Pre-Logic will introduce the student to the components of sound, rational thought, explore the grammatical nature of logic, and enhance his awareness of the more common logical fallacies. He will be encouraged to articulate a rational, Christian worldview through applying the skills he is learning in class debates. [twice weekly for one year; Materials: Critical Thinking: Book I & II] (student workbook, teacherxs guide, answer key) Anita Harnadek, Critical Thinking Books and Software, Pacific Grove, CA.; Supplemental readings and materials supplied by the teacher) Logic I will introduce the student to the terminology and symbolism used in formal logic, focusing on the components and applications of the categorical syllogism, and will guide them through the elementary skills of sound thinking and effective argumentation. He will be encouraged to articulate a rational, Christian worldview through applying the skills he is learning in class debates. [4 days each week for one year; Materials - Traditional Logic I – (student workbook, teacherxs guide, answer key) Martin Cothran, Memoria Press, Louisville, KY.; Supplemental readings and materials supplied by the teacher] Logic II will continue introducing the student to the terminology and symbolism used in formal logic, focusing on the composition and application of the propositional syllogism, and will guide them through the elementary skills of sound thinking and effective argumentation. He will be encouraged to articulate a rational, Christian worldview through applying the skills he is learning in class debates and mock trial. [4 days per week for one year; Materials - Traditional Logic II (student workbook, teacherxs guide, answer key) Martin Cothran, Memoria Press, Louisville, KY.; Supplemental readings and materials] Logic III focuses on the content of reasoning, specifically the areas of epistemology and apologetics. The student will learn what are the ten ways in which something can be said to exist, the five ways in which something can be said of something else, and the four questions one must answer in order to comprehend anything. He will examine the concept of truth and learn the ways in which we discern and persuasively defend truth. He will be encouraged to articulate a rational, Christian worldview through confronting both historic arguments against truth as revealed in the Scriptures and contemporary arguments against the existence of truth altogether. [5 days each week for 1 year; Materials - Material Logic – (student workbook, teacherxs guide, answer key) Martin Cothran, Memoria Press, Louisville, KY.; Supplemental readings and materials] Algebra ½ is offered as a pre-algebra readiness course and covers scientific notation, operations in base 2, conversions by unit multipliers, ratio and proportion, percent equations and word problems. Graphing using rectangular coordinates is introduced and the equation of a line is studied and graphed. Algebraic concepts include signed numbers, order of operations, exponentials, like terms, substitution and evaluation, and the solving of basic equations. Topics from geometry include types and characteristics of triangles, parts of a circle, polygons, perimeter, circumference, area, surface area, and volume of various simple and compound figures. Constructions include copying angles and triangles and bisecting angles. [5 days per week for 1 year; Text— Algebra ½, Saxon] Algebra I reviews skills mastered in Algebra ½ with more depth in topics of scientific notation, rectangular coordinates, and graphing of linear equations. Number classifications are explored as are properties of real numbers. Sets and subsets are studied. Uniform motion problems of various types are solved. More complex exponential operations are studied. Simple and inverse variation, probability and weighed averages are computed. Algebraic expressions and equations are evaluated, simplified or solved using various techniques including factoring, substitution, elimination, and algebraic manipulations. These equations may involve whole numbers, decimals, fraction and simple radicals. Quadratic equations are factored and the quadratic formula developed and used. Functions are introduced. More complex geometric figures are studied. The Pythagorean theorem is used to find distances. [one credit, 5 days per week for 1 year; Text—Algebra I, Saxon] Geometry uses the structure first developed by Euclid to explore the physical properties of one, two, and three-dimensional figures. This structure begins with definitions and postulates for points, lines, and planes, then develops theorems, using previous knowledge to prove each new concept. The process of direct proof will be used at each stage of this development, but some concepts will use indirect proof. Geometric figures studied include segments, angles, lines, triangles, circles, quadrilaterals, and regular polygons. Constructions will be taught as the properties of the various figures are identified. Properties of congruence and similarity will be thoroughly discussed, and the trigonometry of right triangles will be introduced. The course concludes with a review of the area and volume of plane and solid figures. [5 sessions per week for 1 year; Textbook: Geometry. McDougal Littell, Evanston, IL.] Algebra II begins with a review of previous algebraic and geometric topics. Scientific notation is used in more operations and with real-life problems. Graphing includes non-linear equations. Complex numbers and conjugates are studied. The study of sets includes Venn diagrams. More complex proportion, exponential, quadratic, rate, percent, and uniform motion problems are presented. Statistical concepts and variations are studied in more depth. More complex operations with more complex expressions and equations include solving for three unknowns, solving exponential equations, finding complex and irrational roots, and solving non-linear equations. Trigonometric functions and logarithms are studied and used. Geometric topics include corresponding and alternate interior and exterior angles, vectors, and conversions between polar and rectangular coordinates. [5 sessions per week for 1 year; Textbook: Algebra 2. McDougal Littell, Evanston, IL.; Graphing Calculator] Functions, Statistics & Trigonometry gives the student an introduction to the basic principles of statistical analysis, with many real-life examples of the uses of statistics. It also introduces many of the concepts covered in advanced mathematics, including functions and functional notation, graphing, and the basics of trigonometry and the trigonometry of the circle. An introduction to probability is included. Students must obtain a graphing calculator for this course. [5 sessions per week for 1 year; Textbook: Functions, Statistics, and Trigonometry (FST) – UCSMP. Scott, Foresman and Co., Glenview, IL.; Statistics Software: Microsoft EXCEL – provided and licensed by NCS; Graphing Calculator: Texas Instruments TI-83 – purchased by student] Pre-Calculus focuses on a complete study of logarithms, trigonometry, and higher order algebraic operations. Second and third degree equations, arithmetic sequences and series, probability, matrices, and conic sections are all thoroughly discussed. Graphing topics include exponential, logarithmic, and trigonometric functions, as well as the conics. Students also write geometric and trigonometric proofs and proofs by mathematical induction. [one credit, 5 days per week for one year; Text—Saxon, Advanced Math] Calculus (Advanced Placement) is designed to prepare the student to perform successfully on the College Board Advanced Placement Calculus exam. Topics include a thorough treatment of the mechanics and applications of derivatives and integrals in one variable, as well as a detailed study of the uses of a great variety of functions and their graphs. Students must provide a Texas Instruments TI-83 (or above) calculator. [one credit, 5 days per week for 1 year; Text— Calculus: Concepts and Applications by Paul A. Foerster, Key Curriculum Press]