Download Math 105 - School District of Marshfield

School District of Marshfield
Course Syllabus
Course Name: Math 105 – Intermediate Algebra
Length of Course: Semester
Credits: 1/2
Course Description
Intermediate Algebra (Dual enrollment opportunity with UWMarshfield/Wood County): This course is the equivalent of Math 105,
Intermediate Algebra, in the University of Wisconsin system. Although not a
degree credit course, Intermediate Algebra reviews the topics needed to be
mastered before taking College Algebra, the degree credit course for most
Bachelor of Arts degrees. Topics include the real number system, linear
equations and inequalities, operations on polynomials and rational
expressions, factoring, solutions of quadratic equations, Cartesian
coordinates, functions and related applications. Completion of this course
with a C (not a C-) or better qualifies students to take College Algebra in the
Spring semester.
NOTE: This is only offered in the Fall semester. All students who sign up for
this course will sit for the UW System placement tests in Mathematics. Cut
scores determine course placement. Students taking the course for UW
credit will pay half of the current cost of three university credits.
NOTE: A scientific or graphing calculator is required for this course.
This class meets for one semester.
PREREQUISITE: Senior status, completion of three years of math, qualifying
placement score.
Learning Targets
• Perform operations with real numbers
• Solve equations and inequalities
• Use the Cartesian coordinate system
• Solve systems of linear equations and inequalities
• Perform operations with polynomials
• Perform operations on rational expressions and equations
• Use Algebraic relations and functions
• Solve Radical equations
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Solve quadratic equations
Apply properties of exponential and logarithmic functions
Topic/Content Outline-Units and Themes:
First Quarter
1. Perform operations with real numbers (8 days)
A. Identify the different sets of real numbers, finding intersections and
unions of sets, utilizing set notation
B. Identify the order of real numbers
C. Determine the absolute value and reciprocal of a real number
D. Identify and use the commutative, associative, and distributive laws
E. Identify identity and inverse elements for addition and multiplication
F. Add, subtract, multiply, and divide integers and rational numbers
G. Simplify expressions using the laws of exponents
H. Multiply by powers of ten
I. Simplify multiple operation expressions using the appropriate order of
operations
J. Convert numbers between decimal and scientific notation
K. Simplify expressions with numbers in scientific notation
L. Translate phrases to algebraic expressions
M. Evaluate algebraic expressions and formulas
N. Evaluate absolute value expressions
2. Solve equations and inequalities (10 days)
A. Identify constants, variables, and coefficients in algebraic expressions
B. Use both the addition and multiplication axioms to solve linear
equations
C. Check the solution of an equation
D. Use the distributive principle and the combining of like terms to add
and subtract polynomials.
E. Solve equations containing one fraction
F. Solve fractional equations containing an instance of the distributive
principle
G. Solve fractional equations containing two terms on one side
H. Solve linear inequalities
I. Solve absolute equations and inequalities
J. Solve formulas for given variables
K. Solve word problems involving equations, absolute value, and
inequalities
3. Use the Cartesian coordinate system (10 days)
A. Define linear equation
B. Identify ordered pairs and plot points in the Cartesian coordinate
system
C. Find the distance between two points
D. Find the midpoint of two points
E. Calculate the intercepts and slope of a line
F. Use slope to determine if two lines are parallel, perpendicular, or
neither
G. Write linear equations in standard form, slope-intercept form, pointslope form
H. Graph linear equations and inequalities
I. Graph quadratics
J. Use Pythagorean Theorem to solve right triangle problems
4. Algebraic relations and functions (5 days)
A. Define relations and functions
B. Find domain and range of a relation or function
C. Use function notation
D. Extend the definition of functions to formulas
E. Add, subtract, multiply, and divide functions
5. Solve systems of linear equations and inequalities (9 days)
A. Define a system of equations
B. Solve systems of equations using the graphing method
C. Solve systems of equations using the addition method
D. Solve systems of equations using the substitution method
E. Solve systems of equations using Cramer’s Rule
F. Define systems of formulas
G. Eliminate a variable/s from a system of formulas to derive a single
formula
H. Solve systems of linear inequalities
Second Quarter
6. Perform operations with polynomials (10 days)
A. Define the laws of exponents
B. Use the laws of exponents to simplify polynomials
C. Add, subtract, multiply and divide polynomials
D. Square binomials
E. Factor out the greatest common factor
F. Factor trinomials
G. Factor the difference of two squares
H. Factor the sum and difference of two cubes
7. Perform operations on rational expressions and equations (10 days)
A. Multiply algebraic fractions
B. Reduce algebraic fractions to lowest terms
C. Convert algebraic fractions to an equivalent form
D. Add and subtract algebraic fractions
E. Simplify complex fractions
F. Solve rational equations
8. Solve Radical equations (9 days)
A. Convert radical notations to exponential expressions and vice versa
B. Simplify radicals with numerical values and algebraic terms
C. Apply rules of exponents with positive and negative rational exponents
D. Add, subtract, multiply, and divide radicals
E. Interpret a graph of a radical equation
F. Identify complex numbers
G. Simplify radicals that include complex numbers
H. Add, subtract, multiply, and divide complex numbers
I. Solve radical equations
J. Check solution for extraneous roots
K. Use the square root principle to solve pure quadratic equations
9. Solve quadratic equations (8 days)
A. Use the principle of zero to solve equations which have two solutions
B. Define quadratic equations
C. Write quadratic equations in standard form
D. Solve quadratic equations by completing the square or quadratic
formula
E. Rearrange formulas in quadratic form
10. Apply properties of exponential and logarithmic functions (10 days)
A. Find composite functions
B. Identify one-to-one functions
C. Find and graph inverse functions
D. Identify, graph, and evaluate exponential functions
E. Rewrite exponential equations as logarithmic and vice-versa
F. Use properties of logarithmic equations
G. Solve applied problems involving exponential and logarithmic
equations
Resources
Textbook: Intermediate Algebra for College Students, Seventh Edition,
2007, Allen R. Angel – Prentice Hall
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