HSLDA Online Academy | Pre-Calculus and Trigonometry

Pre-Calculus and Trigonometry

Master Teacher:  Elizabeth Shimada

Liz Shimada, High School Classroom Teacher for Pre-CalculusMaster Teacher

Elizabeth Shimada

MS, Santa Clara University
BS, California Polytechnic State University, San Luis Obispo

Elizabeth Shimada earned her bachelor of science in electronic engineering from California Polytechnic State University at San Luis Obispo and her master’s of science in computer engineering from Santa Clara University. Prior to homeschooling her three children, she spent ten years in manufacturing, marketing, and R&D at Hewlett Packard Company’s instrumentation division.

Energized by teaching, she is thrilled to be part of the Academy’s online homeschool community. She enjoys teaching in creative ways, making abstract concepts real and the learning process fun. Besides teaching, she tutors in math and physics. Furthermore, she appreciates math and science as tools to see the “hidden treasures” in God’s creation.

In addition to her family’s year-round basketball activities, Elizabeth enjoys reading, building projects, visiting new places, perusing apologetics, and good literature and theater. She also delights in various Word studies and fellowship, drawing and multimedia activities, and good ol’ company and conversation around a meal.

Elizabeth lives in Northern California with her husband Warren and their children—Eric, Jaclyn, and Kevin—along with their two furry felines, Pachek and Slavna, and a sizeable flock of backyard chickens.

She has been teaching with the Academy since 2016.

Classroom Teacher:  Paige Jackson

Paige Jacks, High School Classroom Teacher for Pre-CalculusClassroom Teacher

Paige Jackson

BS, University of South Florida

Paige Jackson earned her Bachelor of Science degree in Mathematics Education from the University of South Florida in Tampa. Paige has taught high school math and science courses for the past eighteen years.

Four years ago, Paige left the classroom to pursue teaching and tutoring from home while homeschooling her son through high school. She has greatly enjoyed the experience.

Paige lives in Valrico, Florida, with her husband and son. Together, they enjoy spending time with their many friends and nearby relatives. They also enjoy frequent trips to the Orlando area, making use of their theme park passes. As often as possible, they try to travel out of the state of Florida to visit the rest of beautiful North America.

Paige has been teaching with the Academy since 2017.  

Classroom Teacher:  Amber Knapp

Amber Knapp, High School Classroom Teacher for Pre-CalculusClassroom Teacher

Amber Knapp

MEd, Marygrove College
BA, Spring Arbor University

Amber Knapp earned her bachelor's degree in secondary education mathematics from Spring Arbor University and her masters of education degree from Marygrove College. She taught mathematics for ten years at a local high school before moving on to several adjunct professor positions at local colleges. For the past three years Amber has been blessed to teach part-time in these positions while homeschooling her young children.

Along with teaching a variety of math courses at the high school and college levels, Amber has taught online math classes for over a decade, provided regular tutoring to homeschooled students in the area, and has recently begun working with Classical Conversations as a tutor in the Foundations program. Amber enjoys finding creative ways to present material and make it accessible for all students to learn. Coming alongside students and showing them the beauty of God's creation through the application of mathematics is a great joy for Amber—one she is excited to share with students in the Academy's online homeschool community.

In addition to home improvement projects, Amber enjoys running, reading and spending time with friends over a good cup of coffee. She lives in central Michigan with her husband Jesse and three young children, where they love serving in their church and spending time with extended family.

Amber has been teaching with the Academy since 2017.

Duration: Yearlong course offered in fall/spring (32 weeks).
Suggested High School Credit Value: 1 credit.
Suggested Grade Level: 10th grade level and up.
Early Registration Tuition (ends 6/12): $475 $525 for HSLDA Members/$525 $575 for non-members. 

Description: In Pre-Calculus & Trigonometry, students build upon skills learned in Algebra 2 and Geometry while learning about functions and graphs. This course is meant to prepare students for AP® Calculus AB.
Watch a short introduction from Course Developer Elizabeth Shimada.
Watch a sample clip of an Academy live class session. 

Pre-Calculus & Trig. — Live Online Class Session Schedule,
August 27, 2018 - April 26, 2019

Class Section

Weekly Meeting Time


Section 1
Tuesdays AND Thursdays, 10:00 – 10:45 a.m. Eastern

Mrs. Paige Jackson

Section 2
Tuesdays, 2:00 p.m. – 3:30 p.m. Eastern

Ms. Amber Knapp

Section 3
Wednesdays, 11:30 a.m. – 
1:00 p.m. Eastern

Mrs. Elizabeth Shimada

Additional class times will be added as they become available for registration.  If you have questions, please call 540-338-8290.

Frequently Asked Questions about
Pre-Calculus & Trigonometry

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  • What topics will I learn about in Pre-Calculus and Trigonometry?

    Students successfully completing this course will to be able to: 


    • Understand what a function is, understand and determine different properties of functions, evaluate a function at a given value, manipulate the function in a variety of algebraic and graphical ways, learn and work with different families of functions including conics, determine roots both real and complex of polynomial functions using various methods, apply function concepts to application problems, understand how parabolas, ellipses and hyperbola’s are mathematically represented.
    • Understand the basic trigonometric functions and the radian measurement, be able to apply unit circle and angular concepts in trigonometric applications, understand and use various identities, laws and formulas to evaluate and prove trigonometric expressions and equations and to solve trigonometric application problems.
    • Understand and solve linear, nonlinear, and multivariable systems of equations and inequalities both mathematically and graphically, understand and use matrices, matrix operations, their inverses and determinants to solve systems of equations.
    • Understand and use vectors, dot products, complex numbers and the polar coordinates system to solve problems. Understand arithmetic and geometric sequences, their sums, the binomial theorem, counting principles, permutations, combinations, and probability to solve common problems.
  • How much homework is in Pre-Calculus and Trigonometry?

    We estimate that the course workload will take 5-10 hours per week.

    During a typical week in this course, students will complete the following coursework:

    • 60-90 minutes of live class instruction
    • 3-4 lecture videos
    • 15-20 homework problems per lecture (self-graded)
    • 1 quiz
    • Textbook reading

    Throughout the year, students will also complete the following tasks:

    • Unit test about every 4 weeks
    • Midterm exam and final exam
  • Am I ready to take Pre-Calculus and Trigonometry?

    Students who have completed Geometry and Algebra 2 are ready to take Pre-Calculus & Trigonometry at HSLDA Online Academy. 

  • What is a Live Online Class Session in Pre-Calculus and Trigonometry?

    In every HSLDA Academy course, students meet weekly with their instructor and classmates in an online classroom for additional teaching, discussion, Q&A, or group activities. The class sessions are interactive and are conducted using a web meeting software with video, audio, chat, and application sharing capabilities.

    Scheduled, real-time sessions in the online classroom are not the only form of instruction available in a HSLDA Online Academy course, but are offered in addition to lectures or other instructional materials that students are able to access online at their convenience.

    When they register, students will need to select a particular class section and live class meeting time. Additional class sections may be added to the schedule at a later point in the course registration period. Registered students will be notified of any changes to the live session schedule.

  • What if I have a schedule conflict with the listed Pre-Calculus and Trigonometry class time?

    All live class sessions are recorded for later viewing. While it is recommended that students attend each live class session, students can make arrangements to watch the recordings and receive full participation credit.

    Students should contact their instructor at the start of their course to inform the instructor of any foreseen schedule conflicts. 

  • What is the tuition for Pre-Calculus and Trigonometry?

    Please visit our tuition and discounts page for a full summary about course costs.

    HSLDA members save $50 on yearlong high school courses!