Advanced Algebra with Trigonometry
Course description:
Advanced Algebra with Trigonometry is an advanced mathematics
course that extends algebraic concepts and applications and that develops trigonometric
functions and applications. Through meaningful problems and appropriate
technologies, students will study a variety, radical, rational, polynomial,
exponential, circular and logarithmic functions.
Standard 1.0: Algebra
Students will extend algebraic concepts to model and solve
problems in real-world situations by using a variety of functions, equations,
and inequalities.
Learning Expectations:
The student will:
- 1.1 represent
situations that involve variable quantities with expressions, equations,
inequalities, and matrices;
- 1.2 use appropriate
methods and technologies to represent and characterize the solutions for
a variety of equations, inequalities, and systems of equations and systems
of inequalities;
- 1.3 demonstrate
understanding of sequences and series.
Student Performance Indicators:
- represent
(graphically, algebraically, verbally, and numerically) and analyze a variety
of functions (polynomial, rational, exponential, and logarithmic)
and their characteristics
- graph
a variety of functions using transformations;
- solve
a variety of equations using appropriate methods;
- solve
linear, quadratic, and polynomial inequalities using appropriate methods;
- solve
real-world problems modeled by rational, polynomial, exponential, and logarithmic
functions;
- use
data analysis techniques to model real-world phenomena using functions.
- demonstrate
an understanding of operations on matrices;
- solve
real-world problems involving networks, finite graphs, and geometric transformations;
- recognize
the difference between continuous and discrete situations;
- demonstrate
an understanding of recursive and explicit definitions of functions and
sequences;
- use
sigma notation to represent arithmetic and geometric series;
- represent
a sequence using a list, graph, symbols, and words;
- solve
problems using permutations and combinations;
- apply
the Binomial Theorem to expansion of binomials
- use
the discriminants of quadratic equations to characterize the nature of
the solutions to the equations and the x-intercepts of the graphs of the
equations;
- write
equations for conic sections and identify characteristics of the related
graphs;
- recognize
direct- and inverse-variation situations and solve real-world problems
involving variation;
- graphs
equations of the forms y = kx,
 , y = k/x and  .
Standard 2.0: Trigonometry
Students will demonstrate an understanding of trigonometric
functions and apply them to problem situations and real-world phenomena.
Learning Expectations:
- 2.1 apply trigonometry
concepts and applications to problem situations;
- 2.2 connect
trigonometric and circular functions;
- 2.3 interpret
trigonometric functions represented graphically.
Student Performance Indicators:
- define
the trigonometric functions using the unit circle;
- determine
values of the trigonometric functions for special angles using the unit
circle and the symmetry of the circle;
- graph
the trigonometric functions;
- understand
amplitude, period, phase shift, and vertical shift and apply to graphing
trigonometric functions;
- use
trigonometric functions with appropriate technology to model periodic phenomena;
- verify
trigonometric identities graphically and by substitution;
- solve
trigonometric equations graphically
- use
degrees and radians interchangeably to represent angle measure in problems
and explain the advantages/disadvantages of a particular choice;
- solve
real-world problems applying the trigonometric ratios, the Law of Sines,
and the
Law of Cosines;
- apply
the trigonometric formulas for finding the areas of triangles and circular
sectors and segments;
- derive
the Pythagorean Identities.
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