Summer Pre-Calculus

All-Gender Course; Prerequisite - Completion of Geometry and Algebra II or equivalent;  Full-year course credit
COURSE DESCRIPTION
This course covers a full year of Pre-Calculus in eight weeks by addressing the algebraic and trigonometric concepts that lay the foundation for AP® Calculus. Students graph and solve polynomial, rational, exponential, and logarithmic functions, while applying these functions to model the relationship between different quantities in the real world. They explore the unit circle, solve trigonometric equations, and study abstract applications by proving trigonometric identities. Students then examine and apply algebraic representations of matrices, vectors, sequences and series, and conic sections by understanding the patterns and behaviors associated with these concepts. The course concludes with an introduction to calculus through limits. Students preparing for AP® Calculus BC also have the option of studying polar coordinates, parametric functions, and derivatives. Students demonstrate mastery through traditional and alternative assessments, discussion prompts, reflection on their learning, group collaboration, and individual application activities. ​
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Summer courses are for-credit opportunities for ambitious students to get a jump on the next academic year. Students participating in these courses should plan to devote 25-30 hours per week for eight weeks to their course. Students will receive grades and comments in these classes, which are the equivalent of year-long, high-school level courses. Because of the pacing and intensity of for-credit summer courses, there is little flexibility; students must be available and have internet access for all eight weeks of the course. 
WHAT STUDENTS SAY

"The way that One Schoolhouse gives different learning pathways is super helpful. It allows me to play around with how I learn the best wand use this to my advantage. Mrs. Muratore does very good and helpful videos that give me a very comprehensive view of what we're learning."

​"My classmates connect and reply very promptly, they are very respectful and smart, and the group assignments have gone even better than meetings with students face-to-face at a day school!  Mrs. Muratore does such an excellent job of explaining everything so concisely and responding to my questions almost immediately. It feels like she's available to me 24/7, which makes it even better than a day school because of the time flexibility. She has been a supportive, cheerful, and positive presence along the whole course of this term. Overall, I am really satisfied with my experiences this term!"

WHAT STUDENTS DO
Learning is an active process at One Schoolhouse. Students design, create and apply. And, they engage with classmates and connect with their teachers through discussions, video conferences, and projects. Specifically, in this class students will:
  • Set goals that drive their learning. Students reflect regularly on their growth, and meet on video chat with their online teacher to review progress towards their goals.
  • Have choice in how they learn new content and practice new skills. Students are given agency to determine the best ways for them to learn.
  • Apply what they are learning to the real world. Learning is meaningful and connects to concepts outside the classroom.
  • Practice constructive engagement in a diverse and changing world. Students interact with classmates from across the country and around the world.
  • Gain academic maturity. Online learning takes greater discipline and independence than a traditional face-to-face classroom. Teachers support students to build this skill.
MEET A TEACHER FOR THIS COURSE
SIGNATURE ACTIVITIES
Students apply what they learn each week by studying different careers and solving structured modeling problems encountered in these fields.  Students work through project-based learning assignments both individually and collaboratively in teams. These applications lead students to new discoveries and deepen their understanding of the course material.  Some specific examples include:
  • Amusement Park Engineering: Students apply what they learn about trigonometric functions and design a Ferris Wheel.  This is an individual assignment where students create a sinusoid function, specifically a negative cosine function, that models their Ferris Wheel rider's height, based on time (in seconds).  They also create a physical model of their Ferris Wheel in order to visualize their design.
  • Cryptography: Students apply what they learn about matrices and linear algebra to the field of cryptography in order solve a Harry Potter-Themed Cryptography Problem.  They decipher an encrypted message using properties of inverse matrices and a special decoder matrix.
  • Arial and Satellite Engineering: Students design their own reflector (or parabolic dish) for a television satellite.  They decide the schematics of their design, including dish diameter, depth, vertex, and location of the receiver, build a visual representation of the dish, and work out parabolic calculations to ensure their design is mathematically accurate. 
Students reflect on learning, especially in relationship to their goals for the course. Reflections are completed individually and in both small and large groups.  They are weekly assignments in the course that assist students with metacognition at the end of each academic unit. Some examples include:
  • Reflect on your Work this Week: In the medium of their choice, students post something that describes how they feel about their work this week.  Students may choose to write a paragraph, take a picture, post a link to a song, make a video, draw an image, compose a poem, or anything that captures how they feel about their work.  
  • Your Favorite Conic Section: Students think about what particular conic shape and application they found most interesting.  Was it the architectural usage of ellipses? Or maybe the engineering application of a parabola?  Students are instructed to research the various applications of that conic.  Then they post a reflection to our class discussion below about what their Conic is and why they chose it.
COURSE APPROVAL
This course is approved by: the NCAA and the University of California.

​One Schoolhouse is fully accredited with the Middle States Association of Colleges and Schools and the Western Association of Schools and Colleges through December 1, 2025; we are an approved online publisher for the University of California. 
Jacqueline Muratore
Mathematics Teacher
B.A., Cornell University
M.A., Columbia University
M.Ed., Columbia University