## A Student Should Be Able To:

Introduction to Graphs and the Graphing Calculator { REVIEW }*
· Plot points by hand and using a grapher
· Graph equations by hand and using a grapher
· Find the point(s) of intersection of two graphs
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

Chapter R Basic Concepts of Algebra { REVIEW }

R.1 The Real-Number System
· Identify various kinds of real numbers
· Use interval notation to write a set of numbers
· Identify the properties of real numbers
· Find the absolute value of a real number

R.2 Integer Exponents, Scientific Notation, and Order of Operations
· Simplify expressions with integer exponents
· Solve problems using scientific notation
· Use the rules for order of operations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

R.3 Addition, Subtraction, and Multiplication of Polynomials
· Identify the terms, coefficients, and degree of a polynomial
· Add, subtract, and multiply polynomials

R.4 Factoring
· Factor polynomials by removing the common factor
· Factor special products of polynomials

R.5 Rational Expressions
· Determine the domain of a rational expression
· Simplify rational expressions
· Multiply, divide, add, or subtract rational expressions
· Simplify complex rational expressions

R.6 Radical Notation and Rational Exponents
· Rationalize denominators or numerators in rational expressions
· Convert between exponential and radical notation
· Simplify expressions with rational exponents

R.7 The Basics of Equation Solving
· Solve linear and quadratic equations
· Solve a formula for a given variable

Chapter 1 Graphs, Functions, and Models

1.1 Functions, Graphs, and Graphers
· Determine whether a correspondence or relation is a function
· Find function values, or outputs, using a formula
· Find the domain and the range of a function
· Determine whether a graph is that of a functions
· Solve applied problems using functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

1.2 Linear Functions, Slope, and Applications
· Graph linear functions and equations, finding the slope
and the y-intercept
· Determine equations of lines
· Solve applied problems involving linear functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression
· Analyze a set of data to determine whether it can be modeled
by a linear function
· Fit a regression line to a set of data; then use the linear model
to make predictions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

1.4 More on Functions
· Graph functions, looking for intervals on which the function
is increasing, decreasing, or constant, and determine
relative maxima and minima
· Given an application, find a function formula that models the
application; find the domain of the function and function
values, and then graph the function
· Graph functions defined piecewise
· Find the sum, the difference, the product, and the quotient
of two functions, and determine their domains
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

1.5 Symmetry and Transformations
· Determine whether a graph is symmetric with respect to
the x-axis, the y-axis, and the origin
· Determine whether a function is even, odd, or neither
even nor odd
· Given the graph of a function, graph its transformation
under translations, reflections, stretchings, and shrinkings
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

1.6 Variation and Applications [ OPTIONAL ]**
· Find equations of direct, inverse, and combined variation
given values of the variables
· Solve applied problems involving variation

1.7 Distance, Midpoints, and Circles
· Find the distance between two points in the plane and find
the midpoint of a segment
· Find an equation of a circle with a given center and radius, and
given an equation of a circle, find the center and the radius
· Graph equations of circles
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

PROJECT #1

AND/OR

TEST #1 CHAPTERS R AND 1

Chapter 2 Functions and Equations: Zeros and Solutions

2.1 Zeros of Linear Functions and Models
· Find zeros of linear functions and solve linear equations
· Solve applied problems using linear models
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.2 The Complex Numbers
· Perform computations involving complex numbers
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.3 Zeros of Quadratic Functions and Models
equations by completing the square and by using
· Solve equations that are reducible to quadratic
· Solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.4 Analyzing Graphs of Quadratic Functions
· Find the vertex, the line of symmetry, and the maximum
or minimum value of a quadratic function using the
method of completing the square
· Solve applied problems involving maximum and minimum
function values
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression
· Fit quadratic functions to data and make estimates and predictions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.6 Zeros and More Equation Solving
· Solve rational and radical equations and equations with absolute
value and find zeros of their associated functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

2.7 Solving Inequalities
· Solve linear inequalities, using interval notation to express solution sets
· Solve compound inequalities
· Solve inequalities with absolute value
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

PROJECT #2

AND/OR

TEST #2 CHAPTER 2

Chapter 3 Polynomial and Rational Functions

3.1 Polynomial Functions and Modeling
· Use a grapher to graph a polynomial function and find its
real-number zeros relative maximum and minimum
values, and domain and range
· Solve applied problems using polynomial models
· Fit linear, quadratic, power, cubic, and quartic polynomial
functions to date and make predictions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

3.2 Polynomial Division; The Remainder and Factor Theorems
· Perform long division with polynomials and determine whether one polynomial is a factor of another
· Use synthetic division to divide a polynomial by (x - c)
· Use the remainder theorem to find a function value f(c)
· Use the factor theorem to determine whether (x - c) is a factor of f(x)
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

3.3 Theorems about Zeros of Polynomial Functions
· Factor polynomial functions and find the zeros of their multiplicities
· Find a polynomial with specified zeros
· Find a polynomial function with integer coefficients, find the rational
zeros and the other zeros, if possible with this level of algebra
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

3.4 Rational Functions
· Graph a rational function, identifying all asymptotes
· Solve applied problems involving rational functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

3.5 Polynomial and Rational Inequalities
· Solve polynomial and rational inequalities
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

PROJECT #3

AND/OR

TEST #3 CHAPTER 3

Chapter 4 Exponential and Logarithmic Functions

4.1 Composite and Inverse Functions
· Find the composition of two functions and the domain of the
composition; decompose a function as a composition
of two functions
· Determine whether a function is one-to-one, and if it is, find a
formula for its inverse
· Simplify expressions of the type (f • f -1)(x) and (f -1 • f)(x)
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

4.2 Exponential Functions and Graphs
· Graph exponential equations and functions
· Solve applied problems involving exponential functions and their graphs
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

4.3 Logarithmic Functions and Graphs
· Graph logarithmic functions
· Convert between exponential and logarithmic equations
· Find common and natural logarithms using a grapher
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

4.4 Properties of Logarithmic Functions
· Convert from logarithms of products, powers, and quotients to
expressions in terms of individual logarithms, and conversely
· Simplify expressions of the type loga(ax) and alogax
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

4.5 Solving Exponential and Logarithmic Equations
· Solve exponential and logarithmic equations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

4.6 Applications and Models: Growth and Decay
· Solve applied problems involving exponential growth and decay
· Find models involving exponential and logarithmic functions
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

PROJECT #4

AND/OR

TEST #4 CHAPTER 4

Chapter 5 Systems of Equations and Matrices

5.1 Systems of Equations in Two Variables
· Solve a system of two linear equations in two variables by graphing
· Solve a system of two linear equations in two variables by using
the substitution and the elimination methods
· Use systems of two linear equations to solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.2 Systems of Equations in Three Variables
· Solve systems of linear equations in three variables
· Use systems of three equations to solve applied problems
· Model a situation using a quadratic function
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.3 Matrices and Systems of Equations
· Solve systems of equations using matrices
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.4 Matrix Operations
· Add, subtract, and multiply matrices when possible
· Write a matrix equation equivalent to a systems of equations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.5 Inverses of Matrices
· Find the inverse of a square matrix, if it exists
· Use inverses of matrices to solve systems of equations
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.6 Systems of Inequalities and Linear Programming
· Graph linear inequalities
· Graph systems of linear inequalities
· Solve linear programming problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

5.7 Partial Fractions [ OPTIONAL ]
· Decompose rational expressions into partial fractions

PROJECT #5

AND/OR

TEST #5 CHAPTER 5

Chapter 6 Conic Sections

6.1 The Parabola
· Given an equation of a parabola, complete the square, if necessary,
and then find the vertex, the focus, and the directrix and
graph the parabola
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

6.2 The Circle (and the Ellipse [ OPTIONAL ])
· Given an equation of a circle, complete the square, if necessary,
and then find the center and the radius and graph the circle
· Given an equation of an ellipse, complete the square, if necessary,
and then find the center, the vertices, and the foci and graph
the ellipse

6.3 The Hyperbola [ OPTIONAL ]
· Given an equation of a hyperbola, complete the square, if necessary,
and then find the center, the vertices, and the foci and graph
the hyperbola

6.4 Nonlinear Systems of Equations
· Solve a nonlinear system of equations
· Use nonlinear systems of equations to solve applied problems
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

Chapter 7 Sequences, Series, and Combinatorics

7.1 Sequences and Series
· Find terms of sequences given the nth term
· Look for a pattern in a sequence and try to determine a general term
· Convert between sigma notation and other notation for a series
· Construct the terms of a recursively defined sequence
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

7.2 Arithmetic Sequences and Series
· For any arithmetic sequences, find the nth term when n is given
and n when the nth term is given, and given two terms,
find the common difference and construct the sequence
· Find the sum of the first n terms of an arithmetic sequence
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

7.3 Geometric Sequences and Series
· Identify the common ratio of a geometric sequence, and find
a given term and the sum of the first n terms
· Find the sum of an infinite geometric series, if it exists
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

PROJECT #7

7.4 Mathematical Induction [ OPTIONAL ]
· List the statements of an infinite sequence that is defined by a formula
· Do proofs by mathematical induction

7.5 Combinatorics: Permutations [ OPTIONAL ]
· Evaluate factorial and permutation notation and solve
related applied problems

7.6 Combinatorics: Combinations
· Evaluate combination notation and solve related applied problems

7.7 The Binomial Theorem
· Expand a power of a binomial using Pascal's triangle or factorial notation
· Find a specific term of a binomial expansion
· Find the total number of subsets of a set of n objects
FINISH THE ASSIGNMENT OF ALL ODD EXERCISES

7.8 Probability [ OPTIONAL ]
· Compute the probability of a simple event

PROJECT #6

AND/OR

TEST #6 CHAPTERS 6 AND 7

Appendixes [ OPTIONAL ]

A Descartes' Rule of Signs
· Use Descartes' rule of signs to find information about the number
of real zeros of a polynomial function with real coefficients

B Determinants and Cramer's Rule [ OPTIONAL ]
· Evaluate determinants of square matrices
· Use Cramer's rule to solve systems of equations

C Parametric Equations [ OPTIONAL ]
· Graph parametric equations and determine an equivalent rectangular
equation
· Determine parametric equations for a rectangular equation