Download MATH 121 Course Outline - MJC - Curriculum Committee

Modesto Junior College
MATH 121 Course Outline
Effective Date: 05/05/2008
Printed On: 10/30/2007 11:50:42 AM
I. COURSE OVERVIEW
The following information is what will appear in the MJC 2008-2009 Catalog.
MATH 121 - Pre-Calculus 1
5 Unit(s)
Prerequisite: Satisfactory completion of MATH 090 or qualification by the MJC
assessment process.
A one-semester College Algebra course or, together with Math 122, a twosemester Precalculus course sequence. Emphasis on algebra skills essential for
success in calculus. Topics include: review of linear, quadratic, rational, radical,
exponential and logarithmic equations; functions and graphs; synthetic division;
complex roots of polynomials; the Fundamental Theorem of Algebra; applications
of exponential and logarithmic equations; sequences and series; mathematical
induction; combinatorics and probability.
A-F and CR/NC. Applicable to the Associate Degree. Transfer to CSU and UC.
MJC-GE - D2; CSU-GE - B4; IGETC - 2A.
II. LEARNING CONTEXT
Given the following learning context, the student who satisfactorily completes
this course should be able to achieve the goals specified in section III: Desired
Learning.
1. COURSE CONTENT
A. REQUIRED
A.
Algebra Review
1. Radicals; Rational Exponents
2. Polynomials and Rational Expressions
3. Completing the Square; the Quadratic Formula
B.
Equations and Graphs
Topics from Algebra and Geometry
Solving Equations
Setting Up Equations: Applications
Inequalities
Rectangular Coordinates; Graphs; Circles
Lines
Linear Curve Fitting
1.
2.
3.
4.
5.
6.
7.
C.
Functions and Their Graphs
Functions
Graphing Techniques: Transformations
Operations on Functions; Composite Functions
Mathematical Models: Constructing Functions
1.
2.
3.
4.
D.
Polynomial and Rational Functions
Quadratic Functions; Curve Fitting
Polynomial Functions
Rational Functions
Synthetic Division
The Real Zeros of a Polynomial Function
Complex Numbers; Quadratic Equations with a Negative Discriminant
Complex Zeros; Fundamental Theorem of Algebra
1.
2.
3.
4.
5.
6.
7.
E.
Exponential and Logarithmic Functions
1. One-to-One Functions; Inverse Functions
2. Exponential Functions
3. Logarithmic Functions
4. Properties of Logarithms; Curve Fitting
5. Logarithmic and Exponential Equations
6. Compound Interest
7. Growth and Decay
8. Logarithmic Scales
F.
Sequences; Induction; Counting; Probability
1. Sequences
2. Arithmetic Sequences
3. Geometric Sequences; Geometric Series
4. Mathematical Induction
5. The Binomial Theorem
6. Sets and Counting
7. Permutations and Combinations
8. Probability
2. ENROLLMENT RESTRICTIONS
1. Prerequisite(s):
Satisfactory completion of MATH 090 or qualification by the MJC
assessment process
Prerequisite Skills
Before entering the course, the student will be able to:
A.
graph lines and find the equation of a line, given sufficient
information.
B.
effectively use function notation to describe mathematical
relationships.
C.
determine the domain and range of a given function.
D.
given a relation between two variables, determine if the relation is a
function.
E.
graph linear, quadratic, absolute value, and simple cubic functions
using transformations.
F.
solve systems of linear equations in two or three variables by
choosing the most effective method for the given problem.
G.
solve linear, quadratic, absolute value, and rational inequalities.
H.
solve quadratic equations with real and complex solutions by
completing the square and using the quadratic formula.
I.
graph quadratic functions by determining and using the vertex and
stretching constant.
J.
add, subtract, multiply, and divide complex numbers.
K.
convert radicals to rational exponents and vice versa.
L.
add, subtract, multiply, divide, or compose two given functions.
M. find the inverse of a given function.
N.
graph exponential and logarithmic functions using transformations.
O.
solve exponential and logarithmic equations.
P.
simplify expressions using the properties of logarithms.
Q.
identify the equations for and sketch the graphs of conic sections.
R.
list a requisite number of terms of a given arithmetic, geometric, or
recursive sequence.
S.
determine the general term of a given arithmetic or geometric
sequence.
T.
determine the sum of a fixed number of terms of an arithmetic or
geometric series, and determine the sum of an infinite geometric series
when it exists.
U.
solve problems involving permutations, combinations, and
probability.
V.
given an applied problem, analyze the problem, select an appropriate
mathematical model, and use that model to solve the problem. Models
used include: linear, quadratic, exponential, logarithmic, systems, and
conic sections.
3. HOURS OF INSTRUCTION PER TERM
Prorated Hours and Units
TYPE of HOURS TERM HOURS UNITS EARNED
Lecture/Discussion
87.5
Total Units Earned:
5
5
4. TYPICAL METHODS OF INSTRUCTION
Instructors of this course might conduct the course using the following
methods:
Face-to-face education 1.
2.
3.
4.
Lectures, discussions, or other presentations that develop theoretical
material
Demonstrations of mathematical techniques, applications, and problemsolving strategies by both instructor and students
Applications of material to specific problems
(Optional) Demonstrations of concepts using a computer algebra system or
graphing calculator
5. TYPICAL ASSIGNMENTS
A. Quality: Assignments require the appropriate level of critical thinking
1. Given a fourth degree polynomial with integer coefficients, use the
Rational Roots Theorem, the Fundamental Theorem of Algebra, and
synthetic division to find the complete factorization of the polynomial
over the complex number system.
2. Graph a given rational function, citing details including the domain of
the function, the equations of its vertical and/or horizontal
asymptotes, coordinates of all intercepts, and intervals on which the
function is increasing and decreasing.
3. A piece of charcoal is found to contain 30% of the carbon-14 that it is
assumed to have had originally. When did the tree from which the
charcoal came die? (Use 5600 years as the half-life of carbon-14.)
B. Quantity: Hours spent on assignments in addition to hours of instruction
(lecture hours)
1. Weekly homework exercises of approximately two hours per
hour of class
2. Preparation for three to five midterm examinations and the
comprehensive final exam
6. TEXTS AND OTHER READINGS
A.Required Texts: Precalculus, 5th Edition, James Stewart, Lothar Redlin,
and Saleem Watson, 2007
B. Other reading material:
III. DESIRED LEARNING
A. COURSE GOAL
As a result of satisfactory completion of this course, the student should
be prepared to:
effectively manipulate algebraic expressions and solve various types of
equations as will be encountered in a first-semester calculus course. By
significantly strengthening their algebra skills, students successfully
completing this course will be far better prepared for the rigors and
mechanics of calculus.
B. STUDENT LEARNING GOALS
Mastery of the following learning goals will enable the student to achieve
the overall course goal.
REQUIRED LEARNING GOALS
Upon satisfactory completion of this course, the student will be able to:
1.
exhibit the connection between radicals and rational exponents.
2.
add, subtract, multiply, and divide polynomial and rational
expressions.
3.
solve quadratic equations by factoring, completing the square, or
using the quadratic formula.
4.
solve linear, quadratic, absolute value, and rational equations and
inequalities.
5.
solve applied problems of the above types.
6.
graph functions via tables of values, transformations, and
coordinate-wise operations.
7.
add, subtract, multiply, divide, and compose functions.
8.
calculate the two forms of the difference quotient for a given
function.
9.
construct functions to model given problems.
10.
graph quadratic, polynomial, and rational functions.
11.
find all roots (real and complex) of a polynomial by using
synthetic division.
12.
state and effectively use the Fundamental Theorem of Algebra.
13.
find the inverse of a given one-to-one function.
14.
graph exponential and logarithmic functions.
15.
16.
17.
18.
19.
20.
21.
apply the properties of logarithms to various problems.
solve exponential and logarithmic equations.
solve problems involving compound interest, exponential growth
and decay, Newton’s Law of Cooling, and logarithmic scales.
classify sequences as arithmetic, geometric or neither.
calculate general terms and finite sums for arithmetic and
geometric sequences and series, and, when possible, calculate the
sum of an infinite geometric series.
prove theorems using the Principle of Mathematical Induction.
solve probability problems using the Fundamental Principle of
Counting, permutations, and combinations.
IV. METHODS OF MEASURING STUDENT PROGRESS
A. FORMATIVE ASSESSMENT:
1. Regular homework assignments are reviewed in class
2. Question and answer sessions, both specifically related to homework
exercises and broadly related to general concepts being covered.
3. Quizzes, worksheets, or group work.
4. Midterm examinations
B. SUMMATIVE ASSESSMENT:
A comprehensive final examination is required.