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# Strategies for the Math Section

###### Danielle DeLancey

###### Danielle DeLancey

**Harvard University**

PSAT expert

Danielle is a high scorer on the PSAT, National Merit Scholarship finalist and "Teach for America" corps member. She has masters in Education from Harvard University.

So the math section of the PSAT also causes a lot of anxiety with students. So what I’ve done is, I’ve moved over here to the math lab at Brightstorm. And we’re going to go over a little bit about the math section, what to expect. And then we are going to look at a few strategies that are going to help you out, when you actually sit down to take the PSAT.

First things first, let's take a look at the sections. Remember, you have two sections that are each 25 minutes. And in these sections, you’re going to have two types of questions. First, you’re going to have multiple choice questions. These are going to all look pretty much the same. You’re going to have a question, some may have figures, some won’t. You may have lots of definitions and scary numbers, but for these types of questions you’re always going to have five different answer choices, that you’re then going to use and bubble in on your answer sheet.

The other type of question that you’re going to see, besides multiple choice, are something called Grid-in Questions. Now these are really different than other types of questions on the PSAT. Almost every other question, actually every other question is multiple choice; A through E. So it’s pretty important to know what this look like.

Here is an example. What you’re going to have is you’re going to have a question, but no answer choices. You’re going to be required to solve the answer, and then to fill it in the special grid-in box. So for example, the answer to this question is 5/12. So what you would do, is you would simply write at the top, 5 slash 12. And then bubble in the numbers accordingly. You bubble in 5, the slash, 1 and 2.

So they’re a little bit different, and some people think they’re more complicated. And actually, unlike the other questions multiple choice ones, you don’t get any points off if you get this wrong. So that’s an important thing to remember. Now that we’ve seen what these questions look like, let's take a look at a few strategies that are going to help you to solve the maths questions on the PSAT.

So as I mentioned, we are here in the Brightstorm math lab. And we’re going to go over a couple of strategies that are really going to help you out on the math section on the PSAT. First and foremost, it’s really important to read the question. Put otherwise, it’s really important to know what the question is asking. Let’s take a look at what this will look like on the PSAT.

Here we have a typical question, it’s says; if 50% of x is 20, what is 10% of x? Pretty straight forward right? So let’s go ahead and start solving just like would on the PSAT. So we’re going to set up our equation, and we’re going to say 50% of x is equal to 20. If we divide both sides by 50%, we’re going to get that x is equal to 40. Well we check out our answer choices, we have 4, 16, 20, 40, and 80. X is equal to 40 perfect, we’ve got our answer right? Wrong. We need to actually read the question and see what it’s asking. It’s asking what is 10% of x? So if we take 10% of x, and we know that x is 40, we know that our correct answer isn’t 40. It’s actually 4, answer choice A.

You’re going to see all types of questions and this is the one that most people and most students mess up on. So it’s really important to read the question and to figure out exactly what it’s asking.

On the math section of the PSAT, another strategy that you can use, is choosing you own numbers. Now you can use this in two instances. One; you can use it when you’re solving really complicated formulas, and you’re having to put a lot of steps together. It’s actually faster to choose your own numbers. Also, it’s really effective when you’re solving percent problems. Let’s take a look at what I mean.

Here we have a question that’s going to show up on the PSAT. Not necessarily this question itself, but percent increase always shows up on the PSAT and the SAT. So it’s important to know the strategy and to know what they look like. Here we go. Jillian’s salary increased by 10% from 2002 to 2003, and by 20% from 2003 to 2004. By what percent did her salary increase from 2002 to 2004?

We have a range of percents for our answer choices, anywhere from 12 to 32 percent. Now what we could do, is we could set up some complicated formulas, using 10, using 20%, using x and y and etcetera. But it’s actually a lot easier to choose a number, and then just start with that. And then work through what the percent increases are, if you were doing decreases work through that as well.

When working with percents, it’s really easy just to choose the number 100. So let’s say that from 2002 to 2003 that Jillian’s salary started at $100 which is a pretty low salary. But then it increased by 10%, which means that it would multiple times 1.1. Which means at the end of 2003, her salary would actually be $110. So it’s not asking us to find the increase from 2002 to 2003. It’s asking us to find the increase from 2002 to 2004.

So starting in 2003 to 2004, her salary starts at $110, and then it increase by 20%. So we’re going to multiply times 1.20. Now when we multiply this out, you can use your calculator if you like, we find out that her end salary is $132. So she started with a $100, and then she ended in 2004 with $132. Well knowing that 100 is the base and that it increased by 32, an increase of 32 over the base of a 100 is actually 32%.

Let's take a look at our answer choices and see if this makes sense. Well we’ve got 12%, 15%, 20%, 30%, and 32% which is an answer choice. If you wanted to, you can go back an you could plug it in and check your work. It’s highly recommended on the PSAT and SAT to do stuff like this. Let’s take a look our other strategy.

So another strategy that you can use on the math section of the PSAT, and the SAT and the ACT, is actually using figures and diagrams. Now how do you do this? Well, on the SAT and the PSAT, they actually have a lot of figures. Some of them are to drawn to scale and some are not. If there’s not a note that says, note not drawn to scale. It actually is drawn to scale which means that you can use it to estimate some of your answers.

So let’s take a look at this type of question that you might see. In the figure below, a square is inscribed which, means it’s inside, in a circle with an area of 16Pi. What is the area of the square? Well, you could go through a lot of really complicated, computations, and estimations. Using geometry, and area, and figures, and angles. But you can actually estimate. So let’s take some of the information that we were given, to get to just kind of common number and then we can estimate the answer choices.

So here we go. We have a circle with an area of 16Pi as we know area of a circle is equal to Pi r squared. Since our area is 16Pi, we can set the formula is equal to 16Pi. We eliminate Pi from both sides, we get that our radius squared is equal to 16, or that our radius is equal to +/-4. Since we’re dealing with figures and we know that it's +4.

So given that our radius is 4, we can go ahead and we can estimate using our figure. So say that for example we’ve got 4 is from here to here. And the area of the square is side to side. So if this is 4, this a little bit more than 4, let’s say it’s like 5. So we can say that this is a little bit more than 5. 5 times 5 is 25. So we’re going to estimate that the area of our square is approximately 25. So let's take a look at our answer questions choices. Right away we see that 96 is way out there. We learned that in another episode. You can pretty much eliminate outliners right off the bat, let's go ahead and get rid of that.

Now let’s take a look. We’ve got 4, 8, 16 and 32. Well 4 and 8 are nowhere near 25, so we can eliminate those right off the bat as well. Let’s say 16 verses 25 and 32 verses 25, we know it’s a little bit more than 5. 32 is a little bit more 25. So I’m going to a head and guess that my answer is 32, answer choice D. Well it’s not precise, but it is the correct answer. If you went through and solve it. You would have to find the area of right triangle, using geometric properties etcetera. It’s just not worth it when you’re able to eyeball it, and use your diagrams and your figures but only if they’re drawn to scale. Do go ahead eliminate some answer choices, and then choose the correct one. It’s a really helpful strategy for questions involving figures and diagrams.

One of the other strategies that you can use on the math section, of the PSAT, and the SAT, and the ACT and other standardized test, is basically plugging in answers choices. Now what do I mean when I say this? There are two ways you can do this. One, you can actually if the question calls for it, plug in answer choices into your question. You know sometimes up in your question you’ll have variables. What you can also do, is you can plug in numbers into your answer choices. It works really well, when you have answer choices with multiple variables.

Let’s take a look at what this will look like. If x is an even number, and y is an odd number, which of the following must be even? Well, let’s pick a couple of numbers and plug them in. Let’s say that x is 2 and that y is 1. No need to make really difficult numbers, and let’s plug them in and see what happens. X times y is 2 plus 1, is that even? No. It's got to be crossed off. X times y, 2 times 1 minus 1 is that even? No. X divided by y, 2 divided by 1, is that even? Yes it’s 2, let’s keep that for now. X plus y, 2 plus 1, 3 definitely odd. Last one, x times y 2 times 1, that works too. Sometimes when you choose 1 as an answer choice, it gets a little funky. So let's choice another couple of numbers plug them back in to our remaining answer choices, and see which one works.

So this time round, we’re going to say that x is equal to 4 and y is equal to 3. Let’s go ahead and plug it in into our answer choice again. 4 divided by 3 is that even? No. What is that? It's fraction, it doesn’t even matter, definitely not even. 4 times 3 is equal to 12, does E still work? It does, it’s even. So we know that our answer is E.

Now it'll be really complicated if you went through and tried to set up formulas, and equations, and solve and it could get really complicated. So to save time it’s really important to plug in numbers and to answer choices that have variables.

Similarly, if you have answer choice that have numbers and questionable variables, plug these answer choice into the question to see what works.

So there you have it. You have four strategies that are going to work for the math section of the PSAT depending what question type you are on. It’s really important not only to brush up on your content. For example if you’re weak in algebra ,weak or in geometry, pull those textbooks out. But you could know all the content you want. And if you don’t have these sneaky strategies, you’re not going to get as many points as you could if you do know them and practice them a lot. So good luck.

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###### Danielle DeLancey

Harvard University

PSAT expert

Danielle is a high scorer on the PSAT, National Merit Scholarship finalist and "Teach for America" corps member. She has masters in Education from Harvard University.

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