The main purpose of Algebra I is to develop students’ fluency with linear, quadratic, and exponential functions. The critical areas of instruction involve deepening and extending students understanding of linear and exponential relationships by comparing those relationships and by applying linear models to data that exhibit a linear trend. In addition, students engage in methods for analyzing, solving, and using exponential and quadratic functions. Some of the overarching elements of this course include the notion of function, solving equations, rates of change and growth patterns, graphs as representations of functions, and modeling.

Geometry:

The fundamental purpose of the Geometry course is to introduce students to formal geometric proofs and the study of plane figures, culminating in the study of right-triangle trigonometry and circles. Students begin to formally prove results about the geometry of the plane by using previously defined terms and notions. Similarity is explored in greater detail, with an emphasis on developing trigonometric relationships and solving problems with right triangles. The correspondence between the plane and the Cartesian coordinate system is explored when students connect algebra concepts with geometry concepts. Students explore probability concepts and use probability in real-world situations. The major mathematical ideas in the Geometry course include geometric transformations, proving geometric theorems, congruence and similarity, analytic geometry, right-triangle trigonometry, and probability.

Honors Prerequisite: Completion of the prior math course with a year-long grade of 90% or better, meets or exceeds benchmark score on the placement test, and teacher recommendation.

Geometry Honors:

The honors course covers additional topics, incorporates more challenging application and evaluation questions on assessments, and has a higher expectation for abstract reasoning and for the construction of viable arguments. Students will also participate in math competitions.

Algebra II:

The course extends students’ understanding of functions and real numbers and increases the tools students have for modeling the real world. Students in Algebra II extend their notion of number to include complex numbers and see how the introduction of this set of numbers yields the solutions of polynomial equations. Students deepen their understanding of the concept of function and apply equation-solving and function concepts to many different types of functions. The system of polynomial functions, analogous to integers, is extended to the field of rational functions, which is analogous to rational numbers. Students explore the relationship between exponential functions and their inverses, the logarithmic functions. Trigonometric functions are extended to all real numbers, and their graphs and properties are studied. Finally, students’ knowledge of statistics is extended to include understanding the normal distribution, and students are challenged to make inferences based on sampling, experiments, and observational studies. The TI-Nspire calculator is used as a learning tool and is required for the course.

Honors Prerequisite: Completion of the prior math course with a year-long grade of 90% or better, meets or exceeds benchmark score on the placement test, and teacher recommendation.

Algebra II Honors:

The honors course covers additional topics, incorporates more challenging application and evaluation questions on assessments, and has a higher expectation for abstract reasoning and for the construction of viable arguments. Students will also participate in math competitions.

Pre-Calculus:

It combines concepts of trigonometry, geometry, and algebra that are needed to prepare students for the study of calculus, physics, other sciences, and engineering in college. The course strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Topics covered include a review of basic algebraic concepts; analysis of functions and techniques for graphing polynomial, rational, algebraic, exponential, logarithmic and trigonometric functions; identities; probability and statistics; the formation of algebraic proofs; conics; polar coordinates; vectors; limits and derivatives. The TI-Nspire calculator is used as a learning tool and is required for the course.

Honors Prerequisite: Completion of the prior math course with a year-long grade of 90% or better, meets or exceeds benchmark score on the placement test, and teacher recommendation.

Pre-Calculus Honors:

The honors course will also cover introductory topics of differential calculus including differentiation, limits and solve related problems. Besides covering additional topics, this course incorporates more challenging application and evaluation questions on assessments, has a higher expectation for abstract reasoning and for the construction of viable arguments. Students will also participate in math competitions

Calculus is designed for the student who has successfully completed a pre-calculus course but is not ready to advance to AP Calculus. The course will begin with a review of functions and limits. The theory and techniques of differentiation and integration of polynomial and basic trigonometric functions are the primary topics of this course along with applications for both differentiation and integration. This course will provide a strong foundation that will give students the tools to succeed in future mathematics courses. The TI-Nspire calculator is used as a learning tool and is required for the course.

AP Prerequisite: Teacher recommendation and qualifying score on diagnostic test

AP Calculus AB is equivalent to the first semester of college calculus. It is expected that students who take this course will seek college credit, college placement or both from institutions of higher learning. There will be an exam for this course given through the AP College Board in the spring. The course reviews analytic geometry and limits. The theory and techniques of differentiation and integration of polynomial, trigonometric and transcendental functions are covered, and applications are included for both integration and differentiation. A TI-Nspire is required, as the student will be taught to use the calculator as a support for analysis, and graphing calculators are required by the College Board for the AP Calculus AB test.

AP Prerequisite: Teacher recommendation and qualifying score on diagnostic test.

AP BC Calculus is equivalent to the first and second semesters of college calculus. The serious student will be prepared to take the AP Exam in BC Calculus. The theory and techniques of differentiation and integration of polynomial, trigonometric, and transcendental functions are covered, and applications are included for both integration and differentiation. In addition, differential equations, infinite series, and power series are covered. A TI-Nspire is required, as the student will be taught to use the calculator as a support for analysis, and graphing calculators are required by the College Board for the AP Calculus BC test.

Prerequisite: Completion of AP Calculus BC

Multivariable Calculus is for students who have successfully finished AP Calculus BC or have received special consideration from the instructor. Students will explore vector-valued functions, including their differentiation and integration and applications such as velocity, acceleration and as a position function. Differentiating and integrating functions of several variables including partial derivatives and differentials will be covered. Examining area and volume and surface area with multiple integrals will be stressed. The course finishes with vector fields, Green’s Theorem, parametric surfaces, the divergence theorem, Stokes’s Theorem, linear algebra, and probability. The TI-Nspire CX calculator is used as a learning tool and is required for the course.

In the Statistics and Probability course, students continue to develop a more formal and precise understanding of statistical inference, which requires a deeper understanding of probability. Students learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random, and these procedures may be less applicable to non-randomized observational studies. Probability is still viewed as long-run relative frequency, but the emphasis now shifts to conditional probability and independence, and basic rules for calculating probabilities of compound events. Probability is presented as an essential tool for decision making in a world of uncertainty.

AP Prerequisite: Teacher recommendation and qualifying score on diagnostic test.

AP Statistics is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. It is expected that students who take this course will seek college credit, college placement or both from institutions of higher learning. There will be an exam for this course given through the AP College Board in the spring. In this course, students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes.

1. Exploring Data: Describing patterns and departures from patterns
2. Sampling and Experimentation: Planning and conducting a study
3. Anticipating Patterns: Exploring random phenomena using probability and simulation
4. Statistical Inference: Estimating population parameters and testing hypotheses.