Precalculus Full Year (Two Semesters) Prerequisites: Algebra II/Trigonometry or equivalent OR best-fit mathematical placement The major concepts introduced in Algebra II/ Trigonometry – properties of real and complex numbers; polynomial, rational, exponential, logarithmic and trigonometric functions – are examined and investigated in greater depth. Conic sections, probability, and sequences and series are covered on a cursory level, and emphasis is placed on the connection of mathematical ideas using critical thinking to real-world situations. Students explore the concept of a limit and are introduced to the calculus
Topics will be presented graphically, algebraically, and numerically, and real-world applications will be explored whenever possible. Texts and Materials: Graphing calculator; Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN-10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9
Honors Calculus Full Year (Two Semesters)
Prerequisites: Precalculus or equivalent, successful completion of honors prerequisites OR best-fit mathematical placement This course will provide a comprehensive investigation of both differential and integral calculus. Topics of study include limits and continuity, differentiation, integration, and the techniques and applications thereof. Additional topics such as partial fractions and L’Hopital’s Rule will also be introduced, and topics from precalculus — inequalities, functions, trigonometry, and logarithms will be reviewed throughout. The course stresses the importance of critical thinking, and all problems will be approached from algebraic, graphical, and numerical perspectives. Real-world applications to business, engineering, and population growth will be explored, and students will be regularly encouraged to draw their own hypotheses and conjectures, and to speak and write in the language of mathematics in order to justify the veracity of their claims. Texts and Materials: Graphing calculator; Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN- 10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9 Multivariable Calculus Full Year (Two Semesters) Prerequisite: Calculus Honors or equivalent, successful completion of honors prerequisites OR best-fit mathematical placement This course allows students to continue their study of calculus at an accelerated level. Having learned how to evaluate limits, derivatives, and integrals of single- variable functions, students will now study those same concepts in the context of vectors and multivariable functions. Students will also learn the many facets of sequences and series, as well as build upon their understanding of differential equations. Texts and Materials: Graphing calculator; Calculus: Graphical, Numerical, Algebraic, Pearson, by Finney, Ross, 3RD 10 ISBN-10: 0-13-368839-9, ISBN-13: 978-0-13-368839-9
operation of differentiation. Materials: Graphing calculator
Honors Precalculus Full Year (Two Semesters) Prerequisites: Algebra II/Trigonometry or equivalent, successful completion of honors prerequisites OR best-fit mathematical placement This course includes an in-depth examination of coordinate geometry as well as polynomial, exponential, logarithmic and trigonometric functions. Conic sections, vectors, and polar coordinates are introduced and explored. In the second semester, sequences and series are studied as an introduction to the concept of limits, and students will complete the year with a brief look at differential calculus. Throughout the year, graphic solutions to non-routine problems will be explored through the use of the TI-83
or 84 graphing calculator. Materials: graphing calculator Calculus Full Year (Two Semesters)
Prerequisites: Precalculus or equivalent OR best-fit mathematical placement
This course is designed to provide a solid foundation in both differential and integral calculus. Students will learn to evaluate limits and assess function continuity both analytically and graphically, and they will utilize this understanding to uncover the limit-based definition of the first derivative. As the year progresses, students will delve into the many techniques of differentiation, and explore a variety of applications in the form of optimization and related rates problems. The second half of the year will be spent focusing on integration, the techniques thereof, and applications to the calculation of area and volume. Topics from algebra and trigonometry are reviewed throughout the course, and students will have the opportunity to revisit previously learned concepts and problems through a calculus-based lens.
2025-2026 ULS Curriculum Guide
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