How to Tell What Will Be on Your College Math Exam
This lesson discusses one of the most common questions asked by college students:
How do I know what will be on my algebra, calculus, physics, or STEM exam?
The lesson explains how textbooks, lectures, examples, homework problems, and professor expectations work together to determine the material most likely to appear on examinations. :contentReference[oaicite:0]{index=0}
The Purpose of the Textbook
According to the lesson, the textbook is the primary source of information for the course.
Students are encouraged to:
- Read the assigned sections before lecture.
- Work through the examples.
- Review definitions and theorems.
- Attempt the practice problems.
- Use lecture to clarify confusion.
The lecture is presented as a supplement to the reading rather than a replacement for the reading itself. :contentReference[oaicite:1]{index=1}
The textbook introduces the material. The lecture reinforces the material.
Why Example Problems Matter
One of the central themes of the lesson is that example problems are often the strongest indicators of future exam questions.
The reasoning is straightforward:
- The examples define the methods being taught.
- The examples illustrate the intended procedures.
- The examples demonstrate the chapter objectives.
- The examples are already verified and explained.
Because of this, students should carefully study every example problem provided in the assigned reading. :contentReference[oaicite:2]{index=2}
Using the First Exam as a Guide
The lesson recommends carefully analyzing the first examination in a course.
Students should ask:
- Which sections appeared most frequently?
- Which example problems resembled the exam?
- Which homework problems were emphasized?
- What level of difficulty was expected?
The answers often help predict the structure of future examinations throughout the semester. :contentReference[oaicite:3]{index=3}
Sister Problems
The lesson introduces the idea of what are called “sister problems.”
These are problems that:
- Use nearly identical procedures.
- Have similar structures.
- Require the same techniques.
- Differ only by numbers or notation.
If a professor solves one version during lecture, students should pay close attention to related problems appearing elsewhere in the chapter because similar variations often appear on assessments. :contentReference[oaicite:4]{index=4}
When two problems require the same process, mastering one often prepares you for the other.
Definitions and Theorems
Students are reminded that exam questions are not limited to computations.
Many instructors also test:
- Definitions.
- Theorems.
- Notation.
- Vocabulary.
- Conceptual understanding.
Reading the chapter carefully helps students identify the concepts that support the computational work. :contentReference[oaicite:5]{index=5}
The Importance of Verification
The lesson emphasizes that mathematics is not simply about obtaining an answer.
Students should learn how to:
- Verify solutions.
- Check assumptions.
- Confirm procedures.
- Validate conclusions.
A correct answer without understanding may not demonstrate mastery of the material. :contentReference[oaicite:6]{index=6}
Using the Assigned Textbook
The lesson strongly encourages students to focus on the textbook assigned for the course.
Different textbooks may:
- Use different notation.
- Present different solution methods.
- Introduce concepts in a different order.
- Emphasize different examples.
Because examinations are typically aligned with the assigned text, students benefit most from mastering the material presented in that specific book. :contentReference[oaicite:7]{index=7}
How Professors Build Exams
The lesson explains that many examinations are built around:
- Chapter objectives.
- Example problems.
- Lecture demonstrations.
- Homework assignments.
- Core definitions and theorems.
For this reason, students should pay close attention to the problems that repeatedly appear throughout the course materials. :contentReference[oaicite:8]{index=8}
Preparing for STEM Exams
A recommended study strategy includes:
- Read the chapter before lecture.
- Work every example problem.
- Review definitions and theorems.
- Attend lecture and ask questions.
- Practice related homework problems.
- Review previous examinations.
- Verify all solutions.
This approach helps students identify the material most likely to be emphasized during exams. :contentReference[oaicite:9]{index=9}
Final Thoughts
Understanding what appears on an examination is often less mysterious than students believe. By carefully studying the assigned textbook, working through example problems, reviewing lecture material, and analyzing previous assessments, students can make informed predictions about the topics, techniques, and problem types most likely to appear on future math and physics exams. :contentReference[oaicite:10]{index=10}
Original Transcript
All righty, kids. I’m going through and doing some uh some textbook reviewing here and uh to start my playlists for all the different courses. And I’m I’m just going to show you guys how to tell what’s going to be on an algebra text. What’s what’s going to be on an algebra exam? So, how to know what’s going to be on your college algebra exam? For the most part, it’s pretty straightforward. The the professors expect you to be reading these textbooks thoroughly and working all the example questions from the book way before the lectures on them. They have the lecture to go back over the chapter so that you have already gone over it on your own and then you come to the lecture and you have already worked all the example questions in the book and you come to the lecture to the professor. the professor goes back through the chapter and then when they get to certain things like the domain and range of the set of real numbers blah blah blah this and that or or something or they’re working this problem you’re like oh professor in that section I had an issue understanding the shift thing with the negative or something and they’re like excellent let me explain that to you that’s the purpose of the lecture you’re given this book so that you can go through it you’re not you’re not in college to have somebody teach you anything okay you’re in college to learn how to be a self-reliant self-sufficient professional The professor is already an expert at these fields. You’re supposed to go through the books and type up professional documents in Microsoft Word. Not freaking latex type set, not by hand. In Microsoft Word, you’re be training to become a professional. You got five years in college. You need five years of experience using all these tools. You should be doing your homework with these tools. You’re giving it you are given a book in print. You are given Microsoft Office free of charge as a college student. So, you can type in print. It is very easy to type mathematical equations in Microsoft Word. Okay, very easy to do it. And you need to have five years of experience using Microsoft Office tools. So, you might as well do your homework with it. Okay. But if you want to know what’s going to be on your exams for your um algebra test, so how to how to tell what’s going to be on your algebra exam, look these questions here. Nine out of 10 times the questions that they put on the exam are the exact same questions word for word from the examples in the reading. Why? Because this is a subject. This is Sullivan’s Sullivan algebra. This is its own subject. Algebra is a topic. Sullivan algebra is a subject. You are there to study this subject. Okay? They can’t take questions from other books. If they are doing that, they are not doing their job correctly. That this subject has its own rules and definitions and theorems. You can’t mix and match things. And you think getting the answer right is getting the same answer means you’re doing it right. You’re not. It’s not about the answer. It’s about the solution. Besides, how do you even know the answer is right? You’re like, well, it matches a marking on a piece of paper. It’s got to be right. How do you know? You’re not. A scientist does not just trust a marking on a paper. They know how to verify their answer is correct. That’s what we do in Plym Academy. In these books here that I write, the full circle of math, I show you how to verify your answer is correct. So, so, so pay attention, okay? Nine out of 10 times the questions they give you on exams are literally the exact same question from the reading word for word, number for number. One, they can’t take questions from other sources. If they are, they’re doing it wrong. Two, when they tell you when you come to class and you when you come to office hours of class and complain, they never showed us this. They go, “Well, go to page 324, example two. It’s the same question word for word.” Had you been reading the textbook as assigned? Then you would have known that. And you’re like, “Nobody told me I had to read the book. Nobody told me I had to go to lecture.” Yeah, dude. You’re you’re in college to learn how to be a self-sufficient individual. Having a babysitter is not what you’re in college to do. All right? So, you know, grow up immediately. All right. The other way to tell what’s going to be on the exams. So basically, if your exam is chapters three and four and you want to be prepared for the exam, what you need to do is be able to answer all these example questions, okay? Not the super hard, elaborate, longass ones, but the ones that are likely to be on the exams. It’s pretty easy to tell which ones are going to be on the exams, especially if you already have had an exam. You can look at the first exam and be like, “Oh yeah, he took these questions from this part and this section and this chapter using this that.” So you’ll be able to predict where the questions come from for the next exam. The other thing that you need to pay attention to for math exams is the questions in the back of the book. Do you see how this image here looks similar to this image here? Well, if they do this question on the on if they do this question in uh lecture or problem solving sessions, then this question is going to be on the test. I call them sister problems. So, whatever question that you see the sister problem in the back, if they did one of these during lecture, the other one is likely to be on the exam. Uh, the other thing to pay attention to is in the question banks in the back of the books. There are Easter egg formulas. You might need these Easter egg formulas to answer questions on the test. They’re more they’re more evident or prominent in like calculusbased books, but they’re they’re also here in um they are also here in the in the basic algebra books and stuff, but uh these Easter eggs, there’s little formulas in the back of the book that you might have to pay attention to uh to um in order to answer these questions correctly. Some most of the time that’s what professors do. They don’t usually take questions from like like right here like the chapter test. They don’t usually take questions from those because guess what they have to do? They have to write the solutions for those things themselves. And the teacher solution manual does not is not very useful. Okay? It’s not really useful at all. They’re going to have to rewrite the solutions for all this stuff themselves. Why why would they want to do that? Why would they make their life more difficult when the examples that are in the reading already have the solutions done and have been verified and then they can derail the argument with you and say, “Well, if you read the book, kid, you would have no issues. You keep we keep telling you over and over, you can’t leave the textbook.” And you’re like, “So I can go to Khan Academy.” Like, no, you can’t leave the textbook so I can use AI. No, you can’t leave the textbook so I can use a private tutor. No. So I can copy my classmates work? No. Oh, so I can use a different textbook then? No, you can use this book. And you’re like, I don’t understand. That doesn’t make any sense. I I’m paying you thousands of dollars to guide me through this book. Why wouldn’t I be able to use a different book? It doesn’t make any sense to me. Why am I paying you thousands of dollars to guide me through this book when I can use AI to teach me nothing? To have Khan Academy, which plagiarized a bunch of other books, allow me to plagiarize their plagiarized work? Think, kid. Okay, but this is how you can tell what’s going to be on your math exams in college. Uh this I said algebra at the beginning. It’s the same for all of them. How how you can tell what’s going to be on your math or physics exams. This is this is how that is done. Okay, it’s the example questions. Nine out of 10 times. There’s always going to be a case where this is not true. You need to figure out if it is true by looking at your first exam, talking to your professor, asking them if if the questions are likely to come from the book directly because they’ll say, “Well, they shouldn’t lie to you. They should say, well, yeah, they’d have to come from that book because that’s the subject we’re studying. We’re not studying another book. We’re studying this book. So, the questions would have to come from this book.” If they make up a question, they would have to bring the question into the book, prove everything for the solution to that within the book, then prove the answer does satisfy the original question in order to use it in this book. But it’s not in this book. All the questions in this book were solved with this method of this book. Yes, some questions can be solved with other books, but then you have different solutions from that book. Just because you get the same answer doesn’t mean that you’re doing it correctly. [snorts] Anyways, this is how you’ll this is how you can tell what’s on your math exams in college. Have a nice