Algebra 2 - fall 2011

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Unit 1 - Transformation of Functions (2 weeks)


Target 1A - Understanding how to identify transformations.
        1. I can identify transformation(s) when given a function.
        2. I can identify transformation(s) when given a table.
        3. I can identify transformation(s) when given a graph.

Target 1B - Understanding applications of transformations.
        1. I can apply transformation(s) to graphs.
        2. I can apply transformation(s) to functions. (quadratic, exponential, absolute value, and piecewise functions).



Unit 2 - Extending Linear Models (4 weeks)
Target 2A - Understanding the use of linear programming in solving problems.

        1. I can create and interpret constraint equations and their graphs.
        2. I can optimize an objective function given a set of constraints.

Target 2B - Understanding linear equations in three dimensions.
        1. I can write a system of equations in three dimensions.
        2. I can create and interpret matrix equations for linear equations in three dimensions.
        3. I can use matrices to solve a system of linear equations in three dimensions.
        4. I can identify the solution of a 3x3 system of equations as intersecting planes, parallel planes, or coplanar figures.

Target 2C - Extensions.

        1. I can find algebraic solutions to 2x2 systems.
        1. I can perform elimination.
        1. I can perform row reduction.
        1. I can find determinants.



Unit 3 - Extending Exponential Models (4 weeks)

Target 3A - Understanding the application of exponential models to real world situations.

        1. I can identify the rate of change and initial value of an exponential model.
        2. I can model real-world situations with exponential functions.

Target 3B - Understanding the Application of Logarithms to Solve Exponential Equations.

        1. I can use logarithms to solve exponential equations.
        2. I can apply transformations to exponential functions.

Target 3C - Extensions.

        1. I can solve Inverse Functions .
        2. I can solve Logarithmic Functions.



Unit 4 - Extending Quadratic Models (5 weeks)

Target 4A - Understanding the complex number system.

        1. I can perform the three mathematical operations addition, subtraction and multiplication on non-real numbers.

Target 4B - Understanding complex solutions to quadratic equations.

        1. I can solve quadratic equations which have non-real solutions.
        2. I can identify whether the roots of a quadratic function are real or non-real given an equation or a graph.


Target 4C - Understanding vertex form of quadratic equations.

        1. I can write quadratic functions in vertex form.
        2. I can graph quadratic functions in vertex form.
        3. I can apply transformations to quadratic functions.


Target 4D - Extensions.

        1. I can solve quadratic inequalities.



Unit 5 - Higher Degree Polynomial Functions (4 weeks)

Target 5A - Understanding the equivalence of polynomial expressions

        1. I can use the remainder and factor theorems.
        2. I can factor higher order polynomials.
        3. I can use arithmetic operations (add, subtract, multiply, divide) on functions to create equivalent forms.

Target 5B - Understanding the relationship between zeros, analytical or graphical representations of polynomial functions

        1. I can determine a function rule for a function when given the graph.
        2. I can determine the number of real and non-real zeros when given a function.
        3. I can apply transformations to higher degree polynomial functions.


Unit 6 - Rational Expressions & Functions (4 weeks)

Target 6A - Understanding the equivalence of rational expressions.

        1. I can apply properties of exponents to simplify expressions with rational exponents.
        2. I can simplify rational expressions.
        3. I can use arithmetic operations (add, subtract, multiply, divide) on rational expressions to create equivalent forms.
        4. I can solve rational equations in the form of proportions.


Target 6B - Understanding characteristics of rational functions.

        1. I can model problem situations with rational functions.
        2. I can identify the domain of a rational function.
        3. I can graph rational functions.
        4. I can determine the zeros of a rational function.


Target 6C - Extensions.

        1. I can Solve equations in the form (including subtraction/negative).
        2. I can identify Transformations.
        3. I can determine Continuity.
        4. I can identify Horizontal Asymptotes.


Unit 7 - Trigonometric Functions (4 weeks)

Target 7A - Understanding the unit circle.

        1. I can use both radian and degree measure fluently.
        2. I can identify trigonometric values of common angles on the unit circle fluently.


Target 7B - Understanding the application of trigonometric functions.

        1. I can use trigonometric functions to solve non-right triangles.


Target 7C - Understanding trigonometric functions.

        1. I can graph the Sine, Cosine, and Tangent functions.
        2. I can apply transformations to trigonometric functions.


Target 7D - Extensions

        1. I Can recognize cotangent, cosecant, and secant functions.

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