January 2019 Algebra I Regents, THE WHOLE TEST, NY Common Core part 1, 2, 3, and 4

January 2019 Algebra I Regents, THE WHOLE TEST, NY Common Core part 1, 2, 3, and 4


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

89 thoughts on “January 2019 Algebra I Regents, THE WHOLE TEST, NY Common Core part 1, 2, 3, and 4

  • June 18, 2019 at 3:38 pm
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    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

    Reply
  • June 19, 2019 at 12:52 am
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    I just watched every minute of this video … I feel prepared for the test tomorrow but watch me fail anyways 🙁

    Reply
  • June 19, 2019 at 12:57 am
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    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

    Reply
  • June 19, 2019 at 1:03 am
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    The video could have been better without the loud background music

    Reply
  • June 19, 2019 at 1:15 am
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    Thank you sm I needed this

    Reply
  • June 19, 2019 at 1:16 am
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    Will you come out with the June regents 2019

    Reply
  • June 19, 2019 at 1:26 am
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    I’m so scared I already cried 3 times I have to take mine tomorrow 😭😫

    Reply
  • June 19, 2019 at 1:36 am
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    any tips plz? My test starts tomorrow😶

    Reply
  • June 19, 2019 at 1:42 am
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    I’m trying to pass the regents and this man is plugging his Merch 😭😭 like your vids tho

    Reply
  • June 19, 2019 at 1:44 am
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    omg thank you for this i was about to die.

    Reply
  • June 19, 2019 at 1:55 am
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    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

    Reply
  • June 19, 2019 at 1:57 am
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    Thank you for sharing your knowledge to us all, i was very simple and this is all from a teacher which is amazing! Thanks.

    Reply
  • June 19, 2019 at 2:18 am
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    oh my gosh this is really helpful. I feel really confident for my regents tbh

    Reply
  • June 19, 2019 at 2:46 am
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    God bless

    Reply
  • June 19, 2019 at 3:05 am
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    im scared.

    Reply
  • June 19, 2019 at 3:07 am
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    regents is in a couple of hours. pretty helpful

    Reply
  • June 19, 2019 at 3:26 am
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    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.

    Reply
  • June 19, 2019 at 6:00 am
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    I failed the algebra regents last year now I hope i can the regents with your vids thank you so Munch

    Reply
  • June 19, 2019 at 9:50 am
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    When your taking the test today and you rly need to pass

    Reply
  • June 19, 2019 at 10:12 am
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    Thank you for your video its very helpful

    Reply
  • June 19, 2019 at 11:59 am
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    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 👍

    Reply
  • June 19, 2019 at 12:03 pm
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    My regents is in a couple of hours

    Reply
  • June 19, 2019 at 12:56 pm
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    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!

    Reply
  • June 19, 2019 at 1:22 pm
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    I’m gonna kms

    Reply
  • June 19, 2019 at 1:24 pm
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    Im nervous for this test, i just wanna pass to get it over with

    Reply
  • June 19, 2019 at 1:34 pm
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    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

    Reply
  • June 19, 2019 at 1:37 pm
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    Your amazing! I subscribed!

    Reply
  • June 19, 2019 at 1:48 pm
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    You deserve more subs this video was super helpful

    Reply
  • June 19, 2019 at 1:55 pm
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    How many answers do you need to get right to get a 65+?

    Reply
  • June 19, 2019 at 1:57 pm
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    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

    Reply
  • June 19, 2019 at 2:04 pm
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    Have it today this really helped thanks🖒

    Reply
  • June 19, 2019 at 2:13 pm
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    This was so helpful

    Reply
  • June 19, 2019 at 2:18 pm
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    I don't understand the question #33 that you said it's NO! Why it's NO, can u explain ?

    Reply
  • June 19, 2019 at 2:19 pm
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    Who else is here 2 hours before Test

    Reply
  • June 19, 2019 at 2:20 pm
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    I’m about to take the regents in an hour

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  • June 19, 2019 at 2:30 pm
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    It’s A Great Video But The Music In The Background is Really Distracting

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  • June 19, 2019 at 2:47 pm
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    2:07:24

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  • June 19, 2019 at 2:51 pm
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    Who else has their regents in an hour?

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  • June 19, 2019 at 3:02 pm
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    3 brain cells has been gained by this video

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  • June 19, 2019 at 3:10 pm
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    dude,, 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

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  • June 19, 2019 at 3:21 pm
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    For question 27 can I use quadratic formula. Answer quick I’m gonna take test in 30 mins

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  • June 19, 2019 at 4:07 pm
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    Every time I do number 25 I get 8,000

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  • June 19, 2019 at 6:55 pm
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    I just took June regents please go over number 26 and number 30 in detail please

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  • June 19, 2019 at 7:38 pm
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    What happen if you lose the regents

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  • June 19, 2019 at 10:51 pm
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    Talk to me all! How did the JUNE 2019 ALGEBRA 1 REGENTS go?!?

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  • June 20, 2019 at 4:48 am
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    Thanks I pretty sure I did good on this regents part 1 and part2 but not part 3 😅

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  • June 20, 2019 at 9:23 pm
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    My son Juan blessed me yesterday ❤️

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  • June 21, 2019 at 1:17 am
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    Why am I here🤦🏻‍♀️🤦🏻‍♀️🤦🏻‍♀️I should be on geometry vids

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  • June 24, 2019 at 7:55 pm
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    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!

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  • June 26, 2019 at 3:01 am
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    Thank you I passed the regents cause of you

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  • June 26, 2019 at 6:21 am
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    Thanks WFI still going to watch you bc next year I got geometry

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  • June 26, 2019 at 4:43 pm
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    yo juan i got a 96 in the algebra 1

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  • June 26, 2019 at 6:28 pm
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    Is 68 a good score for regent? Should I take it again

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  • June 28, 2019 at 7:32 pm
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    Bro thanks I watched this video and I got a 76 on my regents I’m finally college ready!

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  • July 1, 2019 at 3:20 am
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    The June 2019 algebra 1 regent was so easy that all you have to do is sleep and write and you pass.

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  • July 3, 2019 at 7:03 pm
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    Passed my regents thanks to this vid 😭

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  • July 5, 2019 at 5:19 pm
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    Hi, I am Immanuel, Which instrument do you use to write on screen?

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  • July 5, 2019 at 11:50 pm
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    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.

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  • July 11, 2019 at 8:51 am
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    i failed the regents im taking my regents again august

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  • July 11, 2019 at 9:02 am
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    i forgot do the regents suppose to so january even tho its july

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  • July 19, 2019 at 12:45 am
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    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.

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  • July 21, 2019 at 10:34 pm
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    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😔🤟

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  • July 23, 2019 at 2:53 pm
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    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

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  • July 24, 2019 at 5:50 pm
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    Can you do this for the June 2019 Algebra 1 Regents? I have to retake the test

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  • July 25, 2019 at 8:41 pm
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    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

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  • July 26, 2019 at 2:23 am
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    i failed the algebra 1 test in june , i have to take it again august 13th or 14th 🥺 i failed by one point

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  • August 3, 2019 at 7:32 pm
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    can i contact you for further information? my daughter has to retake the regents on august 12th

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  • August 7, 2019 at 2:03 am
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    I have to retake the test, but the only thing I’m confused on is if the test is going to be the same

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  • August 7, 2019 at 4:32 pm
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    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.

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  • August 7, 2019 at 7:34 pm
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    I failed both of my exam so I really need this.

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  • August 7, 2019 at 11:52 pm
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    For questions like number 4 should i always round down?

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  • August 10, 2019 at 8:58 pm
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    istg im dumb. NOTHING in math makes sense to me not even this. Im screweddd for next week.

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  • August 11, 2019 at 11:58 pm
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    I failed my regents by 1 point hopefully this helps me for me retake

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  • August 12, 2019 at 5:51 am
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    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

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  • August 12, 2019 at 7:06 pm
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    This was so helpful thank you !

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  • August 12, 2019 at 10:02 pm
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    I dont understand how you got 1.52 for number 16

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  • August 13, 2019 at 3:11 am
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    who
    is watching this last minute

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  • August 13, 2019 at 5:31 am
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    ok this is my last chance to get college ready…..am gonna tell you my score soon

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  • December 25, 2019 at 1:01 am
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    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

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  • January 7, 2020 at 2:55 am
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    plz wish me a good luck!!

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  • January 19, 2020 at 7:25 pm
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    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

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  • January 20, 2020 at 4:29 pm
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    How he got 7

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  • January 20, 2020 at 8:04 pm
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    Ik this is free99, but the music ruins the whole vid.

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  • January 21, 2020 at 10:00 pm
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    I have to retake this tomorrow 💀💀💀

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  • January 22, 2020 at 12:17 am
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    Bro your music hurts my head

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  • January 22, 2020 at 3:08 am
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    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!

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  • January 22, 2020 at 2:54 pm
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    i'll be honest but the music is bad, I can't focus on the video without being distracted by this music

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  • January 22, 2020 at 3:35 pm
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    Try not putting the music in your videos

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  • January 23, 2020 at 2:50 pm
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    This regent was too easy, I got a 95, btw I am in college now, Harvard

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  • January 31, 2020 at 9:05 pm
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    Pls can u come to Urban Action Academy at Canarsie campus in Brooklyn 😭😭😭😭

    Reply

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