AP Calc Unit 2 - Rates of Change & Derivatives

Date

Classwork Assigned

Homework Assigned

MAKE SURE YOU ARE SIGNED IN TO YOUR KHAN ACADEMY ACCOUNT BEFORE WATCHING THE VIDEOS!

Learning Objectives

Tues/Wed

Sep 30, Oct 1

(Unit 1 test)

HW 2.1 Videos - Due Thu/Fri

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Slope of a line secant to a curve (7:17)

▶ Examples 1, 2, 3 (optional)

▶ Approximating instantaneous rate of change word problem (6:41)

▶ Approximating equation of tangent line word problem (4:14)

✪ Self Check: Slope of secant lines

▶ HW 2.1 Worksheet - Average and instantaneous rate of change half-sheet

Questions you should be able to answer

What is a secant line?
How can you calculate the average rate of change?
What is an instantaneous rate of change, and how is it calculated?
How can you write a linear equation in point-slope form?

Thu/Fri

Oct 2,3

CW 2.1 worksheet - average and instantaneous rate of change

HW 2.2 Videos - Due Wed/Thu

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Newton, Leibinz, and Usain Bolt (9:07)

▶ Derivative as slope of tangent line (15:42) (new stuff starts at about 5:00)

Questions you should be able to answer

How is rate of change different/interesting in calculus?
What is a differential and how is it used?
What is a derivative?
What is the limit formula for a derivative?
How are f and f’ different?

Mon

Oct 6

CW 2.2 worksheet - Intermediate Value Theorem & Mean Value Theorem

HW 2.3 Videos - due Wed/Thu

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Tangent slope as limiting value of secant slope Ex 1 (5:24)

▶ Tangent slope as limiting value of secant slope Ex 2 (6:04) (optional)

▶ Tangent slope as limiting value of secant slope Ex 3 (3:45)

▶ Calculating slope of tangent line using derivative definition (8:27)

▶ The derivative of f(x) = x2 for any x (11:05)

Questions you should be able to answer

What does f’(x) represent?
What are two different ways I can calculate the slope of a curve at a point using limits?
What is a derivative?
How can I easily calculate the slope of a function at any point?

Tues (sub)/Wed/Thurs

Oct 7-9

CW 2.3 worksheet - limit definitions

HW 2.4 Videos - due Mon

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Formal & alternate form of the derivative (4:53)

▶ Formal & alternate form of the derivative for ln(x) (5:45)

▶ Formal & alternate form of the derivative Example 1 (5:16)

✪ Self-check: The formal & alternate form of the derivative

▶ Derivative intuition module (3:57)

✪ Self-check: Derivative intuition

✪ OPTIONAL Self-check: Tangent slope is the limiting value of secant slope

Questions you should be able to answer

What is h? x+h? f(x+h)?
Why do we take the limit as h→0 or as x→[some number]?
How can we use secant lines to approximate tangent lines?
What does the graph of ln(x) look like?
What is the value of ln(e)? ln(0)?
What can we find from the formal and alternate form of the derivative?
What is a derivative? (Really, do you know? What IS it?? Could you explain it to an Algebra student?)

Mon

Oct 13

CW 2.4 worksheet - speeding up or slowing down

Stanford “How to learn math” videos, Part 2

HW 2.5 Videos - due Tue/Wed

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Binomial Theorem (up to 3:30; stop at Binomial Thm)

▶ Pascal’s Triangle for binomial expansion (8:19 - SKIP the first minute)

Questions you should be able to answer

What is Pascal’s Triangle?
How can we find the coefficients of large powers of (a+b) without doing all the multiplication?

Tue/Wed

Oct 14-15

CW 2.5 worksheet - more on limit definitions

HW 2.6 Videos - due Thu/Fri

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ Power Rule (3:53)

▶ Is the power rule reasonable (6:42)

▶ Derivative properties & polynomial derivatives (9:52)

Also finish CW 2.5

*quiz Thurs/Fri* - rate of change (average & instantaneous), f’(c), f’(x)

Questions you should be able to answer

What is the Power Rule?
What kinds of numbers are allowed in the exponent to use the Power Rule?
What can we do if there is a coefficient?
What can we do if there are multiple terms?

Thu/Fri/ Mon

Oct 16-20

CW 2.6 worksheets - 2.6A: Pascal’s Triangle

2.6B: Power Rule

Quiz #3 - rate of change & derivative definitions

MEMORIZE basic derivatives!

HW 2.7 Videos - due Tue/Wed

I supplemented Khan Academy with YouTube this time. Sal’s Chain Rule explanation was not as clear as he usually is. Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ YouTube: Derivative graphs of sine & cosine (3:36)

▶ Khan: Derivatives of sin x, cos x, tan x, ex, ln x (3:43)

▶ Khan: Chain Rule introduction (5:06)

▶ YouTube: Chain Rule “outside inside rule” (4:14)

▶ Khan: Chain Rule definition & example (5:30)

Questions you should be able to answer

What is the Chain Rule?
When do we need to use the Chain Rule?
What does f’(g(x)) mean?
What does g’(x) mean?

Tue/Wed

Oct 21-22

CW 2.7 worksheet - chain rule

HW 2.8 Videos - due Thu/Fri

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

✪ Self-check: Special derivatives quiz

▶ Applying the product rule for derivatives (2:39)

▶ Quotient rule from product rule (5:15)

▶ Quotient rule for derivative of tan x (3:41)

*Quiz* Thu/Fri on basic derivative memorization!

Questions you should be able to answer

What is the Product Rule?
When do we use the Product Rule?
What is the Quotient Rule?
When do we use the Quotient Rule? (And do we really need it?)
What is another way to write tan x?
What is cos2x + sin2x equivalent to?
What is 1/cos2x equivalent to?

Thu/Fri

Oct 23-24

CW 2.8 worksheet - product & quotient rules

Quiz #4a - basic derivative memorization

HW 2.9 Videos - due Tue/Wed

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

▶ OPTIONAL Quotient rule and common derivatives (9:31)

▶ Product rule for more than two functions (3:34)

▶ Using the product rule and the chain rule (5:52)

▶ Equation of a tangent line (8:08)

*Quiz* again Mon on basic derivative memorization!

Questions you should be able to answer

How can we take the derivative of more than two functions multiplied together?
How does it work when we use the product and chain rules together?
How can we use derivatives to find the equation of a tangent line?

Mon

Oct 27

Finish CW 2.8 worksheet - product & quotient rules

CW 2.9 worksheet - Chain Rule

Quiz #4b - basic derivative memorization

(HW 2.9 Videos - due Tue/Wed - see above for links)

*Quiz* Tue/Wed on derivative rules (power, chain, product, and quotient)!

Tue/Wed

Oct 28-29

Finish CW 2.9 worksheet - Chain Rule

Stations review

Quiz #5 - derivative rules

HW 2.10 Videos - due Mon, Nov 3

Khan Academy *sign in!* Take notes, watch the videos more than once if you need to, and write down any questions you have.

✪ Self-check*: Applications of derivatives: tangent and normal lines (show work for at least 5 practice problems)

▶ OPTIONAL* Y-intercept of tangent line example (5:59)

▶ OPTIONAL* Equation of normal line (5:27)

▶ OPTIONAL* Equation of tangent line Example 1 (7:17)

*If the self-check is too challenging, watch and take notes on all 3 “optional” videos instead.

Questions you should be able to answer

What is the difference between a tangent line and a normal line?
How can we find a perpendicular slope?
How can we use derivative rules to help find the slope of a tangent line?
What else do we need to calculate (besides slope) to find the equation of a tangent or normal line?

Mon

Nov 3

Finish Toolkit

Finish Quiz #5

HW 2.11 (review worksheet) to turn in Thu/Fri

Tues/Wed

Nov 4-5

In-class review

HW 2.11 (review worksheet) to turn in Thu/Fri

HW 2.11 ANSWERS

TUTORING AVAILABLE:

Tuesday after school until 3:45

Wednesday after school until 4:00

Thursday during tutorial

Thu/Fri

Nov 6-7

Test #2 - rates of change & derivatives

If you miss this test, see me any period Friday or come in Monday morning - arrive by 10 am to give yourself enough time to finish before I go to lunch.

HW 3.1 - Unit 3