# PreCalculus with Trigonometry

Teacher: Mr. John Frothingham

Extra Help: Tuesday afternoons 3:00 - 4:00 or by appointment.

### Course Overview

Within this course, we will build a strong and in-depth foundation for Calculus. In the first unit, we will first review lines in planes and then move to examining functions and their graphs which we will shift, reflect translate and stretch.  We will also combine functions and find their inverses. The next unit, we will explore quadratic, polynomial and rational functions and learn how to determine their equations from their graph.  We will review real and complex roots and find them using polynomial division. Next we will learn how to find asymptotes, intercepts and holes in their graphs. In the following unit, we will review and further explore exponential and logarithmic functions. We will model and solve real-world problems such as bacterial growth, compounded interest, radioactive decay. We will manipulate logarithmic and exponential equations in order to solve some seemingly complicated formulas. In the next unit we learn about trigonometric functions.  We will evaluate and graph them, identify basic characteristics and find their inverses and their reciprocals. Using a unit circle  and a reference angle, we find trigonometric ratios of an acute angle. Like with other functions, we will solve real-world problems. In the following unit we will review the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, develop additional trigonometric identities, and solve trigonometric equations. We will find the exact values of trigonometric functions using sums or differences of special angles. Towards the end of the year we will work with Sequences and Series as well as Vectors and Matrices (if time).

Essential Questions:

• How do we think mathematically while problem solving?
• How can we synthesize our knowledge of functions and basic mathematical properties to problem solve?
• How do we communicate effectively our mathematical solutions using appropriate vocabulary and syntax and apply them in terms of real life contexts?
• How do we use mathematics to describe change?

Assessment

Grades for this course consist of four strands: Logic, Accuracy, Application and Work Habits.

Accuracy – 30%

Mathematics is a language that allows people to give exact answers.  When calculations are not made correctly, computers don’t operate, bridges collapse, and checks bounce.  Students are assessed in this strand primarily through their performance on quizzes and tests.

Logic – 30%

Just like accuracy, how one arrives at that answer is also important.  When reviewing student work, teachers look to see how problems are set up before they are solved.  As math concepts become increasingly complex, making sure the logic is clearly communicated takes on greater significance.  Students are assessed in this strand primarily through their performance on quizzes and tests.

Application – 20%

Students participate in several unit projects over the course of a semester where they apply their knowledge to problem solving situations.  Most projects also involve writing about their mathematical thinking, reflecting about their growth as a math students and sharing these in a public forum.  These projects are graded on a variety of content and presentation standards.

Work Habits – 20%

The Work Habits strand reflects the effort students have put into completing homework, studying regularly, and working in class.  Work habits also reflect the level of students’ participation in class, their willingness to take academic risks, and ability to incorporate revisions into their work.  Students with strong work habits grades are putting consistent, effective effort into their schoolwork.

syllabus - In this document you will find a course description, essential questions, student expectations, assessment strand descriptions, honors requirements, how strands are graded, calendar of topics and a overview of major topics.