Mathematics Department

Essential Knowledge and Skills

Students in Algebra II Honors will be able to: identify and graph subsets of the set of real numbers; use the order of operations to evaluate expressions; know and give examples of the axioms for multiplication and addition in the set of real numbers; use axioms and definitions to construct an algebraic direct proof; use subtraction and division of real numbers and algebraic expressions; solve and graph solutions of equations (including fractional and radical equations) and inequalities (including absolute value inequalities) in one variable with integral, rational, or irrational coefficients; set-up and write one or more mathematical sentences to represent the situation presented in varying types of word problems; solve systems of linear equations using graphing, substitution, or linear combinations; add, subtract, multiply, and divide polynomials and rational expressions; factor polynomials including monomials, binomials, trinomials, and factor by grouping terms; use the laws of exponents; solve problems using negative exponents and/or zero as an exponent; set-up and solve problems of direct, inverse, joint, and combined variation; distinguish between the decimal representations of rational and irrational numbers; use the Pythagorean Theorem and the Distance Formula (in two dimensions); add, subtract, multiply, divide, and simplify square root and other root index radicals; solve quadratic equations by using factoring, the completing the square method, and the Quadratic Formula; determine the vertex of a quadratic function and the zeros of all relations and functions studied; define and simplify expressions using complex numbers; use synthetic division; apply the Remainder, Factor, and Rational Root Theorems; study the composition and inverses of functions; define logarithms; use the laws of logarithms; study applications of logarithms; study arithmetic and geometric sequences and series; utilize sigma notation; study infinite geometric series; learn the general binomial expansion; use the definitions of the sine, cosine, and tangent functions and trig tables to obtain trig function values for general angles; solve right triangles; use the Laws of Sines and Cosines; find the area of triangles; analyze statistical data; examine the Normal Distribution; study permutations, combinations, and probability- including the probability of mutually exclusive and of independent events.

Indicators of Student Learning

Upon the completion of the course, students will:

Problem Solving

• Represent and solve problems in written form, verbally, and in graphs or charts. • Select the most efficient method for solving problems- where alternative techniques will produce the same solutions. • Employ a mathematical model to analyze and solve a problem stated in words.
• Identify numerical patterns • Practice problem solving techniques by participating in the national MathFax problem-solving contest.

Reasoning and Proof

• Understand the concepts related to definitions, axioms of real numbers for addition, multiplication, and equality, and theorems developed in the text and in class

Communication

• Use the correct mathematical language and symbols orally and in writing. • Write notes related to the examples, definitions, and other information presented during class time.

• Verbalize ideas by answering questions during entire class or small group situations.

• Relate prior knowledge to broader concepts presented in the course

Technology

• Select online resources, as needed, to supplement and/or review the topics.

• Use graphing calculator and computer program technology to: graph and analyze polynomial, rational, trigonometric, logarithmic, and exponential functions; evaluate trigonometric and logarithmic (common and natural) expressions, permutations, factorials, and combinations; obtain the zeros, the x and y-intercepts, the maximum and minimum points of a graph; investigate sequences, series, and limits, using extensive tables of ordered pairs of numbers and graph.

Assessment

Upon the completion of the course, students will:

• Demonstrate competency in problem solving by identifying patterns that determine specific sets of real numbers.

• Transforming different types of equations in one or two variables (including systems of two linear equations) appropriately to obtain solutions; and utilizing a five step problem-solving process for problems stated in words: 1) determining what quantity/quantities are unknown; 2) representing the unknown(s) with one or more variables; 3) writing equations or inequalities to represent the relationship(s) stated; 4) solving the open sentence or system of open sentences; and 5) verifying the reasonableness of the result

• Demonstrate competency in reasoning and proof by using definitions, axioms, and theorems in algebraic deductive proofs and in the steps needed to simplify expressions and solve or transform equations and systems of equations.

• Demonstrate competency in communication by verbalizing and writing algebraic concepts and the sequences of steps leading to algebraic solutions and by recognizing and naming the different forms of linear and quadratic equations.

• Demonstrate competency in technology by utilizing a graphical calculator’s various programs and capabilities to solve a wide variety of problems.