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 here and here, again i want to see what the output is going to be. so it’s

going to be 1 plus 2 which is 3, ok? and then 2 a of 2 and then i have 2 squared plus 2

times 2 which is 4 plus 4 and the output for 2 days, after 2 days is 8. alright so 3, a

of 3, you’re going to have 3 squared plus 2 times 3, that’s going to be 9 plus 6 and

the output for that is 15. for day 4, a of 4 is 4 squared plus 2 times 4 which is 16

plus 8 and the output is 22. 5, a of 5 is 5 squared plus 2 times 5 which is 25 plus

10 the output is 35, the reason i’m dong this is because you have to be really careful with

quadratic functions because they can change direction, um in this case the vertex is in

the negative area so we’re going to be going in the same direction, but you never know,

if you don’t know what the graph looks like you can’t make assumptions as to what the

pattern, the direction of the change in magnitude is. so let’s finish this up, A of 6 you’re

going to have 6 squared plus 2 times 6 which is 36 plus 12, the output after 6 days is

48 and then for 7, you have a of 7, just input 7 into your function and you have 7 squared

plus 2 times 7 which equals 49 plus 14 and the answer is 63 ok? so you can see that the

output is increasing and the maximum output using this process A is 63 after seven days.

So the second process is a linear process, it’s much easier to generate a table of values,

this one you can just simply plug in 7 since it’s unidirectional, i just want to show you

the pattern ok? so for b of t is 10 t, because if you notice that’s what it says here, b

of t equals 10t so that’s what i’m using alright? so we’re going to start from 1 , this one

you just simply multiply by 10, so b of 1 is 10 times 1 which is 10. And then for 2

b of 2 is 10 times 2 which is 20. And the pattern continues, b of 3 is 10 times 3 which

is 30. And then b of 4 output after 4 days is 40. 5 days, output after 5 days is 50,

6 output after 6 days is 60. and 7 output after 7 days is 70 ok? so I just wanted, you

to see the comparison here, alright? compare them you can see that for these two the outputs

keep increasing, the biggest output for the process A is 63 and the biggest output for

process B is 70 so the winner here is process B at the maximum output after 7 days, up to

7 days is 70 and the answer is E ok? Alright so let’s move on to question number 3, it

says for the 2 functions, f of x and g of x, tables of values are shown below. What

is the value of g of f of 3? ok so g of f of 3 just means that, the value gets inputted

into a function, and then the value of that function gets inputted into another function

alright? so basically starting with x and then um x is inputted into the function f

and when you plug in x into f you end up with f of x. and then f of x gets inputted into

another function, g and then your final output is going to be g of f of x ok? so we’re just

going to do this step wise first thing you take our input plug it into the first function

to get our first output. and what ever output we generate we’ll plug it into our second

function to get our final result which is g of f of 3 ok? alright so let’s go ahead

and do it, so we’re going to start with x, x is um what is x? the innermost value which

is 3, that’s what x is, x is 3 ok? so we got to first of all look for f of 3, so you gotta

use the table that relates, f and x, this is the table that’s going to make this connection

right here, so we look for 3, there goes 3 in the x what is the output, the output for

3 is 2 so f of 3 is 2 ok? so now we know that from 3, this function has taken us to the

value of 2 now we’re going to use this, this 2 now becomes an input ok? and that becomes

our new x so this will be inputted into g to get what the output is, so now we’re going

to look for the chart that relates an input for the function g, so now we’re going to

look for g of f of 3 ok? but wait a minute though, what is f of 3? f of 3 is 2 so what

we’re looking for in essence is g of, let me put it in blue, g of 2 ok? so g of 2 we’re

going to look for an input under x an g table and see what the output is when the input

is 2, so there you have it right here so when x is 2 what is the output? the output is -3

alright so g of 2 is -3. so there goes your final answer, your final answer for number

3 is B ok? alright let’s go ahead and move on to question number 4. Question 4 says for

positive real numbers x,y, and z, which of the following expressions is equivalent to

x to the 1/2 y to the 2/3 and z to the 5/6. now if you look at this um we need to make

all the denominators the same so that we can have a common root. then we extract that root,

so in order to make all the denominators the same we need to take a step back to middle

school and remember the whole idea of lowest common denominator, alright? so the question

is what is the lowest common denominator of 2, the first denominator, 3 the second denominator

and 6. the LCD of all this, of these three numbers is 6 ok? so the goal is to make all

the denominators have the same number, namely the lowest common denominator, make them the

lowest common denominator and then we’re going to extract it and that will be our common

root ok? so let’s do it, so we have x to the 1/2, i need this to be 6, so what do i multiply

it by? i times it by 3, top and bottom, and then for the y component, y to the 2/3 i need

this to be 6 so i multiply it by 2 top and bottom. and then for z 5/6 i need this to

be 6 on the bottom, it’s already 6 so i multiply it by 1 or i could just leave it alone, it

makes no difference alright? so now this becomes, x to the 3/6 y to the 4/6 and z to the 5/6,

ok so this is exactly what we want. We want all of the denominators to be identical and

that’s the case here. so since we have out identical denominator watch this, i’m going

to use the properties of exponents to extract the denominator from all these um three powers

here, so we’re gonna have x to the third, y to the fourth, z to the fifth, factoring

out the denominator equals 1/6 ok? because notice if I distribute 1/6 to all these 3

numbers what am I going to get? i’m going to end up with this, ok so I might as well

just factor it out, so remember the rule that x to the 1 over n equals the nth root of x

ok? this is the root. alright and the numerator is the power, the power here is 1 so it’s

inconsequential. so i’m going to express this using 6 as the root so we’re going to have,

this going to be counted 6 root of x to the 3rd, y to the 4th and z to the 5th ok? so

what answer is that? 3,4,5 the answer is D. alright, now let’s move on to question number

5 this involves operation of matrices, this is a subtraction. so um this question might

look easy but you have to be really careful when you’re carrying out your arithmetic on

the different uh elements in the matrix ok? the different cells in the matrix ok? in this

case you have a subtraction and you also have negative numbers, so you have to be careful

when resolving the signs alright? so i’m going to set it up, A minus B like this, this is

matrix A on the left and matrix B is on the right, you must preserve the order whenever

you carry any operations with matrices because it’s very sensitive to order, matrices are

very sensitive to order of operations ok? Alright so to do that we’re going to be subtracting

B from matrix A so, preserve the order of the elements, we’re going to go 2 minus , don’t

forget that sign there that’s a trap, negative 2 for the first column, first row. first row

second column we’re going to have negative 4 minus 4 ok that completes my first row.

Second row first column we’re going to have 6, minus negative 6 and then for our second

row second column we’re going to have zero minus zero. Now let’s use our arithmetic skills

to finish this off. these two are minuses when you subtract a minus and minus you multiply

the signs so they become plus, so 2 plus 2 is 4, minus 4, minus 4 is negative 8, 6 minus

6, these are two minuses you multiply to be a plus, 6 plus 6 is 12, 0 minus 0 is 0. so

you have 4 negative 8, 12 and 0, answer is option E ok? So thanks so much for paying

attention to this presentation. Please subscribe to my channel for the second part of this

video series and for updates on other cool math videos and you can also feel free to

make requests for math videos on my youtube page. For more videos you can go to mathgotserved.com.

Thanks again and have a wonderful day.

didn't help at all:(

Sorry about that 🙁

You have a good approach to solving problems. You're amazing the way you read the problems and already know and understand so much about what has to be done to solve it. You're brevity(shortcuts) at solving these types of problems is brilliant and very helpful. Thanks so much for your time and for sharing.

You are very welcome. Thanks

i am going to pass my compass test next tuesday because of your videos thank you so much

Thank you so much!!!! You made it so much easier for me to understand this stuff for my compass test :))

You are very welcome 😀

You are welcome. Glad I could help 😀

Ur way of explaining is kind of complicated. I already solve all the problems for my compass test. But thanks anuways

thats great!

hey, did this video end up helping you pass your compass test? I'm going to take it in a few days and am just wondering how much this helped you pass?

did you pass the compass tests? or was the test very different from this?

For number 2 couldn't you just pick E (70) since 70 is the biggest number (output value)?

Thanks, this just made it look easy

You are very welcome!

16+8=22 lol XD

xD

Thank you for the help! Great teacher!

You are very welcome

You were a lot of help, Great Teacher Onizuka. I mean…Great teacher Gotserved.

Oh thanks lol

dude your a boss thank you for your help, a real life saver

Omg THANK YOU SO MUCH, I really needed a review since I'm going to take the test on Monday and for my last year of high school I did not take any math course, you are a LIFE SAVER

Thanks boss 😀

You are welcome! Glad I could help 😀

Thanks for the help. Was very anxious about the placement test. This helped a lot

You are welcome!

Thank you so much I thought I could not learn this. I am ready for my placement test thanks to you.

You are very welcome 😀

Very helpful but I have a question for problem 3 the formular that you used to work out the problem g(f(3)) if I had another problem like number 3 do I always used that formular? If possible can you do another video showing a different example? You videos are very helpful.

Hi for number 5 why did you change the signs from – to + but did not do so in the second column -4 -4 stayed the same.

Thank you so much for this…… i have the test today so lets see what happens 😀

You are welcome

im sooo confused with number 3

for the second problem you did you had 22 as an number when it was supposed to be 24 still it made no big difference to the math problem but still consider to be a mistake.thanks for the help anyway.

16+8 = 24 not 22

Im re-taking the math part next week and i was wondering if you know any websites where i can print or get sample problems to help me for the compass test

@Maths gotserved

16+8 is 24

very useful video. thank you so much!!

Oh thank you so much. You are a wonderful person 😀

You are very welcome!

you have great teaching skills. thank you so much

I am so grateful for these videos!!

Thanks A LOT 🙂

very helpful. thank you

I hope I pass my math test tomorrow, I've been watching a lot of these videos !

Thanks

One thing to note about the COMPASS is that when you go in, choose the highest level you feel most comfortable doing. If you feel OK on college algebra, choose college algebra. This will more accurately place you. As an example, the first time I took the COMPASS I chose algebra, and was placed into college algebra; on a retake, I chose college algebra and placed into pre-calc II.

Wow this is very helpful

I'm an high school student and I'm taking college classes at the same time I placed in college math 175!!!

For the second problem, wouldn't it be easier just to plug in 7 for both of the equations and see which one yields a higher number?

16+8=22 is wrong is 24 in 7:33 a miner detail but still I did find that. By the way Good video it did help me thanks.

thanks to you i passed my math placement test today 🙂

Thank you so much! ❤️

U there? Is college algebra different from regular algebra cause this looks harder

How come for #2 you went through all the numbers 1-7? How come you cant just do times 7 and see the final result?

thank you so much

Man you are such an awesome teacher your explaining is excellent and very clear steps. I wish you were my teacher in high school. You deserve another sub!

I have a TSI test I hope I pass I have watch a lot of these

SO WHAT HAPPEN TO QUESTION #8

#4 I don't get why the "power" is "1"..

You are amazing. You just made this make sense for me. THANK YOUUUUUUU!

it's been 3 years since i did a math problem lol I am going back to school and have to take an assessment test and thanks to you, i think i'm ready! 🙂

thanks bro.

Thank You! 😀

jesus sent me here

3:30 in the morning….after "looking" at about 7different math prep books for 4 months, it popped in my head to find your channel. You're going to help me get where I gotta go. Thank you…..

I have a placement test tomorrow…

thank you!!!

Got 100% on this and I'm in middle school 😂

I just wish I had youtube when I was in middle school and high school…I would have done so much better! Today if your teacher doesn't explain it right for you, you can just come home to youtube and find it here where people make it simple! Using this for my COMPASS to get back into nursing school….nursing math is actually much easier than algebra!

Invaluable revision . Thank you sir .

why is math sooo boring

I had no idea what College Algebra was about until you showed me. Been out of high school for 12 years and this kind of math blew my mind. Im grateful that you shared all of the videos for the math portion of this test. Now I can go back over with ease.

This helped me so much thank you

used to take calculus my junior year in HS, graduated and been working for 4 years going for a long grind for software engineering, forgot all the basic material and just needed a refresher.

You explained it all so well, pretty much remembered everything, understood the concept and etc just from looking at this, good old middleschool lol…

Thanks!

Thumbs Up! Very Helpful. I forgot I knew this stuff!:)

I learned more in these few minutes than i ever did from my teachers xD wow. Thank you so much!

Why do we have to take placement tests anyway? Was 4 years of high school not enough?

On #2 why don't you put rewrite the problems like A(7)=7^2+2(7) and B(7)=10(7) then solve for A or B?

what is the average score to get on algebra compass?

Will this help me study for my CUNY placement test?

complicated but I'm learning

will this help me study for the cuny math test???????

Not even 2 minutes in and I am confused

13:49 How is it 6?????????????????????????????????????

Thank you!

your videos have really helped om studying for my compass test for lpn and i have alot of confidence that ill do great

Got my test in 2 hours pls pray

I'm 11 and I guessed and got #1 right

Dude looking in minute 8 since when is 16 + 8 is 22?

I got a 80 in Pre-Algebra and 34 in Algebra. But because of my Pre-Algebra score I was able to place out of remedial Math and into Mat101.

My college has the same placement test and for #1 it says the correct answer is D. I'm super confused on how 1/8 is the answer so I looked up this video, to confuse me even more to see he also got 1/16. Is my college's test answers wrong??

This Was Great!!

This person is talking too fast and his speech is unclear. He needs to slow down and speak more clearly. I can't understand a word he's saying. This was no help at all.

I'm having my entrance test for the biggest college in my country… This helped refreshing my mind.

People like you are what we need to make this world a better place 📚🙏🏼

Can somebody please explain number three to me like I'm five? I thought the answer was -1…? And I don't quite understand his process

I have to take the Compass test tomorrow and this was a really good refresher. Thank you!

Confusing asf