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A Journey of Mutual Growth: Teaching AP Precalculus to Shriya Balu.

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As a teacher, it's rare to find a student who not only meets you halfway but inspires you to go the extra mile. This year, I had the privilege of teaching AP Precalculus to Shriya Balu, a dedicated and hardworking 11th grader. The 2023-24 academic year marked the introduction of AP Precalculus, a college-level mathematics course designed to pave the way for calculus and other advanced mathematics courses. This was a new challenge for both of us, but together we navigated these uncharted waters with determination and enthusiasm.


In my classes, I've come to understand that before diving into the world of AP Precalculus, students should have a firm grasp on the essentials typically covered in Algebra 1, Geometry, and Algebra 2. These subjects are the backbone of their mathematical journey, ensuring they're ready for the challenges that lie ahead. Mastery of linear and quadratic functions, including polynomial addition and multiplication, factoring quadratic trinomials, and using the quadratic formula, is crucial. Getting a handle on exponential functions and exponent rules is also a must. Students should be adapt at using calculators to perform calculations, graph functions, and analyze graphs. Understanding how to pinpoint the intersection of functions and determine the minima and maxima will serve as vital skills. These fundamental concepts act as the stepping stones to success in AP Precalculus, providing the necessary tools and confidence to tackle more advanced topics. With these basics under their belt, students can hit the ground running and make their AP Precalculus journey a smooth ride.


The AP Precalculus adventure unfolds as a captivating journey, neatly segmented into four distinct units, each filled with its own mathematical marvels and challenges.



In Unit 1, students are equipped with the skills to represent and analyze functions in multiple forms—graphical, numerical, analytical, and verbal—both with and without technology.Key topics include rates of change in linear and quadratic functions, polynomial functions with complex zeros and end behavior, and rational functions with a focus on zeros and holes. Students practice expressing functions in equivalent forms, constructing new functions using transformations and compositions, and supporting conclusions with data.


In Unit 2, the focus shifts to Exponential and Logarithmic Functions, revealing the patterns of exponential growth and decay that we encounter daily. It begins with understanding changes in arithmetic and geometric sequences, followed by exploring changes in linear and exponential functions. You'll then learn about equivalent exponential forms and how to model with exponential functions. The unit progresses to compositions of functions, inverse functions, and logarithms as the inverse of exponentials. You'll delve into logarithmic functions and equivalent forms, and tackle exponential and logarithmic equations and inequalities.


Unit 3 brings you into the domain of Trigonometric and Polar Functions. You'll start with periodic phenomena and radian measure, then delve into sine, cosine, and tangent functions, including their values, graphs, and transformations. We'll model real-world scenarios with sinusoidal functions, explore the tangent function and inverse trigonometric functions, and solve trigonometric equations and inequalities. The unit also introduces the secant, cosecant, and cotangent functions, examines different representations of trigonometric functions, and concludes with an exploration of trigonometry in polar coordinates and graphing polar functions. This unit provides a thorough understanding of trigonometry and its applications.


Finally, Unit 4 explores Functions with Some Extra Flair – Parameters, Vectors, and Matrices. Parameters breathe versatility into equations, allowing you to fine-tune their behavior and explore a spectrum of possibilities. Vectors make their grand entrance, helping you visualize magnitude and direction in three-dimensional space. Matrices provide a powerful framework for solving systems of equations and transforming geometric objects.


From the get-go, Shriya proved to be a star pupil. Her relentless dedication and thirst for knowledge turned our sessions into a dynamic exchange of ideas. It felt like the stars had aligned, bringing us together in a perfect student-teacher match. Each week, I found myself donning the hat of a student, meticulously preparing the material to ensure I delivered my best. As the saying goes, "To teach is to learn twice," and indeed, Shriya's enthusiasm spurred me on to deepen my own understanding of the concepts.Moreover, I cannot overstate the invaluable support provided by Shriya's mother, Parvathi Balu. She was the wind beneath our wings, constantly motivating and encouraging both Shriya and myself. Her unwavering support was a cornerstone of our success, and it highlighted the importance of a collaborative effort between teachers and parents.


As the final exam approached, Shriya’s hard work and determination were truly commendable, and I am confident she will ace the exam with flying colors. This experience has been a feather in my cap, allowing me to spread my wings and soar higher in my teaching journey.

To get a glimpse of my hard work and dedication, here are a few words from Parvathi Balu:

Supriya,


"I Thank you for going above and beyond with your online Math tutoring for my daughter Shriya Balu, 11th grader in High School.

Shriya needed mentoring and confidence to excel in AP Pre Calculus. Your tireless coaching and support made her excel in that class. You showed that genuine care from preparing materials before the class and checking in with her after each class. You provided additional math expertise to Shriya when she needed that extra help in preparing for her SAT exam.


Truly outstanding Math tutor you are, I strongly recommend your coaching to anyone who wants to excel in Math and Ap courses!!!


All the very best in your future endeavors!!!"

This journey with Shriya has reaffirmed my belief that teaching is not just about imparting knowledge; it's about growing together, embracing challenges, and celebrating every milestone. Here’s to many more such enriching experiences and the joy of learning together.


Stay tuned for more inspiring tales in the wonderful world of education, where every student's journey is a masterpiece waiting to unfold.

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