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Using the VSC Algebra II

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Algebra ii

High School VSC TOOLKIT

Tools aligned to HS VSC expectations.

  • Additional Topics
    Additional Topics is content that may be appropriate for the curriculum but is not included in the Core Learning Goals.
  • Skill Statements
    Describes how a student demonstrates an understanding of an indicator
Goal 2
  

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.
    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.
    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.
    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.
    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.
    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
  1. The student will identify linear and nonlinear functions expressed numerically, algebraically, and graphically.
    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
  1. The student will describe or graph notable features of a function using standard mathematical terminology and appropriate technology.
    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
  1. The student will use numerical, algebraic, and graphical representations to solve equations and inequalities.
    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
  1. The student will solve systems of linear equations and inequalities.
    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.
    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.
    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.
    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.
    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
  1. The student will use literal equations and formulas to extract information.
    Assessment limits:
    • Problems may include addition/subtraction and multiplication/division properties of equality, factoring a common factor, and terms that are rational.

June 2007