AP Calculus AB

Pacing Guide: Limits

For a few weeks, this class will be studying concepts with respect to limits, which will lead us to differentiation. The class will be paced with the following schedule:

-Introduction to Unit 2 – September 8

-Section 1.1: A Preview of Calculus - September 9

-Working with Limits and the Area Problem - September 10 through September 11

-Section 1.2: Finding Limits Graphically and Numerically - September 12 to September 16

-Section 1.3: Evaluating Limits Analytically - September 17 through September 19

-Section 1.4: Continuity and One-sided Limits - September 22

-Section 1.5: Infinite Limits - September 23 - September 24

-Review Limits - September 25

-Test on Limits - September 26

All Assignments can be viewed in the Canvas portion of the class. (Two weeks are displayed due to requests from students.) 

This week, we will be continuing a precalculus review. 

Regular homework will be assigned in the classroom. The homework will also be provided in the Canvas class. All of this week's homework will be due on the first school day of the next week.

Remember, this is a senior-level ECA class. No late work will be accepted. 

Monday, September 1:

Labor Day: No School

Tuesday, September 2:

We will be reviewing Law of Sine and Law of Cosine.

Resources:

https://www.mathsisfun.com/algebra/trig-sine-law.html

Links to an external site.

https://www.mathsisfun.com/algebra/trig-cosine-law.html

Links to an external site.

Homework:

Complete #5 - #14 of the Law of Sines worksheet and #1 - #12 of the Law of Cosines worksheet.

(Since this is a test week, you will be provided answers in Canvas to make sure you have properly solved this homework. This work will not be submitted for grading.)

Wednesday, September 3:

We will be reviewing for and discussing the aspects of tomorrow's test.

Homework:

Complete the review handed out in class. Homework (and answers) are in the file in Canvas.

Study for the test. Make sure you bring your notes and test supplies to next class.

Thursday, September 4: 

We will be completing the first half of the first test of the semester.

Friday, September 5: 

We will be completing the second half of the first test of the semester.

This week, we will be starting lessons on limits. Specific work below will be assigned that relates to the lessons of the day. 

Regular homework will be assigned in the classroom. The homework will also be provided in the Canvas class. All of this week's homework will be due on the first school day of the next week.

Remember, this is a senior-level ECA class. No late work will be accepted.

Monday, September 8:

We will studying an introduction to limits (Section 1.1) and discussing two math issues with respect to limits. Complete the following:

1) In the calculus book checked out to you from ECA, read pages 41-46. 

2) In your ECA calculus textbook, complete problems #1 to #10 on page 47. You will be turning this in as part of your classwork to be turned in on Monday, September 16.

Tuesday, September 9:

We will continue our introduction to limits and discuss limit behavior. Complete the following:

1) In the calculus book checked out to you from ECA, read pages 48-54. Some of the last items may be confusing to you...Don't worry, I will explain those concepts to you soon.

2) In your ECA calculus textbook, complete problems #1 to #19 (odd problems only) on pages 54-55. You will be turning this in as part of your classwork to be submitted on Monday, September 16.

Wednesday, September 10:

We will continue our introduction to limits and discuss limit behavior. Complete the following:

1) You will receive three "Area under a Function" worksheets. 

2) On the first sheet of paper, starting at x=0, divide the x-axis into 20 unit sections (make a small mark at x=20, x=40, etc. on the x-axis).

3) For each section, you will make a box that is 20 units wide, has a bottom along the x-axis, and has the upper-left corner of the box touching the function on the worksheet. Look in the textbook at Figure 1.4 on page 46 to see the pattern I want. (Notice that your first box on 0<x<20 will have a height of zero, since the left-most y-value of that section is zero as well. Your second box will have a height of 40, since the left-most y-value of that section is 40.) Keep making boxes until you run out of the function above the x-axis.

4) Calculate the area of each box. Then calculate the total area of the boxes. This is your approximate area calculation if boxes are 20 units wide and area boxes are compared to the left-most function value of each box.

5) For the second "Area Under a Function" worksheet, repeat steps 2-4, except you will create boxes that touch the function on the upper-right corner of each box. Once again, then calculate the area of each box and then compute the total approximate area calculation if boxes are 20 units wide and area boxes are compared to the right-most function value of each box.

6) Make sure each worksheet contains: (a) both worksheets show your boxes, (b) area of each box (on worksheet or separate paper), and (c) total area of boxes from both worksheets. We will add to this tomorrow.

Thursday,  September 11:

We will continue our introduction to limits and discuss limit behavior. Complete the following:

1)On the last sheet of paper for the "Area Under a Function" project, starting at x=0, divide the x-axis into 10 unit sections (make a small mark at x=10, x=20, etc. on the x-axis).

2) For each section, you will make a box that is 10 units wide, has a bottom along the x-axis, and has the upper-left corner of the box touching the function on the worksheet. Look in the textbook at Figure 1.4 on page 46 to see the pattern I want. (Notice that your first box on 0<x<10 will have a height of zero, since the left-most y-value of that section is zero as well. Your second box will have a height of about 20, since the left-most y-value of that section is about 20.) Keep making boxes until you run out of the function above the x-axis.

3) Calculate the area of each box. Then calculate the total area of the boxes. This is your approximate area calculation if boxes are 10 units wide and area boxes are compared to the left-most function value of each box.

4) Look at your results for the three graphs and estimate what you think the area would be if you made another set of boxes over the graph if the boxes were 10 units wide and area boxes are compared to the RIGHT-most function value of each box. 

5) Complete the worksheet given in class. 

6) Take the work from today and combine it with yesterday's work. You will be turning this in as part of your classwork to be submitted on Monday, September 16.

Friday,  September 12:

We will continue our introduction to limits and discuss limit behavior. Complete the following:

1) In the calculus book checked out to you from ECA, read pages 48-54. Some of the last items may be confusing to you...Don't worry, I will explain those concepts to you soon.

2) In your ECA calculus textbook, complete problems #1 to #19 (odd problems only) on pages 54-55. You will be turning this in as part of your classwork to be submitted on Monday, September 16.

Signup and paying for the AP Calculus AB test in May must be completed by October 31, 2025. To sign up for the class, students must access my College Board personal class/website. The instructional are below. Mr. Glaser's College Board AP classroom is: 2LJ7GW (for 2025-26).

STEP 1: Use the class-specific JOIN CODE to join your AP teacher’s classroom on

the MyAP website (http://myap.collegeboard.org) and set your exam decision to

“YES” no later than October 31, 2025.

STEP 2: Starting August 25, 2024, submit payment of $99 for the AP exam that you

are choosing to take at ECA/CEC’s payment website (http://aptsusa.com/eca-cec).

Payment must be received no later than October 31. 2025 . (College Board charges

cancellation/unused exam fees; if a student cancels after November 14th, or fails to take the

exam in May, $40 will be forfeited to pay this charge.)

BOTH Steps 1 & 2 MUST be completed by October 31, 2025 to complete an AP

exam order activation. Orders activated after this will incur an additional

LATE FEE of $40 per exam. (LATE FEE is required by College Board.)

(Students eligible for free/reduced lunch should contact Counselor Alicia Faulds

(alicia.faulds@aps.edu) to obtain the fee reduction code. A $40 deposit will be collected, but $35 of

that fee will be refunded once the exam is completed, resulting in a final fee of $5 per exam.)

ECA/CEC AP Exam Ordering Deadline:

Exam Activation Deadline:  October 31, 2025

Full Exam Payment Deadline:  October 31, 2025

For more information and details as well as assistance and support visit http://aptsusa.com/eca-cec OR contact Ms. Vierra, ECA/CEC Testing Coordinator, at: jessica.vierra@aps.edu.