Upper School Course Descriptions

CCA has two Math tracks that begin at this point in the students’ education:  the Honors level and Academic level.  Both tracks will be taught using the same established course objectives; however, the honors track moves at a faster pace and examines concepts at a deeper level.  Below is a list of courses taken for each of the tracks, as well as a brief description of established objectives.

Pre-Algebra focuses arithmetic operations in mathematics and the real world.  Variables are used as pattern generalizers, abbreviations in formulas, and unknown in problems, and are represented on the number line and graphed in the coordinate plane.  Basic arithmetic and algebraic skills are connected to corresponding geometry topics.  Mathematics is taught from the perspective that God is the Author of math and that through our understanding of it, we may grow in our love for Him, our Great Creator.

Algebra I focuses on patterns, relations, and functions.  Students solve equations with one variable and systems of equations with two or more variables.  Students graph linear equations and inequalities on the Cartesian coordinate system.  Students represent and analyze mathematical situations and structures using algebraic symbols.  Emphasis is placed on operations with polynomials, factoring, and manipulation of algebraic fractions and fractional equations.  Students also use mathematical models to represent and understand quantitative relationships and analyze change in various contexts.

Geometry involves the development of a logical, deductive system through the establishment of rules of argument, definitions, postulates and theorems.  The deductive proof is introduced early in the course and continues to develop as the course progresses.  Topics include congruent and similar figures, parallel and perpendicular lines, polygons, circles, areas and volumes.  Although emphasis is on plane geometry, aspects of solid geometry are included towards the end of the course.  Review of algebra skills is prevalent, and algebra is used extensively to solve geometric problems.

In Algebra II, students study advanced algebraic concepts such as modeling and predicting, linear equations, functions and graphs, polynomials and factoring, quadratic functions, inequalities and linear programming, exponents and radicals, exponential and logarithmic functions, and rational expressions.  Students utilize technology in the form of graphing calculators to help them investigate and solve real-life applications of algebraic concepts.

In Pre-Calculus, students study advanced mathematical concepts such as trigonometry, analytic trigonometry, graphs of common functions, mathematical modeling, rational functions, exponential and logarithmic functions, sequences, series, and probability, and topics in analytic geometry.  Students utilize technology in the form of graphing calculators to help them investigate and solve real-life applications of algebraic concepts.

AB Advanced Placement Calculus enables more capable mathematics students to earn one or two semesters of college credit by taking the AB Advanced Placement exam at the end of the year.  The course begins with an overview of Pre-calculus topics from the year before.  Students first explore limits intuitively and then theoretically.  Derivatives are interpreted as rates of change and local linear approximation.  The definite integral is interpreted as total change over a specific interval as a limit of Riemann sums.  Problem situations are modeled with integrals. Calculus is explored through the interpretation of graphs and tables as well as analytic methods.  The use of technology is integrated throughout the course to provide a balanced approach to the teaching and learning of calculus that involves algebraic, numerical, graphical, verbal, and written methods.  Students use these approaches to investigate and solve problems, to write about their conclusions, and to work in groups to communicate mathematics orally.