all right this is Juan Tutors and we today we
are doing the very brand new Next Gen learning standards Algebra 1 Regents this is the very
first Regent that is from based on the nextg standards the previous one was the common core
standards and if you actually are a teacher and you've looked at the Regents you and the
Regents standards you happen to know that the new standards are actually extremely similar to
the old standards so not much has changed in the test and that's not too surprising so just for
students watching this and for teachers watching this just know I'm going to briefly talk about
what's on the first page and then maybe a few minutes later we're going to get to the problems
so if you just need to fast forward and get to the problems do that but do I advise you to just
take my advice I'm not going to read the entire first page very little has changed here the the
four pieces that I want to address which are not changes here it says the first piece of advice
clearly indicate the necessary steps including the appropriate formulas substitutions diagrams graphs
charts Etc the I want to I want to point out here that that's obviously necessary for part twos
threes and fours but a lot of students think that it's not necessary for part ones in fact a lot
of students say you could focus on just the part ones because you could pass on with just the part
ones but then they show zero work on the part twos threes and fours and then they're they're kind of
gambling whether they passed or not and here's the thing this is what my part one looks like I
don't know let's get it might be a little blurry but you could see all the amount of writing that
I've done and here's another page you could see that there's just a ton a ton of writing
right and as opposed to if you scroll through the test you see it's blank blank except for that
subscribe Now button that's not what that's what this is actually what most students Regents tend
to look like literally almost all blank so here's here's the first piece of advice that I'm going
to give you your you might have fought with your teacher saying I don't want to show work and your
teacher says no you got to show work you got let your your teacher win that fight because on the
part ones here's the thing the part one problems look identical to the part two problems just with
a multiple choice attached to it and actually nearly identical to many part 3es and and very
identical to parts of part four problems so here's the thing if you can't do the part twos threes
and fours because you don't show work you can't do the part ones that it's just not physically
possible vice versa if you know how to do the part ones by showing work then you can actually
you don't have to worry about passing if you know how to do the part ones by showing work
and you can get yourself that 65 you should be able to get an 80 now I know because I happen
to grade the Regents usually January and June and occasionally also August I happen to know what
Regents look like and that's why I said that most students part on look blank but so here's
the proof that I know that students are actually failing often because they just don't show work
there should actually be because it's actually not terribly difficult to pass the Regents
there actually and and I know I know some of you have already failed it before but I do
want you to understand that it it does require you to do the part two three fours and that's
why I actually say it's not terribly difficult not because it's not a difficult test to you but
if if all students do show work on the part ones which means that they do show work on the part
two threes and fours this should actually be a gap of scores between a 65 and an 80 where almost
no students get because if you show all work on the part ones then that amount of work done on
the part twos threes and fours should guarantee you an 80 if you can get a 65 using the multiple
choice only you can get an 80 doing the part two threes and fours there should be no students that
get anywhere between a 65 and an 80 but there's a ton which means I know that that Statewide there's
just a ton of students who are not doing the part of the part twos threes and fours by showing work
and therefore not showing work on the part ones so let your teacher win that battle your teacher has
been right the whole time on showing work part the second part use all the information utilize
the information provided for each question to determine your answer okay so that what that means
is every bit of information in the problem is very likely to be extremely relevant in in like
middle school and definitely Elementary School we kind of trained you to believe that every
single problem is going to have some piece of information in it that's just not relevant and
that's just not true almost every problem has all information that's relevant that's relevant in
fact in almost every Regents every single problem has an only information that's relevant and zero
information that's not relevant and when I say not relevant I mean if they're buying cantaloupes that
doesn't matter if they're buying cantaloups versus they're buying watermelons versus they're buying
oranges or sodas or Waters it doesn't matter like that that's but that may not matter but but like
a cantaloupe versus a bottle of water but every other bit of information is definitely relevant
so basically what we're saying is no math problem has irrelevant information that is actually a
safe assumption to go by and in fact if you're ever stuck in a problem one very wise piece of
advice that you could take is if you're stuck go back to the problem and see if there's any detail
at all read it carefully if there's any detail at all that you haven't used yet because if there is
a detail that you haven't used yet chances are you can use it and it'll get you points okay
and it'll get you the answer statement three that note the diagrams are not necessarily drawn
to scale this is my favorite thing that I like to do with this comment I like to cross it up there
we go cross it up nice straight line there we go okay and now teachers might not agree with me me
when I when I draw this when I cross this out this is the part of me that is a both a teacher
and a tutor here's here's the thing that you got to understand the logic of note the diagrams
are not necessarily drawn to scale is the same logic that the sat company Ed when they took
away a quarter point when you got a question the theory is that that made a wild guest
value less not a punishment value less but not a punishment but what did a lot of students do
they just left a bunch of questions blank even if they could do a lot of really good work with it
or even a little bit of good work with it here a lot of students read note that diagrams are not
necessarily drawn to scale and then they say to themselves well that means that they're not drawn
to scale false in fact almost every algebra one test has every diagram drawn to scale and not only
that almost every test Algebra 1 geometry Algebra 2 has every diagram such that it is illegal for
it to be not drawn to scale because the problem doesn't allow for that and in fact this test that
is the the case every single diagram is not only drawn to scale but it is actually required to be
drawn to scale because the diagram is required as is for the problem so what what is the advice
if you don't know how to do the problem go ahead and assume that it is drawn to scale and see if
that helps because often if you don't know how to do the problem now this is now test taking
strategy not factual advice but test taking strategy if you assume that the diagram is drawn
to scale you might find that you could just get the question right just from that okay and then
of course number four a graphing calculator and a straight edge or ruler must be available to
you for use while taking the exam this test does not require a ruler this one but it does
require a straight edge so if anything you need to to draw a straight line you could use
that okay but you do are they are required to provide you a graphing calculator if you don't
have about the reference sheet this is a new reference sheet but some of the formulas that
are on here we didn't even use on this test so but it is important to know that it is a brand
new ref reference formula reference sheet slightly different conversions slightly
different conversions AC cross measurements and you know some really good formulas here that you
should know you should know every single one of these formulas and you know IQR is new outline
is new on the formula sheet but so it turns out you know the outlier formula especially I
didn't see any on this test for that okay now let's go immediately now we're going to do
problems for the part ones but the very first thing I'm going to do I noticed that it says
note that diagrams are not necessarily drawn to scale and I'm going to cross that out okay and
again if teachers if you disagree with me on that you know you're welcome to but this is the part
where I used to note that but then as a two tutor I started to realize that it's actually better to
tutor students to understand that not necessarily drawn to scale means that it can be drawn to
scale but it doesn't have to be and in fact almost always the diagram is drawn to scale and that's
true for algebra geometry it's true for Algebra 2 it's true for the pre-cal AP it's true for the
Cal AP it's true for the IB tests it's true for the SATs it's true for the acts if you find of
I think I named eight tests there if you find 16 diagrams not drawn to scale combined in eight
in though the next eight of those exams I will gladly send you this hat and I won't I'll get to
keep it because it's not going to happen that's how sure I am that they make nearly every diagram
drawn to scale and it's almost 100% guarantee that every diagram will be drawn to scale all right now
that we've said that we're going to go straight to numo Uno number one of all was launched into the
air and its height above the ground was recorded each second as shown in the table below now when
I read a table I read the I read the table but I don't intake all that information because it's too
much but I but I may be by reading it I might get a little Trend so I read time 0 1 2 3 4 height 11
59 75 59 11 right then based on these data which statements is a valid conclusion the ball lands
on the ground at 4 seconds the ball reaches a maximum height of 11 ft or the ball was launched
from a height of 0t or the ball reaches a maximum height at 2 seconds now some of these are they
contradict each other so luckily some of these will actually just either confirm one confirm
that one is false or confirm the other is false and maybe if we're lucky confirmed they're both
false so for example this one number two the ball reaches the maximum height of 11 ft and by
the way one thing I will say sorry I I know I started speaking half sentence and by the way I
am recording every every cough every sneeze every every every single one of those things
that I'm going to do I'm going to record that and I'm going to publish it that way the reason
I'm going to do that is that I used to record the videos then I used to spend hours and hours and
hours editing the video taking out all those Ms and us and coughs when in fact I could just upload
the video and and spend my time making more videos so now I'm actually me before I used to like
maybe publish one Regents video per season and now I I might be able I might I'm crossing
my fingers I'll be able to record seven of them Algebra 1 geometry Algebra 2 earth science
living environment chemistry and physics if I could do that I'll be very happy but I to do
that I need to not edit videos I'm literally the editor I'm the Creator I'm the writer I'm the doer
like literally all of it so but I'm you know every every faux PA I'm going to keep it there shouldn't
be any faas like literally incorrect answers on the on the test because I've literally confirmed
every answer not just through my own personal math I am a math teacher and tutor but also through the
answer sheet so what what I noticed that number two and number four actually contradict each other
so I should be able to assess whether one of these is wrong or both though this one choice two says
the ball reaches a maximum height of 11 feet and then Choice four says that the ball reaches
its maximum height at 2 seconds so if I look at 2 seconds 11 ft well definitely Choice two is
100% wrong but Choice four actually a maximum height at 2 seconds that is looking nice that is
looking nice there is something that we can maybe address to see if we're actually right it's not a
guarantee just because the maximum number we see is 75 ft that does not mean that the ball reaches
that as its maximum height and we're going to address that in a second so but I put a checkbox
there next to it because I think that that's the right answer I suspect that but now this one
the ball was launched from a height of zero feet according to this the ball was launched
from a height of 11 ft so that's not correct okay now the ball lands on the ground at 4 seconds
actually this does not say that remember valid conclusion this does not say that the ball
the round is at 11 seconds is at 11 me feet in fact it just says its height above the ground the
height above the ground is recorded each second and 11 ft is the height above the ground so it's
not it does not reach the floor because the the ground because the ground would be at zero okay
so now Choice four is looking very good in fact I've confirmed that all the other three choices
are incorrect and by the way every single problem that I do I will do process of elimination this
one blessedly we were able to cross out three choices with 100% certainty so we're actually
going to be guaranteed to get this problem right when we Circle Number Four but we haven't
circled it yet but why is it that we're that the height the maximum height is 75 ft I just said
that it's not guaranteed that just because the the maximum number is 75 that it's that that is
the maximum height after all but here's the thing there's a time of like 1.9 seconds 2.1 seconds
1.5 seconds 2.5 seconds there's times between the times that we took measurements but here's the
thing notice that at Time 1 second and at times 3 seconds the height so let H equal the height okay
h of three is equal to H of one is equal to 59 ft okay h of3 = h of 1 = 59 ft and the path is parabolic therefore the the parabola is symmetric okay about about the time
T equals well the the median between 1 and 3 so 1 + 3 over 2 which is equal to 2 seconds so if
we look that is the maximum the place where the maximum height occurs and that is why Choice 4
is 100% correct okay so every single problem I am going to do some process of elimination okay
so be ready for that do understand my process of elimination May eliminate every answer may not
eliminate some answers we don't know when we until we actually do it okay so number two num a
tuab bus can seed at most 48 passengers an adult ticket costs $18 and a child ticket costs $12 the
bus company must collect at least $650 to make a profit if a represents the number of adult tickets
sold and C represents the number of child tickets sold which system of inequalities models the
situation if they make a profit now I know that this is a lot of of inequalities a plus c is
less than 48 and 18 A + 12 C is greater than 650 or a plus c is less than or equal to 48 and
18 A + 12 C is greater than or equal to 650 or a plus c is less than 48 and 18 A + 12 C is less
than 650 and or or a plus c is less than or equal to 48 and 12 a + 12 C is less than or equal to 12
to 650 now this is what this is an example but it's actually an easier example of what I call
a 2X two problem what do I call a 2 x two problem a 2 x two problem and there be there will be more
examples later on in the multiple choice but what I call a 2 x two problem is is where they have
two pieces of information that are identical in two other problems and then two other pieces of
information that are identical in two two other problem and two other choices sorry yeah two two
pieces of information identical in two choices and two other pieces of information identical in
two choices this is an easier version because it actually has four pieces of information
different in four choices and then two pieces of information that are different in all two choic
notice the difference between this is the equal Choice two and choice four have an equal and
choice one and three have a less than only less than but but not less than an equal so on
the first inequality but they both face the same direction and then the second inequality
one inequality faces to the right to the left greater than greater than greater than or equal
to and this one is less than and less than equal so actually we could all we' have to do is look at
the second inequality to get the answer but if we did want to do some process of elimination
maybe because we don't know how to do the second inequality some process of elimination here it's
the first inequality should a plus b be less than 48 or less than less than or equal to 48 now the
tour bus we go back to the problem it says that a tour bus can seat at most 48 passengers tour
bus can seat at most 48 passengers that includes 48 you can seat 48 and then it says that a
represents the number of adult tickets and C represents the number of children's tickets so
that's the number of adults and that and plus and the number of children the combined number of
adults and children has to be no more than 48 but it can be 48 so 48 is allowed as a solution 48
is allowed as a solution this one does not allow 48 as a solution so Choice one is wrong this one
does not allow 48 as a solution so choice three is wrong now we are at a point where we have
a one and two chance of getting it right and at this point I get to talk about what I call a a
passing problem a passing problem what is a passing problem so on average the number of points
that you need to pass the Regents can vary usually between 25 and 29 Points each multip and and
that's raw score and each multiple choice is worth two points so a if you get half of them right you
get 24 points if you get half of them right you get 12 right time 2 is 24 and what about the other
half well with the other half you can well unfortunately if you get them wrong you can you
can maybe tease out a few points here and there and also on the part twoos threes and fours the
moment you tease out a few points out of the part twoos threes and fours you're basically guaranteed
to pass this reg so why do I call this a pass in problem because if you actually get to the
point where you you have a one and two chance of getting the question right like we just got it to
now if we get so if we get okay so if we have a one and two chance of getting this question right
the point is that statistically speaking it's worth one point half of the two points that it's
worth if we just even wild guess at this point we shouldn't wild guess at this point but it's worth
one out of two points if which on average is the number of points that we need per question per
multiple choice question to get a passing grade so this is now a passing question just by eliminating
two choices now what about the second inequality and by the way one thing I will say about this
one is that if you ever do get a situation like this you may find that it's actually helpful
for part twos threes and fours because now you got a question and you know the format that the
answer should take so if you get an inequality or or system of equations question in the part two
threes and fours you can use the multiple choice to get the answer to the part two three and four
so that's a plus what about this so it seems to be an 18a and a 12C and one the question is
is that going to be greater than or equal to 650 or is that going to be less than or equal
to 650 let's see what they said about the the bus companies tickets the bus company must
collect at least 650 to make a profit okay the so we we have to as a bus company we have to model
if they make a profit okay if they make a profit so they have to make 650 or more 650 or more the
amount of money they collect collected has to be greater than or equal to 650 now let's see what
is the money collected so the money collected from adults a plus not the best
handwriting I know plus the money collected from children has to be greater than or
equal to 650 okay so now the money collected from adults if one adult tickets $18 two adult tickets
18 which is 18 * 2 which is 36 three adult tickets 18 * 3 four adult tickets 18 * 4 so 18 * the
number of adult tickets is the amount collected from adults and then 12 it's $12 for a child
ticket one child $12 two children two times $12 three children three * $12 four children four
times $12 eight children no C children 12 * C that's greater than or equal to 650 and
that matches the inequality Direction matches Choice two okay so that's full credit now for
number two numer and now we're up to numer number three which equation is always true
is it the first one X2 * X Cub is equal to X 5th or x to the 3 x + 3^2 is equal to
9 to the power of 2x or is it let me minimize this a little bit okay or is it umga z^2 is equal
to z^2 or is it 7 a * 7 B is equal to 7 ^ a * B now U I would advise you to get your calculator
out if you don't know how to do this question I would advise you to get your calculator out and
plug in some some answers now I have I like using process of I like using my random number
generator to show you that you could actually do some of these problems by by calculator okay
so my random number generator let me told me to choose to test number three on the on the
calculator so how do I test choice three on the calculator I don't have a z on the calculator
and by the way letter Z is the most common incorrect answer okay now you know it's going to be
incorrect but you know but here how do I know that it's going to be incorrect
well I'm going to choose a random number so this is my recommendation to you
choose a random number to plug in okay choose a random number to plug
in that's one great piece of a device and the second piece of advice
is to choose easy numbers to plug in okay fun fact I I don't know I don't have
an opinion on which of these two pieces of advice is better because there there's benefits and
drawbacks to each one of these easy numbers to plug in just super quick right and but but the
drawback is is that the easy numbers usually don't eliminate every single answer so what are easy
numbers to plug in usually zero or one usually if you plug in zero or one it'll just confirm
which answers are correct or incorrect almost immediately but it won't necessarily confirm
every single answer it does happen to be that plugging in zero will confirm some
of these answers un Choice four has two numbers that you have to plug in so you might
have to choose two numbers and but if you choose zero and one for Choice four that'll be
eliminated Choice two that'll be eliminated and if you plug in zero Choice one and three won't
be eliminated but if you plug in one choice two could choice three could be eliminated you see
so plugging in Easy numbers often gives you an answer right away now I if you choose a random
number a more difficult number to plug in 9 or 8 or 11 those are my two F those are my three
favorite random easy numbers to plug in if I had to choose an easy two digit numbers to plug
in plug in 11 is just so easy to just press right away and in fact that's the one I'm going to
choose to test choice three negative z^2 I'm going to choose 11 11^ squared and I'm oh wait
negative -21 and then I do 11^ SAR is positive 12 huh -21 is not equal to POS 121 look at
this the most common incorrect answer we just confirmed it to be incorrect we just
confirmed it to be incorrect why is it incorrect what why is it why do students
think that it's correct because students insist on sticking the negative sign onto the
Z and then putting the squared and students often really very much insist on just using
minimizing the number of parentheses that they that they use in fact the best one of the better
pieces of advice that I could give you for this test is to use more parentheses that you're
accustomed to using use them legally of course but use them everywhere that if you can use them
if you know you can use them but you're like but I don't want to well if but if you know you can just
use them because it's often the case that you're actually incorrect about the parenthesis not being
able to be used in fact or I'm not I'm sorry you're often incorrect about being allowed to not
use the the parenthesis that's that's what I meant to say a lot of students think that they could
just not use parentheses in places where they're just absolutely required to use them so if you
know you can use the parenthesis use them and in fact that's actually what happens here they
students insist on not using parenthesis around negative numbers and then they grow accustomed to
thinking that they don't need them because of personal stubbornness this about negative numbers
in parenthesis you do need a parenthesis around the negative numbers why because the negative sign
does not attach to the Z the square attaches to the Z and then that gets negated so negative
z^ s means that Z is squared and then that is negated what about the rest of these can I do
these by plugging in yes plug in a equal 9 and b equal 11 that will confirm that choice four is
is incorrect plugin a equal xal 9 into Choice one and you'll find that the left side and
the right side are equal to each other and if you plug in xal 9 onto the right side or if you
don't like it because that there's a nine there plug in xals 8 you'll find that choice two it does
not make sense so what is the rule that allows Choice One to be correct x to the a X to that
a so this is a rule x to the A Time X the B so when you're multiplying Powers with the same base
that's equal to the same base with the exponents added okay and I'll give you another
rule x to the a now that number that power take it to another Power
when you're multiply when you're taking a power to another Power that's
equivalent to multiplying the exponent so as a result Choice 2 3 x * 3 2 is actually
equal to 3 x + 2 and then this one 7 to a * 7 B is actually equal to 7 to the A + B whereas
7 to the a is equal to 7 to the a that to the B okay so that's actually correct that's
actually Inc correct and that's correct all right so numer number four and by the way I
will again do process of elimination but even in cases where I do the problem in some other way I
Comm I'm committing to doing every single problem algebraically because the truth is that you need
to know how to do it algebraically in order to pass the Regents especially or not just to pass
the Regents but to get as many points as possible in the part two threes and fours and I'm going
to show you that the part two threes and fours literally look like part ones with just not
doesn't have a choice one choice two choice three Choice four so you really do have
to know how to do these algebraically so I show how to do these algebraically all right
num number four the expression 2 to the -2 parentheses x^2 - 2x + 1 close + 3x2 + 3x - 5 is
equivalent to X X2 + x - 4 or x^2 - x - 7 or X2 + 7 x - 4 or X2 + 7x - 7 so I would advise you
to again pause the video and try the problem on your own see if you could figure out a way
to eliminate some choices that and then in fact that's the first thing that I'm going to do I'm
going to try to plug in I'm going to plug in in this case I'm going to plug in an easy number
xals 0 so if xals 0 I get -2 time a 0 - 0 + 1+ well5 0 + 0 - 5 is5 which is equal to -2
- 1 is2 plus5 according to my calculator is -7 if you weren't sure on how to do that or if
you actually got that wrong in arithmetic in your head incorrect go to the calculator and do
the arithmetic every single time on a calculator that's another piece of of advice that I have
for you a lot of students like insist on using the calculator right up until the point where
the teacher says use the calculator and then the students are like N I don't want to that's not
correct logic you if you struggle with arithmetic remember you are not taking an arithmetic test
you are taking an algebra test so the arithmetic yes it's meant to be somewhat doable but if you
struggle with the arithmetic let the calculator take over your arithmetic so that you could do the
algebra just let your calculator do the arithmetic for so notice that when I plug in xal 0 Choice one
I get so if xal 0 I get4 which is not correct if I plug in negative if I plug in x
equal z i get4 here so that's not correct but this one I get7 and this one I get ne7 so choice three
and choice four Choice two and choice four might be correct but look at that just really easily
plugging in x equals z I have a passing problem this problem is guaranteed to be a passing
problem even if I did a wild guess on average if every single time every single time
I get a passing problem I don't lose points statistically relative to a passing rate now
if I actually plug in x = 1 okay and I did promis myself I I was trying to choose which
problem I would do strictly on the calculator and I think think this is probably the best
one that I'm going to do that but I am still going to do it algebraically so please do
stick with me while I do it algebraically because again part twos threes and fours
you this problem could easily be a part two right if I literally just the I said the
expression -2X parentheses X2 - 2x + 1 closed Plus open 3x2 + 3x - 5 is equivalent to
deleted all of those covered all of those choices that's literally exactly what a part
two question looks like so do stick with me while I do the problem algebraically too but I am
going to plug in xal 1 in the problem I get -2 parentheses 1 2ar 1 2ar - 2 * 1 + 1 close
parentheses plus parentheses 3 * 1^ 2 + 3 - 5 although and by the way if you know how to plug in
by using the trick of just adding the coefficients you could have literally done -2 * 1 - 2 + 1 plus
parentheses 3 + 3 - 5 because every Power of one is equal to one you got one and then which answer
is going to give you 1 actually Choice 4 1 + 7 - 7 is one and then Choice two so Choice four
is looking good again but Choice two one oh 1 - one I I didn't realize this Min
- 7 okay hold on a second one actually no 1 - one - 7 is not looking good it's ne7 sorry I I
got confused for a second because the previous one we Got7 but this one we should have gotten one
choice two is not the right answer now we actually know that choice four is the answer by plugging in
choices many many many problems can be done that way as you know choice three could be done by
just plugging in numbers in fact if you know how the inequality should be working Choice 4 can
be done this way as well like if you plug in 18 adult tickets if you plug in 48 I'm sorry
48 all adult passengers and check to see if the company made enough money well Cho plugging in all
48 passengers adults and zero children will conf that this one is right choice two and that
choice four is incorrect and that's not Choice one no not quite so how do I do this one
algebraically again every single problem I I commit to doing it by the long way because
again every part 2 3 4 looks like a part one just in pieces -2 x^2 - 2x + 1 from closed
parenthesis Plus open parenthesis 3x^2 + 3x - 5 what I'm going to do in this case I'm going to
distribute the -2 and I get -2 x^2 minus a -4x so + 4x - 2 and then I'm going to distribute
a one here and I'm actually going to put this under this expression so+ 3x^2 + 3x - 5 and I
know that -2 + 3 is 1 so I got 1 x^2 + 4 + 3 is + 7 so + 7 X Plus 4x + 3 x is since plus 4 +
3 is + 7 plus 4x + 3x is + 7 x and then - 2 - 5 -2 - 5 is - 7 and that matches exactly Choice 4
exactly what we expected all right groovy groovy look at that subscribe button H maybe you should
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Place and I was blessed to to to never be in a a situation where I know a lot of my students
who are watching this video have been in and and for you for those of you who are who are
doing what you need to do for yourself to to to get where you need to be in the future for
your for your future and for your kids future I I I I want to support you in that in fact the
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eat too and I started raising my fees as I was raising my fees I started realizing very quickly
that the students who I tutored were a little bit more well healed well healed you know than even
I was and now my fee is actually quite High higher than higher than most tutors I mean I
I'm not going to say I'm the best tutor but I'm among the goats probably because I've
been doing it for so long and and I I make a huge difference in my students and parents know it so
I'm charging quite a lot as of make the making of this video I charge between 2 and 250 an hour
for tutoring I've priced myself out from students who look like me and lived like me and so one of
the reasons why I do these videos for free is that I want students like you to have access to this
knowledge for free but one of the ways that I get to do that is by being able to do things like
put ads before the video and after the video so I do appreciate it if if you do subscribe if you
feel like I've earned it I do appreciate if you would press the Subscribe button on on
that note I'm not I'm not going to advertise much more I'm going to scroll past another two
images of the sub subscribe button and I'm going to mention my tutoring business probably more than
once JuanTutors.com but beyond that I'm not going to do much advertising that said numeral Syle
number five I and I do if you do feel like and you did subscribe I I do appreciate it and thank
you very much for that numero number five which sum is irrational -2 radical 12 plus radical 100
or negative radical 4 plus a third of radical 900 or 1 half radical 25 plus radical 64 or radical
49 + 3 radical 121 I do advise you if you don't know how to do this question don't give up on it
don't just stare at this problem and say I think this one and move on plug it into your calculator
this one is if you don't know how to do this problem you can go into your calculator and
and and get the answer so now my random testing choice for for the for this test for this video is choice three okay so I'm testing choice
three because my random number generator says for the purposes of demonstrating how to plug
into your calculator randomly I'm going to do choice three so now if I plug in
12 1 / 2times the square root of 25 plus the square root of 64 is this number 10.5 so many
of you know that this is a rational number but if you don't know that this is a rational number I'm
going to do it again notice the math button under the green Alpha button the math button press
math and the very first option Arrow Frack Arrow Frack means convert to fraction so if it if I can
convert it to a fraction it's rational with 99.99% certainty there is a bug in the calculator which
I'm not going to address for this video 21/2 is definitely a fraction so this is rational
okay so this is not the answer and in fact if you plug in to two of these these two are both
integers so either integers are rational and they're both not irrational or integers
are are irrational in which case both of these choices would be correct and that can't happen
in a multiple choice question I I as I'm sure you know therefore Choice two and choice
four Once you plug into the calculator will confirm to you that they since they can't both
be right they both have to be wrong so plugging into the calculator will confirm it okay but
how do we actually do this problem the thing that they actually wanted you to know for this
one problem is that the sum okay of a rational number and an irrational number is irrational that's the skill that they're testing
and I will say this there was a test a few a few tests ago that they actually made a
mistake in the grading of the problem in the part twos threes and fours so why why am
I saying that what that means for you is that you could have gotten points in it if you
actually got the wrong answer so even then the part two 3 and fours is really beneficial to
show all work okay so the sum of a rational number and an irrational number is irrational
what is a rational number a rational number can can be written as a ratio of two integers and we just learned that this one is
equal to 21 over2 that's a ratio of two integers 21 and two is a ratio of two integers now what
about Choice two and choice 4 well radical 49 is equal to 7 + 3 radical 121 is equal to 11 and if
you just do the algebra on your calculator again let your calculator be the arithmetic King
seven a lot of students say that this is equal to 110 because they do the calculations in their own
heads let the calculator do it it's plus 33 which is equal to 40 multiplication goes before addition
according to PEMDAS I'm an enemy of PEMDAS by the way but for for for certain reasons pmas is not
a six-step process PEMDAS is a four-step process and that's why I'm an enemy of that acronym
I think I might do a video on it one day because really not the best acronym it can
and it can be fixed so easily anyway here's here it is g d Ms that's the fix the pen blast
and you could just come up with a thousand different acronyms for that in fact if you come
up with a good acronym for that so G grouping symbols exponents e d division M multiplication
s subtraction a addition if you come up with a good acronym for for that please put it in
the in the chat or in the comments okay but let your calculator do 7+ 3 * 11 the calculator knows
that you have to do 3 * 11 first so they do 33 and then 3 + 7 is 40 40 is equal to 40 over one
so it can be written as a ratio of two integers it didn't say that it is written as a ratio of two
integers and in fact 10.5 isn't written as a ratio of two integers but it can be written as a ratio
of two integers 21 over2 same thing happens here negative radical 4 is -2 + 1/3 of radical 900 is
30 so -2 + 10 is equal to 8 which is equal to 8 over 1 can be written as a ratio of two integers
okay so I'm liking that answer it's Choice one it is Choice one so groovy train numeral say number
six the solution to a four parentheses x - 5 Clos parentheses over three + 2 is equal to 14 is
what is the solution to this equation so is it 15 14 6 or 4 OMG talk about a question that
you could just do on your calculator you know plugging in plugging in so I said that
I would demonstrate plugging in by doing by doing specifically choice three I'm going
to try to do four test oops a little bit toy a little bit too high I'm going to test
choice three which is six okay let's see I got four parentheses 6 - 5 Clos parentheses
ID 3 + 2 equal to 14 okay so I could and by the way again use your calculator and use
parentheses obsessively but your calculator says that I guess for the purposes of demonstration
let me just do it on the calculator just to just to teach you muscle memory that's the literally
the only reason that I'm doing this on on on the calculator at this point four parentheses 6 - 5
close parentheses ID 3 + 2 if I don't get 14 this answer's got to be wrong and I get 3.33 repea
okay so that answer is definitely wrong but not only is that answer definitely wrong but so six so
X is not equal to 6 but also X has to be greater than six so now I know that this answer is wrong
but also this answer is wrong now 14 and 15 are so close to each other that I'm not sure which
one is right however I have a strong suspicion personally that 15 isn't correct now I want to
point out my notation here I crossed out choice three and choice four but I put put an X next to
the 15 I didn't cross it out over here because I think that it's wrong you can borrow my notation
and I will explain that notation a few more times as I move through other problems but that's my
notation I suggest that you borrow it cross out the problem if it's 100% definitely super duper
incorrect put an X next to the answer if you think it's incorrect that way you have a quick notation
to look at later on how will we do this problem algebraically 4 parentheses x - 5 / 3 all that
plus 2 is equal to 14 well I know that this is going to be equal to 12 but anyway so I might
actually just look for something that makes this equal to 12 that's why I know it has to be big
but I'm just going to undo this plus two first because that's the last operation done to two to
X I undo the last operation done to X and that's what I keep doing until I'm done so the last
operation done to X is plus two I subtract two subtract two I get 4 pareses x - 5 / 3 is
equal to 12 and I'm going to do that again I'm going to undo the last operation done to X but
why did I but I I should actually say why did I think that 15 was incorrect I said I said
I think 15 is going to be incorrect because I I'm pretty sure I need a multiple of three in
the numerator F student me says I think I need a multiple of three in the numerator real two to
me says I 100% know that I need a multiple of three in the numerator because every because two
is in integer 14 is an integer but fake student me when I say fake student me I'm simulating
myself as a student fake student me says I'm pretty sure that 15 doesn't give me a multiple
of of three in the numerator okay because 15 - 5 is 10 not a multiple of three and four is not a
multiple of anyway so I undid the plus two that was the last operation done to X now I'm going
to undo divide by three because now that's the last operation done to X so times 3 * 3 I get
eliminate those I get four parentheses x - 5 is equal to 36 now students love to distribute
but some students love to Short change the distributive property and only distribute
to the first thing that's lazy you got to distribute to every term so I got to distribute
the 4X to the four to the X I get 4X I got to distribute the four to the minus 5 I get min-2
and that's 36 this is the most common incorrect answer right away if they just don't do
minus 4 * 5 then okay so I add 20 I add 20 and I get 4X is equal to 36 + 20 is
56 and I divide by four and I divide by four that's the last operation done to X and I get that
X is equal to 56 / 4 I'm going to simulate go into my calculator for the the purposes of you getting
to the go to your calculator teaching you that that's the right way to do it 14 real T tutor me
knows that 56 divided 4 is 14 because well 60 divided by 4 is 15 so 56 divided 4 is 14 but fake
student me isn't sure I think it's 14 so I go to my calculator you can't know you can't think
you know something you can only know something or not know it and if you don't believe it think
about the only time that someone has said to you I think I know something it's your parents they
I think I know it you know or I think you know that's when you think you know something but
notice that that is a phrase not a fact I think you know it means you definitely know it I'm
just letting you think about it all right so you can't actually think you know something that said
numer that number seven let's put some more space there on an island a rare breed of rabbit
doubled its population each month for two years which type of function best models the increase in
population at the end of two years linear growth linear Decay exponential growth or exponential
decay now this is the one where I I want you to think look I would as I suggested I would pause
the video choose an answer now a about choosing an answer this is what I will say to you if you say
to yourself I think it's this but you didn't say I'm committing to this answer you didn't really
choose it because I don't know how many times I've been in a situation where I get to a student and
they say I think it's this but I'm going to choose this that is so illogical I think it's this but
I'm going to choose that means I'm going to choose the answer that I think it's not that doesn't make
sense be by switching they're actually convincing themselves that they might actually be wrong but
the other one might be right which means that they never actually committed to it and I've actually
had a student say I think it's this and then I tell them it's not it's this one and they're like
oh I knew it was that one and then I say no I'm lying to you it's this one then I knew it was that
and I literally had them switch four or five times to thinking they were right literally convincing
themselves that they were right despite the fact that they just said that they're right twice
on two different answers including one that was incorrect you have to commit to an answer before
you can confirm that you were right now this one this is a this is a 2X two question this is how is
it a 2 x two question it's either linear or it's exponential and it's either growth or it's Decay
so if you can actually confirm that one of these either linear or exponential or growth or decay
is incorrect you now have a you're down to two choices and you have a passing problem now
the rare readed of rabbit doubled its population every two years that is a definite growth
cross out Decay cross out Decay therefore this one and this one are 100% incorrect okay
so this is 1 three and two and four right two and four are incorrect so it's either one or
three we got a passing problem there's my my process of elimination being super duper now
if you happen to also know that either linear or exponential is the one that makes sense or is
not the one that makes sense then you actually have your answer if it the population doubles
every month for two years we're talking about 1 2 4 8 16 32 64 or maybe it's 3 6 12 24 48
doubling multiplying by two if you plot that that does not look like a linear function 1
2 4 8 16 sorry that's not even 16 81 16 would be like over here and now we're just Bo blow up
blow up blow up that is exponential exponential functions either blow up or they do this right or
they flatten out to to B to zero right whereas linear function just do that that's this is not
linear this is definitely exponential not linear and that's why it's exponential growth okay and in
fact that's actually a really good lesson to know that exponential functions grow by a constant
multiple linear functions grow by a constant sum groovy all right numeral oo number eight
what is the degree of the polinomial 2x - x^2 + 4x cubed is it 1 2 3 or four I think
a lot of students would get this question wrong because they they they start tricking themselves
into believing something that's that's just false most students if I actually tell them don't get
this wrong by convincing yourself of something that's just not true go back to what you know is
true force yourself to do this problem properly they get it right literally by just telling
them to do the problem properly they get it right by not telling them that they start doing
things that just don't quite make sense things that they start adding things that are they
start convincing themselves that some things are plausibly true when they know that they're
false that's why that's actually the big reason why I tell students to force themselves to
make a choice decide if something is correct or incorrect because the truth is that the
moment you choose to force yourself to say this is true or that is true you start to decline
to believe implausible things so a lot of students get this question wrong this is this problem
itself should be a question that almost 95% of students get right when in fact really only like
maybe 75% of students get it right or maybe 70 so what's what is it what is the degree of the
polinomial well the first thing you should do is look at all the exponents and notice
that there is no degree for exponent but there is a constant for that's not
the degree though we know that the exponents are the degrees and then we put
the EXP the exponents in decreasing order and decreasing exponent order so we get 4X
cubed - x^2 + 2x and then we remember the degree is equal to the degree of the leading term we didn't say the degree of the
first term we said the degree of the leading term so wait what's the difference
between the first term and the leading term well as written the first term was
2x but that wasn't the leading term because it wasn't written in standard
form the leading term is in standard form and what is standard form is decreasing exponent order and also expanded so decreasing exponent order now we have
the leading exponent is a three and therefore the degree of this polinomial list scy all right
numer number nine let me go to that page the zeros of the function f ofx = x x x - 5 3x + 6
are 0g5 and two 0 5 and -2 five and -2 only and five and negative and Ne no Nega 5 and
two only and five and negative -2 only this once again is a problem that you could actually
absolutely do by plugging into the calculator and I am going to as you know as you know
I've been doing simulate that but this one instead of plugging into this I'm actually
going to press y equals I need to clear some of this and I'm actually going to
plug it into y1 I get x parentheses x - 5 close and open parentheses 3x + 6 let me
actually get a window that's a little bit bigger so you can see it how's that the size
there we go and then I go to my table Not My Graph but my table I can go to My Graph
Zoom standard okay and I see I could see where it bounces off or goes through and in fact I
see that it goes through -2 0 and five or you five so that actually confirms that choice two should
be correct but in fact if I didn't understand that I can go to my table now my table set is set to
ask so I'm going to go to table set which is above window and I'm going to change my independent
variable to Auto that's something I recommend knowing how to do change your your independent
variable from Auto to ask and vice versa go to my table again now I can scroll up and down
to check my numbers I see that x = -2 is a zero I see that xal 0 is a zero and I see that x = 5 is a
zero so my X my zeros are five 0 and -2 5 0 and -2 now I promised that I and and by the way I would
have eliminate by process of elimination I would eliminate this one and this one because clearly
because a factor of x is0 xal 0 is a is a root okay or a zero okay so what's the difference
between a root and a zero not much root zero X intercepts basically within the real numbers X
Roots zeros and X intercepts are the same thing you only get to a slight difference when you get
to like the complex numbers because an X intercept is real whereas a root in Algebra 2 could
be complex meaning includes an imaginary part so if I have x parentheses x - 5 and 3x + 6 that
equals zero the zero product property zero product property states that if a product equals zero that implies that one of the factors equals zero okay and it could be yes one
or more one or more of the factors equals zero but the fact is that one of the factors equals Zer
this is a product which equals zero therefore one of the factors equals 0o so we have either
x equals z that's a zero step equation that that that and that's why TST three Choice 4 were
eliminated or x - 5 = 0 + 5 + 5 we got x = 5 that eliminates Choice one now for us and 3x
- 6 confirming by the way Choice two is the answer 3x + 6 = 0 - 6 - 6 3x = -6 IDE 3/ 3 you get
that x = -2 confirming again that choice one is not the answer in Choice two is the answer okay
numero yes number 10 what is the Y intercept of the line that passes through the points 15 and
2ga 1 is it1 -2 three or five okay there are some answers that could be eliminated just by
process of elimination here so it says the Y intercept by going through these two points
I could see that the the line is not horizontal the so each y-coordinate is hit exactly once
because it's a line that's not horizontal so the Y intercept they want the Y intercept the Y
intercept is not five because the the it doesn't go through 0 five it goes through negative one5
and the Y intercept is not negative 1 because it doesn't go through 0 Nega 1 it goes through two
negative 1 so we now have a passing problem a passing yeah a passing problem and in fact
3 and -2 are so far from each other that that if I make even the most cursory graph real quick now
I see that it goes through -15 and it goes through 21 and look at this so the Y
intercept is greater than zero by a lot not even close in fact not even close
so how do I actually do this problem though because I said I would do every single problem
algebraically because again this could easily be a part two this is exactly as written a part
two question without the multiple choice to to guide you so you have to you do have to know how
to do it a a part two so let's see I know that Y is equal to mx + b so how do I get m m is equal
to Y2 - y1 over X2 - X1 so if I let this be X1 y1 okay and if I let this be at X2 Y2 then I get
that m is = to -1 - 5 over 2 minus-1 and now I'm going to use parentheses around the numerator
and denominator one of the reasons why I'm not a fan of pendas I told you that pendas is
a four-step method not a six step method but the other reason that I'm not a fan of it is
that notice I put parentheses here but I didn't need them but why did I put them because if I put
this in the calculator now I need them because the horizontal division bar is a grouping symbol the
diagonal fraction bar is not a grouping symbol I'm going to use the diagonal fraction bar so now
I need the grouping symbol parentheses -1 - 5 close parentheses divided by open parentheses 2 -
-1 closed parentheses I get the slope is equal to -2 okay so m is equal to -2 so now I
know that Y is equal to 2x plus b so now how do I get b b is the goal right B
is the goal answer for this question so I'm going to plug in either one of
these two points I'm going to plug in X1 y1 so I get five is equal to so plug in
X1 y1 I get 5 is equal to -2 * X is -1 oops1 close parentheses plus b so use my
calculator just to simulate for you I know that -2 * 1 is 1 so -2 time1 and I better
get one yes two sorry -2 and I misspoke there -2 * ne1 is 2 so not -2 so 5 = 2 + B so one
of the reasons why another reason why I recommend using the calculator to do your arithmetic for you
is that notice that I misspoke if I as a teacher can misspeak what happens sometimes is when
a a student if I can misspeak what a student does is misr so they'll know that -2 * ne1 is is
two but then they somehow replaced that with a one and they write one but let the calculator do
the or for you and you get it right every time Min - 2 min-2 and you get that b is equal to 3 and
there's your answer okay B is three is your answer groy all right num Olen number 11 Nancy has
just been hired for her first job congratulations Dan her company gives her four choices for
how she can collect her annual salary over the first eight years of employment each function
below represents the four choices she has for her annual salary in thousands of dollars where T
represents the number of years after she's hired so AF of is equal to 2 the Power of t + 25 that's
great I'll take that B of t = 10t + 75 C of t equal radical 400 T Clos radical plus 80 and D of
T is equal to 2 parth t + 1^ 2ar - 10t + 50 which plan which pay plan should Nancy choose in order
to have the highest salary in her eighth year AF bft CFT or DFT so I highly suggest that you
try this on your own and see which answer you got I have a strong suspicion already that
it's probably going to be a or D and I have a really strong suspicion that it's going to be a
why because I as a teacher and as a tutor I advise my students to understand that exponentials
blow up fast so fast in fact that they they they catch up to other polinomial and other
functions much faster than you might expect so what is the issue here it says in her eighth
year in so this is the number of years after she's hired so in first year she was hired zero years
ago in her second year she was hired one year ago in her third year she was hired two years ago
so in her eighth year she was hired seven years so what we need to find is a of 7 is equal
to 2 7 + 25 B of 7 is equal to 10 * 7 + 25 C of 7 is equal to radical 400 * 7 + 80 and
D of 7 is equal to 2 parentheses 7 + 1^ 2 - 10 * 7 + 50 so if you plug in to the
calculator plug in tal 7 we see that a is 153 so let's actually bring
this to the C to the slide what's going on why is
it not letting me there we go okay so we see that when
T equals 7 we got a is 153 B is 145 C is 13657 and D is 108 so in fact it is a
sounds good all right number 12 the third term in a sequence is 25 and the
fifth term is 625 which number could be the common ratio of the sequence is it
1/5 5 125th or 25 so as I said before definitely try the problem on your
own this problem we see now if we go to the formula sheet there is there
is second let's get that formula sheet again I just got to get it on another
browser okay we look at the formula sheet they do give us information about
geometric sequence and arithmetic sequences okay now they said that
this the sequence has a common ratio they never said that it's a geometric
sequence but they did say that it has a common ratio the moment they said it's a common has a
common ratio that implies that it's a geometric sequence so now we know that it is a geometric
sequence from the formula sheet we know that a subn is equal to a sub 1 * R to the nus1 so how
do we do this problem well first about process of elimination we see that the third term is 25 and
the fifth term is 625 so we know that the the the terms are increasing so that means that the common
ratio has to be greater than one in absolute value so Choice 1/5 and 125th are guaranteed to be
incorrect okay and I have a strong suspicion that 25 is incorrect my suspicion is based on
the fact that we're multiplying by the common ratio 25 is a quite large number multiplying by
that common ratio implies that we're going to multiply that 25 twice to get 625 that's a bit
too big I think but how do we do this we see that a sub3 is equal to a sub 1 R to now to the 3
minus1 so a sub3 is equal to A1 R 2 we still don't know what A1 is but we do know that A3 is 25 we
also know that A5 is equal to A1 R to the 5 - one and A5 is 625 is equal Al to A1 R to the 4th so
I have these two equations here how do I manage these two equations to get R so I see that or
a possible value of R so I see 25 is equal to A1 R 2 and I say 625 is equal to A1 R to
4th if I actually divide these two equations so I literally divide the second equation by
the first equation divide by 25 and divide by A1 R 2 notice that I have two equations two
unknowns but the A1 actually cancels the the A1 actually cancels so I have on the left side 25 ID
625 happens to be 25 according to my calculator right and then I I have R 4th / R 2 is R 4 minus
2 so 25 is equal to R 2 and if I take the square root of both sides remember to bring in a plus or
minus I get that R is equal to plus or minus 5 now can I eliminate five or neg five well if this
was a part two problem maybe some other piece of information in the problem might tell us but
since there is no other piece of information in the in the part two we it's either plus 5 or it's
minus5 now why do we eliminate minus5 in this case there is no algebraic reason to eliminate minus5
it's only the fact that one of the choices is five so it has to be that one there that it can't be
that neg5 is going to appear on one of the choices because then that answer would also
be incorrect that answer would also be correct they have to choose either five
or Nega five for this problem okay number 13 numer the box plot below summarized the data
for the amount of snowfall in inches during the winter of 2021 for 12 locations in Western
New York and I see the table again I see the Box goes from 50 to 120 winter of 2021 snowfall
inches what is the inter quartile range is it 30 or 50 and or 80 or 110 now I'm might not remember
how to do this problem but the formula sheet does so the inter quti range they actually just tell us
the interquartile range they tell us the formula for it interquartile range is IQR is equal to Q3
minus q1 so you just have to know what Q3 and q1 are so how do I label the box plot this is how
I label it I it's q0 q1 Q2 Q3 and Q4 now some of these go by different names okay q0 is
also called the Min Q2 is also called a median and Q3 is also called a Max q1 is the first
quartile Q3 is the third quartile q1 is also called the lower quartile Q3 is also called the
upper quartile okay but the inter quartile range is Q3 minus q1 now that I have those labeled I see
that it can't be 30 that's too small and if Q3 is 110 and q1 is not zero it can't be four and
it can't be 110 in fact this is also looking too big Q3 minus q1 this is literally testing
whether you know how to use your formula sheet and also if you know how to label q0 q1 Q2
Q3 Q4 and let's see 110 right there minus 60 and that's equal to 50 gravy train Choice two
that one's not so bad not so bad I think number 14 four quadratic functions are represented
below a of x = x - 3^ 2 - 7 C ofx = X2 + 6 x + 3 and then B of X is a graph which I look at
quickly before go moving on and then Choice four is D of X and I just taken it quickly
before reading the rest4 ne32 1 0 and then ne14 54 1 which function has the smallest minimum value
is it Cho is it R in numeral 1 2 3 or four some of this can be done by process of elimination I see
a minimum value here of5 I see a minimum value here of4 minimum value smallest minimum value neg5
is definitely smaller than4 so Roman numeral 2 is definitely not the answer but then out of choice
three and Choice One and choice three I see that this one is in vertex form so if you happen
to know if you happen to know a little bit about Vex form you may suspect that choice one is the
incorrect I'm sorry that maybe is the correct answer and you may suspect now that choice
four is incorrect because you might remember this7 now if you something about the ne7 now
if you remember that in fact this is has a Vertex at three positive3 comma ne7 the negative
of the number being the negative of the number being added to X or rather the number being
subtracted from X and also the number being added to the function then you see that since
this vertex is-7 in fact this is below uh5 here so this is look this is Choice four is looking bad
again now what is it that makes me say that choice four is incorrect remember that quadratics
are symmetric about their vertices since this goes to let's see negative so41 -34 -25
-14 and 01 since this one is symmetric about x = -2 that's the vertex so this is the Min for
this function so5 is not the lowest so Choice 4 is is fully incorrect now what about choice
three choice three right now in principle could be the answer there's nothing telling us whether
it is or not at that point this I promise that choice three would be the one I plug into the
randomly into the calculator and choice three I'm going to plug in oops I'm going to
let do this at y equals Y3 I'm going to do x^2 + 6 x + 3 I go to my table let's
see if I can get it by scrolling this is y35 -65 -2 there's my minimum at -6
okay because I know that that's the minimum because it's symmetric around
xal -3 or I can go to My Graph okay enter enter enter enter to UNG
graph those I go to My Graph Zoom standard okay and I can calculate the [Music] minimum okay I get got get the minimum notice that
above the trace button is the blue cal button so I press the blue second button and then Cal I'm
going to calculate the minimum using three I got to go to the left of that minimum press enter I
got to go to the right of the minimum enter you could just press enter at this point but I'm going
to actually guess I get close to the minimum and I press enter and I see that the minimum is at xal
-3.0 to you unfortunately do need to know that the calculator has a programmed bug into it you need
to know that that X is NE that actually means3 for the calculator and Y is -6 at the minimum and so
the Min is that yal -6 how do you do it by algebra as I mentioned I would do every single Problem by
algebra no matter what so I see that the vertex is at x = b over 2 a so this is a = 1 and b equal
6 so the negative the Min is at the vertex is at6 over 2 * 1 is -6 over 2 which is -3 and C of -3 is
= parentheses -3 2 + 6 * -3 + 3 which is equal to 9 - 18 + 3 which is = to --9 + 3 which is equal
to -6 the Min here is -7 which is bigger this is not the correct answer finally we got a bunch of
ways to do number 14 and we go on to numeral k number 15 the equation that represents the
sequence ne2 5814 dot dot dot is a n = -3 + -2 parentheses nus1 or -2 + -3 nus1 or -3 + 2 plus
I'm sorry 3 + -2 nus1 or -2 + 3 parentheses n - one this is semi 2x2 problem although it's
not really the reason it's a a well it depends on how the way you look at it it is a 2 by two
problem the questions really are separate is the are the coefficients -3 and -2 or switched or
are the coefficients 3 and -2 switched so the questions are what are the two coefficients and
whether they're switched or not or or what or not whether whether they go first or second okay
so it is a truly a 2 by two question but many of you may be able to do it without recognizing
it as a 2 x two question so I notice that this goes down by three subtracting three subtracting
three and then the next number is -4 which again is subtracting three so we're subtracting three
after each term since we're subtracting three after each term we already see the one that
is subtracting three so it's already looking very good for us now you see why this is even
though it's a three a 2 x two problem all four answers are extremely different so by getting one
relevant piece of information you already can get the answer so this is looking very good
but how do I do this by process elimination I plug in numbers A1 I promised that I would always
test Choice one choice three this is just for the person of the video Choice 3 if I say A1 well
that's equal to 3 + -2 1 - 1 which is equal to 3 + -3 * 0 which is equal to 3 + 0 which is equal
to 3 not equal to -2 so choice three is not the answer and in fact because by plugging in
Nal 1 I could actually quickly eliminate this one as well plugging a negative if I plug in X
Nal 1 this one gives us -3 not -2 this one gives us NE -2 when n equal 1 so it Choice
One and choice three don't make sense but then I actually get the the full answer by plugging
an N equals 2 by plugging an N equals 2 because these are linear linear functions can intersect
that at most one point so plugging in to linear functions will give you the right answer every
single time after just plugging in two different numbers so we plug in n equals Nal
2 and we get for the first for the choice one this is Choice two now we plug in
nals 2 we get A2 = -2 + -3 parentheses 2 - 1 which is -2 + -3 * 1 which is -2
- a -3 or you go to your calculator and let your calculator do it for you5 so that one is correct but as I promised every single
question I have to do it algebraically because this this is definitely
a part two question so this is on our formula sheet and that's so this is
literally testing whether you could do it though look at it look at this it is on
our formula sheet so we could do it by the form of the sheet okay make that big so a Nal A1
- DN minus one we found here that D is equal to -3 and we also found A1 by just reading it is -2 so
a n is equal to -2 + D -3 parth n minus one so we just actually read it this is literally did you
go to the formula sheet literally what they're asking for the previous one number 15 did you go
to the formula sheet yes or no or did you have happen to have prior knowledge if you didn't go
to the formula sheet but of course you should go to your formula sheet to check what's on there
okay again here's what's on there definitely go to your formula sheet it is worth knowing what's
on it I may do a video with where we're just reviewing the formul the problems on the formula
sheet in fact I may do that as like my prep for the Regents video I I think it's a really good
idea but that said num says number 16 The Dot Plot shows the number of goals Jessica scored
in each lacrosse game last season Jessica looks to be a very good player because there's a lot
of dots around three goal scored per game which statement about the Dot Plot is correct
mean's greater than the mode mean equals the median mean is greater than the median median
is greater than the mean or mode is equal to the median so this is one that I highly suggest
doing just on your own I I do notice that just in terms of process of elimination Choice
two and choice four have the same quantities so you should actually be able to determine
whether either Choice two or Choice 4 is incorrect simultaneously by by doing some sort of
analysis now suppose that I don't know how to do the problem suppose I'm a student who gets this
problem I just don't know how the mean the median and the mode work well I do remember mode most
often mode most often mode equals most often so in this case that's equal to three because I see
the tallest thing the tallest one is three so now I could put mode I could put three into
all of these for mode now Choice two and choice four don't have the mode in it but I wonder if
there's something in the problem that allows me to to do something with Choice One and choice two
now that I remember the that the mode is three well the I have way more data to the left
of three and way more dots farther than I do on the right which means that the mean is less
than three and I know that the median is less than or equal to three also I just don't know if
it's three or not yet but the mean is less than three Choice One says that the mean is greater
than the mode I have a number that's less than three can't be greater than the mode like 2.5 two
whatever it is can't be greater than the mode so Choice one is definitely incorrect this is not
a passing problem yet because I haven't done I haven't gotten it to the point where I could
eliminate two answers but it is now even if I had to guess at this point a one and three
chance of getting it right makes it worth more than a one and four chance of getting it right so
two point guess while guessing out of four choices that's one worth 1/2 1/4 again 1/4 times the raw
score two is equal to well it's a half but if I eliminate one choice now I have a one and three
chance of getting it right multiply that by two that's equal to 2/3 now if I change this to 36 and
this to 46 you see that 46 is greater than 36 so if you can even eliminate a choice you actually
are guaranteed you're you're guaranteed on average statistically more points and again
why a passing problem is is eliminating two choices because a half times 2 is equal to one
which is the average number of points you need approximately on a multiple choice test to get a
passing grade on average okay so can I eliminate any other choices well actually I could I could
do this one by just calculating what the mean the median and the mode are that's literally all I can
do so I know that the mode is three the median the median now I'm unfortunately I'm going to be
forced to calculate what the median is if if choice three is not the answer so I'm going to
calculate the median the median I cross out a zero and a six a zero and a five a zero and a
five a one and a four a one and a four a one and a three a two and a three two and a three a
two and a three and now here's the thing a two and a three now I'm done with I don't have any
more data points so that means that the median is actually exactly in the middle of the two and
the three which is 2.5 so the median is equal to 2.5 where the mode is equal to three which
means that choice three is not correct I now forced to calculate the mean to find out if the
mean is greater than the median or not so now I have to add up all the data points calculate
the mean okay now a lot of students will stop at that because they're like I you know it's
a lot of work but that's what it's making us do it's the Regents people have the right
to do that now I will also say this what is your time worth on a Regents your time as
now I have a fake it's truly fake but but it's has legitimate logic to it what is your
time worth while you're taking the Regents I I I say it's this it just as a humanistic
thing you T you multiply the amount of time that you work on a problem oh I'm sorry you take
the time that you work on a problem divided by the probability of getting the question right
so if you take two minutes divided by you're wild guessing on the problem so you have no
clue a one and four chance of getting it right then that's equ call that equivalent to
eight minutes but if you get a problem that it takes you three minutes but now you have
a one and three chance of getting it right divided by one and three maybe you worked a
little bit longer but you got it to a 1 and three chance of getting it right that's
equivalent to be being worth 9 minutes so but I'm going to argue that it's still
worth doing that to eliminate a a qu a choice because it usually doesn't take
that much extra time or what if it takes you though four minutes to to go down
to a one and two chance of getting it right that's oops four / parentheses that's
worth like an eight but if you takes if you take five minutes to guarantee you get
the question right that's worth five which is lower so your the time that you spent is
lower if you can it's your the the amount of equivalent time that you spent in this
heuristic argument is lower by doing the work if you're guaranteed to get it right
that's the that's the logic next time I do this this I'll make sure I choose my numbers
well but it is worth spending time if you're going to be guaranteed to get the question
right in fact it's worth spending time if you're guaranteed to go down to two choices if
spending way too much time to go down to three choices well then maybe it's not worth
your time but if spending a little time to go down to three choices then that's worth
it now the median is equal to 2.5 now the mean so what do we have to do for the mean
we have to add add up all the numbers and then divide by how many numbers we have okay
so we're going to add up all the numbers so 0 * 3 0 * 3 plus now how many ones do we
have three plus how many twos do we have two * 4 plus how many threes do we have 3 * 5
plus how many fours do we have four * 2 plus five how many fives do we have time 2 plus six
how many sixes do we have 6 * 1 that's the sum 50 divided by how many data points do we
have 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 50 divided 20 is actually
equal to should be 2.5 ID by 20 2.5 so we got the mean is 2.5 and the median is 2. so
the answer is Choice two it's worth it to go through that because if you're guaranteed
to get the answer then you might as well do the work all right numet the number 17 the
students in Mrs Smith's algebra class were asked to describe the graph of G ofx equal to 2
parentheses x - 3^ 2 compared to the graph of f ofx = x^2 which Student Response is correct
actually said that the graph of G is wider and shifted three units left bth said that
the graph of G is narrower and shifted three units left Carl said the graph of G is wider
and shifted three units right and Don said the graph of G is narrower and shifted three units
right so notice that this is a 2X two problem again the question is is it wider or is it narrower and the question question
is is it shifted three units left or is it shifted right re units okay and then
I see well let's see wider left three units is Choice one now now left three units is Choice two
wider shifted right through units choice three and narrower shifted WR three is Choice four and so
then if I could figure out which of these makes more sense then I can do the problem that way
now if you happen to know one of these has to be wrong then you you can get the question right
now it happens to be many students can get the question right because they know that what
the two does and they know what the minus three does they know that the minus three stretches it
vertically by stretching it vertically you get a narrower Parabola so it has to be narrower so it
can't be wider so now I'm down to two choices and it's a passing question what would I do if I
didn't know how to do this question I would graph it so in other words this is a question that can
be done on the calculator okay going to undo that graph I'm going to put here two parentheses x -
3 squared that's G and this is F is X S so I need to know what G is compared to F okay we're
going to graph these Zoom standard here's G here's F the blue one is G the red
one is f the first one graphed was G the second one graphed is f so I see
from the graph I see that the blue one is three units to the right and I see
that it's also looks a little bit narrower so that means that it is narrower and shifted
three units to the right now how do how would I have done this on paper if I take x s
and I change that to multiply by two outside to 2x^2 this is a vertical stretch which makes it narrower okay also if I take X2 and I subtract
three to X so that's not doesn't look like a plus minus 3 to X I get x - 3^ 2ar okay now
a lot of students are surprised by this but by subtracting three from x I actually shift
three units to the right so by subtracting from x i shifted three units to the right right which
can be counterintuitive but it but it is it does happen that way I'm I'm not going to really
struggle to to make it intuitive at this point because we you know we want to we've been
doing this for years and even even calculus kids struggle with this concept but it does
happen that if you perform an operation on on X it has one effect which is the opposite
of what you what the operation does and if you perform the operation on the entirety of f ofx
then it has the effect in the same direction as the operation so multiplying by two outside
stretches it vertically multiplying by two that only X makes it narrower adding three to F
ofx or subtracting three from F ofx moves it down three but subtracting three from x shifts it to
the right three okay so now we know that it makes it narrower and shifts it three units to the
right so that makes this the answer we eliminated Choice One and choice three but now we know that
choice four is 100% the answer okay and again we did this by graphing number 17 you could have
done it by graphing a lot of students get it wrong again because students want to use the calculator
right up on to the point where the teacher says use the calculator and the students are like n
Go ahead and use the calculator graph it on the calculator you're going to get it right you're
going to get it right okay me take a sip of this drink all right numero number 18 on one Saturday
Dave took a long bike ride the graph below model his trip and I see miles traveled 0 to 60
I see the hours and I see the graph generally going up okay cool and I'm going to go back to
the graph after what was Dave's average rate of change in Miles hour on this trip was it 10 11
11.6 or 14.5 now I would invite you to make a decision on what you how you want to calculate
it like a lot of students basically they know how to do this question but they they invent
new rules that aren't actually accurate to the problem and they end up getting the wrong answer
so how do I go about doing this proc i h well first off I go back to the TR the the problem
and I see that Miles travel go from zero to 55 okay and I see that the hours goes to
from 0 to 5.5 okay then I think the thing that might confuse a lot of students
is is what part of of the of the trip or do we use to calculate the average rate
of change so what part of the trip do we use well we actually have to use the whole
trip don't wor we have to use the whole trip okay so if we have to use the whole
trip then we have to look at this point right up here okay and this point down here to
get the average rate of change where do a lot of students get it wrong well they start to kind
of delete delete little pieces of the trip like they start they start to delete the part where
he was not moving at all but that's not legal the average rate of change no matter how the function
looks assuming it's continuous average rate of change is equal to Y final minus y
initial over xfinal minus X initial and in this case it's equal
to 55 minus 0 / 5.5 minus 0 okay and we I would literally go to your
calculator but another place where students get it wrong is they forget to put Cal
parenthesis luckily for this one if they didn't put parentheses the answer
just wouldn't be there for you but parentheses 55 - 0 / parentheses 5.5 -
0 and then of course I recognize that 5.5 is 10 time or 5 55 is 10 * 5.5
equal to 10 according to our calculator okay all right num number 19
which expression is equivalent to let me scroll this down which expression is
equivalent to x - 5 * 2 2 x + 7 parentheses minus parentheses x + 5 I'm going to I
got to again every four PA including this I great every four part so which expression is
equivalent to that expression is it 2x2 - 2x - 30 or 2x2 - 2x - 40 or 2X - 4x - 30 or 2x2 - 4x -
40 again this is a 2 x two question where the question is -2 or or4 as the coefficient of
x and also -30 or-40 as the as the constant coefficient right so which one is the
answer can be determined by plugging into your calculator and again I said I would
plug in the easy number so I'm going to plug in xal 0 but if you actually plug
in a more difficult number like xal 11 you will confirm which one is the correct answer
in one step okay so if you plug in xals 9 you'll confirm with with your calculator why am I
plugging in x equals z because I like I I like plugging in x equals 0 to quickly eliminate some
choices and I get uh5 * 7 - 5 which is5 -35 -35 let me rewrite that to-35 - 5 which is equal to -40 which means that the constant coefficient
of the answer has got to be -40 so that one's looking good that one's looking good
this one is wrong and this one is wrong so now the benefit of plugging in the easy
number is that now I could plug in like xal 9 or I could plug in another easy number in this
case there is another easy number like x equals 5 you plug in xals 5 the entire first expression
change cancels so that one's actually fairly easy to plug in yeah so that one will confirm
what the correct answer that's fun yeah is doing fun things so how do I do this on paper
x - 5 parenthesis I don't know if you heard that on the A on the microphone my AC
is on the is on the fritz which is why I had to go readjust it but it literally just shot
out ice that's fun 2x + 7 parentheses minus parentheses x + 5 so I have to multiply this out
so I'm going to multiply this out using the box method x - 5 2x + 7 and x * 2x is 2x^ 2
- 5 * 2x is - 10 x and then x * 7 is 7 x and 5 * 7 is - 35 and I could also distribute
this so I'm going to get I could simplify this 2x^2 - 10x + 7 x is - 3x - 35 and then
distribute the minus sign here - x - 5 and I get 2x^2 - 3x - x is - 4x then -
35 - 5 is- 40 so I get the answer is that okay now I'm going to go readjust my AC
please stick around I'll be right back okay fun fun a number 20 num the function
f ofx and g of X are graphed on the set of axes below what is the solution to the equation f
ofx equals g ofx is it 1 and five is it -5 and0 0 or is it -3 and 5 or is it 0 and 4 now
I want you to think about what it means to be a solution to the to the equation f ofx equals
g ofx you may have if you were given algebraic expressions for f ofx and g of X you would set
them equal to each other and you would find the value of x so that's literally what this is it's
asking us for what are the values of X that make this equation true and I see that they intersect
here here and here I don't know if you could hear the AC the AC is still throwing out ice ice
bits so that's going to do that for a little while so if you hear random noises that's what's going
on so I need to find the values of X I noticed that x equals z is very much not a solution to
this so that's not that's not it now I also see that this one has a negative number and I don't
think they intersect anywhere where X where that's negative so my process of elimination is going to
eliminate that choice although I will say this the reason why a lot of students choose this one is
they see the y-coordinates -3 and 5 are the are the intercepts but this is actually asking for
the values of X that satisfy the equation and in fact the values of X that satisfy the equation
are one and five all righty so let's move on to numer number 21 when babysitting Nicole charges
an hour hourly rate and an additional charge for gas she uses the function C of H equal 6 h + 5 to
determine how much to charge for babysitting the constant term of this function represents is
it the additional charge for gas or is it the hourly rate Nicole charges or is it the number of
hours Nicole babysits or is it the total Nicole earns from babysitting so definitely pause
and think about some of these answers now for process of elimination she uses this function
to determine how much to charge they actually told us that how much she charges is C of H so the
constant term is not C of H the constant term is this F so by PR elimination I've eliminated this
one and also well the number of hours she Char that she works that's where the VAR that's the
variable that determines how much she makes isn't it so the variable has to be H so the constant
term is not the number of hours she works it's the H so this is H this is C of H so now I'm down
to two choices is it either is it the additional charge for gas or is it the hourly rate in the
cold charges so I see that c of H is equal to 6h + 5 we know that she charges an hourly rate
and an additional charge for gas staying longer doesn't make gas more expensive did the couple
decide to to go to dinner and then made it made it went to a movie so now they have extra time
so that she makes extra money or did they come back home right away nothing is going to make
gas cost more money so the part of the charge that makes her more money has to be the amount
she makes for the hours so this is the amount she makes for the hours of babysitting and this part this
constant part has to be the gas M okay so we see that she makes she
Mak she gets $5 for gas and she makes 6 h hours for babysitting so this
six which is a common question that they'll ask about this six the
six is equal to her hourly rate which is a very low hourly rate for for if
you're working for strangers but of course if you're working for family what are you going to
do also if you're young what are you going to do so but the point is that the constant term is the
additional charge for gas okay num number 22 when solved for X in terms of a the solution to the
equation 3x - 7 = a x + 5 is so we're solving for a is it 12 over 3 a or is it 12 I'm sorry for x
and we're solving for x in terms of a rather sorry the solution to the equation 3x - 7 = a x + 5
is 12 over 3 a or 12 over 3 - A or 3 a over2 or 3 - A over2 so this is one that you could do
by plugging in a random number you can do it by plugging in a random number I would like remember
let a equals 0 actually eliminates one of the choices eliminates Choice one so that's an easy
one because that would be undefined whereas the original equation would be defined letting a
equal 1 that might eliminate some choices but I'm telling you what you could do letting a equal
the random number like I said before 9 or 11 or eight that'll tell you pretty quickly or 22
that'll tell you very quickly which one of these makes sense how by plugging in that random number
and then solving for x now for example I see that a is a coefficient here's another hint
for elimination I see that a is a coefficient of x so when I'm solving for x I'm going to end
up having to divide by something involving a which means that the bigger a gets the smaller
the value of x is going to get but choice three actually grows as I plug in bigger values of a
choice four goes in the negative Direction but grows in absolute value so when I said grows
I meant actually grows in absolute value as a grows X shrinks in absolute value because I'm
going to divide by something involving a so B Choice 4 grows in absolute value so it actually
only the only one left here is is Choice two so that will tell me that that choice two is the
answer another thing that I could have done to to to eliminate some choices is I might note that in
the process of solving for x I'm going to have to subtract the coefficients of X not multiply
or divide them that eliminates choice three for sure and even if I didn't know how to solve
it fully Choice two or Choice four are the only ones that actually subtract the coefficients of X
so how do I do this algebraically 3x - 7 isal to a x + 5 I need to solve for x so I can get rid of
I'm going to get X on the left side I'm going to and everything without X I'm going to get it
on the right side I'm going to add seven add seven there's the 12 that all the answers have
so 3x = ax + 12 subtract ax subtract ax this is where a lot of students get messed up they combine
the subtraction by multiplication or another thing that I've seen students do is they they subtract
the combine of subtraction by division subtraction is subtraction so you combine subtraction by
subtraction so 3x - ax = 12 the only way to combine these is the distributive property
factor x out the factor pair is 3 minus a is equal to 12 IDE 3 - aide 3 - A and I get that
x = 12 over 3 - A that is Choice two Choice two Ruby all right number 23 Wade Wade van nerk
a runner from South Africa ran 400 m in 43.038157 extremely fast my by the way my my fastest 400 meter was
58 seconds and I was fast I wasn't the fastest on the team but I was fast I was I was
triple jump division champ in high school so to be triple jump division champ you actually
have to be pretty fast 43.3 is significantly faster than so Wade van nerk ran a a runner
from South Africa ran a 400 meters in 43.3 seconds to set a world record which calculation would
determine his average speed in miles per hour so I see a lot of numbers I'm not going to
read all of them because it would take me longer to read them than to analyze what they're really
asking us to do they're asking us to do some what's called dimensional analysis and dimensional
analysis is a big word in chemistry especially but all it is is putting recognizing that dimensions
are being multiplied in other words 400 meters is the number 400 times the unit meters so why does
that matter well it matters because when you're when you're solving and inequality then you can
oh I'm sorry when you're when you're when you're simplifying an expression and changing units you
can if you need to eliminate units that are being multiplied you can divide by those units similarly
if you're dividing by certain units and you need to eliminate them you can multiply by those units
and so that's what this is asking for we do need some units here I'm doing this fully because of
course this easily could be a part two question or a part three question seriously this this
is this is exactly what part twos and threes look like so let's get that there we need
to convert 400 m and 4 43. 3 seconds into miles per hour now I know that my in my dimensional
analysis the numerator and denominator have to have units that cancel not multiply together
so I see that in Choice one I have meters and meters in the numerator somehow you're going to
have meters squared that can't be the answer in the second one let's see meters and seconds
miles and meters and hours and seconds this one has seconds and seconds in the denominator
so you're going to have seconds squared in the denominator when we're canceling seconds and
replacing it with hours that can't be it now this one has meters miles and seconds in the numerator
and seconds meters and hours in the denominator those don't have the same units in the numerator
and in the numerator and not the same unit in the denominator that's looking okay now this one
has meters and meters in the numerator that then that would be me squared that can't be it already
we've eliminated the incorrect choices but let's actually do this by hand as we said we would
for every problem so so excuse me so we have to convert his speed from meters per second to miles
per hour so his average speed is 400 meters in 4303 seconds now we have to eliminate the meters
which means that we have to put meters in the denominator and miles in the numerator which
unit allows us to convert meters to miles let's see they meters to miles meters to miles is it
here inches to centimeters meters to inches miles to kilometers kilometers to miles pounds to
kilogram and kilogram to pounds it not that is not there meters to miles is not there which means
that there's another detail that you do have to know technically this is in the realm of science
but now we know that you do need to know that 1 kilometer is equal to 1,000 M kilo means a
th000 kilometer so 1 kilom means 1,000 M so 1 km is 1,000 M so there we go we actually need
this quantity for and and the knowledge of this you need to know that kilo is 1,000 okay
again 1 kilo is equal to 1,000 1 kilo is just 1,000 yeah so 1 kilo meter 1 kilometer
is 1,000 M so 1,000 m is equal to 06214 mil so if we put that in 06214 miles over 1,000
M that cancels meters in the numerator and denominator and we're left with miles now we
have to eliminate seconds and convert that to hours okay and that one doesn't even appear at
all in the list seconds an hour so that's another thing that we have to know we have
to know that there is 6 seconds is equal to 1 minute and you have to know that 60 Minutes is
equal to 1 hour so that 3,600 seconds is equal to 1 hour so we have to know that you have to know
this so we have to eliminate seconds so where does seconds go seconds was in the denominator so
seconds goes in the numerator to eliminate it and hours goes in the denominator 3,600 seconds
divided by 1 hour and that matches choice three but I I do want to point out again the way I
eliminated the choices for before doing number 24 the way I eliminated the choices was just
going through and speaking out which ones didn't eliminate units CH one had meters and meters
in the numerator and it also actually has so that that that part is incorrect right it also has
seconds and seconds in the denominator that won't eliminate that part is incorrect Choice two had
seconds and seconds in the denominator that won't eliminate and choice one had meters and meters in
the numerator that won't eliminate not bad not bad a lot of students get this one wrong because
it's way too much but we just found out it's actually if you just remember that that the units
have to cancel correctly it's actually not that much in other words you don't have to know how to
do this for part one what I just did for part one you do need to know what I just did for part two
three and four but for part one you could just look for where the units eliminate num number 24
which function has a domain of all real numbers and a range greater than or equal to three this is
Choice One f ofx = x + 3 Choice two G ofx = X2 + 3 Choice 3 H ofx equal to 3 to X or choice 4 M ofx
= absolute x + 3 I I would go ahead and graph this and as you know my my one choice one thing you
could do is literally plug in a number and that might if you're lucky eliminate some choices
like if you plug in x equals z this one it says to have a r it has to have a range
greater than or equal to three right says has a range greater than or equal to three if I plug
in xal 3 I get H of0 I'm sorry if I plug xals 0 I get H of 0 is equal 3 to 0 is equal to 1 which
is lower than three that's pretty lucky but it's the only one that gets eliminated by plugging in x
equals z but if I plug in other numbers I might get lucky this one choice one if I remember
what a line Looks like Choice one has a slope ofx uh1 so this one has the range from negative
Infinity to Infinity it goes all the way down to negative infinity and all the way up to Infinity
so that one's not the answer okay and now I'm kind of stuck maybe as a student I'm stuck between
G ofx = x^2 + 3 and M ofx equals absolute x + 3 valid thing to be stuck on but how do I get past
this this this limit well one thing I could do is well like I said plug in some numbers if
you plug x equals like for example1 you find out the choice four doesn't quite make sense but you
could also graph it I know I'm graphing farther down than you're used to graphing you know
what I'll I'll go ahead and graph at one and two the reason I was trying to graph further down
is that I didn't want to delete anything that I graphed before but in this case I'm going to
I know I'm going to have to later on so how do I graph the absolute if I graph y equals math
if you go to number one space to the right press the math button again one space to the right
is the num number and the very first option is absolute so absolute x + 3 and if I graph this
Zoom standard I see that it goes actually all the way down to the x- axis so the range and before
bouncing back up so the range here is equal to zero including zero to Infinity and here I needed
the range range greater than or equal to three I needed three to Infinity so that choice four is
not the answer choice three Choice two rather is a parabola the standard Parabola y X2 the
parent function of all parabas shifted up three units or equivalently the vertex
form 03 and so the range is 3 to infinity and it's also defined on all real
numbers so the domain is equal to negative Infinity to INF all right and we are done with
the multiple choice questions I hope that that you got so many points on that really do
but we are going to move on to number 25 on part two's and I want you to see that part two's threes
and fours are definitely multiple choice questions with the multiple choices just eliminated you
see like even the first one but now the first thing I want to do before anything I want
to cross out the note that diagrams are not necessarily drawn a scale this is my tutoring
skills at work not you know I used to teach it but then it confused students just like the
whole on the SATs used to penalize you for getting questions wrong they no longer penalize
you for getting questions wrong so you should always answer every question if you literally
out of times to start filling in numbers on the SATs and acts but on this just like
penalizing students actually made students not fill anything in when they actually just
should have here saying not that diagrams are not necessarily drawn to scale convinces
kids that diagrams are aren't drawn to scale when in fact they almost always are drawn to
scale and in almost every test every diagram is drawn to scale and definitely in every
test almost every diagram is drawn to scale so using scale is actually useful if you don't know
how to do the problem that said this is the part for all questions in this part a correct
numerical answer with no work shown will receive only one credit so if you happen to know a way to
do it on your calculator do it on your calculator and if you don't show work you'll get a
point that's great but it does say here it clearly indicate all the necessary steps including
appropriate formula substitutions diagrams graphs and charts Etc so if you show work you're going to
get all the points okay how do we do this solve 5 parentheses xus 2 close parentheses less than
or equal to 3x + 20 algebraically so I like to plug in the number I a number for an estimate
like zero if I plug in x equals 0 I get -10 on the left and I get 20 on the right so zero is in
the solution set zero is is in the solution set okay so and also if I plug in like a huge number
I see that the left side is going to be way bigger than the right side So eventually numbers on the
right are going to stop being in the solution set but all the numbers on the left in the negative
side are going to be in the solution set so the solution is going to look like
this and it's going to stop somewhere but now the question is what that
number is going to be okay this is my estimate but my estimate is fully accurate zero
is in the solution set every negative number is going to be in the solution set some positive
numbers are not going to be so let's find out how to do this we distribute okay this is where a lot
of students lose points right here 5x a lot of students rate minus two that's incorrect because
they have to multiply the five by the -2 by 5 and they getus 10 all right so if you're the kind of
student who gets that question wrong right there keep that in mind when you're taking the Regents 3x
less than or equal to 3x + 20 now I'm going to I'm going to get X on the left I'm going to add X
on the left because a lot of students like it that way but also because it's going to make me avoid
having to divide or multiply by a negative number 2x - 10 less than or equal to 20 add 10 add 10 I
get that 2x is less than or equal to 30 divide by two divide by two I get that X is less than or
equal to 15 and that is my answer so that missing number was 15 okay so that that's very much a
a part two question in fact you've seen questions that exactly like this one already today so
if you feel like this has been helpful do I do appreciate that you clicked the Subscribe button
I told you why I do this for free and I but the benefit that I get from you is the Subscribe
the Subscribe button one thing I didn't actually mention the if you go into the description
of the problem I do have some materials for students some free stuff and some paid stuff so
if you go and for teachers also some free stuff and some paid stuff including a completely free
practice satac assignment 20 minutes a day that's completely completely free for everybody so
if you go down to that you can get that okay you just go into the description and and and click
on the link for that and again free 26 that and that's again for students who who have trouble
affording you know tutor at any cost that is a free service that I provide for everybody
whether you can afford it or not number 26 num says given G of xal to X CU + 2x^2 - x
evaluate G of -3 so this is literally asking you how do you plug in to the how do you plug into
a function as you recall the instructions did say let's go to the instructions real quick
correct numerical answer with no work shown will receive only one credit so if you do not know
how to do this question but you do plug into the calculator y equals I'm going to I don't
like clearing that but I'm going to X Cub + 2x^2 + 2x^2 minus X and you go to the table
and you you could if it's on set to Auto you could scroll to y = x = -3 you get y = -6
if you just write the number -6 that's a point a point you might say but it's only
a point but if you're doing one of those students who's playing the the the points
game on the multiple choice one multiple choice question is only worth two one point
is half a multiple choice question worth it worth it so do plug in and get your point get
your point then find out if you could just do this algebraically in fact you can you I hope
you can do this algebraically by plugging in to the expression in fact if you say G of -3
equals -3 cubed + 2 * -3 2us parentheses -3 let's actually the parentheses minus
parentheses -3 and then you just write right after that equals -6 that's two points you
don't have to do all this simplification on paper you don't have to do all the simplification
on paper that's two points I'm going to do the simplification on paper because I promised
you I would -3 Cub is -27 + 2 * * -3 2 is POS 9 - -3 is + 3 so = -27 + 18 + 3 which
is equal to - 277 + 18 is9 + 39 + 3 is6 done done so but you could just stop at
the red and that'll be two points so those I know that some teachers say focus on the part
ones the multiple choice I I think the reason and I'm not going to I'm not going to denigrate
teachers to say that because the truth is that that that the the often the reason the latal
teachers say that is is that they've fought the Battle to try to get students to show work
they students just insisted on not showing work if you if you insist on not showing work then the
best way to to get your points is by focusing on the part ones but the truth is that if you do
show work then you shouldn't just focus on the part ones you should focus on the part twos
threes and fours and if you can get a 65 on the part ones you can get an 80 so like I said
there should be a gap of students who just don't get anything between a 65 and an 80 that Gap
doesn't exist because there's a ton of students who don't bother showing work so if you show work
immediately your grade is going to blow up if you don't show work and you get an 80 on the part twos
based on just the part ones you can get a 90 on the part twos three with the part twos threes and
fours and if if you can get there you're almost guaranteed to with a little bit of work to get
on 95 98 99 or 100 which is great I have graded a test with 100 it feels great feels great for
the grer I love seeing it okay so given the relation R is R is equal to1 1 0 3 -24 and X5
State a value of x that will make this relation a function and explain why your answer makes this
a function so State a value of x that will make relation of function I remember that a function
has to satisfy the vertical line test so-1 1 03 what just Happ -24 and X5 so any value here any value
of X except except X = -21 or zero oh except I'm writing over my
picture okay except X = -21 or 0 or zero will be one point so how about x = 2 xal 2 xal
3 x.5 xal literally any number except Nega 1a2 or zero now explain why your answer makes
this a function now this is the point where we have to actually use so the and you
don't have to say this value of x makes this a function because you could just start
with the explanation you say none of the x coordinates repeat that's it none of the x coordinates
repeat a relation is just any pairings of X and Y any pairings at all of X
and Y you can pair a bunch of of x's and y's but what makes relation of
function is that none of the x coordinates repeat okay so let's I have to
adjust my AC again unfortunately one second okay okay now I'm back number 28 numero
as I said every FAA every little thing that I have to do to to make this video in one shot I'm
going to do it because now I can make more videos and benefit more students so a survey
of 150 students was taken it was determined that two-thirds of the students play video games of the
students that play video games 85 also use social media of the students who do not play video games
20% do not use social media complete the two-way frequency table students a lot of students
skip this table because they're like this is too much but if you just get one number beyond
the information that they gave you get a point half a multiple choice question now you have to
fill in the rest of the table to get two points but you might but I'll tell you this and this is
something that I have done in the past multiple times students get to this question they're like I
don't know how to do it and then I just tell them is there anything that you can say then they say
the things that they can say and then they're like I don't know how to do the rest and then I say
literally word for word is there anything that you can say so and I just keep saying that over
and over and over until they're done in other words students say they can't do it because they
don't see the final answer in one step but this is not a one-step problem this is literally
a one step at a time problem that's basically every math question is isn't it so you do one
step at a time you just do the thing you can do and suddenly you'll find that you're done and
in fact if you just make a single mistake you'll be fine because if you get one part of it correct
one pro one number beyond what they told you you get a point so 150 students was taken the total
is 150 students the total of out of all things was total it was deter that 2third of the students
play video games so now I'm looking at the table and I see the headers play video games do not
play video games total and also social media no social media total so play video games two-thirds
of the students play video games I'm going to put this in red what number goes here is 2/3 of
50 2/3 of the total so what number goes there 100 just make it a little
bit more legible 2/3 * 150 is 100 then of the students that play video games 85 also use social media of the students that play
video games 85 also use social media so that's 85 then of the students that do not play video
games 20% do not use social media this is the point where now you're starting to get points
complete the two-way frequency table so now let's see what can I do to get some numbers I
already can get the no social media who play video games I know that the total number play
video games is is eight is 100 of those 100 85 play use social media so the number
that do not use social media in the video games column is 100 minus 85 which is equals
to 15 I already got a point I already got a point the rest of the table will give me the
second point so the total here who play video games I'm sorry the total is 150 the the number
play the total only of the people who play video games is 100 so the total of the people who do not
play video games is 150 minus 100 which equals 50 if I hadn't gotten this 15 but I had gotten
this 50 that's also just one point separately okay so now of the students who do not
play video games of the 50 students 20% do not use social media so that's this box
over here here other students who do not play video games 50 do not play social
Med do not use social media so that's 02020 20% of the ones who don't play video games let make that a parenthesis and I go to my calculator
to do 020 * 50 which this is equal to 10 okay now I could actually get the number who
play who do not play video games but do use social media because this column has 50 students
10 of them don't use social media so that means that 50 minus 10 do not play video games but do
use social media that includes me by the way I don't play video games but I do play use social
media 50 - 10 is 40 now the row is how many you social media 85 play video games and 40 don't
play video games so 85 Plus 40 use social media and according to my calculator that is 125 and the
second rle the ones who don't use social media 15 play video games and 10 do not play video games
so the ones who don't use social media is 15 + 10 which is equal to plus 104 to my calculator is
25 and let me just check real quick 85 + 40 is 125 15 + 10 is 25 okay let's see 100 + 50 is
150 85 + 15 is 100 40 + 10 is 50 125 plus plus 25 is 150 so the table works okay the table is
accurate this table only has four degrees of freeway so they have to give you four unique
algebraically independent pieces of information okay and they did 150 students 2third of those
play video games of the ones who play video games 85 use social media and 20% of those who don't
play video games don't use social media for algebraically independent pieces of information
for degrees of freedom eliminated this table can be filled out perly okay so you see that it's
literally just going plotting along and doing the Problems by one piece at a time right this
I have seen this in a multiple choice question I don't think I've seen it as I know I have seen
it as part of a part one on a different test but it was just talking about one column so
it is possible to do this as a part one but this one is definitely like a part one multiple choice
without the choices use the method of completing the square to determine the exact values of X
for the equation x s Plus 10x - 30 = 0 if you use any method other than that you can get
a point again if you just State the answer you can get a point so if you get it any other way
you can get a point so if you don't know how to do it by compet the square but you know like the
quadratic formula go ahead and do the quadratic formula okay so how do I do this
by completing the square so step one this is the steps to to completing
the square get get ax s by plus BX by itself okay so I'm going to add 30 and I get that x^2 + 10 x is equal to 30
notice that Gap two I'm going to divide by a if necessary this one has AAL 1 dividing by
one doesn't change anything so I'm done with that two three sorry right
B B over2 and B over 2^ 2 okay so B equal 10 B over2 = 10 over2 is 5 and
B over2 squared 5 S is 25 okay four add B over2 squar to both sides okay now add 25 so let me put that
[Music] in red here so you see that I did that plus 25 plus 25 and then why did we do
this because the left side is now a perfect square that's why it's called completing the
square the left side used to not be a perfect square and now it is a perfect square we
completed it as a perfect square we completed the square so step five is now to factor the
left side as a perfect square as a perfect square okay let's try like that a little bit neater parentheses x + b/ 2^ 2 okay so that's
what the left side is going to factor as x + 5 parentheses squar equals 30 + 25 is 55 okay and
now step six is to solve via the inverse operation Val okay X appears exactly once in the
problem that means what we could solve by the inverse operation method we just keep
undoing the oper the last operation that was done to X until we're done X+ 5^ squ the last
operation done to X is the squaring so we take the square root of both of both sides putting in
the plus or minus and we get that x + 5 is equal to plus or minus radical 55 then the last thing
that was done to X adding five so we subtract 5 subtract five and we get X = -5 plus or minus
radical 55 and that is our answer and that's two points gravy Trend that's two points if you
did this any other method you would get you know partial credit but this is the method of
completing the square and it works for any quadratic get ax S Plus BX by itself divide by a
if necessary often is necessary write b b over2 b over 2^ 2 right then you add b over2 square
to both sides then you factor the left as a perfect square X Plus B over 2^2 and
then solve via the inverse operation method now this one num number 30 Factor 20x CU
plus 45x completely this one there's a nice clever thing that you could do to to
help you with the factorization as you know if you just write the answer you get partial
credit so what if we did do this 20 x cubed - 45x now we know that the factorization
corresponds to the roots in other words the the roots of the factors are the roots of the original
Expressions so if we graph this Zoom standard we see that this has a root let's see where it has
a root it's it might be a little bit difficult to see where the roots are but we definitely see
a root at xals 0 we see a root somewhere like there and we see a root somewhere there so if we
actually calculate The Roots So Cal is in blue so we press the blue second button and then Cal
then we want to calculate the Zer that's Choice two we want to calculate that that that that this
zero over here enter left to the of that zero to the right of that zero enter we're going to guess
in this case we're off the screen so we're just going to press enter and we see that the zero is
atga 1.5 so one of the Z is going to be at 1.5 it happens to be that that other zero is going to
be at X = positive 1.5 but you could you could do that what we just did calculate the zero to
the left of that zero let's see left of that zero okay to the left of that zero enter
the right of that zero enter yes enter xal 1.5 and then confirm we can confirm that
zero is a root but in fact if you factor 20x Cub - 45x all both of those terms have an X
in it so this definitely has a zero at x equals z so let's actually do the this well let's
bring let's bring in this image into the problem so you have it here but we're going to
do this algebraically as we do with every other problem so we're going to factor I notice that all
the terms have a five in common and all the terms have an X in common x to the first power so I'm
going to factor those out 20 divid 5 is 4 xid x is X2 minus 45 ID 5 is 9 and xid X is just one
okay so now I've already got partial credit I already got partial credit I get a point for that
but I happen to know that 4x2 - 9 is actually a difference of 2 s difference of two squares or
difference of perfect squares p^2 - Q ^2 well this is equal to p + q p minus Q where p is equal
to 2X and Q is equal to 3 so I got 5x parentheses parentheses 2x^ 2 - 3^ 2 and I can Factor this
as a difference of 2 squ is 5X parentheses 2x + 3 Clos parentheses open parentheses 2x - 3 and there
is my factorization completely done and The Roots notice the roots are there the roots are
of this are 1.5 and the root of this negative 1.5 so had I done this with a calculator if
I had done this and said 20 parentheses x parentheses x + 1.5 close open
x - 1.5 that would have been a point without by just writing that the 20 comes
from the leading coefficient and then the rest comes from the roots so this can be done on the
calculator part three again what do I do with this part note that diagrams are not necessarily
drawn to scale notice that we haven't had a single diagram not drawn to SC scale but not only that
we haven't even had a single diagram that even was eligible to be not drawn to scale every diagram so
far had to be drawn to scale so I cross that out because we're going to assume that the diagrams
are drawn to scale okay so unless unless we don't know how to do it we're so in other words
I'm sorry we're going to assume that the diagrams are not drawn to scale if we don't know how to do
the problem if we do know how to do the problem then then do what you can but but if we don't
know assuming the diagram is not try to scale is is fine this is now a four-point question though
which means you might say and I've heard a lot of students say now the fourpoint questions are so
difficult I'm not going to bother with those I'm going to I'm going to bother with the part twos
but the thing is that the part 3es just offer more partial credit so they're worth it and in fact
chances are if you if you're trying to eek out points you can actually eek out more points from
the part twos than you can from the part from the part 3es and the part fours than you can from
the part twos so do focus on the part threes and fours and notice the logic there that means that
if you should focus on the part threes and fours more than the part twos then you should definitely
also focus on the part twos which means you should focus on every part of the test so if anybody
tells you only focus on the part ones that's bad advice and that's the proof okay first one graph
the following system of equations on the set of axes below this one I would highly recommend going
on the calculator because you can get the integer points right there again we ran out of space
so we're going to do delete that y = x^2 - 3x - 6 and there's going to be some
very things that some things that we have to make extremely clear we neatness counts
on graphs what do I mean by neatness counts if you write the letter A but you don't close the
letter A so your a looks like the letter U or you don't close the A and your Loop kind of
is whack and so it comes out sideways and your a looks like a c see but we can read your work
we can just work with what you wrote it has to be neat enough that we could read it so don't
write it so Slappy that we can no longer read it but if we could read it we can do your work
here's the thing about the graph though neatness counts like if you just move a point over because
you think you want to be more clear you're not being more clear that way the location of the
point obsessively matters so if a point is on a line but you're you want to move it over so
you could see it better don't because by moving it over you made it wrong you have to just
if you want to make it more clear just make it darker so I'm going to I can go to the table of
values and I can get t i can get points so let's see I'm going to go down a little bit
there we go and I'm going to use these points to graph these functions now I know that you
don't have colored pens you usually graph with pencils but I'm going to do this with my colors
the first one is blue that's the first y = -3 x^2 - 3x - 6 I see X is -4 I see y = 22
that's off the chart x = -3 y = 12 so I could go up to 1 2 3 four five so I like marking five
and and five and -5 and five on my graph to make it easier to read and I'll make 10 on the graph
and 15 on the graph okay for now I'll stop there but3 12 so -3 x is-3 I go up to Y =
12 I've seen a lot of students move this dot over no if you move it over
it's wrong it's right centered right on the point where the the where
the hash is intersect X is -2 y = 4 x is -2 x is-1 y = -2 x is 0 y = - 6 x is 1 y = 8 x is
2 y = 8 x is 3 y = -6 x is 4 y = -2 X is 5 y = 4 x is 6 y = 12 okay and then I
see it goes off the page after that so what do I do to get full credit for this one graph
I make sure that I go outside of the area and I make sure to put an arrow technically
speaking if you either put the arrows or you go beyond the edge of the graph you get
a point assuming that those points are part of the graph I recommend to students when both
are appropriate do both but now I'm following the graph notice that when I'm doing this I'm trying
my best to go right through the points but it it's a little bit Jagged a little bit jiggly
right I've seen students try to do this graph by using their straight edge but the thing is your
straight edge only graphs perfectly straight lines if the line is perfectly straight you must use
your straight edge if the line is curvy if it's a curve but not straight you can't use your
straight edge so this is a two a full onepoint graph I put the arrows there I went beyond
the edge I've seen students like move the point a little bit to the side to make it more
visible and they lose points I seen students just not be careful and move their points to the
side because they just weren't being careful they lost points look at all this work done
and losing points so easily you want to do that well I should also say that this is
y equals x^2 - 3x - 6 so you do have to label it I should say that too why do you have to
label it because you're graphing two functions okay the second one y = x -1 I see let's see4 534 so I got a line right I got a line Etc okay so if you're careful you now put your ruler down and you end up
getting a line let me see get this carefully get a line that goes like that now does
it straighten it for me yes notice I used the straight edge because it's a perfectly straight
line notice that it goes through all the points that I just graphed and all these other points
that are on the graph are actually part of the function that's this and label this y = x -1
that's a beautiful graph and I it's exactly as neat as it needs to be I suggest not making it
any sloppier than that otherwise you may lose points don't move your points over
to the side to make it easier to read because it doesn't make it easier
to read it makes it just fully incorrect graph your line with a straight edge because
it's perfectly straight graph your Parabola without a straight edge because it's not perfectly
straight and your your hand is not expected to be technologically perfectly arked so that that graph
is and it's a little bit Jagged maybe more Jagged than you're able to do full credit full credit for
that okay number two the last part is to State the coordinates of all solutions now this one is
another point where a lot of students lose points unfortunately a valid question is do
you need the x coordinate and the yord -1 comma -2 is one of the solutions and
the other solution and that's because they intersect you don't have to Circle it
there and the other one they intersect is five and some students some students lose points
on that one because they write the answers like negative 1 and five and it's easy it's easy to
fall into that trap especially since earlier on there was a multiple question that looked exactly
like this one as crazy as it was I think this is a well-written test except for the fact that they
repeated Concepts twice more actually more than twice they repeated Concepts when they could have
just not repeated Concepts and had students who knew more and different things get a high much
higher grade and also students who knew fewer things but knew a broader set of things also
have a bigger chance of passing by asking more things but the other one the answer were just
the x coordinate and this one was the X comma Y coordinates why was this one X comma Y and the
other one was just the x coordinates because this one had the variable y so you had to solve for
y and x combined the other one had didn't have y equals the other one had f ofx equals and g
ofx equals didn't have y as a variable so you only needed the expon so if just remember that if
you have X and Y you got to solve as a point is your solution the solution one solution is NE 1
-2 and the other solution is 54 okay num number 32 the table below shows the amount of money a
popular movie earned in millions of dollars during its first six weeks write the linear regression
equation for the data set rounding all values to the nearest 100 State the correlation coefficient
to the nearest 100 and state what the correlation coefficients indicates about the linear fit of the
data I highly recommend learning how to do this problem why I know a lot of students are like
it doesn't matter in your life but I mean it's impossible to know which ones which ones of these
are really super duper going to matter to you as in your career in real life and which
ones are not it's impossible but the other reason is why I recommend I'm going to
reduce this as the calculator slightly so that you can see all the numbers but
the other reason is this is a four-point question get your points you know get your points
if you this a fourpoint question is worth two multiple choice questions so you literally
get two free multiple choice questions by learning how to do this one question more than
that once you pass the test every extra point is an extra point on your Regents if you get to
and 80 you can get college credit depending on your college if you get way past that like
a 90 95 or 100 then you're going to get to the better class you you'll find that you can learn
more in those classes so how do we do this stat okay we got to put these numbers in a list
so we're going to go to edit okay I was doing some math on a on a different set of problems
I'm going to clear list one and clear list two as well clear list two Now list one I'm going to make weak X so one two
and I'm looking over here if you need somewhere to look two 3 4 five those are the x coordinates
and six those are the x coordinates let's shrink this a little bit more so I can see there
we go and now I now that I tyed them in I check that I tyed them in correctly 1 2 3 4
5 6 great then the list too so I first type them in and then I check to save brain power to
make sure but it is worth your time to check if you plug them in correctly so because a lot
of students do this correctly but mistype and you you'd be surprised it's it's like 10%
of students who mistype and get a long 185 150 I almost missed a zero it's that easy 90
50 25 and five now if I'm looking at this data I see that this is a decreasing function so I'm
going to see I better see a negative correlation coefficient but it actually decreased pretty
strongly like like a like on a on a pretty nice line so I suspect that this is going to
have a strong correlation strong negative correlation so now I just now I check that I typed
it in correctly let's see 185 150 90 50 25 and five now the linear regression equation this is
where we press the stat button and we go to C oh wait click on mode some of you there's one
more detail some of you have in your mode you have diagnostic on and but unfortunately not all
of you stat diagnostic make sure that that's on some of you don't have that though so you have
to go to catalog catalog is above the zero the catalog has every function that this calculator
has so if you scroll down to Diagnostics on you have to press enter twice when you get to it
Diagnostics on enter enter now Diagnostics are on now I go have to do the work stat Cal linear
regression l i n reg ax plus b I'm going to do L1 if you don't if you don't have anything typed
in here you should already have L1 in there but L1 is right up above the one in blue so you
press the blue second Buton button L1 L2 I have to type it in cuz it's not there so the blue
second it's L2 is above the two in blue so I press the blue second button and press two L2 frequency
list there is no frequency list store regression equation I'm going to store this because it
actually is very helpful in many problems although it just happens to be not helpful in
this one but I want you to know how to do it vars press the bars button y variables
function I'm going to store it as Y3 that's not a necessary part of the problem but
sometimes it is so I wanted you to know how to do it and now calculate now this is another
strategy that I use because fixing muscle memory for students is really difficult
but but teaching a new pattern that includes all the muscle memory is helpful so
this is the this is the muscle memory where students struggle if they get it right but they
don't do the nearest 100th or they get the wrong variables so this is what I have students do I
have them write exactly everything that's on the on this picture on the calculator so y equal
a X plus b where a equal - 37.5 714 2857 B is equal to 215. 666666 7 and C is equal to
no r r you don't need R squ for for algeb one R is equal to 9848 1 61359 so I have students
do that and then I have students make sure they write the correct variables X and Y if they said
different variables like H and T you have to use H and T if they said X and Y you have to use X
and Y if they said p and Q you have to use p and Q so y they did Y and X which is convenient
so y equals now a is to the nearest 100.3 no 37.5 7 and then 1 so the seven
stays the same X and now plus b plus 215+ 215 6 the next number six and but the next number
after the six is another six so the six rounds up to seven okay and that is a that's full credit
for the first question okay that's full credit for the first question so what about the second
question the correlation coefficient to the nearest 100 R is equal to .98 and then a four
so the eight stay the same okay what is it that I did that's different from what a lot of students
do I wrote the full answer unrounded and then I rounded why did I do it that way because a lot
of students see one problem says to the nearest 100th but then the other problem might say to
the nearest 10th or the nearest thousandth and they round to the wrong thing or they just always
say my teacher said round to the nearest thousand you have to obey what the book or the test says
so what this does is it fixes the muscle memory now you might say this is a waste of time but
if you actually do the experiment how long it took me to write each number this is a three
hour test 3 * 3 3 * 3,600 you have literally 10,800 seconds to do the test each line took me 6
seconds to right 6 * 6 is 18 so I took 18 seconds out of the 10,000 800 seconds that I have for
the test not not it's not a waste of time and it fixes your muscle memory for the rounding so I
recommend doing it that way so R is equal to .98 to the nearest 100 that's three points already
State what the correlation coefficient indicates about the linear bit of the data all you
have to say so this is a negative .98 this is a strong negative correlation and that's it
strong negative correlation you could say between the variables X and Y but that's it strong negative correlation so
what does that mean what does a strong negative correlation means it means that
if you graph this line and you graph the dots if you graph the line the line is the line is there so look
at this the line is equation three now I'm going to do that for a second
so I'm going to do zoom zoom stat now I recommend not necessarily doing that but if you just to you
could see it notice that the dots are very close to the line that's what a strong correlation
is now why is the correlation negative well R is negative but what that signifies is that
the slope is also negative now the slope and the correlation coefficient don't have the same
value they just have the same sign I don't know what the slope of this line is actually no I
do know what the slope of this line is it's a it's 37.5 7 but notice that the slope is
negative and R is negative the slope and the correlation coefficient will always have
the same sign but you'll have a strong negative cor you'll have a strong correlation
and the number will be close to either one or negative one when you have a strong correlation if
the points are really very very close to the line okay you'll see that if it's a weak correlation
let's say for example like 2 then or negative point2 then the points are very far away from the
line and you'll see that the points are somewhat close but not super duper close to the line if
the correlation coefficient is is moderate okay so and at this point I'm going to suggest
to go to guess Google this guess the correlation guess the correlation that's a pretty fun game
and you'll learn what strong and weak and and and and almost zero correlation looks like
it's a fun game Guess the correlation Google app and of course if you visit JuanTutors.com go
there to to meet your tutoring needs that's for for parents I don't expect students to
pay for that unless you're adult students but you know go to JuanTutors.com to meet your
tutoring needs very little advertising in this video I hope you appreciate that press
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number 33 let's get this use the quadratic formula solve the equation 3x2 - 10x - 5 +
5al 0 express your answer in simplest radical form you I wonder is the quadratic formula on
the formula sheet and let's check look at that the quadratic formula now I'm going to post
both of these here quadratic equation and the quadratic formula quadratic equations need not
be in this exact format y = ax+ BX plus C but they do need to be in that format for you to
use the quadratic formula or rather but you do also need equal Z but they have to be the point
is they have to be in standard form you do need a X2 + BX + Cal 0 you need it in that order and
if it's not in that order you need to do algebra to get it in that order but this one happens
to be in that order does desite being a part three problem I'm shocked that they have it in
that order completely completely this is a part two question in my opinion so why what what's
the benefit now being a part three question if you get it right you get two free multiple
choice questions and if you make little bitty little itty bitty errors you also get a lot of
partial credit so a equal 3 b equal = -10 and C = 5 so lots of partial credit to be had here
and we have x = b +- sare < TK of B ^2 - 4 a c all over 2 a and then we plug in we get -3 and B
will almost always be -10 because they think it's tougher and I think wait I just messed up there
didn't I hey B will almost always be negative because they want to see if you lose a negative
sign parentheses -10 which I lost I lost B so it happens luckily I have it correctly in my in my
work here but plus or minus there's two places where it matters there's a negative sign here
so you in the formula and then B itself happens to be negative in this problem so you got two
negative signs and then the second place where they want to see if you lose a negative sign
is the fact that b is being squared so you actually are required to use a parenthesis for
the squaring and if you don't use a parenthesis for the squaring you get it wrong -4 * 3 * 5 all
of that over 2 a 2 * 3 now why is it wrong without the parentheses because a negative number squared
is positive but without parenthesis the squaring happens first and then the negative happens and
that's not what the problem is doing the number is negating the 10 to make a negative 10 and
then it's squaring that you need parentheses so now we do we could do this by hand you are
allowed to use your calculator as much as you want here but since the calculator probably is
not going to give you a simplified radical you have to be careful you but you could do 10 plus
or minus radical I'm going to do this fully 101 s is 100 with parentheses minus I'm going to
subtract here 60 all of that divided by 2 * 3 is 6 okay so which equal to 10 plus or minus radical
40 over 6 now I just I don't want to stop there they gave full credit for this that's weird
to me that's weird to me it also it even makes me wonder if they'll continue for the rest
of the time that this Regents exist whether they'll continue giving full credit for this why
because this can be simplified for if you actually simplify the radical this is equal to 10 plus or
minus the radical 40 has a perfect square factor of four radical 4 radical 10 over 6 which is equal
to 10 plus or minus 2 radical 10 over 6 and now if you divide the entire numerator by two and
divide the denominator by two you get 5 + or minus 1 radical 10 / 3 this is fully simplified
but they accepted this so if you stop here they'll accept it I don't think that they'll keep doing
that and not only that I think that they will do things to the problem to maybe make
it so that you have to keep going to the point where you get 5 plus or- 10 radical
3 in those cases where where the radical simplifies Frozen it's weird to me that
they said simplest radical form and they didn't expect you to simplify Frozen it's
weird Okay so that's why I kept going do understand though why like maybe on a part six
problem they'll make you keep going for that extra point and then maybe maybe they'll add
some words to make it a Sixpoint problem who knows number 34 graph the system of inequality
on the set of axes below 3 y + 2x is less than equal to 15 and Y - x is greater than 1 I
see when I'm graphing this that Y is going to be greater than something so something is going to
be shaded above something and the other one has Y is going to be less than or equal to something
so we're going to have something shaded below and that's just mentally for me it helps me to to
organize my thoughts both of these though to graph them usually we would we would solve for y
i High I highly recommend doing it that way that way there are other ways of solving of graphing
linear equations in standard form but for now I will solve for y so I got 3 y + 2x less than equal
to 15 15 and I'm going to do this one in red for visual purposes although you will do it in pencil
- 2x - 2x I got that 3 Y is = to -2x + 15 oh sorry less than or equal to ah too many erases less than
or equal to divide by 3 divide by 3 and I got that Y is less than or equal to -23 x + 5 okay and you
could check your answer if you don't like this to you know because if you don't trust yourself you
could say well if x is equal to 0 y should be equal to 5 and 3 * 5 is+ 0 is 15 then you could
also test something like x = 3 -23 * 3 is -2 + 5 is three actually Y is also three three and
three so you got 3 * 9 3 * 3 is 9 and 2 * 3 is 6 9 + 6 is 15 so this is correct so how do I do this
now I have a y intercept of five I have a slope of -2 over3 so I go down 2 over 3 Down 2 over 3 Down
2 over three Up 2 over three3 up two over3 and up two okay so I go there and I now have enough to
now this one is going to be a solid line so I I can feel free to draw this with a straight Ed now
I have software that's going to make me straighten this out for me did I get that good nope I didn't
like it I shifted it up accidentally last minute let's do that okay now let's do this
again well I don't know what just happened there I have software to straightened it out for
me so but you have a straight edge there you go okay now that one's that one's a straight line
and it's solid so I graphed that one with a straight edge and with a straight edge and I
made it solid now this one is y is less than or equal to this number so now to this
expression so I'm going to now shade below Y is less than or equal to I shade below some
students interpret this as shading to the left or to the right we're not shading to the
left or to the right we're shading above or below and Y is less than or equal to the
expression so we're shading below even if the slope is like super extreme shade below or above
depending on what it tells tell you why is less than or equal to we're going to shade below
so how do we shade below we make a bunch of lines okay there we go now the second one is
a little easier to solve for Y is y - x is greater than 1 so we're going to add X+ X we get
Y is greater than x + 1 this is the one where a lot of lose a little Point here and there so
the Y intercept is one right Y intercept is one so they get their points and I I did do that
carefully okay so goes to here but here's the thing this one we're going to use a straight edge
but we have to draw a dotted line so I'm the the software will not let me draw a dotted line
with a straight edge there is a ruler tool unfortunately though the ruler tool is buggy it
like it won't let me get rid of the the ruler after a while so I'm going to simulate drawing
a dotted line here with a straight edge and you just have to you have to remember to do this
with the straight edge on your test so you can get full credit for that graph okay so that
pretend I did that with a straight edge again I can't do it with software that way just
remember you have to do it with a perfect straight edge just like I did the red one with
a perfect straight edge and now this one y is greater than X+ 1 so we're going to shade above
now okay Y is greater than we're going to shade above okay going to shade above so now it doesn't
say to to label the system the solution to the system with a big S but it often does so
and a lot of students already do it so the systems solution is the Regents that's graded
that's shaded twice in blue and red so this is the systems solution I'm going to do that in
a different color so you can see the s a little bit better A lot of students like write the big
S and they kind of make it bold and that's okay too that's that big S is where both Regents are
shaded that is the vast majority of the points I believe so the next one it says to State
the coordinates of a single point in the solution to the system justify your answer this is one
case where justifi technically if you do the algebra you've Justified the answer or if you
do the words you've Justified the answer so you could justify the answer with words or algebra
there I'm going to put that point there why that point because it's in both Regents and
that point is the point -3 comma 4 y = 4 X3 SO3 comma 4 so I'm going to justify it by with
words okay so -3 comma 4 is in the solution set because it is in both shaded Regents okay it's in both shaded Regents that's it okay
so now that now that we know it's in both shaded Regents it is in the solution set this is a
fourpoint solution how could you have done it by doing algebra you could have plugged in the
point -34 so if you want an alternative solution that justifies the answer without without
using words after all Justified doesn't require words explain does fire words but justify doesn't
I could plug in to the original I could get 3 4+ 2 -3 less than equal to 15 and I get 12 -
6 less than or equal to 15 and I get that 6 is less than equal to 15 that's correct and then
the other one I could plug in I could plug in the same point into the second inequality
and I get 4us parentheses -3 greater than 1 or 4 + 3 greater than 1 and I get 7 is
greater than one this is true and I could do put the points34 and I could Circle that and that
counts as justification the black justification or the blue and red justification both serve as
a justification and a statement so each part of this was I think two points if I remember right
and there's a four-point question I think that that this is something something that even many
of you struggling students can get points on if any of these inequalities is graphed correctly
that's a point if the second inequality is graphed correctly that's a second point if a
point in the solution set is graphed that's a point if you graphed one of the inequalities
incorrectly you don't get that point so you only get one point for one graph correctly but
then if you use the correct your graph to identify what would be a correct Point given your
incorrect graph that's a point so you could still get points even with something incorrect here and
if you gave the justification for it like verbal or maybe even made an arithmetic error but count
the justification somehow work I you might get a third point you could get with a with even what
might be considered a a somewhat big error you could still get three out of four points
in this question it's it's really nice so number 35 and I'm going to as you know cross
this out okay because I always I always tell my S to do that not because it's false because I'd
rather you ignore that piece when appropriate which is almost always okay and as you saw on
this test Not only was every diagram drawn to scale but there wasn't even a diagram that was
even legally allowed to be not drawn to scale now this is a sixo question worth three multiple
choice if you think you should not focus on the part twos threes and fours you're literally
giving up three multiple choice questions by not doing number 35 and notice that this one is
broken up into parts so if you get one part you get two points full multiple choice question
if you get one part if you get a second part two multiple choice questions if you get a third
part three multiple choice questions if you get the first part wrong but you use the first part
to get the second part given the error on the first part they don't penalize you twice for
the same error so if you got the wrong answer for part one but you used that for part two you
get the point if you use part one and part two or part two for part three even if there's an
error in part one or part two but you use that to do part three you get a point you get your
points for part three so you can get a lot of partial credit so and again as I mentioned the
multiple choices there was a multiple choice with an inequality that if you notice let's see if
we could find it here I'm going to do some quick scrolling sorry if the scrolling bothers you close your eyes while I'm scrolling
if the scrolling bothers you okay number two there we go I'm done scrolling
for now if you I told you that number two the words in number two can actually help you
with one of the part two threes or fours and it actually can help you with the part four if
you happen to see the format that these take and you say where did these numbers come from a
and C are the number of adult and child tickets and that's less than or equal to the total
number of Tours number of passengers and that the 18a plus 12C the 18 is Multiplied
the cost of an adult ticket is multiplied by the number of adult tickets and the cost of
a child ticket is multiplied by the number of Children's ticket and that H that's combined
to compare with the total profit then you can go now I'm going to back scrolling to number
35 close your eyes if the scrolling bothers you still scrolling still scrolling okay now
I'm at number 35 I'm done scrolling okay so if x repres let's see Courtney went to a
coffee shop to purchase lattes and donuts for her friends one day she spent a total
of ,550 on four lattes and two Donuts the next day she spent a total of 1810 on three
lates and five Donuts all prices included tax if x represents the cost of one latte and
Y represents the cost of one dut write a system of equations that can be used to model the
situation so my the notes that you need for this is how to determine the cost so you
basically what you're going to do is you're going to write a cost equation and then you're
also for one of the situations and you're going to write a cost equation for another
another situation so let X X be what they said the cost of of one latte now I'm not a fan
of letting X be the cost of one latte I like L capital L for the cost of one latte and let y
equal the cost of one donut I would would have preferred using the capital D or something
like that for the cost of one donut but they chose chose the variables for us we don't
have a choice okay so we have to use theirs so what do we have how do we do this we have
the cost for lattes plural plus the cost for donuts is equal to the total cost those are
both actually in this case it's going to be both of our equations so the cost and how do we
get the cost of a lattes it's the cost for one latte for one latte times the number
of lattes and this one is the cost for one dut times the number of donuts okay so we actually do that so
in the first situation she SP she bought four lattes and two Donuts so
she spent on just the lattes 4X plus the cost for the two for the two Donuts is
two times Y and the total that she spent is550 and then the second time she spent a
total of1 1810 that's her total cost and how on what three lattes 3 * X that's how much you
spent on the lattes plus the number of donuts is five so five * the cost of one donut there's
two equations I just got two points I just got a free multiple choice question if I made a
mistake on one of these equations I lose one point if I made a mistake on both equations
but I made the same mistake twice I only lose one point Isn't that cool so you can get a lot
of points and remember one point you're like oh one point is not a lot one point is half a
multiple choice question it's a lot that's a half multiple choice question for those of you
who are like you should focus on the part ones half a multiple choice question so you're doing by
doing the part fours you're focusing on the part ones so part two of this question Courtney
thinks that one latte costs 275 and one donut cost 2725 is Courtney correct justify your answer
you're allowed to skip to the third part using equations to determine algebraically exact cost
of one latte and the exact cost of one donut if you just get the answer to how much a latte cost
and how much one donor costs you could literally go back and justify she's wrong because this is
how much they actually cost but what do I have to do in this case to justify if I don't have
the solution I literally could just plug in and see if if she's if these prices fit the m so I
could do I and I don't necessarily know which one is correct I might do 4 * 2.75 that's the cost
of a latte time four lattes plus 2 * 225 let's see if this is right and we have to check if
this is 1550 I don't know if it is or I Justified it differently on my paper I literally just solved
it so I don't know which one of these is going to be the false one four parenthe es 2.75 plus
2 and I do have I suspect strongly they're going to make this one be true but I don't know it's
equal to, 1550 I I had a suspicion because for the lazy student in other words the student who
doesn't check both equations they're going to stop both of the both equations have to be true
simultaneously though three times parentheses and I actually should have started testing
the second one because I I see based on these prices if these prices were correct the answer
would have to be a multiple of 25 cents and 18 time is not a multiple of 25 cents so this is
going to fail okay 2.25 2.75 plus two nope + 5 time 2.25 equals 1810
and then on the right side let's see what we actually have let's see three and five 1950 1950 equals 1810 B so she's wrong Courtney is wrong
because 1950 does not not equal 1810 two points two points okay
and now I actually now have four points let me see if I can get a copy of these
equations will it let me do that no it won't okay so what about use your equations to determine
algebraically the exact cost of one latte and the exact cost of one donut so I have the equation
4x + 2 y is equal to 1550 and I have that 3x + 5 Y is equal to 1810 so there are a few ways of
going about solving this equ these equations I notice here and any algebraic solution
including some crazy algebraic Solutions like using matrices would would be legal but I
I don't think they expect you to do that using majes using any other method other than algebraic
might get you a point let's see what this says here a correct numerical answer with no work
shown will receive only one credit so in other words if you do get the right answer but you don't
only give the numbers you get one point which is nice but I'm going to do this algebraically h
what am I going to do algebraically so I I don't like the way I did it on paper so I'm going to
do it slightly differently hopefully doing it live doesn't mess me up but I want to get
I want to get two of the coefficients to match okay so I'm going to I'm going to get the
coefficients of x to match so I'm going to multiply this equation by three I'm going
to multiply this equation by four okay so in other words Row one multiply by three and I'm
going to multiply row two by four this notation might look familiar to those of you who know my
Cho methods and I get 12x + 6 Y is equal to go to your calculator get your arithmetic
correct don't lose your points on basic arithmetic this is not an arithmetic test it's
a algebra test so a lot of students get the this question wrong by just not multiplying by three
they say like 4550 when it's actually in fact 4650 and then the next one 4 * 3 is
12x plus 20 Y is equal to now they get the 1810 many more students
get this part right but 1810 * 4 1810 is going to be 6 is 72 40 now that the X coefficients match I'm
going to subtract these two from each other okay let me let me let me leave the AC
because we're almost done we're going to leave the a we're going to subtract the
X's 12x - 12x is 0x I'm going to do keep change change so I'm going to change this to a
plus change all of these to minuses and we get the X's cancel and 6x - 20x don't be scared
of a negative coefficient of Y -14 y equals so 4650 4650 minus 7240 that's equal to - 25909 not 090 90 - 2590 I'm
going to divide this by -14 divide this by14 and I get that Y is equal to this number divided
by -14 and notice that I have to get a positive answer if you don't get a positive answer
don't just like change it to a positive answer the fact if you get a if you get a negative answer use
that as a hint that an error was made and find the error okay so Y is equal to 1 U 85 okay confirming
on my visually that my answer is correct so one donut costs [Music] 1.85 let's make that one
look like the one okay and now that we know that y 1.85 we can actually substitute that into
any of the original equations so I'm going to substitute it into the 4x + 2 y = 1550 so I
got 4 x + 2 y is 1.85 is equal to 1550 I got 4X equals no 4X plus use your calculator to not
get the answers wrong right but I I so your calculator will confirm that 2 * 1.85 is 3.70
okay is equal to 1550 - 3.70 - 3.70 I got the 4X is equal to 11.80 a lot of students
get the subtraction wrong too just by not using their calculator use your calculator
divide by four divide by four and I want to say now before I do this division because we
are done if you appreciate the the work the work that we did on for this test I do would
appreciate it if you hit the Subscribe button at this point if you actually stuck through
the video this long I feel like I did I did earn your subscription but what that
does is it allows me to fund the free channel that I've been providing okay so divide
by four and we get that X is equal to 2.95 okay so one doughnut costs 1.85 and one
latte costs [Music] 2.95 and I want to congratulate you for making it through all
the way to the end of this video do check out the description to see the very free
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