Khan Academy Live: SAT Math

Hello and welcome to Khan Academy live SAT. I'm Eric, I'm an SAT tutor and one of the SAT experts here at Khan Academy, and I'm so excited to be with you today and over the course of the next few weeks as we cover SAT Math, reading, and writing with one class a week. Now before we get into SAT Math, which is our topic for today, I want to give you a quick overview of what's coming up for each of the next few weeks.

Let's take a look. So like I mentioned, today's class is going to cover SAT Math. Next week on Tuesday, May 23rd at 7 PM Eastern, 4 PM Pacific, I'm going to cover SAT writing followed by SAT reading, rather followed by SAT writing. You'll see that all of these classes will happen on Tuesdays at the exact same time. So if you're able to make it today, you'll also be able to make it for the following classes. And you know, if you can't make any of these classes, don't worry! We'll record all of the classes and send out the recordings so that you can watch each of the classes whenever it's most convenient for you.

And so that's a sneak peek at what's coming up over the next few weeks. And for today, let's take a look at what we'll cover within SAT Math. So for today, the first thing I'm going to cover is how to avoid careless mistakes, and the reason I want to cover this is that you know, careless mistakes are a possibility for anyone and on any topic within SAT Math. And so it's a great way to start out with as a foundation.

The next thing I want to cover is function notation, and this is another one of those really common concepts that can show up in a variety of ways in the SAT. And third, I'll cover graph problems, graph and table problems on the SAT. And I'm covering this because not only do graphs and tables show up with SAT Math, but in the evidence-based reading and writing sections, you'll often come across graphs and tables that you'll be asked to interpret and relate back to the author's point.

And then last but not least, I'll wrap up with a Khan Academy badge for attending this class and answer any questions at the end on anything that I covered for the day. And so we've got a lot of topics to cover today, and so let's dive straight in, start doing some math and doing some practice problems.

Ah, so first, how should you avoid careless mistakes in the SAT Math? So what I'll share today is one approach that has really helped me be more organized and methodical and cut down on the number of careless mistakes that I make. And I've found that a lot of other students also find it helpful. So the first step I encourage you to take is to read and understand the question one part at a time.

And so when you break things up and annotate and underline as you go, it'll help you process all of the information and keep you focused on the question. Next, I encourage you to write out the steps you need to take to solve the problem, and so this will prevent you from going one step too far or too short. And so this is really helpful and is almost like a road map for what you want to do first, second, third, and so forth.

Next, you really want to do the math on paper or on the calculator. No matter how confident you might be feeling, I really discourage you from doing this in your head as it really ups the chances that you make a careless mistake. And so put it on paper, type it out in your calculator, and then last but not least, mark down the answer in your test booklet.

And so if you have A, B, C, D like this, you can circle A or you can write out A and block it. And this is all about making sure that once you have the right answer, that answer gets to your bubble sheet. And so four steps that I like to follow: read and understand the question, second write out the steps you need to take, third do the math on paper or on the calculator, and then finally mark down the answer in your test booklet.

And so this process is one that I try and use regardless of what I'm working on, whether it's a quadratic formula or right triangle questions or function notation problems. And so give this process a try. What we'll do now is instead of just walking through the concept, apply this in the context of real SAT Math questions. And so let's take a look at our first one, and I'm going to zoom in here just to make sure that everyone can read it.

So in this first question, I'm going to read the question first. So which of the following expressions is equivalent to the above expression? And so it's a pretty straightforward question, and so I understand that, and then I want to figure out the steps I want to take. And so this is, you've got notice you've got some multiplication and you've got some subtraction, and so I want to do multiply first, and then I want to do the subtraction.

And so this is some good order of operations, and if you want a quick refresher on order of operations, head over to Khan Academy and do a quick search. But for now, I'll just rewrite this here and start doing some of the math: negative 5z minus 2 minus z times 3 minus z. And before I go any further, I want to note that it's important for questions like this to really differentiate your twos and your z's so that you don't get them confused, because if you do, it really does change the answer that you might get.

And so if I go ahead and continue with this problem, negative 5z minus, and then what I'm going to do here is I'm going to foil, to do some foil polynomial multiplication. And so that stands for first, out, inner, last, and so this is foil. And so if I multiply the first terms, the 2 times the 3 is going to be 6, the outer terms, the 2 times the negative z is going to be minus 2z, the inner terms are going to be minus 3z, so the negative z times 3, and then I've got the negative z times negative z, and so that's going to be a positive z squared.

And so I still have this negative sign, but I've done this multiplication, and now I'm just going to combine some like terms and still leave that negative sign out there. So I've got 6 minus 5z plus z squared, and now I can distribute this negative sign. And so if I have this negative 5z, negative times 6 is going to be -6, this negative 1 times this negative 5z is going to be plus 5z, and then this negative times this plus z squared is going to lead to negative z squared.

And now again, I can continue with the second step of subtraction, and I've got this negative 5z and this positive 5z, and so these will cancel out, leaving me with negative 6 minus z squared, which is also the same as negative z squared minus 6. And so then I look over here and I've got negative c z squared minus 6, and so my answer choice is C.

And that last step I do is I will mark down C and make it very clear so there's no chance of making a mistake when I carry it over to the bubble sheet. So that is an example, one example of how you can apply this more organized process within a question that has a few steps and where order matters. Now that question, it may have been straightforward for you; it might have been more challenging, but go ahead and do some practice.

What we'll do next is a slightly different problem with a little bit more information where using a more organized process is even more helpful. So let's take a look.

Okay, so I'm going to zoom out just a little bit here. So let's give this question a read: A distributor ships DVDs to several stores. The shipping boxes contain several DVDs in their cases plus a layer of padding at each end of the boxes. The DVD cases and layers of padding can be arranged neatly inside each box. Each DVD case is 14 millimeters thick, and each layer of padding is 10 millimeters thick, and the length of the interior of the box is 132 millimeters.

If D represents the number of DVDs that this distributor can fit into one box with two layers of padding, which of the following inequalities best models this situation? So I don't know about you, but that was a good bit of information in a lot of sentences, and so what's helpful at this point is to break down the question one part at a time and to pull out the relevant information.

And so we have DVDs that are 14 millimeters thick, and then we have padding, so I'm just going to abbreviate pad as 10 millimeters thick, and then we have the length of the interior of the box, so the box is going to be 132 millimeters thick. And then D is the number of DVDs in one box, and then one box with two layers of padding, so that's important with two layers of padding.

And so now I have all of the information I need from the paragraph, and I can start to process it. And what's even more helpful here is to draw a diagram. And so this goes back to figuring out what steps you need to take and also doing a lot on paper.

And so if I start with this, I know that this box is 132 millimeters thick, and then I've got two layers of padding, and we've got padding at each end of the box, as you see here. And so I've got this padding here, and I've got this padding here, and that's going to be 10 millimeters and 10 millimeters, so that makes sense. And then within this, I've got a number of DVDs being put inside.

And so these are all, you know, DVDs, DVDs, so on and so forth, and each of these is 14 millimeters based on what I have here. And so now with this diagram and these labels, I know that my one side of the inequality is going to be 132 millimeters, since that's the size of the box, and it all has to fit within the box.

And then I have these, the padding that I can work with, and so I've got this, and I've got this, so that feels like something I can start with. And so that is going to be 20. And then within the box, I've got 14 millimeter thick DVDs, and since D represents the number of DVDs, I can write this as 14d plus 20.

So 14 millimeters thick per DVD times the number of DVDs plus 20 for the padding should be less than and equal to 132. And so then that is going to be my final answer B. So in this example, you saw that really breaking down the question into each of its parts, pulling that information out, figuring out how you want to solve the problem, and then drawing a diagram and doing it all on paper was a good way to keep yourself organized as you solve the problem and ensure that you didn't make any mistakes along the way.

Now that's the last careless mistake focus problem, but the same process that we walk through I'm also going to apply in all of the other sample problems that we walk through today since, like I mentioned, it's not just for algebra; it's not just for word problems, it can really help you across the SAT Math test.

And so next up, we're going to look at some function notation. I'm going to do a quick overview and then do some practice problems together.

Okay, let's take a look. So first in this function notation recap, I want to talk about what is a function. So in function notation, a function — and I'll do some abbreviations — takes in an input, does some number crunching, and then creates an output. And so you might have seen this written in your algebra class as f of x or as g of x or h of x.

And in this case, x is going to be your input, and then all of the letters f, g, and h are just different ways of denoting a function. And so an example of a function might be f of x equals x plus 2. A few common ways you might see this on the SAT is within a table format, so you might see something like this.

And so for given values of x, f of x is going to be 2, 3, and 4. Similarly, you can represent this graphically, so x for certain values of x on the x-axis and then f of x on the y-axis. If you have 0, 1, and 2, you have again along the y-axis, one, two, three, four—the same thing, the same function can be represented as this line.

And so for corresponding values of x, you have values of f of x. Now the last thing I want to give a quick overview of is compositions of functions, so F of G of x is another common expression that you'll see on the SAT Math section. This might also be written like this; it all means the same thing though.

And what you want to remember here is that you want to solve this first by solving the inside, so this in this case it would be G of x and then solving for the outside components, which would be F of G of x. So this is a quick overview of function notation that should get you started with SAT Math.

And so what we're going to do next is see what this looks like in the context of real SAT Math questions. And what's coming up are four problems. And so there are two pairs each. So the first pair, the first problem in each pair, I'm going to walk through and work through together.

But if you feel comfortable then in the second question of that pair, go ahead and mute me and go do the problem more independently if you're comfortable, and then check back in to see how I did it. And so you know, only if you're comfortable; otherwise, you can watch me work through it as well. But like I mentioned, four problems total, two pairs each.

And so let's take a look. Okay, so I'll zoom in a little bit more to make sure everyone can see. And so the graphs of the functions f and g are shown to the left. What is the value of f of G of 0, rounded to the nearest whole number? And so I know that, and then I want to look at this graph.

And so I've got F and I've got G and all of their corresponding values. And so the steps I want to take to solve this are to solve for the inside and then the outside. And so I want to solve for G of 0 first, and then I want to solve for f of G of 0.

And like I said, this is kind of my roadmap, and so I've written out the steps, and then it just comes down to following the steps. And so it's easier for me to follow along. So if I look at G of 0, what is the value of G when x is zero? Well, it looks like I'm just right here, and so that y value is zero.

And so what I can do is substitute in that zero, and so then this in the place of G of 0, and so this becomes F of zero. So when x is zero, what is the value of f? It's just going to be right there, five. So you've seen now one example of a function notation question in graphical form.

The next question will be similar to this, and so if you feel like you have a good understanding, go ahead and read the question, read ahead, work ahead, and feel free to mute me if you want to, so you can work independently and then come back here to the livestream after just a minute, and you'll see how I worked through it.

So let's look at the next one, and if you feel comfortable, go ahead and work ahead.

Well, okay, so consider the graphs of the function f and the function G shown above. Which of the following best approximates the value of G of f of three?

Okay, so G of f of three. I've got another composition here. Now how might I solve this? So similar to the last question, and I want to solve for the inner part and then the outer part. And so I've got F over here, and I've got G over here, and so I want to solve for this is G of f of 3.

It just makes it easier; I'm more used to seeing it written like that. So I've got F of 3, and then I've got G of f of 3. And so F of 3: so when x is 3, what is the value of f? Well, it looks like I'm right here, and so I'm going over to 6.

And so then I can substitute in this 6 in the place of f of 3, and this becomes G of six. So when x is 6, I'm now looking at G here. When x is 6, what is the value of F? Well, if I trace our value of G rather, if I trace this up, and I head over here, and that value is going to be 5.

And so again, as a final step, I mark down the right answer so that I don't miss bubble anything to my answer sheet. So you've now seen two graphical examples of function notation questions on the SAT.

Hopefully, you know, if you were working independently on that, you were able to follow along and get to the right answer. But if you want more practice with that kind of question, you can also head to Khan Academy to do that function notation practice.

Now we're going to shift gears a little bit, and the next two problems will be in more of an algebraic context. And again, these two will be, I'll work through the first one, and then for the second one, if you feel comfortable, go ahead and work ahead of me and see if you get to the same answer that I do. Let's take a look.

Oh yes, and ignore the big blue highlighting; I wanted to block out some of the markings there. So let's give this question a read: Let G of x equal 8X minus five. Which of the following is equivalent to G of G of x?

So in this case, there looks like there's going to be some substitution going on, and I'm working now with variables instead of graphs, but I can follow some of the same processes. And so this G of G of x can be simplified to be G of 8X minus 5.

So in place of that G of x, everywhere I see G of x, I'm just substituting this 8X minus 5. And so when I have G of 8X minus 5, I can further simplify this like this: 8 times (8X minus 5) minus 5. So you'll see that this can be rewritten as 8x minus 5, which was G of x just in place of this x, I've substituted this 8X minus 5.

And so now if I solve this, I get 64x minus 40 minus 5, and so I've got 64 x minus 45, and then here I am here, and that is going to be answer choice B. And so in this case, it was just a series of substitutions where I again am working from inside to out and then solving on paper to avoid making any careless mistakes.

So we're going to do one more function notation question, and if you're if you feel pretty comfortable with it, go ahead and work ahead of me. But if you want to just follow along, that is completely fine as well. And then after the function notation, we're going to move on to tables and charts.

So let's take a look here. So let f of x equal x over 1 over X, and let G of x equal 1 over X, assuming X does not equal zero. Which of the following is equivalent to F of g of x?

So F of G of x. So based on the last question, and how that worked, it's probably a safe assumption that there will be some more substitution happening. And so if I solve this in place of this G of x is the first; this is kind of solving from the inside, I can substitute in G of x.

And so this becomes F of 1 over X since this is what G of x equals. And so if F of 1 over X, that means everywhere I see an X, I want to substitute 1 over X and so the algebra, there are a few more variables happening here, but the same principle applies.

And so don't worry too much about that. And so f of x equals is up here: x over 1 over X, and so what that means is I would substitute in place of this x, I'm substituting 1 over X minus 1 over, again I have another X here, and I'm going to substitute in another 1 over X.

Now here again, order of operations matters. And so I've got 1 over X, and I'm going to do this division first before I do the subtraction. And when you're dividing by a fraction, it's really you're multiplying by the reciprocal of that. And so what I've got here is 1 over x minus, and in this case, 1 times x is X, x divided by 1 is X.

1 over x minus X, and that is going to be your final answer there, answer choice D. So the algebra here was a there are a few more variables that you had to work with, but the same principle applied. And so if you have a good understanding of function notation and some of the basics, you can really scale it, no matter regardless of what equation or what format the SAT shows the question as.

So that's it for function notation questions. Now we're going to change now to our final topic of graphs, charts, and tables. And like I mentioned at the start of class, this will not only be relevant for SAT Math but the strategies and the approach that I'm going to walk through will also apply to SAT reading and writing passages that often have tables and charts at the end as well.

So let's take a look at how one way to approach chart, graph, and table questions. Oh, let me zoom out a little bit there. So how should you approach graph and table problems on the SAT Math? Well, it boils down to one sentence, and this is one approach that I found to be really helpful for me and other students, and that is to read the problem and understand the graph or table before you look at the answer choices.

And I want to emphasize that you want to leave those answer choices for the very end after you already have a good understanding of the graph and table. And the reason you do that is that these answer choices can include lots of information that might be overwhelming, or a lot to process; it might be distracting, and it might also lead you down a wrong path.

So it can sometimes be a rabbit hole that can sway your interpretation of the data in front of you. And so the process I encourage you to follow is to read and understand the context from the questions, so that will give you a good kind of background information and then interpret the axes in a graph or the row and column labels in a table.

And so with those axes, you get units, with the labels, you get a lot of information about what the data means to help you interpret. Finally, I encourage you to explain what you see in your own words, and this is a check for understanding.

And so if you're able to explain this to yourself or pretend that you're explaining this to a friend, it's a good check and test that you understand it enough that you could explain it to someone else, and it ensures that you won't be swayed in the wrong direction by any of the answer choices. Then finally, you want to reread the question, and then—and only then—look at the answer choices.

So to recap: read and understand the graph and table, and then look at the answer choices so that you're not swayed or overwhelmed by all of the information. So this might be counterintuitive or might not be exactly how you would have thought about trying these problems before, but we're going to give it a try over the course of some real three SAT practice problems where you get to see it in practice.

And so I encourage you to give it a go if this feels good and comfortable for you; consider practicing it more so that it becomes a habit and you're faster on the real SAT. So let's take a look at a problem.

Okay, I'm going to zoom in to make sure you can read this. And so the graph at the left in the SM plane approximates the average mileage M in miles per gallon that Denise's pickup truck gets when she drives at a speed of S miles per hour. What is the best interpretation of the maximum point on the graph?

So, um, that makes sense. And now I want to shift over to the table and ignore this—so don't pay attention over here. And so if I look at the table, I've got average pickup mileage, and so the title is helpful.

I've got mileage there on my y-axis; I've got mileage in miles per gallon. On the x-axis, I have speed in miles per hour. Okay, so I've got mileage as it varies by speed.

And so that was that step of explaining it in your own words as it varies by speed, and if I interpret the graph then, it looks like as I am going, as Denise is going as she goes faster and faster up until this maximum point here, her mileage is increasing up to a max of 18 miles per gallon, and then it drops off.

So that is that makes sense, and that's kind of my interpretation of the max point. And so let's see which one of these answer choices matches that. So Denise's truck gets a maximum mileage of 18 miles per gallon.

And so I'll erase these X's since they are no longer relevant. Um, so yeah, that matches my interpretation of the graph. And so yeah, her maximum mileage per gallon is this is at 18, and so that works.

Let's take a look at these other answer choices and see what we find. So Denise's truck gets a maximum mileage of 55 miles per gallon. Well, we just said that the maximum mileage is here at 18, and so that 55 is out.

Denise's truck can drive at a maximum speed of 18 miles per hour. Well, no, we know that this x-axis is speed, and we've got 70, and you know, she's still booking it, so that's out.

And then D, Denise's truck can drive at a maximum speed of 55 miles per hour, so that is also not the case since, again, we have this 70 miles per hour. And so we can go ahead and cross that off, and so our final answer is going to be A, and we are good to go.

So in that question, you saw what this process looks like where you read the question, understand it, and then understand the graph before you look at the answer choices and are influenced by them. And so we're going to look at a slightly more complex example in the next question. And again, if you feel comfortable, go ahead and work ahead, mute me, and then compare your answer.

But if you want to follow along, that works as well. So let's take a look at another example of this.

Okay, so let's take a look. The graph at left in the TH plane shows the function used to model height H in feet of the top of a pool toy above the surface of the water T seconds after the toy has been thrown towards the surface. How many seconds after the toy had been thrown did the pool toy resurface?

So how many seconds? Um, okay, so in this example, we can reread that question just to better understand and then hop over here if we still don't understand it to see if the graph helps to clarify. So we've got the TH plane used to model height in feet above the surface of the water T seconds after a toy has been thrown, and the question is, how many seconds after a toy had been thrown did the pool toy resurfaced?

So if I look next, if this is step number one, step number two is to understand the graph. So toy height above the water after T seconds, and so on my axes to understand these, this is height above the surface of the water, and feet, so I've got height over here and then seconds here, and this is time.

And so I'm throwing an object, so I'm throwing, and then based on this, since this is height above the surface of the water—um, POI—so this is above water, above water since this is the height is above and it's positive, and then this is submerged, right? Since I've got these negative feet markers here on the left.

And then if I—that feels like I have a good understanding now of the graph. I know where the toy is above water and below water, and so now I can look back at the question. So how many seconds after the toy had been thrown did the pool toy resurface?

And so resurfacing looks like it's going to be where do you have an idea of where on the graph that might be? So hopefully you've thrown in some answers there.

Well, it seems like it's going to be where it's above this x-axis, right? So that is where—that's almost like if I shade this blue, it almost makes it look like the top of the pool. And so where it's popping back up is going to be right here since this is where the toy is being thrown, this is underwater, and then where it pops back up is where it is now positive and has some positive height, and that looks like it's at 1.1 seconds since it's right between the 1 and 1.2.

And so then my final answer there is going to be C. So in this question, you saw a little bit more of a complex graph, and you know the SAT might have simpler graphs; it might have even more complex graphs. But if you really break down the graph piece by piece, axes by title and all of that, it will help you understand it and ensure that you aren't intimidated or kind of worried and overwhelmed, thinking, oh man, where I have no idea what this means.

If you break it down into its parts, you can build it back up and really strengthen that understanding.

So the final question I'm going to do today is a question on tables. And so tables are a bit like graphs, and so a lot of the principles will apply, but you'll see where there are some differences in this practice question. And again here, if you feel comfortable, go ahead and work ahead; if you want to follow along, go ahead and do that.

Okay, so I'm just going to zoom in here for now, and I'm going to start over here first, the table second, and then these answer choices third.

So an online store's marketing director uses a web-based computer program to tabulate customer responses to a survey, which asks customers whether their priority when buying sneakers was comfort. Okay, that seems important. Comfort, look, or price.

The results are summarized in the table at left. Which of the following claims are supported by the findings in the table?

Okay, so I've got a survey and about shoes and the priorities, so that makes sense. And now I'm going to hop over here to number two, and I've got this sneaker survey, and I'm going to look now at the rows and the column headers to first ground myself.

And so in the rows, I've got gender and age—so male ages 13 to 34, male 35 and over—and so this is exactly like I mentioned: gender and age. So this is some demographic information. And then at the top, these are the priorities that are mentioned over here when buying sneakers: comfort, look, or price—and then I've got my totals.

And my totals. So then this table, if I state my understanding of this is you know, these are customer priorities by gender and age since those are the segments in the rows by gender and age.

So now with that understanding, I can finally go over to number three—the third step there—and look at each of these statements.

So number one: males 35 and older are more likely to purchase sneakers based on price than how the sneaker looks.

And so I want to look at males 35 and over. So males 35 and over are over here, and it says they're more likely to purchase on price. Is price more important than look? So is P greater than L?

And so I've got price and looks, and it does indeed look like price is more important to males ages 35 and over than looks, and so statement number one is going to be true.

Now I'll zoom out a little bit here in case you are here working ahead.

Statement number two: males between 13 and 34 had the highest frequency of responding.

And actually, I'm going to change colors here just to help color code. So males 13 to 34 had the highest frequency of responding to the web-based survey.

So now I'm looking at another demographic: so males age 13 to 34 had the highest frequency. So in this case, highest frequency is the operative word, so I'm not looking just at comfort looking price; I'm looking at their totals. And so that is going to be there on the table.

And now how might I figure out if they had the highest frequency of responding? What number in the table would I be comparing this to? So if you took a moment, I'll be actually comparing it to these numbers here.

And so is 140 greater than 61? Yes. Greater than 89? Yes. Greater than 27? Yes. And so that means males had the most number of responses in this survey, and so statement number two is supported.

Last but not least, we've got statement number three. So the probability that a customer purchases sneakers based on price is approximately 24 percent.

And so in this case, I'm no longer looking at just one segment; I'm looking at all customers. And then I'm looking at price.

And so which elements of the table might I need to see if statement number three is supported? So if you took a moment, you might have said this row here.

And so I want to look at all customers since this is just customers—not male or female or by age—and then I want to look at price here.

And so it looks like this is going to be a key number. So the total number of customers that say price is the most important thing for them.

Now that's one part of the equation, but what about the second part? So how would I know if this is about 24 percent? Well, I would look at the total number of responses.

And so in this case, that's 75 over 3 17, and if you do the math and punch that number in on the calculator, that does get you to right about 24. And so that is also going to be correct and supported by the table, and so then my final answer is going to be D—statements one, two, and three.

Now say you were short on time in this question; there was actually another way you might have done this through a process of elimination. And so say you checked statement number one out first, and you saw that statement number one was correct. Well, then through process of elimination, A does not have number one in it, so you know that's out.

B also does not have one in it, but C and D do, so you'd still—you would have gotten it down to two at least. Then say you were here, and you confirmed that statement number two is also correct. Well then you know that C does not have number two, and so you can also cross that out and by process of elimination get to D as well.

So that's the last practice question that I am going to go through for today on charts and graphs, and so that really is the end of the concepts and the topics for today.

And so I hope that you found some of the work on careless mistakes with SAT Math and function notation and graphs and tables to be helpful. Now to wrap things up in class, I'm going to give out a badge for attending the class and then take some questions.

So let's take a look at the badges and how you'll get that, and then if you have any questions, go ahead and start typing them into the YouTube live chat box, and I'll go ahead and answer as many as I can.

Okay, so for the badge, you're going to get the badge link in the YouTube live chat box and then once you click on the badge, you'll need to log into Khan Academy, and then you'll see a notification in the top right of the screen.

And so keep an eye out for that; it'll pop up and next to this little, like bell icon—that's my best interpretation of a bell—in the top right of your screen. And then like I mentioned, now I'm going to take a minute to go through and answer some questions.

And so the first question we have is around time management strategies on SAT Math. So first thing I would encourage you to do is go to Khan Academy in our tips and strategy sections, and we have two really good articles about time management strategies, not just for SAT Math but also the reading and writing sections.

Now for SAT Math, in particular, what I would encourage you to do is one strategy called the two-pass strategy. And so what you want to do in the first pass is go through and answer the questions—answer as many of the questions as you can, but don't spend too much time on any one question.

And the reason for that is that all of the questions on the SAT on math, reading, and writing—every correct question is worth the same amount of points. So if it's an easy question, it's worth one point. If it's the hardest question you've ever seen, it's still worth one point.

And so investing too much time in a hard question really is not worth it. And so in that first pass, go through and answer as many questions as you can while still being careful and effective. Then in the second pass, you can prioritize your time, and what you want to remember is that in the SAT Math section, the questions go from easy.

So say you have 10 questions or 15 questions in a section, questions one through five or six will be easier than questions 11 through 15. And since these questions are worth all the same amount of points, you can prioritize your time by going through and making sure you get the easy and medium questions absolutely right, since they're all worth the same amount of points, before going on to the hard ones.

And so these are a few things you might do to get better at time management on the SAT Math. The other thing I would suggest is just practicing with a timer at home so that you get a sense for how fast or how slow you need to go.

So let's see—okay, so this was good feedback for the next session: "Can you do more difficult problems? Could you please do some of the hardest passport to advance mathematics questions?" Absolutely. So I can maybe in our next class have a kind of trickier math question to make it a little more challenging, and so we can do that.

And so next question: "Will these questions be on the SAT?" So yes, all of these questions were example problems taken from official SAT practice, taken from official SAT practice and which are all real practice questions from the College Board that will show up on the SAT.

And there are harder ones than these; there are also simpler ones than these, and so everything that you see on official SAT practice—whether through the practice questions, timed mini-sections, or the practice exams—are all official questions that have been on the SAT in the past and that we've built in collaboration with the College Board.

Let's see—we have another one of "When should you start studying for the SAT?" So with that, I would really encourage you to first figure out when you're going to take the SAT. So depending on if you're a junior or senior, and if you're thinking about early admission or early decision, you know, figure out what is the right timing for you to take the SAT.

And then once you know that information, head to official SAT practice and create a personalized practice schedule. There, you'll be able to input your information to say, "I'm taking the SAT in October" or "I'm taking it in August."

And then based on today's date and when you're signed up to take the SAT, we'll then recommend that you study, say, an hour a week, two hours a week, and you can then create that customized schedule to say, "I'm going to study three days a week for an hour a week since I've got some amount of time before the test."

So I can kind of take it easy, or if your exam is in two weeks or three weeks, you might want to step it up. But that practice schedule will really help you decide how many weeks in advance you want to start practicing and how much to study per week. I would say obviously the more time you have and the more leeway you have, the better.

Let's see, so I think we won't be able to finish.

Okay, so this is a great last question: "What if we were running out of time and we know we won't be able to finish? Is it best to guess?" So there is no more guessing penalty on the SAT, and so the answer to that question is yes.

If you get a five-minute warning or realize there's not enough time and you've got, you know, 10 questions left, hopefully that's not the case because you did some time practice and you feel okay. But in that case, absolutely guess!

So I don't know what your—you know, what you want to do—if you want to guess all B's, all C's, or make it random, but you should guess, since there's no penalty for a wrong answer on the SAT.

So I think that's all for SAT Math for today. But for next week, we're going to do SAT reading, and so that class is again on Tuesday. For the next class, I would ask you to think about, you know, when you're on the SAT reading, and you've narrowed down the answer choices to either B or C or C or D down to the final two, how should you pick between those final two answers?

So when it's 50-50, what approach do you use? And so that's going to be one of the things that we'll tackle next week with SAT reading. Again, with some strategies and some real practice problems that you can do.

And so that's it for today for SAT Math, but remember to join us next Tuesday at 7 PM Eastern, 4 PM Pacific for our SAT reading class. I hope this was helpful, and best of luck as you practice for the SAT.