Transcription
In this video, we're going to go over 23 questions, all based on GD ready math problems. Now, the first three are going to be no calculator. So, let's check it out.
When you've got 3^ squared, it's not 3 * 2 squared is always that number times itself. So, 3 * 3 and that'll give us 9. Same thing as adding 3 times. So, let's put that. Okay. So, plus 5^ squared, that's going to be 5 * 5 and that'll be 25. Just imagine you have five nickels. They're worth 5 cents each. So, you've got 25 cents total. So, 9 + 25, it's close to 25 + 10, that'd be 35, but it's one less than that. So, 34 final answer. And that's all for this guy. And these are called exponents. If you want some more practice with these, I have them on my website.
The next type is a number line. What is the distance in units from zero to point Q? Let's highlight that on this number line. Now zero is right here. Q is right here. Let's show that distance. Just imagine how many steps you take. 1 2 3 and a little bit more. Now let's label this because this point here is -3. So the orange point it's right in between -3 -4. That's going to be -3.5. But a distance in math is always going to be positive. So this distance is going to be positive 3.5. That's how many steps you take. 1 2 3 and then half a step to get to that point. So final answer pos3.5 and that's it.
To multiply decimals like this, the easiest way is to round each number. Now imagine this is money. $4.75 that's about $5. $210 again about $2. So we're looking at 5 * 2 and that'll give us 10. So which answer is close to 10? Well, only one of them is this one here. 9.975, $99.97. So, automatically B. That's going to be the correct choice here. But we can go ahead and look at the full steps. The first thing you're going to do is ignore the decimals to start. So, don't even worry about those and just start on the bottom right here. So, 1 * 5, 5, 1 * 7, 7. and 1 * 4 4. When you move to the second number, you're always going to put a zero right here. Let's do it. And then keep going. 2 * 5 is 10. Carry the 1. Then 2 * 7 14 + 1 15. Once again, carry the 1. And then finally, 2 * 4 8 + 1, so 9. Next, we're going to add these all together. Just start on the right side. 5 + 0 5. 7 + 0 7. 4 + 5 9. And drop down the nine. Finally, we're going to deal with the decimals. We just want to count how many numbers are to the right of the decimals in the original problem. We've got two to the right of the decimal here and one to the right here for a total of three. Then just count in three decimal places right to left. So, we'll go ahead and show that. Put the decimal right there. And that's the final answer. So, like we said ahead of time, we knew it was going to be pretty close to 10. So, that's where rounding can help you find it much faster for those ones.
For this one, we're finding an average. Which expression shows the average mass of Mars, Jupiter, Saturn, and Neptune if they're represented by these letters? But to find an average, same thing as the mean, you're always going to add everything up first. So looking at the answers, B does that, adds them all up, and D does as well. But A, that multiplies them together. Same with C. So let's get rid of both of those. Okay. Next, you're going to divide by how many things you have. And we have four planets. Therefore, we want to divide by four. So D, that's going to calculate the average mass. And that's the correct option here. But why does that work? Well, let's say you're in college and you take three exams. These are your scores. What's your average? So, we want to add them up and divide by three since you've taken three tests. Well, let's get the total up top first. We could use the calculator. Those will add to 252. Then dividing that by three, we get 84. So we could find out, okay, you're actually averaging a B in this class, even though you had that one test that wasn't great. So averages are really helpful when you're trying to find out how you're doing in a class.
This pie chart represents an athletes diet. They're eating things in these percentages here. They plan to eat less fat and fruit. Let's highlight those. And they want to eat more protein. which graph represents their new diet plan. So, it's very easy. We just need to take our time here. Let's find out how much fat are they eating, 8% and fruit, 20%. But the only graph that has less fat and less fruit is going to be B with 6 and 18. And same thing with D. So, it could be either of these, but again, they're going to eat more protein. And right now, they're eating 24%. But D, that's the only one that then bumps it up to 28%. So, they're going to eat more protein, less of these two, and the last one has all of those. So, just take your time. You'll be fine with any pie chart question.
This one's going to be a little crazy. Whenever you have backtoback parentheses like this, it's going to be a foil problem. So, let's check out the steps. Now, the first step they tell us is to multiply. But that's where foil comes in. You're going to use f. That means you're going to multiply the first thing here times the first thing here. Let's go ahead and show that. Now, when you do 2x * x, notice you have the same thing times the same thing. That's going to become squared. It's just like we did in the first problem. When you have 3 * 3, you could write it as 3^ 2. So, same with this. When you have x * x, you could rewrite it as x^2. So 2x * x is going to be 2x^2. Okay, let's move to the O. Those are multiplying the outer ones. Well, that's going to be this 2x times this one, which is a -5. It always takes the sign of what's in front of it. So 2 * -5 is -10 and then just keep the x with it. So min - 10 x there. We're going to move to the i. That means the inner ones. That's going to be 3 * x. Just like that. And mush them together. 3 * x is + 3x there. Finally, the last one here, 3 * the last one here, -5. And 3 * -5. So -15. Okay. The next step, you're always going to combine the two middle terms. Those are called like terms. So notice they each have an x. You can add the numbers in front of them. Now -10, imagine you're on a number line at -10. 10 to the left of zero, but then you're going to move to the right three. You're still in the negatives, but you're at -7 instead. So that's how we could combine those. Then just drop down the first thing, drop down the last thing. Final answer is D here. So that's a foil problem. Feel free to look these up on my side as well.
For this one, we're finding the median blade diameter. Let's go ahead and find that in the chart. Now, the median is always the middle number, but you have to put them in order first. And lucky for us, they've already lined them up from smallest to biggest. So, we'll go ahead and find the one that's in the middle. So 21, that is our median here. So very easy to find the median, especially if they're already in the correct order.
For this one, we're finding a circular area of grass. Now, anytime you're finding an area, you could always look up the formula in the formula sheet they give you. And we're looking up the area of a circle. So we'll look up a circle and then a for the area. So, we're going to multiply pi * the radius squared. We just need to find out what is the radius for this circle. Now, we're talking about the size d mower. Let's highlight that. And then up in the chart, we can see, okay, for the size d mower, it's got a diameter of 26. That's the distance that goes all the way across through the center of a circle. That's the diameter, which is 26 for this one. But, we need to find out what the radius is. The radius is always half the diameter. So if we do 26 / 2, cut it in half, that'll get us a radius of 13. And since 13 is the radius, that's what we're going to plug in for r. So we're going to type this in the calculator. Find out the area. Okay, let's do it. Now the pi is on the left side here. And because it's next to r 2, they're being multiplied. So we'll do times our radius which is 13. Now notice this has a little to an exponent. You could do that using this button here. That'll square it. Okay. Then hit enter. It gives us 169 pi. But it hasn't multiplied it by 3.14 or pi yet until you hit the button above enter. So this is what we actually get. 530.9. We're going to round it to the nearest square in. Imagine you're getting change. You have 93 cents. Round it to the nearest dollar. So that'll bump up to 531. So this will be the correct area of grass that's going to be cut by this blade here.
To find a function when you're given these tables, a function is a properly working vending machine. So let's look at these. X is the number that you press and Y is what comes out. Well, let's look at B. Because when you press button four, you get out item one. We'll call that a Coke. But sometimes when you press button four, you get item three. We'll call that a Pepsi. And I've said it before, I'll say it again. Nobody ever really means to get Pepsi. We wanted a Coke. So, there's a problem here. You press one button, but you get two different things out. So, that vending machine is not working correctly. Let's get rid of that one. Which other ones are messed up? Well, C, cuz you press one button, you get four different things out. That's no good. Or D as well, cuz you press button zero. Sometimes you get a Dr. Pepper. Sometimes you get a diet Dr. Pepper. Again, it's not very consistent, but a that's the only one that's not messed up. So that one is our function. So as long as all the x's are different here, it's definitely going to be a function. And again, got more practice. These ones are called determined functions.
To find the perimeter of a shape, the perimeter is the distance around the outside. You're just going to add them all up. So we'll do 5 + 12 plus this. But the problem is some of these are missing. To find anything that's missing, just look opposite of it. Since this one's five, we could slide that over. And that one also has to be five. So, let's add that in. Now, same thing with the bottom here. We don't know this distance, but just look opposite. We've got 10 right there, and we've got 12. If we slide that down and that down, they'll combine correctly to the full thing. So, 12 + 10, 22. So that's the distance right there. Same thing with the 14. Slide that down. So that bottom one, that's 14 as well. And then we just have this length along the side. Once again, we'll look opposite. So we find this one is 16 right there. And plus this one is four. We're going to add both of those guys. 16 + 4. That length is 20. Finally, using the calculator, just start off with 20 + 14 + 5 all the way around until you get to 14 and hit enter. That'll add them up correctly. And that should add up to 122. So that's the correct perimeter for this shape here.
Now, for this problem, they're talking about a rectangular prism and the volume. So, we look that up in the formula sheet and we find this formula. V for volume. Now, we want to plug in things on the right side for the length, the width, and the height. Let's do it. They tell us that the length is 14 12. Same thing as 14.5. Just think of it as 50 cents for half a dollar. So, that's what we're going to plug in for L. For the width, that's 10 and a half. Same thing as 10.5. But what about the height? That's what we want to find out. What is the height of this cooler? But notice they give us these options. So we could try these one by one and plug them in for that h there. Let's start off with six. Because these are next to each other, we're going to multiply these and find out if it gives us the correct volume of 128. So let's go ahead and use the calculator. Okay, let's do 14.5. * 10.5 and times the height of 6. But that only gives us 913. We wanted to get that number. So, unfortunately, it's not the first one. But that's okay. Let's just go ahead and change the height to 8 and we'll reset it. Now, we don't have to type the whole thing in. Just use this up arrow twice and hit enter. That'll grab what you've already typed. And click the left arrow. change that to an eight there. Okay. Then hit enter. That does give us the correct volume. Therefore, eight had to be the correct height here. So, that's all for these problems. You're just going to plug into the formula and see if it gives you the correct thing there.
For this one, we're finding which algebraic expression down below is equivalent to this phrase here. So, let's check it out. The sum. Let's pause there because sum in math always means to add. But what are we adding? Well, we're adding x and two. So, let's look at the answers. The first one does that or B does that. But C and D, these ones are called products. They're being multiplied when you have a number and letter next to each other. So, those would be correct if they said the product here, but let's get rid of those guys. Okay. Next, this is all divided by 5 * the quantity 3 less than x. But you can easily find the answer if you know what quantity means. And that means parentheses. So, as we can see, this one down here does have parentheses or it's multiplying five times the quantity. So, B, that's the correct expression. And that's the final answer here. So, I have a video on algebraic statements that goes over words like sum, quantity, product, and a whole bunch of other ones. So, you can identify these correctly here.
This one is a percent problem. A store plans to increase the price of all their items by 8%. To the nearest cent, how much will a customer save if they buy a 9x12 tablet and cover before the prices increase? So, basically, we're interested in this 8%. Anytime you're doing a percent problem, you could always draw this triangle here. And here's how you're going to label it. If you know the total, that's going to go in the bottom left. The bottom right is going to be the percent. In this case, 8%. And the top part, well, that's actually going to be the smaller amount or part of the price. That's actually the amount that it's going to go up or that we're going to save here. But let's check out what we're buying here. We're buying this 9 by12 tablet and cover. Let's highlight that. It's going to be both of these ones added together here. So, we could add those using the calculator. I've already done that. And they add up to 189.32. But notice we have the total price of the things that we're buying. So, we have the bottom left number. Let's go ahead and draw our triangle. And we'll put the total in the bottom left. We also know the percent is going to increase by 8%. We'll put that in the bottom right. Well, we know we're looking for this part, but these are all connected with these signs here. If they're stacked, it's going to be divided. If they're next to each other, multiplied. So here, these two are going to be multiplied. And let's go ahead and do that. We'll multiply these and actually find out how much we're going to save. So that'll be the same thing as the part the smaller amount that we save. Okay, let's use the calculator. We'll start with our total 189 32 times our 8%. Notice the percent signs right here. You just have to hit the green button and then that one to get to it there. Okay. And then enter. So this is the amount that we save, $15.14. But because of this five, it's going to bump this one up to a five as well. So 15.15. Let's go ahead and add that in. So that's the part. That's the amount that we save. So that's the final answer for this one here.
For this problem, a video game software requires a screen that measures 3x4 dimensions. Basically, we want to find which of these dimensions here are going to be proportional. And that just means basically the same thing. Now, one way to do it is you could just multiply these by the same number. Let's just double these. 2 * 3 6. 2 * 4 8. And we notice the first option is exactly that. So that will be proportional to this value. It's just double it. So this one is definitely good. But another way to do these is using the calculator. And you could just make this a fraction. find out if it reduces to 3 over4. Let's check it out. Now the fraction button n /d is right here. And let's do 6 over8. Okay. Enter. That does simplify to 3 over4. So it has those dimensions. But let's keep going with the other ones. We'll do 8 over 10. And that one has dimensions 4x5. So that's not what we're looking for. We'll put an X there. Okay, the third one. Let's keep going. This time we have 9 by 12. And you may already see these ahead of time, so totally good to do it a different way. But this is one way to check it. That one also is 3x4 dimensions. Just multiply this by 3, 9. This by 3, 12. So it is a multiple of that and it has that same proportion there. Okay. And then the last one, 10 / 12. Let's just clear. So if we simplify this one down, that'll become 5 over 6. So let's get rid of that guy. Okay. Finally, what do we find? And well, what tablet prices are proportional? So this one, that price is right here. We'll highlight that. And this one, and that price is there. So finally, just click on those two. And that's all for this problem here. So these guys are ratios or proportions.
This one is an inequality. We've got a word problem. We're going to match it with one of these down here. Let's check it out. An employee makes $12 per hour and earns 3% commission on all of their sales. The employee works 37 hours this week. Which inequality shows how much money in sales X they must sell to earn more than $500 this week? We know they want to earn more than $500. So which of these symbols is correct? Let's check them out. Well, you could turn these into letters. This one here, you could turn it into a G. And that means greater than. And this one kind of looks like an L. So that one is less than. Which of these do we want? Well, we want to earn more than 500. Same thing as greater than 500. So, this one here is correct. Let's highlight that. Or the third one also correct. But this would earn them less than 500. That's no good. So, we'll get rid of the other two. Okay. Next. Do we want to multiply 37 * 12 or 37 * 3? Well, they're working 37 hours this week and they get $12 per hour. So, those are the two we want to multiply and A does that correctly. And furthermore, we do want to multiply 3 cents. Same thing as 3% time X because they get 3% of their sales and later on they say X represents the number of sales. So, definitely multiply those two. So a everything there fits and that's what we're looking for.
Whenever you're given f parentheses x like this, it's called a function. You're really just going to change this x and this x to the same number. But what is it for this problem? Well, here they tell us that x represents feet. And later on they're changing it to 7 ft. In other words, we're going to change these x's to sevens. And that's going to tell us the cost for this table. So, we're going to go ahead and do a substitution here and substitution here. But when you type it in the calculator, just make sure when you change a letter into a number, put it in parentheses just like this. And this is the full thing we're going to type to find the cost for this problem. So, let's do it. Okay, let's clear. We've got 4.5 parentheses. Got our three and then times x x changing to seven. Put it in parentheses. But notice the squared. It's going to go on the outside of the parenthesis. So we'll put the x^2 right there. Okay. Keep going. - 8 * x again changing to 7 and + 5. Close parentheses. Now that we've got that, just hit enter. And this is the final cost or the final answer. 432. And that's all we're doing for this function problem.
Okay, we've seen one of these before. This is a function, but it's a table. So, we know we're looking at a vending machine here. Once again, x is the number we press and y is what comes out. Add one number to each column of the table so that it shows a function. Do not repeat an ordered pair already in the table. Basically, you don't want to repeat an X because if you put a six here, for instance, six is already assigned to a certain item in the vending machine. So, if we put five right here, that would be a problem because you press this button, you get two different things out, and that's not consistent. The vending machine is definitely messed up. So, let's not do that. We'll get rid of those. Basically, you just want to put a new number here that hasn't been used yet. So, what could we put? Well, we could either put 10 or seven. Neither of those is an X value that's been assigned yet. Another way to say that, assign a new button to press. We'll put 10. And we'll assign anything to come out. It actually doesn't matter what you put here. You could put a new item, an old item, doesn't matter. Only thing that matters is this is a new number that didn't have an assignment. So that's all you're doing for this table. And once again, these are called determined functions.
A teaching assistant is determining how many tests they have left to grade. They can solve the inequality given here to find the number of tests X they have left to grade. Which statement describes the number of tests the teaching assistant has left to grade? Well, we have to solve this to find out which answer is correct. So, let's go ahead and grab that. To solve an inequality, you always want to get x by itself. So, right here. But let's go ahead and put a line wherever the equal sign or the inequality is. That splits it into two halves. Now, to get the x by itself, we don't want the 750. To get rid of it, you could subtract 750. And we have to do that same thing to the other side here. So let's show that because this minus this becomes zero or we say they cancel out. Then you could just drop down the minus5x on the left side. Let's do that. Drop down the greater than or equal to sign. And with the calculator 150 - 750. That'll get us in the negatives and that'll be -600. But notice we're very close to getting x by itself. It's just being multiplied by -15. We want to do the opposite and divide by -15. And we'll do that to the other side as well. Okay. The same thing divided by the same thing becomes 1 or we say it cancels. That leaves us with x by itself. then -600 / -15 using the calculator that'll give us pos40. But there's a trick here. When you divide both sides by a negative, it's going to flip the direction of this thing. So it's going to go the opposite way. Now, how do we say this phrase right here? Well, we say x is less than or equal to 40. But what is x? They tell us it's the number of tests they have left to grade. So let's say that the number of tests left to grade is less than or equal to 40. Same thing as 40 tests or fewer. So see that's saying the same thing as this statement. And that's why we solve this to find out how many they actually have left here. So once again, these are inequalities and this one a word problem inequality.
To find the coordinate of a point, a coordinate is just the location of any point on a grid. X comma Y. But to find that out, it's just like crossing the street. You're always going to look left or right first, up or down second. What do I mean by that? Well, let's practice. You're going to start in the middle. Let's go ahead and get over to this red point. We have to go left or right first. So, the first thing we're going to do, go to the right. One, two. And let's show that because it's to the right, it's positive. That's the first number or the x value. Then we're going to go down to find the y value. That's going to be -1. We'll show that. And then put them in that order. X first, y second, two to the right, down one. And that's the point there. Okay, let's reset it. We'll go to the middle. This time, let's go to the blue point. We're going to go to the left 1 2 3. So x is -3. Let's put that. Then we're going to go up two. Y is positive. So put them in that order. -3, positive2. And that's the location for that coordinate. And finally, we've got the green one. You know what to do. We'll go to the left two this time. But then down four, -2, -4. We go to the left and we go down, which is why both of these are negative. B has all those correct ones. So that's the final for this one. These are called plotting points on my website if you're looking for more practice there.
This one, we're given an equation here. It represents the cost Y per yard X of wool from a company. Which data display represents a company that has less cost per yard than this one? Well, okay. So, this equation here, we have X and Y. What do those represent? Y is the cost and X is the number of yards. Now, you could change X to anything you want. Let's make it easy. Let's change X to one. In other words, how much does one yard of wool cost? Well, plugging in one here, 14 cents * 1 that just stays 14 cents and that's y or the cost. Next, we want to find which of these below is going to have less cost per yard than this one, which is going to be 10, 11, 12 cents, for instance. Now, they give a big hint because they say cost per yard. Per in math always means to divide. So, we could find the answer by doing the cost divided by the number of yards. Same thing as cost per yard. Now, let's use the calculator. That'll give us an answer that we could easily compare to this one. Let's do it. Clear. We'll go ahead and do 16 cost per yard. And this will give us the cost per one yard. So, 16 cents. We'll add that in. Notice we're trying to find one that has less cost than this. So unfortunately it's not the first one. But let's do the same thing. We'll try B. 18 / 150. Let's do it. Cost per yard. So for one yard of wool here, it cost 12. And that's what we wanted. This one has less cost than the one that we have. So, this is going to be a better company to choose from. And it definitely fits. You could double check it for this one or for this graph. Just go straight up and over. One yard is going to cost 15 cents. Let's highlight that. But that's more not less than this one here. So, these are called compare rates. And I have a variety of these ones to practice as well.
For this graph, what is the difference in watts of power output between a solar ariance of 600 and a solar radiance of 300? Even if we're not sure what that means, just look to the graph and it's on the bottom there. Now, we're interested in 600. Let's highlight that. But what we really want to know is what is the power output, and that's on the left side. just find out how high the graph goes and then go straight over. So that one is going to be about 160 there. Okay. What about a solar radiance of 300? Let's find that. What's the power output? But coming straight across, it's right in between 40 and 80. So a good guess there is it's probably about 60. Now finally, we want to find the difference. And in math, that always means to subtract. So we'll do 160 - 60. That'll be the difference. And we get 100. So that's the final answer for this one. Just go step by step and you'll be good for any graph like that.
To solve an equation, we want to get x all by itself here. It's a little complicated because we have x's on both sides, but I'll give you a step by step here. First, just go ahead and copy this over. Next, if you ever have parentheses, you're going to have to distribute. That just means you have to multiply this number in front by what's on the inside. Let's go ahead and show that. We're going to have to do 2 * 8 and that'll give us 16. Then you're going to do 2 *x. Let's show that. Mush them together. That becomes - 2x. Then on the left side, just drop those down and drop down the equal sign. Okay, let's split our equation now. Draw the line in the middle. What's the next step? Well, now we want to get all the x's to the left. We don't want this here. How do we get rid of a minus 2x? You always want to do the opposite to get rid of something. So, we're going to do a plus 2x here. Whatever you do to one side, you have to do to the other. So, plus 2x here. Okay, let's go ahead and find out what happens on the right side. 2x - 2x is 0ero. So those ones cancel out. And on the left side 5x + 2x just add the numbers in front. That becomes 7x there. Drop down the plus 6 equals and 16. Okay. The next step we want to get the numbers to the right. We want to get this x by itself. We don't want a plus 6 there. So we want to do the opposite to get rid of it. We're going to minus six and do it to the other side. So, let's combine these. The sixes, they both cancel. And then we could just drop down the 7x on the left. The right side, 16 - 6 is 10. Now, the last step here, when there's a number in front of x, you're always going to divide it. So, here we're going to divide both sides by seven. Let's do it. Now, the same number divided by the same number is one. So those just cancel. So the final answer, you could leave it as a fraction 10 / 7 here. And that's it. That's solving an equation when you get x all by itself here. So I've got more practice with those guys if you're interested.
And you made it. Just one last one. This one's a word problem. A soda machine is having money taken out of it. Each full section of quarters is worth $15. We'll highlight that. and let's put that down here. Once again, the dimes are worth $10. We'll put that here. If there's $110 total in the machine and nine full sections of either dimes or quarters, then how much of each type are there? Well, we know the total is 110. And that's going to be the most important. So, let's go ahead and use the answers. Now, let's pretend that there's four sections of quarters. We want to multiply that times four right there. and then five sections of dimes. We're going to multiply the 10 * 5. Let's see if these guys add up to 110. Well, using the calculator, 15 * 4, that's going to be 60. And 10 * 5, that'll be 50. And 60 + 50 does give us 110. So, it was nice it was the first one. But by using the answers, we could definitely just multiply these out. See if they total up to what we're interested in there.
Here's another video if you're looking for a fulllength math practice. Check out my website for tons of practice problems for all of these types here. Let me know what questions you have, what else you want me to cover. Good luck. You got these. We'll see you in the next video. Toodles.