Transcription
Hey guys, welcome back to Five Academy. It's Shaheer. So today we're going through 12 super repetitive ACT math problems. These problems aren't necessarily hard or easy, but they show up almost every test, especially you'll notice this as you're practicing for the exam and taking tests over and over again. So if you can make sure you get these problems right every time, then it'll give your score a few points boost, almost guaranteed. So without further ado, let's get into them.
The price of milk is four dollars a gallon. The price decreases by 24%. So what's the new price? With these, all you do is you take your original value, multiply by one plus or minus the percent expressed as a decimal, which in this case is 0.24. And if you do that, you end up getting 3.04 as your answer. Very straightforward.
Rectangular prism is 21 feet tall and has a square base with a width of eight feet. What is one quarter of the volume? So with any rectangular prism or cube problem, remember this formula: volume is equal to length times width times height. You just multiply them together. So our height we know is 21 feet because it's 21 feet tall. Width is going to be eight, and since this is a square base, the width and the length are are going to be the same value; they're both going to be 8. So if you do 8 times 8 times 21, you end up getting 1344. You divide that by 4, and you end up getting your answer of 336.
The greatest common factor of this, this, and this is what? With GCF problems, it's very straightforward. All you do is you take your numbers in the question and you divide them by each of the answer options. Whatever the greatest answer option is that gives you whole numbers for each of those division statements is going to be your answer. So you'll find that 18 divided by 3 works. 45 divided by 3 gives you a whole number as well, and 81 divided by 3 does as well. You do this for a, b, c, and you'll find that they all work, but d and e don't work; these will give you decimals. So C is your answer because it's the greatest factor.
Circle below has a center point C. The length of AC is the radius. The area of the circle is this. So what is the circumference? Remember the two formulas: area equals pi r squared and circumference equals 2 pi r. If you know one, then you know the other. And in this case, we know the area: 30.25 pi equals pi r squared. Divide both sides by pi, take the square root, you get R equals 5.5. Plug that in here, you get circumference equals 11 pi. As long as you remember these two formulas, you'll be good on any circumference or area problem.
In the standard coordinate plane, a line segment has these endpoints. What are the coordinates of the midpoint? So with midpoint, all you do is you average your x value, so 2 and 6. What's the average? It's four; it's the number right in between. And four and zero. What's the average of four and zero? What's the number right in between? It's two. So four comma two is your answer.
In what order should these be listed to be arranged in decreasing order? I recommend that you find the decimal equivalent of each of these just by plugging into your calculator and then order the decimal equivalents and then convert them back to fractions, and you'll get your answer. I plugged all these into my calculator and I got these decimals. I can clearly see this is the biggest, so this should be furthest to the left, and then the after that is going to be five over three, so that means that this has to be the answer.
What is the value of log to base 2 of 16? You can plug this into your calculator as log of 16 over log of 2, because the formula for log is log b y equals x, and that's also the same thing as log of Y divided by log of B. You should remember this. An easy way to remember is that the larger number goes in the numerator and the smaller number goes in the denominator.
According to the measurements given in the figure below, which of the following expressions gives the distance in miles from the house to the car? So for this distance relative to these values and knowing that this is a right angle, right triangle, just remember sohcahtoa, and then relative to your angle, look at which sides you're looking for. You're looking for the opposite side and you're looking for the adjacent side. These are the two known values, so opposite adjacent clearly we have to use a tan ratio. So cancel out these answer options and then plug it in. So tan 41 is equal to opposite, which I'll just call O—that looks like zero—call it x, x over 40. So you know that if you want to solve for x and multiply both sides by 40, and you end up getting 40 tan 41.
What is the product of the complex numbers here? Remember one very simple formula: I squared is equal to negative one. So if I foiled this out and if I want to take the product, I can just multiply them as such: 6i plus six. So 6i times negative 6i will give you negative 36i squared. Negative 6i times six, that's going to be minus 36i, and then positive 36i, and then finally we do six, which is just 36. So these two numbers in the middle cancel out, right? And then this I squared is really just negative one. So if I do negative 36 times negative 1, I end up getting positive 36. So my answer is going to be 36 plus 36, which is 72.
What is the 245th digit after the decimal point in the repeating decimal here? So what we notice is that this decimal is going to look like this, right? One four nine seven one four nine seven one four nine seven, and we see that every fourth digit is going to be a 7, right? The fourth, eighth, twelfth, sixteenth digits are all going to be 7. So if this number is just divisible by 4, just like these here, that means that this should be a seven, but it's not divisible by four unfortunately. But if we find a number right next to it that's divisible by 4, that means that we can track what those numbers will be. So 244, if you plug it into your calculator, is divisible by 4; it gives you 61. That means that the 244th digit is going to be a seven, so the 245th digit would just be whatever shows up right after the 7 typically, and that's a 1.
What is the difference between the median and the mean of this set of numbers? So for the mean, you just add the numbers up; you take the sum and you divide by the number of numbers, okay? For the median, you're going to have to list them all out, so it has to be in order, so it has to be negative 5, negative 3, 9, 14, 20, and you just take the number that's in the middle, so 9 is your median. Your sum divided by the number of numbers is going to be negative 8 added to 9 plus 14 plus 20 divided by 5, and you get 7. Okay, so 7 versus 9, the difference is two.
In a bulb, it's 75 percent of the balls are yellow. If you randomly pick a ball from the pit, what is the probability that the ball picked is not one of the yellow balls? Remember this formula: probability of A is going to be 1 minus probability of B. This is when you have two possibilities. So in this case, property of not yellow will just be 1 minus probability of yellow, and so you'll just get 1 minus 0.75, and that's going to be 0.25, which is A. You should also remember this formula right here that says that probability of any event or anything happening is the number of desired outcomes divided by the number of total outcomes. These two formulas together will cover you from just about any probability problem.