The following chart reflects the general course sequence. It is highly recommended that the student take the Summer Bridge prior
to any move to an AP Prep course.

Course Descriptions

SUMMER MATH BRIDGE
One semester, one credit
This course is offered in summer school and is appropriate for students who would like to get a head start on *AP Prep Algebra II: Advanced Systems, or for a student who has been taking classes at the college prep level who would like to move to the AP prep level. The course content will focus on formal logic, mathematical proof, and algebraic systems. The nature of this course will provide some review of Algebra I concepts and skills, but these will not be the focus of the course. Out-of-class homework assignments are part of the course requirements.

ALGEBRA I
One year, two credits
Prerequisite: Completion of 8th grade math
Content includes: simplifying, factoring, solving equations and inequalities, solving systems of equations, graphing, working with rational expressions, working with radical expressions, solving quadratic expressions, and problem solving. Out-of-class
homework assignments are part of the course requirements.

*AP PREP ALGEBRA I
One year, two credits
This course is for advanced 8th grade students who wish to pursue advanced high school mathematics. The course content will focus on set theory, rigorous development of relations, and functions from a set theoretic perspective, basic algebraic systems, basic number theory, development of the system of integers, and an extension of topics included in the College Prep Algebra I course. Extensions of Algebra I topics will include: factoring, simplifying algebraic expressions, solving linear and quadratic equations, and simplifying and using radical expressions. There will be an emphasis on higher order thinking through providing mathematical arguments and solving problems. Students who earn an A or B in this class are encouraged to take *AP Prep Algebra II: Advanced Systems their freshman year.

ALGEBRA II
One year, two credits
Prerequisite: Algebra I or *AP Prep Algebra I
This course extends the work of College Prep Algebra I. It includes: a study of relations and functions as sets of ordered pairs, a study of the real numbers as a field, a study of the complex numbers as a field, solving systems of linear and quadratic equations, solving inequalities and systems of inequalities, a study of sets of polynomials (defined over a set of numbers) as systems and polynomial equations, introduction to and application of the binomial theorem, an introduction to circular functions, an introduction to arithmetic and geometric progressions. Out-of-class homework assignments are part of the course requirements.

*AP PREP ALGEBRA II
One year, two credits
Prerequisite: Algebra I or *AP Prep Algebra I
This is an extremely rigorous course designed for the most mathematically talented students. This course will cover all the topics covered in Algebra II. This course will also include formal logic, syllogistic proof, set-theoretic approach to the study of relations and functions, an introduction to abstract algebraic systems, and the study of the system of integers and rational numbers. The focus of this course is on higher order thinking skills including: analysis, synthesis, argument building and problem solving. Students should expect to work with other students in study group situation in class and outside of school. Students should expect to spend more than one hour per day outside of class to meet the learning demands of this course.

GEOMETRY
One year, two credits
Prerequisite: Algebra II or *AP Prep Algebra II
Geometry is the logical study of points, lines, angles, polygons, and circles with emphasis on the use of formal deductive reasoning to write proofs. This course will also include right triangle trigonometry. Out-of-class homework assignments are part of the course requirements. The course is demanding in both time and effort. Students should be self-motivated and possess a high level of self-discipline. Out-of-class homework assignments are part of the course requirements. The course is demanding in both time and effort. Students should be self-motivated and possess a high level of self- discipline. Continuation in the second semester of this course requires either a passing grade in the first semester or a grade of “conditional”.

*AP PREP GEOMETRY
One year, two credits
Prerequisite: Algebra II or *AP Prep Algebra II
This course will cover all of the topics covered in Geometry. There will be an emphasis on the use of formal logic and the level of rigor in constructing proofs will be much higher that that in College Prep Geometry. This course will also include Law of Sines, Law of Cosines, non-Euclidian geometries, and some analytic geometry.

STATISTICS WITH FINANCIAL APPLICATIONS
One year, two credits
Prerequisite: Geometry or *AP Prep Geometry
This is an activity-based introduction to statistics. Content includes descriptive statistics, probability, sampling and tests of
statistical significance, and business application of math topics. It is recommended that students have their own TI-83+ calculator, or an equivalent model; however, calculators are available for use in the classroom. Out-of-class homework assignments are part of the course requirements.

COLLEGE ALGEBRA
One year, two credits
Prerequisite: Geometry or *AP Prep Geometry
This course is intended for college-bound students who desire four years of high school mathematics. It consists of an in-depth study of algebraic topics such as linear and quadratic equations, inequalities, functions and their graphs (including polynomial, exponential, inverse, logarithmic, and rational functions), and a study of matrices. Students will use graphing calculators, which will be provided. Students must have a scientific calculator. Out-of-class homework assignments are part of the course requirements.

PRE-CALCULUS/TRIGONOMETRY
One year, two credits
Prerequisite: Geometry or *AP Prep Geometry
This course is intended to prepare strong math students for AP Calculus AB. It will serve as a bridge from high school to college level mathematics. This course is very rigorous in terms of the mathematical content and pace. Topics covered include:
polynomial, rational, trigonometric, inverse trigonometric, logarithmic, and exponential functions along with their graphs; polar
coordinates; parametric equations; sequences and series; proof by induction; vector operations; trig identities; limits and
continuity; matrix transformations; analytic geometry; and polar representations of complex numbers. The course will also focus on applications and problem solving. A graphing calculator, such as a TI-83+ or TI-89, is highly recommended. Out-of-class homework assignments are part of course requirements.

*AP PREP PRE-CALCULUS/TRIGONOMETRY
One year, two credits
Prerequisite: Geometry or *AP Prep Geometry
This course is intended to prepare strong math students for AP Calculus BC and to equip them with the mathematical tools they will find necessary for success in weighted physics (typically taken concurrently). Students are required to do summer preparatory work in pre-calculus and introductory calculus topics. It will serve as a bridge from high school to college level mathematics. This course is very rigorous in terms of the mathematical content and pace. Topics covered include: polynomial, rational, trigonometric, inverse trigonometric, logarithmic, and exponential functions along with their graphs; polar coordinates; parametric equations; sequences and series; proof by induction; vector operations; trig identities; limits and continuity; matrix
transformations; analytic geometry including rotated conic sections; and polar representations of complex numbers. The course will also focus on applications and problem solving. A graphing calculator, such as a TI-83+ or TI-89, is highly recommended. Out-of-class homework assignments are part of course requirements.

*AP CALCULUS AB
One year, two credits
Prerequisite: Pre-Calculus/Trigonometry or *AP Prep Pre-Calculus/Trigonometry
This is a very rigorous, university level course. Students are required to do summer preparatory work in pre-calculus and
introductory calculus topics including matrix theory, parameterizations, conic sections, and limits. Homework is assigned and
collected regularly throughout the school year. The course covers applications, optimization, differential equations, and antidifferentiation, infinite series, calculus using parametric and polar equations, advanced techniques of integration, and many other topics. Students can earn university credit via the Advanced Placement Exam given near the end of the school year. A graphing calculator, such as a TI-83+ or TI-89, is high recommended.

*AP CALCULUS BC
On year, two credits
Prerequisite: *AP Prep Pre-Calculus/Trigonometry
This is a very rigorous, university level course. Students are required to do summer preparatory work in pre-calculus and
introductory calculus topics including matrix theory, parameterizations, conic sections, and limits. Homework is assigned and
collected regularly throughout the school year. The course covers university-level calculus including limits, differentiation
theorems, Riemann sums, business and scientific applications, optimization, differential equations, and anti-differentiation, infinite series, calculus using parametric and polar equations, advanced techniques of integration, and many other topics. Students can earn university credit via the Advanced Placement Exam given near the end of the school year. A graphing calculator, such as a TI-83+ or TI-89, is highly recommended.

Page Updated 10-17-07

Urbana High School
1002 S. Race Street
Urbana, Illinois 61801

Phone: 217-384-3505
Fax: 217-384-3532
Attendance: 384-3522