School Improvement in Maryland

Using the VSC: Algebra II

June 2007

Algebra II Acrobat 96k

Goal 1

The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.

Expectation

1. The student will model and interpret real-world situations, using the language of mathematics and appropriate technology.

Indicators
  1. The student will determine and interpret a linear function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.
    2. Assessment limits:
    • The majority of these items should be in context.
    • Essential characteristics are any points on the line, x- and y-intercepts*, and slope*.
      *Students should be able to perform these skills with and without the use of a graphing calculator.
  2. The student will determine and interpret a quadratic function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.
    3. Assessment limits:
    • The majority of the items should be in context.
    • Essential characteristics are zeros, vertex (maximum or minimum), y-intercept, increasing and decreasing behavior.
    • A table of values must include rational zeros and at least one other point.
    • All have real zeros.
  3. The student will determine and interpret an exponential function when given a graph, table of values, essential characteristics of the function, or a verbal description of a real-world situation.
    4. Assessment limits:
    • The majority of the items should be in context.
    • Essential characteristics are y-intercepts, asymptotes, increasing or decreasing.
    • For f(x) = a bx , b > 0, a and b are rational numbers, b is not 1.
    • The y-values for x =0 and x = 1 will be given.
  4. The student will be able to use logarithms to solve problems that can be modeled using an exponential function.
    5. Assessment limits:
    • The majority of the items should be in context.
    • Properties used to solve problems may include the product, quotient, and/or power properties of logarithms.

Expectation

2. Given an appropriate real-world situation, the student will choose an appropriate linear, quadratic, polynomial, absolute value, piecewise-defined, simple rational or exponential model and apply that model to solve the problem.

Indicators
    Assessment limits:
    • The majority of the items should include a verbal description of a real-world situation.

Expectation

3. The student will communicate the mathematical results in a meaningful manner.

Indicators
  1. The student will describe the reasoning and processes used in order to reach the solution to a problem.
    2. Assessment limits:
    • This indicator is assessed through the implementation of the Core Learning Goal rubric for the constructed response items.
  2. The student will ascribe a meaning to the solution in the context of the problem and consider the reasonableness of the solution.
    3. Assessment limits:
    • This indicator is assessed through the implementation of the Core Learning Goal rubric for the constructed response items.

Goal 2 Mathematical Concepts, Language, and Skills

The student will demonstrate the ability to analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

Expectation

1. The student will be familiar with basic terminology and notation of functions.

Indicators
  1. The student will identify and use alternative representations of linear, piecewise-defined, quadratic, polynomial, simple rational and exponential functions.
    2. Assessment limits:
    • These items are not in context.
  2. The student will identify the domain, range, the rule or other essential characteristics of a function.
    3. Assessment limits:
    • Vertical and horizontal lines are included.
    • Functions with restricted domain and/or range are included.
    • Absolute value, step, and other piecewise-defined functions are included.
    • Rational functions should have denominators that are:
      • linear
      • quadratic
      • sum and/or difference of two cubes in factored form.
    • Essential characteristics of a polynomial function include degree, intercepts, end behavior and symmetry of even or odd power functions.

Expectation

2. The student will perform a variety of operations and geometrical transformations on functions.

Indicators
  1. The student will add, subtract, multiply, and divide functions.
    2. Assessment limits:
    • Items involving factoring will be restricted to quadratics or the sum or difference of two cubes.
    • Long division is restricted to linear, binomial, or monomial terms in the denominator.
  2. The student will find the composition of two functions and determine algebraically and/or graphically if two functions are inverses.
    3. Assessment limits:
    • Functions given in equation form can include linear, quadratic, exponential, logarithmic, or rational functions such as f(x) = (ax+b)/(cx+d).
  3. The student will perform translations, reflections, and dilations on functions.
    4. Assessment limits:
    • Translations are either vertical or horizontal shifts.
    • Dilations either shrink or stretch a function.
    • This indicator assesses recognition of translations, reflections, and dilations on functions.
    • Transformations for absolute value functions are restricted to translations and reflections. They do not include dilations.
    • Exponential functions are restricted to translations.

Expectation

3. The student will identify linear and nonlinear functions expressed numerically, algebraically, and graphically.

Indicators
    Assessment limits:
    • Functions can include linear, quadratic, exponential, logarithmic or functions such as f(x) = (ax + b)/(cx + d)
    • The items may have no real world context given.
    • Graphs may include piece-wise functions.

Expectation

4. The student will describe or graph notable features of a function using standard mathematical terminology and appropriate technology.

Indicators
    Assessment limits:
    • Essential characteristics of a linear, quadratic, or exponential function are those listed for 1.1.1, 1.1.2, and 1.1.3.
    • Transformations for an absolute value function in one variable are restricted to translations and reflections. They do not include dilations.

Expectation

5. The student will use numerical, algebraic, and graphical representations to solve equations and inequalities.

Indicators
    Assessment limits:
    • Equations may be in one or two variables.
    • Quadratic equations and inequalities are included.
    • Higher-order polynomial equations will be factorable.
    • Absolute value equations and inequalities are single variable and may be linear or quadratic.
    • Radical equations will lead to a linear or quadratic equation.
    • Rational equations will lead to a linear or quadratic equation.
    • Simple rational inequalities will lead to a linear inequality.
    • Exponential equations are either of the form f(x) = a bx , b > 0, a and b are rational numbers, b is not 1 or the form cnx+d = gmx +f , where c and g are powers of the same base.

Expectation

6. The student will solve systems of linear equations and inequalities.

Indicators
    Assessment limits:
    • Systems of linear equations will be 2 x 2 or simple 3 x 3 that do not take too much time to solve without a calculator.
    • Systems of linear inequalities will be 2 x 2.

Expectation

7. The student will use the appropriate skills to assist in the analysis of functions.

Indicators
  1. The student will add, subtract, multiply, and divide polynomial expressions.
    2. Assessment limits:
    • Rational expressions may include monomials, quadratics, and the sum and difference of two cubes.
  2. The student will perform operations on complex numbers.
  3. The student will determine the nature of the roots of a quadratic equation and solve quadratic equations of the form y = ax2 + bx + c by factoring and the quadratic formula.
    4. Assessment limits:
    • The solutions may be real or complex numbers.
  4. The student will simplify and evaluate expressions with rational exponents.
  5. The student will perform operations on radical and exponential forms of numerical and algebraic expressions.
    6. Assessment limits:
    • Denominators in problems requiring rationalizing the denominator are restricted to square roots.
    • Radicals containing a numerical coefficient are restricted to square roots and cube roots.
  6. The student will simplify and evaluate expressions and solve equations using properties of logarithms.
    7. Assessment limits:
    • Properties of logarithms include the Change of Base Formula, property of equality for logarithmic functions, and the product, quotient, and power properties of logarithms.

Expectation

8. The student will use literal equations and formulas to extract information.

Indicators
    Assessment limits:
    • Problems may include addition/subtraction and multiplication/division properties of equality, factoring a common factor, and terms that are rational.