The Mathematics Department is committed to providing a quality program in college preparatory mathematics. Our goal is to equip all students graduating from Uni High with the prerequisites in mathematics to succeed in their chosen course of study at any university in the United States. We are also committed to using the NCTM Standards and the Common Core State 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 student’s ability to communicate about mathematics both orally and in writing. We want the students to value the role of both investigation and proof in mathematics, and we use technology where it is helpful in supporting these aims. Calculators are used in all courses, and students use specialized technology such as spreadsheets, dynamic geometry, computer algebra systems, the internet, and other software packages 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 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 entering Uni will automatically be placed into Math 1. Freshmen entering Uni will be placed into
Math 1 unless they take and pass the equivalent of the final exam for Math 1. 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. Students entering Uni who intend to take
Calculus as their first course must either have a grade of B or better recorded for a Precalculus course on a high
school transcript or take placement exams covering trigonometry and algebra.

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 email hcrussel@illinois.edu if these guidelines do not answer your questions, or to arrange for placement tests.

# Courses

__Math 1__

(Subfreshman)
(1 unit)
This first math course for Uni students introduces them to key ideas and skills. This course integrates topics from algebra, geometry, and statistics, with topics that include facility with basic operations on real numbers, modeling, systems of linear equations and inequalities, an introduction to vector and matrix arithmetic, work with linear and exponential functions, the function concept, recursion, congruence, coordinate geometry, geometric proofs, linear regressions, and residual analysis. Use of a graphing calculator and spreadsheets is taught and encouraged throughout the course.

__Math 2__

(9th grade)
(1 unit)
This second integrated course continues the functions strand from Math 1 by adding quadratic functions and radical expressions, absolute value, piecewise, and inverse functions. In the algebra strand, students learn algebraic and graphical techniques for solving quadratic equations, are introduced to complex numbers, and use inverse matrices. In the geometry strand, students work with properties of geometric figures including polygons and circles, similarity, and right triangle trigonometry. They also undertake a study of probability. Students continue to use graphing calculators, spreadsheets, Mathematica, and geometry software.

__Math 3__

(10th grade)
(1 unit)
*Prerequisite: Math 2*

This third integrated course continues the functions strand from Math 1 and Math 2 by adding logarithmic, rational, and circular (trigonometric) functions, further developing the inverse function concept. In the algebra strand, students develop theory of polynomials. In geometry, more work with right triangle and oblique triangle trigonometry (including laws of sines and cosines) and representations in 3-D are explored. In the statistics strand, students explore the normal distribution, experimental design, and simulation. Students continue to use graphing calculators, spreadsheets, Mathematica, and geometry software.

__Advanced Topics in Mathematics__

(1 unit)
*Prerequisite: Algebra 2 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__

(1 unit)
*Prerequisite: Algebra 2 with Trigonometry*

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.

__Accelerated Calculus 1__

(1 unit)
*Prerequisite: Math 3, successful performance on a mastery exam, 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 Math 3 curriculum, and have demonstrated a facility with calculations and swift recall of previously-learned skills. The syllabi for the University of Illinois and Parkland College 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.

__Calculus 1__

(1 unit)
*Prerequisite: Advanced Topics in Mathematics.*

The syllabi for the University of Illinois and Parkland College 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 computer algebra systems and other software.

__Accelerated Calculus 2/3__

(Fall and/or Spring)
(Each 1/2 unit)
*Prerequisite: Acc. Calculus 1*

Accelerated Calculus 2 includes polar coordinates and conic sections, parametric curves in the plane and in space, vectors and surfaces in space, and partial differentiation. Accelerated Calculus 3 is the second semester of this course, with content including multiple integrals, vector analysis, differential equations, infinite sequences and series (convergence, Taylor series, power series) Taylor’s formula, advanced techniques of integration, indeterminate forms and improper integrals. 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 2/3 Calculus & __*Mathematica*

*Mathematica*

*Prerequisite: Calculus 1 or Acc. Calculus 1*

Calculus 2/3 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 2) 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 for each course are separate from normal “concurrent enrollment” tuition, and most likely will NOT be waived for the 2017-2018 school year.

# Faculty

**Ioana Boca**(iboca@illinois.edu) earned her BS in Mathematics from the University of Bucharest, a Ph.D in Mathematics from the University of Southern California, and a MS in Statistics from the University of Illinois. She teaches Geometry, Calculus 1, and Accelerated Calculus 1.

**Emily Buhnerkempe**(emilyeb@illinois.edu) teaches Math 3 first period, Math 3 third period, Math 1 fifth period, and Math 1 eighth period. She holds a master's degree in mathematics from Miami University in Ohio and a bachelor's degree in mathematics from Grand Valley State University in Michigan. At Miami she was a Graduate Assistant for two years and taught Pre-Calculus and Calculus. She has taught in all levels of math from General Education Math to Statistics and Calculus at Parkland College for three years as a tenure-track instructor. She also taught all levels of math at Lake Land College in Mattoon for four years as a tenured professor. In 2015-16, she served as a subject matter expert for textbooks and online course materials for McGraw-Hill.

**Craig Russell**(hcrussel@illinois.edu) is a Teaching Associate and Executive Teacher who earned his B.S. in mathematics at MIT in 1983, then served in Hawk and Patriot units in Germany for seven years before being "assigned" to RPI, where he earned an MS in Applied Mathematics and completed all but dissertation requirements for the PhD in 1992. He was then assigned to teach at the United States Military Academy (West Point), where he taught freshman and sophomore math courses and was the math department leader in a study involving issuing students laptop computers for class work. At West Point, Mr. Russell was bitten by the teaching bug, so he resigned from the Army to become a high school teacher. Mr. Russell's favorite people are his wife and two children, followed by students who like math. He is teaching Geometry and Accelerated Calculus 2/3.

**Erin Smith**(erines3@illinois.edu) is teaching Math 2 and Advanced Topics. She has a degree in secondary education mathematics from Ball State University and is currently working at UI towards a master’s in Educational Administration. Erin has been a math instructor at Parkland Community College and at Bismarck-Henning High School. She most recently taught at Next Generation School, where she was also head track coach.

# Contests

**Parkland/ICTM Contests** These are regional and state competitions featuring individual tests in Algebra 1, Geometry, Algebra 2, and Pre-Calculus, as well as team testing situations with a 5-person "calculating" team, two levels of 8-person team (written) and 2-person team (head-to-head timed contest), and an oral competition. Uni High usually sends three of each team to the regional contest at Parkland (last Saturday in February), and one of each team to the state contest (last Saturday in April). Speak to your math teacher, and watch announcements for grade-level "math team" meetings at lunchtime!

**MathCOUNTS** is a regional and state competition for junior-high level students (subfreshmen). We're limited to a team of about 6 individuals. Speak to Mr. Russell if you're interested.

**Mathematical Talent Search** This is several rounds of difficult problems done by individuals. You generally have a month to complete each round, then mail in results for grading. If you're interested, see Mr. Russell soon--the first round is in September. These problems are very difficult, but they don't generally require calculus. Solutions are in the form of proofs or paragraphs (usually).

**American Mathematics Competition the AMC **is a national contest given at three levels. Subfreshmen compete in the AMC-8 in November; freshmen and sophomores may take the AMC-10 or AMC-12, and juniors and seniors may take the AMC-12, in February. Winners are invited to take the American Invitational Mathematics Exam (AIME) in March, and top scorers on that exam will be invited to participate in the USA Math Olympiad. American Statistics Association High School Project Competition Students enrolled in Statistics submit second semester projects, after making oral presentations to faculty and students in the Statistics Department at the University of Illinois.