Introduction to cellular respiration

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Kind: captions
Language: en

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In my humble opinion, the
single most important

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biochemical reaction, especially
to us, is cellular

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respiration.

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And the reason why I feel so
strongly about that is because

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this is how we derive
energy from what we

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eat, or from our fuel.

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Or if we want to be specific,
from glucose.

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At the end of the day, most of
what we eat, or at least

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carbohydrates, end
up as glucose.

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In future videos I'll talk about
how we derive energy

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from fats or proteins.

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But cellular respiration, let's
us go from glucose to

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energy and some other
byproducts.

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And to be a little bit more
specific about it, let me

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write the chemical reaction
right here.

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So the chemical formula for
glucose, you're going to have

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six carbons, twelve hydrogens
and six oxygens.

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So that's your glucose
right there.

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So if you had one mole of
glucose-- let me write that,

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that's your glucose right
there-- and then to that one

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mole of glucose, if you had six
moles of molecular oxygen

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running around the cell, then--
and this is kind of a

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gross simplification for
cellular respiration.

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I think you're going to
appreciate over the course of

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the next few videos, that one
can get as involved into this

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mechanism as possible.

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But I think it's nice to
get the big picture.

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But if you give me some glucose,
if you have one mole

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of glucose and six moles of
oxygen, through the process of

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cellular respiration-- and so
I'm just writing it as kind of

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a big black box right now,
let me pick a nice color.

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So this is cellular
respiration.

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Which we'll see is
quite involved.

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But I guess anything can be, if
you want to be particular

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enough about it.

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Through cellular respiration
we're going to produce six

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moles of carbon dioxide.

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Six moles of water.

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And-- this is the
super-important part-- we're

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going to produce energy.

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We're going to produce energy.

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And this is the energy that can
be used to do useful work,

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to heat our bodies, to
provide electrical

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impulses in our brains.

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Whatever energy, especially a
human body needs, but it's not

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just humans, is provided
by this

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cellular respiration mechanism.

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And when you say energy, you
might say, hey Sal, on the

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last video didn't you just--
well, if that was the last

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video you watched, you probably
saw that I said ATP

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is the energy currency for
biological systems. And so you

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might say, hey, well it looks
like glucose is the energy

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currency for biological systems.
And to some degree,

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both answers would be correct.

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But to just see how it fits
together is that the process

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of cellular respiration, it does
produce energy directly.

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But that energy is used
to produce ATP.

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So if I were to break down
this energy portion of

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cellular respiration right
there, some of it

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would just be heat.

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You know, it just warms
up the cell.

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And then some of it is used--
and this is what the textbooks

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will tell you.

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The textbooks will say
it produces 38 ATPs.

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It can be more readily used by
cells to contract muscles or

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to generate nerve impulses or
do whatever else-- grow, or

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divide, or whatever else
the cell might need.

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So really, cellular respiration,
to say it

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produces energy, a little
disingenuous.

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It's really the process of
taking glucose and producing

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ATPs, with maybe heat
as a byproduct.

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But it's probably nice to
have that heat around.

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We need to be reasonably warm
in order for our cells to

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operate correctly.

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So the whole point is really to
go from glucose, from one

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mole of glucose-- and
the textbooks will

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tell you-- to 38 ATPs.

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And the reality is, this is in
the ideal circumstances that

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you'll produce 38 ATPs.

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I was reading up a little bit
before doing this video.

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And the reality is, depending on
the efficiency of the cell

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in performing cellular
respiration, it'll probably be

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more on the order of
29 to 30 ATPs.

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But there's a huge variation
here and people are really

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still studying this idea.

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But this is all cellular
respiration is.

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In the next few videos we're
going to break it down into

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its kind of constituent parts.

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And I'm going to introduce them
to you right now, just so

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you realize that these are parts
of cellular respiration.

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The first stage is called
glycolysis.

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Which literally means
breaking up glucose.

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And just so you know, this part,
the glyco for glucose

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and then lysis means
to break up.

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When you saw hydrolysis, it
means using water to break up

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a molecule.

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Glycolysis means we're going
to be breaking up glucose.

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And in case you care about
things like word origins,

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glucose comes from, the gluc
part of glucose comes from

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Greek for sweet.

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And glucose is indeed sweet.

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And then all sugars, we
put this ose ending.

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So that just means sugar.

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So you might think it's kind
of a redundant statement to

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say sweet sugar.

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But there are some sugars
that aren't sweet.

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For example, lactose.

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Milk, it might be a little bit,
but when you actually

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digest lactose then you can turn
it into an actual sweet

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sugar, but it doesn't taste
sweet like glucose or fructose

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or sucrose would taste.

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But anyway, that's an aside.

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But the first step of cellular
respiration is glycolysis,

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breaking up of glucose.

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What it does is, it breaks up
the glucose from a 6-carbon

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molecule-- so it literally
takes it from a 6-carbon

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molecule-- let me draw it like
this-- a 6-carbon molecule

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that looks like this.

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And it's actually a cycle.

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Let me show you what glucose
actually looks like.

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This is glucose right here.

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And notice you have
one, two, three,

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four, five, six carbons.

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I got this off of Wikipedia.

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Just look up glucose and you
can see this diagram if you

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want to kind of see
the details.

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You can see you have six
carbons, six oxygens.

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That's one, two, three,
four, five, six.

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And then all these
little small blue

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things are my hydrogens.

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So that's what glucose
actually looks like.

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But the process of glycolysis,
you're essentially just

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taking-- I'm writing it out
as a string, but you could

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imagine it as a chain-- and it
has oxygens and hydrogens

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added to each of
these carbons.

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But it has a carbon backbone.

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And it breaks that carbon
backbone in two.

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That's what glycolysis
does, right there.

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So you've kind of lysed
the glucose and

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each of these things.

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And I haven't drawn all
the other stuff

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that's added on to that.

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You know, these things are all
bonded to other things, with

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oxygens and hydrogens
and whatever.

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But each of these 3-carbon
backbone

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molecules are called pyruvate.

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We'll go into a lot more
detail on that.

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But glycolysis, it by itself
generates-- well,

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it needs two ATPs.

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And it generates four ATPs.

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So on a net basis, it generates
two-- let me write

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this in a different color--
it generates two net ATPs.

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So that's the first stage.

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And this can occur completely
in the absence of oxygen.

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I'll do a whole video on
glycolysis in the future.

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Then these byproducts, they get

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re-engineered a little bit.

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And then they enter into what's
called the Krebs cycle.

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Which generates another
two ATPs.

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And then, and this is kind of
the interesting point, there's

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another process that
you can say happens

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after the Krebs cycle.

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But we're in a cell and
everything's bumping into

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everything all of the time.

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But it's normally viewed
to be after glycolysis

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and the Krebs cycle.

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And this requires oxygen.

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So let me be clear, glycolysis,
this first step,

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no oxygen required.

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Doesn't need oxygen.

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It can occur with oxygen
or without it.

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Oxygen not needed.

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Or you could say this is called
an anaerobic process.

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This is the anaerobic part
of the respiration.

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Let me write that down too.

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Anaerobic.

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Maybe I'll write
that down here.

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Glycolysis, since it doesn't
need oxygen, we

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can say it's anaerobic.

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You might be familiar with the
idea of aerobic exercise.

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The whole idea of aerobic
exercise is to make you

00:09:11.450 --> 00:09:13.620
breathe hard because you
need a lot of oxygen

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to do aerobic exercise.

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So anaerobic means you
don't need oxygen.

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Aerobic means it needs oxygen.

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Anaerobic means the opposite.

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You don't need oxygen.

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So, glycolysis anaerobic.

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And it produces two ATPs net.

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And then you go to the Krebs
cycle, there's a little bit of

00:09:35.170 --> 00:09:36.150
setup involved here.

00:09:36.150 --> 00:09:38.310
And we'll do the detail
of that in the future.

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But then you move over to the
Krebs cycle, which is aerobic.

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It is aerobic.

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It requires oxygen
to be around.

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And then this produces
two ATPs.

00:09:51.440 --> 00:09:53.650
And then this is the part that,
frankly, when I first

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learned it, confused me a lot.

00:09:54.780 --> 00:09:57.090
But I'll just write it
in order the way it's

00:09:57.090 --> 00:09:57.890
traditionally written.

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Then you have something called--
we're using the same

00:10:00.290 --> 00:10:03.290
colors too much-- you have
something called the electron

00:10:03.290 --> 00:10:04.540
transport chain.

00:10:11.660 --> 00:10:13.920
And this part gets credit
for producing

00:10:13.920 --> 00:10:16.340
the bulk of the ATPs.

00:10:16.340 --> 00:10:19.220
34 ATPs.

00:10:19.220 --> 00:10:22.450
And this is also aerobic.

00:10:22.450 --> 00:10:23.710
It requires oxygen.

00:10:23.710 --> 00:10:26.460
So you can see, if you had no
oxygen, if the cells weren't

00:10:26.460 --> 00:10:28.460
getting enough oxygen,
you can produce a

00:10:28.460 --> 00:10:30.800
little bit of energy.

00:10:30.800 --> 00:10:34.480
But it's nowhere near as much
as you can produce once you

00:10:34.480 --> 00:10:35.980
have the oxygen.

00:10:35.980 --> 00:10:39.230
And actually when you start
running out of oxygen, this

00:10:39.230 --> 00:10:42.500
can't proceed forward, so what
happens is some of these

00:10:42.500 --> 00:10:45.720
byproducts of glycolysis,
instead of going into the

00:10:45.720 --> 00:10:48.010
Krebs cycle and the electron
transport chain, where they

00:10:48.010 --> 00:10:51.620
need oxygen, instead they go
through a side process called

00:10:51.620 --> 00:10:52.870
fermentation.

00:10:55.480 --> 00:10:58.560
For some organisms, this process
of fermentation takes

00:10:58.560 --> 00:11:00.470
your byproducts of
glycolysis and

00:11:00.470 --> 00:11:02.100
literally produces alcohol.

00:11:02.100 --> 00:11:04.260
That's where alcohol
comes from.

00:11:04.260 --> 00:11:06.500
That's called alcohol
fermentation.

00:11:06.500 --> 00:11:09.130
And we, as human beings,
I guess fortunately or

00:11:09.130 --> 00:11:12.410
unfortunately, our muscles do
not directly produce alcohol.

00:11:12.410 --> 00:11:13.900
They produce lactic acid.

00:11:13.900 --> 00:11:17.040
So we do lactic acid
fermentation.

00:11:17.040 --> 00:11:18.150
Let me write that down.

00:11:18.150 --> 00:11:19.250
Lactic acid.

00:11:19.250 --> 00:11:23.540
That's humans and probably
other mammals.

00:11:23.540 --> 00:11:30.230
But other things like yeast will
do alcohol fermentation.

00:11:34.520 --> 00:11:35.650
So this is when you
don't have oxygen.

00:11:35.650 --> 00:11:38.840
It's actually this lactic acid
that if I were to sprint

00:11:38.840 --> 00:11:41.070
really hard and not be able to
get enough oxygen, that my

00:11:41.070 --> 00:11:43.890
muscles start to ache because
this lactic acid

00:11:43.890 --> 00:11:45.370
starts to build up.

00:11:45.370 --> 00:11:46.280
But that's just a side thing.

00:11:46.280 --> 00:11:49.050
If we have oxygen we can move
to the Krebs cycle, get our

00:11:49.050 --> 00:11:51.950
two ATPs, and then go on to the
electron transport chain

00:11:51.950 --> 00:11:56.210
and produce 34 ATPs, which is
really the bulk of what

00:11:56.210 --> 00:11:57.930
happens in respiration.

00:11:57.930 --> 00:12:00.080
Now I said this as an
aside, that to some

00:12:00.080 --> 00:12:01.510
degree this isn't fair.

00:12:01.510 --> 00:12:05.050
Because while these guys are
operating they're also

00:12:05.050 --> 00:12:06.800
producing these other
molecules.

00:12:06.800 --> 00:12:08.670
They're not producing them
entirely, but what they're

00:12:08.670 --> 00:12:11.490
doing is, they're taking-- and
I know this gets complicated

00:12:11.490 --> 00:12:13.470
here, but I think over the
course of the next few videos

00:12:13.470 --> 00:12:16.890
we'll get an intuition for it--
in these two parts of the

00:12:16.890 --> 00:12:20.110
reaction, glycolysis and the
Krebs cycle, we're constantly

00:12:20.110 --> 00:12:24.820
taking NAD-- I'll write it as
NAD plus-- and we're adding

00:12:24.820 --> 00:12:28.470
hydrogens to it to form NADH.

00:12:28.470 --> 00:12:32.670
And this actually happens for
one molecule of glucose, this

00:12:32.670 --> 00:12:34.530
happens to 10 NADs.

00:12:34.530 --> 00:12:38.040
Or 10 NAD plusses
to become NADHs.

00:12:38.040 --> 00:12:40.010
And those are actually
what drive the

00:12:40.010 --> 00:12:41.330
electron transport chain.

00:12:41.330 --> 00:12:43.870
And I'll talk a lot more about
it and kind of how that

00:12:43.870 --> 00:12:47.450
happens and why is energy being
derived and how is this

00:12:47.450 --> 00:12:49.210
an oxidative reaction
and all of that.

00:12:49.210 --> 00:12:51.500
And what's getting oxidized
and what's being reduced.

00:12:51.500 --> 00:12:52.760
But I just wanted to
give due credit.

00:12:52.760 --> 00:12:56.190
These guys aren't just producing
two ATPs in each of

00:12:56.190 --> 00:12:56.680
these stages.

00:12:56.680 --> 00:13:00.930
They're also producing, actually
combined, 10 NADHs,

00:13:00.930 --> 00:13:06.540
which each produce three ATPs
in an ideal situation, the

00:13:06.540 --> 00:13:07.870
electron transport chain.

00:13:07.870 --> 00:13:12.050
And they're also doing it to
this other molecule, FAD,

00:13:12.050 --> 00:13:13.500
which is very similar.

00:13:13.500 --> 00:13:15.030
But they're producing FADH.

00:13:17.610 --> 00:13:19.290
Now I know all of this
is very complicated.

00:13:19.290 --> 00:13:21.010
I'll make videos on this
in the future.

00:13:21.010 --> 00:13:24.030
But the important thing to
remember is cellular

00:13:24.030 --> 00:13:28.350
respiration, all it is is taking
glucose and kind of

00:13:28.350 --> 00:13:31.570
repackaging the energy in
glucose, and repackaging it in

00:13:31.570 --> 00:13:34.345
the form of, your textbooks
will tell you, 38 ATPs.

00:13:34.345 --> 00:13:36.830
If you're doing an exam, that's
a good number to write.

00:13:36.830 --> 00:13:39.340
It tends to, in reality
be a smaller number.

00:13:39.340 --> 00:13:40.440
It's also going to
produce heat.

00:13:40.440 --> 00:13:42.070
Actually most of it is
going to be heat.

00:13:42.070 --> 00:13:45.680
But 38 ATPs, and it does it
through three stages.

00:13:45.680 --> 00:13:48.550
The first stage is glycolysis,
where you're just literally

00:13:48.550 --> 00:13:51.260
splitting the glucose
into two.

00:13:51.260 --> 00:13:52.940
You're generating some ATPs.

00:13:52.940 --> 00:13:54.720
But the more important thing
is, you're generating some

00:13:54.720 --> 00:13:57.400
NADHs that are going to be used
later in the electron

00:13:57.400 --> 00:13:58.670
transport chain.

00:13:58.670 --> 00:14:01.350
Then those byproducts are split
even more in the Krebs

00:14:01.350 --> 00:14:04.240
cycle, directly producing
two ATPs.

00:14:04.240 --> 00:14:06.270
But that produces a
lot more NADHs.

00:14:06.270 --> 00:14:09.710
And all of those NADHs are used
in the electron transport

00:14:09.710 --> 00:14:13.820
chain to produce the
bulk of your energy

00:14:13.820 --> 00:14:17.965
currency, or your 34 ATPs.


ATP: Adenosine Triphosphate

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:03.360
Arguably, one of the most
important molecules in all of

00:00:03.360 --> 00:00:06.150
biology is ATP.

00:00:06.150 --> 00:00:08.620
ATP, which stands for adenosine
triphosphate.

00:00:18.690 --> 00:00:20.340
Which sounds very fancy.

00:00:20.340 --> 00:00:24.270
But all you need to remember,
or any time you see ATP

00:00:24.270 --> 00:00:28.180
hanging around in some type
of biochemical reaction,

00:00:28.180 --> 00:00:30.940
something in your brain should
say, hey, we're dealing with

00:00:30.940 --> 00:00:32.360
biological energy.

00:00:32.360 --> 00:00:38.690
Or another way to think of ATP
is the currency-- I'll put

00:00:38.690 --> 00:00:42.645
that in quotes-- of
biological energy.

00:00:46.820 --> 00:00:49.000
So how is it a currency
of energy?

00:00:49.000 --> 00:00:51.820
Well ATP stores energy
in its bonds.

00:00:51.820 --> 00:00:54.040
And I'll explain what that
means in a second.

00:00:54.040 --> 00:00:56.220
And before we learn what
an adenosine group or a

00:00:56.220 --> 00:00:58.870
3-phosphate group looks like,
you can just take a bit of a

00:00:58.870 --> 00:01:03.010
leap of faith, that you could
imagine ATP as being made up

00:01:03.010 --> 00:01:06.160
of something called-- let me
do it in a nice color-- an

00:01:06.160 --> 00:01:08.950
adenosine group right there.

00:01:08.950 --> 00:01:12.020
And then attached to it you'll
have three phosphates.

00:01:12.020 --> 00:01:13.320
Not might, you will.

00:01:13.320 --> 00:01:18.150
You'll have three phosphates
attached to it just like that.

00:01:18.150 --> 00:01:21.970
And this is ATP.

00:01:21.970 --> 00:01:24.450
Adenosine triphosphate.

00:01:24.450 --> 00:01:27.850
Tri- meaning three
phosphate groups.

00:01:27.850 --> 00:01:31.235
Now if you take adenosine
triphosphate and you hydrolyze

00:01:31.235 --> 00:01:33.460
this bond, which means
if you take this in

00:01:33.460 --> 00:01:34.610
the presence of water.

00:01:34.610 --> 00:01:37.250
So let me just throw
some water in here.

00:01:37.250 --> 00:01:41.610
Let's say I have H2O.

00:01:41.610 --> 00:01:44.450
Then one of these phosphate
groups will break off.

00:01:44.450 --> 00:01:47.100
Essentially part of this water
joins to this phosphate group,

00:01:47.100 --> 00:01:48.900
and then part of it
joins to this

00:01:48.900 --> 00:01:49.900
phosphate group right there.

00:01:49.900 --> 00:01:51.590
And I'll show you that in a
little bit more detail.

00:01:51.590 --> 00:01:53.960
But I want to give you the
big picture first.

00:01:53.960 --> 00:01:57.430
What you're left with is an
adenosine group that now has

00:01:57.430 --> 00:01:58.680
two phosphates on it.

00:02:01.460 --> 00:02:07.520
And this is called adenosine
diphosphate or ADP.

00:02:07.520 --> 00:02:11.860
Before we had triphosphate,
which means three phosphates.

00:02:11.860 --> 00:02:14.330
Now we have diphosphate,
adenosine triphosphate, so

00:02:14.330 --> 00:02:16.650
instead of a tri here
we just write a di.

00:02:16.650 --> 00:02:18.590
Which means you have two
phosphate groups.

00:02:18.590 --> 00:02:22.760
And so the ATP has been
hydrolyzed, or you have broken

00:02:22.760 --> 00:02:24.790
off one of these phosphate
groups.

00:02:24.790 --> 00:02:27.550
And so now you're left with
ADP and then an extra

00:02:27.550 --> 00:02:30.550
phosphate group right here.

00:02:30.550 --> 00:02:33.370
And-- and this is the whole key
to everything that we talk

00:02:33.370 --> 00:02:35.660
about when we're dealing
with ATP-- and

00:02:35.660 --> 00:02:36.910
you have some energy.

00:02:41.440 --> 00:02:45.590
And so when I talk about ATP
being the currency of

00:02:45.590 --> 00:02:48.500
biological energy,
this is why.

00:02:48.500 --> 00:02:52.220
Is that if you have ATP, and if
you were to-- through some

00:02:52.220 --> 00:02:55.960
chemical reaction-- you pop off
this phosphate right here.

00:02:55.960 --> 00:02:57.470
It's going to generate energy.

00:02:57.470 --> 00:02:59.960
That energy can be used
for just general heat.

00:02:59.960 --> 00:03:02.810
Or you could couple this
reaction with other reactions

00:03:02.810 --> 00:03:03.830
that require energy.

00:03:03.830 --> 00:03:07.960
And then those reactions will
be able to move forward.

00:03:07.960 --> 00:03:10.490
So, I draw these circles.

00:03:10.490 --> 00:03:12.040
Adenosine and phosphates.

00:03:12.040 --> 00:03:15.010
And really, this is all
you need to know.

00:03:15.010 --> 00:03:16.780
Already, what I've shown you
right here is really all you

00:03:16.780 --> 00:03:20.660
need to know to operationally
think of how ATP operates in

00:03:20.660 --> 00:03:22.390
most biological systems.
And if you want to

00:03:22.390 --> 00:03:22.740
go the other way.

00:03:22.740 --> 00:03:25.020
If you have energy and you
want to generate ATP, the

00:03:25.020 --> 00:03:26.050
reaction will just
go this way.

00:03:26.050 --> 00:03:29.430
Energy plus a phosphate group
plus some ADP, you

00:03:29.430 --> 00:03:30.610
can go back to ATP.

00:03:30.610 --> 00:03:32.940
And so this is stored energy.

00:03:32.940 --> 00:03:36.520
So this side of the equation
is stored energy.

00:03:36.520 --> 00:03:39.220
And this side of the equation
is used energy.

00:03:39.220 --> 00:03:43.810
And this is really all you--
well this is 95% of what you

00:03:43.810 --> 00:03:46.430
need to know to really
understand the function of ATP

00:03:46.430 --> 00:03:49.450
in biological systems. It's just
a store of energy when

00:03:49.450 --> 00:03:51.150
you-- ATP has energy.

00:03:51.150 --> 00:03:54.070
When you break a phosphate
off, it generates energy.

00:03:54.070 --> 00:03:56.700
And then if you want to go from
ADP and a phosphate back

00:03:56.700 --> 00:03:59.580
to ATP, you have to use
energy up again.

00:03:59.580 --> 00:04:02.040
So if you have ATP, that's
a source of energy.

00:04:02.040 --> 00:04:06.580
If you have ADP and you want
ATP, you need to use energy.

00:04:06.580 --> 00:04:09.500
And so far I've just drawn a
circle with an A around it and

00:04:09.500 --> 00:04:10.460
said that's an adenosine.

00:04:10.460 --> 00:04:12.840
But sometimes I think it's
satisfying to see what the

00:04:12.840 --> 00:04:14.180
molecule actually looks like.

00:04:14.180 --> 00:04:17.010
So I cut and pasted this
from Wikipedia.

00:04:17.010 --> 00:04:19.310
And the reason why I didn't show
this to you initially is

00:04:19.310 --> 00:04:20.829
because this looks
very complicated.

00:04:20.829 --> 00:04:24.780
While the conceptual reason
why ATP is the currency of

00:04:24.780 --> 00:04:26.710
energy, I think is fairly
straightforward.

00:04:26.710 --> 00:04:30.200
When it has three phosphates,
one phosphate can break off.

00:04:30.200 --> 00:04:33.310
And then that'll result
with some energy being

00:04:33.310 --> 00:04:34.640
put into the system.

00:04:34.640 --> 00:04:36.560
Or if you want to attach
that phosphate you

00:04:36.560 --> 00:04:37.560
have to use up energy.

00:04:37.560 --> 00:04:39.910
That's just the basic
principle of ATP.

00:04:39.910 --> 00:04:44.010
But this is its actual
structure.

00:04:44.010 --> 00:04:46.220
But even here we can break it
down and see that it's really

00:04:46.220 --> 00:04:47.740
not too bad.

00:04:47.740 --> 00:04:48.790
We said adenosine.

00:04:48.790 --> 00:04:50.490
Let me draw the adenosine
group.

00:04:50.490 --> 00:04:51.660
We have adenosine.

00:04:51.660 --> 00:04:54.220
This right here is adenosine.

00:04:54.220 --> 00:04:57.070
This part of the molecule
right there.

00:04:57.070 --> 00:04:58.470
That is adenosine.

00:05:01.280 --> 00:05:04.340
And for those of you that have
really paid attention to some

00:05:04.340 --> 00:05:07.560
of the other videos, you might
recognize that this part of

00:05:07.560 --> 00:05:10.660
adenosine-- so this is called
adenosine, but this part right

00:05:10.660 --> 00:05:12.820
here-- is adenine.

00:05:17.130 --> 00:05:21.110
Which is the same adenine that
makes up the nucleotides that

00:05:21.110 --> 00:05:22.460
are the backbone of DNA.

00:05:22.460 --> 00:05:25.870
So some of these molecules in
biological systems have more

00:05:25.870 --> 00:05:26.580
than one use.

00:05:26.580 --> 00:05:27.910
This is the same adenine
where we talk

00:05:27.910 --> 00:05:30.170
about adenine and guanine.

00:05:30.170 --> 00:05:31.100
This is a purine.

00:05:31.100 --> 00:05:33.370
And there's also the
pyrimidines, but I won't go

00:05:33.370 --> 00:05:33.920
into that much.

00:05:33.920 --> 00:05:35.180
But that's the same molecule.

00:05:35.180 --> 00:05:36.380
So that's just an interesting
thing.

00:05:36.380 --> 00:05:39.950
The same thing that makes up DNA
is also part of what makes

00:05:39.950 --> 00:05:42.940
up these energy currency
molecules.

00:05:42.940 --> 00:05:47.700
So the adenine makes part of
the adenosine part of ATP.

00:05:47.700 --> 00:05:50.210
And then the other part
right here is ribose.

00:05:55.330 --> 00:06:00.970
Which you might also recognize
from RNA, ribonucleic acid.

00:06:00.970 --> 00:06:03.040
That's because you have
ribose dealing

00:06:03.040 --> 00:06:05.150
in the whole situation.

00:06:05.150 --> 00:06:06.190
But I won't go into that much.

00:06:06.190 --> 00:06:08.970
But ribose is just
a 5-carbon sugar.

00:06:08.970 --> 00:06:11.340
When they don't draw the
molecule, it's implied that

00:06:11.340 --> 00:06:11.950
it's a carbon.

00:06:11.950 --> 00:06:15.160
So this is one carbon right
there, two carbons, three

00:06:15.160 --> 00:06:18.650
carbons, four carbons,
five carbons.

00:06:18.650 --> 00:06:19.720
And that's just nice to know.

00:06:19.720 --> 00:06:21.840
It's nice to know that they
share parts of their

00:06:21.840 --> 00:06:23.700
molecules with DNA.

00:06:23.700 --> 00:06:26.380
And these are familiar building
blocks that we see

00:06:26.380 --> 00:06:27.260
over and over again.

00:06:27.260 --> 00:06:29.920
But I want to emphasize that
knowing this, or memorizing

00:06:29.920 --> 00:06:32.270
this, in no way will help you
understand the simpler

00:06:32.270 --> 00:06:35.360
understanding of ATP
just being what

00:06:35.360 --> 00:06:37.520
drives biological reactions.

00:06:37.520 --> 00:06:41.520
And then here I drew 3-phosphate
groups, and this

00:06:41.520 --> 00:06:43.350
is their actual molecular
structure.

00:06:43.350 --> 00:06:44.490
Their Lewis structures
right here.

00:06:44.490 --> 00:06:46.170
That's one phosphate group.

00:06:46.170 --> 00:06:48.530
This is the second
phosphate group.

00:06:48.530 --> 00:06:52.320
And this is a third
phosphate group.

00:06:52.320 --> 00:06:54.970
Just like that.

00:06:54.970 --> 00:06:58.830
When I first learned this, my
first question was, OK I can

00:06:58.830 --> 00:07:02.080
take this as a leap of faith
that if you take one of these

00:07:02.080 --> 00:07:05.590
phosphate groups off or if this
bond is hydrolyzed, that

00:07:05.590 --> 00:07:07.020
somehow that releases energy.

00:07:07.020 --> 00:07:08.880
And then I kind of went on and
answered all the questions

00:07:08.880 --> 00:07:09.570
that I had to answer.

00:07:09.570 --> 00:07:10.950
But why does it release
energy?

00:07:10.950 --> 00:07:13.920
What is it about this bond
that releases energy?

00:07:13.920 --> 00:07:16.690
Remember all bonds are are
electrons being shared with

00:07:16.690 --> 00:07:17.830
different atoms.

00:07:17.830 --> 00:07:21.190
So the best way you could think
about it is right here.

00:07:21.190 --> 00:07:24.900
These electrons that are being
shared right across this bond,

00:07:24.900 --> 00:07:27.620
or this electron that's being
shared right across this bond,

00:07:27.620 --> 00:07:29.470
and it's coming from
the phosphate.

00:07:29.470 --> 00:07:31.680
I won't draw the periodic
table right now.

00:07:31.680 --> 00:07:34.490
But you know the phosphate has
five electrons to share.

00:07:34.490 --> 00:07:37.370
It's less electronegative than
oxygen, so oxygen will kind of

00:07:37.370 --> 00:07:39.460
hog the electron.

00:07:39.460 --> 00:07:41.310
But this electron is
very uncomfortable.

00:07:41.310 --> 00:07:43.930
There's a couple of reasons
why it is uncomfortable.

00:07:43.930 --> 00:07:45.700
It's in a high energy state.

00:07:45.700 --> 00:07:47.250
One reason why is, you
have all these

00:07:47.250 --> 00:07:48.720
negative oxygens here.

00:07:48.720 --> 00:07:50.590
So they kind of want to push
away from each other.

00:07:50.590 --> 00:07:55.960
So these electrons in this bond
really can't kind of get

00:07:55.960 --> 00:07:57.220
close to the nucleus.

00:07:57.220 --> 00:07:59.670
They'll go into kind of
a low energy state.

00:07:59.670 --> 00:08:03.000
All of this is more of an
analogy than the reality.

00:08:03.000 --> 00:08:05.210
We all know that electrons
can get quite complex.

00:08:05.210 --> 00:08:07.430
And there's a whole quantum
mechanical world.

00:08:07.430 --> 00:08:08.380
But that's a good way
to think of it.

00:08:08.380 --> 00:08:10.840
That these molecules want to
be away from each other.

00:08:10.840 --> 00:08:13.330
But you have these bonds, so
this electron, it's kind of in

00:08:13.330 --> 00:08:14.395
a high energy state.

00:08:14.395 --> 00:08:17.250
It's further from the nucleuses
of these two atoms

00:08:17.250 --> 00:08:18.580
than it might want to be.

00:08:18.580 --> 00:08:22.220
And when you pop this phosphate
group off, all of a

00:08:22.220 --> 00:08:23.870
sudden these electrons
can enter into a

00:08:23.870 --> 00:08:25.110
lower energy state.

00:08:25.110 --> 00:08:27.080
And that generates energy.

00:08:27.080 --> 00:08:32.030
So this energy right here is
always-- in fact in any

00:08:32.030 --> 00:08:34.409
chemical reaction where they say
energy is generated, it's

00:08:34.409 --> 00:08:37.200
always from electrons going
to a lower energy state.

00:08:47.510 --> 00:08:48.570
That's what it's all about.

00:08:48.570 --> 00:08:50.610
And later in future videos
when we do cellular

00:08:50.610 --> 00:08:54.480
respiration and glycolysis and
all that, whenever we show

00:08:54.480 --> 00:08:57.330
energy, it's really from
electrons going from

00:08:57.330 --> 00:08:59.900
uncomfortable states to more
comfortable states.

00:08:59.900 --> 00:09:02.640
And in the process they
generate energy.

00:09:02.640 --> 00:09:05.620
If I'm in a plane or I'm jumping
out of a plane, I have

00:09:05.620 --> 00:09:07.180
a lot of potential energy
right when I

00:09:07.180 --> 00:09:08.050
jump out of the plane.

00:09:08.050 --> 00:09:10.280
And you can view that as
an uncomfortable state.

00:09:10.280 --> 00:09:13.350
And then when I'm sitting on my
couch watching football, I

00:09:13.350 --> 00:09:15.690
have a lot less potential
energy, so that's a very

00:09:15.690 --> 00:09:16.500
comfortable state.

00:09:16.500 --> 00:09:18.790
And I could have generated
a lot of energy

00:09:18.790 --> 00:09:20.480
falling to my couch.

00:09:20.480 --> 00:09:21.590
But I don't knows.

00:09:21.590 --> 00:09:24.540
My analogies always break
down at some point.

00:09:24.540 --> 00:09:28.230
Now, the last thing I want to go
over for you is exactly how

00:09:28.230 --> 00:09:29.530
this reaction happens.

00:09:29.530 --> 00:09:32.410
So far you could turn off this
video and you could already

00:09:32.410 --> 00:09:35.680
deal with ATP as it is used
in 95% of biology,

00:09:35.680 --> 00:09:36.790
especially AP Bio.

00:09:36.790 --> 00:09:38.630
But I want you to understand
how this

00:09:38.630 --> 00:09:40.320
reaction actually happens.

00:09:40.320 --> 00:09:43.110
So to do that, what I'm going
to do is copy and

00:09:43.110 --> 00:09:44.150
paste parts of these.

00:09:44.150 --> 00:09:46.170
So I already told you that this
guy right here is going

00:09:46.170 --> 00:09:51.280
to break off of the ATP.

00:09:58.490 --> 00:10:01.030
So that's the phosphate
group that breaks off.

00:10:01.030 --> 00:10:02.360
And then you have
the rest of it.

00:10:02.360 --> 00:10:05.310
You have the ADP that's
left over.

00:10:05.310 --> 00:10:07.530
So this is the ADP.

00:10:07.530 --> 00:10:09.340
I don't even have to copy and
paste all of this stuff.

00:10:09.340 --> 00:10:12.000
You can just accept that that's
the adenosine group.

00:10:18.050 --> 00:10:19.500
Just like that.

00:10:19.500 --> 00:10:22.240
So we've already said that this
thing gets hydrolyzed

00:10:22.240 --> 00:10:24.930
off, or gets cut off and
that generates energy.

00:10:24.930 --> 00:10:25.770
But what I want to
do is actually

00:10:25.770 --> 00:10:28.300
show you the mechanism.

00:10:28.300 --> 00:10:30.260
A little bit of hand-wavy
mechanism of how

00:10:30.260 --> 00:10:31.630
this actually happens.

00:10:31.630 --> 00:10:34.825
So I said this reaction occurs
in the presence of water.

00:10:34.825 --> 00:10:37.210
So let me draw some
water here.

00:10:37.210 --> 00:10:40.040
So I have an oxygen
and a hydrogen.

00:10:40.040 --> 00:10:42.100
And then I have another
hydrogen.

00:10:42.100 --> 00:10:43.710
That's water right there.

00:10:43.710 --> 00:10:47.360
So hydrolysis is just a reaction
where you say, hey,

00:10:47.360 --> 00:10:51.420
this guy here, he wants to
bond with something or he

00:10:51.420 --> 00:10:53.920
wants to share someone
else's electrons.

00:10:53.920 --> 00:10:58.500
So maybe this hydrogen right
here goes down here and shares

00:10:58.500 --> 00:11:02.250
its electron with this
oxygen right here.

00:11:02.250 --> 00:11:06.320
And then this phosphorus, it has
an extra electron that it

00:11:06.320 --> 00:11:06.820
needs to share.

00:11:06.820 --> 00:11:09.190
Remember it has five valence
electrons; it wants to share

00:11:09.190 --> 00:11:10.360
them with oxygen.

00:11:10.360 --> 00:11:14.040
It has one, two, three, four
being shared right now.

00:11:14.040 --> 00:11:17.670
Well, if this hydrogen goes to
this guy, then you're left

00:11:17.670 --> 00:11:19.980
with this blue OH right here.

00:11:19.980 --> 00:11:22.460
And this guy can share
one of the

00:11:22.460 --> 00:11:24.810
phosphorus' extra electrons.

00:11:24.810 --> 00:11:27.190
So you get the OH
just like that.

00:11:27.190 --> 00:11:29.230
So that's the actual process
that happens.

00:11:29.230 --> 00:11:31.350
And it could go the
other way as well.

00:11:31.350 --> 00:11:33.040
I could've cleaved it here.

00:11:33.040 --> 00:11:34.740
I could have cleaved the
whole thing here.

00:11:34.740 --> 00:11:37.270
And so this guy would have
kept the oxygen and the

00:11:37.270 --> 00:11:38.890
hydrogen would have
gone to him.

00:11:38.890 --> 00:11:40.820
And then this guy would
have taken the OH.

00:11:40.820 --> 00:11:42.540
It could happen in
either order.

00:11:42.540 --> 00:11:44.765
And so either order
would be fine.

00:11:44.765 --> 00:11:47.010
And there's one other point
I want to make.

00:11:47.010 --> 00:11:48.435
And this is a little
bit more complex.

00:11:48.435 --> 00:11:50.930
And I was even wondering whether
I wanted to make it.

00:11:50.930 --> 00:11:53.310
My whole reason why you're
kind of in a lower energy

00:11:53.310 --> 00:11:56.510
state is, once you break apart--
actually let me go

00:11:56.510 --> 00:12:00.370
down here-- is because I said,
hey, this electron is happier

00:12:00.370 --> 00:12:03.090
when it's-- so let's say this
electron that was part of this

00:12:03.090 --> 00:12:04.760
phosphorus is happier now.

00:12:04.760 --> 00:12:06.540
It's in a lower energy
state because

00:12:06.540 --> 00:12:07.950
it's not being stretched.

00:12:07.950 --> 00:12:10.350
It's not having to spend time
between that guy and that guy

00:12:10.350 --> 00:12:13.050
because this molecule and this
molecule want to spread apart

00:12:13.050 --> 00:12:14.560
because they have negative
charges.

00:12:14.560 --> 00:12:15.910
That's part of the reason.

00:12:15.910 --> 00:12:18.410
The other reason why, and we'll
talk about this in a lot

00:12:18.410 --> 00:12:21.540
more detail when we learn more
about organic chemistry, is

00:12:21.540 --> 00:12:23.940
that this has more resonance.

00:12:23.940 --> 00:12:27.770
More resonance structures or
resonance configurations.

00:12:27.770 --> 00:12:31.360
And all that means is that these
electrons, these extra

00:12:31.360 --> 00:12:34.240
electrons here, they can kind
of move about between the

00:12:34.240 --> 00:12:37.170
different atoms. And that makes
it even more stable.

00:12:37.170 --> 00:12:40.910
So if you imagine that this
oxygen right here has an extra

00:12:40.910 --> 00:12:42.700
electron with it.

00:12:42.700 --> 00:12:47.840
So that extra electron right
there, it could come down here

00:12:47.840 --> 00:12:51.180
and then form a double bond
with the phosphorus.

00:12:51.180 --> 00:12:54.810
And then this electron right
here can then jump back up to

00:12:54.810 --> 00:12:55.870
that oxygen.

00:12:55.870 --> 00:12:58.400
And then that could happen on
this side and on that side.

00:12:58.400 --> 00:12:59.990
And I won't go into the details,
but that's another

00:12:59.990 --> 00:13:01.800
reason why it makes
it more stable.

00:13:01.800 --> 00:13:03.590
If you've already taken organic
chemistry, you can

00:13:03.590 --> 00:13:05.080
kind of appreciate that more.

00:13:05.080 --> 00:13:07.570
But I don't want to get
all into the weeds.

00:13:07.570 --> 00:13:11.120
The most important thing to
remember about ATP is that

00:13:11.120 --> 00:13:14.460
when you cleave off a phosphate
group it generates

00:13:14.460 --> 00:13:17.950
energy that can drive all sorts
of biological functions,

00:13:17.950 --> 00:13:20.570
like growth and movement,
muscle movement, muscle

00:13:20.570 --> 00:13:23.900
contraction, electrical
impulses in

00:13:23.900 --> 00:13:25.290
nerves and the brain.

00:13:25.290 --> 00:13:29.310
So this is the main battery
or currency of energy in

00:13:29.310 --> 00:13:32.540
biological systems. That's the
main thing that you really

00:13:32.540 --> 00:13:33.790
just need to remember
about ATP.


CAHSEE practice: Problems 47-51

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:01.930
Problem 47.

00:00:01.930 --> 00:00:04.059
Which graph represents
the system of

00:00:04.059 --> 00:00:05.990
equations shown below?

00:00:05.990 --> 00:00:08.480
So each of these equations
represents a line.

00:00:08.480 --> 00:00:11.210
So this is going to be a line,
well, both of them have

00:00:11.210 --> 00:00:13.890
y-intercepts of plus 3.

00:00:13.890 --> 00:00:16.580
And this line has a
slope of minus 1.

00:00:16.580 --> 00:00:16.990
So let's see.

00:00:16.990 --> 00:00:19.620
We need a downward sloping
thing that intersects at

00:00:19.620 --> 00:00:20.350
positive 3.

00:00:20.350 --> 00:00:24.890
Actually, they're both going
to intersect at positive 3.

00:00:24.890 --> 00:00:27.900
So choice A, neither of them.

00:00:27.900 --> 00:00:30.940
Both of their y-intercepts
are minus 3.

00:00:30.940 --> 00:00:32.520
We need to see a plus 3 here.

00:00:32.520 --> 00:00:34.400
So it's not choice A.

00:00:34.400 --> 00:00:39.040
In choice C, one of the lines
intersects at positive 3, but

00:00:39.040 --> 00:00:41.540
the other line intersects
at minus 3.

00:00:41.540 --> 00:00:43.990
And they also have the same
slope, and these guys

00:00:43.990 --> 00:00:45.530
obviously don't have
the same slope.

00:00:45.530 --> 00:00:48.410
So it's not going
to be choice C.

00:00:48.410 --> 00:00:50.250
Choice B.

00:00:50.250 --> 00:00:51.230
So I have two lines.

00:00:51.230 --> 00:00:54.140
Both of them have a
y-intercept of 3.

00:00:54.140 --> 00:00:55.760
This looks good so far.

00:00:55.760 --> 00:00:58.290
Both of them have y-intercepts
of 3.

00:00:58.290 --> 00:01:02.400
And then I have one line that
has a positive slope of 1.

00:01:02.400 --> 00:01:05.600
For every 1 I go over,
I go up 1.

00:01:05.600 --> 00:01:09.250
And I have one that has
a negative slope of 1.

00:01:09.250 --> 00:01:12.360
When I move over
1, I go down 1.

00:01:12.360 --> 00:01:16.840
This line right here is y is
equal to x, because I have a

00:01:16.840 --> 00:01:17.630
slope of 1.

00:01:17.630 --> 00:01:19.560
1x plus 3.

00:01:19.560 --> 00:01:21.470
3 is its y-intercept.

00:01:21.470 --> 00:01:24.630
And this line right here
is y is equal to-- its

00:01:24.630 --> 00:01:25.830
slope is minus 1.

00:01:25.830 --> 00:01:28.460
You move to the right
1, you go down 1.

00:01:28.460 --> 00:01:33.560
So minus 1x, or minus x, and
its y-intercept is plus 3.

00:01:33.560 --> 00:01:34.525
So our answer is B.

00:01:34.525 --> 00:01:40.290
These are the two equations
that we have up there.

00:01:40.290 --> 00:01:41.100
You can't see it yet.

00:01:41.100 --> 00:01:42.890
That we have right here.

00:01:42.890 --> 00:01:44.520
Our answer is B.

00:01:44.520 --> 00:01:47.670
And D, both of these guys have
the same slope, so you can't

00:01:47.670 --> 00:01:50.070
have-- clearly it doesn't
apply to the two

00:01:50.070 --> 00:01:50.780
equations up there.

00:01:50.780 --> 00:01:52.540
And they also have two different
y-intercepts, so

00:01:52.540 --> 00:01:54.425
it's definitely not choice D.

00:01:59.200 --> 00:02:01.640
Problem 48.

00:02:01.640 --> 00:02:06.500
Yoshi has exactly $1 in
dimes, which is $0.10,

00:02:06.500 --> 00:02:09.110
and nickels, $0.05.

00:02:09.110 --> 00:02:12.800
If Yoshi has twice as many dimes
as nickels, how many

00:02:12.800 --> 00:02:15.570
nickels does she have?

00:02:15.570 --> 00:02:16.660
So she has $1.

00:02:16.660 --> 00:02:25.240
So let n equal the number of
nickels, and let d is equal to

00:02:25.240 --> 00:02:27.295
the number of the dimes.

00:02:29.840 --> 00:02:34.560
So it says Yoshi has twice
as many dimes as nickels.

00:02:34.560 --> 00:02:38.800
So the dimes are twice as many
as the number of nickels.

00:02:38.800 --> 00:02:39.560
That's what this tells us.

00:02:39.560 --> 00:02:42.120
Yoshi has twice as many
dimes as nickels.

00:02:42.120 --> 00:02:46.980
That translates into the dimes
are 2 times the nickels.

00:02:46.980 --> 00:02:49.790
And then we also know
that she has $1.

00:02:49.790 --> 00:02:52.140
So how do you get $1?

00:02:52.140 --> 00:02:57.630
Well, it's $0.10, so 0.1 times
the number of dimes.

00:03:01.660 --> 00:03:09.190
Plus 0.05 times the number of
nickels is equal to $1.

00:03:09.190 --> 00:03:13.100
Or maybe just so we can avoid
decimals, I could rewrite this

00:03:13.100 --> 00:03:15.075
statement right here,
exactly $1.

00:03:15.075 --> 00:03:17.710
Instead of writing in dollars,
I could write in cents.

00:03:17.710 --> 00:03:23.780
I could write 10 cents times
each dime, plus 5 cents times

00:03:23.780 --> 00:03:28.580
each nickel is equal
to 100 cents.

00:03:28.580 --> 00:03:31.100
So if you compare this equation
and this equation, I

00:03:31.100 --> 00:03:33.310
just multiplied both
sides by 100.

00:03:33.310 --> 00:03:37.010
Here I'm dealing with cents--
$1 is 100 cents.

00:03:37.010 --> 00:03:38.430
Here I'm dealing with dollars.

00:03:38.430 --> 00:03:40.140
A dime is 1/10 of a dollar.

00:03:40.140 --> 00:03:41.950
A dime is 10 cents.

00:03:41.950 --> 00:03:43.930
This one right here is probably
a little bit easier

00:03:43.930 --> 00:03:45.180
to deal with.

00:03:45.180 --> 00:03:45.890
So what are they asking?

00:03:45.890 --> 00:03:47.760
How many nickels
does she have?

00:03:47.760 --> 00:03:51.570
So we want to solve for n, we
want to solve for nickels.

00:03:51.570 --> 00:03:53.680
We have this piece of
information right here.

00:03:53.680 --> 00:03:56.980
The dimes are equal to 2 times
the number of nickels.

00:03:56.980 --> 00:03:58.290
And we have this right here.

00:03:58.290 --> 00:04:00.985
So what we can do is
substitute for d.

00:04:00.985 --> 00:04:04.320
We can replace this d, and we
know that d is equal to 2n.

00:04:04.320 --> 00:04:06.840
So we could put 2n in
the place of that.

00:04:06.840 --> 00:04:08.040
So let me write it over here.

00:04:08.040 --> 00:04:13.990
So I have 10d plus 5n
is equal to 100.

00:04:13.990 --> 00:04:16.730
10 cents times my number of
dimes plus 5 cents times my

00:04:16.730 --> 00:04:19.779
number of nickels is
equal to 100 cents.

00:04:19.779 --> 00:04:21.959
And then my dimes
is equal to 2n.

00:04:21.959 --> 00:04:28.560
So 10 times 2n plus 5n
is equal to 100.

00:04:28.560 --> 00:04:34.660
10 times 2n is just 20n, plus
5n, is equal to 100.

00:04:34.660 --> 00:04:38.820
And then we get 25n
is equal to 100.

00:04:38.820 --> 00:04:44.270
Divide both sides of this
equation by 25, and you get n

00:04:44.270 --> 00:04:47.410
is equal to 100 divided
by 25 is 4.

00:04:47.410 --> 00:04:51.270
Yoshi has 4 nickels.

00:04:51.270 --> 00:04:52.550
And if you want to know
how many dimes, you

00:04:52.550 --> 00:04:54.030
multiply it by 2.

00:04:54.030 --> 00:04:56.350
She has 8 dimes.

00:04:56.350 --> 00:04:59.420
So she has $0.80 in dimes
and she has $0.20 in

00:04:59.420 --> 00:05:02.210
nickels, 4 times 5.

00:05:02.210 --> 00:05:04.040
Problem 49.

00:05:04.040 --> 00:05:08.400
What are all the possible values
of x such that 10 times

00:05:08.400 --> 00:05:13.250
the absolute value of
x is equal to 2.5?

00:05:13.250 --> 00:05:14.480
So we can simplify this.

00:05:14.480 --> 00:05:17.085
So we have 10 times the
absolute value of

00:05:17.085 --> 00:05:19.050
x is equal to 2.5.

00:05:19.050 --> 00:05:22.490
Or if we divide both sides of
this equation by 10, we get--

00:05:22.490 --> 00:05:23.940
let me do it in blue.

00:05:23.940 --> 00:05:27.940
We get the absolute value of
x is equal to-- what's 2.5

00:05:27.940 --> 00:05:32.390
divided by 10?

00:05:32.390 --> 00:05:34.410
You might be able to just
do it in your head.

00:05:34.410 --> 00:05:37.580
You say, oh, you know, there's
4 quarters in $1, or

00:05:37.580 --> 00:05:39.480
25 times 4 is 100.

00:05:39.480 --> 00:05:41.460
But this is 25 divided by 10.

00:05:41.460 --> 00:05:43.800
You multiply 2.5 times 4,
you're going to get 10.

00:05:43.800 --> 00:05:45.920
So you can say this is 1/4.

00:05:45.920 --> 00:05:47.470
If that wasn't obvious
to you, you could

00:05:47.470 --> 00:05:48.500
actually do the division.

00:05:48.500 --> 00:05:54.220
You can divide 10 into 2.5.

00:05:54.220 --> 00:05:56.160
Maybe throw some 0's there.

00:05:56.160 --> 00:05:57.220
Put the decimal there.

00:05:57.220 --> 00:06:00.570
10 goes into 2 zero times.

00:06:00.570 --> 00:06:03.180
0 times 10 is 0.

00:06:03.180 --> 00:06:04.150
Bring down the 2.

00:06:04.150 --> 00:06:05.310
2 minus 0 is 2.

00:06:05.310 --> 00:06:06.790
Bring down the 5.

00:06:06.790 --> 00:06:10.990
10 goes into 25 how
many times?

00:06:10.990 --> 00:06:20.670
10 goes into 25 two times.

00:06:20.670 --> 00:06:22.920
2 times 10 is 20.

00:06:22.920 --> 00:06:24.830
25 minus 20 is 5.

00:06:24.830 --> 00:06:26.510
Bring down another 0.

00:06:26.510 --> 00:06:29.300
10 goes into 50 exactly
five times.

00:06:29.300 --> 00:06:32.820
5 times 10 is 50.

00:06:32.820 --> 00:06:34.030
Subtract, you get 0.

00:06:34.030 --> 00:06:37.180
So 10 goes into 2.5, 0.25
times, which is the

00:06:37.180 --> 00:06:38.430
same thing as 1/4.

00:06:40.590 --> 00:06:45.460
The absolute value of
x is equal to 0.25.

00:06:45.460 --> 00:06:48.970
Now that tells us that x, what
are the two values for x? x

00:06:48.970 --> 00:06:52.820
could definitely be equal to
0.25, because the absolute

00:06:52.820 --> 00:06:54.890
value of 0.25 is 0.25.

00:06:54.890 --> 00:06:57.630
Or what other number,
when I take its

00:06:57.630 --> 00:06:59.400
absolute value, is 0.25?

00:06:59.400 --> 00:07:02.440
Well, it could be minus 0.25.

00:07:02.440 --> 00:07:06.490
I take the absolute value of
minus 0.25, I also get 0.25.

00:07:06.490 --> 00:07:11.400
So my two choices are 0.25 or
minus 0.25, and that is choice

00:07:11.400 --> 00:07:12.770
A right there.

00:07:12.770 --> 00:07:14.680
And when we did this division,
I did it kind of a

00:07:14.680 --> 00:07:15.780
long and slow way.

00:07:15.780 --> 00:07:17.320
And if you didn't recognize
this as 1/4.

00:07:17.320 --> 00:07:19.710
The other way to say it is when
you divide by 10, that's

00:07:19.710 --> 00:07:23.600
equivalent to moving your
decimal 1 slot to the left.

00:07:23.600 --> 00:07:27.610
So you could have just said, oh,
2.5 divided by 10 is equal

00:07:27.610 --> 00:07:30.220
to-- let's just move the decimal
over to the left-- is

00:07:30.220 --> 00:07:32.160
equal to 0.25.

00:07:32.160 --> 00:07:35.200
All of those would have been
equivalent ways of doing it.

00:07:35.200 --> 00:07:36.740
Problem 50.

00:07:36.740 --> 00:07:40.810
Which of the following is
equivalent to 1 minus 2x is

00:07:40.810 --> 00:07:43.830
greater than 3 times
x minus 2?

00:07:43.830 --> 00:07:45.640
So let's solve this.

00:07:45.640 --> 00:07:50.180
So we have 1 minus 2x
is greater than 3

00:07:50.180 --> 00:07:52.370
times x minus 2.

00:07:52.370 --> 00:07:55.850
Or we get 1 minus 2x is
greater than-- let's

00:07:55.850 --> 00:08:00.160
distribute our 3-- 3x minus 6.

00:08:00.160 --> 00:08:03.690
3 times minus 2 is minus 6.

00:08:03.690 --> 00:08:06.880
Now we can subtract
1 from both sides.

00:08:06.880 --> 00:08:09.006
So we have a minus 1 plus
here, and we're going to

00:08:09.006 --> 00:08:11.370
subtract a 1 from that side.

00:08:11.370 --> 00:08:14.230
The whole reason why I'm doing
that is to cancel out that 1

00:08:14.230 --> 00:08:14.790
right there.

00:08:14.790 --> 00:08:17.080
So this side, those cancel out,
so I'm just left with

00:08:17.080 --> 00:08:22.250
minus 2x is greater than
3x, and then minus 6

00:08:22.250 --> 00:08:25.050
minus 1 is minus 7.

00:08:25.050 --> 00:08:28.050
And now here's the vaguely
tricky part.

00:08:28.050 --> 00:08:30.400
No, actually, we're not at the
vaguely tricky part yet.

00:08:30.400 --> 00:08:33.150
Let's subtract 3x
from both sides.

00:08:33.150 --> 00:08:36.730
So we have minus 3x on
that side, and then

00:08:36.730 --> 00:08:38.250
minus 3x on that side.

00:08:38.250 --> 00:08:42.409
And the whole reason why
I'm doing that is to

00:08:42.409 --> 00:08:43.809
cancel out this 3x.

00:08:43.809 --> 00:08:46.460
So that these two guys
obviously cancel out.

00:08:46.460 --> 00:08:52.450
Now minus 3x plus minus 2x,
which is minus 5x, is greater

00:08:52.450 --> 00:08:55.420
than minus 7.

00:08:55.420 --> 00:08:57.340
And now here's the vaguely
tricky part.

00:08:57.340 --> 00:09:00.700
We want to divide both
sides by minus 5.

00:09:00.700 --> 00:09:02.790
But when you have an inequality,
and you're

00:09:02.790 --> 00:09:06.360
dividing or multiplying both
sides by a negative number,

00:09:06.360 --> 00:09:10.000
you need to switch
the inequality.

00:09:10.000 --> 00:09:14.510
So if we divide both sides by
minus 5, so I could multiply

00:09:14.510 --> 00:09:19.210
by a fraction, minus
1/5 times minus 5x.

00:09:19.210 --> 00:09:23.840
And then I'm going to have a
minus 7 times minus 1/5.

00:09:23.840 --> 00:09:26.690
I'm going to switch
the inequality.

00:09:26.690 --> 00:09:28.910
So it goes from greater
than to less than.

00:09:28.910 --> 00:09:31.180
And the whole reason why it's
switched is because I'm

00:09:31.180 --> 00:09:34.040
multiplying both sides, or
depending on how you do it,

00:09:34.040 --> 00:09:36.580
dividing both sides by
a negative number.

00:09:36.580 --> 00:09:40.010
So then this becomes-- I picked
minus 1/5 so this

00:09:40.010 --> 00:09:40.830
cancels out.

00:09:40.830 --> 00:09:45.590
So this just becomes x is less
than, and then minus 7 times

00:09:45.590 --> 00:09:49.630
minus 1/5, the negatives cancel
out, or a negative

00:09:49.630 --> 00:09:51.410
times a negative
is a positive.

00:09:51.410 --> 00:09:55.120
So you're left with 7/5.

00:09:55.120 --> 00:09:57.400
So x is less than 7/5.

00:09:57.400 --> 00:10:00.240
And it shows you that maybe you
don't want to go work out

00:10:00.240 --> 00:10:00.910
the whole problem.

00:10:00.910 --> 00:10:02.990
Because right here, they didn't
expect me to figure out

00:10:02.990 --> 00:10:05.140
the whole problem, so I just
wasted a little bit

00:10:05.140 --> 00:10:06.470
of both of our time.

00:10:06.470 --> 00:10:08.930
They just wanted us to go a
couple of steps into it.

00:10:08.930 --> 00:10:09.960
So what did they just do?

00:10:09.960 --> 00:10:13.100
Well, they just wanted that
first step, where I

00:10:13.100 --> 00:10:14.100
distributed the 3.

00:10:14.100 --> 00:10:17.410
3x minus 6.

00:10:17.410 --> 00:10:18.550
So that's all they did here.

00:10:18.550 --> 00:10:20.430
Because they didn't change the
left-hand side anywhere, they

00:10:20.430 --> 00:10:22.280
didn't change the inequality
anywhere.

00:10:22.280 --> 00:10:25.070
So all I have to do is pick
choice C right there.

00:10:25.070 --> 00:10:26.270
But hopefully you learned
a little bit about

00:10:26.270 --> 00:10:27.900
inequalities as well.

00:10:27.900 --> 00:10:30.040
I hate to waste your time like
that, but this was actually a

00:10:30.040 --> 00:10:31.160
fairly straightforward
problem.

00:10:31.160 --> 00:10:33.700
But actually, the very
first step we did

00:10:33.700 --> 00:10:35.690
got us to the answer.

00:10:35.690 --> 00:10:38.490
So that teaches us both a
lesson: look at the choices

00:10:38.490 --> 00:10:41.020
before you proceed
with the problem.

00:10:41.020 --> 00:10:44.580
51.

00:10:44.580 --> 00:10:49.380
Which equation represents the
line on the graph below?

00:10:49.380 --> 00:10:53.170
So we can look at this, we can
just kind of eyeball it.

00:10:53.170 --> 00:10:55.760
But sometime it's hard
to eyeball it.

00:10:55.760 --> 00:10:58.520
So what we want to do is look
for some point, my first

00:10:58.520 --> 00:11:02.190
intuition is to say, OK, y
is equal to mx plus b.

00:11:02.190 --> 00:11:04.860
Let's look for the y-intercept
and the slope.

00:11:04.860 --> 00:11:07.280
But here the y-intercept,
it's not completely

00:11:07.280 --> 00:11:09.240
obvious where it is.

00:11:09.240 --> 00:11:12.210
Although it looks like
it's at 1.5.

00:11:12.210 --> 00:11:14.660
And we can actually verify that
it's at 1.5, because its

00:11:14.660 --> 00:11:17.300
slope, you can see right here.

00:11:17.300 --> 00:11:22.660
If we start at 1, and if we
go 2 to the right, we go

00:11:22.660 --> 00:11:24.460
down by exactly 1.

00:11:24.460 --> 00:11:32.770
So its slope, m, is equal to
change in y over change in x.

00:11:32.770 --> 00:11:36.480
When your change in x is
positive 2, your change in y

00:11:36.480 --> 00:11:38.420
is minus 1.

00:11:38.420 --> 00:11:40.530
So your slope is minus 1/2.

00:11:40.530 --> 00:11:46.350
So if you go back 1, you're
going to go up 1/2.

00:11:46.350 --> 00:11:47.200
Just like that.

00:11:47.200 --> 00:11:50.410
So our y-intercept is 1.5.

00:11:50.410 --> 00:11:51.200
It's right there.

00:11:51.200 --> 00:11:53.350
It's equal to 1.5.

00:11:53.350 --> 00:11:53.780
Just like that.

00:11:53.780 --> 00:11:56.900
I can verify that
from the slope.

00:11:56.900 --> 00:12:01.390
If I start at 2, and I go 1 to
the right, that means I'm

00:12:01.390 --> 00:12:03.170
going to go 1/2 down.

00:12:03.170 --> 00:12:04.640
Because my slope is minus 1/2.

00:12:04.640 --> 00:12:08.370
So we go 1/2 down, and that'll
get me to 1.5.

00:12:08.370 --> 00:12:15.435
So the equation of this line is
y is equal to minus 1/2 x,

00:12:15.435 --> 00:12:19.290
that's my slope, plus 1.5.

00:12:19.290 --> 00:12:21.870
And that doesn't look like any
of these choices here, so we

00:12:21.870 --> 00:12:23.890
need to simplify this
a little bit.

00:12:23.890 --> 00:12:25.920
Well, the first thing we might
want to do is multiply both

00:12:25.920 --> 00:12:27.600
sides of this equation by 2.

00:12:27.600 --> 00:12:33.370
So you get 2y is equal to 2
times minus 1/2 x, is just

00:12:33.370 --> 00:12:37.310
minus x, and then 2
times 1.5 is 3.

00:12:37.310 --> 00:12:38.530
Plus 3.

00:12:38.530 --> 00:12:41.660
And then if we add x to both
sides of this equation, and

00:12:41.660 --> 00:12:44.440
I'm doing that to get rid of
this minus x on the right-hand

00:12:44.440 --> 00:12:50.900
side, we get x plus
2y is equal to 3.

00:12:50.900 --> 00:12:53.660
And that is choice A right
there, which was completely

00:12:53.660 --> 00:12:56.890
equivalent to what
we did up here.


CAHSEE practice: Problems 28-31

WEBVTT
Kind: captions
Language: en

00:00:00.800 --> 00:00:02.760
Problem 28.

00:00:02.760 --> 00:00:05.930
Which equation best represents
the part of

00:00:05.930 --> 00:00:07.540
the graph shown below?

00:00:07.540 --> 00:00:09.210
So we have a bunch of
equations here.

00:00:09.210 --> 00:00:09.960
Let's see.

00:00:09.960 --> 00:00:12.940
This one is just a linear
equation, so this is just some

00:00:12.940 --> 00:00:14.020
number times x.

00:00:14.020 --> 00:00:17.230
So that graph in general would
be a straight line.

00:00:17.230 --> 00:00:18.910
This one and this one
are straight lines.

00:00:18.910 --> 00:00:22.680
This one would be a straight
line with a positive slope,

00:00:22.680 --> 00:00:24.280
maybe look something
like that.

00:00:24.280 --> 00:00:26.630
This choice C right here would
be a straight line with a

00:00:26.630 --> 00:00:28.550
negative slope, like that.

00:00:28.550 --> 00:00:31.540
They would both go through the
origin, because they don't

00:00:31.540 --> 00:00:33.380
have any y-intercept
right there.

00:00:33.380 --> 00:00:35.220
So neither of these
are the answer.

00:00:35.220 --> 00:00:37.450
So let's look at these two--
I guess we could call them

00:00:37.450 --> 00:00:38.540
quadratics.

00:00:38.540 --> 00:00:42.840
So here we have 1.75x squared.

00:00:42.840 --> 00:00:46.530
So the graph of x squared--
let me do it in a better

00:00:46.530 --> 00:00:49.710
color-- the graph of x squared
looks like this.

00:00:52.230 --> 00:00:53.000
It's a parabola.

00:00:53.000 --> 00:00:54.350
You've seen that before.

00:00:54.350 --> 00:00:56.790
And they're drawing it in the
first quadrant right there,

00:00:56.790 --> 00:00:58.020
and that looks about right.

00:00:58.020 --> 00:01:00.550
And you're like, hey, but
what about the 1.75?

00:01:00.550 --> 00:01:01.940
Well, that's just a
scaling factor.

00:01:01.940 --> 00:01:05.860
If you throw a larger number
there, it'll curve up a little

00:01:05.860 --> 00:01:06.460
bit faster.

00:01:06.460 --> 00:01:08.930
If you throw a smaller number
there, it'll curve up a little

00:01:08.930 --> 00:01:10.210
bit slower.

00:01:10.210 --> 00:01:13.010
But the general idea is that
they all have the general

00:01:13.010 --> 00:01:14.200
shape of a parabola.

00:01:14.200 --> 00:01:15.570
So this one looks pretty good.

00:01:15.570 --> 00:01:17.880
It's an upward opening
parabola.

00:01:17.880 --> 00:01:20.400
It's kind of an upright U.

00:01:20.400 --> 00:01:22.320
So this looks like a pretty
good solution.

00:01:22.320 --> 00:01:25.090
If we were to draw the whole
graph, it would continue on

00:01:25.090 --> 00:01:26.770
this side like that.

00:01:26.770 --> 00:01:30.230
Then choice D, it's just like
choice B, except they have a

00:01:30.230 --> 00:01:31.680
minus here.

00:01:31.680 --> 00:01:33.780
And the reason why I know that's
not going to work is

00:01:33.780 --> 00:01:38.590
that the graph of minus x
squared, or minus anything

00:01:38.590 --> 00:01:41.950
times x squared is going
to look like this.

00:01:41.950 --> 00:01:43.790
It's going to be downward
opening.

00:01:43.790 --> 00:01:47.630
So this is the graph of minus x
squared, the graph of minus

00:01:47.630 --> 00:01:52.530
1.75x squared, might
open up or go down

00:01:52.530 --> 00:01:54.040
a little bit faster.

00:01:54.040 --> 00:01:55.820
So it's going to have the
same general shape.

00:01:55.820 --> 00:01:58.240
So we know that this is also
not the right answer.

00:01:58.240 --> 00:02:02.110
So our choice is B.

00:02:02.110 --> 00:02:03.830
Next question.

00:02:03.830 --> 00:02:05.140
29.

00:02:05.140 --> 00:02:09.180
Lisa typed a 1,000-word essay
at the average rate of 20

00:02:09.180 --> 00:02:10.430
words per minute.

00:02:14.270 --> 00:02:18.660
If she started typing at 6:20
PM and did not take any

00:02:18.660 --> 00:02:23.560
breaks, at what time did Lisa
finish typing the essay?

00:02:23.560 --> 00:02:26.860
So she had a 1,000-word essay
and she was typing at 20 words

00:02:26.860 --> 00:02:27.430
per minute.

00:02:27.430 --> 00:02:29.140
So let me write that down.

00:02:29.140 --> 00:02:34.790
So she had 1,000 words
and she's typing at

00:02:34.790 --> 00:02:38.030
20 words per minute.

00:02:38.030 --> 00:02:41.280
So if you're writing 1,000 words
and you're doing 20 per

00:02:41.280 --> 00:02:43.010
minute, how many minutes
is it going to take?

00:02:43.010 --> 00:02:45.330
Well, what's 1,000
divided by 20?

00:02:45.330 --> 00:02:46.410
You could do this
in your head.

00:02:46.410 --> 00:02:48.920
You say 100 divided
by 20 is 5.

00:02:48.920 --> 00:02:50.480
1,000 is 10 hundreds.

00:02:50.480 --> 00:02:52.010
So it's going to be 50.

00:02:52.010 --> 00:02:53.770
But if you don't want to do it
in your head, you can just say

00:02:53.770 --> 00:03:00.940
20 goes into 1,000-- 20 goes
into 10 zero times.

00:03:00.940 --> 00:03:03.190
20 goes into 100 five times.

00:03:03.190 --> 00:03:08.480
5 times 20 is 100, and then
you bring down the 0.

00:03:13.420 --> 00:03:18.460
20 goes into 0 zero times, and
then 0 times 20 is 0, and then

00:03:18.460 --> 00:03:19.240
you are done.

00:03:19.240 --> 00:03:21.760
20 goes into 1,000
fifty times.

00:03:21.760 --> 00:03:23.830
Or you could say 2 goes
into 100 five times.

00:03:23.830 --> 00:03:24.700
All the same thing.

00:03:24.700 --> 00:03:28.550
Just 20-- and then--
sorry, 50.

00:03:28.550 --> 00:03:29.775
Want to be careful.

00:03:29.775 --> 00:03:31.610
So it'll take her 50 minutes,
and actually

00:03:31.610 --> 00:03:32.620
the units work out.

00:03:32.620 --> 00:03:35.890
You have words divided by words
per minute, or that's

00:03:35.890 --> 00:03:39.540
the same thing as words times
minutes per word.

00:03:39.540 --> 00:03:41.910
They cancel out, and you
end up with 50 minutes.

00:03:41.910 --> 00:03:43.960
If that confuses you, don't
worry about it too much.

00:03:43.960 --> 00:03:45.750
The intuition is what's
important.

00:03:45.750 --> 00:03:49.120
You had a 1,000-word essay, you
did 20 words per minute.

00:03:49.120 --> 00:03:51.490
So it was going to take
you 50 minutes.

00:03:51.490 --> 00:03:53.640
50 minutes times 20 words
per minute is

00:03:53.640 --> 00:03:55.380
equal to 1,000 words.

00:03:55.380 --> 00:04:00.830
So you're going to
have 50 minutes.

00:04:00.830 --> 00:04:05.580
So she starts at 6:20 PM.

00:04:05.580 --> 00:04:12.960
So at 7:00 PM, she's worked
for 40 minutes.

00:04:12.960 --> 00:04:15.290
Because there's 60 minutes
in an hour.

00:04:15.290 --> 00:04:16.640
But she works for 50
minutes, so she

00:04:16.640 --> 00:04:19.829
does another 10 minutes.

00:04:19.829 --> 00:04:22.019
So that gets her to 7:10.

00:04:22.019 --> 00:04:25.800
So the choice is D.

00:04:25.800 --> 00:04:28.900
Problem 30.

00:04:28.900 --> 00:04:31.530
What does-- let me
do it in red.

00:04:31.530 --> 00:04:36.080
What does x to the fifth equal
when x is equal to minus 2?

00:04:36.080 --> 00:04:41.760
So it's minus 2 times minus 2
times minus 2 times minus 2

00:04:41.760 --> 00:04:43.490
times minus 2.

00:04:43.490 --> 00:04:45.180
Now we can just multiply
it all out.

00:04:45.180 --> 00:04:46.670
Let's just do that,
just for fun.

00:04:46.670 --> 00:04:50.570
Minus 2 times minus
2 is positive 4.

00:04:50.570 --> 00:04:54.760
Then positive 4 times
minus 2 is minus 8.

00:04:54.760 --> 00:04:59.910
Minus 8 times minus
2 is positive 16.

00:04:59.910 --> 00:05:04.590
Positive 16 times minus
2 is minus 32.

00:05:04.590 --> 00:05:06.570
So our answer is A.

00:05:06.570 --> 00:05:08.560
Now, if you wanted to do that
really fast, you might

00:05:08.560 --> 00:05:11.400
recognize, well, 2 to
the fifth is 32.

00:05:11.400 --> 00:05:14.120
So it's either going to be that
choice or that choice.

00:05:14.120 --> 00:05:17.520
And then we have
a odd exponent.

00:05:17.520 --> 00:05:19.650
So we're going to be multiplying
a negative times

00:05:19.650 --> 00:05:22.690
itself an even time, and
then one more negative.

00:05:22.690 --> 00:05:23.860
So you're going to get
a negative number.

00:05:23.860 --> 00:05:25.730
When you have an odd exponent,
you're going to

00:05:25.730 --> 00:05:26.490
end up with a negative.

00:05:26.490 --> 00:05:30.140
You have an even exponent,
you'll end up with a positive.

00:05:30.140 --> 00:05:32.570
So that would have been the fast
way to do it, but even if

00:05:32.570 --> 00:05:35.000
you didn't do that, you could
have just multiplied it

00:05:35.000 --> 00:05:36.140
straight out like we just did.

00:05:36.140 --> 00:05:38.080
And just remember a negative
times a negative is a

00:05:38.080 --> 00:05:40.140
positive, and then a
positive times the

00:05:40.140 --> 00:05:41.315
negative is a negative.

00:05:41.315 --> 00:05:44.420
It's minus 32.

00:05:44.420 --> 00:05:47.380
31.

00:05:47.380 --> 00:05:51.250
The graph below compares the
weight of an object on Earth

00:05:51.250 --> 00:05:53.310
to its weight on the Moon.

00:05:53.310 --> 00:05:54.260
Interesting.

00:05:54.260 --> 00:05:56.890
An object's weight on the Moon,
OK, so this is the Moon

00:05:56.890 --> 00:05:58.190
weight, this is the
Earth weight.

00:05:58.190 --> 00:06:00.870
So something that-- let's say--
well, I actually do

00:06:00.870 --> 00:06:02.090
weigh 150 pounds.

00:06:02.090 --> 00:06:04.580
So I weigh 150 pounds on Earth,
and according to this

00:06:04.580 --> 00:06:08.040
chart, I would weigh 25
pounds on the Moon.

00:06:08.040 --> 00:06:11.150
Or I would weigh essentially
1/6 my weight

00:06:11.150 --> 00:06:12.890
that I am on Earth.

00:06:12.890 --> 00:06:14.170
What is it asking me?

00:06:14.170 --> 00:06:17.800
What is the approximate weight
on the Moon of an astronaut

00:06:17.800 --> 00:06:20.410
who weighs 120 pounds
on Earth?

00:06:20.410 --> 00:06:24.660
Well, I just said, essentially
this thing is just taking 1/6.

00:06:24.660 --> 00:06:25.570
You can look at any point.

00:06:25.570 --> 00:06:27.310
When you weigh 10 pounds on
the Moon, you're weighing

00:06:27.310 --> 00:06:33.170
roughly 60 pounds on Earth,
or vice versa.

00:06:33.170 --> 00:06:34.710
So you just take 1/6,
or we could actually

00:06:34.710 --> 00:06:35.340
just look at the chart.

00:06:35.340 --> 00:06:39.370
120 pounds-- so if we go
halfway, that's about 125,

00:06:39.370 --> 00:06:40.550
between 100 and 150.

00:06:40.550 --> 00:06:42.590
120 pounds would
be right there.

00:06:42.590 --> 00:06:45.890
You go up the graph,
just like that.

00:06:45.890 --> 00:06:49.870
And you go there, and it looks
like 18 or 19 pounds.

00:06:49.870 --> 00:06:51.490
And they say, what is the
approximate weight?

00:06:51.490 --> 00:06:53.510
So the closest thing we are
here, let's see, the

00:06:53.510 --> 00:06:56.220
choice of 15 and 20.

00:06:56.220 --> 00:06:58.730
We're definitely closer to
20 than we are to 15.

00:06:58.730 --> 00:07:04.870
So I will go with
20 right here.

00:07:04.870 --> 00:07:06.990
And you know, if we really
wanted to look at it, this is

00:07:06.990 --> 00:07:08.710
actually the point that we
should have looked at, this

00:07:08.710 --> 00:07:12.180
point right here would
have been 120 pounds.

00:07:12.180 --> 00:07:15.160
But you just approximate where
120 is, you read the graph,

00:07:15.160 --> 00:07:16.610
you say, oh, it's closer
to 20 than any

00:07:16.610 --> 00:07:18.000
of these other choices.

00:07:18.000 --> 00:07:20.620
So that'll be our answer.


CAHSEE practice: Problems 52-53

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:01.780
Problem 52.

00:00:01.780 --> 00:00:05.980
Colleen solved the equation 2
times 2x plus 5 is equal to 8

00:00:05.980 --> 00:00:08.300
using the following steps.

00:00:08.300 --> 00:00:09.870
OK, so she has a
bunch of steps.

00:00:09.870 --> 00:00:13.150
To get from Step 2 to Step 3,
Colleen-- so it's good that I

00:00:13.150 --> 00:00:15.850
read the question before I just
started diving into it.

00:00:15.850 --> 00:00:19.476
So to get from Step 2 to Step
3-- so this is her Step 2, and

00:00:19.476 --> 00:00:21.430
this is her Step 3 right here.

00:00:21.430 --> 00:00:25.420
What did she do to get
from here to here?

00:00:25.420 --> 00:00:27.960
Well, she divided
both sides by 4.

00:00:27.960 --> 00:00:28.370
Right?

00:00:28.370 --> 00:00:32.970
You could say 4x is
equal to minus 2.

00:00:32.970 --> 00:00:39.020
If you divide both sides of
this equation by 4, the

00:00:39.020 --> 00:00:42.420
left-hand side-- these cancel
out, you're just left with x.

00:00:42.420 --> 00:00:45.900
And then the right-hand side,
minus 2/4 is just minus 1/2.

00:00:45.900 --> 00:00:48.220
So she just divided
both sides by 4.

00:00:48.220 --> 00:00:51.010
And that is choice A.

00:00:51.010 --> 00:00:53.290
She definitely didn't subtract
4 from both sides.

00:00:53.290 --> 00:00:55.390
She didn't add 4
to both sides.

00:00:55.390 --> 00:00:57.300
And she didn't multiply
both sides by 4.

00:00:57.300 --> 00:00:59.300
Then we would have
had 16x minus 8.

00:00:59.300 --> 00:01:02.000
So that was a pretty
straightforward problem.

00:01:02.000 --> 00:01:03.220
And then 53.

00:01:03.220 --> 00:01:06.240
What is the reciprocal
of ax squared over y?

00:01:06.240 --> 00:01:09.080
This is another, you just have
to know what a reciprocal is.

00:01:09.080 --> 00:01:12.380
A reciprocal of something is
just 1 over that something.

00:01:12.380 --> 00:01:14.530
Or if it's a fraction,
you just flip it.

00:01:14.530 --> 00:01:19.590
So if you have a/b, the
reciprocal is b/a.

00:01:19.590 --> 00:01:26.520
If you have xy/ab,
the reciprocal

00:01:26.520 --> 00:01:29.420
is going to be ab/xy.

00:01:29.420 --> 00:01:34.200
So if you have ax squared over
y, its reciprocal is just

00:01:34.200 --> 00:01:37.390
going to be y over ax squared.

00:01:37.390 --> 00:01:38.510
That easy.

00:01:38.510 --> 00:01:44.120
And that is choice D,
y over ax squared.

00:01:44.120 --> 00:01:47.870
You just have to know to flip
this fraction right there.


CAHSEE practice: Problems 43-46

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:02.280
Problem 43.

00:00:02.280 --> 00:00:05.260
Mia found the area of this
shape by dividing it into

00:00:05.260 --> 00:00:08.180
rectangles as shown.

00:00:08.180 --> 00:00:12.090
Mia could use the same method to
find the area for which of

00:00:12.090 --> 00:00:15.260
these shapes?

00:00:15.260 --> 00:00:19.530
What technique can we use to
figure out the area by

00:00:19.530 --> 00:00:22.200
dividing it into rectangles?

00:00:22.200 --> 00:00:23.280
So let's see.

00:00:23.280 --> 00:00:24.660
What do we have here?

00:00:24.660 --> 00:00:26.340
Can we divide this
into rectangles?

00:00:26.340 --> 00:00:32.090
We can divide into a bunch of
triangles, but we can't divide

00:00:32.090 --> 00:00:34.310
this into a bunch
of rectangles.

00:00:34.310 --> 00:00:36.760
Or we could have done
it this way as well.

00:00:36.760 --> 00:00:38.550
There's multiple ways
to think about it.

00:00:38.550 --> 00:00:42.580
You could have it like this,
and you can draw a bunch of

00:00:42.580 --> 00:00:44.890
triangles like that.

00:00:44.890 --> 00:00:47.410
But you can't divide this
into rectangles.

00:00:47.410 --> 00:00:52.210
This one here, you can't divide
it into rectangles.

00:00:52.210 --> 00:00:54.210
You could divide it into
triangles and rectangles, but

00:00:54.210 --> 00:00:57.160
not necessarily just
rectangles.

00:00:57.160 --> 00:00:59.470
And this here, I really
don't know.

00:00:59.470 --> 00:01:02.550
It looks like there's some
type of typo in my test.

00:01:02.550 --> 00:01:05.890
Because obviously I could divide
both of these things

00:01:05.890 --> 00:01:07.890
right here.

00:01:07.890 --> 00:01:10.270
The way I'm looking at it,
I see squares here.

00:01:10.270 --> 00:01:12.310
So obviously I could divide
that into rectangles.

00:01:12.310 --> 00:01:15.390
But my guess is, if I had to
guess, is that this was a

00:01:15.390 --> 00:01:17.180
triangle, maybe, before.

00:01:17.180 --> 00:01:20.110
If it was a triangle, then I
couldn't divide this into

00:01:20.110 --> 00:01:20.700
rectangles.

00:01:20.700 --> 00:01:22.785
But maybe this was something
like this.

00:01:26.690 --> 00:01:27.130
I don't know.

00:01:27.130 --> 00:01:28.380
I'm only guessing.

00:01:28.380 --> 00:01:30.440
If it did look like this, then
we could divide it into

00:01:30.440 --> 00:01:34.000
rectangles the same way that
she did up here, and figure

00:01:34.000 --> 00:01:34.910
out its area.

00:01:34.910 --> 00:01:38.080
So assuming that there was
some type of typo in this

00:01:38.080 --> 00:01:40.745
problem, I'm going to
go with choice D.

00:01:40.745 --> 00:01:43.170
If choice D was supposed to look
like a figure like that,

00:01:43.170 --> 00:01:46.540
then you could actually divide
it into a bunch of rectangles.

00:01:46.540 --> 00:01:48.100
Problem 44.

00:01:48.100 --> 00:01:48.830
Oh, I see.

00:01:48.830 --> 00:01:49.920
You know what these
probably were?

00:01:49.920 --> 00:01:53.830
These were probably to show us
that these are right angles

00:01:53.830 --> 00:01:55.150
right there.

00:01:55.150 --> 00:01:58.760
So that that's a right angle,
that's a right angle.

00:01:58.760 --> 00:02:00.700
And maybe-- well, I don't
know what else they're

00:02:00.700 --> 00:02:03.590
trying to show us.

00:02:03.590 --> 00:02:04.440
Who knows?

00:02:04.440 --> 00:02:06.610
You see what I'm going at.

00:02:06.610 --> 00:02:09.440
There's clearly some type
of typo on that problem.

00:02:09.440 --> 00:02:10.419
44.

00:02:10.419 --> 00:02:11.500
Simplify.

00:02:11.500 --> 00:02:14.910
x squared minus 3x plus
1, minus x squared

00:02:14.910 --> 00:02:17.840
plus 2x plus 7.

00:02:17.840 --> 00:02:18.980
So let's just write it out.

00:02:18.980 --> 00:02:23.610
We have x squared
minus 3x plus 1.

00:02:23.610 --> 00:02:25.800
Then we have to distribute
this minus sign.

00:02:25.800 --> 00:02:30.970
So minus x squared
minus 2x, right?

00:02:30.970 --> 00:02:32.470
Minus times plus.

00:02:32.470 --> 00:02:34.740
Minus 2x.

00:02:34.740 --> 00:02:39.010
Minus times plus 7 is minus 7.

00:02:39.010 --> 00:02:41.760
So you have an x squared
minus an x squared.

00:02:41.760 --> 00:02:43.230
They cancel out.

00:02:43.230 --> 00:02:46.530
Right? x squared minus
x squared is 0.

00:02:46.530 --> 00:02:49.210
Then you have minus
3x minus 2x.

00:02:51.810 --> 00:02:53.920
Is minus 5x.

00:02:53.920 --> 00:02:58.900
And then you have 1 minus
7, which is minus 6.

00:02:58.900 --> 00:03:05.340
So you're left with minus 5x
minus 6, which is choice C.

00:03:05.340 --> 00:03:07.020
Problem 45.

00:03:07.020 --> 00:03:12.700
What are the coordinates of the
x-intercept of the line 3x

00:03:12.700 --> 00:03:14.660
plus 4y is equal to 12?

00:03:14.660 --> 00:03:17.000
They want to know
the x-intercept.

00:03:17.000 --> 00:03:19.170
Remember, the x-intercept,
if this is a line--

00:03:19.170 --> 00:03:20.510
and this is a line.

00:03:20.510 --> 00:03:22.890
Let me draw the axes.

00:03:22.890 --> 00:03:24.840
Say the line looks-- I don't
know what it looks like.

00:03:24.840 --> 00:03:26.730
Say the line looks something
like this.

00:03:26.730 --> 00:03:33.810
The x-intercept is the value
when y is equal to 0.

00:03:33.810 --> 00:03:39.040
The x-intercept is going to
be some value x and 0.

00:03:39.040 --> 00:03:41.050
So let's figure out what
this x-intercept is.

00:03:41.050 --> 00:03:42.380
So we can even look here.

00:03:42.380 --> 00:03:44.030
This is definitely not
an x-intercept.

00:03:44.030 --> 00:03:45.500
This is a y-intercept.

00:03:45.500 --> 00:03:46.850
This is a y-intercept.

00:03:46.850 --> 00:03:49.910
In order to be an x-intercept,
in order to be on the x-axis,

00:03:49.910 --> 00:03:51.480
your y value has to be 0.

00:03:51.480 --> 00:03:53.880
So the choices are
either B or D.

00:03:53.880 --> 00:03:57.550
And so if y is 0, let's just
solve the equation.

00:03:57.550 --> 00:04:02.680
So 3x plus 4 times
0 is equal to 12.

00:04:02.680 --> 00:04:06.040
Or we get 3x is equal to 12.

00:04:06.040 --> 00:04:08.080
That's just 0 right there.

00:04:08.080 --> 00:04:09.940
So x is equal to 4.

00:04:09.940 --> 00:04:13.260
So the x-intercept
is 4 comma 0.

00:04:13.260 --> 00:04:15.480
x is 5, y is 0.

00:04:15.480 --> 00:04:19.480
So this is our choice
right there.

00:04:19.480 --> 00:04:20.640
46.

00:04:20.640 --> 00:04:21.930
Which of the following
statements

00:04:21.930 --> 00:04:23.630
describes parallel lines?

00:04:23.630 --> 00:04:26.380
And parallel lines are just
two lines that never

00:04:26.380 --> 00:04:29.140
intersect, that have the same
slope an they don't sit on top

00:04:29.140 --> 00:04:29.690
of each other.

00:04:29.690 --> 00:04:32.480
So those would be two parallel
lines right there.

00:04:32.480 --> 00:04:34.830
Same y-intercepts but
different slopes.

00:04:34.830 --> 00:04:37.550
No, I just said, they have to
have the same slope and they

00:04:37.550 --> 00:04:38.110
never intersect.

00:04:38.110 --> 00:04:39.890
So they can't have the
same y-intercepts.

00:04:39.890 --> 00:04:41.300
So it's not that one.

00:04:41.300 --> 00:04:43.510
Same slope but different
y-intercepts.

00:04:43.510 --> 00:04:44.720
That looks right.

00:04:44.720 --> 00:04:47.010
They're parallel, but they're
not on top of each other.

00:04:47.010 --> 00:04:48.450
Or they have the same slope.

00:04:48.450 --> 00:04:49.330
Opposite slopes.

00:04:49.330 --> 00:04:51.880
If they had opposite slopes,
they would intersect.

00:04:51.880 --> 00:04:52.500
Can't be that.

00:04:52.500 --> 00:04:55.160
Opposite x-intercepts but
same y-intercepts.

00:04:55.160 --> 00:04:57.150
No, that's not necessarily
the case.

00:04:57.150 --> 00:05:00.290
So our answer is B.


CAHSEE practice: Problems 38-42

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.110
Problem 38.

00:00:02.110 --> 00:00:05.080
In the drawing below, the figure
formed by the squares

00:00:05.080 --> 00:00:09.650
with sides that are labeled x,
y, and z is a right triangle.

00:00:09.650 --> 00:00:11.680
So the figure, so it's
a right triangle.

00:00:14.550 --> 00:00:16.990
And then they ask us, which
equation is true for all

00:00:16.990 --> 00:00:19.350
values of x, y, and z?

00:00:19.350 --> 00:00:21.870
So really, they're just trying
to see if you remember the

00:00:21.870 --> 00:00:23.190
Pythagorean Theorem.

00:00:31.050 --> 00:00:34.980
And that just tells us that if
we have a right triangle, that

00:00:34.980 --> 00:00:40.050
the sum of the squares of the
two smaller sides, so x

00:00:40.050 --> 00:00:44.440
squared plus y squared, is
going to be equal to the

00:00:44.440 --> 00:00:48.240
square of the longest side, or
the side that's opposite the

00:00:48.240 --> 00:00:49.010
right angle.

00:00:49.010 --> 00:00:50.260
Or we also call that
the hypotenuse.

00:00:53.540 --> 00:00:55.890
So that's equal to z squared.

00:00:55.890 --> 00:00:58.420
That's what the Pythagorean
Theorem tells us.

00:00:58.420 --> 00:01:02.120
And so if we look down here,
only one of those match what I

00:01:02.120 --> 00:01:04.670
just wrote down, are kind
of my restatement of the

00:01:04.670 --> 00:01:06.090
Pythagorean Theorem.

00:01:06.090 --> 00:01:09.570
x squared plus y squared
is equal to z squared.

00:01:09.570 --> 00:01:13.350
And that's this one right
there, choice B.

00:01:13.350 --> 00:01:15.100
Next problem.

00:01:15.100 --> 00:01:18.260
Problem 39.

00:01:18.260 --> 00:01:22.340
A clothing company created the
following diagram for a vest.

00:01:22.340 --> 00:01:25.410
So I guess this is somehow a
vest. Maybe it's half of the

00:01:25.410 --> 00:01:28.830
vest, because I don't see how
I could put that on me.

00:01:28.830 --> 00:01:31.550
To show the other side of the
vest-- OK, right, so this was

00:01:31.550 --> 00:01:38.180
half of the vest-- the company
will reflect the drawing

00:01:38.180 --> 00:01:41.630
across the y-axis.

00:01:41.630 --> 00:01:45.270
What will be the coordinates
of C after the reflection?

00:01:45.270 --> 00:01:47.350
So when they say reflection,
they mean, literally, just

00:01:47.350 --> 00:01:49.860
take the image of this and
you flip it over onto the

00:01:49.860 --> 00:01:50.820
right-hand side.

00:01:50.820 --> 00:01:53.260
So I could draw it out,
and draw it in blue.

00:01:53.260 --> 00:01:56.550
So if I take the reflection,
this line right here is at

00:01:56.550 --> 00:01:57.210
negative 1.

00:01:57.210 --> 00:02:00.270
It's 1 to the left
of the y-axis.

00:02:00.270 --> 00:02:04.220
So when I take its reflection,
I would draw it right here, 1

00:02:04.220 --> 00:02:07.520
to the right of the y-axis.

00:02:07.520 --> 00:02:13.580
This line down here, it goes
from 1 to the left all the way

00:02:13.580 --> 00:02:15.140
to 4 to the left.

00:02:15.140 --> 00:02:17.370
On this side, it's going to go
from 1 to the right all the

00:02:17.370 --> 00:02:20.610
way to 4 to the right.

00:02:20.610 --> 00:02:22.470
I could keep doing it.

00:02:22.470 --> 00:02:26.180
This segment right here, FE,
when I flip it, will become

00:02:26.180 --> 00:02:28.850
this segment right here.

00:02:28.850 --> 00:02:34.800
This segment, DE, right here,
will become this segment.

00:02:34.800 --> 00:02:38.190
It'll just look something like
this when I go onto that side.

00:02:38.190 --> 00:02:43.210
And then C, right here, is 2
to the left of the y-axis.

00:02:43.210 --> 00:02:46.710
So C over here will be 2 to
the right of the y-axis.

00:02:46.710 --> 00:02:48.630
So it's going to look
something like this.

00:02:48.630 --> 00:02:52.130
So the vest is going to look
something like this.

00:02:52.130 --> 00:02:54.030
And then of course, it just
dips down like that.

00:02:54.030 --> 00:02:56.230
So that's the right-hand
side of the vest.

00:02:56.230 --> 00:02:58.240
But they want to know what
are the coordinates of C?

00:02:58.240 --> 00:03:01.330
So this is C, and this is the
C after the reflection.

00:03:01.330 --> 00:03:03.120
Maybe I could call it C prime.

00:03:03.120 --> 00:03:07.440
And so its coordinates are--
its x-coordinate is 2.

00:03:07.440 --> 00:03:09.830
And we're 2 to the right;
before, we were 2 to the left,

00:03:09.830 --> 00:03:10.970
at minus 2.

00:03:10.970 --> 00:03:12.770
And its y-coordinate is
going to be the same,

00:03:12.770 --> 00:03:14.530
it's going to be 7.

00:03:14.530 --> 00:03:16.320
2, 7.

00:03:16.320 --> 00:03:18.065
So that is choice A.

00:03:21.690 --> 00:03:22.960
I'll do it in the next video.

00:03:22.960 --> 00:03:24.870
Well, there's only two problems
in this video.

00:03:24.870 --> 00:03:26.590
So let me go to the next page.

00:03:30.690 --> 00:03:31.880
Number 40.

00:03:31.880 --> 00:03:34.920
What is the area, in
square units, of

00:03:34.920 --> 00:03:38.540
trapezoid QRST shown below?

00:03:38.540 --> 00:03:40.276
So we need to figure out
the area of this.

00:03:40.276 --> 00:03:42.190
And they actually even
give us a formula.

00:03:42.190 --> 00:03:46.090
They gave us the formula
for this trapezoid.

00:03:46.090 --> 00:03:52.810
So they're calling it 1/2 times
the height, times base 1

00:03:52.810 --> 00:03:54.150
plus base 2.

00:03:54.150 --> 00:03:55.980
So essentially, just to give you
an intuition of where this

00:03:55.980 --> 00:03:58.410
comes from, you're essentially
saying, what's the average

00:03:58.410 --> 00:04:00.360
width of this trapezoid?

00:04:00.360 --> 00:04:05.195
So you take 1/2 times the sum of
this guy and that guy, and

00:04:05.195 --> 00:04:06.830
that gives you the
average width.

00:04:06.830 --> 00:04:08.640
And then you multiply that
times the height.

00:04:08.640 --> 00:04:15.450
So just applying this formula,
it is 1/2 times my height-- my

00:04:15.450 --> 00:04:21.500
height is 8-- times base 1,
let's call this base 1, 20.

00:04:21.500 --> 00:04:23.320
Plus base 2.

00:04:23.320 --> 00:04:25.980
Base 2 is this 6 right there.

00:04:25.980 --> 00:04:30.200
So I have 1/2 times 8,
which is 4, times 26.

00:04:30.200 --> 00:04:36.000
And 4 times 26 is equal
to 104 square units.

00:04:36.000 --> 00:04:37.310
So that's that right there.

00:04:37.310 --> 00:04:38.570
So they're really just
testing whether you

00:04:38.570 --> 00:04:39.750
can apply this formula.

00:04:39.750 --> 00:04:42.020
Whether you can recognize what's
the height and what are

00:04:42.020 --> 00:04:44.750
the two bases.

00:04:44.750 --> 00:04:46.230
Problem 41.

00:04:46.230 --> 00:04:47.670
One millimeter is.

00:04:47.670 --> 00:04:52.450
Well, here they're just seeing
if you remember your units.

00:04:52.450 --> 00:04:53.360
Let me write it this way.

00:04:53.360 --> 00:04:57.510
Deci is equal to 1/10.

00:04:57.510 --> 00:05:01.930
Centi is equal to 1/100.

00:05:01.930 --> 00:05:10.030
And then milli is
equal to 1/1000.

00:05:10.030 --> 00:05:15.200
So one millimeter is
1/1000 of a meter.

00:05:15.200 --> 00:05:19.710
They're just making sure you
remember your metric prefixes.

00:05:19.710 --> 00:05:23.030
Problem 42.

00:05:23.030 --> 00:05:30.650
In the diagram below,
hexagon LMNPQR is

00:05:30.650 --> 00:05:33.195
congruent to hexagon STUVWX.

00:05:38.690 --> 00:05:40.780
Congruent just means all the
sides are equal and all the

00:05:40.780 --> 00:05:43.690
measures of their angles
are also equal.

00:05:43.690 --> 00:05:46.920
So they say, which side is
the same length as MN?

00:05:50.500 --> 00:05:53.140
So this is MN right there, and
we want to know what side is

00:05:53.140 --> 00:05:54.900
the same length as that.

00:05:54.900 --> 00:05:56.930
So let me make sure
that they're not

00:05:56.930 --> 00:05:57.900
trying to confuse us.

00:05:57.900 --> 00:06:04.570
So they start here, they
say LMNPQR, and

00:06:04.570 --> 00:06:05.820
then they say STUVWX.

00:06:08.630 --> 00:06:10.010
So they're not confusing us.

00:06:10.010 --> 00:06:11.490
These points do correspond.

00:06:11.490 --> 00:06:14.100
S corresponds to L, M
corresponds to T, and so

00:06:14.100 --> 00:06:15.370
forth and so on.

00:06:15.370 --> 00:06:18.780
So this segment is going to be
congruent to that segment

00:06:18.780 --> 00:06:19.590
right there.

00:06:19.590 --> 00:06:21.510
Segment TU.

00:06:21.510 --> 00:06:25.020
So MN is the same
length as TU.

00:06:25.020 --> 00:06:27.800
That is choice B.