Program of Studies

MATHEMATICS

GRADES 9 - 12

Grades 9 - 12 challenges students at all levels to appreciate mathematics as an independent discipline as well as a tool for the advancement of other disciplines. It builds on skills developed through the instruction system in mathematics in grades K - 8.

Galileo once said, “Mathematics is the language by which God created the universe.” If we want to attempt to understand the structure of God’s creation and glorify God as Creator, then we must understand the language used to create the universe.

Revelation of God in nature involves ideas of number, form, symmetry, system and laws governing the existence and the harmonious working of all things. The concept of numbers and formulas plays a vital role in virtually all aspects of our world. In many fields of study, abstract ideas and symbols must be converted through the mathematical language to communicate information and rules. Thus the study of mathematics as a language has a far broader impact on a student’s life than it may appear on the surface. In fact, it prepares students to communicate mathematically as well as master the art and science of abstraction – a skill that will serve them well in post-graduate studies and in a wide variety of careers. But more importantly, we need mathematicians who boldly confess, ‘How great is the Creator who has made both the mind and nature so compatible!’ (Kepler) We need mathematicians who see the universe, not as a mere mass of mechanistic and impersonal laws, but as the handiwork of God, and delight themselves therein.

Math instruction in grades 9 - 12 helps students:

Develop and appreciation of and a positive attitude toward mathematics.
Understand the structure of mathematical systems--concepts, properties and processes.
Acquire mathematical facts and skills.
Express and interpret mathematical ideas and relationships.
Develop the mathematical reasoning abilities required in problem-solving and decision making situations.
Apply mathematics in personal, social, technological, scientific and career settings.

Because individual students learn math at different rates, the program provides options for students to progress at their own speed. The flow chart, Math Sequence Samples, illustrates the five variety of paths through course offerings the students may select. The entry level into the various paths depends on the students math background and desires, achievement tests, and teacher recommendations.

To keep pace with current and emerging technology, graphing calculators and computers are an integral part of the CVC mathematics program. Students use these tool for tedious manipulations of mechanical skills and research so they can focus their time and energy on developing problem-solving and higher order thinking skills in mathematics.

Students must take a minimum of three senior high courses in mathematics in order to graduate from high school. When planning their schedule, students should keep possible career choice in mind. For example, Algebra 2 or Honors Algebra 2 is often a requirement for college entrance, while many careers require a background of calculus.

CVC offers the following courses in High School (9 - 12): Algebra 1*, Geometry* , Algebra 2, Honors Algebra 2, Precalculus, Honors Precalculus, and AP Calculus AB.
*Required for graduation.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

ALGEBRA 1

Required For Graduation

(Note: Algebra 1 or Honors Algebra 1 taken in Junior High or Middle School will not count as a high school credit.)

Grades 9 - 10

Minimum Entrance Requirements: A "D-" or better each quarter in Prealgebra or similar course

The study of Algebra 1 helps students understand the basic structure relating to real numbers and to recognize and apply mathematics techniques for the solution of linear and quadratic equations. The student will also extend their skills to the study of the graphs associated with liner equations and inequalities; the relationship between two linear equations; equations known as quadratics equations; and the solution of these various equations and inequalities. As students develop these techniques, they apply them to appropriate practical problems such as those involving weather, biology, agriculture, navigation, finances and statistics.

By the end of Algebra 1, the student will be able to:

Compute the value of a numerical expression involving symbols of inclusion and the order of operations rules.
Apply properties of equality and inequality and the concepts of additive and multiplicative inverses to solve equations and inequalities.
Apply the fundamental operations to solve open sentences and word problems involving real numbers.
Factor and solve polynomials.
Solve word problems involving polynomials.
Rewrite a linear equation into slope-intercept forms and graph its solutions.
Determine an equation of a line.
Solve a system of open sentences in two variables.
Solve word problems involving open sentences in two variables.
Add, subtract, multiply and divide algebraic fractions.
Write radical and exponential expressions in simplest form.
Solve quadratic equations.
Solve equations and word problems involving irrational numbers.
Solve trig problems to find unknown angles or sides of right triangles.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

GEOMETRY

Required for Graduation.

Grades 11-12

Minimum Entrance Requirements:

Freshmen whishing to take this course

Grade no lower than a “B-” each quarter in a Junior High Algebra 1 program;
ITBS (or other basic skills test) percentile greater than 80 in all math areas; and
Letter of Recommendation from 8th grade Algebra 1 teacher (Form available upon request or available at http://home.cvc.org/math/form.pdf)

All upper classmen

A "C-" or better each semester in Algebra 1 or similar course as a freshman

Geometry is the study of relationships in planes and space and the development of logical reasoning. Geometry also extends the use of inductive and deductive reasoning in relationship to similarity, triangles, parallel lines, circles, ratio and proportion, and area and volume relationships.

By the end of Geometry, the student will be able to:

Identify congruent segments and angles, and pairs of angles which are adjacent, vertical, complementary and supplementary.
Classify triangles according to the measure of their sides and angles.
Apply the rule of parallel and perpendicular lines and planes.
Develop theorems and postulates for showing triangles congruent.
Apply the rules of ratios and proportion to determine the measures of the side of given similar polygons.
Apply Pythagorean Theorem to determine the length of any side of a right triangle.
Demonstrate the rules about chords, secants and tangent segments of a circle.
Apply the rules for determining areas of polygons.
Apply rules for determining the lateral area, total surface area and volume of solids.
Perform basic geometry constructions.
Solve trig problems to find unknown angles or sides of right triangles.

If you have any questions or concerns contact: The CVC Math Domain

ALGEBRA 2

Grades 10 - 12

Minimum Entrance Requirements: A "C-" or better in Geometry or similar course.

Algebra 2 is a more abstract than that of Algebra 1. It emphasizes problems solving and critical thinking, but at the same time maintains the skills that provides competency in mathematics. Those skills includes computation, operations with positive and negative real numbers, factoring, solving equations and inequalities.

By the end of Algebra 2, the student should be able to:

Solve problems involving systems of equations in two variables, graphically, algebraically, and technologically.
Perform four fundamental operations on real numbers.
Factor or simplify rational expressions.
Use the relationship of the slopes and point to graph lines and solve equations.
To use scatter plots in predicting future outcomes with the assistance of technology.
Collect and analyze various sets of data.
Solve quadratic equations over the set of real numbers manually and with technology.
Sketch graphs of and find solutions for quadratic-linear of quadratic-quadratic systems of equations manually
and with the aid of a graphing calculator.
Sketch graphs of polynomials and find roots, asymptotes, critical points, and other characteristics.
State equivalent exponential and logarithmic equations.
Apply exponential and logarithmic properties to solving problems.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

HONORS ALGEBRA 2 (Carries a 5 point Honors/AP GPA)

Grades 10 - 12

Minimum Entrance Requirements: A "B-" or better every semester in both Honors Algebra 1 and Honors Geometry or a B+ or better every semester in Algebra 1 and Geometry along with teacher recommendation.

Honors Algebra 2 emphasizes the power and beauty of mathematics through the development and application of extended algebraic concepts and skills with the use of technology. Honors Algebra 2 introduces the notion of functions in relation to linear and quadratic equation concepts. It also extends the study of functions to include polynomials, exponential and logarithmic functions, and trigonometric functions. It also includes the study of geometric representation of equations of quadratic functions (conics); systems of equations with the use of linear algebra; and extends the study of number systems to complex numbers.

By the end of Honors Algebra 2, the student should be able to:

Solve problems involving systems of equations in two or three variables, graphically, algebraically, and technologically .
Perform four fundamental operations on real and complex numbers.
Factor or simplify rational expressions.
Use the relationship of the slopes and point to graph lines and solve equations.
To use scatter plots in predicting future outcomes with the assistance of technology.
Collect and analyze various sets of data.
Solve quadratic equations over the set of real and complex numbers manually and with technology.
Identify and graph quadratic relations as a circles, ellipses, hyperbolas and parabolas manually and with the use of a graphing calculator.
Sketch graphs of and find solutions for quadratic-linear of quadratic-quadratic systems of equations manually and
with the use of a graphing calculator.
Sketch graphs of polynomials and find roots, asymptotes, critical points, and other characteristics.
State equivalent exponential and logarithmic equations.
Apply exponential and logarithmic properties to solving problems.
Apply trig functions to the solution of problems.
Sketch the graphs of trig functions.
Solve trig equations.

Precalculus

Grades 11 - 12

Minimum Entrance Requirements: A "B-" or better both semesters in Algebra 2.

Precalculus includes the solutions of triangles and the practical applications of trigonometry to surveying, navigation and other physical measurements, but major emphasis in trigonometry is algebraic. The trigonometric functions are treated as circular functions; algebraic manipulations of their fundamental identities and solutions of trigonometric equations are emphasized as they would be used in mathematics, physics, business, agriculture, science and engineering. This course also includes the study of functions by graphing them and analyzing their graphs to determine relative extreme and roots all with aid of technology, limits and derivatives. It also includes sequences and series and probability and statistics.

By the end of Honors Precalculus, the student should be able to:

Solve problems involving systems of equations in two or three variables, graphically, algebraically, and technologically.
Perform four fundamental operations on real and complex numbers.
Solve quadratic equations over the set of real and complex numbers manually and with technology.
Identify and graph quadratic relations as a circles, ellipses, hyperbolas and parabolas manually and
with the aid of a graphing calculator.
Sketch graphs of and find solutions for quadratic-linear, quadratic-quadratic, and other systems of
equations manually and with the aid of a graphing calculator.
Sketch graphs of polynomials and find roots, asymptotes, critical points, and other characteristics.
State equivalent exponential and logarithmic equations.
Apply exponential and logarithmic properties to solving problems.
Evaluate functions of angles using technology.
Solve problems involving angular measure expressed in radians.
Sketch the graphs of simple and composite trigonometric functions manually and with the aid of technology.
Apply the fundamental relations of composite angles to prove equations to be identities.
Solve trigonometric equations.
Apply the law of sine and cosine to the solution of oblique triangles.
Apply properties of tangents and slope to find the equation of a tangent to the graph of a function,
the equation of perpendicular to a tangent, instantaneous rate or acceleration at a given time.
Solve problems involving arithmetic and geometric sequences and series.
Calculate basic limits, derivatives and integrals to problem solving.
Apply limits, derivatives and integrals to problem solving.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

HONORS PRECALCULUS (Carries a 5 point Honors/AP GPA)

Grades 11 - 12

Minimum Entrance Requirements: A "B-" or better both semesters in Honors Algebra 2.

Honors Precalculus includes the solutions of triangles and the practical applications of trigonometry to surveying, navigation and other physical measurements, but major emphasis in trigonometry is algebraic. The trigonometric functions are treated as circular functions; algebraic manipulations of their fundamental identities and solutions of trigonometric equations are emphasized as they would be used in mathematics, physics, business, agriculture, science and engineering. This course also includes the study of functions by graphing them and analyzing their graphs to determine relative extreme and roots all with aid of technology, limits and derivatives. It also includes sequences and series and probability and statistics. This course culminates with the Precalculus CLEP (College Level Examination Program) exam for college credit.

By the end of Honors Precalculus, the student should be able to:

Apply the fundamental trigonometric relations to verify identities.
Evaluate functions of angles using technology.
Solve problems involving angular measure expressed in radians.
Sketch the graphs of simple and composite trigonometric functions manually and with the aid of technology.
Apply the fundamental relations of composite angles to prove equations to be identities.
Solve trigonometric equations.
Apply the law of sine and cosine to the solution of oblique triangles.
Apply properties of tangents and slope to find the equation of a tangent to the graph of a function, the equation of perpendicular to a tangent, instantaneous rate or acceleration at a given time.
Solve word problems involving arithmetic and geometric sequences and series.
Expand binomials and use the expansion for predicting outcomes.
Compute the probability of a simple and conditional event.
Collect and analyze various sets of data.
Compute central tendencies and standard deviation and apply results.
Calculate basic limits, derivatives and integrals to problem solving.
Apply limits, derivatives and integrals to problem solving.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

ADVANCED PLACEMENT CALCULUS AB (Carries a 5 point Honors/AP GPA)

Grade 12

Minimum Entrance Requirements: A "B-" or better both semesters in Honors Precalculus or similar course or a “B+” or better both semesters in Precalculus along with teacher recommendation.

The topics studied in AP Calculus AB are those traditionally offered in the first semester of Calculus in college. At the end of this program students will be asked to take the College Board AP Math AB Exam. If a student receives a 4 or 5 on a five point test the student will receive college credit for one semester of Calculus (4 credit hours). A student receiving a 3 might receive college credit, depends on the college that will be attended. (Note: The AP Exams are accepted by most colleges, check with your college before taking the exam for requirements.)
The topics developed in AP Calculus AB include limits and continuity of functions; derivatives of algebraic, trigonometric and exponential functions and their applications in problems involving rate; and integration of algebraic, trigonometric and exponential functions and the application in problems involving area and work.

By the end of AP Calculus AB, the student should be able to:

Apply the rules for limits of sums, of products, of quotient, of polynomials; and of a function between two functions which have the same limit when the limit is taken as the variable approaches a constant and as it approaches infinity.
Apply the rules for determining the derivatives of differentiable functions using the sum, product and quotient rules as well as technology.
Apply the rules of implicit differentiations.
Apply the chain rule to find derivatives.
Construct the equations of the tangent line and the normal line at selected points of a function.
Analyze a graph and determine critical points and points of discontinuity as well as increasing and decreasing intervals.
Identify and construct the solution of problems that call for maximums and minimums.
Apply Rolle’s Theorem, Mean Value Theorem and l’Hopital’s Rule, when appropriate.
Apply the Fundamental Theorem of Calculus to determine the area of a given region.
Identify and compute the sum of Riemann integrals.
Apply the definite integral to solve problems involving area, volume of a solid, surface area, and work as the given force moved through a given distance.
Apply the definite integral to determine the length of a curve and determine the center of mass.
Apply the formulas for differentiation to determine instantaneous velocity and acceleration, instantaneous rate of growth or decay and to cost and profit margins.
Apply integration techniques such as trig substitution and integration by parts to solve integration problems.

If you have any questions or concerns contact: The CVC Math Domain

Math Sequence Samples

Four Common Math Sequences for CVC Students

Common Math Sequencing 9th through 12th Grades
Grade	Sequence 1	Sequence 2	Sequence 3	Sequence 4	Sequence 5
9th	Algebra 1	Algebra 1	Algebra 1	Geometry	Geometry
10th	Geometry	Geometry	Geometry / Honors Algebra 2 with Dept Approval	Algebra 2	Honors Algebra 2
11th	Algebra 2	Honors Algebra 2	Honors Precalculus	Precalculus	Honors Precalculus
12th	Precalculus	Honors Precalculus	AP Calculus AB	AP Calculus AB with Dept Approval	AP Calculus AB

If you have any questions or concerns contact: The CVC Math Domain

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