Download Adlai E. Stevenson High School Course Description

Adlai E. Stevenson High School
Course Description
Division:
Mathematics
Course Number:
MTH351
Course Title:
Advanced Algebra
Content Objectives:
By the end of this course, students will be able to:
Algebraically perform operations with matrices, rational expressions, and functions.
Graph and write equations of polynomial, quadratic, piecewise, rational, and operations of
functions.
Model real world situations using quadratic functions, rational functions, operations of functions, piecewise functions, and
systems of linear equations/inequalities.
Solve polynomial, quadratic, rational, and systems of equations.
College Readiness Objectives:
By the end of this course, students will be able to:
Basic Operations & Applications
Expressions, Equations & Inequalities
Functions
Graphical Representations
Numbers: Concepts & Properties
Properties of Plane Figures
Content Learning Targets
Algebraically perform operations with matrices, rational expressions, and functions.
A.
Add, subtract, multiply matrices by hand within context
B.
Add, subtract, multiply matrices using a calculator
C.
Add, subtract, multiply, and divide rational expressions
D.
Evaluate a piecewise function
E.
Factor and solve polynomial equations using the zero product property
F.
Organizing information using matrices and adding/subtracting matrices in context
G.
Perform operations with function notation
H.
Simplify rational expressions
I.
Use the common difference to classify polynomials and complete tables
Graph and write equations of polynomial, quadratic, piecewise, rational, and operations of
functions.
A.
Create a piecewise equation when given its graph
B.
Given the graph of two functions, sketch the graph of its sum, difference, product, or composition
C.
Graph a polynomial in factored form with a vertical shift
D.
Graph a polynomial in standard form
E.
Graph quadratic functions
F.
Graph rational functions
Division:
Mathematics
Course Number:
MTH351
Course Title:
Advanced Algebra
G.
Sketch the graph of a piecewise function
H.
Write the equation of a polynomial in factored form with a vertical shift
I.
Write the equation of quadratic functions
J.
Write the equation of rational functions
Model real world situations using quadratic functions, rational functions, operations of functions,
piecewise functions, and systems of linear equations/inequalities.
A.
Model situations with piecewise graphs and equations
B.
Model situations with rational graphs and equations
C.
Use quadratic functions to model real world situations
D.
Use sums, differences, and compositions to model real world situations
E.
Use systems of inequalities to model maximum/minimum problems
Solve polynomial, quadratic, rational, and systems of equations.
A.
Determine the solvability of a matrix equation
B.
Solve quadratic equations using the zero product property, square root method, and/or quadratic formula
C.
Solve rational equations
D.
Use the inverse, identity, and variable matrices to solve a system of equations
College Readiness target
Basic Operations & Applications
A.
BOA201: Perform one-operation computation with whole numbers and decimals.
B.
BOA202: Solve problems in one or two steps using whole numbers.
C.
BOA302: Solve some routine two-step arithmetic problems.
D.
BOA401: Solve routine two-step or three-step arithmetic problems involving concepts such as rate & proportion, tax
added, percentage off, and computing with a given average.
BOA601: Solve word problems containing several rates, proporations, or percentages.
E.
Expressions, Equations & Inequalities
A.
XEI201: Exhibit knowledge of basic expressions.
B.
XEI301: Substitute whole numbers for unknown quantities to evaluate expressions.
C.
XEI302: Solve one-step equations having integer or decimal answers.
D.
XEI303: Combine like terms.
E.
XEI401: Evaluate algebraic expressions by substituting integers for unknown quantities.
F.
XEI402: Add and subtract simple algebraic expressions.
G.
XEI403: Solve routine first-degree equations.
H.
XEI405: Multiple two binomials.
I.
XEI503: Identify solutions to simple quadratic equations.
J.
XEI504: Add, subtract, and multiply polynomials.
Division:
Mathematics
Course Number:
MTH351
Course Title:
Advanced Algebra
K.
XEI505: Factor simple quadratics.
L.
XEI601: Manipulate expressions and equations.
M.
XEI605: Solve quadratic equations.
N.
XEI606: Find solutions to systems of linear equations.
O.
XEI701: Write expressions that require planning and/or manipulating to accurately model a situation.
P.
XEI702: Write equations and inequalities that require planning, manipulating, and/or solving.
Functions
A.
FUN401: Evaluate quadratic functions, expressed in function notation, at integer values.
B.
FUN501: Evaluate polynomial functions, expressed in function notation, at integer values.
C.
FUN601: Evaluate composite functions at integer values.
D.
FUN701: Write an expression for the composite of two simple functions.
Graphical Representations
A.
GRE201: Identify the location of a point with a positive coordinate on the number line.
B.
GRE301: Locate points on the number line and in the first quadrant.
C.
GRE401: Locate points in the coordinate plane.
D.
GRE402: Comprehend the concept of length on the number line.
E.
GRE403: Exhibit knowledge of slope.
F.
GRE502: Determine the slope of a line from points or equations.
G.
GRE503: Match linear graphs with their equations.
H.
GRE601: Interpret and use information from graphs in the coordinate plane.
I.
GRE703: Solve problems integrating multiple algebraic and/or geometric concepts.
J.
GRE704: Analyze and draw conclusions based on information from graphs in the coordinate plane.
Numbers: Concepts & Properties
A.
NCP301: Recognize one-digit factors of a number.
B.
C.
NCP401: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern
identification, absolute value, primes, and greatest common factor.
NCP505: Work with squares and square roots of numbers.
D.
NCP508: Determine when an expression is undefined.
E.
NCP602: Apply number properties involving even/odd numbers and factors/multiples.
F.
NCP603: Apply number properties involving positive/negative numbers.
Properties of Plane Figures
A.
PPF301: Exhibit some knowledge of the angles associated with parallel lines.
B.
PPF401: Find the measure of an angle using properties of parallel lines.
C.
PPF402: Exhibit knowledge of basic angle properties and special sums of angle measures.
D.
PPF501: Use several angle properties to find an unknown angle measure.
Division:
Mathematics
Course Number:
MTH351
Course Title:
Advanced Algebra
E.
PPF502: Recognize Pythagorean triples.
F.
PPF503: Use properties of isosceles triangles.
G.
PPF601: Appy properties of 30-60-90, 45-45-90, similar, and congruent triangles.
H.
PPF602: Use the Pythagorean Theorem.