Effective Strategies for SAT Math Success

I've gotten perfect 800 scores on back-to-back SAT math sections, and in this video, I show you 54 practical tips and strategies I've curated for the digital SAT math section, each demonstrated on an actual question from digital SAT practice test one. For more digital SAT prep content, make sure to like this video and subscribe to my channel. And with that being said, let's dive into the video. Here's how to answer this SAT math question in under 20 seconds. The question is, what is 10% of 470? we can take 10% and express it as a decimal of 0.1 and then multiply it by 470. And that'll give us our answer of 47. So our answer will be answer choice B. Here's a trick that'll save you time on the SAT math section. Question two says which equation has the same solution as the given equation. If we take a quick glance at our answer choices, we see we have four x in every single one of our answer choices, which means if we look at our equation on top, we have four x plus six equals 18. All we have to do is subtract six from both sides, and we're left with four x is equal to 12. Now, we don't actually have to solve for X because we have 4X in every answer choice. So our answer is answer choice C. Here's a tip to be more efficient on the SAT math section. If you glance at the answer choices of question three, you'll see that all of them are going to be inequalities. So as you read through this word problem, you want to go ahead and write out the inequality to save you time. So if we go ahead and start from the beginning, the total cost in dollars to rent a surfboard consists of a $25 service fee. So we can go ahead and write down that $25. And that's a one-time charge because it's a service fee and a $10 per hour rental fee. So we're going to have plus 10 H. We'll use H to represent hours. A person rents a surfboard for T hours. So we have to replace H with T then and intends to spend a maximum of $75 to rent the surfboard. So they are going to spend a maximum of $75. So this total has to be less than or equal to 75. We find which inequality represents the situation. And as we can see, that is going to be answer choice D. So D would be our answer there. Here's how to solve this SAT math question in less than 30 seconds. The function G is defined by G of X is equal to X squared plus nine for which value of X is G of X equal to 25. Well, since we have g of x equaling 25, we go ahead and plug that in for g of x. Now we have 25 is equal to x squared plus 9. Now we're going to subtract 9 from each side so we can start isolating that x squared value. Now we have 16 is equal to x squared. To isolate x, we need to take the square root of x squared and the square root of 16. The square root of 16 is 4, which means 4 will equal x and our answer will be a. Here's how to solve this probability question on the SAT. Question 5 states each face of a fair 14-sided die is labeled with the number 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a two? Well, only one of the 14 faces has a two on it. So the answer has to be one over 14, which is answer choice A. Here's a trick for converting units on the SAT. Question six states a printer produces posters at a constant rate of 42 posters per minute. At what rate in posters per hour does the printer produce posters? So what we're going to do here is we're going to convert from 42 posters per minute, which I'll represent as P per M, and we have to convert that into posters per hour. So what we're going to do is we're going to multiply by 60 minutes per hour. So as you can see, our minutes, which I'm representing as m, are going to cancel here, and we'll be left with posters p per hour h. So 42 times 60 is going to equal 2,520 posters per hour. So our answer is 2,520. Here's how to solve this SAT math question in under 40 seconds. Question 7 states the function f is defined by the equation f of x equals 7x plus 2. What is the value of f of x when x equals 4? Well, all we have to do is plug in 4 for x. So we do 7 times 4 plus 2. 7 times 4 is going to be 28. 28 plus 2 will be 30. 30 is going to equal our value of f of x and be our answer. Here's how to solve this SAT math question in under 60 seconds. Question 8 states a teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents the situation where x represents the number of 1 point questions and y represents the number of 3 point questions? We know our total number of points is going to be 70, so it's going to have to equal out to 70. Now, for every... x question we get right, which is every one point question, we get one point. So we have x plus now our three point questions, which are represented as y. So x plus three y must equal 70 and our answer will be d. Here's how to answer this similar triangles question on the SAT. Question nine states, right triangles L, M, N, and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has a measure of 53 degrees. What is the measure of angle Q? So what we see here is since we have similar triangles where L and M correspond to P and Q, we also know that. n must correspond to r. Okay, we see that angle M has a measure of 53 degrees. Okay, and then we're asked for the measure of angle Q, we see that M corresponds to angle Q since they're similar triangles. So they're going to have the same angle measure. Okay, so that 53 degrees that we are given for the angle M must also be the angle measure of angle Q. So our answer will be B. Here's a trick for the SAT math section. Question 10 states the solution to the given system of equations is xy. What is the value of x? Whenever you see stacked equations like this on the SAT, It's usually a sign that you're going to be able to add, subtract, or substitute one of the equations with the other in order to get your answer faster. In this case, we're asked for the value of x and we're given that y is equal to negative 3x. So what we're going to do is we're going to substitute in that negative 3x for y in this below equation. So now what we're going to have is we're going to have 4x plus y when we know y is negative 3x. So 4x minus 3x is equal to 15. Now we know that 4x minus 3x is x, which means that x must equal 15 and our answer is answer choice C. Here's how to answer scatterplot questions on the new digital SAT. Question 11 states, which of the following equations is the most appropriate linear model for the data shown in the scatterplot? What you're going to want to do here, since we're looking for a linear model to represent the scatterplot, is go ahead and draw a line just to give you a rough reference. As you can see, we have a negative slope, which means that answer choices C and D cannot be true since they have positive slopes. The next thing we'll look at is the differences between answer choices A and B, which are their y-intercept. We see that we have a positive y-intercept of right around 10. So if we look at answer choice A, it would have a y-intercept of negative 10, which cannot be correct and our answer choice must be answer choice B. Here's how to answer this polynomials question on the SAT. Question 12 states the graph of y equals f of x is shown where the function f is defined by f of x equals ax cubed plus bx squared plus cx plus d, where a, b, c, and d are constants. For how many values of x does f of x equal 0? Well, all we have to do is find where f of x equals 0 and count the number of points. We see we have one here. One here and one here. So our answer will be three, which is answer choice C. Here's a tip to be more efficient on the SAT math section. If you see a word problem like this, you're gonna wanna start writing out the equation as you read it. So watch how I do this problem. Question 13 states, Vivian bought party hats and cupcakes for $71. So 71 is gonna be the total amount she spends. Each package of party hats costs $3. So $3 times our number of packages of party hats, which I'll represent as P. And each cupcake costs $1. So you could make it plus one C, but since... a one in front of C is redundant. We'll just get rid of the one. So now we have our equation. Well, if she bought 10 packages of party hats, that means 10 is equal to P. So we can go ahead and substitute that in. So now I'll go ahead and erase that P and I can put in 10 since we know that's the amount that she had bought of those party hats. We have three times 10. We know that's going to equal 30. So we're going to have 71 is equal to 30 plus C. Now we want to isolate C to solve for it. To do that, we're going to subtract 30 from each side. 71 minus 30 is going to leave us with 41. So now we have 41 is equal to C and our answer will be 41. Here's an example of when you should use your graphing calculator on the SAT math section. If you take a look at question 14, it states, what is one of the solutions to the given equation? Now, you could solve this without a graphing calculator by factoring, but it's really a smarter choice just to go ahead and use the graphing calculator. Now, as you can see here, this is Desmos, and you're going to have essentially a version of Desmos on the Bluebook SAT, on the new digital SAT. Now, what I recommend doing is you just go ahead and put in this equation into the graphing calculator. Now, keep in mind, you want to substitute out Z or any other variable they put in there for X. And once you do that, you see that you have your equation graphed out. And then since it's set equal to zero, all you have to do is find where it equals zero. You can see that that's at negative 12 and at two. So you have two potential answers here. One is negative 12, and that would be correct. And the other answer is two, and that would also be correct. So you could put in one of either of those answers. But I want to quickly touch on why I think it's smart to use the graphing calculator here instead of actually factor this out yourself. If you're factoring this out yourself, the chances of you making a mistake go up versus if you use a graphing calculator. Now keep in mind, using the graphing calculator that's built into the digital SAT only takes a couple of seconds, right? And factoring may save you a couple of seconds, but in my opinion, it's not worth the risk of you actually making a mistake doing multiplication or doing addition or doing subtraction, anything along those lines. In my opinion, with questions like this, it's just much smarter to go ahead and use the graphing calculator. You avoid making many, many, many errors that can be made when factoring. So with questions like these, just use the graphing calculator. Here's how to solve this SAT math question about exponential growth. Question 15 states that bacteria are growing a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every three hours. That's important. How many cells per milliliter will there be 15 hours after the initial observation? So our starting amount is 300,000. So let's go ahead and write that down. Now we're going to be using the equation for exponential growth. Keep in mind, we are doubling every three hours. Since we're doubling, a two is what's going to go in these parentheses. Now... we are going to raise it to the power of 15 over three. And I'm going to explain why here, and it's very important you pay attention because this equation is commonly tested on the SAT math section. So the reason we are raising it to the power of 15 over three, and keep in mind, we're raising this two to the power of 15 over three is because we are doubling every three hours. Since we're doubling every three hours, that gives us that three and that denominator of that exponent. Now we're asked how many there's going to be after 15 hours, which is why we have that 15 in the numerator. Okay. So now, as you can see, we have our equation, we put this in our calculator and we get our answer of D. 9.6 million. Here's how to solve this question about simplifying exponents on the SAT. Question 16 states, which expression is equivalent to 6x to the power of 8 times y squared plus 12x squared y squared? What you're going to do here is you're going to look for common factors that you can pull out of each of these. So as we can see, we have y squared in both of them. We also have 6 and 12, which we can pull out a 6 from 12. We also have x to the power of 8 and x squared. Okay, so the way that we're going to do this is we're going to pull 6 out, we're going to pull x squared out, and we're going to pull y squared out. Now, we still have to multiply, get this equation still. Okay. So what do we have to multiply by here? Well, we're going to need X to the power of six still to get to that X to the power of eight. Keep in mind that this X squared times this X to the six is what's going to give us X to the power of eight. We're still going to have that Y square. We have that six out front. So now we have our first term. Now we know that we also have to have another term because we have six here. But we have 12 up here. Okay, so to get to that 12 there, we're gonna have to add two. And we still have x squared and y squared here as well. So we see that we're ultimately gonna end up with 6x squared y squared times x to the power of 6 plus 2, which we see is gonna be answer choice C. Here's how to better interpret word problems on the SAT math section. Question 17 states a neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x plus 35y is equal to 3934 represents this situation. Which of the following is the best interpretation of x in this context? Well, what we have to look at here is what does this total represent? Well, it represents the total amount of trees. Now, we also have to look at what gets us to that total. Okay, we have 35 times y. Well, 35 is our area, but we have to multiply by the number of trees per unit of area. Now, keep in mind, we're asked to solve for x here. So we're looking at the amount of trees per hectare in the park. Okay, so X must be the average number of trees per hectare in the park, which is answer choice A. Here's a tip to solve SAT math questions when your answer choices aren't in point-slope form. If we take a look at this question, it says the graph shows the relationship between the number of shares of stock from company A, which is represented as X, and the number of shares of stock from company B, which is represented as Y, that Simone can purchase. Which equation could represent this relationship? And we see we have company B and company A, and obviously we have the correct correspondence of X to A and Y to B, so that's good to know. Now, Now in this case, I see that A and C both are in point slope form. So I'm gonna go ahead and just check if they're correct since that's the easiest thing to do. So here I see that both of these have y-intercepts that are not correct. I have 12 and 8, but the actual y-intercept is 40. So I can go ahead and get rid of A and I can get rid of C. Now you could go ahead and convert B and D into point slope form and there's not an issue with that, but it does take longer than what I'm about to show you. Instead what you could do is you could know that the slope, which we'll represent as M, is equal to negative A over B when we have our equation set up like this. where we have a coefficient in front of x plus a coefficient in front of y equals some constant. Now, the next thing I'm going to do is I'm going to check what my slopes are for each one. Okay, so for answer choice B here, we see that our slope would be negative 8 since 8 is our a value over 12. Okay, and then for our d value, we see that we would have negative 12 over 8. Now, I'm going to see what my actual slope is. Okay, my actual slope is I go down 40 and I go over 60. So that'd be negative 40 over 60, which we know we can simplify to negative 4 over 6. Okay, negative 4 over 6 is equal to negative 8 over 12 when we simplify negative 8 over 12. So our answer there is going to be answer choice B. Here's how to solve this SAT math question in under 60 seconds. Question 19 states circle A has a radius of 3n and circle B has a radius of 129n where n is a positive constant. The area of circle B is how many times the area of circle A? Well, let's start by finding the area of circle B then. So circle B has a radius of 129n. Now keep in mind the formula for the area of a circle is pi r squared. We know our radius is 129. and all of that is going to get squared. Now we have to divide that then by the area of circle A to find out how many times bigger it is. So we know that the radius of circle A is 3n squared. Now keep in mind that n here is going to end up being squared in both the top and the bottom. Okay, so first thing, it's very obvious that those pi's cancels most people will get that. Now the next thing we need to understand is that 129 squared times n squared is equal to what we have here of 129 times n all to the power of 2. Now on the bottom then we end up with 3 squared times n squared as well and we see that those n squareds are going to cancel. Okay that's really important to know because now the question becomes very easy we can just plug it into our calculator and when we plug into our calculator 129 squared divided by 3 squared which you can also just know is 9 then you're going to end up with answer choice d. Here's how to avoid this tricky question on the SAT. Question 20 states the frequency table summarizes the 57 data values in a data set. What is the maximum data value in the data set? Now most people when they look at this might think that the answer is 11 because it has the highest frequency. And they think that that's the maximum since it's the highest value in the frequency section of the table, but that's incorrect. The actual answer here is 14. Now, the reason why is because they're asking for the maximum data value. They're not asking for the highest frequency value. Okay. That would be 11 because the data value there is 11, but they are asking for the maximum data value, which means our answer has to be 14. Here's how to answer this question about circles on the SAT. Question 21 says a circle in the XY plane is a diameter with end points 2, 4 and 2, 14. An equation of the circle is X minus 2 squared plus Y minus 9 squared equals R squared, where R is a positive constant. What is the value of R? Okay. What you need to understand here is that this is a question dealing with the circle equation. So it's important you know the circle equation going into the SAT because it is tested fairly often. Now, as far as how you answer this, it's actually pretty easy as long as you can recognize this simple trick. When you're given a circle question, you're given end points. Oftentimes, There are endpoints that are specifically designed to make the question easier. So you want to look at them pretty closely. And here what we notice is that we have an X coordinate that is the same in both of these. Sometimes it'll be a Y coordinate that is the same in both, but either way, try to find if you can see either the X coordinates are the same or the Y coordinates are the same because it'll make the question a lot easier. In this case, since our X coordinates are the same, we're going to look at how far apart are our Y coordinates. And we see that from 4 to 14 is a difference of 10. Now keep in mind that the circle has a diameter with these endpoints. Okay. So if the circles like this, and this is our diameter between our points and it's 10, well that means our radius must be 5 because our diameter is double our radius. So the value of r, and keep in mind that this is the equation of a circle where r is representing our radius and we're asked for the value of r, not r squared, the value of r then must be 5. So our answer is 5. Here's how to solve questions that ask you to convert from radians to degrees on the SAT. Question 22 states the measure of angle r is 2 pi over 3 radians. The measure of angle t is 5 pi over 12 radians greater than the measure of angle r. What is the measure of angle t in degrees? So we have to start by finding the measure of angle t in radians, and then after that we'll convert to degrees. So we know that the angle r is 2 pi over 3 radians. Now we have to add on to that the 5 pi over 12 radians, since 5 pi over 12 is the amount of radians that we are greater than the angle measure of r to get to angle t. From here we need to have a common denominator in order to add these fractions. So to do that, I'm just going to go, I see three and 12. I'm just going to go ahead and make it 12. I know that you could sort of simplify it, but I'm not going to. So I'm going to multiply three by four to get to 12 and I'm going to multiply with two by four, which will give me eight. So now I have eight pi over 12. Now I can go and add these together and I'm going to see that that's going to get me 13 pi over 12. Now from here, I need to go ahead and convert 13 pi over 12 in two degrees. Now this is really easy, but some people can get tripped up on it if they don't know this trick. In order to convert from radians to degrees, you need to multiply by 180 degrees over pi radians. Now keep in mind that we have radians as our units in here with this 13 pi over 12. So to get rid of those radians, we have to have radians in the denominator right here, which is why we have pi on the bottom. Okay. So when we go ahead and do this, we're going to end up getting rid of our pi on each one. Sorry, I did not mean to erase that. Let me go and put that back. Okay. We're going to end up canceling out those pies and we're going to end up with 13 times 180 over 12, which we're going to go ahead and put into our calculator. And once we do that, we're going to see that that turns out to be 195 degrees, which is answer choice C. Here's how to answer questions about converting units on the SAT. Question 23 states a certain town has an area of 4.36 square miles. What is the area in square yards of this town? Now, when you're converting area as your unit, you have to keep in mind that you end up squaring it, right? Since we have square miles and square yards. So when we make this conversion of one mile equaling 1,760 yards, What we have to actually do is we have to take our first, our 4.36 square miles, and then we have to actually multiply that by 1760 squared. Since we're converting from square miles to square yards, we have to square the unit that we are converting. Okay. And when we do that, we put it in our calculator and we end up with an answer of answer choice D, 13,505,536. Here's how to solve this difficult SAT math question. Question 24 states for line H, the table shows three values of X and their corresponding values of Y. Line k is the result of translating line h down 5 units in the xy plane. What is the x-intercept of line k? Well, in order to get to line k, we need to first know the equation for line h. So let's go ahead and find that. So let's start by finding our slope. We see that we go over 5 and we go up 30. So we have 30 over 5 as our slope. So let's go ahead and write that down. We're going to get 30 over 5, which we know is equal to 6, is equal to our slope, which we'll call m. Now, in order to solve for our full equation, we're going to... go ahead and put in some of these points to get our y intercept. Okay, so we see that x is 18, when y is one. So y is 130. So we're gonna have 130 is equal to six times 18, plus some constant B. Now let's go and solve for this. So six times 18 is going to give us 108. So let's go ahead and subtract 108 from each side here. 130 minus 108 is going to leave us with 22 is equal to B. Okay, so now we have our equation. So let's go ahead and write out our equation. All right, so we have y is equal to 6x plus 22. Now, we don't use this to find our answer here because we have to keep in mind that line h is translated down five units. So if we're going down five units instead of plus 22, we would have plus 17. Okay, so let's go ahead and put in that plus 17. Okay, so now we have our equation for line h. Now we can go ahead and find our x-intercept. Well, where's our x-intercept? That is where y is equal to zero. So let's go ahead and take out y. We'll put in zero. Now, all we gotta do is track 17 from both sides. When we do that, we're going to end up with negative 17 is equal to 6x. Now we're going to go ahead and divide both sides by 6, and we're going to get that x is equal to negative 17 over 6, which we see is going to be answer choice D. Here's a great example of an SAT question that is made way easier by using the graphing calculator that is available on the digital SAT. Question 25 says, in the xy plane, the graph of the equation y equals negative x squared plus 9x minus 100 intersects the line y equals c at exactly one point. What is the value of C? Now the key thing here is that it intersects at exactly one point, which is what is going to allow us to do this super easily using Desmos. So as you can see, what I did here is I went ahead and I plugged in this equation into Desmos. Now, as you can see from this negative X squared, and also from the graph, it's going to open down. So in order for us to, to intersect at exactly one point with the equation. Y equals C. That's going to have to happen right at this maximum value. So if we take a look at the graph, all we got to do is find that point. We see that point is negative 79.75. We just have to match that up with one of our answer choices now. Now I see with our answer choices, they're all negative, but this is obviously going to be way too small a value. Negative 100 we know is not equal to negative 79.75. Negative 481 over four would be something below negative 100. So it can't be correct. And our answer would have to be C. Here's how to make this really difficult SAT math question much easier. If you take a look at question 26, it states for each real number r, which of the following points lies on the graph of each equation in the xy plane for the given system? Now, if you see stacked equations like this, oftentimes you'll be looking to sort of add or subtract to get to your answer. But in this case, since we're asked for which of the following points lies on the graph of each equation, what we're actually going to do is check if something lies in the first equation, if it also will be a solution to the second equation. So the way we're going to do this is, in this case, we have 2x plus 3y equals 7. We have 10x plus 15y equals 35. I'm going to look for proportions or ratios here. I see that to get from 7 to 35, I'd be multiplying by 5. I see to get from 2 to 10, I'd multiply by 5. I see to get from 3 to 15, I would multiply by 5. So in this case, I know that since all of those numbers, if they're multiplied by 5, will get me that next equation. I know that if a solution set, it works on the first equation, it will also be true on the second equation, right? So now in this case, I only have to actually check on one of the equations. And if it is true, then it means that it will work for the other equation as well. So that's going to save me half the time. Now, the next important thing to help you here is the order at which you're going to check these, because the reason this question is so difficult is because it's time consuming. It's not necessarily that is extremely complex, but the real only way to check these is substitution, which is obviously not ideal at all. Substitution takes a very long time, but thankfully we already gotten rid of half the work. Let's be smart about the way we go about this. So what I'm going to look for here is which of these answer choices I would start with. Because if you start with the wrong answer choices, oftentimes it's going to be a little bit more lengthy to figure out that it's actually wrong. And the reason why is because typically the correct answer choices will just fit nicely. It's just kind of the way it works usually most of the time, not always, but most of the time. So the way that I'm going to choose which answer choice to actually substitute in first here is I'm going to look for things that will cancel out. Okay. So the first thing I'm going to do is since I see three out of my four answer choices are dealing with sort of denominators of two or three, I'm going to be working with this first equation. Okay. And I would usually pick that one anyways, just because it's smaller numbers than sort of 10, 15 and 35. So that's where I'm going to be checking these possible solutions. Now, the next thing I'm going to look at is which ones will cancel out night nicely. Right. And the way that I look at that is I'm going to look for X values that are divided by two, since I have this two and I'm looking for Y values that are divided by three, cause I have that three. Okay. So I see here by X values are over two. Okay. So that is one that I would probably start with. And if I look at B or I'm sorry, if I look at number C. I see that in this Y value, I have ones that are over three. So that's the one that I would check next. And then I have D and A, and I'd probably just check D third and then A fourth. I'm checking A fourth because it's the most complex. I'm checking D third because it doesn't have something that nicely cancels out. Okay. So from here, this is the order that I would check these in on a substitution question. Now, from this point, I would just go ahead and start substituting. So let's go ahead and do that. So we're going to have two multiplied by negative three R over two plus seven over two. And then we are also going to have that. plus three times y, we know that y is going to be r. So plus three r is going to equal seven. Now let's find out if this is true. So we can go ahead and cancel this two out with this two and that two out as well with this two, because we know that we would distribute this. Okay. So once we do that, we end up with negative three r plus seven, and then plus three r is equal to seven. Now we have a negative three r and a plus three r, which will cancel out to zero. So we're going to end up with seven is equal to seven. Okay, we end up with 7 is equal to 7. Now is that true? Yes. So is that a solution? Yes. So is our answer B? Yes. Here's a really difficult SAT math question made super easy. Question 27 states the perimeter of an equilateral triangle is 624 centimeters. The height of the triangle is k times root 3 centimeters where k is a constant. What is the value of k? Well, if we go ahead and draw this out, it's going to make us a lot easier to visualize. So we have our equilateral triangle, we have our height, which is going to form a right angle there. Since it's equilateral, we know that we have side lengths 60 and 60. And we also know that since we have a 90 degree angle and a 60 degree angle, this angle has to be 30 degrees. The next thing we know is that our perimeter is 624. Okay. And that's perimeter. Since we have an equilateral triangle, if we divide it by three, we're going to get our side lengths. So that's going to be 208 as our side length. Now the next thing to note is that we have our height in K times root three. Now this is important because when we have a 60 30 90 triangle, we know that the value here must actually be K. And the reason why, if I go ahead and draw this out very quickly, okay, is that in a 60, 30, 90 triangle, which I'll go ahead and just put those numbers there so you can recognize them. And you should try to memorize this for the SAT. If you have side length X there, you're gonna have side length X. times root 3 there and you're going to have 2x here. So in order to actually solve for the value of k, I just have to divide this 208 by 2 to get the value of k right here. Okay, so 208 over 2 is going to leave me with 104 as my answer and I'll just go ahead and put 104 as the value of k. Here's how to solve this oddly worded SAT math question. Question 1 states that Tilly earns p dollars for every w hours of work. Which expression represents the amount of money in dollars Tilly earns for 39 w hours of work? Well, we know that she's earning P dollars per every W hours of work. And we know that we can set that proportion equal to the amount that she's earning per 39 W hours of work. And now on our numerator, we'll just have that labeled as X. And that's what we need to solve for here. So to isolate X, we'll multiply both sides by 39 W to isolate X. So now we have 39 W times P all over W is equal to X. Now we see our W's are going to cancel and we're going to be left with 39 P. Keep in mind that that is P, so I'm going to put it parentheses just to make it clear. So 39 times P is equal to X. And we see that that is going to be answer choice A. Here's how to solve this seemingly simple SAT math problem. Question two states, for a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function M models the number of minutes it will take Juan to ride X miles at this rate? Now, the reason this question can be troublesome for some people taking the SAT is because it really does deal in details. So. let's go ahead and focus on the details that we need to pay attention to. In this case, we are asked for the model of the number of minutes it will take to ride X miles at this rate. Now we have to keep in mind that our units were given for our rate is 5.7 minutes per mile. So this is actually very easy, but you have to pay attention to the details. Like I said, now we're modeling the amount of time it takes him to ride X amount of miles. So we're already given that ratio. And our answer is D M of X equals 5.7 X. You have to make sure here. They're paying attention to the details because some people would fall for the misconception that you have to convert minutes per mile into miles per minute or miles per hour, and you do not need to do that in this case. Your answer is, here's an SAT math tip that can save you a ton of time. Question three states the solution to the given system of equations is xy. What is the value of y? Since we want to solve for y and we see that we have stacked equations, we're going to look for a way to get rid of x. To do that in this case, I see we can add these two equations together because 3x plus negative 3x is going to give us 0x. So what we're going to end up with then is y is equal to 12 plus negative 6, which is the same as 12 minus 6, which is 6. So our answer there will be b for the value of y. Here's how to solve this SAT math question in under 60 seconds. Question four states, the equation gives the speed s in miles per hour of a certain car t seconds after it began to accelerate. What is the speed in miles per hour of the car five seconds after it began to accelerate? Well, given our equation, we want to know how fast is it going five seconds after it begins to accelerate. We know that the amount of time after it begins to accelerate is represented as t. So we plug in 5 for t, and we're going to have our speed is equal to 40 plus 3 times 5. 3 times 5 is going to be 15. 15 plus 40 is going to equal 55, and our answer will be answer choice d. Here's how to solve this question that deals with the Pythagorean theorem on the SAT. Question 5 states, for the right triangle shown, a equals 4 and b equals 5. Which expression represents the value of c? Well, when you're given a triangle question on the SAT, it's often helpful to go ahead and label your sides. So as you can see, we go ahead and do that. We're asked for the value of C. We're going to use the Pythagorean theorem, which means that we're going to take A squared plus B squared and make it equal to C squared. And when you do that, you're going to get your value of C as the square root of 4 squared plus 5 squared, which we see is going to be answer choice D. Here's how to solve this SAT math question in under 60 seconds. Question 6 states, what is the solution to the given equation? We have 4x plus 5 equals 165. We want to isolate x, so we're going to subtract 5 from both sides. We're going to end up with 160 is equal to 4x. Then we'll divide both sides by 4 to isolate x. When we do that, we have 160 over 4, which is going to end up giving us 40 as our value of x. So our answer there is 40. Here's how to solve this SAT math question in under 30 seconds. The question states the x-intercept of the graph is x0. What is the value of x? In this case, since we're asked for the value of x and 0, we know that our y-coordinate is 0. At y being 0, we have our x value of 7. So the value of x is 7. Here's how to solve this SAT math question that deals with slope intercept form. The function f is defined by f of x equals 1 10th x minus 2. What is the y-intercept of the graph of y equals f of x in the xy plane? Well, all that this means is you have an equation y equals 1 10 x minus 2. All you got to do is find the y-intercept. Your y-intercept is where x is 0. If you substitute in 0 for x, you're going to end up with y is equal to negative 2. So as you can see, your answer has to be where x is 0. and where y is negative 2 and your answer has to be answer choice b. Here's how to solve this SAT math question that deals with transformations. Question 9 says the function f is defined by f of x equals 7x cubed and the xy plane the graph of y equals g of x is the result of shifting the graph of y equals f of x down two units. Which equation defines the function g? Well the function g of x is the same as f of x except we are moving it down two units which means that g of x will equal 7x cubed minus 2. We can see that that is answer choice d. Here's how to solve this system of equations question really easily. The question states which ordered pair xy is a solution to the given system of equations. Now as we can see, we have one equation x plus 7 equals 10. We know that in that case, we can subtract 7 from both sides and we're going to get that x is equal to 3. Now that we have the value of x, we can go ahead and plug that in on our second equation. We will end up with 3 plus 7 squared, which is equal to 10 squared, which is equal to 100 is equal to y. So we know that it will have to be 3 and 100, which is answer choice A. Here's how to solve this SAT math question that deals with adding and subtracting variables with exponents. The question states which expression is equivalent to 7x cubed plus 7x, in parentheses, minus 6x cubed minus 3x. What we're going to go ahead and do here is distribute this minus sign to both that 6x cubed and that minus 3x. Once we do that, we're going to go ahead and combine like terms. So we have 7x minus negative 3x, which is same as plus 3x. And then we also have a 7x cubed plus 7x cubed. minus 6x cubed. Now, keep in mind that these are going to get summed together. I just didn't have room on one line to write them, but that is ultimately going to give us 10x plus our x cubed value for a total of x cubed plus 10x, which we see as answer choice A. So A is our answer there. Here's how to solve this SAT math question in under 60 seconds. Question 12 states the function p is defined by p of n is equal to 7n cubed. What is the value of n when p of n is equal to 56? Well, when P of N is equal to 56 means we just substitute in that 56 for P of N in our equation and we get 56 is equal to 7N cubed. Next thing we're going to do is try to isolate N because that's what we need to solve for is the value of N. Now we got 56 over 7. That's going to leave us with 8 is equal to N cubed. Now from here, you should hopefully be able to recognize that if we take the third root of each side, we'll be able to isolate the value of N and we will also have the third root of 8, which is 2. So So two is equal to the value of n and our answer will be a. Here's how to solve SAT math questions that deal with intersecting lines. This question states in the figure shown, line C intersects parallel lines S and T, what is the value of X? Well, since we have parallel lines S and T with something intersecting them, we know that this angle next to X also has to be 110. The next thing that we can notice is that since we have the straight line here, that has to sum to 180. So we can go ahead and do 180 minus 110. And that will give us our answer for the value of X as 70 degrees. So our answer will be 70. Here's how to solve questions that ask you to find the mean of a dataset on the SAT. Question 14 states, a list of 10 data values is shown. What is the mean of these data? Since the SAT has gone digital, you will be able to use a calculator on each part of the test as of the filming of this video. So in that case, if you're asked to find the mean, I will 100% recommend that you use a calculator exclusively because you can. And it makes much more sense to find the mean of a data set using a calculator rather than doing it by handwritten math because you're less likely to make an error. So what you would do is you would take all of these values and you would sum them together, and then you would take that sum and you would divide it by the number of values, and that will get you your mean. So that is how you would solve this question. And once you do that, you will end up with an answer of 10. Here's how to answer this question that asks about the exponential growth formula on the SAT. Question 15 states, the equation E of T is equal to 5 times 1.8 to the power of T gives the estimated number of employees at a restaurant where T is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context? The number 5 is our initial value. It is our starting value. It is the amount that when T is 0, we will have because any number raised to the power of 0 is 1. So this is our initial amount. And that is a very important thing to know for the SAT math section. Let's go ahead and run through our answer choices. We have A, the estimated number of employees when the restaurant opened. That is the correct answer. Here's how to solve this S18 math question super quickly. Question 16 states, what is the minimum value of the given function? We have g of x equals x squared plus 55. Now, since we have an x squared value, we don't have any sort of minus 5x value or anything like that. We know that any number that is squared is going to be positive and that's just being added to 55. So our minimum value will be 55. Now, if you come across a question like this, and it's a little bit more complicated, for example, say that the question was something like x squared minus 12x plus 55, then in that case, what you should do is you should go ahead and graph it. Use on the digital SAT, you pretty much have access to Desmos within sort of the testing environment. And you should use that and then just find the minimum on the graph. But in this case, this is a trick you can use since you know that x squared will always be positive. You're not subtracting anything as x changes. So in this case, this is a trick you can use to move faster. Here's something you need to know about exponential and linear functions for the SAT. Question 17 states, each year the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time? Now, since it is dependent on the value of the investment the previous year, since we are going up by 0.49% each year, that is exponential growth. So that is increasing exponential. Now, I want to cover these other three options as well so you know them and you can answer them correctly on the SAT if they come up on a different question. So let's go over it. Increasing exponential. In this case, since we're going up by 0.49% of our previous year's value, the number that would be within our exponential growth equation for the growth rate would be 1.0049. Now, what if that number, instead of being above one, what if it was below one? Let's say that our rate, instead of being that, our rate was 0.09. Well, 0.09 is a decreasing exponential function. So in that case, it would be A. Now, what if instead of being dependent on the previous year's value, it was independent of the previous year's value? So in that case, let's say that we just went up by $50. So we went up by $50 each day. It's a dollar sign. We're going up by $50. each day. Well, that would be increasing linear. And what if we were going down by $50 each day? That'd be decreasing linear. If we are not dependent on the previous year's value, then it's likely going to be, then it will be linear. Now, if we are dependent on the previous year's value, then it will be exponential. And then you can use the rate of growth to determine if it's increasing or decreasing. Here's how to solve this SAT math question about percentages. Question 18 states the population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is K times the 2015 population, what is the value of K? Well, if we're increasing by 7%, then the way we would represent this is the 2015 population, which we're just going to label as P multiplied by K, which is how many times we are bigger than the 2015 population will give us our new population. Now we have to solve for K and we know we're increasing by 7%. And since we're increasing by 7%, we would represent that as 1.07. So our answer will be answer choice C. Here's how to answer this. tricky SAT math question about exponents. The question states, which expression is equivalent to a to the power of 11 over 12, where a is positive. Now, the first thing I would immediately check for is if we have a to the 11 over 12, just rewritten in the same format, which would be the 12th root of a to the 11th power. But we see that that's not the case. So instead, what we're going to do is we're going to go ahead and multiply by 12 over 12 to this exponent up here. And the reason why we're doing that is because I see that all of these have 132 on the power on the you know, what a is being raised with power as, and I know to get to 132, I ultimately have to multiply by 12. So we're going to go ahead and multiply by 12 over 12. Now, why is this okay? Well, it's okay because we're multiplying by one. So we're taking that 11, 12, we're multiplying by one. So it would stay the same. We're just making it a larger number. So when we do that 11 times 12, we know is going to equal 132. And we know in our denominator, 12 times 12 will equal 144. So now we're going to find our answer choice. It will be answer choice B, which is 144th root of a to the power of 132. Here's how to solve this SAT math question that deals with an inequality. The question states, an event planner is planning a party. It costs the event planner a one-time fee of $35. Now, keep in mind when you're dealing with a word problem like this, you want to start writing out equations as you come across the numbers. So in this case, we have a one-time fee of $35. That's not reoccurring, so I can just go ahead and add that. To rent the venue and 1025 per attendee, so that's going to be our cost will be plus 10. two five per attendee, which I'm just going to call a for now, unless I'm given a variable, it needs to be the event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget? So since we cannot exceed the budget, it has to be less than or equal to 200. Now from here, I want to go ahead and solve for the maximum amount of attendees I can have without going over. So I need to solve for a, so I'm gonna go ahead and subtract 35 from both sides that will cancel to zero subtract 35 here. So now I'm going to end up with 10.25A and then 200 minus 35 is going to end up giving us 165. From here, I will divide both sides by 10.25. So I divide both sides by 10.25. Now, 165 divided by 10.25 is going to give me 16.09. Now, since I know I can't have a partial amount of a person and I can't go over my budget, since that gives me 16.09, I know that A must equal 16. Okay, and I got that by using my calculator on the new digital SAT. You can use your calculator on the section. So our answer will be A is equal to 16. So our answer would just be 16. Here's how to solve this SAT math question that deals with absolute value. Question 21 states if the absolute value of 4x minus 4 is equal to 112, what is the positive value of x minus 1? Now keep in mind here that when you have an absolute value question like this, you can have two answers for the value of x. But in this case, we are asked for the positive value of x minus 1. So there is only one right answer here. there are two answers for the value of x. So let's go ahead and talk about why that is and how you can approach this question. So the first thing I would do is I would do 4x minus 4 is equal to 112. Then I will add 4 to both sides. Add four to both sides. This will cancel the zero 112 plus four will give us 116. So I can just go ahead and write this as four X is equal to one 16. And then from there, I divide both sides by four and we are going to get that X is equal to see what that is in my calculator. That'll be 29. Okay. So X is equal to 29. Now we see that if we plug in 29 for X, we're going to get 29 minus one. That's positive. That's 28. So 28 will be our answer. Okay. So 28 is our answer. Now I want to show you what would happen. if we came across the negative number first, okay? Because the other way to get x, because there are two values that x can be here, is you would do negative, and I'm just going to actually erase this so you can see how you would do this, right? So you saw me get one of the values of x. There is another value of x, however, because when you have absolute value like this, you also have to do this to find the other solution, okay? So negative 4x minus 4, you distribute your negative sign, okay? And notice how I'm... distributing that negative sign to everything that was within that absolute value. And that gets us negative four X plus four is equal to 112. We will subtract four and we will get 108. Okay. So now we have negative four X is equal to 108. I'm just going to go ahead and write that neater. Negative four X is equal to 108. We divide both sides by negative four, divide both sides by negative four. Okay. And we see that X is going to equal 108 divided by negative four, which if we go ahead and put that in our calculator, 108 divided by negative four, That's going to give us negative 27. Okay. And then in that case, you would see negative 27 minus one is negative 28. That is not a positive solution, which is why our answer there has to be 28. Okay. So it's important that you understand absolute value on the SAT math section, which is why I wanted to go over this, even though we got to the answer sooner without having to get this other value for X. Here's how to solve this difficult SAT math question that deals with volume. Question 22 states that a cube has an edge length of 68 inches, a solid sphere with a radius of 34. Inches is inside the cube such that the sphere touches the center of each face of the cube to the nearest cubic inch What is the volume of the space in the cube that is not? Taken up by the sphere and just a quick note anytime you have something that is underlined on the SAT pay close attention to it Because they are underlining it for a reason because in a sense, it's almost trying to trick you they're telling you hey This is important. It sticks out from the rest because it is different and you need to pay attention to it So anytime you see that pay close attention to it Now since we're asked to find the volume of the space in the cube not taken up by the sphere we have to calculate first the volume of the cube. Then we have to subtract the volume of the sphere. So let's start with the volume of the cube. We know that a cube has an edge length of 68 inches. So what we're going to do is we're going to go ahead and have 68 inches. Now the volume of a cube, okay, all the side lengths are the same. So that's going to be 68 to the power of three is the volume of the cube. Now let's subtract the volume of the sphere. So the volume of a sphere is four thirds times pi. times the radius cubed. We know our radius is 34 inches, so I'll go ahead and put 34 in parentheses cubed. Now, all you have to do is put this into your calculator and you will ultimately get your answer of 149,796. So our answer there will be answer choice A. Here's how to solve this question on the SAT about circles super easily. Question 23 states, what is the diameter of the circle in the XY plane with this equation? Now, if you know the circle equation, you know that this value of 16 is equal to the radius squared. Now, if 16 is equal to the radius squared, all you have to do is take the square root of the radius squared to isolate the radius. The square root of 16 we know is 4, so we know that 4 is equal to the radius. To get the diameter, we know that the diameter, which we'll just call D, is equal to 2 times the radius. So that's going to be 2 times 4, which will equal 8, and our answer there will be answer choice B. Here's a trick to make this difficult SAC math question super simple. Question 24 states, for the exponential function f, the value of f of 1 is k. Where k is a constant, which of the following equivalent forms the function f shows the value of k as the coefficient or the base? Well, in this case, all of our answer choices are in the exponential growth formula or the exponential growth equation. So our coefficients are going to be 50, 80, 128, and 204.8. Now in order for the value of f of one, to be that in a situation where we have exponential growth like this, we need to have the exponent be zero, because if the exponent is zero, and we're multiplying it by 1.6, that's going to give us one, which means that our value will just be that of the coefficient. So f of x will equal the value of the coefficient when x is equal to one, which is what we need. So all we got to do is do find the answer choice where we are raising it to the power of zero. So one plus one would be two. So we can go and get rid of a if we just have one that's not zero, if we have one minus one, we get that equal to zero as the exponent. So our answer there has to be answer choice C. And I will just quickly show you how this works just to prove it to you in case you are in disbelief. 128 times 1.6 raised to the power of zero. Well, 1.6 to the power of zero is going to be one. So that will equal 128 when we have F of one. We know that we have 128 as our coefficient. Therefore our answer has to be C. So there's just some quick proof in case you were doubting me. Here's a really difficult SAT math question made super simple just by knowing the exponential growth formula. So question 25 states a model estimates that at the end of each year from 2015 to 2020, the number of squirrels in population was 150% more than the number of squirrels in the population at the end of the previous year. Model estimates that at the end of 2016, now the reason that I'm underlining this is because I noticed that here we had 2015 to 2020, now we have 2016. So we are moving one year in to this growth. There were 180 squirrels in the population, which of the following equations represents this model, where N is the estimated number of squirrels in the population T years after the end of 2015. And T must be less than or equal to five. Key thing here is they're kind of trying to throw you off with answer choices C and D because we are modeling it after the end of 2015. And that 180 number that they gave us is at the end of 2016. So that's one year in. So our initial value is not 180. Our initial value is 72. Now, as far as the rate of increase, they're also trying to throw you off with answer choice A, because they know that you're going to see that 150% and think, oh, that's just 1.5, but it's not. You have to keep in mind that it's 150% more than the number of squirrels in the population at the end of the previous year, right? So if we were multiplying by, let's say we're increasing by 50%, then it would be 1.5, but we're not increasing by 50%. We're increasing by 150%, which means we have to multiply that by 2.5. So our answer there has to be B. So if you know the exponential growth formula, this question is really easy. If you don't, you're probably going to get it wrong. Here's one of the most difficult SAT math questions made super simple. Question 26 states that in the given pair of equations, a and b are constants. The graph of the pair of equations at the xy plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines? So the key thing here is that you understand what perpendicular lines mean. It means that these slopes are negative reciprocals of each other. So for example, if we look at our equations that we are given, we have 5x plus 7y equals 1, ax plus by equals 1. Now the slope of this first one, I'm going to call m our slope, So, m is going to equal negative a over b. Now, the form negative a over b works when you have the form of a coefficient in front of x plus a coefficient in front of y is equal to some constant, which we have in both of these equations, so we can use it. Okay, so that means that our slope is going to equal, let me go ahead and get that, it's going to equal negative 5 over 7. Now, our slope for this bottom equation is going to be m is going to equal, well, m is that's going to have to equal seven over five. And how do we know that? Well, we need the opposite sign and the reciprocal. Okay. So that's going to have to be seven over five. Let me go and write that a little bit bigger so you can see it better. Seven over five. Okay. And I'll just draw the arrow that that's there. All right. Well, if that's going to be seven over five, we know that our a value then, well, that must be negative seven. Okay. And the reason we don't ask to be negative seven is because we know that the formula for our slope is negative a over B in this form. We know our b value then has to be 5. So I'm just going to go ahead and write that down, that our b value is going to equal 5. Because we need to know that in order to solve this. Now, the other thing that I think is important to notice here, and that will ultimately help you solve this extremely quickly once you know this trick, is that if you look at our equations up top here, we have negative 7x plus 5y is equal to 1. Now, what I want you to notice here is that when you're dealing with perpendicular lines in this format of the format where you have them set equal to a constant, notice how we have 5x and 5x. And then notice how we have 7y and 7y. Obviously, they are changed places, right? That coefficient of 7 has now changed from being attached to the y to being attached to the x. And then we have one singular change in sign. So that change in sign, it can be out in front of this a value, or it could also be in front of the b value. But either way, we have that one change in sign. So now that we've noticed that, we can pretty much solve these pretty quickly, right? So if we look at answer choice a, if we were to plug in for a, we know our value of a is negative 7. So we can go ahead and do that. So negative seven, we know that we have the sign change, right? We're switching from that seven being in front of the Y being in front of the X, that part's good. But then we have minus two times B. We know that our B value is five, right? So we're gonna end up getting minus 10 Y. Now the problem with that is that we changed both signs. We can only change one of the signs. So A is going to be wrong. And then we look at B, we've got 10 X plus seven Y. And then down here, we know that our A value is negative seven. So once again, we're changing the sign. That looks good. And then we got plus two times B, we know B is five. So that's going to end up giving us plus 10 Y, right? And now we see. That both of the, you know, the coefficient in front of X is now in front of Y coefficient that wasn't in front of Y is now in front of X. And we only changed one of the signs. So that means that B has to be our correct answer. Okay. So I know it took a little while for me to explain that, but I wanted to make sure that you guys understand how this works and why this works, because once you understand this trick, you can then apply it and it becomes very, very quick to find the right answer. And also, I will just note that this is one of the more difficult questions on the SAT. So being able to save time by understanding this trick is going to be very, very beneficial, especially for, especially for. students who are looking to score high in the math section, in particular above 700. Here's what you need to know about calculating the number of real solutions on the SAT math section, along with a problem to help you apply it. Question 27 says, in the equation above, C is a constant. The equation has no real solutions if C is greater than N. What is the least possible value of N? Well, let's start by discussing how you know the number of real solutions. The way you know that for a quadratic equation like this is by using the value of b squared minus 4ac. Now, one thing I want to have you make note of is that in the quadratic equation, it is set equal to zero. That's very important. Okay, so b squared minus 4ac. If that value is greater than zero, then that means that you're going to have two real solutions, which I'll represent as rs. Now, if b squared minus 4ac is equal to zero, then that means you're going to have one. real solution. Now, if you can kind of figure out where I'm going with this, b squared minus 4ac, if that is less than zero, then you're going to have no real solutions. Okay, so now that we know this, and we know that in our question, we are asked to find the equation having no real solutions if c is greater than n, we know that we can go ahead and set up this equation. So we know our a value is one, we know our b value is going to be negative 34, and we know our c value is just going to be represented as c in this case. So we have b squared, we know b is negative 34. So we'll go ahead and take that and square it. We're going to subtract four times a, a is one, and then we'll multiply it by c. Next thing we have to do is we have to set that as less than zero. So negative 34 squared is going to become 11, I believe. Let me just quick check on the calculator. 11 56, 11 56. Okay, so 11 56 minus 4c is going to be less than zero. I'm going to go ahead and add 4c to each side. Okay, so I'll add 4c to each side. And then next thing I'm going to have to do is I'm going to have to divide by four in order to isolate c so we can get it all alone. So let's go ahead and do that. We'll divide both sides by four. We'll get that C must be greater than 1156 over four, which is going to be 289. All right. So now that we have this, we know that C has to be greater than N. Okay. And we know that N, if we go ahead and let me just draw this, right, this inequality is going to equal this other inequality of C being greater than N. Well, in that case, N is going to have to equal 289. Okay. So our answer for the least possible value of N is 289. If you enjoyed this video, please like, subscribe, and consider sending a super thanks to help support my channel. Additionally, please drop a comment below letting me know what videos you want me to make in the future. And if you are looking for additional educational services that I offer, please check out my website, HaydenRoddy.com.

Here's how to answer this SAT math question in under 20 seconds. The question is, what is 10% of 470? we can take 10% and express it as a decimal of 0.1 and then multiply it by 470. And that'll give us our answer of 47. So our answer will be answer choice B. Here's a trick that'll save you time on the SAT math section. Question two says which equation has the same solution as the given equation.

If we take a quick glance at our answer choices, we see we have four x in every single one of our answer choices, which means if we look at our equation on top, we have four x plus six equals 18. All we have to do is subtract six from both sides, and we're left with four x is equal to 12. Now, we don't actually have to solve for X because we have 4X in every answer choice. So our answer is answer choice C. Here's a tip to be more efficient on the SAT math section. If you glance at the answer choices of question three, you'll see that all of them are going to be inequalities.

So as you read through this word problem, you want to go ahead and write out the inequality to save you time. So if we go ahead and start from the beginning, the total cost in dollars to rent a surfboard consists of a $25 service fee. So we can go ahead and write down that $25.

And that's a one-time charge because it's a service fee and a $10 per hour rental fee. So we're going to have plus 10 H. We'll use H to represent hours. A person rents a surfboard for T hours. So we have to replace H with T then and intends to spend a maximum of $75 to rent the surfboard.

So they are going to spend a maximum of $75. So this total has to be less than or equal to 75. We find which inequality represents the situation. And as we can see, that is going to be answer choice D. So D would be our answer there.

Here's how to solve this SAT math question in less than 30 seconds. The function G is defined by G of X is equal to X squared plus nine for which value of X is G of X equal to 25. Well, since we have g of x equaling 25, we go ahead and plug that in for g of x. Now we have 25 is equal to x squared plus 9. Now we're going to subtract 9 from each side so we can start isolating that x squared value. Now we have 16 is equal to x squared. To isolate x, we need to take the square root of x squared and the square root of 16. The square root of 16 is 4, which means 4 will equal x and our answer will be a.

Here's how to solve this probability question on the SAT. Question 5 states each face of a fair 14-sided die is labeled with the number 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a two?

Well, only one of the 14 faces has a two on it. So the answer has to be one over 14, which is answer choice A. Here's a trick for converting units on the SAT. Question six states a printer produces posters at a constant rate of 42 posters per minute. At what rate in posters per hour does the printer produce posters?

So what we're going to do here is we're going to convert from 42 posters per minute, which I'll represent as P per M, and we have to convert that into posters per hour. So what we're going to do is we're going to multiply by 60 minutes per hour. So as you can see, our minutes, which I'm representing as m, are going to cancel here, and we'll be left with posters p per hour h. So 42 times 60 is going to equal 2,520 posters per hour. So our answer is 2,520.

Here's how to solve this SAT math question in under 40 seconds. Question 7 states the function f is defined by the equation f of x equals 7x plus 2. What is the value of f of x when x equals 4? Well, all we have to do is plug in 4 for x. So we do 7 times 4 plus 2. 7 times 4 is going to be 28. 28 plus 2 will be 30. 30 is going to equal our value of f of x and be our answer. Here's how to solve this SAT math question in under 60 seconds.

Question 8 states a teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents the situation where x represents the number of 1 point questions and y represents the number of 3 point questions?

We know our total number of points is going to be 70, so it's going to have to equal out to 70. Now, for every... x question we get right, which is every one point question, we get one point. So we have x plus now our three point questions, which are represented as y.

So x plus three y must equal 70 and our answer will be d. Here's how to answer this similar triangles question on the SAT. Question nine states, right triangles L, M, N, and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has a measure of 53 degrees.

What is the measure of angle Q? So what we see here is since we have similar triangles where L and M correspond to P and Q, we also know that. n must correspond to r.

Okay, we see that angle M has a measure of 53 degrees. Okay, and then we're asked for the measure of angle Q, we see that M corresponds to angle Q since they're similar triangles. So they're going to have the same angle measure. Okay, so that 53 degrees that we are given for the angle M must also be the angle measure of angle Q. So our answer will be B.

Here's a trick for the SAT math section. Question 10 states the solution to the given system of equations is xy. What is the value of x? Whenever you see stacked equations like this on the SAT, It's usually a sign that you're going to be able to add, subtract, or substitute one of the equations with the other in order to get your answer faster. In this case, we're asked for the value of x and we're given that y is equal to negative 3x.

So what we're going to do is we're going to substitute in that negative 3x for y in this below equation. So now what we're going to have is we're going to have 4x plus y when we know y is negative 3x. So 4x minus 3x is equal to 15. Now we know that 4x minus 3x is x, which means that x must equal 15 and our answer is answer choice C. Here's how to answer scatterplot questions on the new digital SAT.

Question 11 states, which of the following equations is the most appropriate linear model for the data shown in the scatterplot? What you're going to want to do here, since we're looking for a linear model to represent the scatterplot, is go ahead and draw a line just to give you a rough reference. As you can see, we have a negative slope, which means that answer choices C and D cannot be true since they have positive slopes.

The next thing we'll look at is the differences between answer choices A and B, which are their y-intercept. We see that we have a positive y-intercept of right around 10. So if we look at answer choice A, it would have a y-intercept of negative 10, which cannot be correct and our answer choice must be answer choice B. Here's how to answer this polynomials question on the SAT. Question 12 states the graph of y equals f of x is shown where the function f is defined by f of x equals ax cubed plus bx squared plus cx plus d, where a, b, c, and d are constants.

For how many values of x does f of x equal 0? Well, all we have to do is find where f of x equals 0 and count the number of points. We see we have one here. One here and one here.

So our answer will be three, which is answer choice C. Here's a tip to be more efficient on the SAT math section. If you see a word problem like this, you're gonna wanna start writing out the equation as you read it. So watch how I do this problem. Question 13 states, Vivian bought party hats and cupcakes for $71.

So 71 is gonna be the total amount she spends. Each package of party hats costs $3. So $3 times our number of packages of party hats, which I'll represent as P. And each cupcake costs $1. So you could make it plus one C, but since...

a one in front of C is redundant. We'll just get rid of the one. So now we have our equation.

Well, if she bought 10 packages of party hats, that means 10 is equal to P. So we can go ahead and substitute that in. So now I'll go ahead and erase that P and I can put in 10 since we know that's the amount that she had bought of those party hats. We have three times 10. We know that's going to equal 30. So we're going to have 71 is equal to 30 plus C.

Now we want to isolate C to solve for it. To do that, we're going to subtract 30 from each side. 71 minus 30 is going to leave us with 41. So now we have 41 is equal to C and our answer will be 41. Here's an example of when you should use your graphing calculator on the SAT math section. If you take a look at question 14, it states, what is one of the solutions to the given equation?

Now, you could solve this without a graphing calculator by factoring, but it's really a smarter choice just to go ahead and use the graphing calculator. Now, as you can see here, this is Desmos, and you're going to have essentially a version of Desmos on the Bluebook SAT, on the new digital SAT. Now, what I recommend doing is you just go ahead and put in this equation into the graphing calculator. Now, keep in mind, you want to substitute out Z or any other variable they put in there for X.

And once you do that, you see that you have your equation graphed out. And then since it's set equal to zero, all you have to do is find where it equals zero. You can see that that's at negative 12 and at two.

So you have two potential answers here. One is negative 12, and that would be correct. And the other answer is two, and that would also be correct. So you could put in one of either of those answers. But I want to quickly touch on why I think it's smart to use the graphing calculator here instead of actually factor this out yourself.

If you're factoring this out yourself, the chances of you making a mistake go up versus if you use a graphing calculator. Now keep in mind, using the graphing calculator that's built into the digital SAT only takes a couple of seconds, right? And factoring may save you a couple of seconds, but in my opinion, it's not worth the risk of you actually making a mistake doing multiplication or doing addition or doing subtraction, anything along those lines.

In my opinion, with questions like this, it's just much smarter to go ahead and use the graphing calculator. You avoid making many, many, many errors that can be made when factoring. So with questions like these, just use the graphing calculator.

Here's how to solve this SAT math question about exponential growth. Question 15 states that bacteria are growing a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every three hours.

That's important. How many cells per milliliter will there be 15 hours after the initial observation? So our starting amount is 300,000.

So let's go ahead and write that down. Now we're going to be using the equation for exponential growth. Keep in mind, we are doubling every three hours.

Since we're doubling, a two is what's going to go in these parentheses. Now... we are going to raise it to the power of 15 over three. And I'm going to explain why here, and it's very important you pay attention because this equation is commonly tested on the SAT math section. So the reason we are raising it to the power of 15 over three, and keep in mind, we're raising this two to the power of 15 over three is because we are doubling every three hours.

Since we're doubling every three hours, that gives us that three and that denominator of that exponent. Now we're asked how many there's going to be after 15 hours, which is why we have that 15 in the numerator. Okay. So now, as you can see, we have our equation, we put this in our calculator and we get our answer of D. 9.6 million.

Here's how to solve this question about simplifying exponents on the SAT. Question 16 states, which expression is equivalent to 6x to the power of 8 times y squared plus 12x squared y squared? What you're going to do here is you're going to look for common factors that you can pull out of each of these. So as we can see, we have y squared in both of them. We also have 6 and 12, which we can pull out a 6 from 12. We also have x to the power of 8 and x squared.

Okay, so the way that we're going to do this is we're going to pull 6 out, we're going to pull x squared out, and we're going to pull y squared out. Now, we still have to multiply, get this equation still. Okay. So what do we have to multiply by here? Well, we're going to need X to the power of six still to get to that X to the power of eight.

Keep in mind that this X squared times this X to the six is what's going to give us X to the power of eight. We're still going to have that Y square. We have that six out front. So now we have our first term. Now we know that we also have to have another term because we have six here.

But we have 12 up here. Okay, so to get to that 12 there, we're gonna have to add two. And we still have x squared and y squared here as well. So we see that we're ultimately gonna end up with 6x squared y squared times x to the power of 6 plus 2, which we see is gonna be answer choice C.

Here's how to better interpret word problems on the SAT math section. Question 17 states a neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934.

The equation 2x plus 35y is equal to 3934 represents this situation. Which of the following is the best interpretation of x in this context? Well, what we have to look at here is what does this total represent?

Well, it represents the total amount of trees. Now, we also have to look at what gets us to that total. Okay, we have 35 times y. Well, 35 is our area, but we have to multiply by the number of trees per unit of area.

Now, keep in mind, we're asked to solve for x here. So we're looking at the amount of trees per hectare in the park. Okay, so X must be the average number of trees per hectare in the park, which is answer choice A.

Here's a tip to solve SAT math questions when your answer choices aren't in point-slope form. If we take a look at this question, it says the graph shows the relationship between the number of shares of stock from company A, which is represented as X, and the number of shares of stock from company B, which is represented as Y, that Simone can purchase. Which equation could represent this relationship? And we see we have company B and company A, and obviously we have the correct correspondence of X to A and Y to B, so that's good to know. Now, Now in this case, I see that A and C both are in point slope form.

So I'm gonna go ahead and just check if they're correct since that's the easiest thing to do. So here I see that both of these have y-intercepts that are not correct. I have 12 and 8, but the actual y-intercept is 40. So I can go ahead and get rid of A and I can get rid of C.

Now you could go ahead and convert B and D into point slope form and there's not an issue with that, but it does take longer than what I'm about to show you. Instead what you could do is you could know that the slope, which we'll represent as M, is equal to negative A over B when we have our equation set up like this. where we have a coefficient in front of x plus a coefficient in front of y equals some constant. Now, the next thing I'm going to do is I'm going to check what my slopes are for each one. Okay, so for answer choice B here, we see that our slope would be negative 8 since 8 is our a value over 12. Okay, and then for our d value, we see that we would have negative 12 over 8. Now, I'm going to see what my actual slope is.

Okay, my actual slope is I go down 40 and I go over 60. So that'd be negative 40 over 60, which we know we can simplify to negative 4 over 6. Okay, negative 4 over 6 is equal to negative 8 over 12 when we simplify negative 8 over 12. So our answer there is going to be answer choice B. Here's how to solve this SAT math question in under 60 seconds. Question 19 states circle A has a radius of 3n and circle B has a radius of 129n where n is a positive constant.

The area of circle B is how many times the area of circle A? Well, let's start by finding the area of circle B then. So circle B has a radius of 129n. Now keep in mind the formula for the area of a circle is pi r squared. We know our radius is 129. and all of that is going to get squared.

Now we have to divide that then by the area of circle A to find out how many times bigger it is. So we know that the radius of circle A is 3n squared. Now keep in mind that n here is going to end up being squared in both the top and the bottom.

Okay, so first thing, it's very obvious that those pi's cancels most people will get that. Now the next thing we need to understand is that 129 squared times n squared is equal to what we have here of 129 times n all to the power of 2. Now on the bottom then we end up with 3 squared times n squared as well and we see that those n squareds are going to cancel. Okay that's really important to know because now the question becomes very easy we can just plug it into our calculator and when we plug into our calculator 129 squared divided by 3 squared which you can also just know is 9 then you're going to end up with answer choice d. Here's how to avoid this tricky question on the SAT. Question 20 states the frequency table summarizes the 57 data values in a data set.

What is the maximum data value in the data set? Now most people when they look at this might think that the answer is 11 because it has the highest frequency. And they think that that's the maximum since it's the highest value in the frequency section of the table, but that's incorrect. The actual answer here is 14. Now, the reason why is because they're asking for the maximum data value.

They're not asking for the highest frequency value. Okay. That would be 11 because the data value there is 11, but they are asking for the maximum data value, which means our answer has to be 14. Here's how to answer this question about circles on the SAT.

Question 21 says a circle in the XY plane is a diameter with end points 2, 4 and 2, 14. An equation of the circle is X minus 2 squared plus Y minus 9 squared equals R squared, where R is a positive constant. What is the value of R? Okay. What you need to understand here is that this is a question dealing with the circle equation.

So it's important you know the circle equation going into the SAT because it is tested fairly often. Now, as far as how you answer this, it's actually pretty easy as long as you can recognize this simple trick. When you're given a circle question, you're given end points.

Oftentimes, There are endpoints that are specifically designed to make the question easier. So you want to look at them pretty closely. And here what we notice is that we have an X coordinate that is the same in both of these. Sometimes it'll be a Y coordinate that is the same in both, but either way, try to find if you can see either the X coordinates are the same or the Y coordinates are the same because it'll make the question a lot easier.

In this case, since our X coordinates are the same, we're going to look at how far apart are our Y coordinates. And we see that from 4 to 14 is a difference of 10. Now keep in mind that the circle has a diameter with these endpoints. Okay.

So if the circles like this, and this is our diameter between our points and it's 10, well that means our radius must be 5 because our diameter is double our radius. So the value of r, and keep in mind that this is the equation of a circle where r is representing our radius and we're asked for the value of r, not r squared, the value of r then must be 5. So our answer is 5. Here's how to solve questions that ask you to convert from radians to degrees on the SAT. Question 22 states the measure of angle r is 2 pi over 3 radians. The measure of angle t is 5 pi over 12 radians greater than the measure of angle r.

What is the measure of angle t in degrees? So we have to start by finding the measure of angle t in radians, and then after that we'll convert to degrees. So we know that the angle r is 2 pi over 3 radians.

Now we have to add on to that the 5 pi over 12 radians, since 5 pi over 12 is the amount of radians that we are greater than the angle measure of r to get to angle t. From here we need to have a common denominator in order to add these fractions. So to do that, I'm just going to go, I see three and 12. I'm just going to go ahead and make it 12. I know that you could sort of simplify it, but I'm not going to.

So I'm going to multiply three by four to get to 12 and I'm going to multiply with two by four, which will give me eight. So now I have eight pi over 12. Now I can go and add these together and I'm going to see that that's going to get me 13 pi over 12. Now from here, I need to go ahead and convert 13 pi over 12 in two degrees. Now this is really easy, but some people can get tripped up on it if they don't know this trick. In order to convert from radians to degrees, you need to multiply by 180 degrees over pi radians.

Now keep in mind that we have radians as our units in here with this 13 pi over 12. So to get rid of those radians, we have to have radians in the denominator right here, which is why we have pi on the bottom. Okay. So when we go ahead and do this, we're going to end up getting rid of our pi on each one. Sorry, I did not mean to erase that. Let me go and put that back.

Okay. We're going to end up canceling out those pies and we're going to end up with 13 times 180 over 12, which we're going to go ahead and put into our calculator. And once we do that, we're going to see that that turns out to be 195 degrees, which is answer choice C. Here's how to answer questions about converting units on the SAT. Question 23 states a certain town has an area of 4.36 square miles.

What is the area in square yards of this town? Now, when you're converting area as your unit, you have to keep in mind that you end up squaring it, right? Since we have square miles and square yards.

So when we make this conversion of one mile equaling 1,760 yards, What we have to actually do is we have to take our first, our 4.36 square miles, and then we have to actually multiply that by 1760 squared. Since we're converting from square miles to square yards, we have to square the unit that we are converting. Okay. And when we do that, we put it in our calculator and we end up with an answer of answer choice D, 13,505,536.

Here's how to solve this difficult SAT math question. Question 24 states for line H, the table shows three values of X and their corresponding values of Y. Line k is the result of translating line h down 5 units in the xy plane.

What is the x-intercept of line k? Well, in order to get to line k, we need to first know the equation for line h. So let's go ahead and find that.

So let's start by finding our slope. We see that we go over 5 and we go up 30. So we have 30 over 5 as our slope. So let's go ahead and write that down. We're going to get 30 over 5, which we know is equal to 6, is equal to our slope, which we'll call m. Now, in order to solve for our full equation, we're going to...

go ahead and put in some of these points to get our y intercept. Okay, so we see that x is 18, when y is one. So y is 130. So we're gonna have 130 is equal to six times 18, plus some constant B. Now let's go and solve for this.

So six times 18 is going to give us 108. So let's go ahead and subtract 108 from each side here. 130 minus 108 is going to leave us with 22 is equal to B. Okay, so now we have our equation.

So let's go ahead and write out our equation. All right, so we have y is equal to 6x plus 22. Now, we don't use this to find our answer here because we have to keep in mind that line h is translated down five units. So if we're going down five units instead of plus 22, we would have plus 17. Okay, so let's go ahead and put in that plus 17. Okay, so now we have our equation for line h.

Now we can go ahead and find our x-intercept. Well, where's our x-intercept? That is where y is equal to zero.

So let's go ahead and take out y. We'll put in zero. Now, all we gotta do is track 17 from both sides. When we do that, we're going to end up with negative 17 is equal to 6x. Now we're going to go ahead and divide both sides by 6, and we're going to get that x is equal to negative 17 over 6, which we see is going to be answer choice D.

Here's a great example of an SAT question that is made way easier by using the graphing calculator that is available on the digital SAT. Question 25 says, in the xy plane, the graph of the equation y equals negative x squared plus 9x minus 100 intersects the line y equals c at exactly one point. What is the value of C? Now the key thing here is that it intersects at exactly one point, which is what is going to allow us to do this super easily using Desmos. So as you can see, what I did here is I went ahead and I plugged in this equation into Desmos.

Now, as you can see from this negative X squared, and also from the graph, it's going to open down. So in order for us to, to intersect at exactly one point with the equation. Y equals C. That's going to have to happen right at this maximum value. So if we take a look at the graph, all we got to do is find that point.

We see that point is negative 79.75. We just have to match that up with one of our answer choices now. Now I see with our answer choices, they're all negative, but this is obviously going to be way too small a value. Negative 100 we know is not equal to negative 79.75. Negative 481 over four would be something below negative 100. So it can't be correct.

And our answer would have to be C. Here's how to make this really difficult SAT math question much easier. If you take a look at question 26, it states for each real number r, which of the following points lies on the graph of each equation in the xy plane for the given system?

Now, if you see stacked equations like this, oftentimes you'll be looking to sort of add or subtract to get to your answer. But in this case, since we're asked for which of the following points lies on the graph of each equation, what we're actually going to do is check if something lies in the first equation, if it also will be a solution to the second equation. So the way we're going to do this is, in this case, we have 2x plus 3y equals 7. We have 10x plus 15y equals 35. I'm going to look for proportions or ratios here. I see that to get from 7 to 35, I'd be multiplying by 5. I see to get from 2 to 10, I'd multiply by 5. I see to get from 3 to 15, I would multiply by 5. So in this case, I know that since all of those numbers, if they're multiplied by 5, will get me that next equation.

I know that if a solution set, it works on the first equation, it will also be true on the second equation, right? So now in this case, I only have to actually check on one of the equations. And if it is true, then it means that it will work for the other equation as well. So that's going to save me half the time. Now, the next important thing to help you here is the order at which you're going to check these, because the reason this question is so difficult is because it's time consuming.

It's not necessarily that is extremely complex, but the real only way to check these is substitution, which is obviously not ideal at all. Substitution takes a very long time, but thankfully we already gotten rid of half the work. Let's be smart about the way we go about this. So what I'm going to look for here is which of these answer choices I would start with.

Because if you start with the wrong answer choices, oftentimes it's going to be a little bit more lengthy to figure out that it's actually wrong. And the reason why is because typically the correct answer choices will just fit nicely. It's just kind of the way it works usually most of the time, not always, but most of the time. So the way that I'm going to choose which answer choice to actually substitute in first here is I'm going to look for things that will cancel out.

Okay. So the first thing I'm going to do is since I see three out of my four answer choices are dealing with sort of denominators of two or three, I'm going to be working with this first equation. Okay.

And I would usually pick that one anyways, just because it's smaller numbers than sort of 10, 15 and 35. So that's where I'm going to be checking these possible solutions. Now, the next thing I'm going to look at is which ones will cancel out night nicely. Right. And the way that I look at that is I'm going to look for X values that are divided by two, since I have this two and I'm looking for Y values that are divided by three, cause I have that three. Okay.

So I see here by X values are over two. Okay. So that is one that I would probably start with.

And if I look at B or I'm sorry, if I look at number C. I see that in this Y value, I have ones that are over three. So that's the one that I would check next.

And then I have D and A, and I'd probably just check D third and then A fourth. I'm checking A fourth because it's the most complex. I'm checking D third because it doesn't have something that nicely cancels out.

Okay. So from here, this is the order that I would check these in on a substitution question. Now, from this point, I would just go ahead and start substituting. So let's go ahead and do that.

So we're going to have two multiplied by negative three R over two plus seven over two. And then we are also going to have that. plus three times y, we know that y is going to be r. So plus three r is going to equal seven.

Now let's find out if this is true. So we can go ahead and cancel this two out with this two and that two out as well with this two, because we know that we would distribute this. Okay. So once we do that, we end up with negative three r plus seven, and then plus three r is equal to seven. Now we have a negative three r and a plus three r, which will cancel out to zero.

So we're going to end up with seven is equal to seven. Okay, we end up with 7 is equal to 7. Now is that true? Yes. So is that a solution?

Yes. So is our answer B? Yes. Here's a really difficult SAT math question made super easy. Question 27 states the perimeter of an equilateral triangle is 624 centimeters.

The height of the triangle is k times root 3 centimeters where k is a constant. What is the value of k? Well, if we go ahead and draw this out, it's going to make us a lot easier to visualize.

So we have our equilateral triangle, we have our height, which is going to form a right angle there. Since it's equilateral, we know that we have side lengths 60 and 60. And we also know that since we have a 90 degree angle and a 60 degree angle, this angle has to be 30 degrees. The next thing we know is that our perimeter is 624. Okay.

And that's perimeter. Since we have an equilateral triangle, if we divide it by three, we're going to get our side lengths. So that's going to be 208 as our side length. Now the next thing to note is that we have our height in K times root three. Now this is important because when we have a 60 30 90 triangle, we know that the value here must actually be K.

And the reason why, if I go ahead and draw this out very quickly, okay, is that in a 60, 30, 90 triangle, which I'll go ahead and just put those numbers there so you can recognize them. And you should try to memorize this for the SAT. If you have side length X there, you're gonna have side length X.

times root 3 there and you're going to have 2x here. So in order to actually solve for the value of k, I just have to divide this 208 by 2 to get the value of k right here. Okay, so 208 over 2 is going to leave me with 104 as my answer and I'll just go ahead and put 104 as the value of k. Here's how to solve this oddly worded SAT math question. Question 1 states that Tilly earns p dollars for every w hours of work.

Which expression represents the amount of money in dollars Tilly earns for 39 w hours of work? Well, we know that she's earning P dollars per every W hours of work. And we know that we can set that proportion equal to the amount that she's earning per 39 W hours of work.

And now on our numerator, we'll just have that labeled as X. And that's what we need to solve for here. So to isolate X, we'll multiply both sides by 39 W to isolate X. So now we have 39 W times P all over W is equal to X.

Now we see our W's are going to cancel and we're going to be left with 39 P. Keep in mind that that is P, so I'm going to put it parentheses just to make it clear. So 39 times P is equal to X.

And we see that that is going to be answer choice A. Here's how to solve this seemingly simple SAT math problem. Question two states, for a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function M models the number of minutes it will take Juan to ride X miles at this rate? Now, the reason this question can be troublesome for some people taking the SAT is because it really does deal in details.

So. let's go ahead and focus on the details that we need to pay attention to. In this case, we are asked for the model of the number of minutes it will take to ride X miles at this rate.

Now we have to keep in mind that our units were given for our rate is 5.7 minutes per mile. So this is actually very easy, but you have to pay attention to the details. Like I said, now we're modeling the amount of time it takes him to ride X amount of miles. So we're already given that ratio. And our answer is D M of X equals 5.7 X.

You have to make sure here. They're paying attention to the details because some people would fall for the misconception that you have to convert minutes per mile into miles per minute or miles per hour, and you do not need to do that in this case. Your answer is, here's an SAT math tip that can save you a ton of time.

Question three states the solution to the given system of equations is xy. What is the value of y? Since we want to solve for y and we see that we have stacked equations, we're going to look for a way to get rid of x. To do that in this case, I see we can add these two equations together because 3x plus negative 3x is going to give us 0x.

So what we're going to end up with then is y is equal to 12 plus negative 6, which is the same as 12 minus 6, which is 6. So our answer there will be b for the value of y. Here's how to solve this SAT math question in under 60 seconds. Question four states, the equation gives the speed s in miles per hour of a certain car t seconds after it began to accelerate. What is the speed in miles per hour of the car five seconds after it began to accelerate? Well, given our equation, we want to know how fast is it going five seconds after it begins to accelerate.

We know that the amount of time after it begins to accelerate is represented as t. So we plug in 5 for t, and we're going to have our speed is equal to 40 plus 3 times 5. 3 times 5 is going to be 15. 15 plus 40 is going to equal 55, and our answer will be answer choice d. Here's how to solve this question that deals with the Pythagorean theorem on the SAT.

Question 5 states, for the right triangle shown, a equals 4 and b equals 5. Which expression represents the value of c? Well, when you're given a triangle question on the SAT, it's often helpful to go ahead and label your sides. So as you can see, we go ahead and do that.

We're asked for the value of C. We're going to use the Pythagorean theorem, which means that we're going to take A squared plus B squared and make it equal to C squared. And when you do that, you're going to get your value of C as the square root of 4 squared plus 5 squared, which we see is going to be answer choice D.

Here's how to solve this SAT math question in under 60 seconds. Question 6 states, what is the solution to the given equation? We have 4x plus 5 equals 165. We want to isolate x, so we're going to subtract 5 from both sides. We're going to end up with 160 is equal to 4x.

Then we'll divide both sides by 4 to isolate x. When we do that, we have 160 over 4, which is going to end up giving us 40 as our value of x. So our answer there is 40. Here's how to solve this SAT math question in under 30 seconds.

The question states the x-intercept of the graph is x0. What is the value of x? In this case, since we're asked for the value of x and 0, we know that our y-coordinate is 0. At y being 0, we have our x value of 7. So the value of x is 7. Here's how to solve this SAT math question that deals with slope intercept form. The function f is defined by f of x equals 1 10th x minus 2. What is the y-intercept of the graph of y equals f of x in the xy plane? Well, all that this means is you have an equation y equals 1 10 x minus 2. All you got to do is find the y-intercept.

Your y-intercept is where x is 0. If you substitute in 0 for x, you're going to end up with y is equal to negative 2. So as you can see, your answer has to be where x is 0. and where y is negative 2 and your answer has to be answer choice b. Here's how to solve this SAT math question that deals with transformations. Question 9 says the function f is defined by f of x equals 7x cubed and the xy plane the graph of y equals g of x is the result of shifting the graph of y equals f of x down two units.

Which equation defines the function g? Well the function g of x is the same as f of x except we are moving it down two units which means that g of x will equal 7x cubed minus 2. We can see that that is answer choice d. Here's how to solve this system of equations question really easily.

The question states which ordered pair xy is a solution to the given system of equations. Now as we can see, we have one equation x plus 7 equals 10. We know that in that case, we can subtract 7 from both sides and we're going to get that x is equal to 3. Now that we have the value of x, we can go ahead and plug that in on our second equation. We will end up with 3 plus 7 squared, which is equal to 10 squared, which is equal to 100 is equal to y. So we know that it will have to be 3 and 100, which is answer choice A. Here's how to solve this SAT math question that deals with adding and subtracting variables with exponents.

The question states which expression is equivalent to 7x cubed plus 7x, in parentheses, minus 6x cubed minus 3x. What we're going to go ahead and do here is distribute this minus sign to both that 6x cubed and that minus 3x. Once we do that, we're going to go ahead and combine like terms. So we have 7x minus negative 3x, which is same as plus 3x. And then we also have a 7x cubed plus 7x cubed.

minus 6x cubed. Now, keep in mind that these are going to get summed together. I just didn't have room on one line to write them, but that is ultimately going to give us 10x plus our x cubed value for a total of x cubed plus 10x, which we see as answer choice A. So A is our answer there. Here's how to solve this SAT math question in under 60 seconds.

Question 12 states the function p is defined by p of n is equal to 7n cubed. What is the value of n when p of n is equal to 56? Well, when P of N is equal to 56 means we just substitute in that 56 for P of N in our equation and we get 56 is equal to 7N cubed.

Next thing we're going to do is try to isolate N because that's what we need to solve for is the value of N. Now we got 56 over 7. That's going to leave us with 8 is equal to N cubed. Now from here, you should hopefully be able to recognize that if we take the third root of each side, we'll be able to isolate the value of N and we will also have the third root of 8, which is 2. So So two is equal to the value of n and our answer will be a. Here's how to solve SAT math questions that deal with intersecting lines. This question states in the figure shown, line C intersects parallel lines S and T, what is the value of X?

Well, since we have parallel lines S and T with something intersecting them, we know that this angle next to X also has to be 110. The next thing that we can notice is that since we have the straight line here, that has to sum to 180. So we can go ahead and do 180 minus 110. And that will give us our answer for the value of X as 70 degrees. So our answer will be 70. Here's how to solve questions that ask you to find the mean of a dataset on the SAT. Question 14 states, a list of 10 data values is shown. What is the mean of these data? Since the SAT has gone digital, you will be able to use a calculator on each part of the test as of the filming of this video.

So in that case, if you're asked to find the mean, I will 100% recommend that you use a calculator exclusively because you can. And it makes much more sense to find the mean of a data set using a calculator rather than doing it by handwritten math because you're less likely to make an error. So what you would do is you would take all of these values and you would sum them together, and then you would take that sum and you would divide it by the number of values, and that will get you your mean. So that is how you would solve this question.

And once you do that, you will end up with an answer of 10. Here's how to answer this question that asks about the exponential growth formula on the SAT. Question 15 states, the equation E of T is equal to 5 times 1.8 to the power of T gives the estimated number of employees at a restaurant where T is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

The number 5 is our initial value. It is our starting value. It is the amount that when T is 0, we will have because any number raised to the power of 0 is 1. So this is our initial amount. And that is a very important thing to know for the SAT math section. Let's go ahead and run through our answer choices.

We have A, the estimated number of employees when the restaurant opened. That is the correct answer. Here's how to solve this S18 math question super quickly. Question 16 states, what is the minimum value of the given function?

We have g of x equals x squared plus 55. Now, since we have an x squared value, we don't have any sort of minus 5x value or anything like that. We know that any number that is squared is going to be positive and that's just being added to 55. So our minimum value will be 55. Now, if you come across a question like this, and it's a little bit more complicated, for example, say that the question was something like x squared minus 12x plus 55, then in that case, what you should do is you should go ahead and graph it. Use on the digital SAT, you pretty much have access to Desmos within sort of the testing environment.

And you should use that and then just find the minimum on the graph. But in this case, this is a trick you can use since you know that x squared will always be positive. You're not subtracting anything as x changes. So in this case, this is a trick you can use to move faster. Here's something you need to know about exponential and linear functions for the SAT.

Question 17 states, each year the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time? Now, since it is dependent on the value of the investment the previous year, since we are going up by 0.49% each year, that is exponential growth. So that is increasing exponential. Now, I want to cover these other three options as well so you know them and you can answer them correctly on the SAT if they come up on a different question.

So let's go over it. Increasing exponential. In this case, since we're going up by 0.49% of our previous year's value, the number that would be within our exponential growth equation for the growth rate would be 1.0049. Now, what if that number, instead of being above one, what if it was below one?

Let's say that our rate, instead of being that, our rate was 0.09. Well, 0.09 is a decreasing exponential function. So in that case, it would be A.

Now, what if instead of being dependent on the previous year's value, it was independent of the previous year's value? So in that case, let's say that we just went up by $50. So we went up by $50 each day. It's a dollar sign. We're going up by $50.

each day. Well, that would be increasing linear. And what if we were going down by $50 each day?

That'd be decreasing linear. If we are not dependent on the previous year's value, then it's likely going to be, then it will be linear. Now, if we are dependent on the previous year's value, then it will be exponential.

And then you can use the rate of growth to determine if it's increasing or decreasing. Here's how to solve this SAT math question about percentages. Question 18 states the population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is K times the 2015 population, what is the value of K?

Well, if we're increasing by 7%, then the way we would represent this is the 2015 population, which we're just going to label as P multiplied by K, which is how many times we are bigger than the 2015 population will give us our new population. Now we have to solve for K and we know we're increasing by 7%. And since we're increasing by 7%, we would represent that as 1.07. So our answer will be answer choice C. Here's how to answer this.

tricky SAT math question about exponents. The question states, which expression is equivalent to a to the power of 11 over 12, where a is positive. Now, the first thing I would immediately check for is if we have a to the 11 over 12, just rewritten in the same format, which would be the 12th root of a to the 11th power. But we see that that's not the case. So instead, what we're going to do is we're going to go ahead and multiply by 12 over 12 to this exponent up here.

And the reason why we're doing that is because I see that all of these have 132 on the power on the you know, what a is being raised with power as, and I know to get to 132, I ultimately have to multiply by 12. So we're going to go ahead and multiply by 12 over 12. Now, why is this okay? Well, it's okay because we're multiplying by one. So we're taking that 11, 12, we're multiplying by one. So it would stay the same.

We're just making it a larger number. So when we do that 11 times 12, we know is going to equal 132. And we know in our denominator, 12 times 12 will equal 144. So now we're going to find our answer choice. It will be answer choice B, which is 144th root of a to the power of 132. Here's how to solve this SAT math question that deals with an inequality. The question states, an event planner is planning a party.

It costs the event planner a one-time fee of $35. Now, keep in mind when you're dealing with a word problem like this, you want to start writing out equations as you come across the numbers. So in this case, we have a one-time fee of $35. That's not reoccurring, so I can just go ahead and add that.

To rent the venue and 1025 per attendee, so that's going to be our cost will be plus 10. two five per attendee, which I'm just going to call a for now, unless I'm given a variable, it needs to be the event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget? So since we cannot exceed the budget, it has to be less than or equal to 200. Now from here, I want to go ahead and solve for the maximum amount of attendees I can have without going over. So I need to solve for a, so I'm gonna go ahead and subtract 35 from both sides that will cancel to zero subtract 35 here. So now I'm going to end up with 10.25A and then 200 minus 35 is going to end up giving us 165. From here, I will divide both sides by 10.25.

So I divide both sides by 10.25. Now, 165 divided by 10.25 is going to give me 16.09. Now, since I know I can't have a partial amount of a person and I can't go over my budget, since that gives me 16.09, I know that A must equal 16. Okay, and I got that by using my calculator on the new digital SAT.

You can use your calculator on the section. So our answer will be A is equal to 16. So our answer would just be 16. Here's how to solve this SAT math question that deals with absolute value. Question 21 states if the absolute value of 4x minus 4 is equal to 112, what is the positive value of x minus 1?

Now keep in mind here that when you have an absolute value question like this, you can have two answers for the value of x. But in this case, we are asked for the positive value of x minus 1. So there is only one right answer here. there are two answers for the value of x.

So let's go ahead and talk about why that is and how you can approach this question. So the first thing I would do is I would do 4x minus 4 is equal to 112. Then I will add 4 to both sides. Add four to both sides.

This will cancel the zero 112 plus four will give us 116. So I can just go ahead and write this as four X is equal to one 16. And then from there, I divide both sides by four and we are going to get that X is equal to see what that is in my calculator. That'll be 29. Okay. So X is equal to 29. Now we see that if we plug in 29 for X, we're going to get 29 minus one. That's positive. That's 28. So 28 will be our answer.

Okay. So 28 is our answer. Now I want to show you what would happen. if we came across the negative number first, okay?

Because the other way to get x, because there are two values that x can be here, is you would do negative, and I'm just going to actually erase this so you can see how you would do this, right? So you saw me get one of the values of x. There is another value of x, however, because when you have absolute value like this, you also have to do this to find the other solution, okay?

So negative 4x minus 4, you distribute your negative sign, okay? And notice how I'm... distributing that negative sign to everything that was within that absolute value.

And that gets us negative four X plus four is equal to 112. We will subtract four and we will get 108. Okay. So now we have negative four X is equal to 108. I'm just going to go ahead and write that neater. Negative four X is equal to 108. We divide both sides by negative four, divide both sides by negative four.

Okay. And we see that X is going to equal 108 divided by negative four, which if we go ahead and put that in our calculator, 108 divided by negative four, That's going to give us negative 27. Okay. And then in that case, you would see negative 27 minus one is negative 28. That is not a positive solution, which is why our answer there has to be 28. Okay. So it's important that you understand absolute value on the SAT math section, which is why I wanted to go over this, even though we got to the answer sooner without having to get this other value for X.

Here's how to solve this difficult SAT math question that deals with volume. Question 22 states that a cube has an edge length of 68 inches, a solid sphere with a radius of 34. Inches is inside the cube such that the sphere touches the center of each face of the cube to the nearest cubic inch What is the volume of the space in the cube that is not? Taken up by the sphere and just a quick note anytime you have something that is underlined on the SAT pay close attention to it Because they are underlining it for a reason because in a sense, it's almost trying to trick you they're telling you hey This is important.

It sticks out from the rest because it is different and you need to pay attention to it So anytime you see that pay close attention to it Now since we're asked to find the volume of the space in the cube not taken up by the sphere we have to calculate first the volume of the cube. Then we have to subtract the volume of the sphere. So let's start with the volume of the cube. We know that a cube has an edge length of 68 inches.

So what we're going to do is we're going to go ahead and have 68 inches. Now the volume of a cube, okay, all the side lengths are the same. So that's going to be 68 to the power of three is the volume of the cube. Now let's subtract the volume of the sphere.

So the volume of a sphere is four thirds times pi. times the radius cubed. We know our radius is 34 inches, so I'll go ahead and put 34 in parentheses cubed.

Now, all you have to do is put this into your calculator and you will ultimately get your answer of 149,796. So our answer there will be answer choice A. Here's how to solve this question on the SAT about circles super easily. Question 23 states, what is the diameter of the circle in the XY plane with this equation?

Now, if you know the circle equation, you know that this value of 16 is equal to the radius squared. Now, if 16 is equal to the radius squared, all you have to do is take the square root of the radius squared to isolate the radius. The square root of 16 we know is 4, so we know that 4 is equal to the radius.

To get the diameter, we know that the diameter, which we'll just call D, is equal to 2 times the radius. So that's going to be 2 times 4, which will equal 8, and our answer there will be answer choice B. Here's a trick to make this difficult SAC math question super simple. Question 24 states, for the exponential function f, the value of f of 1 is k.

Where k is a constant, which of the following equivalent forms the function f shows the value of k as the coefficient or the base? Well, in this case, all of our answer choices are in the exponential growth formula or the exponential growth equation. So our coefficients are going to be 50, 80, 128, and 204.8.

Now in order for the value of f of one, to be that in a situation where we have exponential growth like this, we need to have the exponent be zero, because if the exponent is zero, and we're multiplying it by 1.6, that's going to give us one, which means that our value will just be that of the coefficient. So f of x will equal the value of the coefficient when x is equal to one, which is what we need. So all we got to do is do find the answer choice where we are raising it to the power of zero.

So one plus one would be two. So we can go and get rid of a if we just have one that's not zero, if we have one minus one, we get that equal to zero as the exponent. So our answer there has to be answer choice C.

And I will just quickly show you how this works just to prove it to you in case you are in disbelief. 128 times 1.6 raised to the power of zero. Well, 1.6 to the power of zero is going to be one. So that will equal 128 when we have F of one. We know that we have 128 as our coefficient.

Therefore our answer has to be C. So there's just some quick proof in case you were doubting me. Here's a really difficult SAT math question made super simple just by knowing the exponential growth formula.

So question 25 states a model estimates that at the end of each year from 2015 to 2020, the number of squirrels in population was 150% more than the number of squirrels in the population at the end of the previous year. Model estimates that at the end of 2016, now the reason that I'm underlining this is because I noticed that here we had 2015 to 2020, now we have 2016. So we are moving one year in to this growth. There were 180 squirrels in the population, which of the following equations represents this model, where N is the estimated number of squirrels in the population T years after the end of 2015. And T must be less than or equal to five. Key thing here is they're kind of trying to throw you off with answer choices C and D because we are modeling it after the end of 2015. And that 180 number that they gave us is at the end of 2016. So that's one year in.

So our initial value is not 180. Our initial value is 72. Now, as far as the rate of increase, they're also trying to throw you off with answer choice A, because they know that you're going to see that 150% and think, oh, that's just 1.5, but it's not. You have to keep in mind that it's 150% more than the number of squirrels in the population at the end of the previous year, right? So if we were multiplying by, let's say we're increasing by 50%, then it would be 1.5, but we're not increasing by 50%.

We're increasing by 150%, which means we have to multiply that by 2.5. So our answer there has to be B. So if you know the exponential growth formula, this question is really easy. If you don't, you're probably going to get it wrong. Here's one of the most difficult SAT math questions made super simple.

Question 26 states that in the given pair of equations, a and b are constants. The graph of the pair of equations at the xy plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines?

So the key thing here is that you understand what perpendicular lines mean. It means that these slopes are negative reciprocals of each other. So for example, if we look at our equations that we are given, we have 5x plus 7y equals 1, ax plus by equals 1. Now the slope of this first one, I'm going to call m our slope, So, m is going to equal negative a over b. Now, the form negative a over b works when you have the form of a coefficient in front of x plus a coefficient in front of y is equal to some constant, which we have in both of these equations, so we can use it.

Okay, so that means that our slope is going to equal, let me go ahead and get that, it's going to equal negative 5 over 7. Now, our slope for this bottom equation is going to be m is going to equal, well, m is that's going to have to equal seven over five. And how do we know that? Well, we need the opposite sign and the reciprocal. Okay.

So that's going to have to be seven over five. Let me go and write that a little bit bigger so you can see it better. Seven over five.

Okay. And I'll just draw the arrow that that's there. All right.

Well, if that's going to be seven over five, we know that our a value then, well, that must be negative seven. Okay. And the reason we don't ask to be negative seven is because we know that the formula for our slope is negative a over B in this form.

We know our b value then has to be 5. So I'm just going to go ahead and write that down, that our b value is going to equal 5. Because we need to know that in order to solve this. Now, the other thing that I think is important to notice here, and that will ultimately help you solve this extremely quickly once you know this trick, is that if you look at our equations up top here, we have negative 7x plus 5y is equal to 1. Now, what I want you to notice here is that when you're dealing with perpendicular lines in this format of the format where you have them set equal to a constant, notice how we have 5x and 5x. And then notice how we have 7y and 7y. Obviously, they are changed places, right?

That coefficient of 7 has now changed from being attached to the y to being attached to the x. And then we have one singular change in sign. So that change in sign, it can be out in front of this a value, or it could also be in front of the b value.

But either way, we have that one change in sign. So now that we've noticed that, we can pretty much solve these pretty quickly, right? So if we look at answer choice a, if we were to plug in for a, we know our value of a is negative 7. So we can go ahead and do that.

So negative seven, we know that we have the sign change, right? We're switching from that seven being in front of the Y being in front of the X, that part's good. But then we have minus two times B.

We know that our B value is five, right? So we're gonna end up getting minus 10 Y. Now the problem with that is that we changed both signs. We can only change one of the signs. So A is going to be wrong.

And then we look at B, we've got 10 X plus seven Y. And then down here, we know that our A value is negative seven. So once again, we're changing the sign.

That looks good. And then we got plus two times B, we know B is five. So that's going to end up giving us plus 10 Y, right? And now we see. That both of the, you know, the coefficient in front of X is now in front of Y coefficient that wasn't in front of Y is now in front of X.

And we only changed one of the signs. So that means that B has to be our correct answer. Okay.

So I know it took a little while for me to explain that, but I wanted to make sure that you guys understand how this works and why this works, because once you understand this trick, you can then apply it and it becomes very, very quick to find the right answer. And also, I will just note that this is one of the more difficult questions on the SAT. So being able to save time by understanding this trick is going to be very, very beneficial, especially for, especially for. students who are looking to score high in the math section, in particular above 700. Here's what you need to know about calculating the number of real solutions on the SAT math section, along with a problem to help you apply it.

Question 27 says, in the equation above, C is a constant. The equation has no real solutions if C is greater than N. What is the least possible value of N?

Well, let's start by discussing how you know the number of real solutions. The way you know that for a quadratic equation like this is by using the value of b squared minus 4ac. Now, one thing I want to have you make note of is that in the quadratic equation, it is set equal to zero.

That's very important. Okay, so b squared minus 4ac. If that value is greater than zero, then that means that you're going to have two real solutions, which I'll represent as rs.

Now, if b squared minus 4ac is equal to zero, then that means you're going to have one. real solution. Now, if you can kind of figure out where I'm going with this, b squared minus 4ac, if that is less than zero, then you're going to have no real solutions. Okay, so now that we know this, and we know that in our question, we are asked to find the equation having no real solutions if c is greater than n, we know that we can go ahead and set up this equation.

So we know our a value is one, we know our b value is going to be negative 34, and we know our c value is just going to be represented as c in this case. So we have b squared, we know b is negative 34. So we'll go ahead and take that and square it. We're going to subtract four times a, a is one, and then we'll multiply it by c.

Next thing we have to do is we have to set that as less than zero. So negative 34 squared is going to become 11, I believe. Let me just quick check on the calculator.

11 56, 11 56. Okay, so 11 56 minus 4c is going to be less than zero. I'm going to go ahead and add 4c to each side. Okay, so I'll add 4c to each side. And then next thing I'm going to have to do is I'm going to have to divide by four in order to isolate c so we can get it all alone.

So let's go ahead and do that. We'll divide both sides by four. We'll get that C must be greater than 1156 over four, which is going to be 289. All right.

So now that we have this, we know that C has to be greater than N. Okay. And we know that N, if we go ahead and let me just draw this, right, this inequality is going to equal this other inequality of C being greater than N.

Well, in that case, N is going to have to equal 289. Okay. So our answer for the least possible value of N is 289. If you enjoyed this video, please like, subscribe, and consider sending a super thanks to help support my channel. Additionally, please drop a comment below letting me know what videos you want me to make in the future. And if you are looking for additional educational services that I offer, please check out my website, HaydenRoddy.com.

Transcript for:Effective Strategies for SAT Math Success

Transcript for:
Effective Strategies for SAT Math Success