Mathematics

The University of Chicago Laboratory Schools

Mathematics

University High School requires that every student successfully complete three years of mathematics while in high school. Students who have questions about the mathematics requirements are urged to see their mathematics teacher or the chairperson of the Mathematics Department.

Credit And Placement
The normal policy of the Mathematics Department is not to award partial credit (credit of less than one unit) for work in mathematics of less than one year. Any senior who is registered in a Math course and plans to graduate early should notify the department as soon as possible, but certainly by the beginning of their last quarter at University High School. Seniors who leave school early for May Project will receive 1 credit for AP Calculus or AP Statistics and 7/8 of a credit for any other mathematics course.

Problems concerning prerequisites and placement should be discussed with the department chairperson. All new students must check their placement with the department before final registration.

Texts And Equipment
Scientific calculators are required in Algebra and Geometry. Graphing calculators are required and used extensively in all courses starting at Advanced Algebra or Accelerated Advanced Algebra/Trigonometry. The TI-84 Plus is recommended for students purchasing calculators for these courses.

Notes on the Sequential Flow Chart
Most of the students entering our high school as freshmen have had a year of algebra, and many have also had a year of geometry. These students begin the freshman year with Geometry, Advanced Algebra, or Accelerated Advanced Algebra. We provide opportunities for students of differing backgrounds to accelerate their studies if they wish. Students interested in such a program should discuss their plans with their teacher or the department chairperson.

Note 1: The Mathematics Department is careful to place each student in a course appropriate to the student's background and interests. Placements other than those indicated in the diagram are occasionally recommended.

Note 2: Solid lines indicate the traditional sequence of courses. Students electing to move from Functions, Statistics, and Trigonometry to Accelerated Pre-Calculus may be required to do independent work in preparation for the next course.

Note 3: Students who have successfully completed Algebra in 7th grade take Geometry in 8th grade. Students who have successfully completed Algebra in 8th grade or high school take Summer School Geometry, or Geometry. See below for course descriptions.

Note 4: Any 11th or 12th grade student who has completed or is currently enrolled in either Pre-Calculus course may take AP Statistics.

Note 5: Any student who has completed either Pre-Calculus course may take Math Seminar.

Note 6: Any student who has successfully completed BC Calculus and earned a grade 5 on the AP exam is eligible to take the University of Chicago's exam for placement into one of its Math courses.

Algebra 1
Course Number: 1410
Credit: 1
Pre-requisite: Placement by the department

Topics include: an intuitive transition from arithmetic to Algebra, with special emphasis on equations; solution of linear equations; introduction to coordinate Geometry; solution of systems of equations by algebraic and graphical methods; solution of second degree equations; operations with polynomials and with radicals and exponents. Applications are stressed throughout.

Summer School Geometry
Course Number: 2450
Credit: 1
Pre-requisite: Algebra 1 and placement by the department

This class is designed for students entering grades 9-12 who have already completed a year of Algebra in 8th grade or high school and wish to advance in mathematics. The course includes congruence and similarity; properties of polygons, circles, and solids, and proof. Both Euclidean and algebraic approaches are explored. Constructions and applications of Geometer's Sketchpad are integral parts of this course.

Geometry
Course Number: 1420
Credit: 1
Pre-requisite: Algebra 1 and placement by the department

This course includes congruence and similarity; properties of polygons, circles, and solids, and proof. Both Euclidean and algebraic approaches are explored. Constructions and applications of Geometer's Sketchpad are integral parts of this course.

Advanced Algebra
Course Number: 1430
Credit: 1
Pre-requisite: Geometry or placement by the department

Topics include: number systems, including complex numbers; equations and inequalities; linear, quadratic, polynomial, and rational functions, their properties and graphs; radicals, exponents, and logarithms; systems of equations; matrices; applications.

Accelerated Advanced Algebra/Trigonometry
Course Number: 1431
Credit: 1
Pre-requisite: Completion of both Algebra and Geometry with a final grade of at least B or placement by the department

This course provides a thorough introduction to mathematical functions. Topics include: linear, quadratic, exponential, logarithmic, rational, irrational, polynomial, and trigonometric functions, applications, and proofs.

Discrete Mathematics and Statistics
Course Number: 1440
Credit: 1
Pre-requisite: Accelerated Advanced Algebra/Trigonometry with at least a final grade of at least B or placement by the department

Topics include: matrices, sequences and series, mathematical induction, combinatorics, the binomial theorem, probability and statistics, and fractals. Students prepare two written papers: a short biography of a prominent mathematician, and an independent mathematical investigation.

Trigonometry, Statistics and Discrete Math Topics
Course Number: 1450
Credit: 1
Pre-requisite: Advanced Algebra or placement by the department

Topics include: Trigonometry, sequences and series, mathematical induction, binomial theorem, combinatorics, introductory probability and statistics, and matrices. Applications are emphasized.

Pre-calculus
Course Number: 1460
Credit: 1
Pre-requisite: Functions, Statistics, Trigonometry or placement by the department

Topics include: polynomial and rational functions and inequalities; exponential and logarithmic functions; trigonometry, polar coordinates, and complex numbers; conic sections; vectors; limits; introduction to calculus.

Accelerated Pre-calculus
Course Number: 1461
Credit: 1
Pre-requisite: Discrete Mathematics with a final grade of at least B or placement by the department

This course is designed for students who plan to complete the AP Calculus BC course. Topics include: polynomial, rational, exponential, and logarithmic functions; trigonometry; conic sections; polar coordinates and polar form of complex numbers; vectors and parametric equations. The spring quarter is devoted to beginning calculus, covering limits and derivatives and their applications.

AP Calculus AB
Course Number: 1470
Credit: 1
Pre-requisite: Accelerated Pre-calculus with a final grade of at least C, or Pre-calculus with a final grade of at least B, or placement by the department

This course follows the Advanced Placement AB Calculus syllabus including limits, derivatives, integrals, and differential equations. Success on the AP Calculus AB examination normally leads to advanced placement and/or credit in college mathematics.

AP Calculus BC
Course Number: 1472
Credit: 1
Pre-requisite: Accelerated Pre-calculus with a final grade of at least B or placement by the department

This course follows the Advanced Placement BC Calculus syllabus. Besides all AB topics, topics include analysis of vector, polar, and parametric functions, and sequences and series. Success on the AP Calculus BC examination normally leads to advanced placement and/or credit in college mathematics.

Math Seminar
Course Number: 1475
Credit: 1
Pre-requisite: Pre-calculus or placement by the department

Topics to be chosen by the class. In recent years, among the topics chosen have been linear algebra, basic number theory, and an introduction to functions of one real variable. One of the objectives of the course is to bridge the gap between high school mathematics and the mathematics curriculum at the university level for students in the physical sciences. Note: this course will be offered if there is sufficient enrollment.

AP Statistics
Course Number: 1477
Credit: 1
Pre-requisite: Two years of laboratory science, currently enrolled in 11th or 12th grade and, completion of or concurrent enrollment in Pre-calculus or Accelerated Pre-calculus

This course follows the AP Statistics syllabus, which is built around four main topics: exploring data, planning a study, probability as it relates to distributions of data, and inferential reasoning. TI-83 or TI-83 Plus calculator (no substitutions) required.

Independent Study in Mathematics
Course Number: 1476
Credit: 1/3 per quarter
Pre-requisite: Consent of instructor and placement by the department

A student may arrange an independent study project with any department member. In accordance with the School's Independent Study policy, the student must submit a written proposal for the approval of the department. Proposals must center on topics beyond the scope of regular courses.

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