- Kevin Liddiard
- 2017-2018 School Year
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.
No upcoming assignments.
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.
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.
I.P. 9.7 #5,7,13
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
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
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
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
Ch 8 Assessment
Entry: 5-10 minutes review with table groups.
Task: Ch 8 test.
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
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
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
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
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
Task: Ch 5 test on transformations.
Eval: 5.5 #3,5,13,17,25
Task: Chapter 5 review # 3,5,7,9,13,15,19,39,47
Test on Tuesday
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
I.P. 5.5 #3,5,13,17,25
Horizontal Stretch and Compression
Task: transform functions with horizontal stretches and compressions-notes
G.P. 5.4 #2,8,16
I.P. 5.5 #1,9,19,21
Function Transformation Quiz
Entry: Check 5.3 #5,9,11
Task: Quiz on function Transforms- No Calculators!
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.
I.P. 5.3 #5,9,11,
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,
Vertical and Horizontal shifts
Entry: What would f(X) +k do the original function f(x)?
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
Test on Logs
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.
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
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.
I.P. 4.3 # 1, 5,13,17,21,23,33,35
Note we will finish this on Monda.y.
Eval: problems from 4.2
Task: Quiz on Logs and properties.
Finish HW from section 4.2, read section 4.3
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
I.P. 4.2 #9,13,21,37,41
Finish next period.
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.
Exit: 4.2 #2
I.P. 4.2 #3,5,23,27,29.
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 #12,18,26,32,36I.P. 4.1 #13,15,33,37 and expand log(x2y/z4) contract log x +2log y - 3log z
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
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.
Eval: Review problems from ch 3
Task: Exponential assessment.
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.
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.
I.P 3.4 #1,9,11,19, 25 ,29
Eval: 3.3 #1-9odd, 13,15,33
Task: Quiz on Exponentials
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
I.P. 3.3 #1-9 odd 13,15,33
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
I.P.: 3.2 #3,7,9,11,15,31
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
Task: Chapter 2 Test
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.
Entry: What do you remember from Quadratics?
Eval: 2.5 Problems
I.P. 2.6 #1,9,13,15,17,21
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
I.P. 2.5 #1,3,7,11,15,17
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
I.P. 2.4 #1,3,9,21
Entry: Tell your neighbor one item on test.
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
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
I.P.:Study for quiz!
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)
I.P. 2.2. #3,11,23,25,29
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
I.P.: Section 2.1 #7,11,23,27
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.
Read over syllabus- available to the right.
Do the Puzzlers Presentation.
Complete the "Railroad Rates" problem for tomorrow.