Algebra I and Descriptive Statistics

(Subfreshman)(1 unit)
This first math course for Uni students introduces them to key ideas and skills. The Algebra course topics include: facility with basic operations on real numbers, operations with polynomials, factoring polynomials, solving linear and quadratic equations, the quadratic formula, graphing linear and quadratic functions, exponential functions, the function concept, recursion, and proportional reasoning. The Descriptive Statistics component includes frequency tables, charts and graphs, measures of central tendency, measures of variation, linear regression, and introductory statistical reasoning. Use of a graphing calculator and spreadsheets is taught and encouraged throughout the course.

Geometry and Trigonometry

(9th grade)(1 unit)
The Geometry course has two major components. Approximately three-fourths of the year is devoted to standard plane and solid geometry in the tradition of Euclid. The second component is a study of trigonometry focusing on right and oblique triangles and the unit circle. The Euclidean portion of the course emphasizes the concept of mathematical proof. Starting with a small number of axioms which establish certain basic properties of geometric objects, the theorems generally covered in a first year course are logically deduced. The geometric objects are generated from a few undefined terms by means of definitions. While understanding proofs is a primary objective of the course, all of the basic geometric facts and computations which will be of use in subsequent courses are covered. Students reinforce their earlier work with graphing calculators and use dynamic geometry software to make and test conjectures.

Algebra II with Trigonometry

(10th grade)(1 unit)
Algebra II is taught at a more advanced level than traditional Algebra II courses. Many topics from Algebra I are extended to more complex applications. New topics include: matrices, complex numbers, rational exponents, radicals, rational functions and expressions, inequalities, logarithms, power functions, conic sections, solving systems, and various application problems. The course also includes a study of trigonometry focusing on modeling with periodic functions and trigonometric identities and equations. Graphing calculators are used extensively throughout the course, and students may use other technologies at times.

Advanced Topics in Mathematics

(11th - 12th grade)(1 unit)
Prerequisite: Algebra II with Trigonometry
This course will give students further preparation for a successful study of calculus and will introduce students to concepts of discrete mathematics which are vital in the study of computer science, social sciences, and other fields. Precalculus topics include vectors, complex numbers, polar graphs, and polynomial theory, with extensive work on trigonometric identities, rational functions, and function algebra. Discrete topics include mathematical induction, elementary logic, fractals, combinatorics, and probability. Graphing calculator use is integral to the course.

Statistics

(11th - 12th grade)(1 unit)
Prerequisite: Algebra 2/Trig
This course is roughly equivalent to Statistics 100 at UIUC, and incorporates all topics on the Advanced Placement Statistics syllabus. The major theme of the course is "interpreting the world around us;" tools developed include the design of experiments, hypothesis testing, and analysis of variation. Students use graphing calculators, statistical software packages, spreadsheets, and simulation software to explore concepts and analyze results. Individual and team projects each semester, as well as several analyses of articles in the media, help students both to apply the concepts and to see how others have applied them.

Calculus I

(12th grade)(1 unit)
Prerequisite: Advanced Topics in Mathematics.
The syllabi for the University of Illinois first semester calculus and for the Advanced Placement Exam in Calculus (AB) will be used as guides for course content. Emphasis will be placed on an understanding of concepts and mastery of the techniques and applications of differentiation and integration. Students use graphing calculators as well as spreadsheets and specialized software.

Accelerated Calculus I

(11th grade)(1 unit)
Prerequisite: Algebra 2/Trig and permission of the Math Department chair
This course is offered to qualified students who have shown consistently strong performance throughout their first three math courses, to include mastery of additional topics in the Geometry and Algebra 2 curricula, and have demonstrated a facility with calculations and swift recall of previously-learned skills. The syllabi for the University of Illinois first semester calculus and for the Advanced Placement Exam in Calculus (AB) will be used as a guide for course content, but additional topics of a more theoretical nature, such as a more careful consideration of limits are also included. Content includes techniques and applications of differentiation and integration.

Accelerated Calculus II/III

(12th grade)(Each 1/2 unit)
Accelerated Calculus II is the sequel to the Accelerated Calculus I course. Course content includes advanced techniques of integration, polar coordinates and conic sections, indeterminate forms, Taylor's formula, improper integrals, infinite sequences and series (convergence, Taylor series, power series), and parametric curves of vectors in the plane. Accelerated Calculus III is the second semester of this course, with content including vectors, curves, surfaces in space, partial differentiation, multiple integrals, vector analysis, and differential equations. The syllabi for the University of Illinois second and third semester calculus courses and the Advanced Placement Exam in Calculus (BC) serve as guides for course content. Technology used includes graphing calculators and computer algebra systems.

Calculus II/III Calculus & Mathematica

(12th grade)
Prerequisite: Calculus 1 or Acc. Calculus 1
Calculus II/III can be taken through the Calculus & Mathematica Distance Education Program for college credit at the University of Illinois. Calculus II (Math 231) can be taken the first semester or over two semesters for 3 hours credit. If Math 231 (or Accelerated Calculus II) is completed during the first semester, Multivariable Calculus (Math 241) can be taken the second semester for 3 hours credit. Students wishing to take C&M must indicate their preference on their Uni High course request form and complete the Distance Education registration form available from the Student Services Office. Fees of around $800 per semester were waived for the 2007-2008 school year but may be re-instated