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College Algebra

Instructor
Kevin Liddiard
Term
2017-2018 School Year
Department
Mathematics
Description
This is an advanced mathematics course that is offered for joint high school/college credit through Columbia Gorge Community College.  The course corresponds to College Algebra (MTH 111).  Topics to be studied include functions and relations of one and two variables with emphasis on polynomial and rational functions; exponential and logarithmic functions and complex numbers.

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Past Assignments

Due:

FINAL EXAM
 
Today period 3, tomorrow period 4

Due:

Final Review

Review for final- old quiz and tests, comp notebook etc.

one side of  3"x5" notecard can be used on final if NOT taking class for CGCC credit.

Test is on Tuesday for period 5, Wednesday for period 4.

Due:

Curve Fitting with Data

Entry: How can you tell if a model needs a linear, exponential or power function?

Eval: Section 9.4 work

TASK: Use Excel to curvefit, and determine the best fit for a given set of data.

G.P.9.7 #4,6,14

I.P. 9.7 #5,7,13

Due:

Rational Functions- short run

Entry: What does discontinuous mean?

Eval: Section 9.4 problems

Task: define vertical asymptotes functions, divide by zero errors.

G.P.  9.5 #2,4,12

I.P. 9.5 # 1,3,11,16

Due:

Rational Functions

Entry: What is a rational number? a rational function?

TASK: define rational functions, examine asymptotes and long-run behavior

G.P. 9.4 #5,12,14

I.P:  9.4 # 1,7,15,16

Due:

Polynomials - short run

Eval: section 9.2 problems

Task: Look at zeros, short run behavior of polynomials

G.P. 9.3 #2,8,12,14

I.P. 9.3 # 1,5,11,13,19

Due:

Polynomials

Entry: Sketch a cubic and quartic polynomial.

Eval: section 9.1 problems

TAsk: Review polynomials, discuss long-run behavior

G.P. 9.2 #2,4,10,20,22?

I.P. 9.2 #1,5,9,21,27

Due:

Ch 8 Assessment

Entry: 5-10 minutes review with table groups.

Task: Ch 8 test.

Due:

Chapter 8 Review

Eval: 8.3 problems

Task: review for  Quiz on Ch 8 functions

I.P. Ch 8 Review #1,3,5,7a-d,8,16,35,36,38,40

Due:

Power Functions

Entry: Define direct and inverse relationships.

Task: Define and model with power functions

G.P. 9.1 #2,4,8,10,12,16,30?

I.P. 9.1 #1,3,7,9,11,17,31

Due:

Combinations of Functions

Entry: r(x) is revenue, c(x) is cost  Why would you find p(x) = r(x) - c(x)?

Eval: 8.2 problems

Task: Combine functions to create new functions- NOTES

G.P. 8.3 #2,4,8,14,31

I.P. 8.3 #1,3,5,7,15,21

Due:

Inverses

Entry: f(2) = -5, f-1(3)= 0, What other values do you know for f(x) and f-1(x)?

Eval: 8.1 problems

Task: Find inverse formulas or values from f(x)

G.P 8.2 #6,10,22,32

I.P. 8.2 #7,9,16,23,29

Due:

Composition of Functions

Eval: CH 5 Test.

Task: Define the composition of functions. notes.

G.P. 8.1 #2,4,6,18,28,29

I.P. 8.1 #1,5,11,19,23,59

Due:

Transformation Assessment

Entry: Questions?

Task: Ch 5 test on transformations.

Due:

Transformation Review

Eval: 5.5 #3,5,13,17,25

Task: Chapter 5 review # 3,5,7,9,13,15,19,39,47

Test on Tuesday

Due:

Quadratic Transforms

Entry: Write the vertex form of a quadratic function.

Task. Use tranforms on the family of quadratics.

G.P. 5.5 #4,7,12,26

Exit:

I.P. 5.5 #3,5,13,17,25

Due:

Horizontal Stretch and Compression

Task: transform functions with horizontal stretches and compressions-notes

G.P. 5.4 #2,8,16

Exit: #20

I.P. 5.5 #1,9,19,21

Due:

Function Transformation Quiz

Entry: Check 5.3 #5,9,11

Task: Quiz on function Transforms- No Calculators!

Due:

Vertical Stretch and Compression.

Entry: Given this sketch of f(x), draw -f(x) and f(-x) on the same axes.

Eval: Problems from 5.2

Task: Examine outside- vertical- stretches on functions expressed in different formats.

G.P. 4,6,8,10

Exit: 12

I.P. 5.3 #5,9,11,

Due:

Reflective Symmetry

Entry: Graph f(x) = 2x, g(x) = -2x, h(x) = 2-x  on the same set of axes. How are g(x) and h(X) related to f(x)?

Eval: Problems from section 5.1, Ch 4 Test

Task: Describe odd and even functions via graphs and equations.

G.P. 5.2 # 2,4,8,18,26

I.P. 5.2 #1,5,7,11,19,21,27,

Due:

Vertical and Horizontal shifts

Entry: What would f(X) +k do the original function f(x)?

Eval:

TASK:  Define horizontal and vertical transformations with h, k.

G.P. 5.1 #2,12,34

I.P.: 5.1 #1,17,19,21,31,33

Due:

Log Test

Questions?

Test on Logs

Due:

Logarithmic Review

Entry: When will $125 at 3.9% compounded monthly reach $150?

Eval: 4.4 #1,3,9,13

Task: Review problems 1,5,7,9,11,17,19,23,29,37

I.P. Study old quiz.

Test Thursday.

Due:

Log Scales

Entry: Find the ion concentration of Baking Soda with a pH of 8.3

Eval: 4.3 Problems

Task. Graphing a wide spread of values.

G.P.  Demo 2,4,10,14

I.P 4.4 #1,3,9,13

Due:

Logarithmic Models

Entry: What does the graph of an exponential and a logarithmic  function look like? Sketch both on a the same set of axes.

Eval: Quiz on Logs

G.P Log graphs, pH, Earthquakes, and Sound Intensity.

demo #2,6,16,20,22,34

I.P. 4.3 # 1, 5,13,17,21,23,33,35

Note we will finish this on Monda.y.

Due:

Logarithms Quiz

Eval: problems from 4.2

Task: Quiz on Logs and properties.

Finish HW from section 4.2, read section 4.3

Due:

Logarithms and Exponential Modeling: 2

Eval: 4.2 Problems from yesterday.

Task: converting between annual and continuous rates.

G.P. 4.2 #8,14,20,32

Exit: 22

I.P. 4.2 #9,13,21,37,41

Finish next period.

Due:

Logarithms and Exponential Modeling: 1

Entry: Expand log(x2y/z3), Contract log 2 + log x - 2 log y.

Eval: 4.1 problems from last lesson

Task: Doubling time, Half life.

G.P. 4,6,24,26,28

Exit: 4.2 #2

I.P. 4.2 #3,5,23,27,29.

Due:

Logarithms and their Properties

Entry: find log 100, log2 8, ln e w/o a calculator.

Eval: 4.1 #1-9 odd, 21,25

Task: Write the properties of logarithms (exponents)

G.P. 4.1 #12,18,26,32,36

I.P. 4.1 #13,15,33,37 and expand log(x2y/z4) contract log x +2log y - 3log z

Due:

Logarithms and their Properties

Entry: Solve 10x = 1000, 2x = 1/4, 9x = 3 w/o a calculator.

Task: Define log as as exponents, change forms.

G.P. 4.1 #2,6,8,10,20

I.P. 4.1 #1,3,7,9,21

Due:

Exponential Project:

Entry: Where might you see exponential growth, besides a bank account?

Eval: Chapter 3 test.

Task: Model with exponentials using project handout, due Wednesday 10/4 at the end of the period.

We will be in the library this week.

Due:

Exponential Assessment

Eval: Review problems from ch 3

Task: Exponential assessment.

Due:

Exponential Review: Day 1

Entry: Describe how to see which investment option will provide the highest return.  Use terms like rate, frequency of interest paid, length of investment, etc.

Eval: 3.4 #1,9,11,19,25 ,29

Task: Review for test. Use quiz and problems #1,2,3,5,8,12,13,25,39,45 from the chapter review.

Discuss " Check your Understanding" statements #1-32 on page 137 if you need more practice.

Finish next class period.

Due:

The natural log, base e.

Entry: Do you recall interest formulas form Alg 2?  Compounding monthly, daily, continuously?  

G.P. Read section 3.4 notes on e,continous growth, compounding interest.

3.4 #8,12,18,24,32

I.P 3.4 #1,9,11,19, 25 ,29

Due:

Exponential Check

Eval: 3.3 #1-9odd, 13,15,33

Task: Quiz on Exponentials

Due:

Exponential Graphs

Entry:  What do graphs of exponential growth and decay look like?

Task: Fitting data with Excel, take notes.

G.P. 3.3 #2,4,14,16

Exit: #18

I.P. 3.3 #1-9 odd 13,15,33

Due:

Linear vs Exponential

Entry:  Is this a linear or exponential? Construct a table of the other.

Eval: 3.1 assignment from Monday. Ch 2 test.

Task: Model rabbits with linear and exponential if t = 3, r = 120 and t=6, r= 300.

G.P 3.2 # 10,12,16

Exit #1

I.P.: 3.2 #3,7,9,11,15,31

Due:

Exponential Introduction

Entry:  Is increasing at a constant rate the same as increasing by a constant amount? Explain.

G.P. 3.1 #4,6,8,10,12

I.P. 3.1 #3,5,7,13,15,23

Due:

Function Assessment

Eval: Questions?

Task: Chapter 2 Test

Due:

Review Functions

Entry: What don't I know?

Eval: Section 2.6 problems

Task:Review Problems #1,5,7,13,17,27,33, Review quiz, Check Understanding #1-33

I.P. Finish Check Understanding Problems

We will finish this on tomorrow.

Due:

Review Quadratics

Entry: What do you remember from Quadratics?

Eval: 2.5 Problems

G.P. #4,10b,12,16

Exit: #18

I.P. 2.6 #1,9,13,15,17,21

Due:

Concavity

 

Entry: Define concave and convex

Eval: Section 2.4 problems

Task: Define concave up and down mathematically.

G.P. 2.5 #2,4,6,8,12,16

Exit: #18

I.P. 2.5 #1,3,7,11,15,17

Due:

Inverse Functions

Entry: Using previous work- find a function  that relates gallons of paint ot area covered.

Eval: Section 2.3 problems

Task: Define f(x) and inverse

G.P.  #2,4,10,20.

I.P. 2.4 #1,3,9,21

Due:

Piece-Wise Functions: Day 2

Entry: Tell your neighbor one item on test.

EVAL: Questions?

Task: QUIZ ON 1.1,2.1,2.2

G.P :2.3 #2,6,12,14

I.P:  2.3 #1,5,9,15

Due:

Piece-Wise Functions: Day 1

Entry: f(x) = x2, x≤ 2;x +1 x> 2. Find f(0) f(3) f(2).

Eval: 2.2 problems

Task: Modeling with pieces section 2.3

G.P. Prepare for quiz

Exit: None

I.P.:Study for quiz!

Due:

Domain and Range

Entry: Find a way to remember Domain → x = inputs, Range → y = outputs.

Eval: 2.1 # 7,11,23,27

Task: Read 2.2 Demo Notes on 4,10,16, 33 (need online grapher, see links page, or TI)

watch: https://www.khanacademy.org/math/algebra-home/alg-functions/alg-domain-and-range/v/domain-of-a-function-intro

I.P. 2.2. #3,11,23,25,29

Due:

 Evaluate Functions

Entry: f(x) = x2 - 4 Find f(x) = 5, f(5), f(x-2)

Eval: Section 1.1 # 1,3,5,19

Task: Section 2.1 and examples 2,4,6,12,20

Exit: #19

I.P.: Section 2.1 #7,11,23,27

Due:

Define Functions 

Entry: What do you think a "function" is?

Eval: Do the Drive Solutions explanations, railroad rates.

Task: Read Section 1.1, work #16,18 together.

Exit: Problem #13

I.P.: Section 1.1 #1,3,5,19.

Due:

First Day! 

Read over syllabus- available to the right.

Do the Puzzlers Presentation.

Complete the "Railroad Rates"  problem for tomorrow.