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Compass College Algebra Math Test Prep Part I Placement test ACT community college

Xuất bản 29/06/2016
good day students and welcome to the compass practice test, sample questions college algebra. i'm going to be going over the release questions, they are available online. so let's go ahead and take a look at question 1, there are nine questions, in this, on the release questions, i'm going to go over all of them. so number one says what is the next term in the geometric sequence 16, -4,1,-1/4? now for geometric sequences, the first, the next term differs from the other by something called the common ratio ok, so this is the general form for writing a list of geometric sequences. so generally it can be expressed as A1 and then the next one is a1 times r as a2 and then a1 times r squared and then a3 i mean a1 times r to the third, and then it goes on and on and on like that. so the whole idea behind geometric sequence is that every time you multiply by a number called the common ratio, so to go from the first term to the second term you multiply by r and then to get from the second one to the third you multiply by r, notice you keep multiplying by exactly the same thing, ok? so that is exactly what's happening here, where multiplying by the same number. ok? so from here to here i multiply by a certain number and then from negative 4 to one i need to multiply by a certain number and then the same process here and when i figure out what that number is, when i multiply negative one fourth by that number, that will tell me what the answer is, so that number is called the common ratio alright? so how do you find the common ratio? to find the common ratio all you simply do is you can divide the second term and the first term or the third term by the second term or the fourth term by the third term the general formula is simply an divided by an minus 1 so term divided by the term before it to give you the common ratio alright? so in this problem to find the common ratio i'm just going to pick this is a1, a1 is 16 and a2 is -4 so to find the common ratio, i'll, let's just use this a2 and a1, i could use a3 and a2 or a4 and a3, it doesn't matter, you get exactly the same ratio, ok? so to get your common ratio i'll divide a2 which is -4 by a1 which is 16, if you divide that out you get, reduces to -1/4. so what on earth does this mean, this means that every single time i'm multiplying by -1/4 ok? so we multiply 16 by -1/4 you get -4, when you multiply -4 by -1/4 guess what you get 1, and then when you multiply 1 by -1/4 you get -1/4 and to get the next term just simply multiply by -1/4 again, ok? so to get the answer to this problem, what i'm going to do , see i'm looking for a5, so to get a5, the fifth term or the next term, i'm just going to take a4 which is -1/4 and i'm going to multiply by what? the common ratio which is -1/4 ok? so what is -1/4 times -1/4? just multiply across, top to top 1, minus and minus is a plus, 4 times 4 is 16, so your final answer for number 1 is option c. ok? so there you have it. now let's take a look at number 2. it says a manufacturing company processes raw ore. The number of tons of refined material the company can produce during t days using Process A is A of t equals t squared plus 2t and using Process B is b of t equals 10t. the company has only 7 days to process ore and must choose the processes. What is the maximum output of refined material, in tons for this time period? so we have two processes here represented by two different processes. so the question is which of these two functions will produce the biggest output, the maximum output. So there are two approaches that we can use to solve this problem. we can use the graphical approach and compare the graphs, think about what the graphs of these two look like as they approach infinity, or we can use a numerical approach ok? so these are the functions that we get a of t and b of t, now um i'm going to use a numerical approach for this problem because it's less complicated, the graphical approach um is a little bit more evolved, i'm trying to keep it easy here so that you do well on your compass test ok? so if you can use a numerical approach anytime, it's good to just make sure that you see exactly what's going on ok? alright so what I'm going to do is I'm going to generate a table of values, and i'm going to compare the output of the values of these two, um for the seven days and see which one generates the maximum output ok? alright so lets go ahead and do it. alright so i'm going to start out with the quadratic function, to make a table of values and then complete the output value, so for the quadratic function we're going to have t column here and then um a of t equals t squared plus 2t. so we're going to start out from 1, time is unidirectional just goes positive, it doesn't go negative, so we're going to go from 1 all the way to 7. ok so let's start from 1, so from 1 it's a of 1 which is going to be 1 squared plus 2 times 1, what did i just do? I just plugged in 1 for t