Download precalculus compentencies on core standards 2011

Mathematics Department Competencies and Assessments
Precalculus
Course description: This is a course dealing with algebraic, geometric, and trigonometric concepts, with considerable emphasis on problemsolving. The theory of factoring, structure of complex numbers, and solutions of logarithmic equations are also covered. The utilization of
graphing technology will be emphasized.
Course Power Standards
Assessment Tools
The Real Number System: Students demonstrate understanding of:
 Quizzes
 Extending the properties of exponents to rational exponents;
 Homework
 Use properties of rational and irrational numbers.
 Classwork
 Tests
 Projects
The Complex Number System: Students demonstrate understanding of:
 Quizzes
 Performing operations with complex numbers, including conjugation;
 Homework
 Use of complex numbers in polynomial identities and equations: solve quadratic
 Classwork
equations with real coefficients that have complex solutions.
 Tests
 Projects
Arithmetic with polynomials and rational expressions: Students demonstrate
 Quizzes
understanding of:
 Homework
 Performing arithmetic operations on polynomials.
 Classwork
 Understanding the relationship between zeros and factors of polynomials: know
 Tests
and apply the remainder theorem; identify zeros of polynomials when suitable
 Projects
factorizations are available, and use the zeros to construct a rough graph of the
function defined by the polynomial;
 Rewriting rational expressions;
 Solving rational equations.
Creating Equations: Students demonstrate understanding of:
 Creating equations that describe numbers or relationships: representing constraints
by equations or inequalities, and by systems of equations and/or inequalities, and
interpreting solutions as viable or non-viable options in a modeling context;
rearranging formulas to highlight a quantity of interest using the same reasoning
as in solving equations.
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Quizzes
Homework
Classwork
Tests
Projects
Reasoning with Equations and Inequalities: Students demonstrate understanding of:
 Solving quadratic equations in one variable: use the method of completing the
square to transform any quadratic equation in x into an equation of the form (xp)2=q that has the same solutions; solve quadratic equations by inspection taking
square roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation;
 Solving systems of equations;
 Representing and solving equations and inequalities graphically.
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Quizzes
Homework
Classwork
Tests
Projects
Interpreting Functions: Students demonstrate understanding of:
 Understanding the concept of a function and use of function notation: Use
function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context;
 Analyzing functions using different representations: Graphing functions
expressed symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases; Graphing quadratic
functions, square root functions, cube root functions, piecewise-defined
functions, polynomial functions, exponential, logarithmic, and trigonometric
functions.
 Writing a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function: Use the process of
factoring and completing the square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and interpret these in terms of a
context.
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Quizzes
Homework
Classwork
Tests
Projects
Linear and Exponential Models: Students demonstrate understanding of:
 Constructing and comparing linear and exponential models and solving problems,
including proving that linear functions grow by equal differences over equal
intervals, and that exponential functions grow by equal factors over equal
intervals;
 Recognizing situations in which a quantity grows or decays by a constant rate;
 Exponential models, expressing as a logarithm the solution, or evaluating the
logarithm using technology.
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Quizzes
Homework
Classwork
Tests
Projects
Trigonometric Functions: Students demonstrate understanding of:
 Trigonometric ratios and solving problems involving right triangles;
 Use of special triangles to determine the values of sine, cosine, and tangent;
 Extending the domain of the trigonometric functions using the unit circle;
 Radian measure of an angle;
 Modeling periodic phenomena with trigonometric functions;
 Proving and applying trigonometric identities;
 Applying trigonometry to general triangles, including use of the Law of Sines and
Cosines.
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Quizzes
Homework
Classwork
Tests
Projects
Vector and Matrix Quantities: Students demonstrate understanding of:
 Representing and modeling with vector quantities, recognizing that vectors have
both a magnitude and direction;
 Finding the components of a vector;
 Performing operations on vectors, including addition, subtraction, and scalar
multiplication;
 Performing operations on matrices and using matrices in applications, including
adding, subtracting, scalar and matrix multiplication, finding and using the
determinant, and representing and manipulating data.
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Quizzes
Homework
Classwork
Tests
Projects
All prospective students must complete all three assessment types to the standards listed below and subsequent attachments.
Assessment #1- Projects and Summative Assessments
These are based on concepts and projects that are covered with all Precalculus classes during the course of each year. Prospective Students must
complete all components of each project. The cooperating teacher must sign off on each component with a label of “mastery”.
Assessment #2- Homework, Classwork, and Formative Assessments
Daily assessments of student performance and understanding used to inform instructional decisions.
Assessment #3- Exam
These are based on concepts and information that all Precalculus students are exposed to each year. Each must be completed with the prospective
student attaining a 70% or higher proficiency.