AZTEC HIGH SCHOOL

MATHEMATICS DEPARTMENT STANDARDS

 

TRIGONOMETRY / PRE-CALCULUS

11/12/04

 

 

 

PREREQUISITE – Algebra II with a C- or better.

 

DESCRIPTION - This course will build upon the student’s knowledge of Algebra II to prepare the student for Calculus or college mathematics.

 

POWER STANDARDS – Skills and knowledge needed to be prepared for Trigonometry/Pre-Calc.

1.   Know and use the basic rules of Algebra with expressions and equations

2.   Simplify radicals and rational exponents

3.            Rationalize denominators

4.   Factor using the greatest common factor, trinomials, by grouping, squares, and cubes

5.   Simplify rational expressions

6.   Use operations with rational expressions

7.   Solve equations involving 1 and 2 variables, quadratics by all four methods, radicals, and absolute value            .

8.   Solve and graph inequalities

9.   Graph a line from the equation, one point and the slope, and two points

 

COMMON STANDARDS – These standards will be included in every math class at Aztec High School.

1.   Learn to communicate mathematically

2.   Learn to use mathematics in their daily lives.

3.   Become proficient with appropriate computational tools and techniques.

4.   Learn to reason mathematically.

5.   Become mathematical problem solvers.

 

PERFORMANCE STANDARDS – Skills and content that students will learn in this course.

  1. Possess a working knowledge of trigonometry.
    1. Know Radians and Unit circle.
    2. Know common identities.
    3. Be able to graph using the six trigonometric functions and variable.
    4. Know about and how to find amplitude, period and phase.
    5. Know the results of combining functions.
    6. Be able to solve triangles using trigonometric laws.
    7. Be able to solve trig equations.

 

  1. Be able to apply trigonometry to find solutions.
    1. Know the polar coordinate system.
    2. Know complex numbers.

 

 

TRIGONOMETRY / PRE-CALCULUS PERFORMANCE STANDARDS (cont.)

 

  1. Be able to use logarithms and exponential functions.
    1. Know real number exponents.
    2. Know what a logarithmic function and exponential function is.
    3. Know the relationship between a logarithmic and exponential function.
    4. Know the laws and properties of a logarithmic and exponential function.
    5. Be able to solve logarithmic and exponential equations.

 

  1. Understand the basics of analytic geometry.
    1. Know the four different conic sections.
    2. Be able to identify the equations of the conic sections.
    3. Be able to graph the conic sections by using the major components of each.

 

  1. Understand vectors and matrices.
    1. Know what a vector and a matrix are.
    2. Know the operations of vectors and matrices.
    3. Be able to solve systems using Gaussian elimination.
    4. Be able to solve systems using Cramers Rule.

 

  1. Understand sequences and series.
    1. Know the difference between arithmetic and geometric sequences and series.
    2. Know what a sequence and series is.
    3. Know the difference between finite and infinite series.
    4. Know and apply properties of factoring to exponents to expand polynomials.

 

  1. Be able to understand Polynomials and Rational Functions
    1. Quadratic functions
    2. Higher degree functions.
    3. Be able to find zeros/ rational/ irrational/ complex.
    4. Be able to graph all.

 

  1. Understand Systems of Equations
    1. Be able to solve, graph substitute, and eliminate.
    2. Be able to multiply variable systems.
    3. Know what an inequality is.
    4. Know linear programming / optimization. 

 

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