New this year: a live course in Precalculus, taught according to Charlotte Mason's principles, using the Algebra II/Trig text by Paul Foerster.  

Our rigorous, calculus-preparatory course that deepens students’ understanding of functions while strengthening trigonometric reasoning and analytical thinking. This course prepares students to move directly into Calculus the following year.

This approach includes the introduction of "captain ideas" from great thinkers or from history to pique the interest of the students and grab their attention. Through carefully graduated lessons, students are engaged and guided to wonder, explore, and consider concepts on their own — moving beyond procedural fluency toward genuine mathematical insight.

This course constitutes one high school math credit.**

**Climbing Higher Math teaches students from different states and countries and is not responsible for ensuring every state's standards are met.

Course Details

Course Description

This course is a comprehensive study of advanced function analysis and trigonometric structure, designed to prepare students for the study of calculus. Building upon prior work in Algebra II and Trigonometry, students revisit familiar function families with greater depth, examining behavior, composition, inverses, transformations, and modeling with increased mathematical maturity. The course continues to utilize Paul Foerster’s Algebra and Trigonometry: Functions and Applications textbook, supplemented with additional units to extend and unify key concepts.

Key topics include advanced polynomial and rational function analysis, trigonometric identities and equations, sinusoidal modeling, triangle applications and vectors, sequences and series, probability and random variables, parametric equations, polar coordinates, and an introduction to the conceptual foundations of limits. Throughout the course, students emphasize structural reasoning, strategic problem solving, and the interpretation of multiple representations of functions, preparing them for success in calculus and other advanced mathematics courses.

Prerequisites

A course of Algebra 1, a course of High School Geometry, and a course of Algebra 2/Trigonometry

Structure 

• Live, online class meets on Mondays and Wednesdays via Zoom. This class is taught by Dr. Julie Ryle.

• Assignments will be given to be completed independently on Tuesdays and Thursdays.

• Self-guided lessons will be posted on Fridays, continuing to build on the topics learned through the week.

Logistics

Class assignments and links will be posted in a Canvas Classroom to which students will be added.  In this environment, students have the opportunity to easily ask the teacher for help, converse with their classmates, as well as use tools to turn in assignments and re-watch lessons. The instructor will be available to answer questions, including personalized video answers to problems, as needed.

Materials Required 

• access to a device on which to stream Zoom classes, and upload and download assignments from Canvas Classroom

  • a computer, or laptop, is suggested for using Zoom as students often need to access another classroom platform such as Desmos or Quizizz while running Zoom

  • a phone is suggested for taking pictures of assignments and uploading them  

• Algebra & Trigonometry textbook by Paul Foerster

• Solutions manual for the text (out of print -- you may find a used copy, or a pdf version is available here)

• a scientific calculator (like this one)

• a gridded notebook, or a lined notebook plus graph paper

Course Types offered

Climbing Higher Math only offer Precalculus as a live course (taught by Dr. Julie).