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
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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
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R.3 Addition, Subtraction, and Multiplication of Polynomials
· Identify the terms, coefficients, and degree of a polynomial
· Add, subtract, and multiply polynomials
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R.4
Factoring
· Factor polynomials by removing the common factor
· Factor special products of polynomials
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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
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R.6 Radical Notation and Rational Exponents
· Simplify radical expressions
· Rationalize denominators or numerators in rational expressions
· Convert between exponential and radical notation
· Simplify expressions with rational exponents
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R.7 The Basics of Equation Solving
· Solve linear and quadratic equations
· Solve a formula for a given variable
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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
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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
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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
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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
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1.6 Variation and Applications [ OPTIONAL ]**
· Find equations of direct, inverse, and combined variation
given values of the variables
· Solve applied problems involving variation
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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
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2.2 The Complex Numbers
· Perform computations involving complex numbers
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2.3 Zeros of Quadratic Functions and Models
· Find zeros of quadratic functions and solve quadratic
equations by completing the square and by using
the quadratic formula
· Solve equations that are reducible to quadratic
· Solve applied problems
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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
· Graph quadratic functions
· Solve applied problems involving maximum and minimum
function values
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2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression
· Fit quadratic functions to data and make estimates and predictions
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2.6 Zeros and More Equation Solving
· Solve rational and radical equations and equations with absolute
value and find zeros of their associated functions
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2.7 Solving Inequalities
· Solve linear inequalities, using interval notation to express solution sets
· Solve compound inequalities
· Solve inequalities with absolute value
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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
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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)
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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
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3.4 Rational Functions
· Graph a rational function, identifying all asymptotes
· Solve applied problems involving rational functions
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3.5 Polynomial and Rational Inequalities
· Solve polynomial and rational inequalities
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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)
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4.2 Exponential Functions and Graphs
· Graph exponential equations and functions
· Solve applied problems involving exponential functions and their graphs
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4.3 Logarithmic Functions and Graphs
· Graph logarithmic functions
· Convert between exponential and logarithmic equations
· Find common and natural logarithms using a grapher
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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
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4.5 Solving Exponential and Logarithmic Equations
· Solve exponential and logarithmic equations
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4.6 Applications and Models: Growth and Decay
· Solve applied problems involving exponential growth and decay
· Find models involving exponential and logarithmic functions
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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
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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
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5.3 Matrices and Systems of Equations
· Solve systems of equations using matrices
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5.4 Matrix Operations
· Add, subtract, and multiply matrices when possible
· Write a matrix equation equivalent to a systems of equations
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5.5 Inverses of Matrices
· Find the inverse of a square matrix, if it exists
· Use inverses of matrices to solve systems of equations
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5.6 Systems of Inequalities and Linear Programming
· Graph linear inequalities
· Graph systems of linear inequalities
· Solve linear programming problems
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5.7 Partial Fractions [ OPTIONAL ]
· Decompose rational expressions into partial fractions
FINISH THE ASSIGNMENT OF: (ask your professor)
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
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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
FINISH THE ASSIGNMENT OF: (ask your professor)
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
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6.4 Nonlinear Systems of Equations
· Solve a nonlinear system of equations
· Use nonlinear systems of equations to solve applied problems
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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
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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
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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
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7.5 Combinatorics: Permutations [ OPTIONAL ]
· Evaluate factorial and permutation notation and solve
related applied problems
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7.6 Combinatorics: Combinations
· Evaluate combination notation and solve related applied problems
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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
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7.8 Probability [ OPTIONAL ]
· Compute the probability of a simple event
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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
FINISH THE ASSIGNMENT OF: (ASK YOUR PROFESSOR)
B Determinants and Cramer's Rule [ OPTIONAL ]
· Evaluate determinants of square matrices
· Use Cramer's rule to solve systems of equations
FINISH THE ASSIGNMENT OF: (ASK YOUR PROFESSOR)
C Parametric Equations [ OPTIONAL ]
· Graph parametric equations and determine an equivalent rectangular
equation
· Determine parametric equations for a rectangular equation
FINISH THE ASSIGNMENT OF: (ASK YOUR PROFESSOR)
Notes:
* { REVIEW } topics covered in prerequisite courses and skills needed for this course. Students are expected to brush up on these topics to the point of knowing the concepts at a problem solving conversational level every day of the course.
** [ OPTIONAL ] means your professor will determine the need for covering this OPTIONAL topic based on the types of projects selected in your professor's syllabus.
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