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Order of Difficulty

Teacher/Instructor Eva Holtz
Eva Holtz

Harvard University
Perfect scores on the SAT and 4 SATIIs

Eva is a certified admissions counselor and the founder of PrepPoint, a premier test prep company in the San Francisco Bay Area.

In this episode we're going to talk about a really important concept for the Math section of the SAT, the idea that you should pay attention to the order of difficulty and this is based on the concept that Math questions come in blocks and within those blocks the questions are in order of difficulty and based on this fact there are three strategies that are really worth keeping in mind. First of all easy questions are easy, second of all hard questions are hard and finally you should have a target and really stick with it on the Math section. Let's look at that idea up here and the three strategies based on it in more detail.
So questions first of all come in blocks of two types. The first type is multiple choice, so you might get a cluster of questions that are like the ones you're used to seeing on standardized tests, multiple choice. There is one other kind of block of questions that you'll also see and that's grid-ins which you could also call free response. They look like this and the idea is for each of these ten questions, you're going to have to look at each one and say grid-in your answer. So for instance if the answer is five point two, you would bubble in five period two. If the answer is eleven thirteenths actually that one wouldn't fit. So let's say you got one thirteenth as an answer, you get one divided by one three and bubble that in. So these are the two kinds of blocks you'll encounter and within each one it will go from easy to hard. Now since there are three sections on math here's what you'll see more specifically. One section is going to give you 20 multiple choice questions, strangely enough they give you up to 40 bubbles but you would actually quit at 20. Another section is going to give you 16 multiple choice questions, so even though they're very generous and give you 40, you'd quit right here after 16 and then one final section would mix the multiple choice with the fill ins. So you'd have eight multiple choice and you'd quit after these eight and then with the rest of your time you would have the ten free responses to deal with. Now, like I said within these blocks you're dealing with an order of difficulty, so the first one third of a block is easy, the next one third is medium and the final one third is hard. So let's have a look at what that means. There are going to be three strategies and I mentioned these at the offset; easy questions are easy, hard questions are hard and you're going to want to stick to your target. Let's look at each of these in more detail.
First of all easy questions are easy. Questions appearing in the first third of a question block are easy, so if you're on that section that has 20 multiple choice, the first third which is about seven questions you should expect to be really doable. So what's the implication of that, you should not hurry up and fast-forward through those first seven or so questions, they're the easiest points you will get on the entire SAT. So really give them a shot and even if the question that you see in the first third that gives you trouble, you know inspires you to want to skip it stop read it again and give it a try. A lot of times students will block at a question early on and they'll say really, like have another look and when they do have another look they can't believe they were thinking of skipping it or can't believe they actually skipped it 'cause it was doable. So it's nice when you're in the first third of a block of questions, whether it's the first third of a multiple choice block or the first third of a free response block, you know the question is easy so you know to give it another shot if you at first think it's hard 'cause it's probably not. Let me give you an example of a question that is early and people might be inclined to skip but they definitely shouldn't. So we know we're in the beginning of a section 'cause here we are at number three, number three is pretty close to number one and a lot of people will see a question like this and immediately will say "Oh I'm so bad with exponents I totally don't remember that chapter from algebra two." But first of all you might be able to think through it and second of all, there is a strategy that works really well here and that's plugging in. And it turns out to be the case that if you plugged in the answer choices you'd very quickly find out that B worked, because two to power of three times one is two to the power of three and whether you understand how exponents work or you know how to work a calculator you'd find out that that would give you eight. So don't immediately shut down when you see an early problem that seems hard, chances are it's totally doable if you give the time and the energy and then there is another strategy which is to remember that hard questions are hard.
So questions appearing in the last third of block of questions are hard, so definitely do not be in a hurry to get to these questions. They are way more difficult so you're more likely to get them wrong, they're way more difficult so they'll stress you out and they're way more difficult, so they're going to be more time consuming. All these are bad things and yet you don't get more points for doing the difficult problems. So really take your time on the easy questions and the medium questions, but don't be in a hurry to get to the hard questions 'cause they're not going to treat you well anyway. And when you do get there, assuming you get there, remember that whenever you're attempting a hard question you should expect it to have a trick or require some really challenging calculations. So if you look at a math question that's in the last third you should know it's hard and if you see it and say like "Huh I kind of feel like the answer might be ten," that's probably telling you that you haven't found the trick and you haven't done the hard calculations, so you're getting it wrong. Let's look at an example for what might be a hard question in the last third of the test and might be counter intuitive. So, 'Melinda jogs to school at the rate of 6 miles per hour and she walks home at the rate of 4 miles per hour. What is her average speed in miles per hour?' So in the last third of any block of questions you shouldn't expect a question to be easy and if you just breeze in and say, "Oh I guess it's probably B," you probably got it wrong. So keep in mind that you should be either skipping the hardest questions or understanding why they're hard rather than just thinking you see what's going on when it's not like that. Let me give one more example of this concept, here we are at number fifteen so whether we are in a block of 20 or a block of 16 multiple choice where towards the end and we know it's a hard question, 'A stock's price dropped 20%. From this new price, it then rose 25%. The final price was what percent of the original price?' Now what most people naturally think is let's see, it dropped 20 but then it rose 25, so I guess it ended up 5 percent over where it started, if it's 5 percent over where it started it must be 105% and so that is a very natural response but it's wrong. That's not how percents works and you should know that because if you're at the end of the section like number 15 out 16, or 15 out of 20 a question should not be that easy. So sure enough the answer is not D 105%.
Let's look at our third idea which is that you're going to have to pick a target and stick with it. So you're going to need a target Math score that's slightly higher than you're current Math score. So you should take a practice SAT and see where your Math is at or look at an old SAT for where your Math is at or maybe a PSAT, those will all give you an idea of your Math starting point. And then from there you want to pick a score slightly higher maybe 40, 50 or 60 points higher that will be your new goal. You don't want to pick a goal that's too ambitious right away but work your way up gradually, so somewhere around 50 points higher. Then you're going to take that target, your new goal and determine the target number of questions to answer that corresponds to that goal and you're going to find that in the pacing charts that available in the bonus materials. So go find that and look up the number of questions you should be attempting in each section. This is really important, you may remember from the general introduction to the SAT that we talked about how the average performance on the SAT is about 55 percent right and even if you skip 30 percent of the questions you can still get an above average score. So if you just walk into the Math section expecting that you should attempt a 100 percent of the questions or 95 percent of the questions, that's actually probably going to backfire because you're better served by attempting less remember the hard questions are at the end and they're time consuming and stressful and you're likely to get then wrong and they're not worth any more points, instead focus on the easy to medium, and exactly how many you can focus on, the pacing charts will direct you to. And then stick with that target, practice, really focusing on doing that number of questions and not more and if you start really nailing that target and doing an excellent job with it you can gradually ratchet it up. So if you set a goal that's 50 points higher and you start really nailing, that you can bump it up another 50 points and practice performing at that level. So let's summarize what we've learned about the order of difficulty and the three strategies that emerge from that.
So bottom line it's really important to remember that the Math questions come in order of difficulty with the easy questions towards the beginning, the medium questions in the middle and the hard questions towards the end of each block and a block can be a block of multiple choice or a block of free response questions. So within that block of free response or within that block of multiple choice, easy at the beginning, hard at the end and that useful for three reasons. First of all you can remember that easy questions are easy so you should really give them short and take your time on them and hard questions are hard so you shouldn't just breeze through them but attempt them if you really think you know what's going on and you work carefully and finally you should stick to your target. Some students are meant to try attempt 100 percent of the test 'cause they're going for perfect scores but the vast majority of students are better served by doing a much smaller portion and that portion is determined by the pacing chart again it's in the bonus materials. So if you want to score a 500 on the math for instance, you're only supposed to do the first 11 out 20, the first five out eight here, the first five out 10 here and the first eight out 16 here and of course by the time you're attempting a perfect 800 you're going to have to try a lot more but for the majority of students the amount of math you're supposed to do is a heck of a lot less than 100 percent. So check out the chart and practice for this target, it will have a huge pay off if you stick with it and that's what you need to know about the order of difficulty on Math.