Maui Community College
Course Outline
1. Course Title:
MATH 25 – Elementary Algebra II
Number of credits:
3
Abbreviated Course Title:
Elem Algebra II
Date of Outline:
February 19, 2004
2. Course Description:
Prepares student for sequence of math courses which
lead to calculus. Teaches exponents, polynomials,
factoring, rational expressions and equations, radical
expressions and equations, and quadratic equations.
Uses mathematical skills to solve application
problems.
3. Credits/ Contact Hours:
3 Hours/Lecture
4. Prerequisites:
MATH 23 or 24 with at least a C or placement at MATH
25 and ENG 19 with at least a C or concurrent
enrollment in ENG 22 or 55, or consent
Corequisites:
Recommended Preparation:
Approved by
At least 10th grade reading skills
Date
Math 25 – Course Outline – February 19, 2004
page
5. General Course Objectives:
Prepares student for sequence of math courses which lead to calculus. Teaches exponents,
polynomials, factoring, rational expressions and equations, radical expressions and equations, and
quadratic equations. Uses mathematical skills to solve application problems.
6. Student Learning Outcomes:
For assessment purposes, these are linked to #7. Recommended Course Content.
On successful completion of this course, students will be able to:
a. define the mathematical terms of exponent, base, and exponential notation;
b. identify and apply the laws of exponents to simplify expressions with integral
exponents;
c. use scientific notation in calculations and in applications;
d. define the following mathematical terms: monomial, binomial, trinomial,
polynomial, descending order, ascending order, missing terms, degree of a
term, degree of the polynomial, like terms, coefficient;
e. evaluate a polynomial for a given value of several variables;
f. collect and combine like terms and arrange them in descending order;
g. identify the degree of each term of a polynomial and the degree of the polynomial;
h. categorize a polynomial as a monomial, binomial, trinomial, or none of these;
i. use polynomials to represent perimeter and area of geometric figures;
j. add, subtract, multiply, and divide polynomials in one or more variables;
k. factor the greatest common factor from a polynomial expression;
l. factor general trinomials of the form: ax2 + bx + c where a, b, and c are
integers;
m. recognize and factor the difference of two squares;
n. recognize and factor a perfect square trinomial;
o. factor expressions with four terms using factoring by grouping;
p. solve quadratic equations by factoring;
q. solve application problems involving quadratic equations that can be solved by
factoring, including number problems, areas of geometric figure problems,
product of consecutive integer problems, the Pythagorean Theorem and
problems where a formula is given;
r. define and write rational expressions in lowest terms; understand the terminology;
s. add, subtract, multiply, and divide rational expressions;
t. solve equations involving rational expressions;
u. simplify complex rational expressions;
v. solve a rational formula for a specific variable;
w. solve word problems that lead to equations containing rational expressions
including direct and indirect variation, problems that involve distance, rate and
time, and problems that use the work principle;
x. define square roots and positive or principal square roots of number;
y. identify the square root or radical symbol and radicands of radical expressions
z. state the principal square roots and their opposites of the whole numbers from
zero squared to 25 squared;
aa. state the approximate square roots of real numbers using a calculator;
bb. solve applied problems involving square roots;
cc. evaluate and simplify a radical expression;
dd. identify a given radical as rational, irrational, or not real;
ee. add, subtract, multiply, and divide radical expressions;
ff. solve equations containing radicals, using the principle of squaring;
gg. solve application problems that lead to equations containing radical expressions;
hh. write a quadratic equation in standard form;
ii. solve quadratic equations by factoring;
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jj. solve equations of the form (ax + b)2 = c, using the square root property of equations;
kk. solve quadratic equations by completing the square;
ll. state and use the quadratic formula to solve quadratic equations;
mm.solve a formula for a given variable, including problems which require using the quadratic
formula;
nn. solve applied problems using quadratic equations, including problems involving areas of
geometric figures, problems that use the Pythagorean Theorem, and problems that involve
distance, rate and time;
oo. identify the graph of a quadratic equation as a parabola;
pp. state the line of symmetry and the vertex of the graph of a parabola;
qq. graph a quadratic equation;
rr. state the x-intercepts and the y-intercept of a quadratic equation;
ss. define the mathematical terms: function, relation, domain, range, linear function, quadratic
function, function values;
tt. decide whether a correspondence is a function;
uu. given a function described by an equation, state function values (outputs) for specified values
(inputs);
vv. draw the graph of a function;
ww. decide whether a graph is that of a function using the vertical line test;
xx. solve applied problems involving functions and their graphs.
7. Recommended Course Content and Approximate Time Spent
Linked top #6. Student Learning Outcomes.
A. Exponents and polynomials (3 weeks)
1. Exponents
a. Define the mathematical terms of exponent, base, and exponential
notation (a)
b. Identify and apply the laws of exponents to simplify expressions with
integral exponents (b)
c. Use scientific notation in calculations and in applications (c)
2. Polynomials
a. Define the following mathematical terms: monomial, binomial,
trinomial, polynomial, descending order, ascending order, missing
terms, degree of a term, degree of the polynomial, like terms,
coefficient (d)
b. Evaluate a polynomial for a given value of several variables (e)
c. Collect and combine like terms and arrange them in descending order (f)
d. Identify the degree of each term of a polynomial and the degree of the
polynomial (g)
e. Categorize a polynomial as a monomial, binomial, trinomial, or none of
these (h)
f. Use polynomials to represent perimeter and area of geometric figures (i)
g. Add, subtract, multiply, and divide polynomials in one or more
variables (j)
B. Factoring polynomials (3 weeks)
1. Factoring
a. Factor the greatest common factor from a polynomial expression (k)
b. Factor general trinomials of the form: ax2 + bx + c where a, b, and c
are integers (l)
c. Recognize and factor the difference of two squares (m)
d. Recognize and factor a perfect square trinomial (n)
e. Factor expressions with four terms using factoring by grouping (o)
f. Solve quadratic equations by factoring (p)
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2. Solve application problems involving quadratic equations that can be
solved by factoring including:
a. number problems (q)
b. areas of geometric figure problems (q)
c. product of consecutive integer problems (q)
d. problems using the Pythagorean Theorem (q)
e. problems where a formula is given (q)
C. Rational Expressions and Equations (3 weeks)
1. Rational expressions
a. Definitions and terminology (r)
b. Reduce algebraic fractions (r)
c. Complex fractions (u)
d. Operations (r)
e. Multiplication and division with canceling (s)
f. Addition and subtraction using lowest common denominator (s)
2. Solve equations involving rational expressions
a. Find an allowable solution set (t)
b. Solve a formula for a specified unknown (v)
c. Solve application problems including direct and indirect variation,
problems that involve distance, rate and time, and problems that use the
work principle (w)
D. Radical Expressions and Equations (2 weeks)
1. Radical expressions
a. Definitions and terminology: square roots and positive or principal
square roots of numbers, radical symbol, radicand (x, y, z)
b. State the approximate square roots of real numbers using a calculator (aa)
c. Identify a given radical as rational, irrational, or not real (dd)
d. Evaluate and simplify a radical expression (cc)
2. Operations
a. Addition and subtraction (ee)
b. Multiplication and division (ee)
3. Solving equations containing radical expressions
a. Solve equations containing radicals, using the principle of squaring and
checking for extraneous roots (ff)
b. Solve application problems which result in equations containing radical
expressions (bb, gg)
E. Quadratic equations (4 weeks)
1. Standard form of a quadratic equation (hh)
2. Solve quadratic equations
a. Solve quadratic equations by factoring (ii)
b. Solve equations of the form (ax + b)2 = c, using the square root
property of equations (jj)
c. Solve quadratic equations by completing the square (kk)
d. State and use the quadratic formula to solve quadratic equations (ll)
e. Solve a formula for a given variable, including problems which require
using the quadratic formula (mm)
3. Solve applied problems using quadratic equations, including problems
involving areas of geometric figures, problems that use the Pythagorean
Theorem, and problems that involve distance, rate and time (nn)
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4. Graph quadratic equations (qq)
a. Identify the graph of a quadratic equation as a parabola (oo)
b. State the line of symmetry and the vertex of the graph of a parabola (pp)
c. State the x-intercepts and the y-intercept of a quadratic equation (rr)
5. Functions
a. Define the mathematical terms: function, relation, domain, range,
linear function, quadratic function, function values (ss)
b. Decide whether a correspondence is a function (tt)
c. Given a function described by an equation, state function values (outputs)
for specified values (inputs) (uu)
d. Draw the graph of a function (vv)
e. Decide whether a graph is that of a function using the vertical line test
(ww)
f. Solve applied problems involving functions and their graphs (xx)
8. Recommended Course Requirements:
Recommended course requirements include regularly assigned homework problems, along with
regular quizzes, unit tests, and a final exam.
9. Text and Materials:
An appropriate text(s) and materials will be chosen at the time the course is to be offered from those
currently available in the field.Examples include:
Introductory Algebra, 9th edition, Marvin Bittinger, Addison-Wesley Publishing
Company, 2003
Optional textbook: Student Solutions Manual for the above textbook
10. Evaluation and Grading
A student's grade in the course is determined by computing an average of the
semester's course work which would include the quizzes (5% - 15%), the unit
tests (55% - 65%), and the final exam (25% - 35%). It is not appropriate to evaluate
student competency in a mathematics course by using only a mid-term and final
exam. The homework may be included in the final grade (0% - 5%).
In the math department, grades are usually assigned according to the following scale:
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
0% - 59% = F or N
The student may select to receive a "credit/no credit" for the course instead of a letter
grade. If he/she wishes to select this option, he/she must inform the instructor.
Some flexibility is given to instructors in these matters. Each instructor will clearly
inform students on his/her syllabus what the forthcoming course work will entail and
how it will be weighted and graded respectively.
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11. Methods of Instruction: This course may be taught in a traditional lecture format or
in an individualized study format in a math lab. In the lecture class, use is made of
cooperative learning, lecture sessions involving much student participation and
feedback, self-checking homework assignments, frequent quizzes and tests to inform
students of their progress and a final exam at the end of the semester.
In the individualized study lab class, similar methods of instruction are used, but in
place of the lecture sessions, the students work for short periods of time one-on-one
with an instructor or tutor. The student would be expected to learn more on his/her
own by reading the textbook and watching video tapes of the lessons.
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