# Andrew Jeung Tutoring > 1:1 Personalized Math and Science Help for High School and College Students ## Pages - [CCPA – California Consumer Privacy Act](https://andrewjeungtutoring.com/ccpa-california-consumer-privacy-act/): Definitions Website https://andrewjeungtutoring. com or Andrew Jeung , doing business as “Andrew Jeung Tutoring” The owner (or We) Indicates the... - [Privacy Policy](https://andrewjeungtutoring.com/privacy-policy/): Welcome to https://andrewjeungtutoring. com (the “Site”). We understand that privacy online is important to users of our Site, especially when... - [Terms of Use](https://andrewjeungtutoring.com/terms-of-use/): These Terms govern your access to, and usage of all content, Products, and Services available at https://andrewjeungtutoring. com website (the... - [College Tutoring](https://andrewjeungtutoring.com/college/): Need help with your college math or physics class? Get the help of a patient, experienced, and professional tutor with no long-term commitment. - [Blog](https://andrewjeungtutoring.com/blog/) - [Tutoring Rates](https://andrewjeungtutoring.com/tutoring-rates/): Current rates for all tutoring services. Expensive? Possibly. Worth it? Definitely! - [Summer Previews](https://andrewjeungtutoring.com/summer-previews/): Imagine your child entering class on the first day of school, confident because they will have seen the material already through Summer Previews! - [About Me](https://andrewjeungtutoring.com/about-me/): How I came to be in this business, my general philosophy about tutoring, and why I think there is no such thing as "not a math person". - [Frequently Asked Questions](https://andrewjeungtutoring.com/frequently-asked-questions/): Get answers to the most frequently asked questions about my services. Something not on the list? Please reach out to me on the Contact page. - [Contact](https://andrewjeungtutoring.com/contact/): Request new tutoring services or ask for more information here. I would love to tell you more about my services! I usually get back to you within 24 hours. - [One-on-One Math and Science Tutoring for High School and College Students](https://andrewjeungtutoring.com/): Is your child struggling in any of the following areas: Math? Biology? Chemistry? Physics? Computer Science? Get math and science tutoring help today! ## Posts - [READ THIS Before Solving Word Problems](https://andrewjeungtutoring.com/read-this-before-solving-word-problems/): Many of my tutoring clients who work with me on Algebra tell me that they have difficulty with word problems.... - [What You Need to Know To Understand TAYLOR SERIES](https://andrewjeungtutoring.com/what-you-need-to-know-to-understand-taylor-series/): One Calculus topic that seems to challenge my tutoring clients every year is the topic of Taylor series. It usually... - [Read THIS Before Buying an AP® Physics 1 Test Prep Book](https://andrewjeungtutoring.com/read-this-before-buying-an-ap-physics-1-test-prep-book/): The AP® Physics 1 exam is one of many Advanced Placement exams offered by the College Board. If you are... - [The RIGHT Way To Think About Moles in Chemistry](https://andrewjeungtutoring.com/the-right-way-to-think-about-moles-in-chemistry/): One of the big ideas that Chemistry students are introduced to pretty early in the class is the concept of... - [Five Reasons Why YOU Should Consider ONLINE TUTORING](https://andrewjeungtutoring.com/five-reasons-why-you-should-consider-online-tutoring/): “Do you offer in-person sessions? ” This is by far the most common question that prospective parents ask me as... - [A Totally Different Way To Approach Electric Fields and Electric Potential](https://andrewjeungtutoring.com/a-totally-different-way-to-approach-electric-fields-and-electric-potential/): Many Physics students get overwhelmed when they start their first Electricity & Magnetism (E&M) class, even if they were pretty... - [Why You Need The EIGHT BLANKS METHOD To Make Trigonometry Graphs A Snap, Part 2: Tangent, Cotangent, Secant, and Cosecant](https://andrewjeungtutoring.com/why-you-need-the-eight-blanks-method-to-make-trigonometry-graphs-a-snap-part-2-tangent-cotangent-secant-and-cosecant/): In part 1 of this blog series, I shared a foolproof method for graphing transformed sine and cosine functions using... - [Why You Need The EIGHT BLANKS METHOD To Make Trigonometry Graphs A Snap, Part 1](https://andrewjeungtutoring.com/why-you-need-the-eight-blanks-method-to-make-trigonometry-graphs-a-snap-part-1/): One of the big challenges my tutoring clients often face in Trigonometry class comes when they are asked to graph... - [The RIGHT Way To Solve Optimization Problems](https://andrewjeungtutoring.com/the-right-way-to-solve-optimization-problems/): Your Math class may have introduced you to a type of word problem called an optimization problem, sometimes referred to... - [The Way You SHOULD Be Solving Stoichiometry Problems, Part 2: Using Dimensional Analysis](https://andrewjeungtutoring.com/the-way-you-should-be-solving-stoichiometry-problems-part-2/): In the first blog post of this series, I showed you a method to solve stoichiometry problems that helps you... - [The Way You SHOULD Be Solving Stoichiometry Problems, Part 1](https://andrewjeungtutoring.com/the-way-you-should-be-solving-stoichiometry-problems-part-1/): If you are taking Chemistry for the first time, you may encounter a class of problems known as stoichiometry problems.... - [Solving Kinematics Problems The Way Your Teacher Did NOT Show You, Part 3 : Projectile Motion](https://andrewjeungtutoring.com/solving-kinematics-problems-the-way-your-teacher-did-not-show-you-part-3-projectile-motion/): In Part 1 of this blog series, I showed you a way to approach kinematics problems for horizontal motion, and... - [Solving Kinematics Problems The Way Your Teacher Did NOT Show You, Part 2 : Vertical Motion](https://andrewjeungtutoring.com/solving-kinematics-problems-the-way-your-teacher-did-not-show-you-part-2-vertical-motion/): In Part 1 of this series, I showed you a new way of looking at horizontal kinematics problems and of... - [Solving Kinematics Problems (The Way Your Teacher Did NOT Show You), Part 1](https://andrewjeungtutoring.com/solving-kinematics-problems-part-1/): If you are starting out in a new Physics class, you may have come across (or will come across) a... ## All FAQ Items # # Detailed Content ## Pages - Published: 2025-07-09 - Modified: 2025-07-09 - URL: https://andrewjeungtutoring.com/ccpa-california-consumer-privacy-act/ Definitions Website https://andrewjeungtutoring. com or Andrew Jeung , doing business as "Andrew Jeung Tutoring" The owner (or We) Indicates the natural person(s) or legal entity that provides this Website to Users. User (or You) Indicates any natural person or legal entity using this Website. This Privacy Notice for California Residents supplements the information contained in the Website's Privacy Policy and applies solely to all visitors, users, and others who reside in the State of California. We adopted this notice to comply with the California Consumer Privacy Act of 2018 (CCPA), and any terms defined in the CCPA have the same meaning when used in this notice. Information We Collect The Website collects information that identifies, relates to, describes, references, is capable of being associated with, or could reasonably be linked, directly or indirectly, with a particular consumer or device ("personal information"). In particular, the website has collected the following categories of personal information from its consumers within the last 12 months: Category Examples Collected A. Identifiers. A real name, alias, postal address, unique personal identifier, online identifier, Internet Protocol address, email address, account name, Social Security number, driver's license number, passport number, or other similar identifiers. YES B. Personal information categories. A name, a signature, a Social Security Number, physical characteristics or description, address, telephone number, passport number, driver's license or state identification card number, insurance policy number, education, employment, employment history, bank account number, credit card number, debit card number, or any other financial information, medical information, or health... - Published: 2025-07-09 - Modified: 2025-07-09 - URL: https://andrewjeungtutoring.com/privacy-policy/ Welcome to https://andrewjeungtutoring. com (the “Site”). We understand that privacy online is important to users of our Site, especially when conducting business. This statement governs our privacy policies concerning those users of the Site (“Visitors”) who visit without transacting business and Visitors who register to transact business on the Site and make use of the various services offered by Andrew Jeung , doing business as "Andrew Jeung Tutoring" (collectively, “Services”) (“Authorized Customers”). “Personally Identifiable Information” Refers to any information that can be used to identify, contact, or locate the person to whom such information pertains, including, but not limited to, name, address, phone number, fax number, email address, financial profile, social security number, and credit card information. Personally Identifiable Information does not include information that is collected anonymously (that is, without identification of the individual user) or demographic information not connected to an identified individual. What Personally Identifiable Information is collected? We may collect basic user profile information from all of our Visitors. We collect the following additional information from our Authorized Customers: the name, email address, phone number, What organizations are collecting the information? In addition to our direct collection of information, our third-party service vendors (such as credit card companies, clearinghouses, and banks) who may provide such services as credit, insurance, and escrow services may collect this information from our Visitors and Authorized Customers. We do not control how these third parties use such information, but we do ask them to disclose how they use personal information provided... - Published: 2025-07-08 - Modified: 2025-07-08 - URL: https://andrewjeungtutoring.com/terms-of-use/ These Terms govern your access to, and usage of all content, Products, and Services available at https://andrewjeungtutoring. com website (the “Service”) operated by Andrew Jeung , doing business as "Andrew Jeung Tutoring" (“us”, “we”, or “our”). Your access to our services is subject to your acceptance, without modification, of all of the terms and conditions contained herein and all other operating rules and policies published and that may be published from time to time by us. Please read the Agreement carefully before accessing or using our Services. By accessing or using any part of our Services, you agree to be bound by these Terms. If you do not agree to any part of the terms of the Agreement, then you may not access or use our Services. Intellectual Property The Agreement does not transfer from Us to you any of Ours or third-party intellectual property, and all rights, titles, and interests in and to such property will remain (as between the parties) solely with Andrew Jeung , doing business as "Andrew Jeung Tutoring" and its licensors. Third-Party Services In using the Services, you may use third-party services, products, software, embeds, or applications developed by a third-party (“Third-Party Services”). If you use any third-party services, you understand that: Any use of a third-party service is at your own risk, and we shall not be responsible or liable to anyone for third-party websites or services. You acknowledge and agree that we shall not be responsible or liable for any damage or loss... > Need help with your college math or physics class? Get the help of a patient, experienced, and professional tutor with no long-term commitment. - Published: 2024-07-03 - Modified: 2024-07-04 - URL: https://andrewjeungtutoring.com/college/ Need a boost for your college math or physics class? BOOK A COLLEGE TUTORING QUICK SESSION Are you a college student in a math or physics class, who is facing one of the following: You are struggling with one particular homework assignment or lab and need just a couple of questions answered to get unstuck You are having a hard time making it to your professor or T. A. 's extremely limited office hours You need to catch up on the material from that one crucial lecture that you missed You would like to boost your understanding on certain topics just before that important midterm or final -- BUT -- you don't have the time (or funds) to spend on regular sessions with an outside tutor? College Tutoring Quick Sessions are a great way to get those immediate questions from your college math and physics classes answered. All tutoring sessions are 100% online over Zoom, so you can take the session from the privacy of your dorm room, at a coffee shop, inside the library, or anywhere that you have Internet access. Each Quick Session is individually scheduled and charged, so you will only pay for sessions that you need and want. There is no long-term commitment and no contract to sign. And you can schedule them as little as 2 hours before the session begins! BOOK A COLLEGE TUTORING QUICK SESSION Quick Sessions are available for the following subjects at this time: College Precalculus First-year lower division Calculus (for... > Current rates for all tutoring services. Expensive? Possibly. Worth it? Definitely! - Published: 2022-01-16 - Modified: 2026-05-24 - URL: https://andrewjeungtutoring.com/tutoring-rates/ Current rates High school classes (below AP level) $110 / hour College-level classes in high school, including AP and Middle College $120 / hour AP Test prep $125 / hour College and university classes starting at $130 / hour Early Bird Special! 20% off weekday sessions that start before 4:00 PM Pacific Time. Does not apply on weekends. Great choice for Central and Eastern time zones! Pricing for college classes depends on level of difficulty. Please contact Andrew to get rates for a specific class. Group rates for groups of 2 or 3 clients sharing one session are available upon request. info@andrewjeungtutoring. com (650) 937-9821 > Imagine your child entering class on the first day of school, confident because they will have seen the material already through Summer Previews! - Published: 2020-04-11 - Modified: 2024-07-04 - URL: https://andrewjeungtutoring.com/summer-previews/ What are Summer Previews? Imagine your child confidently entering their Biology, Calculus, Physics, or Chemistry class on the first day of school -- assured that they will do well because they will have been introduced to the material already! Summer Previews are a convenient, low-stress way to get a head start on challenging classes that your child will be facing next school year. Each Summer Preview consists of a set of fully customizable, private, one-on-one tutoring sessions over the summer that provide an introductory look at the material covered in a class to be taken in the fall. Summer Previews are not a replacement for a class, but can provide a helpful overview or offer background information to make the class easier. CONTACT US TODAY FOR SUMMER AVAILABILITY Summer Previews are: Tailored to your child’s specific needs Scheduled individually between you and the tutor, so you will only pay for sessions that accommodate your child’s work and vacation schedule over the summer Low-stress Homework-free (unless parent requests otherwise) You might consider a Summer Preview if your child: is going to be a freshman in high school and would like to know what their first high school science class (Biology or Bio Honors) might be like will be taking Calculus-based Physics next year, but has not formally taken Calculus yet will be going into AP Biology, Pre-Calculus, Calculus, Multivariable Calculus, Chemistry, or Physics, and has heard that it is a challenging class will be attending college next year and would like... > How I came to be in this business, my general philosophy about tutoring, and why I think there is no such thing as "not a math person". - Published: 2018-05-20 - Modified: 2024-07-04 - URL: https://andrewjeungtutoring.com/about-me/ Andrew Jeung Andrew has a Ph. D. in Physics from Stanford University, and he has over twenty-five years of industry experience in the Silicon Valley. In 2012, he became hooked on tutoring after serving as a volunteer tutor at his local public high school. After a number of years of volunteering in order to perfect his craft, he founded Andrew Jeung Tutoring in early 2018 so that he could serve the wider community of students in the Mountain View, Los Altos, and Palo Alto CA areas. Andrew's Philosophy Ever since I started tutoring in 2012, I have been struck by how much material today’s students are expected to learn at the high school and college levels. High schools now cover a multitude of topics in math, science, and other fields that used to be taught only in college. While on the one hand students are blessed to have the opportunity to learn these additional topics, they are also challenged by the burden of a much denser curriculum than previous generations faced, with the same amount of school time available to complete it. Teachers are now forced to keep the pace of the class in lockstep with this demanding curriculum, and don’t have the luxury of making sure each student’s individual educational needs are met. The unfortunate result is that many students, who might otherwise have done just fine had they been allowed a slightly slower pace or a little more emphasis on certain topics, are left thinking that they are... > Get answers to the most frequently asked questions about my services. Something not on the list? Please reach out to me on the Contact page. - Published: 2018-05-20 - Modified: 2026-07-25 - URL: https://andrewjeungtutoring.com/frequently-asked-questions/ What subjects do you offer tutoring for? I tutor math, statistics, biology, chemistry, physics, and computer science at the high school and introductory college levels. I can also help with test prep for Advanced Placement tests in the above areas. What areas do you serve? Because I offer online tutoring, I can literally serve all areas within the United States! Online tutoring? How does that work? Online tutoring occurs over the Zoom platform with an online whiteboard. In my experience, the vast majority of clients take to the online format very well. I don't know -- both my child and I thought online school during the pandemic was miserable. I agree with you about online school! My daughter was in high school during the pandemic and it was pretty awful. 1:1 online tutoring is nothing like online school. Online tutoring is very personable, collaborative, and interactive. Because the work that I do is personalized to the individual student, there is no concern of a student getting lost or ignored. I have an online whiteboard that both the student and I can write on, add pictures and diagrams, and upload assignments to -- a great improvement over just using pencil and paper. Moreover, all students have access to PDF copies of all of their own whiteboards afterwards so they don't have to take any additional notes unless they want to. I have asked my current online clients how they feel about online tutoring, and all of them prefer it once they... > Request new tutoring services or ask for more information here. I would love to tell you more about my services! I usually get back to you within 24 hours. - Published: 2018-05-17 - Modified: 2024-07-04 - URL: https://andrewjeungtutoring.com/contact/ If you are interested in tutoring services or would like more information, please send an e-mail to info@andrewjeungtutoring. com or fill out this form. I will get back to you as soon as possible. Your name * Your phone number * Your e-mail * Student's name * Name of school / college * Class FreshmanSophomoreJuniorSeniorOther I am interested in SUMMER PREVIEWS Find out more about SUMMER PREVIEWS Subject (please indicate honors or AP if applicable) * Please describe your situation and what you would like to get out of tutoring: * Required fields info@andrewjeungtutoring. com (650) 937-9821 > Is your child struggling in any of the following areas: Math? Biology? Chemistry? Physics? Computer Science? Get math and science tutoring help today! - Published: 2018-05-12 - Modified: 2026-07-11 - URL: https://andrewjeungtutoring.com/ Is your child frustrated by school? Is he or she struggling in any of the following areas: • Math? • Biology? Chemistry? Physics? • Computer Science? You and your child are not alone, and your child deserves to be freed from frustration by having the guidance of a patient, experienced tutor. Since 2018, I have been helping clients just like your child achieve their academic goals, whether it be a firmer grasp of the fundamentals, a better grade, or even less time spent struggling on schoolwork so that they have more time for what matters to them. Select the school subject of interest to learn more! Biology Freshman Biology or Biology Honors is often the first science class that high school students experience, and it is often seen as a big jump from Middle School. Andrew can help ease that transition by clarifying challenging concepts and providing opportunities for knowledge checking. Chemistry Andrew has worked with students on Chemistry from the introductory sophomore class all the way through first-year college level classes. He is equally comfortable working with students on regular Chemistry, Chem Honors, or AP Chemistry as needed. Computer Science Andrew has over twenty years of experience creating software code for a company in the Silicon Valley. He has industry experience writing and debugging software in C++, C#, Python, and Matlab, and can show your student how to do the same. He is also able to help students with their computer science classes in Java. Math Andrew has extensive... ## Posts - Published: 2026-07-25 - Modified: 2026-07-25 - URL: https://andrewjeungtutoring.com/read-this-before-solving-word-problems/ - Categories: Math, Algebra - Tags: age problems, money problems, word problems Many of my tutoring clients who work with me on Algebra tell me that they have difficulty with word problems. They can do the math, they say, they just have a hard time figuring out what the question is asking them. If this applies to you, please read on because I will show you a way to make sense of these types of problems. What I tell my tutoring clients is that a word problem is really just a translation problem. Just like in foreign language class, you are translating a sentence in English into "math language". If math is a language that you can translate to, then it makes sense that it would include: Common nouns: we call these variables: x, y, z Proper nouns: refer to a specific number: 2 3 27 Verbs: = < > ≤ ≥ Conjunctions: + - × ÷ and Prepositional phrases: +3 -1 ×4 Let's look at an example:  Currently, Bob is three times John's age. In six years, Bob will be twice John’s age. What are their ages now? Before I start translating, I need a dictionary of terms, and that's where the variable definitions come in. The objective is to identify quantities in the problem whose value is not known, and make a variable name for each one. Since the question is asking about their ages (which are numbers that are in the problem but whose values we don't know), I can create a variable for each one: x = Bob's... - Published: 2026-04-09 - Modified: 2026-04-14 - URL: https://andrewjeungtutoring.com/what-you-need-to-know-to-understand-taylor-series/ - Categories: Calculus, Math One Calculus topic that seems to challenge my tutoring clients every year is the topic of Taylor series. It usually comes up near the tail end of their Calculus class, and it is touted as a method to come up with an “approximation” to a function. Most Calculus textbooks introduce Taylor series with a scary-looking formula like \sum\limits_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n! } \cdot (x-a)^n Often, clients tell me that they can plug in the right numbers into the formula more or less adequately, but they have no idea what the formula means or why this would even generate an approximation of the original function. If you feel this way, then you have come to the right place! I will show you a way of thinking about Taylor series so that the formula to generate them won’t be such a mystery anymore. To start, let’s imagine that we have a function f(x), which is continuous and differentiable in a region around x = a: What I would like to do is to come up with a power series p(x) that exactly mimics the original function f(x) at a. I don’t care if the power series mimics the original function anywhere else, but it has to be a perfect match for the function at a: If your Calculus class has not gone over power series, please be assured that a power series is just a polynomial, except that it has an infinite number of terms. This is not as crazy as it sounds! You... - Published: 2026-02-10 - Modified: 2026-02-10 - URL: https://andrewjeungtutoring.com/read-this-before-buying-an-ap-physics-1-test-prep-book/ - Categories: Test Prep, Physics - Tags: 5 Steps To A 5, AP Physics 1, Barron's, Princeton Review, Test Prep The AP® Physics 1 exam is one of many Advanced Placement exams offered by the College Board. If you are taking AP Physics 1, you may be wondering if it’s the right time to purchase a test prep book for your upcoming exam in May. Perhaps you have already started looking on Amazon or elsewhere, and have discovered that there are a lot of choices for test prep materials out there. If this is the case, then you have come to the right place! I have read three of the most popular test prep books, all geared towards the 2026 administration of the AP Physics 1 exam. I will be sharing with you my thoughts on the benefits and drawbacks of each. Do I even need a test prep book? It depends. If your AP Physics teacher has been doing a good job conveying the material to you, and has prepared you for the format of the exam, then you should be able to do well on the AP exam without a prep book. However, it is not a bad idea for you to have a supplemental source if: There are content areas that you are still confused about Your teacher has not explained to your class how the test is structured, what the four types of FRQs (Free Response Questions) on the exam are, and what task verbs are used on the FRQs Your class assignments have been focused on calculations, and you have not had much chance to... - Published: 2026-01-07 - Modified: 2026-01-12 - URL: https://andrewjeungtutoring.com/the-right-way-to-think-about-moles-in-chemistry/ - Categories: Chemistry One of the big ideas that Chemistry students are introduced to pretty early in the class is the concept of the mole. A significant percentage of the calculations in Chemistry class depend on this concept, so a clear understanding of moles is really helpful not just for its own sake, but for understanding large portions of the rest of the class as a whole. If you are reading this, maybe you are learning about moles in Chemistry class for the first time. Or maybe you never quite fully understood moles when your teacher or professor introduced it, and now you are discovering that this is getting in the way of your understanding of subsequent parts of Chemistry. Either way, you have come to the right place! I will discuss moles in this blog post in a way that is easy to understand. What is a mole, anyway? At its core, the mole is actually a pretty simple idea. A mole is just a word that represents a certain number of things. Note that a mole is not a unit, like meters or grams. It represents a certain number of things. What things? Well, in principle it could be anything, as long as the things are separate objects that can be counted. If that seems strange, consider the fact that we have words to mean a certain number of things already. For instance, we have the word “dozen” which refers to twelve things. The things could be anything: a dozen eggs,... - Published: 2025-07-27 - Modified: 2025-07-27 - URL: https://andrewjeungtutoring.com/five-reasons-why-you-should-consider-online-tutoring/ - Categories: Art of Tutoring - Tags: in-person tutoring, online tutoring “Do you offer in-person sessions? ” This is by far the most common question that prospective parents ask me as an online tutor. And I can see why. We are not so far removed from the COVID pandemic of 2020 that parents and students have forgotten what it was like to experience distance learning. Students joylessly looking into a grid of their classmates’ faces, teachers having no means and little incentive to enforce class rules, and everyone having to endure awkward breakout rooms where nobody wanted to contribute anything. It is natural, sensible even, to want to avoid anything that seems to be remotely connected to that. But the truth is that online tutoring is very different from the distance learning we remember from a few years ago. In fact, online tutoring provides numerous advantages that make it a highly attractive option for both students and parents. I’d like to take this blog post to explore these key benefits. 1. Online Tutoring ≠ Online School Online tutoring is nothing like online school. There is a very different dynamic online when the interaction is one tutor to one client, as opposed to one teacher to thirty (or more) students. When I am acting as an online tutor, the student client has my full undivided attention, and our interaction is both personable and interactive. I make sure that clients have the chance to ask questions, express their areas of confusion, and talk through their developing ideas, just the same as if I... - Published: 2025-07-11 - Modified: 2025-07-27 - URL: https://andrewjeungtutoring.com/a-totally-different-way-to-approach-electric-fields-and-electric-potential/ - Categories: E&M, Physics - Tags: electric field, electric potential Many Physics students get overwhelmed when they start their first Electricity & Magnetism (E&M) class, even if they were pretty good at Mechanics. And it is hard to blame them. Most of them have at least an intuitive feel for concepts like mass, velocity, momentum, and gravity, and they feel that these ideas in Mechanics are more concrete, even if the math takes some getting used to. But once E&M begins, they are suddenly introduced to much more abstract elements, such as electric fields and electric potential. They don’t have the same intuitive feel for what these things even are, and so E&M as a subject seems that much harder. If you fit the description above, no worries! Over the years of tutoring clients who need help with Physics, I have developed an easy way of thinking about electric fields and potentials that makes electrostatics problems a snap. First Things First -- Electric Charges If you are enrolled in an E&M class right now, you have probably already learned that objects have a property called charge, a scalar that can take either positive or negative values. You most likely also know that like charges (two positive charges or two negative charges) will repel (push each other away), whereas opposite charges (one positive and one negative charge) will attract (pull towards each other). You may even have been introduced to an equation that allows you to compute the force exerted by a charged particle on another charge. This is known as... - Published: 2025-06-08 - Modified: 2025-06-08 - URL: https://andrewjeungtutoring.com/why-you-need-the-eight-blanks-method-to-make-trigonometry-graphs-a-snap-part-2-tangent-cotangent-secant-and-cosecant/ - Categories: Math, Trigonometry - Tags: cosecant graph, cotangent graph, secant graph, tangent graph In part 1 of this blog series, I shared a foolproof method for graphing transformed sine and cosine functions using the Eight Blanks method. I am going to show you how to extend this method to cover the other four trigonometric functions you typically encounter in Trig class: tangent, cotangent, secant, and cosecant. The base tangent and cotangent graphs As before, I want to start by first examining the base graphs for tangent and cotangent. If you have never seen these in class, there are several websites where you can learn the basics of them, including MathHints and Purplemath. Here is the base tangent curve: Base tangent curve. Generated by Desmos. Like the sine and cosine curves, the tangent curve can be characterized by five landmark positions, marked in the graph above with green arrows. However, there are several differences between the landmarks here and the ones for sine and cosine: At Landmarks 1 and 5, the curve crosses the centerline, just like sine, but Landmark 3 is a vertical asymptote, and the actual curve does not touch this asymptote. The tangent curve does not have an amplitude, as such, since it goes all the way to positive and negative infinity in the vertical direction. However, at Landmark 2, the curve is exactly one unit above the centerline, and at Landmark 4 the curve is exactly one unit below the centerline. So in the Eight Blanks method, these locations are going to fill in for our “amplitude”. Important! The period... - Published: 2025-04-18 - Modified: 2026-01-07 - URL: https://andrewjeungtutoring.com/why-you-need-the-eight-blanks-method-to-make-trigonometry-graphs-a-snap-part-1/ - Categories: Math, Trigonometry - Tags: cosine graph, math, sine graph, trigonometry One of the big challenges my tutoring clients often face in Trigonometry class comes when they are asked to graph trigonometric functions with different amplitudes, periods, and shifts. Even when clients understand the basic principles, they often find it hard to keep track of and condense all the information they are given into one single graph. If you are facing these kinds of problems in your Trig class, you are not alone! I will show you a trick that I have dubbed the “Eight Blanks” method, which is a system for organizing all the information about amplitude, period, and shifts so that drawing the actual graph of the trig function will be very easy. I will start with sine and cosine graphs, which are the most common, and progress to graphs of other trig functions in later blog entries. A small disclaimer: While most of my blog entries contain original methods and techniques that I created myself, in this case I cannot take credit for coming up with this method. It was taught to me by a client, and I thought it deserved to be spread around more widely. The base sine and cosine graphs Before I show you the method, let’s take a moment to look at the base parent graph for sine. If you have not yet seen in class what the base graph for sine looks like, you can learn all about it from a website such as Purplemath, Khan Academy, or MathHints. Base sine curve. Generated... - Published: 2025-01-18 - Modified: 2025-01-22 - URL: https://andrewjeungtutoring.com/the-right-way-to-solve-optimization-problems/ - Categories: Math, Algebra, Calculus - Tags: algebra, Calculus, Optimization Your Math class may have introduced you to a type of word problem called an optimization problem, sometimes referred to as a min / max problem. The objective of these is always the same: to find the maximum or minimum possible value of some quantity named in the problem. The weird thing about these problems is that you typically encounter them TWICE during your math career -- once in Algebra class, and then again in Calculus class. The only difference is that once you get to Calculus, you have more advanced math techniques to handle one particular step in the process. And other than that one step, the procedure to handle these problems is exactly the same between the two math classes. Since the process for solving these problems is almost exactly the same, I am going to describe a way to handle them that will apply to your situation equally well whether you are in Algebra or Calculus class. The general process is as follows: Define all the variables that you are going to use -- draw a picture if necessary. Create two statements: an OPTIMIZATION Statement, and a CONSTRAINT Statement. Use the Constraint Statement to eliminate one of the variables in the Optimization Statement so there is only one variable on the right side of the Optimization Statement. Perform the optimization -- either by using the Vertex Formula in Algebra class, or the First Derivative Test in Calculus class. Let’s look at an example to illustrate the method.... - Published: 2025-01-07 - Modified: 2025-01-07 - URL: https://andrewjeungtutoring.com/the-way-you-should-be-solving-stoichiometry-problems-part-2/ - Categories: Chemistry - Tags: dimensional analysis, stoichiometry In the first blog post of this series, I showed you a method to solve stoichiometry problems that helps you keep organized and avoid getting confused. Most of my clients like this approach. However, one of my clients told me, “I think your method makes sense, but my teacher won’t let me do it this way. ” I am not going to address the question of why any technique that consistently gives the right answer should even be a problem for a teacher. Instead, I will point out that it is thankfully not too much trouble to use the process I showed and report the answer in a way that would be acceptable to most teachers. Most Chemistry teachers use a method called dimensional analysis, which looks like a series of multiplied fractions. Each fraction in the series is just a way of expressing one of the arrow conversions that we looked at in Part 1 of this series. So we can think of these fractions as just a way of reporting all the conversions that we used to get from the initial quantity given in the problem all the way to the final answer. Let’s redo one of the stoichiometry problems we worked on in the last post, only this time reporting the answer using dimensional analysis. As a reminder, the first problem we looked at last time was: Fe2O3 (s) + 2 Al (s) → 2 Fe (s) + Al2O3 (s) The above equation refers to the thermite... - Published: 2024-12-01 - Modified: 2026-03-14 - URL: https://andrewjeungtutoring.com/the-way-you-should-be-solving-stoichiometry-problems-part-1/ - Categories: Chemistry - Tags: stoichiometry problems If you are taking Chemistry for the first time, you may encounter a class of problems known as stoichiometry problems. These are problems to calculate the amount of product generated (or reactant required) in a particular chemical reaction, given the quantity of some other product or reactant in the reaction. Most Chemistry teachers teach students to solve these problems using something called dimensional analysis, which looks like a series of multiplied fractions: And, truth be told, this is not a bad way to work through this type of problem. What I have discovered, however, is that some of my tutoring clients find this method confusing in the beginning, as they were not properly shown the strategy for deciding which fractions to use and what order to put them in. I am going to show you a method that will get you the same answer as if you had used dimensional analysis, but in a way which makes the strategy more understandable. When solving a stoichiometry problem, there are only two actions I am allowed to take: I can convert from moles of one substance to any other unit of the same substance (and vice versa) using a conversion factor. The conversion factor I have to use depends on what units I am converting between: If I am converting between moles and grams, the conversion factor is the molar mass. Molar masses are always given in grams / mole. If I am converting between moles and liters of gas at STP... - Published: 2024-11-10 - Modified: 2024-12-17 - URL: https://andrewjeungtutoring.com/solving-kinematics-problems-the-way-your-teacher-did-not-show-you-part-3-projectile-motion/ - Categories: Kinematics, Physics In Part 1 of this blog series, I showed you a way to approach kinematics problems for horizontal motion, and in Part 2, I did the same for vertical motion. Now it is time to put it all together so that we can solve kinematics problems for arbitrary two-dimensional projectile motion problems. You may have learned from your Physics teacher or professor that motion in the horizontal direction and motion in the vertical direction are independent -- that is, what happens with the motion in x has nothing to do with the motion in y, and vice versa. (If you are not familiar with this concept, there are lots of resources online to learn about it, such as OpenStax or The Physics Classroom. ) This implies that I will need one set of the three kinematic equations for the x direction, and a second, separate set of the three kinematic equations for the y direction, like so: xf = xi + vxi∙t + ½∙ax∙t2 (1) vxf = vxi + ax∙t (2) vxf2 = vxi2 + 2∙ax∙(xf - xi) (3) yf = yi + vyi∙t + ½∙ay∙t2 (4) vyf = vyi + ay∙t (5) vyf2 = vyi2 + 2∙ay∙(yf - yi) (6) Note that the first three equations only deal with x, while the last three equations only deal with y. I have also made some changes to some of the variable names: Since there is an initial velocity for x and a separate initial velocity for y, I have made... - Published: 2024-10-10 - Modified: 2026-01-07 - URL: https://andrewjeungtutoring.com/solving-kinematics-problems-the-way-your-teacher-did-not-show-you-part-2-vertical-motion/ - Categories: Kinematics, Physics - Tags: kinematics, physics, solving kinematics problems, vertical kinematics In Part 1 of this series, I showed you a new way of looking at horizontal kinematics problems and of organizing your information so that you could avoid confusion and get the right answer every time. In this post, I am going to demonstrate how you can use the same method to make vertical motion kinematics problems just as easy! There are two main differences between a vertical motion problem and the horizontal motion problems from Part 1: Since we are talking about vertical motion, it makes sense to rewrite the kinematics equations from Part 1 using y instead of x: yf = yi + vi∙t + ½∙a∙t2 (1) vf = vi + a∙t (2) vf2 = vi2 + 2∙a∙(yf - yi) (3) Usually, vertical motion problems involve free fall motion -- this is motion where the only influence on the object is gravity. (If you would like some background on free fall motion, you can read about it at The Physics Classroom. ) The upshot of this is that the acceleration is always a fixed value -- in particular, the value of a will always be 9. 8 m/s2 downward. Some of my tutoring clients ask me if acceleration is always negative, that is, a = -9. 8 m/s2. The answer is: it depends! Acceleration is always 9. 8 m/s2 downward, but whether it is negative depends on whether I choose up or down to be the positive direction. Either choice is legitimate, but a = -9. 8 m/s2... - Published: 2024-09-15 - Modified: 2024-10-10 - URL: https://andrewjeungtutoring.com/solving-kinematics-problems-part-1/ - Categories: Physics, Kinematics - Tags: horizontal kinematics, kinematics, physics, solving kinematics problems If you are starting out in a new Physics class, you may have come across (or will come across) a class of physics problems known as kinematics  problems. These have to do with the relationship between position, velocity, and acceleration, and are often the first heavy calculation problems that students encounter in their study of Physics. If the methods that you learned in class for solving kinematics problems aren’t quite working for you, please know that you are not alone. And I’m here to show you a new way to approach them that your teacher or professor probably has not shown you! I am going to assume that your physics teacher / professor has already introduced you to some form of the kinematic equations. (If not, there are great places for you to learn about these -- The Physics Classroom and Khan Academy are just two examples. ) Here is the form of the kinematic equations that I’ll be using in this post: xf = xi + vi∙t + ½∙a∙t2 (1) vf = vi + a∙t (2) vf2 = vi2 + 2∙a∙(xf - xi) (3) where: xi is the initial position xf is the final position vi is the initial velocity vf is the final velocity a is the constant acceleration t is the time interval between the initial and final events Some teachers might use slightly different notation (for example, v0 for initial velocity and v with no subscript for final velocity) and may even write some of the... ## All FAQ Items