Pre-Calculus
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
- Working with Linear Functions: 8/22/2013
- Bringing Water to a Boil Lab
- Linear Model 1: Due 8/28/2013
- Inclined to Roll activity
Grading
- Quarterly Exams: 60%
- Projects: 40%
Functions
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)
- General Forms
- slope-intercept
- Slope
- Intercept
- point-slope form
- slope-intercept
- Transformations
- parallel lines
- perpendicular lines
- Bringing Water to a Boil Lab
- Modeling
- Graphing
- Combining
Quadratic Equations
Additional Info
Apps
- Plotting Points Practice - simple plotting points on a co-ordinate plain (About).
- Straight Lines/Linear Equations - draw straight lines from two points, or from equations in slope/intercept and point/slope forms(About).
- Parabolas - draw parabolas from standard and vertex form equations (About).
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
- 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:
- Using two of your measured points.
- Linear Regression: Using a calculator or spreadsheet function.
- 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
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 5
- 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 6
- 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 7
- 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
- Chapter 8