Math Department Philosophy

The Mathematics Department is committed to providing a quality program in college preparatory mathematics.  Our goal is to equip every student graduating from Uni High with the prerequisites in mathematics to be able to enter any university in the United States without having to take a remedial course in mathematics.  We are also committed to using the NCTM Standards and the Illinois Learning Standards as guidelines for our curriculum.  At all course levels, we emphasize approaching problems from the numerical, geometric, and analytic points of view and developing the students' ability to communicate about mathematics both orally and in writing.  We want the students to value the role of both investigation and proof of mathematics, and we use technology where it is helpful in supporting these aims – calculators are used in all courses, and students use specialized technology for data collection and analysis.  Spreadsheets, dynamic geometry, computer algebra systems, the internet, and other software packages are used at various times to represent information, form conjectures, solve problems, and communicate results.

Mathematics is a language for describing patterns in the world around us.  We believe that when students recognize that mathematics comes from a rich historical development, and that new mathematical ideas, applications, and algorithms are continually being generated, they will learn to value mathematics not only for what it can do but for what it is.  If students experience the wonder of mathematics and are intrigued by a mathematical curiosity, they will come to appreciate and even enjoy the process.  Although mathematics is a useful subject that helps us find the amount spent on groceries, communicate scientific relationships, and model problems involving interest, it is also a wonderful subject in itself, with startling relationships and connections that are fascinating to think about.

Math Department Placement Procedures

All subfreshmen and freshmen entering Uni will automatically be placed into Algebra I, unless they demonstrate proficiency in Uni math courses by passing one or more placement exams. Placement Examinations were created for the express purpose of placing incoming students into the appropriate mathematics courses. Students entering in sophomore, junior, or senior years may automatically place out of a Uni math course only if they have received a grade of C or better on a high school transcript for a substantially equivalent course.  Otherwise, they must take placement exams.  A passing score on a placement exam qualifies the student to take the next course in the Uni sequence.  Placement exams (50 minute, multiple-choice/short answer format) are available in the following subjects:

• Algebra I  (graphing calculator allowed, but not required)
• Geometry (graphing calculator allowed, but not required)
• Algebra II  (graphing calculator required)
• Trigonometry (graphing calculator required)

•  In addition, new students with grades of B or better in an Algebra 2-equivalent courses who wish to enter Calculus must take and pass both an Algebra 2 competency exam and a Trigonometry proficiency exam.

Our experience with students taking Algebra I in 6^th or 7^th grades before coming to Uni has been that only the most exceptional will place out of Algebra I and into Geometry.  Students who begin a study of algebra before they are cognitively ready for the level of abstraction required tend to learn only mechanical processes, and our goal is to get students beyond the mechanical and into real understanding.   

Note: These proficiency guidelines are directed towards students just entering University High School. Please contact a member of the Mathematics Department (tel. 333-6034 or 244-4804, or email  hcrussel @uni.uiuc.edu) if these guidelines do not answer your questions, or to arrange for placement tests.

Requirements for Graduation/Courses Offered

Course names are linked to brief descriptions of the course content.

All students are required to complete a minimum of 3 units of math beyond Algebra I, including:

• Geometry
• Algebra II with Trigonometry

and a choice of one of the following:

• Advanced Topics in Math
• Calculus
• Statistics
• In exceptional circumstances, another higher-level course approved by the Executive Teacher of the Math Department.

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Maintained by UNIMATH.  Last update:  July 25, 2008
University of Illinois Laboratory High School, Urbana

Algebra I

(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.  In addition to algebraic content, students are introduced to data interpretation (statistics), including use of 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.  

Textbook and materials list
Course list

Geometry and Trigonometry

(9^th 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

(10^th grade)

(1 unit)

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.

Textbook and materials list
Course list

Advanced Topics in Mathematics

(11^th - 12^th 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

(11^th - 12^th 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

(12^th grade)

(1 unit)

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

(11^th grade)

(1 unit)

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

(12^th 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.  The syllabi for the University of Illinois second semester calculus course and the Advanced Placement Exam in Calculus (BC) serve as guides for course content.   Technology used includes graphing calculators and computer algebra systems.Accelerated Calculus III is the second semester of this course.  The content includes vectors, curves, surfaces in space, partial differentiation, multiple integrals, vector analysis, differential equations.

Calculus II/III Calculus & Mathematica

(12^th 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 230) can be taken the first semester or over two semesters for 3 hours credit.  If Math 230  (or Accelerated Calculus II) is completed during the first semester, Multivariable Calculus (Math 242) 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. 

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