Math Info for CVCHS | The CVC Math Domain | The CVC Home Page
Course
Descriptions
Algebra 1 | Geometry | Geometry Plus | Honors
Algebra 2 | Precalculus | Honors Precalculus
| AP Calculus AB
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, mathematics helps them to better understand His
marvelous design and handiwork – His creation.
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* , Geometry Plus, Algebra
2, Honors Algebra 2, Precalculus, Honors Precalculus,
Statistic, and AP Calculus AB.
*Required for
graduation.
If you have any questions or concerns contact: The CVC Math Domain
Math Sequence Samples
Math Info for
CVCHS | The CVC Math
Domain
Top of Page | The CVC Home Page
Other
Course Descriptions
Geometry | Geometry
Plus | Algebra 2 | Honors Algebra 2 | Precalculus | Honors
Precalculus | AP Calculus
AB
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
Math Info
for CVCHS | The CVC Math
Domain
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Other
Course Descriptions
Algebra 1 | Geometry Plus | Algebra
2 | Honors Algebra 2 | Precalculus | Honors
Precalculus | AP Calculus
AB
GEOMETRY
Required for Graduation.
Grades 10-12
Minimum Entrance Requirements:
- "C-" or better each semester in Algebra 1 or similar course
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
Math Info
for CVCHS | The CVC Math
Domain
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Other
Course Descriptions
Algebra 1 | Geometry | Geometry
Plus | Algebra 2 | Honors Algebra 2 | Precalculus | Honors
Precalculus | AP Calculus
AB
GEOMETRY Plus
Required for Graduation.
Grades
9-10Minimum Entrance Requirements:
Freshmen whishing to take this course
- Grade no lower than a “A-” each quarter in a Junior High Algebra 1
program; and
- 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 "A-" or better each semester in Algebra 1 or similar course as a
freshman
Geometry Plus is the study of relationships in planes and space and
the development of logical reasoning. Geometry Plus 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. Geometry Plus also places an emphasis on higher level
Algebra skills and the maintenance of those skills..
By the end of
Geometry Plus, 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
Math Info
for CVCHS | The CVC Math
Domain
Top of Page | The CVC Home Page
Other
Course Descriptions
Algebra 1 | Geometry | Geometry
Plus | Honors Algebra 2 |
Precalculus | Honors Precalculus | AP Calculus AB
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
Math Info
for CVCHS | The CVC Math
Domain
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Course
Descriptions
Algebra 1 | Geometry | Geometry Plus | Algebra
2 | Precalculus | Honors Precalculus | AP Calculus AB
HONORS ALGEBRA 2 (Carries a 5 point Honors/AP GPA)
Grades 10 -
11
Minimum Entrance Requirements: An "A-" 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 . 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.
Math Info
for CVCHS | The CVC Math
Domain
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Other
Course Descriptions
Algebra 1 | Geometry | Geometry Plus | Algebra
2 | Honors Algebra 2 | Honors Precalculus | AP Calculus AB
Precalculus
Grades 11 - 12
Minimum Entrance Requirements: A "B-" or better both semesters in Algebra 2
along with teacher recommendation.
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
Math Info
for CVCHS | The CVC Math
Domain
Top of Page | The CVC Home Page
Course
Descriptions
Algebra
1 | Geometry | Geometry Plus | Algebra
2 | Honors Algebra 2 | Precalculus | AP Calculus
AB
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 along with teacher recommendation.
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
Math Info
for CVCHS | The CVC Math
Domain
Top of Page | The CVC Home Page
Course
Descriptions
Algebra 1 | Geometry | Geometry Plus | Algebra 2 | Honors Algebra 2
| Precalculus | Honors
Precalculus
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
Math Info for
CVCHS | The CVC Math
Domain
Top of Page | The CVC Home Page
Course
Descriptions
Algebra 1 | Geometry | Geometry Plus | Algebra
2 | Honors Algebra 2 | Precalculus | Honors Precalculus | AP Calculus AB
Four Common Math Sequences for CVC Students
If you have any questions or concerns contact: The CVC Math Domain
Math Info for CVCHS | The CVC Math Domain
Program of Studies | The CVC Home Page