include rational numbers
  
• Real Number Exponents
  To extend the meaning of exponents to include irrational numbers and to define exponential functions
  
• Composition and Inverses of Functions
  To find the composite of two given functions and to find the inverse of a given function
  
• Definition of Logarithms
  To define logarithmic functions and to learn how they are realted to exponential functions
  
• Laws of Logarithms
  To learn and apply the basic properties of logarithms
  
• Applications of Logarithms
  To use common logarithms to solve equations involving powers and to evaluate logarithms with any given base
  
• Problem Solving:  Exponential Growth and Decay
  To use exponential and logarithmic functions to solve growth and decay problems
  
• The Natural Logarithmic Function
  To define and use the natural logarithm function
  

Chapter 11:  Sequences and Series

• Types of Sequences
  To determine whether a sequence is arithmetic, geometric, or neither and to supply missing terms of a sequence
  
• Arithmetic Sequences
  To find a formula for the nth term of an arithmetic sequence and to find specified terms of arithmetic sequences
  
• Geometric Sequences
  To find a formula for the nth term of a geometric sequence and to find specified terms of geometric sequences
  
• Series and Sigma Notation
  To identify series and to use sigma notation
  
• Sums of Arithmetic and Geometric Series
  To find sums of finite arithmetic and geometric series
  
• Infinite Geometric Series
  To find sums of infinite geomtric series having rations with absolute value less than one
  
• Powers of Binomials
  To expand powers of binomials
  
• The General Binomial Expansion
  To sue the binomial theorem to find a particular term of a binomail expansion
  

Chapter 12:  Triangle Trigonometry

• Angles and Degree Measure
  To use degrees to measure angles
  
• Trigonometric Functions of Acute Angles
  To define trigonometric functions of acute angles
  
• Trigonometric Functions of General Angles
  To define trigonometric functions of general angles
  
• Values of Trigonometric Functions
  To use a calculator or trigonometric tables to find values of trigonometric functions
  
• Solving Right Triangles
  To find the sides and angles of a right triangle
  
• The Law of Cosines
  To use the law of cosines to find sides and angles of triangles
  
• The Law of Sines
  To use the law of sines to find sides and angles of triangles
  
• Solving General Triangles
  To solve any given triangle
  
• Areas of Triangles
  To apply triangle area formulas
  

Chapter 13:  Trigonometric Graphs; Identities

• Radian Measure
  To use radians to measure angles
  
• Circular Functions
  To define the circular functions
  
• Periodicity and Symmetry
  To use periodicity and symmetry in graphing functions
  
• Graphs of Sine and Cosine
  To graph the sine, cosine, and related functions
  
• Graphs of the Other Functions
  To graph the tangent, cotangent, secant, cosecant, and related functions
  
• The Fundamental Identities
  To simplify trigonometric expressions and to prove identities
  
• Trigonometric Addition Formulas
  To use formulas for the sine and cosine of a sum or difference
  
• Double-Angle and Half-Angle Formulas
  To use the double-angle and half-angle formulas for the sine and cosine
  
• Formulas for the Tangent
  To use addition, double-angle, and half-angle formulas for the tangent
  

Chapter 14:  Trigonometric Applications

• Vector Operations
  To define vector operations and apply the resultant of two vectors
  
• Vectors in the Plane
  To find vectors in component form and to apply the dot product
  
• Polar Coordinates
  To define polar coordinates and graph polar equations
  
• The Geometry of Complex Numbers
  To plot complex numbers in the complex plane and to use the polar form of complex numbers
  
• De Moivre's Theorem
  To use De Moivre's theorem
  
• The Inverse Cosine and Inverse Sine
  To evaluate expressions involving the inverse cosine and inverse sine
  
• Other Inverse Functions
  To evaluate expressions involving the inverse trigonometric functions
  
• Trigonometric Equations
  To solve trigonometric equations
  

Chapter 15:  Statistics and Probability

• Presenting Statistical Data
  To display data using frequency distributions, hisitograms, and stem-and-leaf plots, and to compute measures of central tendency
  
• Analyzing Statistical Data
  To compute measures of dispersion and, together with measures of central tendency, to describe and compare distributions using these statistics
  
• The Normal Distribution
  To recognize and analyze normal distributions
  
• Correlation
  To draw a scatter plot, determine the correlation coefficient, and use the regression line for a set of ordered pairs of data
  
• Fundamental Counting Principles
  To apply fundamental counting principles
  
• Permutations
  To find the number of permutations of the elements of a set
  
• Combinations
  To find the combinations of a set of elements
  
• Sample Spaces and Events
  To specify sample spaces and events for random experiments
  
• Probability
  To find the probability that an event will occur
  
• Mutually Exclusive and Independent Events
  To identify mutually exclusive and independent events and find the probability of such events
  

Chapter 16:  Matrices and Determinants

• Definition of Terms
  To learn and apply matrix terminology
  
• Addition and Scalar Multiplication
  To find sums and differences of matrices and products of a scalar and a matrix
  
• Matrix Multiplication
  To find the product of two matrices
  
• Applications of Matrices
  To solve problems using matrices
  
• Determinants
  To find the determinant of a 2x2 or 3x3 matrix
  
• Inverses of Matrices
  To solve systems of equations using inverses of matrices
  
• Expansion of Determinants by Minors
  To evaluate third-order determinants using expansion by minors
  
• Properties of Determinants
  To sue the properties of determinants to simplify the expansion of determinants by minors
  
• Cramer's Rule
  To solve systems of equations using determinants
  

This Page was last update: Thursday, January 21, 2010 at 7:25:41 AM
This page was originally posted: 5/31/2006; 5:37:06 PM.
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