Subject: Mathematics

Honors Pre-Calculus

Course Type: Honors High School

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Credits: 1.0

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Course Description

Exploring the relationship between advanced algebra topics and trigonometry, Honors Pre-Calculus is an informative introduction to calculus that challenges students to discover and comprehend the nature of graphs, nonlinear systems, and polynomial and rational functions. Encouraging logarithmic knowledge and application, this course covers many interesting and advanced subject areas in a thoughtful and supportive format, providing students a deeper understanding of topics, including limits, continuity, derivatives, and the Fundamental Theorem of Calculus.

Textbook: Pre-Calculus ISBN-13: 978-1-938168-34-5

Course Objectives

Extend on previous coursework with functions with a more in-depth analysis of polynomial and transcendental functions.

Use matrices and vectors to solve mathematical and real-world problems.

Use parametric equations to describe functions and model real-world concepts.

Analyze conic sections and their rotations in Cartesian and polar coordinate systems.

Perform statistical analysis using normal distribution approximations.

Understand the concepts of a limit, a derivative, and an integral and how they are related via the Fundamental Theorem of Calculus.

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Course Contents

Module TitleModule Topic(s)
1: Functions & Their Graphs
2: Polynomial & Rational Functions
3: Exponential and Logarithmic Functions
4: Trigonometric Functions
5: Analytic Trigonometry
6: Additional Topics in Trigonometry
7: Linear Systems & Matrices
8: Sequences, Series, & Probability
9: Topics in Analytic Geometry
10: Analytic Geometry in Three Dimensions
11: Limits & an Introduction to Calculus

Recommended Prerequisites

Carnegie Credits Explained: Our Approach vs. Trimester Credits

Carnegie Credit System
Excel High School follows the Carnegie Credit system, a widely recognized method of measuring student progress based on instructional hours. A single Carnegie credit reflects approximately 120 hours of coursework, typically completed over a full academic year.

Carnegie Credit vs. Trimester Credit
While Carnegie credits are awarded based on total hours over a year, trimester credits divide the school year into three terms. In a trimester system, students complete courses in shorter, intensive sessions, often earning partial credits (e.g., 0.33 or 0.5 per term). In contrast, Excel’s use of Carnegie credits ensures students have ample time to engage deeply with the material and develop a well-rounded understanding at a consistent pace.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.