North Carolina Department of Public Instruction

Web Links to NC DPI Web Site:

• Algebra II Indicators for use through 2004-2005
• Algebra 2 Goals and Indicators (beginning 2005-2006)
• Comparison of Goals Through 2004-2005 and Goals Beginning 2005-2006

Number Sense, Numeration, and Numerical Operations

Competency Goal 1: The learner will perform operations with numbers and polynomials to solve problems.

1.01 Operate with numbers to solve problems.

1. Simplify expressions involving rational exponents.
2. Use logarithms and exponents to solve problems.
3. Define complex numbers and perform basic operations with them.

1.02 Operate with algebraic expressions to solve problems.

1. Expand powers of binomials using Pascal's triangle or the binomial theorem.
2. Divide one polynomial by another of a lower degree using either synthetic division or the division algorithm.
3. Factor polynomials and other algebraic expressions completely over the real numbers.
4. Find sums, differences, products and quotients of rational algebraic expressions.
5. Simplify complex fractions.
6. Solve problems using direct, inverse, combined and joint variation.

Spatial Sense, Measurement, and Geometry

Competency Goal 2: The learner will describe geometric figures algebraically in the coordinate plane.

2.01 Write the equations in standard form of circles and parabolas; graph.

2.02 Graph ellipses and hyperbolas given the equations.

Patterns, Relationships, and Functions

Competency Goal 3:  The learner will use relations and functions to solve problems.

3.01 Describe graphically, algebraically and verbally real-world phenomena as functions; identify the independent and dependent variables.

3.02 Translate among graphic, algebraic, and verbal representations of relations.

3.03 Graph relations and functions and find the zeros of functions.

3.04 Find the composition and inverse of functions.

3.05 Use quadratic equations and inequalities to solve problems. Solve by:

1. Graphing.
2. Factoring.
3. Completing the square.
4. Using the quadratic formula.
5. Using properties of equality; justify steps needed.

3.06 Find and interpret the maximum and minimum values and the intercepts of a quadratic function.

3.07 Use polynomial equations (up to 4^th degree) to solve problems. Solve by:

1. Graphing.
2. Factoring;
3. Using properties of equality; justify steps used.

3.08 Find zeros, intercepts, and approximate the turning points of polynomial functions; describe them in the context of the problem.

3.09 Write a polynomial equation given its solutions.

3.10 Use rational equations to solve problems. Solve by:

1. Graphing; identify the asymptotes and intercepts.
2. Factoring.
3. Finding the zeros and asymptotes through analysis of the polynomials in the numerator and denominator.
4. Using properties of equality; justify steps used.

3.11 Use equations which contain radical expressions to solve problems. Solve by:

1. Graphing.
2. Factoring.
3. Using properties of equality; justify steps used.

3.12 Use systems of two or more equations to solve problems. Solve by:

1. Elimination and/or substitution.
2. Graphing.
3. Using matrix equations of the form AX = B.

3.13 Use linear programming (systems of three or more inequalities) to solve problems.

3.14 Use equations and inequalities with absolute value to solve problems. Solve by:

1. Locating points on the number line.
2. Locating points on the coordinate plane.
3. Using properties of equality; justify steps used.

3.15 Write and graph exponential functions of the form f(x) = a b^x.

3.16 Recognize as inverses the exponential and logarithmic functions.

3.17 Use logarithmic and exponential equations to solve problems. Solve by:

1. Graphing.
2. Substitution.
3. Applying the inverse relationship.
4. Using properties of equality; justify steps used.

Data, Probability, and Statistics

Competency Goal 4:  The learner will collect, organize, and interpret data with functions of best-fit and matrices to solve problems.

4.01 Write and interpret an equation of a curve (linear, exponential, quadratic) which models a set of data.

4.02 Find the equation of the curve of best-fit (linear, exponential, quadratic) for a set of data. Interpret the constants, coefficients, and bases in the context of the data. Check the equation for goodness-of-fit and use the equation for predictions.

4.03 Use exponential equations of the form f(x) = (1+ r)^x where r is given as a rate of growth or decay to solve problems.

4.04 Operate with matrices to solve problems.

1. Add, subtract, and multiply matrices.
2. Find the inverse and determinant of a matrix.