Mrs. DeCosta - heidi.decosta@ct.gov's Website

Cycle Objectives

1. Calculate slope and write the equation of a linear function
2. Determine the domain, range and graph of a function
1. Linear
2. Polynomial
3. Piecewise

9/6 – Hand out books and stuff

9/7–Lines and Slope

1. Review class policies and procedures
2. Calculate Slope
3. Graph a line
4. Write the equation of a line

• Get Policy and Rules signed (due 9/8)
• PG 16-17: 1-14, 27-43 odd, 69-72

9/8 – How well do you know your function?

1. Use function notation
2. Find the domain and range of a function
3. Graph a function
4. Use the vertical line test

• Mini quiz
• PG 27 1, 3, 5, 7, 8, 11, 12, 15, 21-32

9/9 – Piecewise  functions

PG 27 17-18, 20, 51

Calculus Cycle 3 Schedule 9/27-10/11

 

9/27 – Review Functions

• WS pg 20-22 1, 5-8, 27-43, 4.8B all

 

9/28 –Rational Functions

• Simplifying and Domain restrictions
• WS 11.2

 

9/29 – Combination Functions

• Adding, subtracting and composing functions

• WS pg 44: 29-37, 41-46, 50&52

 

9/30 – Functions Quiz

 

10/3 – Why Calculus/Tangent Line problem

• Introduction to limits

• Pg 47 #9

 

10/4 – Introduction to limits

• Pg 54: 1-4, 7

 

10/5 – When a limit does not exist

• Behavior differs from L to R, oscillating behavior, infinite limits

• pg 55: 9-18

 

10/6 – Evaluating a limit analytically

• pg 65 1-4, 5, 12, 18, 22, 45-48

 

10/7 – Review - limits

 

10/11 – Quiz - limits

 

next cycle: right and left hand limits, continuity, Intermediate value theorem, revisit tangent line problem/intro to derivatives

Calculus Cycle 7 Schedule 12/7-12/23

 

Cycle Objectives

1. “Derive” differentiation rules
2. Investigate the relationship between position
3. , velocity and time
4. Use differentiation rules to find the derivative of a function
5. Understand the derivative as the slope giving function,  and use it to describe the rate of change of a function

 

12/7 – Definition of a derivative (review)

Objectives:

1. use the definition of a derivative to discover the power rule

Activity:

• Review test
• Pg 113 1-2, 3-17 odd, 53-56

 

12/8 – Application of power rule: Ball Bounce Activity

Objectives:

1. Graph the position vs time of a falling object
2. Use manual fit and regression techniques to fine the equation of a free falling object
3. Calculate the derivative of the height vs time equation using the power rule

Activity:

• Ball bounce activity part 1

 

12/9 – Ball Bounce continued…

Objectives:

1. Graph velocity vs. time
2. Find the velocity equation of a free falling object
3. Graph acceleration vs time
4. Find the acceleration of a free falling object
5. Relate position, velocity and acceleration using the power rule

Activity:

• Ball bounce activity part 2 and conclusions

 

12/12 – Derivatives as a rate of change

Objectives:

1. Use the derivative as a rate of change

Activity:

• Pg 113 92-94, 95 - 97

 

 

 

 

 

 

12/13 - Derivative as a slope giving function

Objectives:

1. Use derivative to find the slope at a point
2. Find and use the derivative of sin and cos

Activity:

• Pg 113 19-22, 31-41 odd, 71-72

 

12/14 – Product and Quotient Rule

• Rational Function WS
• pg 124-125: 1-17 odd, 25, 31, 32, 63-67

 

 

12/15 – Review Product and Quotient Rule

• Review HW
• Derivatives WS

 

12/16 – Quiz

 

12/19 – Chain Rule

Objectives:

1. Recognize functions as composite functions
2. “Derive” and use the chain rule

Activity:

• Pg 133-135 1-6, 7, 9, 11, 25, 29, 31, 47, 48, 51, 59

 

12/20 – more on Chain Rule

Activity:

• HW quiz
• Pg 133-135 87, 92-94

 

12/21 – Higher Order Derivatives

Objectives:

1. find higher order derivatives of a function

Activity:

• Pg 83, 85, 87, 89-92

 

12/22 – Implicit Differentiation

Objectives:

1. Understand derivative operator notation
2. Recognize functions written in implicit form
3. Use implicit differentiation to find the derivative of a function

Activity:

• Pg 142 1-11 odd, 21, 24, 25, 29, 31, 35, 39

 

12/23 – Derivatives Quiz

Calculus Cycle 9 Schedule 1/8-1/26

Cycle Objectives

1. Use the derivative as a rate of change to model and solve problems
2. Find critical numbers of a function
3. Use the first and second derivative test to find the max/min(s) of  a function 

 

1/12 – Intro to related rates

Objectives:

1. Define related rates
2. Use the chain rule and implicit differentiation to differentiated problems involving related rates
3. Use related rates to solve problems

Activity:

1. Pg  149 5, 8, 15, 19, 22, 23

 

1/13 –More Related Rates

• PG 149-150 #27, 28, 31, 32, 35

 

1/17 – Related Rates day 3

• HW Quiz
• WS #11-14, 33-34

 

1/18– Review

 

1/19 – Quiz on Related Rates

 

1/20 - Finding max/min of a function using critical numbers

• Pg 165 1-15 odd, 17, 25, 29, 55

 

 

1/23 - Rolle’s Theorem and Mean Value Theorem

• Pg 172 7-15 odd, 22, 25, 31-37 odd, 43

 

 

1/24 - 1^st Derivative Test       

• In class pg 181 #43-48
• Pg 181 #1-4, 11-31 EOO

 

 

1/25 – Quiz 1^st derivative test

 

1/26 - TBD

Calculus Cycle 11 Schedule 2/8-2/24 

Cycle Objectives

1. Find critical numbers of a function
2. Use the first and second derivative test to find the max/min(s) of  a function
3. Use the second derivative test to find the concavity of a curve.
4. Application: Use the tests to sketch the graph of a function (curves).
5. Application: use maximum and minimum to solve optimization problems

 

       

2/8 – Rolle’s Theorem and Mean Value Theorem

• Objective 22-23

 2/9 - 1^st Derivative Test         

• In class pg 181 #43-48
• Obj 24-25

 

2/10 - 2^nd Derivative Test

• Pg 189 1-7, 11, 15, 19, 21, 27, 33, 39

 2/14 – Curve Sketching

• Pg. 208-209 #1-7, 9, 27, 51, 52

 2/15 – More Curve sketching

 2/16 – Optimization

• Obj 30

 2/17 – QUIZ on curve sketching and optimization

 

 2/22 – Review

 2/23 – Review

2/24 – DWA Final