Pre-Calculus - Part 1 (Semester 1)
In this 18 week online class students will prepare their skills for Calculus after successfully completing Algebra II.
Ellen Hulliberger (Highly Qualified —MI)
Average rating:
4.7
Number of reviews:(73)
What's included
18 live meetings
18 in-class hoursHomework
2-4 hours per week. Homework Policy • Homework will be assigned during every weekly meeting. • and checked by me and returned as soon as possible, • The problems must be written on your paper and have all work shown with answers to receive credit. • If you are unable to complete a problem, you must show evidence of effort. • Late assignments will be accepted for reduced credit.Assessment
Assessments: * weekly formative assessments to check for understanding including an interactive approach and a traditional paper pencil exit quiz. * at the end of a unit students will complete a guided review, then a summative assessment.Class Experience
US Grade 9 - 12
TEACHING and LEARNING My style of teaching is a Blended Model which includes differentiated instruction that meets the needs of all students, interactive learning, student driven problem solving, and demonstration techniques. Students will be responsible for weekly lessons and exit quizzes of 2-4 lessons per week. COURSE DESCRIPTION Pre-Calculus intertwines together previous study of algebra, geometry, and mathematical functions into a preparatory course for calculus. The course focuses on mastery of critical skills and exposure to new skills necessary for success in successive math courses. Throughout the course, Common Core standards are taught and reinforced as the student learns how to apply the concepts in real life situations. Topics include fundamental concepts of Algebra, functions and graphs, polynomials and rational functions, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, topics in trigonometry, systems of equations and inequalities, matrices and determinants, conic sections and analytic geometry, sequences, induction, probability, and an introduction to Calculus. Pre-Calculus Part I includes five lesson tests and a midterm written exam that requires the student to demonstrate understanding by showing work. Week 1 - Operations with Complex Numbers Week 2 - nth Roots and Real Numbers Week 3 - Systems of Linear Equations and Matrices Week 4 - Statistics Week 5 - Functions and Relations Week 6 - Continuity, End Behavior and Limits Week 7 - Parent Functions and Transformations Week 8 - Composition and Inverse Functions Week 9 - Power, Radical and Polynomial Functions Week 10 - Remainder and Factor Theorems, Rational Functions Week 11 - Non Linear Inequalities Week 12 - Exponential and Logarithmic Functions Week 13 - Modeling Non Linear Regression Week 14 - Right Triangle Trigonometry and Radians Week 15 - Trigonometric Functions and Graphing Week 16 - Inverse Trigonometric Functions and Law of Sines and Cosines Week 17 - Trigonometric Identities and Operations of Identities Week 18 - Final Semester 2 Exam Review COURSE SYNOPSIS – Semester 1 * Functions and Their Graphs Students learn fundamentally important definitions and notations related to functions. They evaluate functions and find their domains. They analyze graphs of functions, identify graph translations, reflections, and non-rigid transformations of functions. Students find arithmetic combinations and compositions of functions as well as finding the inverse of functions graphically and algebraically. * Polynomial and Rational Functions Students sketch and analyze graphs of quadratic and polynomial functions. They use long division and synthetic division to divide polynomials by other polynomials. They will use the Fundamental Theorem of Algebra determine the number of rational, real, and non-real zeros of polynomial functions and find them. Students perform operations with complex numbers. They determine the domain, find asymptotes and intercepts, and sketch the graphs of rational functions. * Exponential and Logarithmic Functions Students learn to recognize, evaluate, and graph exponential and logarithmic functions. They will rewrite logarithmic functions with different bases, use properties of logarithms to evaluate, rewrite, expand, or condense logarithmic expressions. Students will solve exponential and logarithmic equations, use exponential growth and decay models, and use logarithms to solve real-life problems. * Trigonometric Functions Students learn to describe an angle using degree and radian measure. They will identify a unit circle and its relationship to real numbers and evaluate trigonometric functions of any angle. Students will explore fundamental trigonometric identities, sketch their graphs, evaluate their inverses, and evaluate the composition of trigonometric functions. Students will then use trigonometric functions to model and solve real-life problems. GRADE WEIGHT • Attendance: 5% • Assignments: 10% • Exit Quizzes: 30% • Tests: 55% FINAL GRADE • Semester Grade: 80% • Final Exam: 20%
Learning Goals
LEARNING OBJECTIVES After completing Pre-Calculus, students will be able to:
• Recall and apply basic algebra skills.
• Explore symmetries of graphs, determine continuity and average rates of change of functions, use limits to describe end behavior, and find inverse functions algebraically and graphically.
• Model real-world data with polynomial functions, use the Remainder and Factor Theorems, find real and complex zeros of polynomial functions, analyze and graph rational functions, and solve polynomial and rational inequalities.
• Evaluate, analyze and graph exponential and logarithmic functions, apply properties of Logarithms, solve exponential and logarithmic equations, and model data using exponential, logarithmic and logistic functions.
• Use trigonometric functions to solve right triangles, find values of trigonometric functions for any angle, and graph trigonometric and inverse trigonometric functions.
• Use and verify trigonometric identities, solve trigonometric equations, use sum and difference identities to evaluate trigonometric expressions and solve equations, and use double-angle, power-reducing, half-angle, and product-sum identities to evaluate trigonometric expressions and solve equations.
Other Details
Supply List
Supplies • Graphing Calculator DESMOS • Whiteboard , marker, and eraser • Pencils and Pens • Graph paper and Straight Edge • Binder, dividers, notebook paper for own purpose
2 files available upon enrollment
Language of Instruction
English
External Resources
In addition to the Outschool classroom, this class uses:
Sources
For student reference purposes only:
* Glenco Precalculus textbook McGraw-Hill Education ISBN: 978-0-07-664183-3 (student edition)
Joined April, 2018
4.7
73reviews
Teacher expertise and credentials
Michigan Teaching Certificate in Mathematics
2 Degrees
Master's Degree in Secondary School Administration/Principalship from Grand Valley State University
Bachelor's Degree in Mathematics from Grand Valley State University
I am a highly qualified mathematics and chemistry teacher. I taught 10 years in the middle school and 10 years at the high school. I love teaching and believe in innovative ways to keep students motivated and engaged.
I graduated from Grand Valley State University with a Major in Mathematics and Minor in Chemistry. I also, have a Masters Degree in Middle Level Education and a Specialist Degree in Central Office Curriculum. I worked hard to get these degrees since I did not attend college until after my children were raised. I have 1 son and 3 daughters (1 of which is deceased). They are all adults now and they have given me 3 grand daughters.
Reviews
Live Group Class
$378
for 18 classes1x per week, 18 weeks
60 min
Completed by 7 learners
Live video meetings
Ages: 14-18
3-6 learners per class
