Mathematics Department

Essential Knowledge and Skills

Students in Pre-Calculus will study: how to identify and solve equations, inequalities, and systems of the same given in algebraic form or derived from word sentences, including: systems of linear equations using linear combinations, substitution, graphical, and matrix methods; linear inequalities and linear programming; trigonometric, logarithmic, and exponential equations; conversion formulas; second order matrix equations; radical and fractional equations. Students will also study: how to use algebraic operations (including addition, subtraction, multiplication, division, raising to powers, finding roots, the process of factoring, etc.) to simplify expressions involving: matrices (including inverses of second order) and determinants; trigonometric identities; slope of secant and tangent lines to any point on the graph of a polynomial function (obtaining the first derivative); how to determine continuity of a graph; normal and polar form of a linear equation; complex numbers in rectangular or polar form; powers and roots of complex numbers; terms or sums of arithmetic or geometric sequences; how to use and evaluate sigma notation; norm of a vector; dot product or cross product of two vectors in two or three dimensions; and how to obtain the Euler number "e" and Euler's Formulas.

Indicators of Student Learning

Upon the completion of the course, students will:

Problem Solving

• Represent and solve problems in written form, verbally, and by using graphs or charts.

• Select the most efficient method for solving problems when alternative techniques will produce the same solutions.

• Employ a mathematical model to analyze and solve a problem stated in words.

• Identify numerical patterns

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.

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

• Relate prior knowledge to broader concepts presented in the course.

• Recognize relationships between arithmetic, algebraic, and geometric concepts and how the language of mathematics relates to real world issues.

Technology

• Use graphing calculator and computer program technology to graph and analyze polynomial, rational, trigonometric, inverses of trigonometric, logarithmic, and exponential functions and polar graphs; evaluate trigonometric and logarithmic (common and natural) expressions, permutations, factorials, and combinations; convert between degree and radian measures; convert between rectangular and polar coordinates; obtain critical points, zeros of a graph, and x and y-intercepts and examine end behavior, asymptotes, and symmetry of graphs; investigate sequences, series, and limits, using extensive tables of ordered pairs of numbers and graphs.

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

Assessment

Upon completion of the course students will:

• Demonstrate competency in problem solving by: utilizing the diagram of the unit circle and its important arc lengths to illustrate concepts of trigonometry; analyzing sets of points (especially those of a line) from different perspectives (i.e. vector, polar, parametric, or normal form); graphing functions and identifying major characteristics; applying various theorems; and identifying patterns that determine specific sequences of numbers.

• Demonstrate competency in reasoning and proof by using definitions and previously acquired knowledge to justify conclusions in deductive proofs of new theorems and by performing 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 new forms of a linear equation: parametric, vector, matrix, normal, and polar forms.

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