PERT Math Diagnostic Test Walkthrough Part 1

Hey guys, welcome back to Super math for you. This is Mr. and today we're working on PERT exam. am the Valencia's website for the PERT. I'm only leaving link in the description. I'm going to scroll down because there's something specific that want to work on today. please visit all this practice. I'm going to go to math review guide. Here I'm going to go to modules on the left side and under modules I'm going to go to diagnostic test. There you go. That diagnostic test is done on software that is called math AAS. Right now went through because already logged in. you guys there's directions for you too how to open that if you want to practice this. Now downloaded this on Goodnotes. So we're going to work on it here. PERT diagnostic test. Let's go. My first question is -3 + 4. So when I'm adding or subtracting two numbers with different sign okay, what do is subtract the big number minus the small number. 4 - 3 is 1. And then keep the sign of the bigger number because the four is bigger then my answer is going to be positive. Number two, am dividing 24 / -4. If there's no sign on the 24 that means it's positive. The rules of signs are the following. When every every time you're multiplying or dividing two signs that have the same sign, two positives give you positive, two negatives give you positive. If they have different sign, your answer will be negative. This is multiplying or dividing, okay? So my answer here positive divided by negative is going to give me negative and 24 divided by four gives me six. Make sure you practice these rules. Next problem. You notice put in my screenshot the directions. Please always read the directions. See what they want you to do. They're asking me to write this as an improper fraction. How can do that? To write an improper fraction, what you do is you get the whole number times the denominator. That's going to give you 15. And then to this answer, you add the numerator. 5 15 + 4 is going to give you 19, and then you keep the same denominator. So now this is my improper fraction. Number four, they're asking me to add 1/3 + 1/4. Again, here are the tools, right? click on this area and right away they're going to open up. Now the first thing that need to do is need to get the same denominator. Every time I'm adding or subtracting two fractions, need the same denominator. The easiest way how to do this is by multiplying the two denominators. 3 * 4 is going to give me 12. And what's going to happen is I'm going to find out by what number do need to multiply each of these numbers that gives me 12. In this case, 3 * 4 gives me 12. If multiply my denominator by four, need to multiply my numerator by four. So 4 * 1 is going to give me four, and then 4 * 3 is going to give me 12. Same idea on the other side. By what number do need to multiply the four to give me 12? Times three. If do on the bottom, do on the top. 1 * 3 is going to give me three, 4 * 3 is going to give me 12. Once have the same denominator, keep denominator. Again, this is when adding or subtracting. And then solve whatever have here. In this case it's an addition, so 4 + 3 is 7, and this is the answer for that. Okay? Adding fractions. Multiply. Multiply is much easier, okay? Because when you're multiplying two fractions, basically is you multiply across. Top with top and bottom with bottom. Okay? 13 * 5 is going to give you 65. And 14 * 12, have no idea. So, let's do it on the side. All right. 2 * 4 gives you 8. 2 * 1 gives you 2. And then, 1 * 4 gives you 4 and 1 * 1 gives you 1. If you notice, skip position. Normally, what you do is in your second lane, when I'm multiplying the 1, my first here add zero. And then, start multiplying. 1 * 4 gives me 4. And then, 1 * 1 gives me 1. Once have that, let me put it on the side. 28 and have 140, right? 8 + 0 is 8. This is going to give me 6 and this is going to be 1. So, 14 * 12 is going to give me 168. Okay? Please always read the directions. Enter reduced fraction or integer, not mixed numbers. need to make sure that this is reduced, simplified. So, you need to find out if can simplify this fraction. And you always do is you try to divide by two on the top, by two on the bottom. If that doesn't work, what about three? What about five? You try all the prime numbers. Okay? An easy way how to do this is the following. When you're multiplying two fractions, okay? You see if can reduce number from the top with number from the bottom. Okay? Let's pretend, just pretending, that instead of 13, let's pretend that had an 18. Okay? And have to do the same product again. Now, before doing all this, want to know if can reduce the number from the top and from the bottom. Meaning, mean, do mean by that? Can divide by two the top and by two in the bottom? That means simplifying or reducing. yes, can divide this by two. If divide this by two, it's going to give me nine. And if divide by two on the bottom, it's going to give me seven. But now this fraction is simplified. And these numbers are way easier to multiply. Okay, so this is something that you can do when you multiply fractions. And I'm saying all this just in case you're not allowed to use calculator. Okay? All right. I'm subtracting 9.26 minus 5.31. You see that there's no more decimals. So, what do is cover the empty spaces with zeros. And now do one at time. 6 minus 0 gives me 6. 2 minus 1 gives you 1. 5 minus 3 gives you 2. Period. 9 minus 5 gives you 4. All right. This was the little trick that you have to add zero for position right there. And now we're dividing. We're dividing 372 divided by 6. So, decimal divided by whole number. If you do this in calculator, this is simple. If you do this by hand, it's not as simple. So, to get rid of this decimal point, what you do is you count how many decimal places you have here. You have two decimal places. Therefore, what I'm going to do is I'm going to add the same amount of decimal places, two decimal places, add two zeros on the bottom. And now this number becomes 372 because moved the decimal place once and twice. That's why added the two zeros for every single one place that moved. And now have 372 divided by 600. Let's pretend that you have to do this by hand. Okay? So, long division. So, I'm going to do 372 divided by 600. How do you start? You say, "How many times does the 600 inside the 372?" As you notice, 600 is bigger than 372, so there's none. So, you write none. How do you write none? Zero. It's not there. You put period. Once you do this, the whole idea is to keep working on the division, so you add zero to this number. And use that again. Is the 600 inside the 3,720? Yes. Six inside the three? No. Six inside the 37? Yes, six times. So, I'm going to try six times and see how it goes. Now, I'm going to multiply back. You start 6 * 0, which is zero. 6 * 0, which is zero. 6 * 6 is 36. And now we subtract. 0 - 0, 2 - 0, 7 - 6 is 1, 3 - 3 is 0. And now have this is my answer. If want to keep going, then keep adding zeros because now I'm working with decimal place. All right? If need to keep going, add more zeros and start dividing again. How many times is the 600 into the 1,200? You notice the six goes into 12 twice, so say twice, okay? And I'm going to multiply back. 2 * 0 is 0. 2 * 0 is 0. 2 * 6 is 12. 12. You subtract 1,200 - 1,200, you get zero. And now my final answer here is going to be .62. If you have to do this by hand, so we just review long division. Let's go next. Here now we have in some kind of subtraction and as we notice, we have an absolute value. Look at this thing. We have an absolute value line, okay? So, the absolute value it becomes like grouping symbol. But inside the grouping symbol, there's another parenthesis, so we got to work here inside the parenthesis. So, let's do this one step at time. So, once have this, this are the absolute value. Okay, but within the absolute value, have parenthesis, so need to work on this. So, I'm going to do 8 - 7 is going to give me 1. So, I'm going to keep everything else. 9 - absolute value 9 - 2, and this parenthesis becomes 1. Okay, and keep going. Close - 1. I'm going to do one step at time. Now, have to multiply this 2 * 1 because right now what we're doing is we're following PEMDAS within this absolute value. Right? We follow PEMDAS within this absolute value. We did parenthesis, and now we did parenthesis, and I'm going to do multiplication. So, have 12 - absolute value 9. Now, 2 * 1 is going to give me 2. All right? Within Now, I'm going to do this subtraction because I'm still inside the absolute value. have 12 - absolute value 9 - 2 gives me 7 absolute value - 1. still have to solve the absolute value to keep going on the outside. So, now have 12 - absolute value 7. Absolute value of any number is always positive value. So, absolute value of 7 gives me 7. This negative stays on the outside. Keep that in mind. And now just complete that. do 12 - 7 is going to give me 5 - 1 is going to give me 4. Okay, so my answer is going to be 4. Let's go next. Now, we have word problem. Okay, they're saying garden 35 by 30. How many feet of fence are needed to enclose it? So, they're giving me only two dimensions for the garden, so I'm assuming it's some kind of rectangle. Okay? Let's just pretend that those are straight lines. And one side is 30 ft, and the other one is 30. I'm sorry, 35 and 30 ft. How many feet of fence fence fence means fence is all around it. It's not area, it's perimeter. Okay, that's my fence. So, if go back, know that if this is 35, this side is 35. If this is 30, then this side is 30. Okay? Because rectangle, opposite sides are congruent. All right, those little marks. And now if I'm doing the perimeter, all the fence around it, just need to add 30 + 35 + 30 + 25. Okay? 30 and 30 60. 35 and 35 is 70. And that's equal to 130. So, in this case it's 130 ft. Okay? Let's go next. Question 10. The table below shows student quiz on six quizzes. Find the median. Okay. The median is the middle number, but need to see if all these values are organized. need to organize those values. The smallest one is eight. Next one is nine. Next one is 10. Next one is 13. Next one 14. Next one is 18. So, the first thing is need to organize the data. All right, organize. Now they're asking me for the median. Median is the middle number. Okay? But let me see how many values have. 1 2 3 4 5 and 6. If had seven number here, you know, another value, then the median would be the middle value. But because this is even number of values, which is six, my median is going to be the average of the middle two. All right? The median is the mean of the middle two. Mean is average. So, got to do the average of those two. So, do 10 + 13 / 2. That's what average means. 23 / 2 and it's going to give me 11.5. So, that's my median. Let's pretend we're done with the problem. Let's pretend that by any chance we had different value. Let's pretend that we had 20. And now, let's pretend that this is different problem, okay? Different problem, and they're asking me for the same thing. So, organize my data. All right, count how many values have. 1 2 3 4 5 6 and 7. have seven values. And because they're asking me for the mean median, then the median is the middle value. If have seven, the value number four is the median. So, in this new problem, my median will be number 13, okay? All right. Next one. Now, they're asking me perform the subtraction. Okay, and they give me two polynomials. Let's do that. Every time Every time they're adding or subtracting, okay, and what do is the idea in these polynomials is to get rid of those parentheses, okay? Now, because this parenthesis has minus in front of it, then this negative is going to affect each one of them. have to distribute though that negative. My first parenthesis stays the same, and now negative negative is going to become positive 10 5. Negative and positive is going to come become negative 7 squared, and negative and negative is going to become positive. These are the rules that we did in the previous problem, so keep that in mind. Once solve all, and now have there's no parenthesis, what do is I'm going to combine like terms. And start with the exponent, highest exponent. have five here, and have five there. So, I'm going to combine this with this, and that's going to give me 19 to the fifth power, and already used those two. Next value, squared with squared. So, it's going to be -7 -7. Does not zero. -7 -7 is -14. When they have the same sign, you add the numbers, seven and seven, and then you keep the sign. And that's how you got -14 squared. Every time you're combining like terms, keep the same variable with the the exponent. fifth, fifth. When I'm combining like terms, keep them. And used this already and used this already. The last value that I'm going to use is the there's no on the eight. So, I'm going to bring down minus 9X, right? Because this has no no no other like terms. And the last value that haven't used is the eight. have zero of eight. And this is the answer that you have to type in. Again, screenshot all the directions and here are the tools that you're going to use. All right? There's basic functions and trig. Play around with those. Next. Now they're asking me to multiply two binomials. So, when I'm multiplying, okay, got to multiply times the first value and times the second value. And then use the five times the first value and five to the second value. This is called foil. Okay? That's the process that I'm going to do. Let's start. times 3X is going to give me 3X squared. How come? Don't forget that the has one as an exponent and one as an exponent. And if there's no number in front, you have one. So, 1 times 3 gives you 3. to the first times to the first is to the second. You add the exponent. Next is 1X times 3. 1 times 3 is 3 and you bring down the And now go with the -5. -5 times 3X is going to give me negative 15X. And -5 times positive 3, negative positive gives me negative. 5 times 3 is 15. Once you multiply, you see you can combine like terms. Most of the times, the middle values are like terms. Okay? So, you keep the same first term. And now 3X minus 15, 3 minus 15, you different signs, so you subtract. 15 minus 3 gives me 12 and keep the sign of the bigger number. The 15 is bigger and is negative, therefore keep the negative. Last number least, bring the constant. There's nothing else to combine it and this is my answer. Okay, I'm reviewing lot of basic topics, you know, with this diagnostic test. Next, now have this division, okay? But because there's only one term on the on the bottom, then you don't have to do long division. just can simplify. What's going to happen is that this term on the bottom is going to divide every single term on the top. Okay? So, I'm going to simplify this with this and then the middle one with this and then the last one with this. Let's start from the beginning. -12 / 3 is going to give me -4. ^ 7 / ^ 3, keep the same variable and subtract the exponents. 7 - 3 gives me 4. Next, positive divided by positive 9 divided by positive 3 is going to give me positive 3. ^ 4 / ^ 3, keep the same variable, subtract 4 - 3 and that's going to give me 1. Last, 6 / 3 is positive 2. ^ 3 / ^ 3, because they have the same variable, same exponent, they cancel out. ^ 3 / ^ 3, they cancel out and you don't have to write anything. Now, we're working with exponents. Okay, so we're working with the exponents, have parenthesis here. There's an exponent on the outside, so that's the first thing you want to do. After that, I'm going to have bunch of negative exponents, all right? There's two choices. One of them is just to flip the negative exponents or we multiply. Let's Let's get rid of this exponent first. ^ 1 times, now this exponent multiplies the exponents on both on the inside. So, I'm going to have 2 * -2 is going to give me -4. And then the is going to give me 2 * -1 is going to be -2 and I'm going to write everything else the same. 8 * cube * 4. All right. Something that suggest, because there's lot of people that are going to get confused with this, is flip the negative exponents. All right? So, on the top, you flip only whoever has the negative exponent. The to the first stays the same. The goes down. Because it has negative exponent, so you flip it and it goes down. The it goes down. This it went down because it has negative exponent. All right? Now, I'm going to go on the bottom and I'm going to write whatever is on the bottom. If you notice the bottom, forgot this on the on the this has negative exponent. So, this has positive exponent, this has positive exponent, so that stays the same. 8 cube and all of them are multiplying. So, and this because it has negative exponent, goes to the top. All right? So, think this is an easy way how to do this thing. And make it line over here and let me get working on the bottom. Okay. So, let's multiply on the top. You have to the first, to the fourth stays the same. On the bottom, you can multiply those Ys. keep the to the 8 and then third times to the fourth, when you multiply these two Ys, when you multiply, you add the exponents. All right? So, that's going to give me to the 7 and I'll bring down to the second. Okay. My last step is divide. All right, let's divide. When you divide, you subtract the exponents of the same variables. with right? Subtract the exponents. And that's going to give you 1 - 8 is going to give you -7. Then the is on the bottom, there's no other on the top, so stays on the bottom. And then the Zs, you have what? to the fourth, to the second, you subtract that and that's going to give you to the second. 4 minus 2 is 2. One more thing, if you notice there's fraction line. Every time you're dividing, whatever answer you get, it goes on the top. You notice that divided the X's, my answer's on the top. divided the Z's, my answer's on top. The only thing that put on the denominator was the because the was in the denominator. All right, keep that in mind. As my final answer, I'm not allowed to have any negative exponents. So, any negative exponents at the end, have to flip them. Everything else stays the same. So, the is going to go down, the is on the top and the is on the bottom. And that should be my final answer. Next, I'm going to stop here because these questions now are factoring and there's bunch of questions in unit 2 15. So, because of the factoring, want to do this together. So, I'm going to stop here and the second part of the this review diagnostic test is coming next. Please make sure you check the playlist. All right, if you're doing you're studying for the pert, you need to study this playlist. All right, it's right here. Click on it. Take care and I'll see you next one. Make sure you subscribe. Bye.