AB - Week 12 Update

Hello Calculus Families!

Hello everyone! Welcome to this week's edition of Classroom Highlights.

🧠 What Did We Learn This Week?

We covered Lesson 5.3: Local Extrema and Concavity. Students explored how the second derivative (f'') reveals where a graph opens upward like a cup (concave up) or downward like an umbrella (concave down). We also mastered identifying inflection points (where concavity changes) and utilizing the Second Derivative Test to classify local maxima and minima.

• Unit 5 Quiz: Demonstrating our mastery of concavity, extrema, and derivative tests.

• Lesson 5.4: Using Calculus to Graph Functions — Putting all the pieces together (intercepts, asymptotes, critical points, and concavity) to sketch precise curves without relying on a graphing calculator!

• Lesson 5.5: Introduction to Optimization — Using derivatives to solve real-world problems: finding maximum profits, minimum costs, optimal volumes, and perfect efficiency.

If your learner scores below 85% on a test, they are expected to meet with me within 3 school days of receiving their test results to complete test corrections.

Available times include:

• Before school
• During Advisory
• During lunch

Please note: I will not be able to provide class time for test corrections.

If test corrections are not completed within the 3-day window, the original score will be entered into Skyward and will not be changed afterward.

For minor grades, learners may complete corrections once to review their mistakes and improve their understanding of the material. However, minor-grade test corrections will not result in an increase to the recorded score.

Learners, please take advantage of this opportunity! Test corrections are not just about improving a grade — they are a chance to identify misconceptions and learn from mistakes. 🧠✨

To help keep everyone on track for success, all major grades during this nine-week period will be counted.

Here is what to expect for our major assessments this grading period:

• Unit 4 Test: Worth 100 points (completed today!)

• Unit 5 Test: Worth 100 points (coming up later this unit)

Encourage your learner to stay consistent with their homework assignments and quiz prep—these major tests are great opportunities to showcase everything they've mastered!

We will have more than 8 minor grades throughout the nine weeks, and I will drop only one minor grade. Therefore, every assignment counts!

Learners, please be intentional about completing all homework and class assignments. Although these assignments may seem less important than tests, they provide valuable opportunities to practice, learn from mistakes, ask questions, and build the skills needed to succeed on major assessments.

Consistency beats cramming! Stay on top of your assignments, and your hard work will pay off.🚀

🌅 Morning Tutorials

I’m available for individual/small-group tutorials: Monday • Tuesday • Friday- ⏰ 8:15 AM

📌 By appointment

Learners who would like extra practice, clarification, or help preparing for an assessment are welcome to schedule a tutorial.

⭐ Mandatory Tutorials

Learners who score below 85% on an assessment are required to attend tutorials beginning Thursday, 09/03, during Advisory.

These tutorials are designed to help learners identify areas of difficulty, correct misconceptions, and strengthen their understanding of the material.

Remember: Asking for help is a strength, not a weakness! 💪📐

Engage your learner in a quick conversation over the break about how linear approximations work in the real world:

• "If a car's speed is increasing, but it's increasing slower and slower, is that concave up or concave down?" (Hint: Concave down—the rate of growth is slowing down!)

• "What is an 'inflection point' in real life, outside of math class?" (Think: The moment a growing trend or project shifts from accelerating to leveling off.)

• Fully Charged Chromebook: Essential for accessing Webdesk, our BFW eBook, AP Classroom, and DeltaMath during class.

• Writing Utensils: Pens and pencils for daily note-taking and working through practice problems.

• Note-taking Materials: A dedicated notebook or loose-leaf paper to take daily notes and show work for AP-level problems.

• Binder: A 1-inch binder (if using loose-leaf paper) to keep handouts, notes, and returned assignments neatly organized.

• Daily AP Classroom Practice: Essential for skill-building; these check-ins may or may not be scored for a grade.

• BFW Assignments: Accessible directly through Webdesk.

• Unit Worksheets: Completed for the corresponding lesson.

• AB (5.3) - AP® Practice Problems & Review Exercises - Friday, Nov 6 (Midnight)
• AB Day 12 (5.4) - AP® Practice Problems and Review Exercises - Sunday, Nov 15 (Midnight)

📅 Unit 5 Quiz - Monday, November 9, 2026

Unit 5 Test - Thursday, November 19, 2026

In economics and business strategy, an inflection point on a growth curve is known as the Point of Diminishing Returns. It marks the precise moment where adding more resources continues to increase output, but at a slower rate than before!

Meanwhile, in roller coaster engineering, designers rely heavily on inflection points and concavity changes to engineer smooth transitions between drops and loops—calculating the exact moments where g-forces shift to keep the ride thrilling yet completely safe!

उद्यमेन हि सिध्यन्ति कार्याणि न मनोरथैः।
न हि सुप्तस्य सिंहस्य प्रविशन्ति मुखे मृगाः॥

Transliteration:
Udyamena hi sidhyanti kāryāṇi na manorathaiḥ,
Na hi suptasya siṃhasya praviśanti mukhe mṛgāḥ.

Translation:
“Success comes through effort, not mere wishes.
Even a lion cannot have deer walk into its mouth while it sleeps.”

Applicability:

This sloka reminds us that achievement requires consistent effort and perseverance — a perfect message for learners striving to understand complex concepts through practice and curiosity.

It is a privilege to partner with you through AP Calculus this year! Thank you all for your understanding and support as I recover—I look forward to a fantastic week ahead in our math lab together. If anyone ever has questions, please feel free to reach out.

Have a wonderful weekend everyone!

Mrs J