Pre Calculus - US - StudyForge

Pre-Calculus

This course aligns with the learning outcomes for:

United States

This course aligns with the learning outcomes for:

United States

Are your students intimidated about the prospect of having to take the “dreaded” Calculus course at some point in their future? Are you searching for a Pre-Calculus curriculum that will help your students master its topics and not only survive Calculus but even thrive? And all the while still enjoying the course? Your search is over.

StudyForge proudly presents: Pre-Calculus.

Pre-Calculus is the culmination of a students’ high school mathematical journey, as they learn the fundamentals of advanced functions, trigonometry, logarithms and more. The course thoroughly prepares students for the oncoming rigor of Calculus, yet does so in a manner that is compelling and rewarding, and fosters an appreciation for the real-life applications of each topic explored, as well as for math itself.

The course also supports diverse learners by incorporating auditory, visual, and hands-on elements. Interactive videos allow students to learn at their own pace, with engaging applets and graphs to reinforce concepts. Each instructional video includes a student-friendly note package, and students have access to plenty of practice questions with detailed solutions. Quizzes and tests can be retaken to help solidify understanding and promote mastery.

This course is a prerequisite for students who might take Calculus (or AP Calculus) in the future.

Not all schools and jurisdictions will require students to complete all 11 units, as curriculum standards vary by region. Teachers will need to customize their course by removing any units that are not required by their jurisdiction. Teachers can then adjust the semester exams accordingly.

Core units are highlighted in blue and included for all jurisdictions. Elective units are highlighted in green and vary by jurisdiction. Lessons marked (Enrichment) are optional.

Unit 1: Review of Functions

Lesson 1: The Coordinate Plane and Graphs

Lesson 2: Domain and Range

Lesson 3: Functions

Lesson 4: Applications of Functions

Unit 2: Exploring Functions

Lesson 1: Modeling With Common Functions

Lesson 2: More Common Functions

Lesson 3: Key Features of Functions

Lesson 4: Transformations of Functions Part I: Stretches and Reflections

Lesson 5: Transformations of Functions Part II: Translations

Lesson 6: Combinations of Transformations

Lesson 7: Inverse Functions

Lesson 8: (Enrichment) Modeling Situations Using Regression

Unit 3: Quadratic Functions

Lesson 1: Graphing Quadratic Functions Part 1

Lesson 2: Graphing Quadratic Functions Part 2

Lesson 3: Completing the Square

Lesson 4: Maximum and Minimum Problems

Lesson 5: The Quadratic Formula

Unit 4: Polynomial and Rational Functions

Lesson 1: Dividing Polynomials

Lesson 2: The Remainder Theorem

Lesson 3: Solving Polynomials Using the Factor Theorem

Lesson 4: Rational Expressions

Lesson 5: Operations With Rational Expressions

Lesson 6: Rational Equations and Applications

Lesson 7: (Enrichment) Sketching Polynomials Using Zeros

Lesson 8: (Enrichment) Graphing Rational Functions

Unit 5: Exponential and Logarithmic Functions

Lesson 1: From Linear to Exponential Functions

Lesson 2: Exponential Functions and Equations

Lesson 3: Graphing Exponential Functions

Lesson 4: Continuous Exponential Growth

Lesson 5: Introduction to Logarithms

Lesson 6: The Product and Quotient Laws

Lesson 7: Solving Equations Using Logarithms

Lesson 8: Graphing Logarithmic Functions

Unit 6: Sequences and Series

Lesson 1: Arithmetic Sequences

Lesson 2: Arithmetic Series

Lesson 3: Geometric Sequences

Lesson 4: Finite Geometric Series

Lesson 5: Infinite Geometric Series

Lesson 6: (Enrichment) Recursive Sequences

Lesson 7: (Enrichment) Sigma Notation

Lesson 8: (Enrichment) Pascal’s Triangle and the Binomial Theorem

Unit 7: Solving Triangles and Trigonometric Equations

Lesson 1: Trigonometry Review

Lesson 2: The Sine Law

Lesson 3: The Cosine Law

Lesson 4: A New Angular Measure: Radians

Lesson 5: Angles and the Coordinate Plane

Lesson 6: Trigonometric Ratios of Any Angle

Lesson 7: Special Angles and Trig Ratios

Lesson 8: Solving Trigonometric Equations

Lesson 9: (Enrichment) Sine Law: The Ambiguous Case

Lesson 10: (Enrichment) Graphing Trigonometric Functions

Unit 8: Trigonometric Functions and Identities

Lesson 1: Graphing Sine and Cosine Functions

Lesson 2: Graphing Tangent Functions

Lesson 3: Graphing Inverse Trigonometric Functions

Lesson 4: Applications of Trigonometric Functions

Lesson 5: Trigonometric Identities

Lesson 6: Sum, Difference, and Double Angle Identities

Lesson 7: Solving Advanced Trigonometric Equations

Lesson 8: (Enrichment) Using Technology to Solve Complex Trig Equations

Unit 9: Analytic Geometry

Lesson 1: Parabolas

Lesson 2: Circles

Lesson 3: Ellipses

Lesson 4: Hyperbolas

Lesson 5: Parametric Curves

Lesson 6: Polar Curves

Unit 10: Vectors and Matrices

Lesson 1: Introduction to Vectors

Lesson 2: Vectors With Trigonometry

Lesson 3: Vector Operations

Lesson 4: Solving Systems of Equations

Lesson 5: Introduction to Matrices and Matrix Operations

Lesson 6: Matrix Multiplication, Inverses, and Determinants

Lesson 7: Applications of Matrices

Lesson 8: (Enrichment) Solving Systems Involving Quadratics

Unit 11: Limits

Lesson 1: Introduction to Limits

Lesson 2: Properties of Limits

Lesson 3: Limits Involving Infinity

Lesson 4: Continuity

Lesson 5: Applications of Limits

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StudyForge has been an effective instructional program for students who are learning math. There are many visual representations as well as audio explanations on all the topics. Most of the practice questions provide both an answer and a solution to help students understand the procedures. From the teacher’s perspective, the course instruction can be easily rearranged for students who need a review of concepts from a previous grade.

SONYA

Online Teacher at EBUS Academy

I have been using the StudyForge math videos for a year now. The benefits were immediate as I was able to free up the time spent with my students to better track their progress and construct personalized learning goals. My students love the ease of use of the system and most of all, the increase in their test scores! I can’t ever imagine going back to a traditional classroom!

Scott

Blended Teacher at Brampton Christian School

I think the videos are excellent. Unlike lectures, I can actually rewind back and forth as much as I want. In class, students kind of miss important information because they are busy writing notes.

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StudyForge Student

I love the reporting tool. In my distributed learning context, seeing student’s work habits in a helpful format has become invaluable to me. I wouldn’t ever want to give one on one help to students again without the course overview report handy!