Pre-Calculus

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In pre-Calculus we will learn how to use different classes of functions. Researchers use functions to describe different types of behavior in the natural world: how a body cools over time; the shape of the path of a ball through the air; how the demand for a product decreases as you increase the price; and, the relationship between hours of practice and test scores, are just a few examples.

In this class we will collect or acquire data and identify the functions that best describe them.

Spring Test Schedule

  • Exam S1: Trigonometric Functions: Jan. 17th.
  • Exam S2: Analytic Trigonometry: Jan 31st.
  • Exam S3: Matrices: Feb 22nd.
  • Exam S4: Probability and Sequences: March 6th.
  • Exam S5: Analytic Geometry: April 12th.
  • Exam S6: 3D Geometry: April 22nd.
  • Exam S7: Additional Trigonometry: May 10th.
  • Exam S8: Intro to Limits: March 19th.
  • Final Exam: During the Final Exam period (Week of May 18th).


Contents

Assignments

Portfolio

Over the course of the year you will create a portfolio of the different function types you encounter. You will dedicate one page for each of the types of functions and major topics listed here.

Projects

Grading

  • Quarterly Exams: 60%
  • Projects: 40%

Functions

General Principles for Working with Functions

Concept map of general principles for working with functions


  • general form of an equation
  • transformations
    • shifts
    • reflections
    • non-rigid transformations
  • graphing
    • domain and range
    • maxima and minima (relative and absolute)
    • rate of change (increasing, decreasing, or constant)
  • combining
    • arithmetic
    • compositions
    • piecewise defined functions
  • inverse of a function
  • modeling
    • algebraic
    • numerical
      • regression (least squares)

Linear equations (y=mx+b)

Linear equations concept map.
  • General Forms
    • slope-intercept
      • Slope
      • Intercept
    • point-slope form
  • Transformations
    • parallel lines
    • perpendicular lines


Quadratic Equations


Additional Info

Apps


Data Analysis Methods (with Linear Functions)

We'll start with a simple function you should be familiar with:

y = mx + b

where:

  • y = dependent variable
  • m = slope
  • x = independent variable
  • b = intercept

Data Collection

  1. Observations of how the temperature (T) of liquid in a beaker changes with time (t) as it is heated up on a hot plate. (Use the same beaker of liquid and start the clock at the same time, but different groups/students will take measurements at different times)
    • Model: T = mt + b

Data Analysis

Find the equation of the line using a linear model by these methods:

  1. Using two of your measured points.
  2. Linear Regression: Using a calculator or spreadsheet function.
  3. Linear Regression: Direct calculations using a spreadsheet.

Prediction

  • Compare equations to the other groups that used the same beaker and liquid

Review of Linear Equations

Section 1.1

Forms of the equation:

  • slope intercept
  • point slope
  • general form

Uses of the coefficients:

  • intercept
  • parallel and perpendicular lines


Functions

Section 1.2

  • Definition of a function.
    • vertical line test
  • function notation: f(x)
  • piecewise functions
  • Domain and Range of functions
  • Difference Quotient

Graphs of Functions

Section 1.3

  • Increasing or decreasing functions
  • Maximums and minimums
  • Step and piecewise-defined Functions
  • Odd and Even functions

Transforming Graphs

Section 1.4 - (graphing resources: Straight lines and Parabolas)

  • Vertical and Horizontal shifts
  • Reflecting
  • Stretching

Combining Functions

Section 1.5

  • Arithmetic Combination
  • Composition of Functions

Inverse Functions

  • Graphing Inverse functions
  • Checking if the Inverse Function exists
  • Finding the inverse algebraically

Q1 Test Question

  • Blog Post Problem: find the equation for the best-fit inverse function? That way I could estimate how many hits my 20th or 100th ranked post gets per month.

Old Stuff

Pre-Calculus 2011

Homework

    • Chapter 5
      • 5.1:1-11 odd
      • 5.2:1-11 odd
      • 5.2:21-37 odd
      • 5.3:1-29 odd
      • 5.4:1-57 odd
      • 5.5:1-101 odd
      • Chapter 5 Review Exercise 1-105 every other odd
    • Chapter 6
      • 6.1:1-25 odd; Jessica-27, Jincy-28, Bowen-37, Alex-29.
      • 6.2:1-11 odd
      • 6.3:1-45 odd
      • 6.4:1-51 odd Alex-55, Lena-53, Bowen-57, Jess-59, Jincy-60, Mathew-56
      • review 2.4
    • Chapter 7
      • 7.1: 15-27 odd, Pick one: 61-78
      • 7.2: 7-15 odd, Pick one: 61-68
      • 7.2: 1-25 odd, Pick one: 87-94
      • 7.3: 1-25 odd, Pick one: 87-94
      • 7.4: 1-27 odd, 47-59 odd, 67, Pick one: 71-80
      • 7.5: 1-57 odd, Pick one: 65-72
      • 7.6: 1-51 odd, 57
      • 7.7: 1-53 odd
      • 7.8: 1-15 odd, Pick one: 23-34
    • Chapter 8
      • 8.1: 1-105 other odd, Pick one: 109-114
      • 8.2: 1-69 other odd, Pick one: 75-90
      • 8.3: 1-73 other odd
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