Download School District of Marshfield Course Syllabus

School District of Marshfield
Course Syllabus
Course Name: AS Technical Mathematics
Length of Course: Year
Credits: 1
Course Description:
Algebraic content with applications including properties of real numbers,
order of operations, linear equations and inequalities, operations with
polynomial and rational expressions, operations with rational exponents and
radicals, algebra of inverse, logarithmic and exponential functions. This
course includes competencies and performance standards for Intermediate
Algebra with Applications which is part of the General Studies Core offered
throughout the Wisconsin Technical College System (WTCS). Upon
successful completion of Technical Mathematics at Marshfield Senior High
(earning a B or better in both semesters) and obtaining the required
Accuplacer scores, students will earn Wisconsin Technical College Advanced
Standing for Intermediate Algebra with Applications. The course
competencies are consistent among the colleges and are at baccalaureate
level to accommodate student success in transfer to four-year colleges.
PREREQUISITE: Senior Status having completed either Geometry (211) or
Advanced Math Applications (202)
Learning Targets:
• Perform operations with real numbers
• Solve linear, quadratic, and algebraic fractional equations and inequalities
• Factor and solve polynomials
• Use Cartesian coordinate system involving lines, parabolas, and circles
• Apply function notation and properties of exponential and logarithmic
equations
Topic/Content Outline-Units and Themes:
First Quarter
1. Perform operations with real numbers (3 weeks)
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 basic and pure quadratic equations (2 weeks)
A. Identify constants, variables, and coefficients in algebraic expressions
B. Use both the addition and multiplication axioms to solve linear
equations
C. Use the distributive principle and the combining of like terms to add
and subtract multinomials
D. Use the square root principle to solve pure quadratic equations
3. Solve rational equations (3 weeks)
A. Solve equations containing one fraction
B. Solve fractional equations containing an instance of the distributive
principle
C. Solve fractional equations containing two terms on one side
D. Define ratio and proportion, solve proportions
E. Solve formulas
F. Check the solution of an equation
4. Solve linear inequalities (1 week)
A. Solve simple and compound inequalities
B. Solve absolute value equations and inequalities
C. Solve word problems involving equations, absolute value, and
inequalities
D. Use internal notation and set builder notation
Second Quarter
5. Perform calculator steps to solve formulas with combined operations
(1 week)
A. Use a calculator to evaluate formulas involving addition, subtraction,
and division
B. Use a calculator to evaluate formulas containing squares
C. Use a calculator to evaluate formulas containing square roots
D. Use a calculator to evaluate formulas containing cubes
E. Use a calculator to evaluate formulas containing cubic roots
F. Use a calculator to evaluate formulas containing numbers in scientific
notation
G. Use a calculator to evaluate formulas containing parentheses
6. Perform operations with algebraic fractions (2 weeks)
A. Multiply algebraic fractions
B. Reduce algebraic fractions to lowest terms
C. Divide algebraic fractions
D. Convert algebraic fractions to an equivalent form
7. Rearrange formulas (2 weeks)
A. Identify terms and coefficients
B. Rearrange formulas with one non-fractional term on each side
C. Rearrange formulas containing fractions
D. Solve for a variable that is squared in a formula
E. Solve formulas which contain more than one term on a side
F. Rearrange formulas that involve the distributive principle
G. Solve for a variable that appears in more than one term of a formula
8. Perform operations with polynomials (1 week)
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
Third Quarter
9. Factor polynomials (4 weeks)
A. Factor monomials
B. Factor binomials
C. Factor trinomials
D. Factor the difference of two squares
E. Factor the sum and difference of two cubes
F. Reduce fractions to lowest terms after factoring
G. Multiply and divide fractions and use factoring to simplify to lowest
terms
H. Add and subtract polynomial fractions and factor to simplify to lowest
terms
I. Solve polynomial fractions
10. Solve quadratic equations (2 weeks)
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
E. Rearrange formulas in quadratic form
11. Use the Cartesian coordinate system (3 weeks)
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. Graph absolute value inequalities
K. Recognize equations of circles in standard and nonstandard form
L. Graph circles
M. Use Pythagorean Theorem to solve right triangle problems
12. Algebraic relations and functions (3 weeks)
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
F. Find composite functions
G. Identify one-to-one functions
H. Find and graph inverse functions
Fourth Quarter
13. Solve systems of linear equations (4 weeks)
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 the determinant method
F. Define systems of formulas
G. Eliminate a variable/s from a system of formulas to derive a single
formula
14. Solve Radical equations (3 weeks)
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. Check solution for extraneous roots
15. Apply properties of exponential and logarithmic functions (2 weeks)
A. Identify, graph, and evaluate exponential functions
B. Rewrite exponential equations as logarithmic and vice-versa
C. Use properties of logarithmic equations
D. Solve applied problems involving exponential and logarithmic
equations
Resources:
Textbook: Technical Mathematics I, McHale/Witzke 1989
Technical Mathematics II, McHale/Witzke 1989
Algebra 1, Glencoe 2010
Algebra 2, Glencoe 2010