IB Math AA HL Paper 3 - Finding EASY marks!

Indexé : 2026-05-19

[00:00:01]So, welcome back to the channel and this short video on finding easy marks in paper three questions for higher level analysis and approaches. So, this is a short exam that is just two questions with multiple parts for each of those questions totaling 55 marks total, okay?

[00:00:17]So, it's real important to be strategic with your time and part of that is finding things that are quick and easy to do and independent of the previous parts of the problem so you can stay in these questions longer and grab more marks, okay? We're going to look at question one from May 2024 time zone one paper three and look at how we can do that on a probability distributions problem. Let's get right into it. All right, so here we are with the exam and we got a calculator up in case we need it, but we'll scoot on down to question one and we're not going to do every single part of this question.

[00:00:49]We're just going to look for the easy marks here. So, you can pause the video and read this if you want, but it's talking about a computer game where there's boosts and there's non-boosts and it's some kind of tree diagram probability kind of thing, okay? Again, the purpose here is not to solve these problems. I may do a full video on that over the summer, but I want to look for easy marks here, okay?

[00:01:11]So, we've got boosts happening.

[00:01:14]Um It's explaining that in the first few parts, but I want to come down to part C, okay? So, part C, they give us this expression for the sum of an infinite geometric sequence, first term A, common ratio R. We should be familiar with this and I want to look at C part one here, okay? So, look at this instruction. By differentiating both sides of the above equation with respect to R, find an expression for this summation which some people may be scared of, but we don't really need to be and I really want to focus in on how this question is worded. It's telling us exactly what to do. Take a derivative.

[00:01:50]So, there's easy marks sitting right here, even if we haven't understood anything in in previous part of the question, okay? Take a derivative of both sides. Well, the derivative of A with respect to R is just zero.

[00:02:02]The derivative of AR will just be A. The next one will be 2 AR + 3 AR squared, so on and so on and so on.

[00:02:13]And that should equal the derivative of the right side. Well, the right side we can rewrite it as A * 1 - R to the -1 and just apply a chain rule. So, that's -1 * A 1 - R. Drop that power down to -2. Okay? Multiply by the derivative of the inner function. The derivative of 1 - R will be -1. So, this will just simplify to A over 1 - R squared. Okay? And then our left side is A + 2 R + 3 AR squared, so on and so on. So, again, we can kind of see that it's giving us a very clear instruction here on how to approach this part. So, I want to look for things like that in the paper three that I know that I can do or at least stop without any prior knowledge.

[00:03:06]So, this part C has a part two and it show it tells us to show that E to the X is equal to 1 over P and we only get two marks for that. So, let's say that we don't know how to do that, but we come down to the top of the next page where they give us Var X in terms of P. Okay?

[00:03:21]Well, in part D, there's two marks for just finding E to the X and Var X when X is equal to when P is equal to 0.1.

[00:03:30]Okay? So, these might be the easiest two marks on the exam. All you need to do is take these two equations that they fed you for E to the X and Var X and just substitute 0.1 into these guys and you have a calculator to do this number crunching for you. So, that's at least four easy marks. I think we found two for doing those derivatives and two for substituting in here. So, without even reading the question, we got four freebies on this one.

[00:03:58]If we come down a little further, it talks about this second model and this table should be something we're very familiar with for a discrete random variable, okay? We have to show that the probability the first boost occurs on the third action with this probability.

[00:04:12]We're not going to do that. Explain why the number of actions until the boost has to be less than or equal to five.

[00:04:19]Well, if you read this carefully, the probability of being boosted is just going up by 0.2 each time. So, if you do it five times, 0.2 + 0.2 + 0.2 + 0.2 + 0.2 You do it five times, it's equal to one, so it's guaranteed to happen, okay? So, that's another free mark in there if you don't know how to do parts A, B, C, D, or E, Uh we get to the table. We're asked to find the values of M and N, okay? Well, M is the probability of being boosted on the second go. So, if you get boosted on the first, that's a 0.2, meaning a 0.8 for a not boost, okay? Boosted on the second, that's simply going to be 0.8 * 0.2. That's another easy mark, okay?

[00:05:03]You can find N by continuing this tree diagram idea on here. Let me zoom out a little bit so everybody can see that.

[00:05:09]Or, we know that all these probabilities have to add up to one, so we know that N is equal to 1 - 0.2 - M - 0.

[00:05:18]288 - 0.0384.

[00:05:22]And that's another easy mark, okay?

[00:05:24]The expected value of Y equaling this.

[00:05:26]Again, that's just multiplying the top row and the bottom row and adding them all together. That's another easy mark, okay? Variance of Y is a formula given as well. So, sitting here in part G, I would view this as six pretty easy marks that we can get independent of whether we understand the rest of the question, okay? So, these problems have these little sections built in that you can work them independent of knowing what's going on in the rest of the question.

[00:05:56]All right. So, hopefully in this short video in just looking at one paper three question, we've seen how we can find easy marks in there even deep into the question. So, try and apply this idea to all the paper three questions you try and tackle and try and stay in those questions as long as you can. Don't tap out when there's easy marks waiting for you later on.

[00:06:17]Thanks again for watching the channel.

[00:06:18]Please like and subscribe and we'll see you again hopefully after IB exams.