Subject: Mathematics

Pre-Calculus

Northgate Academy’s Pre-Calculus course bridges the gap between advanced algebra topics and trigonometry, preparing students for calculus through an exploration of graphs, nonlinear systems, and various functions. This course emphasizes the understanding of polynomial, rational, logarithmic, quadratic, exponential, and periodic functions, equipping students with the skills to tackle real-world problems. By engaging with topics like limits, continuity, derivatives, and the Fundamental Theorem of Calculus, students gain a deeper insight into the mathematical concepts that underpin calculus.

Credits: 1.0

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Course Description

Exploring the relationship between advanced algebra topics and trigonometry, 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

Expands on previous coursework around 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

Modules
Functions and Their Graphs
Polynomial and Rational Functions
Exponential and Logarithmic Functions
Trigonometric Functions
Analytic Trigonometry
Additional Topics in Trigonometry
Linear Systems and Matrices
Sequences, Series, Probability
Topics in Analytic Geometry
Analytic Geometry in 3D
Limits and an Intro to Calculus

Recommended Prerequisites

Carnegie Credits Explained: Our Approach vs. Trimester Credits

Carnegie Credit System
Northgate Academy 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, Northgate’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.