The Mathematics Department of Lake Forest High School will prepare students for life in a increasingly technological world inthe following core areas: problem solving, logical reasoning,communicating mathematical ideas, applying mathematics to realworldsituations and using technology as a mathematical tool to solve mathematical problems. We will maintain learning environments and classroom situations in which students can develop confidence in the above endeavors.

ADVANCED ALGEBRA — 1 Unit of credit Juniors, Seniors
Prerequisite: Plane and Solid Geometry with current teacher or Instructional Director recommendation
This course assumes the student understands the concepts, and exhibits competency in the skills of Algebra l. It is designed for the serious math student who will take additional math courses at a higher level. In addition to studying the traditional topics of Algebra 1 at a more advanced level, there is study of the field of real numbers, the field of complex numbers, conic sections, and exponential and logarithmic functions. Students will learn to visualize various relations and functions through graphing on the coordinate plane both manually and by using graphing calculators and computer programs. Successful completion of this course will satisfy the prerequisite for enrollment in College Algebra and Trigonometry.

ADVANCED ALGEBRA ACCELERATED – 1 Unit of credit Freshmen
Prerequisite: Student has mastered Algebra 1 in the middle school and has not previously taken a geometry course. This course is designed for the serious math student who will take additional math courses at a higher level and assumes the student has mastered the concepts and exhibits competency in the skills of Algebra 1. In addition to Algebra 1, there is a study of real numbers, the field of complex numbers, rational expressions, and exponential and logarithmic functions. Students learn to visualize various relations and functions through graphing on the coordinate plane both manually and by using graphing calculators and computer programs. Successful completion of this course will satisfy the prerequisite for enrollment in Plane and Solid Geometry Accelerated. This course is similar to our present Advanced Algebra course but is designed for accelerated freshmen in our new math sequence. It will not require the concept of proof that is taught in geometry.

ADVANCED ALGEBRA AND TRIGONOMETRY H — 1 Unit of credit Freshmen
Prerequisite: Student has mastered Algebra 1 in the middle school with current teacher or Instructional Director recommendation
This course is designed for very talented mathematics students who plan at least a four-year sequence in mathematics. The content of this course is similar to Advanced Algebra but it is a more challenging course in that the topics are covered in a more rigorous way. There is an increased emphasis on proof and analytical methods. Considerable time is spent on trigonometry which is presented as a class of periodic functions. Trigonometric identities are studied and applications are made using the law of sines and the law of cosines. Problem solving is a major strand of this course. Successful completion of this course will satisfy the prerequisite for enrollment in Plane and Solid Geometry Accelerated
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ADVANCED COMPUTER SCIENCE HONORS – 1 Unit of credit Juniors, Seniors
Prerequisite: AP Computer Science or significant programming experience and current teacher or instructional Director recommendation
This course is the next course taken after AP Computer Science. Advanced data structures are covered including stacks, queues, linked lists and trees. Also, advanced algorithms are analyzed. Design, documentation and testing of programs will be emphasized.

ADVANCED TOPICS IN MATHEMATICS H — 1?2 Unit of credit Seniors Prerequisite: Multivariable Calculus and current teacher or Instructional Director recommendation This semester course builds on the concepts of multivariable calculus, and challenges students to apply the calculus of higher dimensions and principles of linear algebra to a variety of problems in science and business. Students will use computer software to discover and demonstrate relevant theory and concepts, and will engage in problem based learning activities. Students will also have the opportunity to do independent research in other areas of advanced mathematical study, such as: computer animation, chaos, fractals, electronic privacy, telecommunications, code encryption and cracking, computer simulations, and market analysis.

ALGEBRA 2 — 1 Unit of credit Juniors, Seniors Prerequisite: Plane Geometry (or Plane and Solid Geometry) with recommendation of current teacher or Instructional Director This course is designed for those students who do not intend to pursue a math-related course of study at the college level. A review of Algebra 1 concepts and skills will be followed by topics studied in Advanced Algebra but presented in a less rigorous manner. These will include inequalities, graphing, probability and simple statistics, trigonometry of the right triangle and the conic sections. Successful completion of this course will satisfy the prerequisite for enrollment in Trigonometry/Statistics.

AP CALCULUS (AB) — 1 Unit of credit Juniors, Seniors Prerequisite: Precalculus and current teacher or Instructional Director recommendation This course is intended for students who have a thorough knowledge of algebra, axiomatic geometry, trigonometry and analytic geometry. Topics include functions, graphs, limits, continuity, derivatives, applications of derivatives, anti-derivatives, applications of anti derivatives and the definite integral. Students are expected to take the Advanced Placement Exam as part of this course.

AP CALCULUS (BC) — 1 Unit of credit Juniors, Seniors Prerequisite: Math Analysis H and current teacher or Instructional Director recommendation All of the topics in Calculus AB are taught. Additional topics include: vector functions, parametric equations, a rigorous definition of limit, complex integration techniques, areas bounded by polar curves, differential equations and a thorough study of sequences and series. The content of Calculus BC is designed to qualify students for placement and credit one semester beyond that granted for Calculus AB. Students are expected to take the Advanced Placement Exam as part of this course.

CALCULUS CP — 1 Unit of credit Seniors Prerequisite: Precalculus or College Algebra/Trigonometry with current teacher or Instructional Director recommendation This course is intended for students who have a knowledge of algebra, geometry, trigonometry, and precalculus. Topics include: functions, graphs, limits, continuity, derivatives, applications of derivatives, anti-derivatives, applications of anti-derivatives, definite integrals, and applications of the definite integrals. There will also be topics on combinatorics, graph theory, trees, counting techniques, and logic. This course will emphasize the use of technology to solve real world applications.

COLLEGE ALGEBRA AND TRIGONOMETRY — 1 Unit of credit Juniors, Seniors Prerequisite: Advanced Algebra or Plane & Solid Geometry Accelerated with current teacher or Instructional Director recommendation This precalculus course is designed for students preparing to take Calculus CP. Topics include: properties, graphs and applications of polynomial, rational, exponential, logarithmic and trigonometric functions; complex numbers, sequences, and series. The graphing calculator will be used extensively as both an instructional and a problem-solving tool. This course does not meet the prerequisite for Advanced Placement Calculus.

AP COMPUTER SCIENCE — 1 Unit of credit Sophomores, Juniors, Seniors Prerequisite: Plane and Solid Geometry or current teacher or Instructional Director recommendation The curriculum and course content will be the College Boards’ Advanced Placement Computer Science course. Topics covered include problem solving, object oriented programming and data structures. Design, documentation, and testing of programs will be emphasized. Students are expected to take the Advanced Placement Exam as part of this course.

ALGEBRA — 1 Unit of credit Freshmen, Sophomores, Juniors Prerequisite: Current teacher or Instructional Director recommendation This course is designed for students who have basic arithmetic skills but who need additional practice to master algebraic concepts. The curriculum of this course will be limited to the essential topics of a first-year Algebra course; however, these select topics will be covered in greater depth. The topics will include: (1) solving linear equations and inequalities, (2) graphs of linear equations and other topics related to the Cartesian coordinate system, (3) solving systems of equations, (4) basic operations with polynomials, (5) factoring and solving quadratic equations. Successful completion of this course will satisfy the prerequisite for enrollment in Plane Geometry.

INTERMEDIATE ALGEBRA — 1 Unit of credit Freshmen Prerequisite: Current teacher or Instructional Director recommendation This is the first high school mathematics course for students who plan three or four years of college preparatory mathematics. Students who take this course should be competent in basic arithmetic skills, abstract reasoning, and working with the symbols of mathematics. Also, the student has received significant exposure to algebra topics. In this course, topics include: (1) the real number system, (2) operations with polynomials, (3) solving first and second degree equations and inequalities in one and two variables, (4) solving systems of equations and inequalities, (5) factoring and solving quadratic equations, (6) rational expressions, (7) graphing in one and two dimensions, (8) word problems, (9) operations with radicals, (10) laws of exponents, and (11) functions and relations. Problem solving techniques are emphasized throughout the course. Successful completion of this course will satisfy the prerequisite for enrollment in Plane and Solid Geometry.

MATH 1 — 1 Unit of credit Freshmen Prerequisite: Current teacher or Instructional Director recommendatio This laboratory course is designed primarily for freshmen who require a review of the basic skills necessary for Algebra A. The major emphasis will be to develop and reinforce skills in performing the four arithmetic operations on whole numbers, fractions and decimals. It also includes a comprehensive treatment of the metric system, informal geometry, statistics and basic consumer applications of earning, spending, borrowing and investing money. A considerable amount of daily work is assigned in order to develop the necessary skills. Successful completion of this course will provide the preparation necessary for Math 2 or Algebra 1.

MATH 2 — 1 Unit of credit Sophomores Prerequisite: Math 1 with current teacher of Instructional Director recommendation This course is designed for the student who has successfully completed Math 1 and is not ready for the abstractions of Algebra 1. Nonsequential units of length one, two or three weeks developed around topics of real world applications will be the major thrust. The topics will include estimation, rounding, calculator skills, following and giving directions, formula usage, tables and charts, statistics, problem solving, probability, measurement and geometric constructions. Successful completion of this course will provide the preparation necessary for success in Algebra 1 and/or Consumer Math.

MATH ANALYSIS H — 1 Unit of credit Sophomores, Juniors Prerequisite: Plane & Solid Geometry H with current teacher or Instructional Director recommendation This is a Precalculus course for mathematically talented students. It reviews and extends topics covered in previous math courses. New topics include an in-depth study of elementary functions and their limits, vector analysis, polar coordinates and polar equations, mathematical induction, and derivatives of polynomial, logarithmic, trigonometric and exponential functions. Successful completion of this course will satisfy the prerequisite for enrollment in AP Calculus (BC).

MULTIVARIABLE CALCULUS H — 1?2 Unit of credit Seniors Prerequisite: AP Calculus (BC) and current teacher or Instructional Director recommendation Multivariable Calculus is a third semester of calculus. Its topics include: vectors in a plane and space, partial differentiation, multiple integration and vector calculus.

PLANE GEOMETRY — 1 Unit of credit Sophomores, Juniors, Seniors Prerequisite: Algebra 1 or Algebra B with current teacher or Instructional Director recommendation This course covers traditional geometry topics through observation, measurement, intuition and induction. Students are also introduced to the methods of deductive proof. Successful completion of this course will satisfy the prerequisite for enrollment in Algebra 2.

PLANE AND SOLID GEOMETRY — 1 Unit of credit Sophomores Prerequisite: Algebra or Intermediate Algebra with current teacher or Instructional Director recommendation This course covers traditional Euclidean geometry topics with emphasis on synthetic, deductive proofs. Some topics from three-dimensional geometry are also studied. Topics from coordinate geometry are covered to show an alternative approach to studying the content of geometry. Successful completion of this course will satisfy the prerequisite for enrollment in Advanced Algebra.

PLANE AND SOLID GEOMETRY ACCELERATED – 1 Unit of credit Sophomore Prerequisite: Advanced Algebra Accelerated or Advanced Algebra Trig H This course assumes that the student understands the concepts and exhibits competency in the skills of Advanced Algebra Accelerated. It covers traditional Euclidean geometry topics with emphasis on synthetic deductive proofs. Some topics from three-dimensional geometry are also studies. Topics from coordinate geometry are covered to show an alternative approach to studying the content of geometry. Successful completion of this course will satisfy the prerequisite for enrollment in Precalculus or College Algebra and Trigonometry.

PLANE AND SOLID GEOMETRY H — 1 Unit of credit Freshmen, Sophomores Prerequisite: Advanced Algebra Trigonometry H with current teacher or Instructional Director recommendation Students who request this course should have high ability and achievement in both mathematics and reading. In addition to the topics covered in the Plane and Solid Geometry course, non Euclidean geometry, right triangle trigonometry and transformation geometry are studied. Inductive methods and reasoning are used extensively to introduce concepts, logic, deductive proofs, and problem-solving techniques are emphasized. Projects are assigned. Successful completion of this course will satisfy the prerequisite for enrollment in Math Analysis

H. PRE CALCULUS — 1 Unit of credit Juniors, Seniors Prerequisite: Plane & Solid Geometry Accelerated or Plane & Solid Geometry Honors with current teacher or Instructional Director recommendation This is a third year of algebra and a full course in trigonometry. It enhances the knowledge and skills for students who are very strong in the concepts of Advanced Algebra. New topics include an introduction to polar coordinates and equations, convergence and divergence of series, mathematical induction and functions and their limits. Because of the content of this course, students should be prepared to spend more time and effort than in previous courses. Successful completion of this course will satisfy the prerequisite for enrollment in AP Calculus (AB), AP Statistics or Calculus CP.

SENIOR MATH TOPICS – 1 Unit of credit Seniors Prerequisite: Trig/Stats/Quantitative Literacy, Precalculus, or College Algebra/Trigonometry This course consists of the study of Non-Western mathematics, the development of calculus, mathematics of the 18th and 19th centuries, Non- Euclidean geometry, number theory, Diophantine equations, probability theory, and set theory. Topics will also include the mathematics of art, music, and architecture.

AP STATISTICS — 1 Unit of credit Seniors Prerequisite: College Algebra/Trigonometry or Precalculus with current teacher or Instructional Director recommendation This semester course is a non-calculus-based introduction to statistics exposing students to four broad conceptual themes: exploring data, planning studies, probability and simulation, and statistical inference. While this course is not as mathematically rigorous as the AP Calculus courses, students must read, write, and analyze at the college level. Students are expected to take the Advanced Placement Exam as part of this course.

TRIGONOMETRY, STATISTICS & QUANTITATIVE LITERACY — 1 Unit of credit Seniors Prerequisite: Algebra 2 or Advanced Algebra with current teacher or Instructional Director recommendation This course consists of three areas of study. The three areas will be: 1.) topics of trigonometry, 2.) topics of statistics/quantitative literacy and 3.) an introduction to the mathematics of finance. The topics of trigonometry will include angles and triangles, trigonometric ratios, solving triangles, radian measure, circular functions, unit circle, graphs of trigonometry functions, trigonometric identities and solving trigonometric equations. The majority of the course will be spent on quantitative literacy and statistics in areas including: exploring data using graphs, twoway tables, measures of center and spread, producing data through sampling and experiments, scatterplots, regression analysis, residuals, correlation coefficients, probability, normal distributions, binomial distributions, sampling distributions, tests of significance and confidence intervals. The introduction of the mathematics of finance will employ spreadsheet software to study topics related to mortgages and other debt instruments