alright guys today we’re doing something

really special we’re doing the New York State Algebra one Regents from January

2019 that just occurred a couple days ago. my name is Juan tutors. my goal is to

get you the highest rate on the ACT so that you can get into the College

of your choice and the career you deserve. now you might be wondering this

is the algebra one Regents from New York State Why are we doing this for the ACT? is one of the biggest states in the

country so the ACT builds its curriculum largely

on on what the bigger states do with Texas Florida California and of course

New York so a lot of what’s on the ACT actually comes from New York as a bonus

for you guys watching this video in the description below have some really

exciting content I have three practice tests for the New York State Algebra 1

Regents a baseline a midterm and a final with a student ready solution set so

that if you do the testing you want to grade it you can actually grade it on

your own and also it gives you resources where to go for each individual problem

if you have trouble on any individual problems this is definitely for you and it’s

a super low price and I’m really excited about something else

ready this t-shirt I’ve never sold a t-shirt that got so much traction

compared to this t-shirt everyone who sees this shirt loves it you see it’s

actually it’s not just a pie it’s actually the digits of pi 3.14159 on the

first 500 digits of pi on this t-shirt and you can get it for a

super low price the link is also in the description below if you bought that

you’d be supporting my site I use that itself to get better technology and make

better videos if you want to support me definitely go get that t-shirt you know

Pi Bay is coming up March 14th it’s almost here so that’s another good

reason and if you want to support me by supporting yourself definitely get the

elgible one baseline the midterm and the final and there might be a little

surprise there for you too let’s get started my name Juan Tutors

school name JuanTutors.com or JuanTutors on YouTube problem one they

love asking questions about scatterplot so pay attention the scatterplot below

shows the relationship between the number of members in a family and the

amount of a family’s weekly grocery bill so what I’m looking at the chart I see a

general upward trend it looks kind of like this good I see the numbers grocery

billion dollars 100 to 600 number of family members 1 to 9 I always read the

labels and I do a quick cursory glance at the graph I know I’m gonna have to go

back to look at the graph again that’s why I do a quick glance so then I go on

with the rest of the problem the most appropriate prediction of the grocery

bill for a family that consists of six members is $100 $300 or $400 or $500 so

let’s look at this problem it’s asking for the most appropriate prediction for

the grocery bill for a family that consists of six members so I have used

the grocery bill and here’s the number of family members I see that these

answers are actually quite far away from each other when they ask you

multiple-choice questions on quick scatterplot problem the numbers have to

be far apart because you see that line that I made that general trend line it

kind of cuts through the middle of the data have two points approximately on

the table below in fact that could even improve it a little bit but the truth is

that there’s so much variation your estimate of your trendline that

that they can put the numbers close to each other the only there’s only gonna

be one answer that makes sense in the multiple choice so we go to six family

members we go up to that the backs writing line that we drew this is how to

draw do every trendline problem draw a really quick trendline so we go up to

that a quick trend line that we drew that is the point and then we call a saw

I have 6 family members and then we go to the right to figure out how much that

cost you thought might have been so for me it’s between two hundred three

hundred dollars so whichever is closest to that is gonna be my answer and it

looks to be three hundred so definitely not way too far away you might feel a little bit iffy because

250 it’s like almost in between 100 and 300 but it is costly hundred that’s one

point the second point is if you don’t like the answer this is close enough

don’t fudge the line so that it fits 300 because you want it to be fit 300 just redo the line let me pick a new color sorry for the we’ve

jumped in the screen I see that there’s fewer points on bottom

top so I’m going to actually move the line up a little bit and then I’m gonna

draw the line up so the right line now and in fact this is closer for the 300

for me so I’m extremely confident now but the answer is definitely 300 the

answer is definitely 300 numero dos number two the function g(x) is defined as G

of X is equal to -2x ^ 2 + 3x the value of G of -3 is

-27 -927 or 45 let me tell you the point of this problem it’s

literally it’s number two it’s really meant to see if you know how to do some

of the easy problems it separates you if you’re a struggling student from Steve

don’t struggle so much and vice-versa if you don’t struggle at all it separates

you from from students who struggle a little bit and how does it separate you

one you have to know what a function is and to even have to know how to

substitute a number into a function and three you have to know your order of

operations and four you have to know how to work with negative numbers so you

have to do all of those things so that’s how I’m gonna do the problem you can do

this one on the calculator by putting missing y=putting this function

to y=and then plugging into the number -3 in your graph but

I’m gonna do this algebraic way because I do need to point out all the little

details that they want so the g(x) means that G is the function which takes

excellent does all this crazy stuff to it so G of -3 means okay

-2 * -3 X is -3 ^ 2 + 3 * negative

3 is now the next step do you know how to square negative numbers and multiply

negative numbers and use your order of operations yes PEMDAS, spelled GEMDAS. G for grouping symbols symbols include all parentheses and all

other things that food things separately exponents then multiplication divisions

an addition and subtraction and I’m gonna hold this strictly I know some of

you know some gesture to go quicker but if you don’t don’t trick yourself into

believing you’re going quicker and messing up an accident where did it go

there’s no those parentheses but there’s nothing to do in the parentheses so

there’s no more parentheses no grouping symbols we go to exponents (-3)^2 we know that’s how to square we multiply a number by itself

most students get that if they got this wrong they say -3 ^ 2 is

-9 it’s not it’s nine a negative ^ 2 is positive learned

that as a rule it’s a law (-2)(9)+(3)(-3) no more exponents so I’m noticeable obeying these rules of operations strictly then multiplication and division whatever

happens first this multiplication here this multiplication here let’s do those

-2*9=-18 + and I well we could actually do

this multiplication now since its saturated so 3*-3

gives -9 okay and now adding negative numbers all the other part

words to get this wrong they get to this point then they say -18 +

-9=-9 because they subtracted 9 but they didn’t they didn’t

subtract nothing I did nine can -18 on the number

line is to the left of 0 so if you go to -9you’re actually

going to the right so you’re adding 9 okay so on this side -8eenth

here’s 0, -18 + 9 goes this way – nine goes that way

so -20 -18 + negative 9 is actually -27 we move to the

left when we subtract so it’s -27 here we go number three which

expression results in a rational number hmm sqrt(121)- sqrt(21), sqrt(25)*sqrt(50), sqrt(36)/sqrt(225) sqrt(225) / okay and number 4

3 radical 5 + 2 radical 5 so just fair warning I was doing this video for

number 3 in a different way I was using the calculator and they gave me the

wrong answer and the calculator was wrong this is an interesting case of the

software having a button and I’m gonna post a video later on I already recorded

the video I’m opposed to video later on about me and countering that bug but for

now I’m gonna do the so first you do need to know and they’re testing you to

see do you know what irrational numbers yes or no and do you like are you sure

so here’s one good a definition on rational number is a number that can be

written as a ratio of two integers yes they have to be positive or negative

whole numbers the denominator can’t be 0 you know that because dividing by

0 is undefined so that’s it so one of these can be written as a ratio of two

integers so let’s see what we can do number one right sqrt(121) – sqrt(21) so

a lot of students don’t get tricked by this one and combined sqrt(121) -sqrt(21) is rational done no false that’s why they put these numbers here you have to

know that radicals don’t obey the distributive property over subtraction

the distributive property is a property of multiplication over addition or

subtraction multiplication over addition or subtraction not every operation

radicals don’t distribute over subtraction so this number is actually

equal to sqrt(121) does simplify it’s 11 – sqrt(21) 21

is not a perfect square okay so that this means that this is a

rational number 11 – an irrational number which it makes it irrational a

rational number + an irrational number is irrational because the number

that can be converted into a fraction times a number that can’t plot – a

number that can’t there’s no way to combine to make the second number into a

fraction to the bottom so that’s so number two right 25 * radical

this is the one where the calculator actually give me the wrong answer right

at 25 is five * now radical 50 has a very large perfect square factor radical

25 * radical 2 so 25 * 2 is 50 so radical 50 is right for $25 radical 2

you might notice I used a distributive property type thing the radical does

distribute over multiplication if you have multiplication only okay it does

not distribute over addition the radical does not ship it over subtraction the

radical does distribute over multiplication and the radical does

distribute over division okay it’s because it’s an exponent okay so now

this is five * right out to me five is five * right – okay and – five

times five is 25 right – now this is a rational number * an irrational

number so this is irrational why because if you have a number that can be

written as a fraction or another number that can’t do we multiply fractions by

multiplying horizontally multiply the numerators and multiply the denominators

so if this number was rational it would mean that that the irrational number was

also rational and that’s not a thing a number either can be written as a ratio

of two integers or it can’t right let’s go to number three and so let’s cross

these out soon number three okay so number 3 says radical 36 /

radical 225 this one actually simplifies here quite

nicely radical 36 is 6 / 225 if you go to your calculator if you don’t

trust me to 225 is a perfect square 225 square rooted is 15 okay so this is 6

/ 6 15 also known as 6/15 this whole this sure looks like a ratio

of two integers right 6 designed to do 15 but you got it

number 3 is the choice number 3 black was too radical 5 is equal to 5 radical

5 it’s not rational for the same reason that choice to is not rational so that’s

not it numero cuatro, number 4 the math

department needs to buy new textbooks and laptops for the computer science

classroom the textbooks cost $116 each and the laptops

cost $439 each if the math department has

$6500 to spend and purchases 30 textbooks

how many laptops can they buy six seven 11 or 12 I would you have a lot

of options on how to do this problem test numbers I hope you know how they’re

by 30 laptops so a lot of the cost of 30 laptops and then figure out how many

labs which you can buy to get the cost to maximize that the amount that you

spend below or at sixty five dollars that’s a great money

however the life students don’t even know how to do that a little bit getting

how much 30 laptops cost you do need to know this and this is one of those

places where we’re working on a little bit of your intuition really helps you

look if you buy something that cost you $8 dollars how much does each two books

cost you $16 right $8 + $8=$16 how much does 3 books cost you okay

if you follow me here and follow me here you’re eight + eight + eight is $24

right and if I can’t ask you how much those four books cost you but you stop

you’re boring me eight + eight + eight + eight is $32 again but if I

said to you how much does 20 books cost you all of a sudden for eight dollars

20 * sure go ahead I’ll wait or or you can know what the definition

of multiplication is why do you use the word * historically speaking the

reason we use the word * is because times multiplication is a repeated

addition that’s what it is so so buying an $8 book 20 * 8+8+8+8 … etc 20 *

8 * 20 these problems oh they’re always asking you

the same question sometimes you need a variable source sometimes you need

numbers but always is the cost * the number of things that you buy always

always always so let’s do that here the textbooks cost one hundred and 16

dollars each and the laptops cost four hundred thirty-nine dollars each the

math department has 65 million dollars to spend purchases 30 textbooks

how many laptops can they buy well first we need to know how much we have left to

spend after we purchased the 30 * books

okay so how much the textbooks cost and the textbooks cost 116 dollars each

two textbooks I’ll add three textbooks add three for textbooks oh and the

number for time thirty textbooks add a number three

times 30 * 30 * 116 so textbooks cost 116 * 30 let’s get the

calculator out cool 116 * 30 okay so that’s 34 434

80 3480 cool yeah textbook her expensive cool remaining money=so well it’s

a 65 margin – the 3480 and this one I can do my head but you could do on the

calculator and you should do on a cap here if you don’t want to mess up so 3020 okay so that’s how much money’s left so how much – how many laptops can they buy now so it’s again this is where we introduce

our variable the cost of laptops * the number of the cost of the laptop

system cost of 1 laptops * the number of laptops we buy we know the

cost of one laptop so we need a variable for the to be the number of laptops so

that equal the number of laptops but ok ok so the cost of one laptop for 39 times L has to be equal to three 0 to

0 now if you’re smart you might know that no it doesn’t have to be equal to

three 0 to 0 because you can’t buy a third or a fifth or .7 or 83%

of a laptop so actually so we solve for L we solve for L we divide by four

thirty nine sorry for the space I’m actually running out of batteries in my

camera and for 39 I think it’s happened when you’re making videos for thirty

nine l=item thank you for for for having patience for me I’m doing the

best that I can for you guys you know to get decided for us as soon as possible

while being of course legally within to the time limits that I’m allowed for 39

okay so six .8 seven nine laptops and if you could buy .8

seven nine laptops then great if you could figure out how let me know so six

.8 seven nine so L is actually equal to six and a lot of these problems

actually purposely make it so that you have to round down even though the

number is big just to see if you know that you were supposed to round down

because you can’t buy .8 seven nine of a laptop and that’s true for any

physical unit object so the answer is six okay well just interesting the right

when I’m finished recording number five the camera actually died on me so I’m

actually I really appreciate it but you guys

we’re piecing with me while I did number four so rushed with all the weird random

mistakes the reason I want to do so many edits of ways because I really want

these videos to be out for you as soon as possible as soon as illegally allowed

to post the solutions change here’s the t-shirt in the baseball style again the

link is below if you want to support me these t-shirts and also just represent

your nerdy style you can purchase one of those from from the link below if I use

the money that I make to purchase new equipment for example I need a new

battery attachment for the for this GoPro so that so that I could actually

record for longer periods of time between breaks and also if you want to

support yourself while supporting me you could purchase the study guides that I

have based on the midterm of the final now with the student ready solution sets

I’ll tell you exactly where to go to study stuff that you don’t know how to

do and they’re super affordable and just for you guys since since you were

supporting me by watching this video and by a Calista tolerating the way I record

at number four I’m gonna lower the price bites when you put up by 20% for the

next week so you can definitely check that link out and that’s just for you

thank you for watching this video and listen I know you could do it I’m doing

this for you and you would be doing that for yourself

too so I’m glad you’re here with me let’s go out to number five what is the

solution to the equation 3/5 X 3/5 parentheses x + 4/3=one point

0 four so these are weird answers I’ve never seen a problem like this and

I like it three point 0 six repeating 0 .4 -.4

eight repeating and -.7 0 nine three repeating just the three

of being the highlights question I’ve never seen a person exactly like this on

the regions before they can ask this on the AC TSM SATs I

mean but they can because they do on the state tests right so there’s a few ways

of doing this you could do with the algebraic method / multiplied

by five thirds subtract four thirds got and see what the calculator tells you

you can do this by plugging in each answer or any approximation of the

answer and see if you get really really close to 1.0 four and that’s what those

are two options and both of those will work I want to show you as many methods

as possible because again I’m doing this for you and I want you to get the

highest rate possible on this on this test sorry for that flicker that was my

recording apparatus so I’m gonna do this by the calculator method so I’m gonna

press y=and what I’m gonna do is a trick a really useful trick on the a

CTS SATs and and on state tests to have the calculator solve algebraic when you

don’t necessarily know how to do the algebra so and even though the

calculator doesn’t know how to do algebra so what we do is three it only

knows arithmetic it only knows what you typed in 3/5 * parenthesis

X + 4/3 okay that’s the left side of the equal sign and then the second

equation is gonna be y=the right side 1.0

okay what I’m going to do with this I’m gonna presume standard to reset our

graph bounds and this is this is the value of the left side of the equation

and this is the value of the right side of the equation the first graph of the

value of the right side of the equation for all values of x from -10 to

10 in this graph and if I expanded the graph that’s as much as I want and the

right side the second graph that horizontal line is the right side of the

equation so it’s 1.04 because it’s constantly 1.04 for every single value

of X there’s no X there so it doesn’t change so how can we get it done

calculator to do that before us well here’s the thing the the graph the first

graph is the set of X values that make the left side true for a given x and

y-coordinate and then the right side the second graph is a set of what x and y

values that make the second equation true so the intersection of these two

graphs is the set of Y values x and y values that make both equations as we

type them shoot and in this case what it implies is that it’s actually the

x-coordinate of this is the solution to the equation the left side equaling the

right side so how do we get an intersection we we can estimate we drag

it around here it looks around .4 but I mean we got a .4 we got a

.4 8 negative .4 8 repeating the negative put something on line 3 I

suspect that the answer is gonna be .4 I really think it’s gonna be

because it looks like the intersection is positive but how can we get the

intersection exactly the calculator does the intersection exactly look at this in

calc so it’s in blue so you press the blue second button second count

intersect is the this one there’s only two curves on the first curve enter the

second curve there’s two curves guess get close to this intersection press

ENTER and X is .4 four so this is the exact answer nice right

the Catholic into algebra force numero seis number six the area of the

rectangle is represented by 3x ^ 2 – 9x – 8 which expression can

also be used to represent the area of the same rectangle let’s see 3 X

+ 2 * X – 4 3 X + 2 * X + 4 3 X + 4 * X – 2 & 3

X – 4 * X + 2 it’s one of these so if this is the area

of the rectangle right this is the area it says it’s the area of the rectangle

it seems it’s weird because they’re saying there isn’t 42 it’s not 57 it’s

not 8 it’s this expression right so this is the area and so then they’re saying

which expression can also be used to represent the area okay so we’re not

trying to solve for the base we’re not trying to solve for the height that that

is semi arbitrary most of the time when they asked you to do this problem baby

what I want you to factor but they’re asking for the area okay so in this case

that they actually are saying can you factor this polynomial to get these to

get on the answer there’s a like I said there’s a few ways to do this I just did

number 5 by graphing you can graph 3x ^ 2 – 10x – 8 and then graph

each one of these choices and see if the graphs match if you get the same graph

the answer is right so but what I’m gonna do is I’m gonna actually do the

algebra for you I’m gonna show you have to do this algebraically how factors

it’s a really cool man I like to call it the AC method a lot of teachers call it

something different but it’s a method it’s an expansion of the method of like

looking for numbers that add up to be in multiply C so we’re going to do 3x

^ 2 – 10x – 8 know how do I know that I’m going to factor this

because these four expressions are all factored polynomials factored quadratic

equations and there is only one way to factor this polynomial right so there’s

only one way to do this so though the method of doing this is saying that B so

there are two numbers two mystery numbers okay item to be which is equal to

-10 okay so two numbers add up to be those same two numbers when

multiplied have a product equal to not see because a is the food when it’s C

and a would have to be equal to one in fact we need to be equal to AC okay so

AC is three * -8 which is equal to -24 okay two numbers

whose product is -24 and some is -10 there’s infinitely many

choices of integers whose sum is -10 there’s only a finite number

of integers whose product is 24 I like to do what’s called the factory MO 24

Connect one in 20 for the next number after 24 I 1 is 2 2 is a factor of 24

with a factor pair of 12 2 * 12 is 24 3 is also a factor of 24 3 days a

factor of 24 3 * 8 is 24 for another factor of 24 cool for you see why I call

it the factor rainbow 4 is a factor of 24 with a factor pair of 6 cool 5 is not

a factor of 24 so we don’t use it and then 6 6 is already on the list it’s

written right here that’s the hint that’s the exact time you stopped these

are the only factor pairs of 24 so again you start from one go until you can

actually get a repeated number and one of the repeated number is actually the

last bigger over the 6 in this case so these are the factor pairs whose product

is in 24 we need one of them to be positive one of them to be negative for

the product to be negative but there’s some has to be negative x so

let’s see 1 -24 is -23 -1 and 24 is positive 23 okay so

two and 12 -2 and 12 that’s ten that’s positive ten okay

positive to a -12 there it is positive 2 * -12

is -24 and 2 + -12 is so -10 so 2 and -12 is

-24 2 + -12 is -10 those are the numbers how

are you using we we can’t just factor right away unfortunately like the other

method but we can use this to factor by grouping

I know some students factor by having people just by intuition looking for the

numbers until they find them this method this AC method is factoring by grouping

by it actually algebraically finds the numbers for you there is no guessing

check the numbers are 4 2 and negative 12 so 3x ^ 2 + 2x – 12 X so

there’s the two of the -12 and then – 8 these are the exact number

choices that allow you a factor by grouping we found them we actually

actually calculated them a lot of students guess and check

I like this so the greatest common factor of 3x when two axis x *

factor pair through x * 3x is 3x^2 and x * 2 is 2x and then we need a + something * 3x + 2 is gonna

be the factor pair and what factor pair is this this is the only player that

gets a little tricky sometimes you have to factor out before or some number or

the negative of a number in this case if i factor out a -4 I have a

correct factor pair of 3x + 2 so that way that works four * negative then

-4 * 3x is -12 and then your 4 * 2 is -8

perfect and now I factor by distributive property X – 4 * 3x + 2 and

one of these is exactly that X – 4 times 3x + 2 this is it isn’t it cool

I like it no one else here in number 7 which relation does not represent a

function this list of x and y values this one

expression involving Y and X number this graph and then this is the set of arrows

look so if you know the answer discussion congratulations because

because they’re gonna keep asking you this question they’re not then they keep

doing it you know that so if you don’t know what a function is and you gotta

you’ve gotta know what a function is e there’s no excuse for it because really

they don’t really ask many questions about what is a function right and they

don’t say what is a function and say it’s a this other thing about the

problem if we’re one for one multiple choice question we always ask which

relations is not represent a function hand

what does not represent a function so you this is what a function is so far a

function is a relation does not does not repeat s values with a giant diet period at the end of

the sentence that’s all that function is you pair a bunch(x) and y-coordinates

you could do without all you want for any relation in fact that’s all the

relation is it’s a bunch of pairs of x and y-coordinates every graph is a

relation every table of values is a relation or a scribble on a graph paper

is a relation because that graph that scribble contains points and those

points are part of the relation but a function just doesn’t repeat

x-coordinates that’s all it is so functions function graphs

pass the vertical line test okay test so let’s look at number three this says

ritually which relation does not represent a function so for example if I

draw every single vertical that’s sort of vertical every single vertical line

that I draw through this graph only crosses the graph once has to be

vertical line only crosses the graph once so in other words what is the

vertical line test and make sure that every single x coordinate there’s only

one black border it does not repeat X values so this one this first one look

at one not repeated two not repeated three it doesn’t appear for not repeated

five not repeated six not repeated cool no I never said you think about Y

coordinates X that’s the end of the sentence X can’t repeat that’s the end

of the sentence so this is a function this is also function number three y

equals radical three radical X + one – two well if you don’t believe that

that’s a function let’s graph it oops y=let’s clear out that algebra

problem we did okay and let’s say y equals three square root X + one out of square root and then – two

let’s graph it does this path the vertical line test so these are these

dis passes the vertical line test in other words if you put a plug in an x

coordinate you only get one y coordinate so it

doesn’t P X values so now this one so this is a function so it has to be this

one does not so this is yes yes yes and no how why is this or no look at that

look at this one it gets repeated to number four it also gets repeated to the

the five so one gets repeated twice to repeat it once and again three gets

repeated once and again so these each actually get repeated

twice so this is not a function okay that’s all it is carotene expertise

number eight Britney is solving a quadratic equation

her first step is shown below problem one 3x ^ 2 – 8 – 10 x=3

parentheses 2x + 3 step 1 3x ^ 2 – 10x – 8 is equal to 6x + 9

which two properties did Britain use to get to step 1 and the properties are

let’s see addition property of equality commutative property of addition

multiplication property of equality distributive property multiplication

over addition and then the choice is 1/3 1 & 4 2 & 3 or 2 & 4 so we know without

me using either 1 or 2 and we’re also using 3 or 4 based on the choices the

combinations of the sources so let’s see what she did we do need to know what

each of these are the addition property of equality the addition property of

equality says that if you have an A and equals of B and then you add a C to both

sides that you’re allowed to do that and you frequently do that too to solve

equations a + C=B + C but normally what you end up doing is not to

add our mysterious see sometimes rarely you do like in completing the square but

what you normally do is you actually use this property to eliminate something so

you usually effect if it’s a a – C equals B – C you do + C + + C on

both sides to cancel out the C but the point is that you can always do that if

you have two numbers are equal and you modify the same by adding the same

number you’ve got to remove equal things of the other property

and on this one I don’t see her adding two things to both sides okay so two or

one thing to both sides so it’s not the add addition property of equality so

wasn’t eliminate number one and choice to suppose so we know what she’s going

to use to the commutative property of addition and it might feel like well

she’s not adding him but remember that addition is subtraction are equivalent

operations they’re inverse operations of each other because they’re equivalent to

each other subtraction if he went to adding a

-right so see what she did here the Commuter property of addition she

took this – 8 which is + negative 8 she moved it to the end and his –

10 acts she moved it to the middle so she literally communities to commute

means to move so that she she definitely used the commutative property of

addition okay so that part is right in that part is

right now let’s look at the third and fourth choice the multiplication

property of equality so the multiplication property of equality is

similar to this one like if you have an A=B and you want to multiply both

sides by the same number let’s say * D * D that you could do that and

then you get Ad Bede and normally of course we do this

to cancel out an addition but if the point is that you can do this any time

the left side=the right side and you get two equal things so we’ve got

multiple but in this case she did not multiply both sides of the equation by

the same number so it’s definitely not gonna be this so it’s not gonna need

this and so it’s not gonna be twice three distributive property of

multiplication over addition she did do that she is the distributive property

here so it is number four number nine the graph of y=one-half x ^ 2

– X – four is shown below the points a -2 0 B 0 -4 and

C 4 0 lie on this graph which of these points can determine the 0s of the

equation y=1/2 x ^ 2 – X – 4 any only be only a and C only or

a B and C not a fan of this question I want to be surprised if they eliminate

this question from the test but I wouldn’t be surprised if they do

because technically there are two answers and they’re usually quite

careful about how they were this question the reason there’s two answers

is that any parabola is uniquely determined by three points so a B and C

would be a good answer however I would be the answer if they didn’t give you

the 0es of this parabola now quadratic equation can only have two

0s so that’s why in this case there’s actually another answer that this is

that this problem has point a negative two so that does say that these points

lie on the graph and it confirms that they do point a -2 0 is on

the x axis because the y coordinate is 0 so that is a 0 okay that’s a

0 and then point B is 0 negative for a lot of * students see this and

fixes it think it’s a 0 it’s not that’s a y intercept okay it’s not a 0 a

0 is a point where the graph crosses the x axis more and more specifically it’s

an x coordinate where the graph crosses the x axis or in other words a pool and

an x coordinate where the y value is equal to 0 so in this case they gave us

a 0 if this is point a so -2 is a 0 B this is a y intercept this is not

a 0 so -4 is not a 0 0 is not a 0 and the Third Point C for 0

is right here this is C so 4 is also a 0 of this equation so so we have two

0s a -2 and C at 4 so a and C do give you the 0s of the equation so

3 is the answer and a a is definitely not enough not a single point could

never determine all the 0s of that equation a single point can’t do it ah

so Hayes wrong but because a and C Katie the C are the 0s then 4 is enough now

for is not the right answer again this purse specifically uses a

quadratic the fact that this is a quadratic equation if it were something

else a cubic quartic then you need more points but this is a quadratic equation

up around only has two 0s new male yes number 10 given the parent function

f(x)=x cubed the function G of x=x – 1 cubed – 2 is the

result of a shift of f(x) let’s see one unit left two units down or when you

left some two units oh or winning it right and two minutes down

or one unit and write and tune it up so you should by the way you should always

do these problems on your own you can definitely do this problem by applying

graphing it and I highly recommend graph I mean if you don’t know the answer and

I will I will graph it but I will tell you the answer based on the graph

because if you don’t know how to do it based on the graph then you’ve got to

move on to another method which is I’m gonna give you the more algebraic method

beat which is an extremely relevant method I’m gonna clear this out so G of

f(x)=x cubed okay and then G of X is equal to its delia transformation

of the original X – 1 cubed – 2 okay and now I’m gonna zoom zoom

standard so that it gives me the standard graph and I’ll just assume if I

need to that was the first graph that was y=x cubed in the second one

that it just graphed is y=X – 1 cubed – 2 so if that one tells you

the answer agreed if not better listen to this conversation in the way I’m

gonna explain it is this and this every time I explain it to students this way

they get so listen any transformation that you perform in the Y Direction

using numbers is done as you would naturally expect it adding one should

stop vertically adding C shift the shift the graph up vertically C units

subtracting C shifts the graph down C units

multiplying by C cos C stretches the graph by a factor of C vertically

and then so on the other side of it if you do if you work with the numbers

seeing on the x coordinate on the I literally performed the operation on

just X by itself it does exactly the opposite of what you would expect it to

do on the Y in the Y direction and there is a reason for that but it’s a little

bit too deep for now but for example if we take X and we add C to X we would

expect the graph to move C C units to the right no but if we add C it actually

moves C units to the left and the menu dress okay

which is the opposite of what happens that we’re in the vertical direction if

we subtract C we like intuitively expect just like the graph would move down if

we subtracted see from the whole thing if we subtract C from X the graph

actually moves in the positive direction okay and then if we multiply X by C if

we multiply the whole expression by C vertically we expect it to stretch by

seen vertically but if we actually multiply X by C it actually narrows the

graph so it does exactly the opposite if you perform the operation on X

horizontally as what happens if you do the if you do the same operation on the

entire expression vertically so in this case subtracting two we expect

subtracting two from the entire expression X – 1 cubed two shifted

downward two spaces so down to cool so it’s definite gonna be two units down so

if this is right so far this is wrong good this is right so far and this is

wrong so so worn out the answers are now are 50/50 which is great taking our

problem for one and she was great I uses a 50% chance of

getting a write this on the acct it’s a one-point question so that is equivalent

to getting a half point on the Regents is actually a two-point question so it’s

equivalent to getting one point now so now is a unit isn’t one unit left or one

unit right so this we’re subtracting one so we expect it to go in the negative

direction but it actually goes into the positive direction you always thought

the opposite in the horizontal direction so this is actually one unit right if

you subtract one from anything it goes down in the negative direction so in the

horizontal direction we it does the opposite or would normally expect so

instead of going in the negative direction it goes in the positive

direction when you get right so it is this kind not this so not that in this

okay no middle answer number 11 if C equals 2a ^ 2 of -5 and D=3

– a then C – 2 D=2 a ^ 2 + a – 8y ^ 2 – a

– a 2 a ^ 2 + 2a – 11 or 2 a ^ 2 – a – 11 so let’s

see if we can do some process of elimination here

process of elimination could take you a really long way to getting an extremely

good grade on the SAT on the AC T so my process of elimination says C it’s C

– 2 D so it’s C – 2 D so I’m subtracting 2 * this from this and I

see immediately that if I have subtract 2 D I subtract 2 * 3 is 6 so I

subtract 6 so – 5 and – 6 is gonna be – 11 so immediately I see

these might be the answer this is good so far this is good so far

this is good this is not good so it’s not one

it’s not two so quickly I want from one unfortunate event in this question right

to a one in two chance of getting it right

so this problem went from being valued out of a half a point or two to being

valued 1.2 big deal because they don’t require that many points to

pass this reaches 27 points for this Regis which is crazy it’s it’s literally

getting 14 questions right in the multiple choice and gain nothing else

right anyway I think it should be more realistic in terms of okay let’s keep

going so which one of these is it I’m subtracting and negatives which you

think it’s gonna be + so I think it’s gonna be this I like this so let’s see

let’s actually do the algebra though let’s go up here C – 2 D=to a

^ 2 – 5 – – 2 parentheses three months Hey and this

tests if you could do the distributive property if you know that this is true

at this point you just perform the distributive property carefully let’s

see two a ^ 2 – five two mistakes that are common distributive

property so you that you know distributing the – two to the three

but not to the a that’s the biggest most common mistake the second most common

mistake is distributing the – two to a – a and somehow keeping the

negative sign because there’s one there’s two negative signs already

sometimes as well keep 101 when in fact two negative signs when multiplied

cancel the product of two negative is a positive so distribute the -2

to that and three and to the negative a -2 * 3 is – 6 -2

to the negative a is + 2a and now we combine like terms and put a decreasing

exponent order to a ^ 2 and then the 8 rows + 2a

and then – 5 in the – 6 is – 11 so that’s it number three and I was

right about that + gosh it’s almost like I actually know what I’m doing when

I when I saw that + but it’s not meant to be a humble brag it’s actually

meant to be to show you what I do to solve some of these questions the

process of elimination is an extremely important skill to have and it actually

isn’t that tough even for students who struggle with it with a lot of the basic

math you could be at 50 % level on the AC T and you could actually perform

process of elimination one of the things that I used to tutor students to do on

the AC T is process of elimination looking at the answers they know one

wrong looking at the answers they think are wrong looking at the answers that

look for me I’m just crossing those out and then guessing from there if they

didn’t know how to do the question if they didn’t know how to do the question

they should do it if they know how to do the question

partially they should do the question partially and then if they still can’t

finish it then they should eliminate the answers they know are wrong and

eliminate in answers that they think are wrong eliminate the answers that you

think are wrong that would that look funny and then guess from there I was

able to eliminate two answers because I knew they were wrong because -5

– 6 is negative ugh you see 50% chance of getting it right at that point

and if I could quickly speak about expected value the expected value of the

question is the probability but the number of points that it’s worth *

the probability of you’re getting it right so it’s extremely relevant thing

to calculate when you’re performing but when you’re taking the test because

you’re not gonna know how to do every single question so the it’s the expected

value that you want to increase the expected value of a question you exactly

know how to do definitely one point on the a CT the

expected value of a question that you leave blank is 0 so you should never

leave a question blank and that’s true on the a SAT to the expected value of a

question that has five choices four to five choices is 1/5 * the value 1

which is 1 so if you were learning three other choices and you have two left the

expected value of that is 1/2 1/2 that’s actually 150% increasing the value of

that question seemed weird that’s the way it works let’s do number 12 more

bought a new laptop for one thousand two hundred and fifty dollars he kept track

of the value of the laptop over the next three years as shown in the table below

years after purchase value in dollars and I look at tables personally cuz I

know I’m gonna have to look at them later even have to purchase volume

dollars one two three thousand eight hundred six forty okay which function

can be used to determine the value of the laptop for X years up to the

purchase f(x)=a thousand * 1.2^X if X equal a thousand

times 0.8 ^ x f(x)=one .2 five one thousand fifty *

one point to do X and f(x)=one thousand 50 * 0.8 ^ x do this

purchase on your own see if you can use that process of elimination that I just

taught you to eliminate a question and then see what I do

so either I do the value of the laptop so now I have to look at the value he

bought a new laptop for a thousand to infinity so that’s gonna be a relevant

number and then he kept trying the valuable app top it looks like your won

a thousand your to 836 forty so it looks like it’s going down in value down in

value over time that’s an extremely relevant thing to

note and in fact if you want to pause now and guess I highly recommend so now

what do I do I notice that I see the value of this 1.2 ^ x

power 1.2 is better than one so the exponential function is actually

going to increase as time goes on so this is not a right answer and the same

deal here one point ^ x this is going to increase as time goes on so

this is not the answer now I got a 50/50 chance of getting it right so it’s

either a thousand * 0 point e to the X or 1250 to 0.8 ^ x at this

point I’m starting suspect that this one versus this one versus this one this one

uses a thousand and fifty as the initial value of the laptop so I actually

suspect that this is gonna be the right answer

because of the thousand two hundred and 15 now let’s see if I’m right

the the equation for an exponential decay of a value is equal to a so f(x)

is equal to f of 0 the initial value okay * one – the rate of

decrease ^ X or our X’s in years okay so this is equal to f of 0

is 1250 and now I could see that big deal amount that it decreases is

actually well I actually know it’s gonna be 20% because these bases are the same

and I can confirm it by doing let’s see let’s quit here 1,250 because it’s a product so final /

initial so 1 2 500 is 0.8 not confirm to the .8 0.8 okay and then ^ the

year and so this is the answer and a half(x)=this okay no choice for

what I just talked about is extremely important the answer is not the

important thing the method is what’s important I tell it to all my two new

students and the ones who accept that progress more quickly all my students

progress eventually but the ones who accept that and really progress fast

I’ve taken so many students from the 70% level to the 90% level in just a few

days literally a few days I’ve taken students that are getting done 18s

on the AC T’s to getting thirty ones on their AC T’s and a week and a half so

frequently not even rarely so that’s relevant

so take the advice that I give you all the little hints I give you along the

way that’s 399 knowledge you should take it

number 13 a height of a ball doreen tossed into the air continue modeled by

the function h(x)=-4 .9 x ^ 2 + 6x + 5

where X is the time elapsed and seconds h(x) is the height in meters

and yes yes in that number of five in the function represents the initial

height the time it was the body to the ground the time at which the ball is at

its highest point and the maximum height the ball at a me alone yeah try the

problem if you know your physics you might be able to answer this question

let’s look at the problem and see if we get some information because it does

tell us some of the information the H of X is behind the hiney at all * okay so this is bhai right the X is the time

elapsed okay and then so let’s see what we can eliminate here the initial height

of the ball that seems to make sense since since this is by itself its units

are the same as the original function so it’s a height okay so this looks good

the time at which the ball reaches the ground this is not X X is the time so X

is time okay excess time so the time what’s the

bondage ground enough the time at which the ball is at a point

no I X is the time okay so now and the maximum height of the ball a team goes

thrown into the air this might seem like okay and then you can graph it because

it is a high knee but if you graph it you find out that that’s not the case

the second thing is that if you plug in x=0 with these

0 time you get for Megan 4.9 * 0 is 0 + 6 * 0 0 + 5 so this is

5 is the value of the function at X equal 0 so this is so 5 is equal to H 0

which is the initial height so it’s definitely this one and in fact the

maximum height of the ball doesn’t occur at this constant if this is actually an

extremely common question the maximum height occurs at the vertex vertex and

where is the vertex x=negative B over 2a which is equal to -6

over 2 * -4 . 9 get the calculator out and find out what that is

equal to and then the MaxLite max height equals H of whatever -6/2

times 4.9 is so -6/2 * -4 . 9 whatever that happens

to be that’s the maximum height and that height is bigger than 5 because it’s

initially being thrown up in the air the function f(x)=2x ^ 2 +

6x – 12 has a domain consisting of the integers from -2 to 1

inclusive the integers from -2 to 1 inclusive okay which set represents

the corresponding range values for f of X well let’s see -2 -28

9 phone for 16 4 or -2 & 4 native 16 in metaphor

but definitely try this problem on your own see what you think about it I think

that you should give yourself the chance to think about this question because if

you think about it for a little while you might find that it’s actually not as

hard as you think take your guess at what you think is

right and then try to do everything right by this problem okay

I’m gonna continue now though so this the domain is the integers from negative

2 to 1 inclusive so the domain is equal to the set -2 -1 0 & 1

and that’s the full domain for numbers in the domain not the full interval for

just those 4 numbers okay so what’s the range the range if we repeat numbers

this might repeat numbers but then the repeated numbers aren’t really repeated

they’re just beyond once in a set they appear twice in a graph but once in a

set so this is -2 F of negative 1 of 0 & 1 okay this is commonly denoted

as and after the full domain so this is a

sad it’s a shorter notation okay so how do I evaluate this I’m gonna show you my

without it’s using the top and here in a very good way you can plug in the one of

these numbers to eliminate some choices like I see that all of these have

-4 in them so I plug in though x equals 0 I can quickly evaluate this

function f of 0=0 0 – 12 there’s my process of elimination choice

3 and choice floor are eliminated and could be two -12

so I can show you how to do it but a process of elimination that’s what

you’re paying me 0 dollars for to give you the best advice possible what

I’ve started a very large amount of money to tell students so=2x

^ 2 + 6x – 12 the table let’s see how the table looks the table I’m

going to show you what I did table set is in blue so second table set

I make sure we feed the pivot value right now it’s Auto and usually people

started using SEPTA’s you’re automatically slide those at 0 0 0 1

Otto Otto and I can school so -2 F of -2 is equal

to the -16 okay so this is the set containing -16 comma

-1 is actually also -16 so where that’s already on the list

great and then after 0s -12 -12 1 is equal to -4

therefore and this is the range okay so it’s choice to I want to be honest with

you I’ve just if I could take a + for the reason that I suggest purchasing the

resources I have for the regions inaudible Warren also for the s 18 for

the AC T is that actually offer one extra hands work whatever product that you sell in your

business me I sell my knowledge and my my teaching ability and also the

products that I that I create and publish online and I do that with the

goal of producing quality not with the goal of producing money for me because

if I try to produce money for me I know that I won’t make money because the

purchaser will look at the product I bought and not like if not buy anything

else and I recommend me to anybody else in this case I want you to have the best

product that’s possible and I’m selling it for a very low price and I want you

to do the best as possible on this test and on any future tests so I do highly

recommend that you purchased those to do yourself a favor you support yourself by

supporting me I believe that you can do it I know that you can do it and I

believe in you so definitely check those out number 15 which equation has the

same solution as x ^ 2 + 8x – 33=0 now let’s see there’s a

bunch of these X + 4 ^ 2 equals -49 X – 4 ^ 2 equals

-49 X + 4 ^ 2=17 or X – 4 ^ 2=17 so

definitely try this problem on your own like I said you can do this problem by

graphing all of these one at a time I’m gonna show you a quick cool trick to

graphing because I know that graphing calculator doesn’t differentiate

especially if you have the non color one they have a really cool color calculator

now she’s phenomenal if you if you graph these two functions let’s say I’m going

to graph one and the original in choice 1 x ^ 2 okay + eight X – 33

equals 0 so which equation has the same solutions are these as these and

then X for parentheses x + 4 ^ 2 equals

49 so I need to I need to have equal 0 so – 49 – 49 – 49 so to get 0 on the

right okay – 49 okay now I’m gonna trick come when he uses this I’m gonna if this

will happen to be the left side the right side happen to be the same exact

expression you might notice that then while the calculator wouldn’t

differentiate between the two because the thickness of the lines are the

different so what I do is I actually make one thin in one thing and then i

graph them and if they overlap you’ll see that the line gets thicker alright

so there’s the pass that graph and then that new graph so it looked like the

graph that I just chose happened to be the right answer

so let’s do zoom it zoom fit is a nice little tool that’s change the Y

coordinates about min line the max Y to fit the graph so let’s see BAM that’s

the original function and this is choice one notice just one Humber is exactly on

top and you can actually see that graph being created so this one so it seems to

be right in terms of process of elimination this is a – sign so and

this sauce + if you do if you get you can get these equations by completing

the square so the when you complete the square this

+ is gonna be maintained so it’s gonna be the choice 1 or choice 3 this

has a – sign so less than and this is a – sign so that’s not it because

no – sign so it does turn out as we checked on the graph that it’s that it’s

number 1 ok done feel free to ask any questions in the comments below I will

respond to your comments number 16 one of the essays the table below shows the

weights of Liam’s pumpkins I love W weights of pumpkins in power

Patricius pumpkins PFW here over a four-week period where W represents the

number of weeks so what W weeks okay Liam’s pumpkins grow at a constant rate

okay Patricius pumpkin grow at a weekly rate of approximately four fifty two

% okay let’s see so these grow at a constant rate 2.4 five

.5 eight .6 seven point seven so that’s a linear function okay

because they said it’s a constant rate and then patricia pumpkin wrote breyer

weekly rate of approximately two birth fifty-two %

okay this is exponential okay so cool so assume that the pumpkins continue to

grow at these rates through week 13 mm-hmm when comparing the

weights of both Liam’s and Patricia’s pumpkins in week ten and week 13

which statement is true Leo’s pumpkins will weigh more in week

tournament and and week 13 Patricius pumpkins will weigh more in

week ten and week 13 or Liam’s pumpkins will weigh more in return at

Patricia’s well pumpkins will weigh more in week 13 or Patricia’s pumpkins will

weigh more in week ten and Liam’s Logan’s upload way more meters in other

words which one’s gonna be which way in would ten which week 13 they

literally could have said Patricia’s weights are gonna be this and this at

these weeks their pictures and Liam’s are gonna be one of these weeks because

that’s really kind of the only way to do this for a question you have to find out

how much they weigh every ten in week 13 so how do I do this

I do 11 12 13 and then I do

let’s see get my calculator out how much this one is a the liam’s is growing at a

constant rate of two point from two .4 two three five .5

let’s confirm that this is let’s see so the difference here five .5 nine

support for is three .1 let’s confirm that that kana that difference

is constant eight .6 – five .5 is three .1 according

to my calculator I have one installed in my brain 11 .7 – eight

.6 is three .1 cool and these grow by approximately two point

52% so this is we know that this is * 1.50 five two and of

course there’s some decimal approximation so that’s I’m gonna get to

the next one this one has to be calculated so I’m gonna do we are liam’s

first so I’m gonna do that 11 .7 good the next week is

gonna be dot + three .1 enter 14 .8 to do this way

because to get the next one it’s answers + three .1 so

into this answer + three .1 enter 17 .9 the next one 12 17 .9

+ two from one is 2121 and then the next one is 24 .1 24 .1 okay now I suspect strongly better than Patricia’s are

gonna be way bigger because hers grow metric teacher % exponential

functions grow faster than the linear functions and eventually a growing

exponential function will surpass any growing linear function that’s how fast

exponential functions eventually grow 52% is extremely fast so I

need to do eight .8 * 0.5 to so eight .8 five two *

one * 1.5 to 13 .3 seven six 13 point

three seven six so I’m gonna circle the one that’s bigger picture so in other

words it weighs more so Liam’s weighs more and me ten so here these will wait

more week ten this is so far away the Tricia’s will weigh more than eight ten

no I won’t so that’s number two is wrong the unspoken one we turn this looks good

it Patricia’s probably way more anytime this is wrong okay so it’s not me before

I suspect for me that all Patricia’s is gonna weigh more weight for a team by a

whole lot in fact so I think that this is gonna be the case okay I think it’s

gonna be choice three let’s find out so the technique * 1.5 to enter

let’s see 20 .3 list for twenty .3

because the computers gonna store on the decimal so 20.3 and it’s already which

is already heavier and now you see 17 .9 twenty point let’s

see the next one if I’m right kind of exponential functions grow extremely

fast the next number should be way bigger than the twelfth week for our for

Liam’s 21 weeks this is thirty point nine pounds 3.9 ODS completed so compare

week 11 week alone they’re different five up to five pounds

week 12 they’re different by about ten or 11 pounds week 13 forty

six .9 seven pounds of sixty forty seven forty seven lbs you know

they’re different by almost a factor of two so I was definitely right Patricia’s

gonna be way more way way way more she heard what pumpkins are way way more

13 so that stuffing right answer this is not a numeral they cease yet the

number 17 and the function f(x) is graphed below okay cool Raph it’s

like avi maybe an absolute value type thing but there’s a point so it doesn’t

go forever on on the left side okay then the domain of this function is all

positive real numbers and integers or Ashe greater than equal

to 0 or X greater than equal to negative 1

so it’s important to know what the domain of associated what domain means

it’s the domain and I’ll definitely do this problem on your own and look at

this very suspiciously is my hint that should allow you to get eliminate

choices in fact process of elimination might actually give me the answer so

definitely try it on your own and see what you get so here’s one thing I see

all positive real numbers all positive integers all ex-criminal to 0 X is

greater than equal to -1 so here’s the thing positive integers this

is defined on way more than the integers I mean look at actually like a negative

1/2 go off there’s a point on the graph so it’s defined at x=-1/2

x=3 .1 4 pi around here go up to the point we’ve gone to the graph

there’s a point on the graph so it’s defined as those numbers so find

everywhere in fact weigh between between any square especially on the right so

it’s not that now all positive real numbers it’s asking what the domain is

so if it’s all positive real numbers it means that it’s defined there and

nowhere else so all positive real numbers this means

that it’s defined at all positive real numbers but not defined at 0 not fun for

any negative numbers but at 0 I go up and there’s a point on the graph I go to

the negative numbers I go up and there’s a point on the graph for some negative

numbers so that’s not it for X greater than equal to 0 this means that it’s

defined at 0 and all positive real numbers but not below it which means no

negative numbers but if again if negative or -1 I go to the

graph and there it is that that’s the negative numbers where the function is

defined so it’s not x=0 so it is X greater than equal to

negative one as a challenge I invite you to think about what the actual equation

for this absolute value function is my game is that is an absolute value

function but it’s not a restricted domain for X greater than equal to

negative one but it’s still an absolute value function put in the comments below

what you think the functions new window the SEO of show number 18 which pair of

equations would have -1/2 as a solution y=x + 3 and y equals

2 ^ X or Y X -1 to Y becomes 2x or whitewalls x ^ 2 –

3 – 2 and y + 4 X + 6 or 2x + 3y=-4 and y equals

-1/2 X – 3 halves definitely probably try the problem on

your own this is a problem that you might find that you could do on your own

I mean there’s no reason to think that you couldn’t if you you might feel like

you can but you have to have some intuition on this problem you do no

matter what your skill is no matter I haven’t had a student in life and I had

all of those of student you have never had a level of student life that didn’t

have enough ability to answer something about this equation no not I mean this

not at this level so let’s see if we can get the answer ourselves but again try

it on your own plug in x=-1 and see you

find it – sounds good so I plug in x equals -1 again so I get 2y

equals -1 + 2 this one’s good and next one I plug in to the -1

so 2 to the -1 is actually 1 over 2 ok which is not equal to 2 so

this is not it number the this one let’s see -1 2 choices 2 so y equals

-1 – 1 is -2 not 2 ok done not it that’s the next one I’m

gonna plug into the linear equation to see because this one’s harder smart

thing to do y=4x + 6 1 4 x equals -1 4 * -1 is

-4 and -4 + 6 is 2 so this one looks good so far so now I am

gonna plug into the quadratic equation I think these are a little bit weird with

fractions and what is on the left so I’m gonna put into this one so I’m gonna see

y=x ^ 2 – 3x – 2 and if you allows you to see what I do with

that -1 the pesky -1 cause a lot of students to get squish me

wrong if you listen to what I’m saying you’ll let the question right and

actually elevates your score relative to other students so 2 is equal to when X

is -1 -1 ^ 2 notice I put the -1 in parentheses then

the parentheses are necessary it’s not optional it’s not us being pedantic

they’re required if you don’t put the -1 it’s actually 1 okay so

another 1 ^ 2 – 3 * negative 1 – 2 and this is a multiplication

of a negative number and a subtraction of a positive so that’s gonna also have

some operations so -1 ^ 2 is positive 1 – 3 * -2

-1 is negative three which is three so +

three – two so I 1 + 3 is 4 – 2 which is equal to 2 2=2

definitely right so it is choice 3 and therefore we can eliminate choice for I

had a feeling that it wasn’t kind of before because I see so many this

negative sign overpowering this negative this whether it’s just positive or

negative this one would satisfy the point but this one again the negative

three-halves overpowers the expression on the right and this becomes negative

new middle eocene where in number 19 which function could be used to

represent the sequence 820 5125 1/3 12.5 comma

given given that 80=8 so I know no soy these are some expressions let’s

let’s actually cysts are some things about these expressions let’s see if we

could actually say something about I noticed that this increases by 12 then

by 30 then by a bigger number than by an even bigger number so this this sequence

is not linear okay so it’s not an arithmetic sequence no choice 1 a n

equals a M – 1 + a 1 this might not seem like a dramatic sequence but

remember then an arithmetic sequence can be written as recursively defined

sequences in terms of previous elements or a N=n – 1 so previous term

previous term + a 1 now N 1 is 8 it’s a fixed constant + constant okay

so this in fact is is arithmetic also called linear okay so it’s not choice 1

because this is not grow linearly it doesn’t grow by the same number each

step so it could be exponential now this was an exponential not for a sequence B

and I know this one because it’s the previous term multiplied by a fixed

number this one is a previous term multiplied by a fixed number look at

choice 3 it’s a previous term multiplied by a fixed number and then + another

number so this is actually not even it’s not magic nor is it

exponential it’s something to us okay so which one of it is this so I think the

only way to do this is to evaluate now the the expressions are so long I have a

feeling it’s gonna be this one let me tell you why I’m gonna eliminate choice

for before I even an odd way this is a N equals a 1 * n – 1 so this is a

n is equal to this is an 8 4=a times a and – 1 so in other words to

take the previous term multiplied by 8 which is a big number 8 the next one

would be 8 * 8 is 64 which is not 20 the next one if that is just to check

again the second term * 8 is would be 13 20 * 8 though is 169 51 huh

number 50 so it’s not this one so it’s either choice 3 or choice to my process

of elimination let’s test choice 2 a 2 is equal to 2 . 5 * a 1 let C

equals 2.5 * 8 which=20 good a 3=2.5 * a 2 but so there’s

some works out=2.5 * 20 which is equal to 50 so this one is

looking good I suspect that this is the answer if we keep going we’ll be able to

verify now let’s test this one to see if this is the answer because I suspect

that they chose the numbers right so that the first term will work to see if

I soon would look at the first one go for me to 20 and realize that works and

done and in fact like 8 * 1.5 is 12 + 8 is 20 20 * 1.5 is 30 but +

8 is not 30 it’s 38 is not 50 so this is not the answer

so so this one would go 8 comma 20 the next one goes again 20 * 1 . 5

is 30 + 8 is 38 not 50 so this is not the answer so it is a choice number 20

the formula for electrical power if you know your physics is P=I ^ 2

R don’t be scared this is an algebra test they don’t expect you to know this

what each thing is tell Tony when they are where I is current and R is

resistance electrical power P eyes current R’s resistance the formula for I

in terms of P and R is is P/R ^ 2

I was radical PR I=P – R ^ 2 or I=radical P miners are

definitely try this problem on your own this is what I’ll tell you a lot of students who can solve

equations in fact equations with some more complicated numbers but the modern

UI had numbers that are a little bit too complicated they start to fail at

solving the equations so I’m gonna tell you the exact reason why I’m talking

about like this for example two point three like yeah 2.3 let me

scroll down so I don’t have to hide my face again 2.3 X + eight

.4=1.7 and a lot of students don’t know how to solve

this equation but if I told them to X + e=one

they wouldn’t know how to solve this equation and then I realize they don’t

really know how to solve the equation they’ve just done that stuff so

frequently that they just kind of follow the steps like they always have the

truth is if they know how to solve the equation they would be able to do the

first one that I did a 2.3 X + eight .4=one point

seven so I’m actually in an effort to explain number 20 I’m gonna solve this

equation I subtract eight .4 – eight .4 – eight point

four and solvers and I get two point three X is equal to well whatever one

.7 – eight .4 is so eight .4 seven .4 six

.4 six .7 so negative six .7 and then / two

.3 / a 2.3 get ax is equal to I guess I’m gonna

have to have to hide my face whatever this happens to be -67/23

which is an ugly number but let’s see if you know why I said that if they know

how to solve the first equation they should know how to solve this one like

if they truly did look at this 2 X + 8=1 – 8 – 8 2 x equals

-7 / 2 / 2 X is equal to -7/2 if you

look at this question the way to solve this equation is by performing the

inverse operation with the same number that’s written it wasn’t the numbers

that told you what to do it never is the numbers that tell you

how to solve it equation it never is it’s the operation it’s always the

equation of the operation that tells you how to solve the equation of the numbers

so I saw student C at 2.3 and eight .4 what’s up I don’t

know what to do the operation is when you do you imprint the operation do you

see a + I don’t care that’s at a point for it

invert the SAP lusts with – I don’t care that it’s a 2.3 that’s a

multiplication between that’s the point 3 in the X and run the time supply a by

dividing and you get the answer it’s the same thing on the left side it’s the

same thing on the right side that said that’s exactly what we’re doing in this

question we’re solving for I in terms of P and R look at this and if you wait if

you think you’ve got what I just said this is this is clutch right here try to

get the question right see if right now I don’t care what long you I don’t care

if you think you’re horrible imagine if you think you’re great at math

you know a lot kids were great at math who can’t do this question and all I

think some struggling math that I tell them what I just told you and they can

do this so pause the trial problem all right cool

let me do this I hope you try it so I’m gonna invert operations I don’t care

that they’re letters they’re letters but it’s not about the letters it’s about

the operations and I know operations and then letters are next to each other

multiplication if there’s a square that’s squaring that’s a power so I’m

gonna invert those so I need to solve for R for I P P=I ^ 2 R

according to my order of operations Pam – it starts with G grouping symbols

right parenthesis but also any other grouping symbol okay there is no

parenthesis but there’s nobody simple song so i inverting operations in fact

so I’m actually going backwards when you invert operations you invert them in the

inverse order i by itself here but it’s being ^ 2 and that is being

multiplied by R okay I need to invert our I need to invert the multiplication

by our not because there’s an R but because there’s a multiplication get

what I’m saying I need to invert the multiplication it could have been a Q a

P a dog you arrival to eight .4 five .7 this is a

multiplication I need to divide / r / r and I get I ^ 2 is equal to P/R

and now I is all by itself except for that pesky square and I know how to

invert a square because I know the inverse operation of a spraying

operation the inverse operation of a square an operation is the square root

operation doesn’t matter that that’s an eye event the left side are letters

there’s some division there this is the squaring operation I invert

that with a square root operation okay that’s in fact the definition of the

square root in themed version of the squaring operation so I is equal to

radical pink over are his choice to that’s it if I wanted to do some

elimination by osq subtraction here subtraction here that’s not gonna being

a subtraction so it’s not going to be this or this that’s it I really love

number 20 but let’s let’s move on to number 21 the function f(x) Q(x) and

P(x) are shown below so I see f(x) is this graph over here I see P Q(x)

is this expression and I say I see P of X is this table function so when the

input for when the input is for which functions have the same output value hmm

so – am I gonna have the same output value at least and possibly all three –

qfn P cubed P Q and P or F Q and P so let’s see I think the only way to really

do this is to evaluate the functions and I think evaluating the easiest ones is

easier so I’m gonna evaluate the easier ones I noticed that three out of four

contain F so if I happen to evaluate F and F is not well doesn’t match anything

others that I know immediately that choice one two or four I’m for I’m gonna

be eliminated so let’s see so f of 4 we need F of 4 so I need 1 2 3

4 ok so I’m gonna go up here here right to find nothing floor so this is 4 – 4

which=3 ok now I go to black and Q by P(x) is

the easiest around here at x=4 because I could you read it ok and then

I see that the P of 4 is equal to 3 ok so anyone any a choice that contains

f(x) and P(x) could be right if it doesn’t contain f(x) and P are X it’s

wrong so Q(x) is wrong and Q and P is wrong and also F and Q is wrong because

it doesn’t continue P this is actually some zucchini P so these are F and P or

F Q and P so I wish they give it to us for free and we didn’t have to validate

Cuba we do so let’s do that Q 4 is equal to after careful order of operations

PEMDAS which starts with P stands for grouping symbols right p OMG symbols d

yes hey why do I put the M and Venus to each other in the ASX each other tell me

in the comments CP enough for our thumbs up

so Q 4 is equal to X – 1 ^ 2 – 6 so 4 – 1 ^ 2 – 6 hmm

4 – 1 is 3 3 ^ 2 – 6 and that cuz I have parentheses cookie

symbols first then exponents 3 ^ 2 is 9 – 6 and 9 9 6 is equal to 3 number 22 using the substitution method

video is solving the following system of equations algebraically substitution

method ok y + 3x=-4 and 2x – 3y=-21 which

equivalent equation could be don’t use the choice policy there’s some

complicated ones let’s see 2 * -3x – 4a + 3x=I

think the important thing to do is to think about how they did this is a

question they did this question by the substitution method right so that means

that they substituted something from one equation into the other equation

normally in the substitution I think you just pick one of the equations solve for

one of the variables in terms of the other variables you know you’re not

gonna get a numerical answer but you’re gonna get an expression for one variable

in terms of the other and then you’re gonna take that expression and plug it

into the other equation if you know is a smart kid he would actually to choose

the first equation and solve for y why because this one has a 3 so we divide

things by 3 and introduce fractions this one has a 2 and none of these numbers

are divisible by 3 by two so even introduced fractions by

solving for x this one has a 3 this is divisible by 3 but this one is not so

we’ve introduced fractions again by solving for y in this case so the first

one is the one that’s easiest to solve for y in terms of X so y + 3x equals

-4 miss subtract 3x I’m going to subtract 3x on both sides and I get y

equals -3x – 4 right okay the second one I need to replace y

substitute Y with Disick’s known expression let’s see what I can let’s

see if it’s one of the choices I hope it is because I don’t know if it’s gonna be

that’s the truth because when it’s substitution you’re kind of guessing and

which one they might do so 2x but this is the most logical one I wouldn’t die

if I were doing this problem I wouldn’t do any other substitution so – 3y is

equal to -3x – 4 so negative 3x – 4=-21 let’s see

if this is one of the choices look at it 2x – 3 * -3x – 4

equals -21 this is choice 3 choice for is here for the students step

kind of shifted the 3x to the other side and there is no moving operation moving

it’s not an operation subtracting is an operation that’s where you get the –

sign so it’s not this one it’s not this one it’s not this week

nobody wait to the lighting change oh my shirt changed – it must be today

when you’re recording videos in general it takes a lot longer to record them

then to actually watch them this is actually taking for me nor 23 materials

a and B decay over time the function for the amount of material a is a of T

equals a thousand * 0.5 x to the power of 2 T and for the amount of

material B is B of T=a thousand times at 0.25 ^ T where T

represents time and days on which day will be amount of material be equal and

it’s their leading to only day 5 only or every day ok let me try the problem on

your own see what you got there’s a lot of ways of doing this problem

graphically numerically if you actually know your exponents but I think you can

actually get this question immediately I suspect a so if I plug in 0 I son the

initial day only said the time T equals 0 so I got a of 0 is equal to a

thousand * 0.5 ^ 2 times 0 and then you need to need to

know that any number to the 0 power is 1 so this is one so this is a

thousand * 1 is a thousand and then B of 0 is a thousand * 0.25 to the

power of 0 and again any numbers of the 0 power is you can do 1 so I found

which is also a thousand okay so the initial day the the numbers are the same

so Vince eliminates day two only in a limited state five only at leaves the

emotional day only or every day now we have fifty % chance of getting it

right and that’s something that you should know that any number to the 0

power is equal to one they do test on that they do tests to see if you think

that it’s actually equal to 0 any number to the 0 power 0 it’s not

it’s not any number to the 0 power is one so now we’re left with a 50/50

chance of getting it right just from basic exponent rules super basic

exponent rules now for the more complicated stuff you could graph these

that’s a great way of doing it if you got this one graph this one or number of

checks watch your project with our minecraft server and you might see that

they do or do not overlap if they don’t overlap then it’s one if they do overlap

completely and if it’s every time so I’m gonna do this algebraically so using my

exponent all so that I can give you a little bit of overview a of T is 1000

times 0.5 ^ two T the exponent it’s also equal to so the rule

for exponents is that that I’m gonna use here is that if base is taken to two

different powers it’s equivalent to taking it to a power and then to another

power normally this you means useful in the

reverse direction that’s cool if you wanna erase my just role 0.5 to the

power of 2 and then to parity normally we use this rule to

combine exponents but in this case we’re going to use it to split exponents and

this is equal to a thousand two . 5 ^ 2 .5 to twenty

five .2 five .2 five the power of team which is actually the

exact expression for B of T so not only are they equal to each other every devil

we’ve confirmed that they have they can be simplified to the same expression

so let’s every day twenty-four the following conversion was done correctly

so we know the conversion is correct we assuming three miles in one hour *

one hour/60 minutes * 5,280 feet/one mile * 12 inches

to one foot/one foot what is one of the final units for this conversion

minutes per foot minutes per inch feet per minute or inches per minute so

definitely try the problem on your own this is not that tough if you really

just think about what you do know about fractions and your shortchanging

yourself if you think you know nothing or not enough about fractions you think

you know enough so try it on your own this is what I see I see the first this

is a conversion so this is converting the original amount to two different

units the numerator of this one is miles the denominator of this one is hours of

saw distance/time these are * these are distances and these are

distances so the units are gonna be distance/time so that in the

minutes this one this one and it leaves feet for a minute or inches per minute

so now we have a 50-50 chance of getting it right now we do for this one is

of how multiplying fractions works multiplying fractions is the one that

students confuse of bagging fractions because they think it should be as easy

as moving horizontally it’s not you have to do if you criss cross body or getting

a common denominator but multiplying fractions is done that way

you multiply horizontally so multiply this way okay and multiply this way now

there’s a corollary to that the correlated to that is that doing a

factor in the numerator and a factor in the denominator factors that multiply

then they cancel so now how are in the Dominator kiss the numerator this

vaccine minute does not cancel with anything

my on the denominator can smile in the numerator okay and then feet in the

denominator cancel feet in the numerator okay and then those of these inches does

not cancel it so we’re left with minutes in the denominator and inches in the

numerator inches per minute inches per minute it’s number four so it’s not

number thank you might be single number 25 solve algebraically 4x 3600 + one

final 2x is less than 2,000 + 1.0 4x so talk about the AC tease the a CTS

does not for the black questions but if you’re

taking a CTS chances are you’re going to take the SATs too and SATs do have fill

in the blanks I don’t know if you know that the blacks are not answer if the

fill in the blank is just give the answer and the relevant thing is that

that actually makes it harder not easier the this New York State Regents does

great but with partial credit but the SATs is not rated with partial

credit and then on the AC T’s it’s a multiple-choice question

but either way you really have to know how to solve these algebraically – in

order to be able to get the answer anyway there are tricks with multiple

choice that you can use like testing the end points but if you saw and testing in

between well besides that knowing the method for more difficult problems it’s

going to become relevant now how to do this one it’s uh say algebraically force

for this Regents if you if you take you’re from New York

it does say algebraic we saw a numerical method does not work the bravely means

you know inverse operations combining like terms if you have a distributive

property those kinds of things you’ve got tell you that is this answer but it

has to be through performing inverse operations basically so I need to get X

by itself on and usually I get it on the left and so I’m gonna get X on the left

so I’m actually you might not like that I’d get a negative number one point all

for X – one point O for X and then so I get 3,600

1.02 – 1.04 is – point all 2x is less than 2000 and you might not like again

that I get a negative number for the X but usually students get confused when

they do inequalities or even equations when X is not on the left

you shouldn’t I do think you shouldn’t but at the same time since students try

so hard to get the number of the X on the left and then they get confused when

they have to get it on the left and it’s already on the right I’m gonna get it on

the left even if it’s a negative number I subtract 3,600 I subtract 3,600 and

then what do I get I you that can use a calculator here so I get -0.02 X

is less than -1600 and if you don’t know that you should use a

calculator you should do 2,000 – thirty-six hundred and subtracting to

get a negative number is another place that students super get wrong even

students who are in the 90s and 95 so if these numbers confusion you should get

used to them but if you’re not used to them use the calculator okay so now I

need to divide by negative point on to a lot of another place where students get

things wrong as they were they they had one or two could they see a negative

sign forgetting that it’s nothing it’s not the negative sign it’s not the

number that tells you what to do it’s the operation this is a multiplication

break in so we need to divide so we do need to divide by negative .2

/ negative point oh two and now another place the final place where

students get confused is that since they’re / a negative number the

so they’re / -0.02 that actually flips the direction of the

inequality so this becomes a greater than and now 1,600 divided

– I do know the answer 16 / 2 is 8 the decimal place over twice and so

and then also a negative / a negative is a positive but if you don’t

know that -16 hundred / -0.02 okay they’re just maybe

thousand positive 80,000 and that’s another place where students good things

on a negative / a negative somehow becomes a negative it’s not it’s

a positive negative / a negative is a positive

80,000 and that’s a full to credit answer and it’s actually not that long

of a process is it I would recommend that you do this on your own see if you

if you do this on your own you could see where you got it wrong correct that

error for future problems no matter what they say is number 26 all right these

problems getting wider let me just shrink myself and oh sorry the number of

people who attended our schools last six basketball games increased as the team

needs the states sessional games this table below shows the data game on top

30 42 18 okay attendance 348 forth so a bunch of numbers and government hundreds

the state the type of function that best fits the data justifier choice of a

function type so this this is a interesting problem that they like to

give now they’ve been using given us one so so definitely understand where this

answers coming from all right there’s two types of functions that

they’re really gonna ask for linear or exponential but the reason there’s

really only two types that they’re going to ask for is that once you start going

for the curved functions you have to have a lot more data points before you

can differentiate between a lot of exponential function is a quadratic

function for example it’s really too many too tough too many points so really

purnima or exponential so here what we’re gonna do is we’re gonna calculate

the first difference and that’s the way to do it the first difference or the

first ratio if the first difference is constant then the first ratio then then

its linear the first ratio scales and on the y axis then the that a function is

is expert someone 1 so we know that these are going linearly okay so these

should be drawn linearly if this function is a linear so briefly – 4:35

okay and we do need the characters of 4 for 35 – 348 okay 87 okay so then 522 –

4 3580 son looking good so far 522 – 605 so 609 609 I’m sorry – 522 any son and if in fact I see 187 +

609 is this in fact left from 696 so this is 87 as well and 596 + 80 is 776 okay and 776 + seven is 783 so in

fact asleep so okay so a function that that’s the data just fired split choice

of a function type the function sign is linear and don’t skip the problem after

I’m done writing because there’s something extremely important that needs

to be said because the first difference is constant okay so the very extremely

important things that that needs to be said is that this first difference

didn’t have to be exactly exactly constant for this problem and there

wasn’t a very good question it could have been the first difference could

have been 87 86 88 85 89 88 that’s still fairly constant it’s almost exactly

constant and this is this answer what a stupid linear because the first

differences are almost constant the other side of it if you got the first

difference not being constant and then you calculated the first ratio for 33/348

but to me too old for three and he got outdated whatever the

numbers were you copy the first ratio so instead of subtracting them you divide

them and you got a nearly a constant then that would have been an exponential

function of the function that would have been exponential because the first ratio

is nearly constant that’s not a question that they really can ask that and it’s

actually a completely fair question on an AC T SAT or regions when I mean

algebra two they will ask that one numero n piece yet they’re number 27

solve for x ^ 2 – 8 X – 9 equals 0 algebraically explain and

explain the first step that you used to solve the given equation so things to

know if you’re taking the SAT or a CT they don’t care about the method they

just care about the answer so if you know the the quadratic formula for

example if you want to do it that way you could do it that way if you wanted

to guess and check out the SAT or a CT you could do that in fact this one might

not even be that hard to guess and check but if the thing is that those don’t

count as algebraic methods for the purposes of this test so they they count

as numerical method the quadratic formula and and guessing checking both

count as numerical methods not algebraic methods I don’t agree with that but

that’s the case so how do we how do we do this one but there’s two ways of

doing it algebraically that I know if there’s many more one is finding two

numbers that add up to -8 into the same two numbers whose product

is -9 use those to factor x ^ 2 – 8x – done as two factors

and then solve for Mary using the 0 product property that’s one the other

one is completing the square that was completing the square I think is a

little bit harder but the test loves to ask about completing the square and we

haven’t really gotten some practice completing the square on this test yet

so I’m gonna actually do this one by that method cleaning the square

pay attention away I do this because every completing the square problem is

exactly the same 100% of them exactly the same if a is equal to one every

single one the same steps so the first thing we’re gonna do is we’re gonna

isolate x ^ 2 – ax – isolate the terms that have an X by adding 9 to

both sides okay and then x ^ 2 – 8x=9

now I highly recommend this part some students find stiffness writing but

there’s no reason why I want you to write this be write the value be

negative or 8 like the value of B/2 equals of -4 and write the value

of B/2 ^ 2=16 why are we doing this because these two numbers not

just the one of them but these two numbers are the exact values that are

gonna allow you to complete the square on the left there’s one unique way of

completing the square on the left these are the numbers that we’re gonna use so

first we’re gonna add B/2 ^ 2 to both sides so + 16 + 16 and we

got x ^ 2 – 8x + 16=25 okay why do we do that because this now

so we use 16 not 18 – 4 this adding 16 is the exact number the only number

the unique number that allows us to complete describe the left side and how

do we complete the square it’s using this number so it’s X – 4 ^ 2

this is the unique way of factoring the left side has a perfect square 25 okay

so that’s why these numbers are extremely important okay so now on the

left side the variable appears exactly once so we can actually solve this

equation using the inverse operation method invert all the operations in the

reverse order that they were performed and using the inverse operation so first

– 4 was subtracted men for was subtracting then the squaring operation

was performed we invert the last operation the squaring operation with

the square root operation okay this is exactly the place where

where where a lot of us up because the squaring operation is an information

destroyer the in squaring operation destroys the information about whether

the original number was positive or not here so by taking the square when we

take the square root we have to consider both cases if the number was negative

originally and or if the number was positive originally so we got an X –

4 is equal to + or – 5 okay now we just Affordable son size like the X

+ 4 and we get X is equal to 4 + or – 5=in other words 4 +

5 or 4 – 5 which simplifies as 9 or 4 minutes 5 is -1 let’s check

our answer okay if you want to check out what advise you to use the positive

number if you’re not comfortable with negative numbers I’m gonna actually use

that the -1 to give you practice with negative numbers so -1

^ 2 – 8 * -1 – 9 equals 0 -1 ^ 2 is a

positive 1 not a -1 – 8 times -1 is + 8 and then

– 9=0 and this should have a question mark here 1 + 8 is 9 – 9

equals 0 you might think it’s obvious that this is 0 but you don’t stop until

the left side expression is exactly the same as the right side expression 0 on

the left here on the right done so this is right notice I’m not checking the

other number than 9 if you if you’re doing a quadratic equation problem and

if you just check one of the numbers and that one happened to work generally the

the answer is correct the reason is that if you made a mistake at any point in

the process of solving this equation you usually would get both answers

one of the answers is right so most likely be both answers are right so

that’s not the hard and fast fact most likely it’s true if you want to check

the other number you can but remember that sometimes time is a factor on the

ECT MSgt time is an extreme factor and then other regions it can be a factor

depending on you and now the second part explained the first step you use to

solve this equation that’s this uh + 9 over here that we added so we added

added 9 to both sides of the equation to isolate the x ^ 2 on tax term x

^ 2 and X term in order to complete the square okay numero and Theo show number 28 of

the graph of F of T models the height in feet that the that Abby is flying above

the ground with respect to the time and traveled in T seconds

okay the height above the ground with respect to the time so height in feet I

see two and a four feet and I see two four six eight ten 12 14 time

and seconds and I see a jagged line and so so it goes it looks like the bees

going up and down I don’t look at the graph more thoroughly than that until

later too but I do take a quick glance because it helped me understand the

problem better state all the time intervals where the bees rate of change

is 0 feet per second explain your reasoning okay so rate of change if you

you don’t know how to do this problem if you don’t know what the rate of change

is and we need the rate of change to be 0 okay so so what is the rate of

change in this case since it’s a high and a time yeah so the rate of change is equal to change in the height divided

by the change in time for any cool for any sub interval for any interval any

sub interval so is equal to height final – height initial / a T

final – T initial so in this case notice that that for this to be 0 it

means that this fraction has to be 0 so we need this to be 0 which means

that the height final is equal to the height initial okay so now we look at

the graphs a little bit more thoroughly this graph is representing the B’s

height/time so the following this graph is going up which means the graph

the the B is actually gone up from a 0 feet to one feet/two seconds

then it kind of stays there at the same level that’s the rate of change so the

height is not changes that the rate of change is 0 this slope is positive in

other words the function is increasing over time so the rate of change is

positive the slope is positive the rate of change is positive real quick easy

where to see it then all of a sudden beasts are stopping the rate of change

is negative so and then the region is suddenly positive again and then the

rate of change is flat okay so and it says explain your reasoning right so

we’re gonna say the rate of change so let’s put that there

okay change see these these are notes for you this is not part of the problem

you do need to know this but you could put this on your test and in fact you

probably should so the rate of change is 0 okay so the height is not

increasing okay and the slope slope is 0 okay so

that’s the explanation there we go and an explanation we need

words okay if it says justify justified needs words

I don’t know explain needs words and justify needs any anything algebra or

words okay but where you explain does require words so the slope is 0 okay

the slope is 0 on the interval let’s see 2 2 6 2 2 6 and on the interval let’s

see if time 14 to 15 so the other two intervals 14 to 15 okay you might you

might write doing that as this T such that 2 less than or equal to T less than

or equal to 6 or 14 less than or equal to T less than or equal to 15 okay

either one of these answers would have been correct okay that’s it numero NP

limit number 29 graph of function f(x) equals 2 ^ x – 7 on these set

of axes below nice set of axes and if G of x=1.5 X – 3 determine if f

of X is greater than g(x) when X is equal to 4 justify your answer

I see the word justifies justify requires some algebra or numerical

justification but doesn’t require words but we do have to justify

it explain requires works so first we graph the function while f(x) equals

two ^ x – seven so just numerically speaking I see that two to

the X this is a base greater than one so I know that this is going to be an

increasing exponential function as x increases and of course two ^ x for

negative exponents gets closer and closer to 0 so when we subtract seven

from it it’s gonna have an asymptote a horizontal asymptote of -7

so it’s gonna it’s gonna get flatter and flatter and flatter as X gets closer to

negative something now here’s a question do we have to

label all the numbers negative ten to 0 to ten and also negative ten to

0 to ten ten upwards we don’t the rule about labeling the graph is if you

assume that each box represents one unit you don’t have to label it however if

you wanna expand the graph at all so that each box represents anything other

than one you do have to label the boxes so I’m gonna use each box and

representing one so one two three and I don’t have to label it so I didn’t even

have to write this I just want this is me explaining what I’m doing and of

course they’re here one -2 negative three so that -7 is

negative one -2 -3 negative four -5 -6

negative seven that’s over here okay number seven and I’m gonna make a dotted

line here okay now you might not be like me but I’m not using a

graphic operator but I actually let’s do that I already know what it’s gonna look

like though y=let’s clear this let’s clear this and this is y equals

two ^ X – seven and let’s zoom standard six look at it it’s

kind of flat so the form where you think it’s a line and then suddenly it blows

up break that that hockey stick effect these is what an exponential function

looks like a hockey stick goes straight but then it kind of curves on the bottom

so this is a this is what we call hockey stick effect and exponential functions

our hockey stick curves it’s a nice visual to let you remember that

exponential functions our hockey sticks so where is this asymptote we said it’s

at y=-7 in fact it is and if you want need points to graph at

the table they do that for you you just have to make sure to remember to go to

the table set make sure that table set is set to auto and auto and table start

you can put it at 0 and table Delta table is equal to one play putting the

independent variable a task is actually a really good tool because if you put it

I ask you could choose the number set of tests but then it’s left blank and it

won’t give you any values until you test them so it’s giving me the values so

that I can make it easier to graph let’s see 0 -6 0 -6 let’s see

1 -5 okay 2 -3 notice is hopping off by 2 then by 4/3 four nine four nine and then five and I

beyond are too big 25:57 and one of the big numbers right so now let’s go back

to the negative direction and we should expect this to get closer to negative

seven so -6 let’s see negative one -6 .5 ninety-two

six .7 five -6 point eight nine eight seven five .9

eight you see it’s getting closer and closer to -7 so we do in

fact an asymptote so here here here here here and it’s getting closer and closer

but it’s not touching so now we do a curve another place where students get

stop points lost on this is that they connect the dots with straight lines all

these straight lines get connected with certain very nice straight edge that

you’re required to be given on the New York State there were one regions but

this is not a straight line this is a curve so I am using curved arc okay

and I’m connecting to all the dots that I have okay and then with with curve

okay and I put it down here it’s gonna keep blowing up and I put an arrow here

because it’s gonna keep getting flatter okay the second player if g(x) is

equal to and that’s a point that’s a lot for a point but it’s a point here if G

of X is equal to 1.5 X – 3 determine if f(x) is greater than G

of X when X is equal to four justify your answer this is normally a three

pointer for a four point question but here it’s a three point question its

grade is f(x) greater than g(x) when x=4 justify your answer you don’t

have to graph this you can you’re allowed and in justification is allowed

so if you graph this and look at the breath to see where they’re located

that’s that’s good enough we’re gonna perform do I’m gonna do this

algebraically but I will graphic to the shack y=let’s go 1.5 x 1.5 X -3

and we’re talking about when X is equal to 4 so we’re gonna graph this when X is

even before and we could use the trace button one to look at the x value 3 4

oops so he’s about 4 so this line is here and the exponential function is

higher it so that shows that the exponential function is higher but let’s

actually do it by by calculating just sum or confirmed but what they’re saying

is f of 4 f of 4 we’re comparing it to G of 4 F of 4 is equal to 2 to the 4th

– son okay which is equal to 16 – 7 which is equal to 9 okay and

then let’s scroll down a little bit let’s see and G of 4 is equal to 1.5

times 4 – 3 which is equal to 6 – 3 which is equal to 3 so f of 4 is

greater than G of 4 yes okay

ah there is no purple explanation they needed we sodargye algebraic

justification and as justification does not require work so does not require

words explanation requires words justification doesn’t thirty determine

how to break Li the 0s of f(x) equals 3x cubed + 21x ^ 2 + 36

X this says algebraically I know a lot of people are fans of the quadratic

formula quadratic formula counts as a numeric method so we can’t use it here

and guessing and checking counts as a numerical method again we can’t use it

here so we have to use factoring by our usual methods either the AC method or

the BC method or completing the square I did one pre couple of steps above which

was I completed the square so we will do this by the other method the AC method

because we need a D method I’m sorry the BC method because you can so let’s see

so we need to do is find the 0s of this in other words they want us to find

3x cubed + 21x ^ 2 + 36 x equals 0 now some eagle-eyed members of

you might have noticed that this is number is equal to 3 this is 21 and this

is 36 so they have a common factor of 3 right so and they have a common factor

of s and we should factor out so 3x and it makes it easier for us

I wish they didn’t make it quite this easy for us because it would have

allowed us to practice something else and they just gave us this problem

earlier so it’s a repeat of the question there’s a rumor that that is this

current version of the Algebra one Regents is going to disappear soon soon

meaning five years unfortunately for you guys but what it means is usually when

that starts to happen the quality of the test starts to go down I think they

should maybe have fewer people working on this test and they just gave us a

quadratic formula problem where a is not equal to one and growl or a fashion

method I’m sorry where a is not equal to one and they wanted it algebraically too

so they’re actually repeating the same skill but the factor out of three x

times x ^ 2 + 7x + 12 parentheses=0 now the other

one I did by completing the square so I’m gonna do this one by the BC method

so be blank + blank to mystery numbers=seven and the product of

those same two numbers is equal to 12 okay now how do I find these numbers I

teach kids to do the factoring Bo one is that so this is a method of laying the

numbers that I learned from a student actually one and * 12 is 12

go to the next number two 2 * 6 is 12 3 is three a factor of 12 yes 3 *

4 is 12 and then the next number is 4 but for is already on the list you never

have to skip anything we’re done we found all the factor pairs of 12 one of

these numbers since this is and this is positive two of these

parents have to add up one of these parents has to add up to 7 so 3 & 4 3 &

4 7 3 + 4 7 so here is 3 & 4 & 3 & 4 so how do we use that it turns out in 3 x

times parenthesis parenthesis=0 this quadratic equation expression

factors as X + 3 * X + 4 these two numbers are the unique numbers that

allow us to do it that’s what to do this to factor 3x ^ 2 + 7x + 12 as

a factor of two monomials so that’s why we do it this way

monic monomials with a coefficient of 1 so now we need to use the 0 product

property a lot of students will stop and say the answers are 0 3 & 4 and they’re

wrong and immediately they lost a point we have this step that will that

teachers seem to take and we seem to think as necessary it’s necessary that

answers are not 0 3 & 4 3 x=0 / 3 / 3 so x=0

is one of the solutions but the next one X + 3=0 another thing that

seems to like move the 3 over that’s not of operation moving a number over to the

other side of an equal sign is not an operation it’s like having a balanced

scale taking the RAM off of 1 putting in the other and thinking it’s gonna stay

there it’s not right so – 3 – 3 so we’re actually taking away 3 from

both sides so we got X is equal to -3 okay and then also X + 4

equals 0 – 4 – 4 and we got X is equal to -4 and these are for

three answers and we’re done with this problem nu-metal plantino number 31

Santina is considering a vacation and has obtained high temperature data for

the last two weeks for Miami and Los Angeles so Miami you have a

whole bunch of temperatures okay and Los Angeles we have a whole bunch of

temperatures cool and then which location has the least variability and

temperature explain how you arrived at your answer okay so before we even start

this problem we do need to understand that this can it have this variability

can be interpreted in two different ways one is the standard deviation deviation

and if you don’t know if you don’t know what that is then a calculator does

calculator for you but it’s a measure of how spread out the data is okay and then

number two is just a max – the min and and the truth is that there’s other

ones q3 – q1 okay but we’re gonna focus especially on these two because if

the standard deviation for them happens to be the same then we need to go up to

max – min let’s see let’s see let’s go to the calculator though we do need

the calculator than some of these numbers so we go to stat press the stop

button and then we see the first thing that says and that’s the edit button to

go into the list I’ve actually typed in both lists very

carefully into this problem I’ve already typed the data in

just to save us a little bit of time one of the things that I advise you to do is

it’s really easy to accidentally miss type of a number so definitely check

that you typed all the numbers correctly I just did check that and I’d type them

all correctly so now I want a minute goal to do now I’m gonna go I’m gonna

press I’m gonna go to the catalog okay this is an extremely thing necessary

thing to do for someone using Diagnostics is not usually turned on our

calculators Diagnostics really should be automatic I mean the Diagnostics tell

you a lot of information about the data so let’s go to Diagnostics on it should

be the default there’s no reason to keep it off in other words in fact there’s

just no reason to have it off I think all four you can be an option on these

copiers but it is and it’s usually off so we have to remember to turn it on

as students okay so now that the Diagnostics is on so now I’m gonna go to

calc one variable statistics okay because each one of these is separate

from the other one variable statistics list one frequency this there is no

frequency list calculate okay so looking at these number number so here’s the Sun you know

the first one is the average the second one is the Sun the third one is the sum

squares those are relevant numbers for the average of course is a very relevant

number those are that the Sun is relevant to saw the square is relevant

for other things as accents Sigma s s s X is the sample standard deviation and

Sigma X is the potted is the population standard deviation the difference

between the concepts this is not a time important for this problem but I will

tell you for completeness sake the SS the sample standard deviation is it goes

on to the assumption that we’ve taken that this is only a sample of the ah the

full data this Sigma X is it goes under the assumption that this is the entirety

of the data that there are no other days so a sax is the more element number for

us so so for Miami okay as X is equal to 7.49 and in seven and then uh nine which

causes to round out the seven so seven .4 nine eight okay

and we could even put sigma x if you want to just be complete if you’re not

if you’re nervous about what you learn seven .2 to five the next ones

are to seven .2 to five okay now let’s go keep going the number of data

points 14 and then the min and the max if the min is sixty-two q1o seventy five

million million is 83 is 83 that series sound so we’re gonna do the

minimum the max – the min so max – the min is equal to 87 – 60 is equal to 27 okay

now let’s go for Los Angeles okay so aspects=Sigma X=and let’s

pull down here a little bit a little bit too much and then max – min equals

okay so stat calculate one variable statistics list is l2 l2 is right here

of them are the two button it’s in blue so we press the blue second button L to

enter there is no frequency this frequency list tells you how frequently

each data point occurs each sample occurs once cuz we put it that way

economy so SAS X is 3.77 in this case 3.77 the next one is a six and a seven so son

the next of the Sigma X is 3.639 3.639 I don’t care Samsung and then max –

the min but it’s gonna the max – the min so sixty 74-61 74-61=13

okay notice that this number is smaller and these numbers are actually also

smaller okay so by both definitions the standard deviation and the max – min

definition the variability in los angeles this temperature is lower so

that’s gotta be the answer if these were if these were opposites like this one

was bigger this one was smaller but you have to think a lot that that’s rare for

that to happen you have to think which one you want to

use as the definition but then I couldn’t do that to you because there’s

since there’s two definitions that are not going to shake you and to happen to

choose one versus the other it’s not meant to be a coin flip for the right

answer so the variability in temperature for our Los Angeles is lower because the

standard deviation deviation Tevi a tion is smaller that’s it

all right let’s deviate to number 32 thank tylose solve the quadratic

equation below for the exact value of x for x ^ 2 – 5=75 I

misread this problem multiple * that I said 4x ^ 2 – 5x so watch out

for that 4 * I misread okay let’s move so how do we solve this equation

you can actually do this by any method that you want completing the square

quadratic it’s already completed though technically you could use the quadratic

formula you can use numerical methods now because this one does not say to

that we have to use a specific method I see that there isn’t an X term in fact I

see that actually appears once in the equations so this one I actually I’m

gonna do it using the inverse operation method I think it’s the easiest way to

do it we haven’t used the quadratic formula yeah I know but a lot of

students get confused on the quadratic formula when there isn’t an X term I

will know this if you do want to use the quadratic formula okay I will say this that you get ax ^ 2

+ BX + C=0 so you have to get 0 by itself so you have to

subtract 75 and then notice that there is no X term B=0 okay that’s

what students that get sidetracked a lot so we’re not gonna use this method

though because actually appears once we’re gonna use the inverse operation

method so we’re gonna salt and we’re gonna add five

we’re gonna add five and we get 4x ^ 2=80 why did I do that

first because X is being ^ 2 then it’s being multiplied by four and then

five is being subtracted from that the last operation performed is a

subtracting five so we’re gonna undo that as the first operation by adding

five now the last operation performed on X is a multiplication by four we’re

gonna undo that by dividing by four so we’re going to divide by four /

four then we’re gonna get x ^ 2 equals 80 / 4 is twenty

okay and now we invert the squaring operation by the square root operation

okay and we got remember that squaring operation is an information destroyer we

don’t know if the original number was positive or if it was negative because

the string operation destroys the sign it turns it the number positive so

unless the number was originally 0 then it just turns it to 0 so we do

need to take into account all possibilities ax is actually equal to

+ or – radical 20 and this is worth a point already this is not worth

perfect two points is worth one point why because the radical 20 can be

simplified and they do expect us to simplify this by factoring out the

biggest perfect square factor of 20 so equals + or – and inside the

radical nothing comes out of the radical there is no taking something out

that’s never been an operation if an operation is written you do it if an

operation is not written you probably don’t have a reason to do it so radical

four is the biggest perfect square factor of 20 * radical five and four

times five is 20 and now we don’t take a four out of the radical we don’t take

the two out of the radical we performed the radical operations for root

operation the square root of 4 is 2 so + or – two radical five okay and

I’m not just being being tactical that’s where students lose points

let’s roll ourselves at number 33 this is the first four-point question for us

on this test Marylyn collects old dolls she purchased

a doll for $450 research shows that this doll value will increase by 2.5 %

each year write an equation that determines the value V of the doll t

years after purchase and then assume that the dolls rate of appreciation

remains the same will the dolls value be doubled in 20 years

justify your reasoning if I may can make some quick estimates well if which is

what I advise you to do if it increases by two and a half % each year two

and a half * 20 is is fifty okay so it’s not that it’s gonna increase by 50

% but that is a fairly okay estimate so 50 % is quite far from

a harness so I suspect that it’s gonna be close to 100 but not quite now that I

calculation that I did 2.5 * 20 equals 50 that is actually always

guaranteed to be an underestimate so we do have to be careful I just made an

estimate and I’m making the not be not sure what the answer is gonna

be so keep that in mind that 2.5 * 50 * 20 is 50 is only an estimate

for the girl theme the growth is guaranteed to be more so they’re also

the equation the equation in fact they want you to know here’s=80 equals

P * 1 + R ^ T a in fact I’m gonna put the over N and the N

here T where a is equal to final Valley okay P is equal to the principal also

known as initial value okay R is equal to the rate of increase increase n is

equal to the number of comp odd times compounded per year basis okay this this number is

only relevant when we’re doing finances like if you have an investment that

grows at a certain number of times compounded quarterly quarterly means

four * per year semi-annually twice a year monthly there’s 12 months of

the year and daily this severe than sixty five days in the year weekly

there’s 52 weeks of the year right so it would be 52 in the case of weeks by this

case it’s not being compounded at all because they don’t say that it’s being

compounded they tell us how free for me it’s compounded in a per year okay maybe

you just do 2,000 all things that compound that every quarter means that

there’s four quarters in a year so that then is four or if it’s monthly you do

need to go out there are 12 months in here that’s common knowledge or that

there are 365 days I mean you do have to know these things so n is not another

number for us and then of course T equals time and then for finances K in

cases it’s in years okay for non finance cases so you could be in days weeks

whatever it happens to be in the specific problem and in non finance

cases then n is guaranteed to be one so the equation simplifies a whole lot so

now write an equation of the value V so V is the value so in this case a is V

and then P is the sole and it’s an unknown value make changes over time but

the initial value is 450 so P is 450 okay there’s a one to the + now two and

a half % is as a decimal point 0 to five you move the decimal place

over twice 30 point 0 to five over one there’s no we don’t write the 1

because it’s this case it’s not number times

compounded and is one again same added here and then T is unknown value T T

changes over time so this is the equation for part one of this problem

stressed two points done let’s scroll down a little bit here assuming that

dollars rate of appreciation remains the same will the dollars value be doubled

in 20 years justify your reasoning they said justify

numbers and by the numbers and calculations are enough he didn’t say

explained so 20 years this is at T is equal to 20 we estimated that he would

grow by 50% that’s an under estimate and be the

actual estimate of complete for the linear sum it is only higher but 50%

could pick to more than double which is more than a hundred % that’s

that’s a big jump so let’s see I suspected me know so we in 20 years 450

times 1 + 0.025 ^ 20 and this is equal to this is not

something I can do one that come in my head I can maybe make an estimate to

this in my head but not not good enough to answer this question so 450 * 1

+ 0.025 ^ 20 that’s what this is 7:37 3037 sapling

seven cents so seven thirty seven and thirty seven and seven cents so

thirty-eight cents okay so now the % growth is equal to final –

initial over initial also equal to V – P/P * a honey

in this case it’s V – P or a – P over P * a hundred so let’s see five

us seven thirty seven .3 eight – initial 450/450 100 I only

need to in this case but I do need to have a calculator okay so for the C’s

because the diagonal fraction bar is not a grouping symbol but the horizontal

fraction bar is so this fraction bar and this fast bar are actually different 737

and in that one this one is not a grouping symbol about this with not the

only difference one three eight – 450 and I can

already tell that it is be the darling so but we do need

to confirm we do need to confirm algebraically so * 100 and just

saying it is not enough so 63% so this is sixty three .8 six five

sixty three .9 % sixty three .9 % growth okay and

then we could say no so no the reason is we do have to say yes or no we don’t

have to give a verbal reasoning but explanation because this is justified

not explained but the reason is that this number is not 100 % you could

say the value grew by sixty three point nine % which is less than a

hundred % so the price did not double no matter when people at number

34 I’ll get another four point question the

data given in the table below show some of the results of a study comparing the

height of a certain breed of dog based applies in there so I see maddis and I

see some numbers and then I see height and I see some numbers right a linear

regression equation for these data where X is the mass and Y is the height round

all values to the nearest 10 years you do not surround to the nearest tenth if

you don’t round correctly don’t take a point if you don’t round at all they’ll

take a point if you round to the nearest thousandth they’ll take a point so

definitely obey when they see it around to a fixed number and then state the

value of the correlation coefficient to the nearest tenth again and explain what

this indicates almost always this data will have a strong correlation almost

always for some reason on this test they don’t give data that has a low

correlation so let’s see we’re gonna get the calculator and this is a question

that they love to ask so you just follow the procedure and it’s for free points

on this region so let’s follow the procedure it’s the stat button

and then we go to edit okay now these already have our data for the previous

problem we used l1 and l2 you can go down to use l3 and l4 but if that

confuses you you to clear l1 and l2 the drawback by doing what I’m doing right

now clearing l1 and l2 is that now the data is gone so you can’t go back and

check your previous answer unless you retype everything so I would if you know

how to go to l3 and l4 I would do that and that might be a better idea I don’t

do that because I don’t want to have another layer of things you need to know

so what did we do we press the stop button and we got to edit and now we

clear this and now we’re using the data so the mass we already did Diagnostics

on the per member icaralot scroll down to Diagnostics on and turn it on you

have to do that there you’re required to do that that you won’t get this answer

for the second part if you don’t do that so Diagnostics time now we’re gonna put

in the data for .5 for the first for the mass five four three .5

five .5 five five four four six three .5 five .5 oops

and now I made an error you do want to check if you made a mistake or not so

five .5 keep on five six four four five five

five .5 three .5 four five four .5 good you always

want to check it’s just a quick thing quick quick chat because if this answer

will come out wrong for you mistyped you won’t know because there’s no reason to

know and in fact that everything everything will change very little if

you mistyped something unless you completely put a 55 705 but even that

isn’t changing much so now L 2 41 40 35 38 43 44 37 39 42 44 31 and 30

okay so 30 31 and 44 or 42 39:37 44 43 38 35 40 41

all right so now we have to quit and or we have to let get the linear regression

equation but this does that for us stat tell now it’s the little red bang s

+ B I would say put em here they don’t Limerick ax + B l1 is the

first element it’s usually put and someone else ooh the second element okay

notice how if you notice I was mislabeled here so I had to put it in

its I wanted blue above the one button so I press the blue side button to put

on one okay I’ll – frequency is very low frequencies store there with the

equation I like to store the equation so what I do is bars and this is where you

store it go to Y variables function one if you’re sorted six or seven or three

whatever you want to infinite be stored in the y equal sections okay and then

continuity okay and here’s the equation y=x for B where a is been five

nine seven so we have to round to the nearest tenth so aims one forty nine one

seven 81.9 so let Y be the heights of y is equal to

1.9 1.9 1.917 years these points

X if you have to sort of sesame + B + 29 .7 the

next numbers 19 it’s round up to seven 26 29 20+

29 23 okay so now stake the value of the correlation

coefficient to the nearest tenth and explain what it mean indicates this is

almost always strongly correlated this is actually the first time in years that

I’ve seen a low correlation coefficient this is our so let’s see R is equal to

0.32 near seven three three so R equals .3 so what does this mean so it

means so much with this is uh knows so if R is between as of salsa .7

is less than the absolute value of art including -r could be -r

and less than number one less than equal to one this is this is a strong

correlation okay then if .2 is less than or

equal to absolute R is less than or equal to .7 okay then this is

on a weak correlation and then if 0 is less than or equal

to ask them R is less than or equal to .2 this is usually no correlation okay so what does this what does that

mean it means that the data points are strongly related to each other or weekly

relate to each other are not related to each other so the fact that our point

three B means that that this will be correlation so this means there is a

weak a weak correlation between the mass of

what are we ready mass and height of let’s see certain certain breeds of dogs

the breed dog breeds cool noodle belly sink or number 35

Miranda received a movie gift card for $100 to her local theater matinee

tickets cost seven dollars and fifty cents each and evening tickets cost

$12.50 each if X represents the number of matinee tickets she could purchase

and Y represents the number of evening tickets she could purchase write an

inequality that represents all the possible ways Miranda could spend her

gift card on movie theater tickets then on the set of axes below graph the

center quality they were nice and still able in for us and then what is the

maximum number of matinee tickets Miranda could purchase with her gift

card so let’s let’s actually just go one piece at a time here

Miranda received a movie gift card for $100 to our local theater matinee

tickets cost 750 and evening tickets cost 12 fifty each and if X

represents the number of matinee tickets you could purchase so X is equal to the

number of marinated that she could purchase okay and y represents the

number of evening to kiss chica purchase so right

and inequality that represents all the possible wave Miranda could spend her

gift cards on movies back to the theater so it looks like she could buy a bunch

of men they think is a bunch of evening tickets and she helped until the point

where her gift card runs out we talked about above I had some previous problem

how a cost is related to the number of the same projects that you buy we and we

talked about how that if one ticket costs 752 costs 15 three cost twenty to

fifty and it gets harder and harder then to get the final number because after a

while I hang up a number of multiple times gets difficult but we talked about

that adding a number multiple * is where the multiplication operation

originally came from the wheat the reason we used to work * is because

we went somewhere we say like 750 * 8 we mean 750 + 750 + 750 added 8

times so in this case this having 50 is not added 8 * because 750th the cost

of a man a ticket and the number of matinee tickets we bought is unknown X

value it’s an unknown variable s which we called we got we inherited at that

name so if we buy 707 dollar 50 tickets $7.50 tickets x * the cost is equal

to 4 the madness tickets at 7:15 X you see them none the cost for one ticket

times the number of tickets it’s always the same the same deal here that one of

them evening tickets cost 1250 so the cost for all the evening tickets it’s 12

15 * how many tickets we bought is why

and now this cost has to be less than or equal to the amount of money that

Miranda received so less than or equal to 100 okay all right so how do we graph

this there’s I do I want to teach you a new way I do I think I do want to teach

you a new way of graphing this because the thing is that a lot of * were

used to graphing the y=MX + B way of graphing an equation and then we

have an equation that it’s not written in y=MX + b form and then we

get confused especially in for the consu who struggles with the y=MX +

b form so if you know how to do y equals MX + B go ahead and do y=MX

+ B I’m gonna actually show you how to do this a different way because this

is an actual it’s called the standard form why it’s called standard form is a

little esoteric and that’s to do with quadratic equations and things are not

platonic at all but we’re gonna use the method of noting that if X is 0 the

only term here is y so so the y intercept is equal to a hundred over the

coefficient of Y is 1250 then we can use the calculator to get this one hundred

/ 12 50 is actually eight okay so being y intercept is 8 okay so one

two three four five six seven eight okay now the x-intercept it’s equal to so if this is the case

when vehicles on the x axis y equals 0 so if y=0 this is 0 so

750 ax is less than equal to hundred so we actually got a hundred / the

coefficient of x is 750 and I do need a calculator for this one it is a decimal

so 750 and it’s 13.33 so what do we do here so let’s see 1 2 3 4 5 6 7 8 9 10

11 12 13 20 3 3 so it starts another third okay now notice I didn’t label the

numbers as 1 2 3 4 5 6 7 8 and I didn’t know the numbers here if you count up by

one you don’t have to if you cannot buy anything other than one

have to okay so I’ve got the line you know using the software on on my side

you have to use a straightedge again because the line is a straight line if

you don’t use a straightedge you’ve got the question wrong now you might also

notice that this is an inequality right so how do I decide if I if I should make

it into quality with a dotted line or a solid line if you draw the side line if

equality is violet so if it’s less than or equal to or greater than or equal to

and you draw it with a dotted line it could be if the applauding it’s a less

than or a greater than inequality this isn’t less of a equal to in a class

so I know it’s a solid line so now how do I decide so this the way we could do

this is by testing a point we could the way you test a point is by saying

choosing them on a point below or above and seeing if it’s a valid point

in the city of quality so I’m going to choose a point if we buy one man a

ticket one evening today so one s one so sunny fifty + 12 fifty is mention

dollars twenty dollars and she’s less able to operate this point is in is in

the solution of unify so every point below God is in the solution of the

employee so he actually stood below I don’t know because the methods not

released yet so I don’t know if you graph the line company but your children

stayed here if it’s worth a point or two points but this is a complete graph yet

so notice nothing has changed above you notice a couple to the left of the graph

is below the graph okay so now we go to the system at the next plot what is the

maximum number of mandates afisma to purchase with a gift card so in explain

your reasoning it’s only now we have to use words okay the words words are

required so let’s give words so we maximize so we can really maximize matinee tickets bye well if we but if we mark something

if we buy any evening tickets then we weren’t spending money on that so which

leaves less money to buy their next tickets so we’ve maximized the mandates

and it’s by a number of many tickets okay bye and bye bye bye

0 evening – it’s okay okay so let’s go back to the inner quality so 750 X

+ 12 50 Y is less than or equal to hundred so 750 s + 1250 Y is less

than equal to wonder did we like Y is 0 so 715 X + 12 15 *

0 is less than a dollar so this is 0 so 750 ax is less wrinkled all

right / 750 / 750 then we got an X is less than or equal to and

stop using for 13 .3 repeating three repeating if we stop

here we don’t get the point that we wanted because you can’t buy a third of

a matinee ticket you can’t five .3 repeating

automatic if you so either by nineteen to this and a very common strategy for

that Isis if this number is bigger than five then you would think you’d round up

it and if you don’t have the money don’t buy like .8 of a ticket either

you still can’t buy that ticket so that’s this number so we can buy

13 matinee tickets I hope this videos loving you like I

think it is if it is click the subscribe button and also I again invite you to

click on the the review packets that I created for you there really are that

good and they’re really an affordable price and then on top of that I’ve

lowered the price by 20% – thank you for watching this video let’s go on to the

next problem nobody says second-to-last problem one

spring day Elroy noted the title day and the temperature and degrees Fahrenheit

his findings are stated below at 6 a.m. the temperature was 50 degrees for the

next four hours temperature rose three degrees per hour

the next six hours it rose two degrees per hour the temperature then stayed

steady until 6:00 p.m. from there but from the next for the next two hours

temperature dropped one degree per hour the temperature then dropped steadily

until the temperature was 56 degrees Fahrenheit and midnight on a set of axes

below breath Elroy’s data there’s a lot of little bitty pitfalls here but I

don’t expect you to keep all that extra info in mind they don’t expect you to do

that either the way to do this problem is not to keep all that crazy stuff in

mind it’s there so you can refer to it so let’s look at the

don’t forget to subscribe the sandbox is below graph Elroy’s data the interpreter

I see it goes up from 50 to 60 in five boxes so Street County and good for them

prefer for labeling the graph for us then soda skipping

skip counting the temperature back to the bees each time and the temperature

looks like it’s nasty beyond this exam 7:00 a.m. 8:00 9:00 a.m. 10:00 so it’s

going by one hour and so now we carefully graph to do the details using

dots and then we should connect with straight lines with straight lines and

connect what we should connect with programs with curved lines fair warning

they don’t want you to assume somehow the curves curve in some weird way just

because if they don’t give us information of the time in between we

should assume that the curve is is straight layer for the pieces so let’s

see at 6 a.m. the temperature was 50 degrees let’s go for the red pen 6 a.m.

the temperature was 50 degrees okay keeping in mind the boxes to the right

count per hour upward count to degrees so then for the next 4 hours the

temperature rolls three degrees for the next 4 hours so until 10 o’clock the

temperature rose 3 degrees per hour so 7 a.m. going up 3 degrees remember this is

skin counting by 2 so 3 is not here it’s here ok

8 o’clock 3 degrees more that’s 2 hours not 3 just because it’s read us 2 hours

remember an hour is a gap hours a gap not about 9 o’clock a 3 more 2 bees

ten o’clock three more degrees okay now the next six hours it rose to

degrees per hour so from 10 o’clock + four hours is four o’clock p.m. + six

hours at four o’clock p.m. so it rose two degrees per hour so now we’re gonna

go back two degrees each hour remember this is the boxes are script counting by

two so one hour two hours to two hours two peas third hour two degrees fourth

hour two degrees fifth hour two degrees and sixth hour two degrees and let’s

just make sure that we skip counted correctly this is 4:00 p.m. then that’s

the last dot then the temperature stayed steady until 6:00 p.m. 6:00 p.m. is two

hours later so stayed steady stay steady cool then for the next two hours so

until 8:00 p.m. the temperature dropped by one degree per hour

remember don’t stir don’t ever lose compounding by two so half a box is one

there half a box is one half a box is one and then the temperatures then drop

steadily until the temperature was 56 degrees at midnight so right now we’re

at 72 degrees and we’re gonna go down to 56 degrees at midnight this is the only

plumber recently have to do a little bit of algebra okay so we have to do the

rate of change from from 8:00 p.m. to midnight so let’s see delta cavinti for

temperature/delta little t why’s my printer making noises so delta T over

delta T is final – initial so 56 – 72 and / the time 12

– 8 so this is equal to 56 – 72 if you’re not comfortable with -r

numbers that’s you could use a calculator but you can also count up and

then negate it so -56 to 60 is for 270 is 14 to 72 is 16

12 dot but the Tollman is a is four so this is a change of -4

degrees per hour so we’re gonna drop by for de beans and let’s use it as a check

we should definitely end up exactly here by dropping four degrees per hour so

let’s see four degrees down one hour this is looking good already four

degrees down one hour four degrees down one hour and four degrees down one hour

perfect and then we stop okay so now do we connect these with straight lines or

curves we connect them with straight lines because there is no information

that says let me just go and blue for a second there is no information that says

that this thing is like some weird curvy thing you see how I’m drawing a conic RV

there’s no information that says that that’s the case

so in fact we do need to use a straightedge in this problem so instead

of wrestling with the software I’m gonna skip right to the point where we have

the straight lines and here they are and so the straight lines have to be

drawn with a straight edge the straight lines go from here to here stops another

straight line from here to here stops another straight line from here to here

stops another straight line from here to here stops another straight line from

here to here okay so we’ve grabbed the data cool so let’s keep going now to

state the entire interval for which the temperature was increasing so I just

have to state it it was increasing from 6 a.m. all the way up to 74 degrees at

4:00 p.m. okay so from 6 a.m. a.m. to 4 p.m. and that’s it no full sentences you

don’t need the temperature was increasing from 6 a.m. to 4 p.m. if you

want a full sentence you don’t need it good

good so now determine the average rate of change in degrees per hour from 6:00

p.m. to midnight 6:00 p.m. to midnight so the average rate of change this is an

important topic and they do ask this question on multiple-choice part twos

and on the SATs and a CT so average rate of change rate of change is equal to T

final – T initial/time final – time initial okay so T final

temperature final is and notice the ordering of that it’s always that don’t

like change it just cuz you got a -r number the temperature is

dropping the average rate of change is -right so the temperature final

is 60 it’s 56 degrees it’s 56 degrees – it’s the same calculation that we did be

formal with two slightly different numbers the top temperature was 74

degrees okay 74 and then the T at that time final was 12 so and then – the

6:00 p.m. 6:00 p.m. so this is equal to 56 – 74 which again you should use a

calculator if you’re not comfortable with the -r number by 56-74 if I

come from 56 to 76 I get 20 go down I get 18 so -18 / 12

– 6 is 6 which is equal to -3 degrees per hour I’m gonna change my

answer as a hint to you if you’re taking the Regents if they gave you the unit’s

okay unis given then don’t give you this

do not ok this is a protip do not give unis I gave them and I gave them

correctly so I’m gonna cross them out 3 degrees -3y if they give you the

units they’re already stated you don’t have to give them if they didn’t say

penis or if they ask you for the unit’s you do have to state them but no one

thing gave us the units so now why do I say don’t state them -3 is a

correct answer why because the units are do please per hour because they said so

however if I give the units please degrees per hour I’m not wrong on the

other side of it if I make a mistake which happens all over the regions and

I’m talking about I’ve read so many of these thing and you get the unit’s wrong

you lose a point so there is no point in ever giving the unit’s in algebra 1

regions unless it’s clear that they want you to give them and how do you know if

they want you to give them if they say so so they say give me the units they

didn’t say that here so I’m not giving them done -3 is the answer

that’s a protic no teacher might not like me when I say that I’m a teacher

too though trust me and we finally made some last question of this test number

37 if you appreciate the work that I’ve done for you if you even remotely like

the quality of work that I’ve done please hit the like button so that other

students can see it please click the subscribe on

gotta get other videos and the higher tests I’m making them as we go and of

course like I said check out the the stuff that I had even if you don’t plan

on buying it just go check it out see if it might be worth it for you you might

be surprised the price is really not that high I’m not charging like 30 bucks

for that one that one review package it’s very small as I as I go in the

future and I start creating a actual class that might be a little bit more

expensive but this this is a prelim this is just baseline it’s a midterm it’s a

final and and then a few days because I have I’m handing it to my students

enough in about January 15th I’m sorry February 15

I’ll have another packet and it’s gonna be there too so if you after February 15

it’s gonna be there too check those out and love the t-shirt pie

a 3.14 March 14 it’s coming up definitely check out the t-shirt too

let’s go for the prize of this test number 37

six points okay six points is a lot out of 86 points in fact on this region’s if

you get full credit on this question which only requires the test only

requires 27 points so you’re and you’re actually it’s about it’s a little over

20 % of the points that you need to pass the test if you get a full

credit on this cup question believe it or not twenty % of more than 20

% of the way towards towards getting a fool for a

passing grade 20 about 20 to 23 % so let’s do the winter plan this year

that number 37 recreation center ordered a total of 15 tricycles and bicycles

from a sporting goods store so total of 15 tricycles and bicycles the number of

wheels the number of wheels for all the transfers and bicycles total 38 right

all linear system of equations that models this scenario where T represents

the number of tricycles and B represents a number of bicycles order okay I know

this question is is tough for a lot of students right but let’s go convert B

questions the words into equations okay and I’m not gonna continue reading with

the rest of it let’s just focus on this one part because this is actually an

important scope not just in general but also for this test so a recreation

center and they love asking this question recreation center ordered a

total of 15 tricycles and bicycles so the total number of combined tricycles

and bicycles is equal to 15 so number of trikes + number of bikes=15

and there we have it the words converted into an equation T is the number of

tricycles t + the number of biiss B equals 15 then we got a point

right the next part so let me move this over

something I did something I can do I can’t apparently I can’t do I thought I

could do it either no I can’t do it so I’m gonna go over here and I’m gonna

talk about the wheels okay this this is the part that that couldn’t cause a

little bit difficulty the total number of wheels is equal to 38 so this is how

it is the number of trike wheels + the number of light wheels equals

38 now this might seem tough but if you go back to what I’ve been talking about

throughout this video it’s that if you actually think about what multiplication

is multiplication is a repeated addition you can actually get an expression for

this quantity remember if one tricycle has three wheels

oh that’s something they do expect you to know about a tricycle has three

wheels and a bicycle has two wheels try so the prefix tri is three the prefix

binds to okay so what tricycle has one tricycle has three wheels two tricycle

s63 tricycle has nine four tricycle as well oh wait but if I ask you for 30

trustable what would you do you died 330 times no three but three thirty *

three thirty * three * 30 so you take the number of wheels in one

tricycle * the number of tricycles that’s it so three * the number of

tricycles is T + the same deal with the bikes two wheels per bicycle *

the number of bicycles that you have so two * a number bicycles that’s a

beam okay let’s make that clear B is equal to 38

there goes our equity let me write them a little bit neater here so T flood B

equals 15 and 3 T + 2 B=38 nice right and then on a Sun that and

let’s go to the graph on the set of axes below graph the systems of a system of

equations you can turn it into a so B is the the y axis and you so you can what

you can do is and I’ll show you both ways let me go and blue ok so you could

turn into a y=MX + B type of situation solve for B because b is the y

axis so B=15 let me MX + B so -t + 15 I subtracted B from

both I subtract 50 from both sides and then I have a slope of -1 and a

y-intercept of 15 BAM slope of -1 then I got you here

okay um they’re there they’re there

ok so I keep going and I don’t need you just to see me wrestling with the

software so I’m just gonna draw this and there’s a straight line you do have to do this with the

straightedge so the second one I’m gonna do it the other way because I know a lot

of students mess up the the y-intercept form instead I’m gonna do it the other

way because this is the standard form the standard form is there’s a switch

back to write the standard form there’s a nice easy way of getting the

intercepts let one value be 0 so on the y intercept on the B intercept

two T is 0 so to be=38 so B intercept to B=38 or should I say

let’s let’s make it clear three * 0 + 2 B=38 this is a 0 so

this is gone so / 2 / 2 and this is gone I don’t need to

divide this by 2 because it’s not there right 0 is + 2 B is 2 B so B is equal

to 19 ok so the V axis is 19 to be intercept is 19 and also the team is

sent okay so I got 3t someone on the teen or Sun B is equal to 0 so 3t + 2

times 0 is 38 so 3t=38 that’s a 0 right so

divide by 3 divide by 3 and I got T is equal to 38/3 is 13 – 1/3 so 12.6 repeating okay 12 .6

repeating good let’s confirm that with the calculator I don’t want to be make

problem 37 the point where I where I messed up for you guys but I do know the

answer so 38 cuz nine / three is 13 right

so there is 2.6 repeating so that’s the T intercept and now I’m going to connect

this one line and there it is okay so um do you have to connect this one with the

straightedge also yes you do but here it is

now the next step based on your graph in this scenario could the represent the

recreation sector have ordered ten tricycles explain your reasoning

so I let’s see ten tricycles if we go to ten tricycles that means we go up let’s

see so the number of wheels total 38 can we convey of order ten so here’s the

thing this is not even an inequality question so it’s not below a lot this

big can ask you to do quality question below so they can graph this quantity

this region but they’re not asking an inequality that it’s saying that it’s

actual equality so this is the exact scenario that that corresponds to this

problem now I see that the problem is kind of its kind of not on a corner and

it looks like it Rana is on the corner like it may be a tricycles and seven

bicycles and that happens when we draw with a pencil we might be a little bit

inaccurate without with our broth but um if you

look down here to the seat down if the slope is -3 and -3 over

2 so 3 & 2 3 & 2 & 3 & 2 so this so this graph does cross here okay so if this is

the correct corner Sun and 8 so 8 comma 7 so that is the point that is the only

point this is the point the only point so the question is could the recreation

center I ordered 10 bicycles explain their reasoning so the answer is no

because if they order 10 principles so this time is not on it on that point

that it’s eight in fact so and it says based on the graph okay so we have to

use the Brad I was about to give an explanation that involved the algebra

like if they ordered ten tricycles then they ordered five bicycles then the

number of wheels is 10 * 3 is 30 + 5 * 2 is 10 is 40 but that’s

not a valid explanation because the SI based on the graph make in order to

tricycles they ordered 5 bicycles ok bye ok I can’t spell bicycles buying see

Cole’s right by the graphs intersect at the . 8

comma 7 which means they order eight tricycles and seven bicycles and

that’s the full explanation there’s a lot of explanations that say why they

can couldn’t have ordered ten tricycles but again they did insist that we do the

graph I hope that this this video was as rewarding for you as it was fun for me

to make I really appreciate you watching this video listen and I know you can do

it I actually know I fully believe in your abilities if you appreciate the

video that we created definitely hit the like button you click the subscribe

button cuz we have way more videos coming we hang our videos in the past

you know they’re gonna keep coming and check out the review packets that we’ll

have right on bottom and check out the t-shirt I think it’s a really awesome

t-shirt this one t-shirt has gotten more compliments from from friends and family

than anyone any t-shirt that I’ve ever worn that have created myself so I’ll

definitely check out thanks for watching stay tuned for the next video coming up

wow, I usually HATTEEE watching these vids for practice because they are so boring and I feel like they do nothing. BUT THISS!! you are so entertaining and actually make me wanna finish the video and practice. Thankyou so much you actually helped me not only in hopefully passing the regent but in a way that I want to learn loll. If I do good its bc of this vid. I learned more in this vid then I ever learned in all my terms of taking algebra classes

I just watched every minute of this video … I feel prepared for the test tomorrow but watch me fail anyways 🙁

One more question sorry because I have my regents tomorrow, how many can be done on calculator? Can you make a video ASAP and show us which ones and how? If not it’s okay

The video could have been better without the loud background music

Thank you sm I needed this

Will you come out with the June regents 2019

I’m so scared I already cried 3 times I have to take mine tomorrow 😭😫

any tips plz? My test starts tomorrow😶

I’m trying to pass the regents and this man is plugging his Merch 😭😭 like your vids tho

omg thank you for this i was about to die.

Omg you are literally my last hope. I’m going to wake up early and rewatch this tomorrow before the test. If I fail would you be up to tutor me over the summer lol? I attend a private school and is one of the worst schools. We can’t afford to pay teachers anything but minimum wage so they all really suck. There is literally a giant hole in at least one of the classrooms with a tarp and a hose connected to a bucket to catch water from the roof. We’ve had four math teachers this year all of which obviously can’t teach or flat out won’t. We didn’t even get through the algebra book. I am a resource student- I can’t really teach myself anything. Im probably going to fail this test. Throughout the school year I didn’t have the time for a math tutor and keep up with the rest of my classes. Don’t even get me started on our six earth science teachers! I’m miraculously very well passing all of my classes so I don’t qualify for summer school. I’m not allowed to leave my school parent wise. I’m probably not going to pass high school. I apologize about this long paragraph of a comment, I just needed to rant

Thank you for sharing your knowledge to us all, i was very simple and this is all from a teacher which is amazing! Thanks.

oh my gosh this is really helpful. I feel really confident for my regents tbh

God bless

im scared.

regents is in a couple of hours. pretty helpful

Does every school provide that type of calculator during the regents or do you need to bring your own? because I only have a scientific calculator and I'm worried I won't be able to do some of the problems.

I failed the algebra regents last year now I hope i can the regents with your vids thank you so Munch

When your taking the test today and you rly need to pass

Thank you for your video its very helpful

Mine is today thank you have watched this video twice and taken notes on all problems to solve them you have helped me so much you earned a sub 👍

My regents is in a couple of hours

Hi kids! I know you're working hard between now and the test in a few hours. I just wanted to give you the biggest pointer you all are asking for: what do you do between now and test time? What you do is this: do problem 1 on this video until you get an answer. If you get it wrong, write down everything I do to get it right. Then retry the problem without notes until you get it right. Then go to problem 2 and do the same thing. After that, problem 3, etc. I know you can do it, and I believe in you! Knock this one out of the park for me! Also sorry about the loud music! I seriously and honestly don't know what caused it to get loud. Please hit like anyway, and don't be afraid to subscribe! You could be studying from a book right now, but you chose to study with me, and I appreciate that and thank you for that. Let's go!

I’m gonna kms

Im nervous for this test, i just wanna pass to get it over with

I’m a 12th grader trying to score a higher grade than I did before (I got a 67) this is actually helping considering o haven’t had math this whole year

Your amazing! I subscribed!

You deserve more subs this video was super helpful

How many answers do you need to get right to get a 65+?

Please drop the music sir i need quiet and i just need to hear you not that music that im pretty sure no one listens to but other than that great review you have helped me big time so i thank you so much

Have it today this really helped thanks🖒

This was so helpful

I don't understand the question #33 that you said it's NO! Why it's NO, can u explain ?

Who else is here 2 hours before Test

I’m about to take the regents in an hour

It’s A Great Video But The Music In The Background is Really Distracting

2:07:24

Who else has their regents in an hour?

3 brain cells has been gained by this videodude,, i got algebra regents in less than an hour, i just finished this video,,,, i feel so much better about this test holy shit thank you so much

For question 27 can I use quadratic formula. Answer quick I’m gonna take test in 30 mins

Every time I do number 25 I get 8,000

I just took June regents please go over number 26 and number 30 in detail please

What happen if you lose the regents

Talk to me all! How did the JUNE 2019 ALGEBRA 1 REGENTS go?!?

Thanks I pretty sure I did good on this regents part 1 and part2 but not part 3 😅

My son Juan blessed me yesterday ❤️

Why am I here🤦🏻♀️🤦🏻♀️🤦🏻♀️I should be on geometry vids

Hey, I’m in 8th grade and I took the algebra regents. This video was very helpful and I got 100!!! I was so happy.. (I scored pretty good in my other regents) Thanks for everything!

Thank you I passed the regents cause of you

Thanks WFI still going to watch you bc next year I got geometry

yo juan i got a 96 in the algebra 1

Is 68 a good score for regent? Should I take it again

Bro thanks I watched this video and I got a 76 on my regents I’m finally college ready!

The June 2019 algebra 1 regent was so easy that all you have to do is sleep and write and you pass.

Passed my regents thanks to this vid 😭

Hi, I am Immanuel, Which instrument do you use to write on screen?

I liked the way you are explaining math problems. The board you are using is incredible. Can you tell what is the name of the board you are using it.

i failed the regents im taking my regents again august

i forgot do the regents suppose to so january even tho its july

Jesus please help me. I am going into my senior year and going to summer school for this. Hopefully I pass by this video and by the grace of GOD. WISH ME LUCK.

Thank you so much I learned so much here then in school!!im watching this cause I failed it on June by 4 points now I needa retake it😔🤟

these videos very helpful especially as an 8th grader who hasn't really learned theses concepts and has 2 regents coming up in less than a month

Can you do this for the June 2019 Algebra 1 Regents? I have to retake the test

Juan I have trouble with algebra 1 don’t k what to do i feel so stress I can’t play or anything until I pass it I’m literally home studying all day stressing please tell me what I can do

i failed the algebra 1 test in june , i have to take it again august 13th or 14th 🥺 i failed by one point

can i contact you for further information? my daughter has to retake the regents on august 12th

I have to retake the test, but the only thing I’m confused on is if the test is going to be the same

I really want to get a good mark, I got a 75 but I want to retake it, it would make me so much more confident but the more I try the more it seems impossible! My brain doesn’t work well with math, I don’t know what to do or how I’m get into a good college if it takes me hours to understand simple math.

I failed both of my exam so I really need this.

For questions like number 4 should i always round down?

istg im dumb. NOTHING in math makes sense to me not even this. Im screweddd for next week.

I failed my regents by 1 point hopefully this helps me for me retake

Vivo en New York estoy en MHS y es una escuela que se habla más español que inglés podrías hacer el proceso del regente pero en español please

This was so helpful thank you !

I dont understand how you got 1.52 for number 16

who

is watching this last minute

ok this is my last chance to get college ready…..am gonna tell you my score soon

hopefully this helps for the algebra 1 regents i’m taking in january 2020

i need to get at least a 70 or over to pass so i’m reviewing over everything during the christmas break

plz wish me a good luck!!

You teach better than my teacher omg, you arent boring and you really make me understand it thank you.. I'm taking my test in 3 days and this video is gonna help me alot thanks once again

How he got 7

Ik this is free99, but the music ruins the whole vid.

I have to retake this tomorrow 💀💀💀

Bro your music hurts my head

I have my algebra regent tomorrow for the first time and i dont know what to expect but this really helped me to review and make sure that i know at least most of the material needed to pass the test. Thank you!

i'll be honest but the music is bad, I can't focus on the video without being distracted by this music

Try not putting the music in your videos

This regent was too easy, I got a 95, btw I am in college now, Harvard

Pls can u come to Urban Action Academy at Canarsie campus in Brooklyn 😭😭😭😭