ALGEBRA 2

BENCHMARKS

2002

1. Basic Arithmetic, Estimation, and Accurate Computations	Benchmarks o Students add, subtract, multiply, and divide real and complex numbers. o Students understand the properties of the real and complex number systems o Students calculate squares and square roots o Students understand error accumulation in a computation when there is rounding in intermediate steps.
2. Mathematical Reasoning and Problem Solving	Benchmarks o Students use mathematical structures such as field properties to prove elementary theorems. o Students apply functions in problems involving exponential growth and decay. o Students write equations to represent real world scenarios.
3. Concepts and Principles of Measurement	Benchmarks o Students understand and use ratios, proportions, and scaling.
4. Concepts and Language of Algebra	Benchmarks	Objectives o Students understand and use variables, expressions, equations, and inequalities. o Students solve absolute value problems. o Students understand and apply the binomial theorem o Students solve equations and inequalities analytically, graphically, and with calculators, including those with complex solutions. (Polynomial, Rational, Exponential, o Logarithmic, Absolute value, Compound, Radical) o Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. o Students are adept at operations on polynomials, including long division. o Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. o Students add, subtract, multiply, divide, reduce and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. o Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula in both the real and complex number systems. o Students graph quadratic functions and determine the maxima, minima, and zeros of the function. o Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems. o Students know the laws of fractional exponents and understand exponential functions. o Students use the definition of logarithms to translate between logarithms in any base. o Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. o Students can manipulate an equation of the form ax2 + by2 + cx +dy + e to recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. o Students find the general term and the sums of arithmetic series and both finite and infinite geometric series.
5. Concepts and Principles of Geometry	Benchmarks	Objectives o Students understand concepts of the Cartesian coordinate system
6. Data Analysis, Probability, and Statistics	Benchmarks	Objectives o Students use fundamental counting principles to compute combinations and permutations. o Students use combinations and permutations to compute probabilities. o Students find the probability of both dependent and independent events o Students determine the number of possible outcomes for a limited number of choices or with a limited number to choose from. o Students understand and apply the basic concepts of probability. o Students understand and use the binomial theorem to expand binomial expressions that are raised to positive integer powers
7. Functions and Mathematical Models	Benchmarks	Objectives o Students find the domain and range of functions from ordered pairs, rule or graph; find compositions and inverses of functions; find distance, midpoint and equations of lines given two points. o Apply concepts of function, inverse, composition, asymptotes, symmetry, and end behavior to polynomial, rational, exponential and logarithmic equations