2015 AP Calculus BC 2c

WEBVTT
Kind: captions
Language: en

00:00:00.272 --> 00:00:02.965
- [Voiceover] Part c,
find the time at which the

00:00:02.965 --> 00:00:06.410
speed of the particle is three.

00:00:06.410 --> 00:00:09.131
So let's just remind
ourselves what speed is.

00:00:09.131 --> 00:00:12.207
It's the magnitude of velocity.

00:00:12.207 --> 00:00:16.205
So, if you have the x,

00:00:16.205 --> 00:00:17.575
actually let me draw it this way,

00:00:17.575 --> 00:00:21.661
if you have the x dimension of,

00:00:21.661 --> 00:00:23.094
or the x component of

00:00:23.094 --> 00:00:24.941
a velocity, right over there,

00:00:24.941 --> 00:00:27.635
so this is the rate
of, which x is changing

00:00:27.635 --> 00:00:29.190
with respect to time.

00:00:29.190 --> 00:00:32.347
And you have the y
component of the velocity

00:00:32.347 --> 00:00:34.756
you have the y component of the velocity,

00:00:34.756 --> 00:00:36.562
let's say it looks something like that.

00:00:36.562 --> 00:00:39.636
That is dy dt.

00:00:39.636 --> 00:00:44.000
Then the, then the speed is
going to be the magnitude

00:00:44.000 --> 00:00:47.238
of the sum of those two vectors.

00:00:47.238 --> 00:00:49.768
So, this right over here
the magnitude of this,

00:00:49.768 --> 00:00:51.441
of this vector right over here,

00:00:51.441 --> 00:00:52.563
is going to be the speed.

00:00:52.563 --> 00:00:54.353
Well, what's the magnitude of that?

00:00:54.353 --> 00:00:55.895
Well, the Pythagorean theorem tells us

00:00:55.895 --> 00:00:58.613
it's going to be the square root of

00:00:58.613 --> 00:01:01.550
your x component of velocity squared,

00:01:01.550 --> 00:01:03.697
so dx dt, the rate at which

00:01:03.697 --> 00:01:07.866
x is changing with
respect to time, squared.

00:01:07.866 --> 00:01:12.866
Plus your y component, dy dt, squared.

00:01:13.323 --> 00:01:15.726
This right here is the speed.

00:01:15.726 --> 00:01:17.221
And we need to figure out at what time

00:01:17.221 --> 00:01:19.053
is this thing equal to three?

00:01:19.053 --> 00:01:20.711
So let's figure that out.

00:01:20.711 --> 00:01:22.559
So the square root of,

00:01:22.559 --> 00:01:25.051
what's the x component of our velocity?

00:01:25.051 --> 00:01:26.131
Well, they told us over here,

00:01:26.131 --> 00:01:27.845
the x component of our velocity

00:01:27.845 --> 00:01:30.775
is cosine of t squared.

00:01:30.775 --> 00:01:35.605
So, cosine of t squared,

00:01:35.605 --> 00:01:37.866
we're gonna square that whole thing.

00:01:37.866 --> 00:01:41.551
And then plus the y
component of the velocity,

00:01:41.551 --> 00:01:44.322
the rate of change, the
rate at which y's changing

00:01:44.322 --> 00:01:45.613
with respect to time.

00:01:45.613 --> 00:01:47.400
That's e to the zero point five t,

00:01:47.400 --> 00:01:49.032
and we're going to square that.

00:01:49.032 --> 00:01:53.896
So plus e to the zero point five t,

00:01:53.896 --> 00:01:56.253
and we're going to square that.

00:01:56.253 --> 00:01:58.784
This right over here is
our expression for speed,

00:01:58.784 --> 00:02:00.293
as a function of time.

00:02:00.293 --> 00:02:01.269
And we still have to figure out,

00:02:01.269 --> 00:02:02.825
when does this thing,

00:02:02.825 --> 00:02:06.571
when does this thing equal nine?

00:02:06.571 --> 00:02:07.596
So there's a couple of ways,

00:02:07.596 --> 00:02:09.964
we could just subtract nine, or sorry

00:02:09.964 --> 00:02:11.601
when does this equal three?

00:02:11.601 --> 00:02:14.492
When does this equal three?

00:02:14.492 --> 00:02:17.151
And so we could try to, we
could just subtract three from

00:02:17.151 --> 00:02:20.495
both sides and input this into our solver,

00:02:20.495 --> 00:02:22.410
or we could begin to
simplify this a little bit,

00:02:22.410 --> 00:02:24.581
we could square both sides,

00:02:24.581 --> 00:02:28.972
and you would get cosine,
let me write it this way,

00:02:28.972 --> 00:02:33.775
you could get cosine of t squared, squared

00:02:35.125 --> 00:02:38.746
plus e to the zero point five
t, and then squaring that,

00:02:38.746 --> 00:02:40.742
well two times zero
point five is just one,

00:02:40.742 --> 00:02:43.041
so this is the same thing as e to the t,

00:02:43.041 --> 00:02:45.298
is equal to nine.

00:02:45.298 --> 00:02:47.144
And now we can subtract
nine from both sides,

00:02:47.144 --> 00:02:51.971
and we get cosine of t squared, squared,

00:02:51.971 --> 00:02:53.719
I could've written cosine
squared of t squared,

00:02:53.719 --> 00:02:55.671
but this makes it a little
bit clearer, I think.

00:02:55.671 --> 00:03:00.232
Plus e to the t minus
nine is equal to zero,

00:03:00.232 --> 00:03:02.391
and now once again, in
this part of the AP exam,

00:03:02.391 --> 00:03:03.657
we can use our calculators.

00:03:03.657 --> 00:03:07.115
So let's use our calculators to solve

00:03:07.115 --> 00:03:10.767
let's use it to solve for, in this case,

00:03:10.767 --> 00:03:14.470
t, but I'll do everything in terms of x.

00:03:14.470 --> 00:03:18.907
So, the equation, zero is equal to

00:03:18.907 --> 00:03:20.737
is equal to,

00:03:20.737 --> 00:03:22.267
let me just delete all of this actually,

00:03:22.267 --> 00:03:24.375
just to get it out of the way.

00:03:24.375 --> 00:03:26.856
Alright, is equal to cosine,

00:03:26.856 --> 00:03:28.574
and I'm gonna use x as my variable,

00:03:28.574 --> 00:03:33.380
cosine of x squared,

00:03:33.380 --> 00:03:34.918
close that parenthesis,

00:03:34.918 --> 00:03:37.330
and then I wanna square the cosine,

00:03:37.330 --> 00:03:38.635
the whole thing,

00:03:38.635 --> 00:03:41.700
plus e to the t.

00:03:41.700 --> 00:03:44.637
So second e to the,

00:03:44.637 --> 00:03:46.586
but my variable that I'm
gonna solve for is x,

00:03:46.586 --> 00:03:48.120
I'm just replacing all the t's with x

00:03:48.120 --> 00:03:50.059
just for inputting into the calculator,

00:03:50.059 --> 00:03:52.784
e to the x minus nine,

00:03:52.784 --> 00:03:56.106
minus nine is equal to zero,

00:03:56.106 --> 00:03:57.589
is equal to zero.

00:03:57.589 --> 00:03:59.830
We already have this set equal to zero,

00:03:59.830 --> 00:04:01.949
and so we click enter,

00:04:01.949 --> 00:04:04.234
and then we could,

00:04:04.234 --> 00:04:08.462
we could just use our previous
answer as our initial guess,

00:04:08.462 --> 00:04:10.834
and we click, we have to do
this little blue solve there,

00:04:10.834 --> 00:04:13.736
so I click alpha, solve,

00:04:13.736 --> 00:04:16.279
let the calculator munch
on it a little bit,

00:04:16.279 --> 00:04:18.647
and it gets t is equal to,

00:04:18.647 --> 00:04:20.900
or x is equal to, but this is really t,

00:04:20.900 --> 00:04:24.371
two point one nine six.

00:04:24.371 --> 00:04:27.382
So we get t is approximately

00:04:27.382 --> 00:04:30.332
two point one nine six.

00:04:30.332 --> 00:04:31.769
Did I type that in right?

00:04:31.769 --> 00:04:34.611
Two point one nine, yep
and then round that up.

00:04:34.611 --> 00:04:38.321
And we are all done.


2015 AP Calculus BC 2b

WEBVTT
Kind: captions
Language: en

00:00:00.110 --> 00:00:01.370
- [Voiceover] Part b.

00:00:01.370 --> 00:00:04.510
"For zero is less than t is less than one,

00:00:04.510 --> 00:00:07.160
"there is a point on the
curve at which the line

00:00:07.160 --> 00:00:10.940
"tangent to the curve has a slope of two."

00:00:10.940 --> 00:00:13.750
The line tangent to the curve

00:00:13.750 --> 00:00:15.580
has a slope of two.

00:00:15.580 --> 00:00:19.259
"At what time is the
object at that point?"

00:00:19.259 --> 00:00:22.310
So, the slope of the tangent line is two.

00:00:22.310 --> 00:00:24.940
That means that the rate of change of y

00:00:24.940 --> 00:00:28.135
with respect to x is equal to two.

00:00:28.135 --> 00:00:31.060
Well, they don't directly
give us the derivative of y

00:00:31.060 --> 00:00:34.880
with respect to x, but they
do give us the derivative of x

00:00:34.880 --> 00:00:35.880
with respect to t.

00:00:35.880 --> 00:00:38.200
That's the derivative
of x with respect to t.

00:00:38.200 --> 00:00:41.627
And they give us the derivative
of y with respect to t.

00:00:41.627 --> 00:00:44.140
The x component of the
velocity function is the rate

00:00:44.140 --> 00:00:46.000
of change of x with respect to time,

00:00:46.000 --> 00:00:48.490
and the y component of
the velocity function

00:00:48.490 --> 00:00:51.190
is the rate of change of
y with respect to time.

00:00:51.190 --> 00:00:53.370
And using those two, we can figure out

00:00:53.370 --> 00:00:56.918
the rate of change of y with respect to x.

00:00:56.918 --> 00:01:01.120
If you were to take the
derivative of y with respect to t

00:01:01.120 --> 00:01:05.520
and divide it by the derivative
of x with respect to t,

00:01:05.520 --> 00:01:08.234
derivative of x with respect to t,

00:01:08.234 --> 00:01:11.930
well, if you, for the sake of,

00:01:11.930 --> 00:01:13.400
I guess conceptually understanding it,

00:01:13.400 --> 00:01:16.630
if you view the differentials
the way that you would view

00:01:16.630 --> 00:01:18.330
traditional numbers and fractions,

00:01:18.330 --> 00:01:20.330
well, the dt's would cancel out

00:01:20.330 --> 00:01:24.460
and you'd be left with dy divided by dx.

00:01:24.460 --> 00:01:25.760
Or a little bit more formally,

00:01:25.760 --> 00:01:27.320
you could go to the
chain rule and you'd say,

00:01:27.320 --> 00:01:30.350
all right, the derivative
of y with respect to t

00:01:30.350 --> 00:01:33.800
is equal to the derivative
of y with respect to x

00:01:33.800 --> 00:01:37.280
times the derivative
of x with respect to t.

00:01:37.280 --> 00:01:40.460
This comes straight out of the chain rule.

00:01:40.460 --> 00:01:43.458
So this is the chain rule right over here.

00:01:43.458 --> 00:01:45.800
That is the chain rule.

00:01:45.800 --> 00:01:47.840
And then if you divide both
sides by the derivative

00:01:47.840 --> 00:01:50.420
of x with respect to
t, you're going to get

00:01:50.420 --> 00:01:53.134
that original expression right over here.

00:01:53.134 --> 00:01:55.479
Well, how is this useful?

00:01:55.479 --> 00:01:58.160
Well, we know what the derivative
of y with respect to t is.

00:01:58.160 --> 00:02:00.270
We know the derivative of
x with respect to t is.

00:02:00.270 --> 00:02:02.748
We know them as functions of t,

00:02:02.748 --> 00:02:04.900
and then we can set them equal to two

00:02:04.900 --> 00:02:07.210
and then use our
calculators to solve for t.

00:02:07.210 --> 00:02:08.334
So let's do that.

00:02:08.334 --> 00:02:10.970
The derivative of y with respect to t,

00:02:10.970 --> 00:02:13.230
that is, e to the point .5t.

00:02:13.230 --> 00:02:17.780
So we have e to the 0.5t

00:02:17.780 --> 00:02:20.300
and then we divide it
by the derivative of x

00:02:20.300 --> 00:02:22.900
with respect to t, so that's
going to be the x component

00:02:22.900 --> 00:02:24.390
of the velocity function.

00:02:24.390 --> 00:02:29.334
So cosine of t squared.

00:02:29.334 --> 00:02:31.140
And so this is the derivative of y

00:02:31.140 --> 00:02:33.720
with respect to x and
we need to figure out

00:02:33.720 --> 00:02:37.949
at what t does this equal to two.

00:02:37.949 --> 00:02:42.170
Or if we want to simplify this,

00:02:42.170 --> 00:02:44.200
and in our calculator,
we need to set this up

00:02:44.200 --> 00:02:45.990
so it's some expression,

00:02:45.990 --> 00:02:48.180
you know, some function of x

00:02:48.180 --> 00:02:50.220
is equal to zero.

00:02:50.220 --> 00:02:53.390
So let me rearrange this equation.

00:02:53.390 --> 00:02:57.060
So I have a bunch of things equaling zero.

00:02:57.060 --> 00:02:59.290
So let's see, I could just subtract two

00:02:59.290 --> 00:03:02.100
from both sides, or actually,

00:03:02.100 --> 00:03:04.880
what I could do is I
could multiply both sides

00:03:04.880 --> 00:03:06.520
times cosine of t squared.

00:03:06.520 --> 00:03:10.220
And so I'll have e to the 0.5t

00:03:10.220 --> 00:03:14.980
is equal to two, cosine of t squared.

00:03:14.980 --> 00:03:17.350
Then I could subtract
this from both sides,

00:03:17.350 --> 00:03:21.940
and I will get e to the 0.5t

00:03:21.940 --> 00:03:25.740
minus two, cosine of t squared

00:03:25.740 --> 00:03:27.338
is equal to zero.

00:03:27.338 --> 00:03:29.660
And now I could use the
solver on my calculator

00:03:29.660 --> 00:03:31.149
to figure this out.

00:03:31.149 --> 00:03:33.455
So let's get the calculator out,

00:03:33.455 --> 00:03:37.950
and let's go to Math.

00:03:37.950 --> 00:03:39.700
Whoops, let me make sure it's on.

00:03:39.700 --> 00:03:41.032
So, Math.

00:03:41.032 --> 00:03:42.790
Let me go all the way down

00:03:42.790 --> 00:03:45.720
to the solver.

00:03:45.720 --> 00:03:47.270
So, select that.

00:03:47.270 --> 00:03:49.740
My equation is zero is equal to,

00:03:49.740 --> 00:03:51.519
so I'm gonna say,

00:03:51.519 --> 00:03:55.060
e to the 0.5,

00:03:55.060 --> 00:03:56.480
and the variable that I'm gonna solve for,

00:03:56.480 --> 00:03:58.460
I'm gonna use x instead of t.

00:03:58.460 --> 00:04:00.220
The same thing, I'll get the same answer.

00:04:00.220 --> 00:04:04.545
e to the 0.5x.

00:04:04.545 --> 00:04:05.845
All right.

00:04:05.845 --> 00:04:09.472
And then I'm gonna have minus two

00:04:09.472 --> 00:04:11.120
times cosine

00:04:11.120 --> 00:04:14.761
of x squared

00:04:14.761 --> 00:04:17.690
is equal to zero.

00:04:17.690 --> 00:04:18.820
All right, so there you have it.

00:04:18.820 --> 00:04:22.520
Zero is equal to e to the 0.5x

00:04:22.520 --> 00:04:25.965
minus two, cosine of x squared.

00:04:25.965 --> 00:04:27.070
Click Enter.

00:04:27.070 --> 00:04:28.600
And then we put our initial guess.

00:04:28.600 --> 00:04:31.500
And they tell us that for
t is between zero and one.

00:04:31.500 --> 00:04:33.400
So maybe a good guess
would be right in between.

00:04:33.400 --> 00:04:35.020
So let's put .5 there.

00:04:35.020 --> 00:04:37.650
And then we press Alpha, at
least, on this calculator,

00:04:37.650 --> 00:04:39.430
and then you see that
little blue Solve there.

00:04:39.430 --> 00:04:41.340
That will actually solve it.

00:04:41.340 --> 00:04:43.560
Let it munch on it for a little bit.

00:04:43.560 --> 00:04:44.530
And I get

00:04:44.530 --> 00:04:48.830
t is equal to 0.840.

00:04:48.830 --> 00:04:51.350
0.840.

00:04:52.900 --> 00:04:57.900
t is approximately 0.840.

00:04:57.900 --> 00:05:01.100
And we are done.


2015 AP Calculus BC 2a

WEBVTT
Kind: captions
Language: en

00:00:00.270 --> 00:00:02.720
- [Voiceover] "At time t is
greater than or equal to zero,

00:00:02.720 --> 00:00:05.550
"a particle moving along
a curve in the xy-plane

00:00:05.550 --> 00:00:09.290
"has position x of t and y of t."

00:00:09.290 --> 00:00:11.460
So its coordinate is given
by the parametric function

00:00:11.460 --> 00:00:14.640
x of t, and y-coordinate by the
parametric function, y of t.

00:00:14.640 --> 00:00:17.990
"With velocity vector v of t is equal to,"

00:00:17.990 --> 00:00:20.090
and the x component of the velocity vector

00:00:20.090 --> 00:00:21.730
is cosine of t squared,

00:00:21.730 --> 00:00:23.570
and the y component of the velocity vector

00:00:23.570 --> 00:00:25.920
is e to the 0.5t.

00:00:25.920 --> 00:00:27.660
"At t equals one,

00:00:27.660 --> 00:00:32.198
"the particle is at
the point 3, comma, 5."

00:00:32.198 --> 00:00:34.200
Is at the point 3, comma, five.

00:00:34.200 --> 00:00:35.387
All right.

00:00:35.387 --> 00:00:39.467
"Find the x-coordinate of
the position of the particle

00:00:39.467 --> 00:00:43.683
"at time t is equal to two."

00:00:43.683 --> 00:00:45.709
All right, so how do we think about this?

00:00:45.709 --> 00:00:48.640
Well, you could view the
x-coordinate at time t equals two.

00:00:48.640 --> 00:00:52.600
So let's say, so we
could say x at time two,

00:00:52.600 --> 00:00:56.276
which they don't give that to us directly,

00:00:56.276 --> 00:01:01.270
but we could say that's
going to be x of one

00:01:01.270 --> 00:01:04.540
plus some change in x

00:01:04.540 --> 00:01:08.130
as we go from t equals
one to t equals two.

00:01:08.130 --> 00:01:10.218
But what is this going to be?

00:01:10.218 --> 00:01:12.920
Well, we know what the velocity is.

00:01:12.920 --> 00:01:15.500
And so the velocity,
especially the x component,

00:01:15.500 --> 00:01:17.180
and we can really focus on the x component

00:01:17.180 --> 00:01:18.740
for this first part
'cause we only wanna know

00:01:18.740 --> 00:01:21.472
the x-coordinate of the
position of the particle.

00:01:21.472 --> 00:01:26.010
Well, we know the x component of velocity

00:01:26.010 --> 00:01:27.160
as a function of t

00:01:27.160 --> 00:01:32.160
is cosine of t squared.

00:01:32.160 --> 00:01:35.000
And if you take your velocity
in a certain dimension

00:01:35.000 --> 00:01:38.737
and then multiply it times
a very small change in time,

00:01:38.737 --> 00:01:41.800
in a very small change in time, dt,

00:01:41.800 --> 00:01:44.450
this would give you your
very small change in x.

00:01:44.450 --> 00:01:46.610
If you multiply velocity
times change in time,

00:01:46.610 --> 00:01:50.092
it'll give you a displacement.

00:01:50.092 --> 00:01:53.000
But what we can do is we can
sum up all of the changes

00:01:53.000 --> 00:01:56.930
in time from t equals one to t equals two.

00:01:56.930 --> 00:01:58.855
Remember, this is the change in x

00:01:58.855 --> 00:02:02.510
from t equals one

00:02:02.510 --> 00:02:05.115
to t is equal to two.

00:02:05.115 --> 00:02:06.570
So what we have right over here,

00:02:06.570 --> 00:02:08.160
we can say that x of two,

00:02:08.160 --> 00:02:10.013
which is what we're trying to solve,

00:02:10.013 --> 00:02:11.860
is going to be x of one,

00:02:11.860 --> 00:02:14.160
and they give that at time equals one,

00:02:14.160 --> 00:02:16.600
the particle is at the
point three, comma, five.

00:02:16.600 --> 00:02:18.454
Its x-coordinate is three.

00:02:18.454 --> 00:02:20.950
So this right over here is three.

00:02:20.950 --> 00:02:23.930
And then our change in x from t equals one

00:02:23.930 --> 00:02:25.940
to t equals two is going
to be this integral.

00:02:25.940 --> 00:02:29.540
The integral from t
equals one to t equal two

00:02:29.540 --> 00:02:33.420
of cosine of t squared, dt.

00:02:33.420 --> 00:02:35.330
And just to make sure we
understand what's going on here,

00:02:35.330 --> 00:02:38.800
remember, how much are we
moving over a very small dt?

00:02:38.800 --> 00:02:41.000
Well, you take your
velocity in that dimension

00:02:41.000 --> 00:02:43.800
times dt, it'll give you a
displacement in that dimension,

00:02:43.800 --> 00:02:46.030
and then we sum 'em all
up from t equals one

00:02:46.030 --> 00:02:48.022
to t equals two.

00:02:48.022 --> 00:02:49.730
And in this part of the AP test,

00:02:49.730 --> 00:02:51.360
we're allowed to use calculators

00:02:51.360 --> 00:02:53.494
and so let's use one.

00:02:53.494 --> 00:02:54.902
All right.

00:02:54.902 --> 00:02:57.808
So there's my calculator.

00:02:57.808 --> 00:03:00.590
And I can evaluate.

00:03:00.590 --> 00:03:03.192
So let's see, I wanna evaluate three

00:03:03.192 --> 00:03:05.050
plus the definite integral.

00:03:05.050 --> 00:03:06.470
I click on Math,

00:03:06.470 --> 00:03:08.732
and then I can scroll down

00:03:08.732 --> 00:03:11.680
to function integral, right there.

00:03:11.680 --> 00:03:13.865
The definite integral of,

00:03:13.865 --> 00:03:15.790
and I make sure I'm in radian mode,

00:03:15.790 --> 00:03:18.172
that's what you should assume,

00:03:18.172 --> 00:03:19.900
unless they tell you otherwise.

00:03:19.900 --> 00:03:23.050
Cosine of t squared, now
I'll use x as my variable

00:03:23.050 --> 00:03:25.900
of integration, so I'll say cosine of x,

00:03:25.900 --> 00:03:28.707
cosine of x squared.

00:03:28.707 --> 00:03:31.370
And then my variable of integration is x,

00:03:31.370 --> 00:03:33.290
so I'm really integrating
of x squared, dx,

00:03:33.290 --> 00:03:35.280
but it'll give the same value,

00:03:35.280 --> 00:03:38.515
comma, from one

00:03:38.515 --> 00:03:40.903
until two,

00:03:40.903 --> 00:03:44.390
and now let the calculator
munch on it a little bit,

00:03:44.390 --> 00:03:49.207
and I get approximately 2.557.

00:03:49.207 --> 00:03:51.950
So this is approximately

00:03:51.950 --> 00:03:55.541
2.55,

00:03:55.541 --> 00:03:58.197
2.557.

00:03:58.197 --> 00:04:00.620
Let me make sure that I added the three.

00:04:00.620 --> 00:04:03.180
Yeah, three plus that definite integral

00:04:03.180 --> 00:04:04.040
from one to two.

00:04:04.040 --> 00:04:06.810
2.557.

00:04:06.810 --> 00:04:07.920
And I just rounded that.

00:04:07.920 --> 00:04:09.040
So there you go.


AP US history long essay example 3

WEBVTT
Kind: captions
Language: en

00:00:00.423 --> 00:00:02.753
- [Voiceover] This is the
third video in a series

00:00:02.753 --> 00:00:05.473
about tackling the Long Essay Question

00:00:05.473 --> 00:00:09.129
on the AP U.S. History exam.

00:00:09.129 --> 00:00:10.967
Now in the last video we were kind of

00:00:10.967 --> 00:00:14.235
weighing the evidence about the New Deal.

00:00:14.235 --> 00:00:16.859
Considering the ways in
which the government,

00:00:16.859 --> 00:00:20.236
the economy and race, class and gender,

00:00:20.236 --> 00:00:22.186
may have been either conservative during

00:00:22.186 --> 00:00:25.158
the New Deal or radical.

00:00:25.158 --> 00:00:27.003
And we came up with some good evidence

00:00:27.003 --> 00:00:28.930
to support either side.

00:00:28.930 --> 00:00:32.228
And now it's up to me to choose which way

00:00:32.228 --> 00:00:33.412
I'm going to go.

00:00:33.412 --> 00:00:35.293
So I think I'm actually
going to choose the

00:00:35.293 --> 00:00:37.956
conservative side here
because I think it's

00:00:37.956 --> 00:00:40.133
just a tiny bit more convincing.

00:00:40.133 --> 00:00:41.895
And if you're wondering why I think it's

00:00:41.895 --> 00:00:43.325
a tiny bit more convincing,

00:00:43.325 --> 00:00:46.454
I think the part about
Eleanor Roosevelt being

00:00:46.454 --> 00:00:51.009
an advocate for race and
Frances Perkins being a

00:00:51.009 --> 00:00:54.123
visible woman in a government cabinet,

00:00:54.123 --> 00:00:57.079
they to me don't seem like
maybe substantive changes.

00:00:57.079 --> 00:00:58.827
They seem maybe like they're
a little bit more like

00:00:58.827 --> 00:01:01.496
figure heads like things
went well for this one person

00:01:01.496 --> 00:01:03.469
or maybe just a tiny group of people,

00:01:03.469 --> 00:01:05.581
but in the grand scheme
of things it wasn't

00:01:05.581 --> 00:01:07.067
that big of a change.

00:01:07.067 --> 00:01:09.110
Anyway, you may feel different from me.

00:01:09.110 --> 00:01:10.844
You may decide that you would have written

00:01:10.844 --> 00:01:13.793
an article about how
radical the New Deal was,

00:01:13.793 --> 00:01:17.369
but I'm going to do an example
of a conservative argument

00:01:17.369 --> 00:01:18.948
about the New Deal.

00:01:18.948 --> 00:01:22.617
Now our task here is take
these themes that we've noticed

00:01:22.617 --> 00:01:25.659
and the evidence that
we have assembled about

00:01:25.659 --> 00:01:28.945
these themes and turn it
into a five paragraph essay.

00:01:28.945 --> 00:01:33.065
And that essay is going
to include an introduction

00:01:33.065 --> 00:01:34.794
with a thesis statement

00:01:42.126 --> 00:01:47.126
and a paragraph that
explores one of these themes,

00:01:47.419 --> 00:01:52.237
and I think I might start
with the government theme.

00:01:55.377 --> 00:01:57.853
A paragraph that explores another one.

00:01:57.853 --> 00:02:01.475
I think I'll go with the economic theme.

00:02:01.475 --> 00:02:04.480
And because we're talking
about economics here,

00:02:04.480 --> 00:02:07.895
I actually think we're going
to roll class into that one

00:02:07.895 --> 00:02:09.706
because it's about people who are rich

00:02:09.706 --> 00:02:10.989
and people who are poor.

00:02:10.989 --> 00:02:14.418
And lastly I want to
talk about the effect on

00:02:14.418 --> 00:02:15.951
woman and minorities.

00:02:15.951 --> 00:02:18.044
So that's our last theme.

00:02:23.458 --> 00:02:26.321
And then we'll finish it
all up with a conclusion

00:02:26.321 --> 00:02:29.724
where we talk about how right we were.

00:02:29.724 --> 00:02:31.179
All right. Are you ready for this?

00:02:31.179 --> 00:02:33.083
So let's start with our thesis statement.

00:02:33.083 --> 00:02:36.079
So we've decided that we
think that the New Deal

00:02:36.079 --> 00:02:37.890
was ultimately conservative.

00:02:37.890 --> 00:02:40.165
So we could start our
introduction by saying,

00:02:40.165 --> 00:02:45.165
"Although the New Deal
seems really radical

00:02:48.547 --> 00:02:53.547
"because it brought on a
new relationship between

00:02:54.275 --> 00:02:58.505
"the federal government
and the economy and

00:02:58.505 --> 00:03:01.059
"there were so many new programs.

00:03:01.059 --> 00:03:06.059
"In fact, it was actually
essentially conservative.

00:03:09.625 --> 00:03:14.625
"And it was conservative
because it did not really change

00:03:18.496 --> 00:03:23.496
"the essence of American government,

00:03:23.809 --> 00:03:27.264
"the America economy,

00:03:27.264 --> 00:03:31.822
"or the lives of ordinary
Americans including

00:03:31.822 --> 00:03:36.157
"women and minorities."

00:03:36.157 --> 00:03:37.612
All right. I think that's pretty good.

00:03:37.612 --> 00:03:39.214
So let's move into our first paragraph

00:03:39.214 --> 00:03:40.143
about the government.

00:03:40.143 --> 00:03:42.465
Now with our thesis
statement here we've kind of

00:03:42.465 --> 00:03:45.948
set up a pattern for
ourselves to say the things

00:03:45.948 --> 00:03:48.827
that seem radical,

00:03:48.827 --> 00:03:51.939
but really are conservative.

00:03:51.939 --> 00:03:54.843
And we're going to do that
in each of these paragraphs.

00:03:59.323 --> 00:04:04.210
So we can say what seems radical.

00:04:04.210 --> 00:04:08.343
Specific examples of things
that might seem radical.

00:04:08.343 --> 00:04:10.758
And it's in giving these
specific examples where

00:04:10.758 --> 00:04:13.601
you're going to really
wow the reader by showing

00:04:13.601 --> 00:04:15.203
the breadth of your knowledge.

00:04:15.203 --> 00:04:18.397
So it might seem radical that there's

00:04:18.397 --> 00:04:23.397
a whole new government
bureaucracy around the economy.

00:04:26.431 --> 00:04:29.726
It might even seem radical
that there are women

00:04:29.726 --> 00:04:32.344
in cabinet positions.

00:04:36.409 --> 00:04:39.621
It might even seem radical
that FDR had this kind of

00:04:39.621 --> 00:04:42.964
first 100 days thing where he said,

00:04:42.964 --> 00:04:46.122
"I'm going to achieve so
much in my first 100 days.

00:04:46.122 --> 00:04:47.887
"I'm going to hit the ground running."

00:04:47.887 --> 00:04:50.348
So that seems like a very
different form of government

00:04:50.348 --> 00:04:52.750
than what you might have had in the 1920s.

00:04:52.750 --> 00:04:56.813
In fact you can even
say that FDR is such a

00:04:56.813 --> 00:04:59.251
active President, right?

00:04:59.251 --> 00:05:03.338
Mean he is bringing a force of personality

00:05:03.338 --> 00:05:07.587
and also governing
ability to this role that

00:05:07.587 --> 00:05:10.308
really hadn't been established that much

00:05:10.308 --> 00:05:12.430
except for, you know, a few people say

00:05:12.430 --> 00:05:14.520
Lincoln or Teddy Roosevelt.

00:05:14.520 --> 00:05:17.005
So it does seem like
he's changing the office

00:05:17.005 --> 00:05:18.895
of President quite a bit,

00:05:18.895 --> 00:05:22.689
but in fact it's really
conservative because they're not

00:05:22.689 --> 00:05:25.359
throwing the baby out
with the bathwater, right.

00:05:25.359 --> 00:05:29.328
They're saying that essentially
the democratic system works,

00:05:29.328 --> 00:05:31.743
and you can even compare
the American government

00:05:31.743 --> 00:05:34.413
with governments in other
parts of the world right now.

00:05:34.413 --> 00:05:38.894
I mean think about Germany
where this economic depression

00:05:38.894 --> 00:05:40.752
leads to the rise of Hitler.

00:05:40.752 --> 00:05:44.096
So the United States could
conceivably have become

00:05:44.096 --> 00:05:46.486
a fascist government in this time period,

00:05:46.486 --> 00:05:47.570
but they did not.

00:05:47.570 --> 00:05:49.515
All right. Let's talk about economics and

00:05:49.515 --> 00:05:51.791
the class system in the United States.

00:05:51.791 --> 00:05:54.716
So first let's think about
things that might seem radical.

00:05:54.716 --> 00:05:58.989
Well it's radical that the
government puts together

00:05:58.989 --> 00:06:03.989
all of these new economic
initiatives like social security,

00:06:05.792 --> 00:06:10.436
or the federal deposit
insurance corporation, the FDIC,

00:06:10.436 --> 00:06:14.012
which are new regulations
about the banking and

00:06:14.012 --> 00:06:16.311
economic system that are kind of designed

00:06:16.311 --> 00:06:20.444
to make sure that ordinary
people don't lose everything

00:06:20.444 --> 00:06:23.718
if the banking system
crashes or maybe if they're

00:06:23.718 --> 00:06:26.179
in old age and lose their job.

00:06:26.179 --> 00:06:30.920
And there's also a new
sense that being wealthy is

00:06:30.920 --> 00:06:34.245
not something that's
necessarily deserved, right.

00:06:34.245 --> 00:06:37.063
That there's an element
of chance that goes

00:06:37.063 --> 00:06:39.013
into your economic status.

00:06:39.013 --> 00:06:42.891
So I think it really
tears down a long standing

00:06:42.891 --> 00:06:47.891
stereotype in the United
States that the wealthy

00:06:47.918 --> 00:06:51.960
deserve to be wealthy and
the poor deserve to be poor,

00:06:51.960 --> 00:06:56.593
this is a very popular
notion in the gilded age.

00:06:56.593 --> 00:06:58.280
And instead says,

00:06:58.280 --> 00:07:00.811
"You know, sometimes bad
things happen to good people."

00:07:00.811 --> 00:07:03.481
It's not everyone's fault
if there's a depression

00:07:03.481 --> 00:07:05.385
because we couldn't have stopped it.

00:07:05.385 --> 00:07:08.205
Now we can to talk about how
it was really conservative.

00:07:08.205 --> 00:07:10.524
And what we're saying here is that the

00:07:10.524 --> 00:07:14.966
capitalist system itself
didn't fall apart.

00:07:14.966 --> 00:07:19.588
If you compare the New
Deal to a true revolution,

00:07:19.588 --> 00:07:22.119
like for example the French Revolution,

00:07:22.119 --> 00:07:24.162
or the Russian Revolution,

00:07:24.162 --> 00:07:25.996
and these are examples where the poor

00:07:25.996 --> 00:07:28.736
rose up against the rich
and were cutting people's

00:07:28.736 --> 00:07:30.919
heads off and taking their land.

00:07:30.919 --> 00:07:33.520
Then the New Deal seems very conservative.

00:07:33.520 --> 00:07:34.286
In fact,

00:07:34.286 --> 00:07:36.422
what most of these New Deal programs

00:07:36.422 --> 00:07:39.952
are trying to do is not
to demolish capitalism,

00:07:39.952 --> 00:07:41.809
but to fix capitalism.

00:07:41.809 --> 00:07:45.836
So they accept the basic
premise that capitalism is good.

00:07:45.836 --> 00:07:48.204
And that certainly wasn't the
case in many other countries

00:07:48.204 --> 00:07:49.296
in the time period.

00:07:49.296 --> 00:07:50.874
Okay, last paragraph.

00:07:50.874 --> 00:07:53.313
So again we're looking
at things that seem like

00:07:53.313 --> 00:07:54.404
they might be radical.

00:07:54.404 --> 00:07:55.263
And you could say,

00:07:55.263 --> 00:08:00.263
"It seems like Frances
Perkins and Eleanor Roosevelt

00:08:01.811 --> 00:08:06.811
"are women that have
established a real presence

00:08:07.407 --> 00:08:10.124
"in the government."

00:08:10.124 --> 00:08:11.587
And you could say that,

00:08:11.587 --> 00:08:16.388
"New Deal programs did
employ many African Americans

00:08:16.388 --> 00:08:19.105
"and at the national
level were not intended

00:08:19.105 --> 00:08:21.906
"to be discriminatory."

00:08:21.906 --> 00:08:23.534
But you could say,

00:08:23.534 --> 00:08:27.946
"At the local level administrators
are often preventing

00:08:27.946 --> 00:08:30.941
"African Americans and other
minorities from getting jobs."

00:08:30.941 --> 00:08:34.238
And you could also say that,
"A lot of the New Deal programs

00:08:34.238 --> 00:08:37.907
"were really definitely intended for men."

00:08:37.907 --> 00:08:40.252
And you could, for example, say,

00:08:40.252 --> 00:08:45.252
"The Civilian Conservation
Core was a program only

00:08:45.268 --> 00:08:46.638
"for young men."

00:08:46.638 --> 00:08:48.588
So women are often
booted out of these jobs

00:08:48.588 --> 00:08:51.444
or they're not even
actually eligible for them

00:08:51.444 --> 00:08:52.679
in the first place.

00:08:52.679 --> 00:08:55.372
So even though the New
Deal is supposed to be

00:08:55.372 --> 00:08:58.530
this great economic turnaround
in the United States,

00:08:58.530 --> 00:09:01.270
it really doesn't change
the status of women

00:09:01.270 --> 00:09:03.502
and minorities much at all.

00:09:03.502 --> 00:09:05.040
Okay, time to conclude.

00:09:05.040 --> 00:09:07.037
So I think we can pretty much just sum up

00:09:07.037 --> 00:09:08.476
what we've said here.

00:09:08.476 --> 00:09:12.076
That there are a lot of things
that look really radical

00:09:12.076 --> 00:09:13.260
about the New Deal,

00:09:13.260 --> 00:09:17.061
but in the end it doesn't
actually change that much

00:09:17.061 --> 00:09:20.041
about the basic assumptions
and basic structure

00:09:20.041 --> 00:09:22.503
of the American society and economy.

00:09:22.503 --> 00:09:24.031
And you might even mention that it's not

00:09:24.031 --> 00:09:26.910
going to be for another 20 or 30 years

00:09:26.910 --> 00:09:30.114
that things like this change
for women and minorities.

00:09:30.114 --> 00:09:33.958
And even during the 1940s things,
things kind off go back to

00:09:33.958 --> 00:09:36.547
the status quo before the
great depression, right.

00:09:36.547 --> 00:09:39.291
It's this moment during the New Deal

00:09:39.291 --> 00:09:42.240
where there are a lot of
government experiments

00:09:42.240 --> 00:09:45.468
about how to reorganize American society

00:09:45.468 --> 00:09:47.999
and reorganize the American economy,

00:09:47.999 --> 00:09:51.249
but by 1940 things kind
of go back to the way

00:09:51.249 --> 00:09:52.447
that they had been.

00:09:52.447 --> 00:09:55.041
They're only a few things
that still remain with us

00:09:55.041 --> 00:09:56.922
from the New Deal and I think those things

00:09:56.922 --> 00:10:01.078
are important like the
FDIC, social security,

00:10:01.078 --> 00:10:03.888
and the idea of an
interventionist government

00:10:03.888 --> 00:10:05.049
in the first place.

00:10:05.049 --> 00:10:08.058
But from the 1920s to the 1940s,

00:10:08.058 --> 00:10:10.452
there's not a gigantic revolution,

00:10:10.452 --> 00:10:13.997
an American Democracy, capitalism,

00:10:13.997 --> 00:10:15.516
or social structure.

00:10:15.516 --> 00:10:17.490
Things continue the way that they were

00:10:17.490 --> 00:10:20.416
and that's why the New Deal
is essentially conservative.

00:10:20.416 --> 00:10:22.469
Okay, well I hope this
example helped you with a

00:10:22.469 --> 00:10:26.950
Long Essay portion of
the AP U.S. History exam

00:10:26.950 --> 00:10:28.309
and good luck.


AP US history long essay example 2

WEBVTT
Kind: captions
Language: en

00:00:00.214 --> 00:00:02.568
- [Voiceover] We're talking
about the long essay section

00:00:02.568 --> 00:00:05.598
on the AP US History exam.

00:00:05.598 --> 00:00:07.421
In the first video on this essay,

00:00:07.421 --> 00:00:10.335
we talked about general strategy

00:00:10.335 --> 00:00:12.061
for how to approach the essay.

00:00:12.061 --> 00:00:14.023
You've got 35 minutes to write it.

00:00:14.023 --> 00:00:15.462
So, I recommend you spend

00:00:15.462 --> 00:00:17.214
5-10 minutes planning,

00:00:17.214 --> 00:00:19.898
and 25-30 minutes writing.

00:00:19.898 --> 00:00:22.266
The question we've decided to answer is

00:00:22.266 --> 00:00:24.437
"Some historians have argued"

00:00:24.437 --> 00:00:26.016
"that the New Deal was ultimately"

00:00:26.016 --> 00:00:27.676
"conservative in nature."

00:00:27.676 --> 00:00:31.566
"Support, modify, or refute
this interpretation,"

00:00:31.566 --> 00:00:33.563
"providing specific evidence"

00:00:33.563 --> 00:00:35.258
"to justify your answer."

00:00:35.258 --> 00:00:36.789
So, we've come to the conclusion that

00:00:36.789 --> 00:00:39.530
there are three different ways we could go

00:00:39.530 --> 00:00:41.144
with answering this question.

00:00:41.144 --> 00:00:42.177
We could say,

00:00:42.177 --> 00:00:43.744
yes we think that the New Deal

00:00:43.744 --> 00:00:45.544
was ultimately conservative.

00:00:45.544 --> 00:00:46.763
We could say,

00:00:46.763 --> 00:00:49.689
no, actually the New
Deal was quite radical.

00:00:49.689 --> 00:00:53.086
Or, we could say it was both or neither.

00:00:53.086 --> 00:00:54.306
Somewhere in between.

00:00:54.306 --> 00:00:56.582
So, we then took the opportunity to just

00:00:56.582 --> 00:01:00.366
brainstorm things that we might bring up

00:01:00.366 --> 00:01:01.655
in an essay like that.

00:01:01.655 --> 00:01:04.488
What kind of facts are
related to the New Deal?

00:01:04.488 --> 00:01:07.913
We recall that the New Deal
was this series of programs

00:01:07.913 --> 00:01:11.129
implemented by President
Franklin Delano Roosevelt

00:01:11.129 --> 00:01:12.336
and his administration,

00:01:12.336 --> 00:01:15.088
to try to combat the Great Depression.

00:01:15.088 --> 00:01:18.246
It contained a real
alphabet soup of agencies

00:01:18.246 --> 00:01:20.173
which aimed at trying to

00:01:20.173 --> 00:01:22.239
get work to Americans.

00:01:22.239 --> 00:01:24.353
To help Americans who were struggling.

00:01:24.353 --> 00:01:26.315
And, also to try to make sure

00:01:26.315 --> 00:01:28.419
that something like this
never happened again.

00:01:28.419 --> 00:01:29.905
But, we noted that

00:01:29.905 --> 00:01:33.226
the New Deal ultimately
didn't really work.

00:01:34.196 --> 00:01:35.967
Partly because the Supreme Court

00:01:35.967 --> 00:01:38.349
rolled back some of its agencies

00:01:38.349 --> 00:01:40.010
as being unconstitutional.

00:01:40.010 --> 00:01:41.832
And partly because,

00:01:41.832 --> 00:01:44.001
it was actually World War II

00:01:44.001 --> 00:01:45.044
that got the United States

00:01:45.044 --> 00:01:46.659
out of the Great Depression.

00:01:46.659 --> 00:01:48.958
Let's take a minute an just pin-point

00:01:48.958 --> 00:01:50.827
some of the themes that have come up

00:01:50.827 --> 00:01:52.708
as we've brainstormed these possible

00:01:52.708 --> 00:01:53.997
pieces of evidence.

00:01:53.997 --> 00:01:56.713
It seems like we definitely
want to talk about

00:01:56.713 --> 00:02:00.080
the system of government, in general.

00:02:05.470 --> 00:02:07.512
And, definitely the economy.

00:02:07.512 --> 00:02:11.596
The economy is really the
heart of the Great Depression.

00:02:11.596 --> 00:02:13.021
What else can we think about?

00:02:13.021 --> 00:02:14.790
Well, as historians,

00:02:14.790 --> 00:02:16.450
we're always interested

00:02:16.450 --> 00:02:20.426
in questions of race and class,

00:02:20.426 --> 00:02:22.394
and gender.

00:02:25.058 --> 00:02:26.359
We're always wondering

00:02:26.359 --> 00:02:29.620
how did things affect
people who were White

00:02:29.620 --> 00:02:31.630
differently than people who were Black?

00:02:31.630 --> 00:02:33.116
How did it affect rich people

00:02:33.116 --> 00:02:34.776
differently than poor people?

00:02:34.776 --> 00:02:36.853
Or, women differently than men?

00:02:36.853 --> 00:02:39.524
It's just a really useful
way of thinking about

00:02:39.524 --> 00:02:41.997
how benefits in American society

00:02:41.997 --> 00:02:44.900
might not necessarily accrue to everyone.

00:02:44.900 --> 00:02:46.920
Okay, so these are some possible themes

00:02:46.920 --> 00:02:48.090
we can cover.

00:02:48.090 --> 00:02:49.634
Now, let's ask ourselves,

00:02:49.634 --> 00:02:52.455
whether in each of these themes,

00:02:52.455 --> 00:02:54.440
the New Deal was something that was

00:02:54.440 --> 00:02:57.505
radical or something
that was conservative?

00:03:03.225 --> 00:03:04.423
Okay, government.

00:03:04.423 --> 00:03:08.485
Was government, in general, radical?

00:03:08.485 --> 00:03:11.295
Or, was it conservative
in this time period?

00:03:11.295 --> 00:03:13.338
Well, I think there's a
good argument to be made

00:03:13.338 --> 00:03:15.045
that government was conservative

00:03:15.045 --> 00:03:16.624
in this time period.

00:03:16.624 --> 00:03:18.876
Because the United States didn't give up

00:03:18.876 --> 00:03:20.467
the democratic system.

00:03:20.467 --> 00:03:22.556
Many nations in the world did

00:03:22.556 --> 00:03:23.975
in this time period.

00:03:23.975 --> 00:03:26.578
Think about Germany, which became Fascist

00:03:26.578 --> 00:03:28.052
in this time period.

00:03:28.052 --> 00:03:30.105
So, there's still a commitment

00:03:30.105 --> 00:03:32.266
in the New Deal to keeping

00:03:32.266 --> 00:03:35.146
the governmental system
of democracy alive.

00:03:35.146 --> 00:03:36.841
Even though the economy has tanked,

00:03:36.841 --> 00:03:37.874
no one has said,

00:03:37.874 --> 00:03:40.939
"Well, this is a clear example
that democracy doesn't work."

00:03:40.939 --> 00:03:42.948
"So, let's try being Fascist."

00:03:42.948 --> 00:03:45.432
You could also say that
there is a radical change

00:03:45.432 --> 00:03:47.208
in government in this time period.

00:03:47.208 --> 00:03:50.064
Because, the government
is now taking on roles

00:03:50.064 --> 00:03:52.398
it has never taken on before.

00:03:52.398 --> 00:03:54.624
There is just a completely new level

00:03:54.624 --> 00:03:57.561
of intervention in the economy

00:03:57.561 --> 00:03:59.837
by the government that you could say

00:03:59.837 --> 00:04:02.031
is completely radical.

00:04:02.031 --> 00:04:03.691
All right. How about the economy?

00:04:03.691 --> 00:04:05.839
Well, I think there's a good
argument to be made that

00:04:05.839 --> 00:04:08.962
the New Deal was
conservative in the economy.

00:04:08.962 --> 00:04:12.503
Because, the United States
didn't give up capitalism.

00:04:13.503 --> 00:04:16.992
Just like the United
States decided that they

00:04:16.992 --> 00:04:18.734
weren't going to give up democracy,

00:04:18.734 --> 00:04:20.288
they weren't going to give up

00:04:20.288 --> 00:04:22.983
the system of capitalism itself.

00:04:22.983 --> 00:04:25.421
The New Deal instead, with things like,

00:04:25.421 --> 00:04:28.869
the NRA, or maybe social security,

00:04:28.869 --> 00:04:32.886
was instead designed
to sure up capitalism.

00:04:32.886 --> 00:04:35.369
To solve the problems of capitalism.

00:04:35.369 --> 00:04:37.691
Instead of maybe going
towards a completely

00:04:37.691 --> 00:04:39.156
government-run economy.

00:04:39.156 --> 00:04:41.055
Or, a completely people-led economy

00:04:41.055 --> 00:04:42.589
like in Communism.

00:04:42.589 --> 00:04:44.048
But, you could also say that the economy

00:04:44.048 --> 00:04:46.311
in this time period is really radical.

00:04:46.311 --> 00:04:48.402
Because again, there's this massive

00:04:48.402 --> 00:04:50.097
government intervention.

00:04:50.097 --> 00:04:52.174
There's a complete re-write

00:04:52.174 --> 00:04:54.915
of how the United States thinks about

00:04:54.915 --> 00:04:57.806
what the role of government
in the economy is.

00:04:57.806 --> 00:04:59.884
Okay, how about race?

00:04:59.884 --> 00:05:02.843
I think it's pretty easy to argue that

00:05:02.843 --> 00:05:04.215
the New Deal was conservative

00:05:04.215 --> 00:05:05.689
in terms of race.

00:05:05.689 --> 00:05:07.500
Because very few people

00:05:07.500 --> 00:05:11.030
think of the 1930s as
this major turning-point

00:05:11.030 --> 00:05:13.047
for civil rights for African-Americans,

00:05:13.047 --> 00:05:14.532
or any other group.

00:05:14.532 --> 00:05:16.112
In most cases,

00:05:16.112 --> 00:05:19.442
the economic pressure
of the Great Depression

00:05:19.442 --> 00:05:22.707
meant that many people who are minorities,

00:05:22.707 --> 00:05:25.040
many women actually lost their jobs

00:05:25.040 --> 00:05:27.490
because of a racist idea that White men

00:05:27.490 --> 00:05:29.661
were more deserving of those jobs.

00:05:29.661 --> 00:05:31.004
So, you might say that,

00:05:31.004 --> 00:05:34.289
the Civil Rights Movement
doesn't happen until later.

00:05:39.199 --> 00:05:42.423
You could also talk about the job loss.

00:05:43.794 --> 00:05:45.763
On the flip side, you might talk about

00:05:45.763 --> 00:05:49.304
the opportunity that the
Great Depression gave

00:05:49.304 --> 00:05:52.892
to talk about real economic disparities

00:05:52.892 --> 00:05:55.258
between Whites and other races.

00:05:55.258 --> 00:05:56.398
You might even say

00:05:56.398 --> 00:05:59.382
Eleanor Roosevelt in this time period

00:06:00.902 --> 00:06:04.369
was an essential

00:06:05.419 --> 00:06:07.108
advocate for civil rights.

00:06:07.108 --> 00:06:09.453
Especially, making sure
that the benefits of

00:06:09.453 --> 00:06:11.113
the New Deal trickled down

00:06:11.113 --> 00:06:13.421
in whatever way they could to minorities.

00:06:13.421 --> 00:06:15.380
And that the New Deal itself

00:06:15.380 --> 00:06:20.293
was not intended to separate
African-Americans and Whites

00:06:20.293 --> 00:06:22.500
in jobs, in its benefits.

00:06:22.500 --> 00:06:25.764
It was mostly administrators
at the local level

00:06:25.764 --> 00:06:28.260
who might have prevented African-Americans

00:06:28.260 --> 00:06:30.466
from reaping those benefits.

00:06:30.466 --> 00:06:32.068
Okay, what about class?

00:06:32.068 --> 00:06:33.838
I think this is a really important one

00:06:33.838 --> 00:06:36.695
because the New Deal is
all about the relationship

00:06:36.695 --> 00:06:38.332
between the rich and the poor.

00:06:38.332 --> 00:06:40.460
I think one thing that the New Deal does

00:06:40.460 --> 00:06:43.083
that is very revolutionary,

00:06:43.083 --> 00:06:45.196
I know I'm flipping the order here,

00:06:45.196 --> 00:06:49.028
is it really makes people
question the idea that

00:06:49.028 --> 00:06:50.966
wealth is earned

00:06:50.966 --> 00:06:55.947
completely without relationship
to one's status in life.

00:06:55.947 --> 00:06:59.314
Right. In the period of the Gilded Age,

00:06:59.314 --> 00:07:01.334
many people said things like,

00:07:01.334 --> 00:07:04.922
"Oh well, the wealthy
people, the White people,"

00:07:04.922 --> 00:07:07.581
"They are in a better position in life"

00:07:07.581 --> 00:07:09.461
"because they're more deserving."

00:07:09.461 --> 00:07:10.588
"They've worked harder."

00:07:10.588 --> 00:07:13.208
"They've may even be racially superior."

00:07:13.208 --> 00:07:14.923
According to the logic of the time.

00:07:14.923 --> 00:07:16.572
And then, the Great Depression

00:07:16.572 --> 00:07:18.406
which affects so many people

00:07:18.406 --> 00:07:21.936
really makes people
re-think this idea that

00:07:21.936 --> 00:07:26.839
wealth and status are connected
to one's personal worth.

00:07:26.839 --> 00:07:30.798
So you can say it really
up-ends this idea of

00:07:30.798 --> 00:07:33.178
social Darwinism that

00:07:33.178 --> 00:07:36.209
the fittest, the best in society

00:07:36.209 --> 00:07:38.786
are the ones who are prospering.

00:07:38.786 --> 00:07:40.422
But you can also say that

00:07:40.422 --> 00:07:41.886
in terms of class,

00:07:41.886 --> 00:07:44.661
once again, the New Deal was nothing like

00:07:44.661 --> 00:07:46.669
the revolution in Russia.

00:07:46.669 --> 00:07:49.617
There was no massive
redistribution of land.

00:07:49.617 --> 00:07:52.799
There wasn't this great
sense of class consciousness

00:07:52.799 --> 00:07:54.402
and workers uprising.

00:07:54.402 --> 00:07:56.175
Instead, it pretty much

00:07:56.175 --> 00:07:59.321
continued the patterns of social classes

00:07:59.321 --> 00:08:01.039
that existed before.

00:08:07.749 --> 00:08:09.689
In therms of women's
lives in the New Deal,

00:08:09.689 --> 00:08:11.738
you might say that

00:08:11.738 --> 00:08:14.437
things for women might
even have been worse

00:08:14.437 --> 00:08:17.966
in this time period than in the 1920s.

00:08:17.966 --> 00:08:20.834
Because again, as jobs contracted,

00:08:20.834 --> 00:08:23.748
those jobs were often
reserved for White men.

00:08:23.748 --> 00:08:25.583
In fact, some of these programs

00:08:25.583 --> 00:08:27.603
like the Civilian Conservation Corps

00:08:27.603 --> 00:08:29.252
were only for men.

00:08:29.252 --> 00:08:31.585
Only for people who were
considered bread-winners.

00:08:31.585 --> 00:08:33.002
On the radical side,

00:08:33.002 --> 00:08:34.035
you could say that

00:08:34.035 --> 00:08:36.868
the New Deal opened up many new positions

00:08:36.868 --> 00:08:38.608
for women in the federal government.

00:08:38.608 --> 00:08:41.499
For example, Franklin Delano Roosevelt

00:08:41.499 --> 00:08:43.172
appointed Francis Perkins,

00:08:43.172 --> 00:08:46.678
the first ever cabinet
secretary who was a woman.

00:08:47.778 --> 00:08:49.139
You might also even talk about

00:08:49.139 --> 00:08:51.136
Eleanor Roosevelt and her own prominence.

00:08:51.136 --> 00:08:54.387
She really transformed the
position of First Lady.

00:08:54.387 --> 00:08:56.686
Which is something that
is going to be important

00:08:56.686 --> 00:08:59.054
throughout the rest of the 20th century.

00:08:59.054 --> 00:09:00.970
You may be noticing here that

00:09:00.970 --> 00:09:02.793
there are good arguements

00:09:02.793 --> 00:09:05.289
for going either way.

00:09:05.289 --> 00:09:06.705
And the fact is,

00:09:06.705 --> 00:09:08.423
either way you argue this

00:09:08.423 --> 00:09:11.872
or even if you choose to
go this route of modifying

00:09:11.872 --> 00:09:16.125
or saying either or both,
radical and conservative.

00:09:16.125 --> 00:09:17.422
They're both right.

00:09:17.422 --> 00:09:19.095
So, at this point, you just have to decide

00:09:19.095 --> 00:09:20.685
which way you want to write about,

00:09:20.685 --> 00:09:23.797
and then marshal your
evidence for your essay.

00:09:23.797 --> 00:09:26.245
And, we'll get to that in the next video.


AP US history long essay example 1

WEBVTT
Kind: captions
Language: en

00:00:00.283 --> 00:00:01.559
- [Voiceover] Okay, this video is about

00:00:01.559 --> 00:00:05.786
the long essay section on
the AP U.S. History exam.

00:00:05.786 --> 00:00:07.597
Now you might also have heard this called

00:00:07.597 --> 00:00:11.102
the free response question or FRQ.

00:00:11.102 --> 00:00:14.300
I think it is officially
called the long essay question,

00:00:14.300 --> 00:00:16.413
so that's what we're
gonna go with for now.

00:00:16.413 --> 00:00:19.619
Now this is the last essay
that you'll be writing

00:00:19.619 --> 00:00:21.499
on the AP exam,

00:00:21.499 --> 00:00:24.356
and you get 35 minutes to do it,

00:00:24.356 --> 00:00:27.839
which is considerably
shorter than the DBQ section,

00:00:27.839 --> 00:00:29.371
but the nice part about this is that

00:00:29.371 --> 00:00:31.531
you don't have so spend so much time

00:00:31.531 --> 00:00:34.014
looking at all of those primary documents.

00:00:34.014 --> 00:00:35.523
The more challenging part, however,

00:00:35.523 --> 00:00:38.938
is that it's drawing on
your own personal knowledge

00:00:38.938 --> 00:00:40.794
of the subject matter.

00:00:40.794 --> 00:00:43.650
So unlike the DBQ where
you're analyzing documents

00:00:43.650 --> 00:00:46.019
and looking at just
what's in front of you,

00:00:46.019 --> 00:00:48.991
here you're really using
your own background

00:00:48.991 --> 00:00:51.314
understanding of U.S. history

00:00:51.314 --> 00:00:54.192
and also bringing up specific details

00:00:54.192 --> 00:00:56.631
to help you make an argument.

00:00:56.631 --> 00:00:58.302
So on this section of the exam

00:00:58.302 --> 00:01:00.138
you're gonna have the option to choose

00:01:00.138 --> 00:01:02.877
between two different essay prompts

00:01:02.877 --> 00:01:04.689
and you can choose which of them

00:01:04.689 --> 00:01:06.244
you want to write about.

00:01:06.244 --> 00:01:07.963
You only have to write about one.

00:01:07.963 --> 00:01:10.446
And of course, I recommend
writing about the one

00:01:10.446 --> 00:01:13.164
where you feel most confident.

00:01:13.164 --> 00:01:16.019
Maybe it's about a
topic that you like more

00:01:16.019 --> 00:01:18.179
or maybe it's a topic
about what you feel like

00:01:18.179 --> 00:01:20.176
you can give more information,

00:01:20.176 --> 00:01:23.031
but in these cases always
play to your strengths.

00:01:23.031 --> 00:01:25.586
So out of the two prompts that I was given

00:01:25.586 --> 00:01:29.510
there was one about whether
the American Revolution

00:01:29.510 --> 00:01:31.717
was actually revolutionary,

00:01:31.717 --> 00:01:33.760
and then there was this question about

00:01:33.760 --> 00:01:36.011
whether the New Deal was actually new

00:01:36.011 --> 00:01:38.426
or whether it was more
conservative in nature.

00:01:38.426 --> 00:01:39.983
Now I love the New Deal,

00:01:39.983 --> 00:01:42.607
so that is the question
that I want to take on here.

00:01:42.607 --> 00:01:44.580
Plus I can remember a
lot about the New Deal

00:01:44.580 --> 00:01:46.113
off the top of my head,

00:01:46.113 --> 00:01:47.320
so that's gonna give me a lot

00:01:47.320 --> 00:01:49.456
of extra information to work with.

00:01:49.456 --> 00:01:52.080
So of this 35 minutes that you have on

00:01:52.080 --> 00:01:53.497
the long essay question,

00:01:53.497 --> 00:01:55.400
I would recommend that you spend maybe

00:01:55.400 --> 00:01:58.094
five to 10 minutes of that

00:01:58.094 --> 00:02:01.044
and I think 10 minutes would really be max

00:02:01.044 --> 00:02:03.807
to plan your essay.

00:02:03.807 --> 00:02:05.920
To write a little outline for yourself,

00:02:05.920 --> 00:02:07.940
to decide what your thesis is going to be,

00:02:07.940 --> 00:02:10.448
and come up with a game
plan that is gonna direct

00:02:10.448 --> 00:02:12.444
the rest of your writing time,

00:02:12.444 --> 00:02:17.041
which should be the rest
of the time that you spend.

00:02:17.041 --> 00:02:21.819
The 25 to 30 minutes in this exam period.

00:02:23.450 --> 00:02:27.282
Now again, your mileage may vary on this.

00:02:27.282 --> 00:02:30.671
You might be the sort of
person who can plan really fast

00:02:30.671 --> 00:02:32.343
and take a lot of time writing,

00:02:32.343 --> 00:02:34.642
or you might be the sort of person who

00:02:34.642 --> 00:02:36.779
knows that they can write pretty fast

00:02:36.779 --> 00:02:38.752
so they can spend some more time planning,

00:02:38.752 --> 00:02:41.677
but I think this is just
kind of a good overall

00:02:41.677 --> 00:02:45.532
guideline for how you want
to be spending your time.

00:02:45.532 --> 00:02:47.854
Okay, so once you've taken a look

00:02:47.854 --> 00:02:50.571
at each of the topics
for the essay prompts

00:02:50.571 --> 00:02:52.591
and decided which one you want,

00:02:52.591 --> 00:02:55.888
the next step is to read the prompt itself

00:02:55.888 --> 00:02:57.816
really carefully.

00:02:57.816 --> 00:02:59.417
You want to make sure
that there aren't any

00:02:59.417 --> 00:03:03.203
sort of hidden strictures
in there that might

00:03:03.203 --> 00:03:06.267
direct what you are allowed
to write about in the prompt

00:03:06.267 --> 00:03:09.171
and what you aren't allowed
to write about in the prompt.

00:03:09.171 --> 00:03:11.863
Okay, so let's take a
look at this question.

00:03:11.863 --> 00:03:15.533
"Some historians have
argued that the New Deal

00:03:15.533 --> 00:03:19.433
"was ultimately conservative in nature.

00:03:19.433 --> 00:03:23.312
"Support, modify, or
refute this interpretation,

00:03:23.312 --> 00:03:27.792
"providing specific evidence
to justify your answer."

00:03:27.792 --> 00:03:30.882
Okay, so it seems like
the heart of this is about

00:03:30.882 --> 00:03:33.319
whether the New Deal

00:03:33.319 --> 00:03:37.028
was conservative

00:03:38.288 --> 00:03:41.813
or radical.

00:03:45.115 --> 00:03:48.180
And I think in this context
the word conservative

00:03:48.180 --> 00:03:51.616
doesn't mean politically
conservative or right-leaning,

00:03:51.616 --> 00:03:54.867
but rather conservative as in the sense of

00:03:54.867 --> 00:03:58.235
keeping something that existed before.

00:03:58.235 --> 00:04:01.693
So were the ways of a society conserved

00:04:01.693 --> 00:04:04.876
over time or did they change over time?

00:04:04.876 --> 00:04:06.408
One thing I notice about this question

00:04:06.408 --> 00:04:09.936
is that it really doesn't
give us much in the way

00:04:09.936 --> 00:04:13.536
of a specific timeframe to talk about.

00:04:13.536 --> 00:04:16.764
So it doesn't say talk
about whether the New Deal

00:04:16.764 --> 00:04:20.293
was conservative or radical in the period

00:04:20.293 --> 00:04:23.404
between 1920 and 1940,

00:04:23.404 --> 00:04:26.307
it just asks us to say in
the grand scheme of things

00:04:26.307 --> 00:04:28.373
do you think the New Deal was ultimately

00:04:28.373 --> 00:04:30.998
a conservative or radical movement.

00:04:30.998 --> 00:04:33.111
So that means if we want
to we could actually

00:04:33.111 --> 00:04:35.865
talk about a lot of different things

00:04:35.865 --> 00:04:37.608
really up to the present.

00:04:37.608 --> 00:04:39.372
And it doesn't even say that we only have

00:04:39.372 --> 00:04:41.322
to talk about the United States.

00:04:41.322 --> 00:04:43.529
I mean, this is AP U.S. History,

00:04:43.529 --> 00:04:45.619
so the bases of everything you're writing

00:04:45.619 --> 00:04:47.917
has to be about American society,

00:04:47.917 --> 00:04:50.263
but there's nothing
saying you can't compare

00:04:50.263 --> 00:04:54.001
American society to other
nations in this time period.

00:04:54.001 --> 00:04:58.058
Okay, so our time scope is broad

00:05:01.431 --> 00:05:05.722
and even our geography
is relatively broad.

00:05:09.535 --> 00:05:11.996
All right, so how do we decide
what we're gonna write about?

00:05:11.996 --> 00:05:15.571
Well, I think it's given
us three main options here.

00:05:15.571 --> 00:05:18.173
Can support this idea.

00:05:18.173 --> 00:05:22.230
So we could argue that yes
the New Deal was conservative.

00:05:29.853 --> 00:05:33.075
We can refute and say no

00:05:33.075 --> 00:05:36.650
the New Deal was radical.

00:05:36.650 --> 00:05:39.043
It's not conservative at all.

00:05:39.043 --> 00:05:40.900
Or we can modify,

00:05:40.900 --> 00:05:43.175
which might take the form of saying

00:05:43.175 --> 00:05:46.148
oh, maybe it was both
conservative and radical

00:05:46.148 --> 00:05:48.633
or maybe you even want to say

00:05:48.633 --> 00:05:50.723
this is not the right question to ask.

00:05:50.723 --> 00:05:52.836
So the modify option is kind of like a

00:05:52.836 --> 00:05:56.795
both or neither

00:05:56.795 --> 00:05:59.349
kind of way of looking at things.

00:05:59.349 --> 00:06:01.438
Now how do we decide which of these three

00:06:01.438 --> 00:06:03.111
arguments we want to make?

00:06:03.111 --> 00:06:04.643
I think one of the most useful things

00:06:04.643 --> 00:06:08.172
you can do at this stage
is just make a list

00:06:08.172 --> 00:06:11.191
of things that you
might want to talk about

00:06:11.191 --> 00:06:12.422
in this essay.

00:06:12.422 --> 00:06:15.207
So if we're thinking
about the conservativeness

00:06:15.207 --> 00:06:17.901
or the radicalness of the New Deal,

00:06:17.901 --> 00:06:20.990
what sorts of things might we bring up?

00:06:20.990 --> 00:06:23.125
So first let's just refresh ourselves

00:06:23.125 --> 00:06:25.564
on what the New Deal was about.

00:06:25.564 --> 00:06:29.256
And the New Deal was this package

00:06:29.256 --> 00:06:32.502
of programs

00:06:34.179 --> 00:06:38.492
which were passed during
the Great Depression

00:06:43.003 --> 00:06:46.206
by Franklin Delano Roosevelt

00:06:46.206 --> 00:06:50.421
as a means to try to restart
the American economy.

00:06:50.421 --> 00:06:53.115
And people often talk about the New Deal

00:06:53.115 --> 00:06:56.943
kind of taking the three forms of relief,

00:06:58.483 --> 00:07:00.444
for people who are suffering,

00:07:00.444 --> 00:07:03.748
for people who need immediate aid.

00:07:03.748 --> 00:07:05.138
Recovery,

00:07:05.138 --> 00:07:08.761
to try to get the economy

00:07:08.761 --> 00:07:10.456
back on track.

00:07:10.456 --> 00:07:12.360
And reform.

00:07:12.360 --> 00:07:14.380
Ways to try to change laws,

00:07:14.380 --> 00:07:16.191
change the way the economy worked

00:07:16.191 --> 00:07:18.072
so that something like
the Great Depression

00:07:18.072 --> 00:07:19.720
didn't happen again.

00:07:19.720 --> 00:07:21.509
And with the New Deal we often think about

00:07:21.509 --> 00:07:24.410
this kind of alphabet soup of agencies.

00:07:24.410 --> 00:07:28.497
There's the CCC, the
Civilian Conservation Corps.

00:07:28.497 --> 00:07:32.746
There's the TVA, the
Tennessee Valley Authority.

00:07:32.746 --> 00:07:36.834
There's the NRA, the National
Recovery Administration.

00:07:36.834 --> 00:07:40.873
And the WPA, the Works
Progress Administration.

00:07:40.873 --> 00:07:43.033
And these were all
programs that were intended

00:07:43.033 --> 00:07:45.007
to get people back to work,

00:07:45.007 --> 00:07:46.934
to try to modernize the country,

00:07:46.934 --> 00:07:49.930
and to try to moderate relationships

00:07:49.930 --> 00:07:53.018
between workers and corporations.

00:07:53.018 --> 00:07:54.504
So what are some of the
other things we know

00:07:54.504 --> 00:07:56.036
about the New Deal?

00:07:56.036 --> 00:08:00.485
Well, the New Deal was a
reaction to the Great Depression,

00:08:00.485 --> 00:08:04.745
which was brought on by some irresponsible

00:08:04.745 --> 00:08:07.765
banking in the 1920s,

00:08:07.765 --> 00:08:10.551
a time of what was known

00:08:10.551 --> 00:08:13.453
as laissez-faire economics,

00:08:13.453 --> 00:08:15.287
which kind of said the government

00:08:15.287 --> 00:08:18.282
was to keep its hands out of the economy.

00:08:18.282 --> 00:08:21.325
Laissez-faire is French for
let them do what they will,

00:08:21.325 --> 00:08:23.530
so let the economy do whatever it wants.

00:08:23.530 --> 00:08:26.131
Well, this all right came crashing down

00:08:26.131 --> 00:08:30.329
somewhat literally in 1929
with the stock market crash.

00:08:31.193 --> 00:08:33.887
And then for another three years

00:08:33.887 --> 00:08:36.673
the Depression continued
to get worse and worse.

00:08:36.673 --> 00:08:38.949
Hoover had a largely hands-off approach

00:08:38.949 --> 00:08:40.434
to the Great Depression,

00:08:40.434 --> 00:08:43.383
and so he's creamed in
the election of 1932

00:08:43.383 --> 00:08:45.125
by Franklin Delano Roosevelt,

00:08:45.125 --> 00:08:47.842
who promises that he's gonna
get things back on track.

00:08:47.842 --> 00:08:50.999
And so Roosevelt had a really experimental

00:08:50.999 --> 00:08:52.973
response to the Great Depression.

00:08:52.973 --> 00:08:56.641
It was kind of a try something
and see if it works approach.

00:08:56.641 --> 00:08:58.593
So he and his administration just kind of

00:08:58.593 --> 00:09:02.075
threw a lot of different
experimental solutions

00:09:02.075 --> 00:09:06.093
at the problem to see what they could do

00:09:06.093 --> 00:09:08.938
about the Great Depression.

00:09:08.938 --> 00:09:11.236
But the other thing we
know about the New Deal

00:09:11.236 --> 00:09:14.255
is that in the end it didn't really work.

00:09:14.255 --> 00:09:17.576
Now this was partly
because the Supreme Court

00:09:17.576 --> 00:09:21.059
rolled back a lot of the New Deal programs

00:09:21.059 --> 00:09:23.845
saying that they weren't constitutional,

00:09:23.845 --> 00:09:27.978
which led FDR into his
famous court packing scheme

00:09:27.978 --> 00:09:30.486
where he tried to add new justices

00:09:30.486 --> 00:09:31.869
to the Supreme Court,

00:09:31.869 --> 00:09:34.145
basically tilting it in his favor.

00:09:34.145 --> 00:09:35.887
And he failed at that.

00:09:35.887 --> 00:09:37.373
And the Depression continued to get worse

00:09:37.373 --> 00:09:40.112
throughout the end of the 1930s.

00:09:40.112 --> 00:09:43.291
It really wasn't until World War II

00:09:43.291 --> 00:09:46.820
that the mobilization for war,

00:09:46.820 --> 00:09:49.584
the American manufacturing for the war,

00:09:49.584 --> 00:09:53.665
got the United States out
of the Great Depression.

00:09:59.242 --> 00:10:00.868
So I think it's clear that the New Deal

00:10:00.868 --> 00:10:04.258
was this really unique
period in the United States

00:10:04.258 --> 00:10:07.276
when the government just tried whatever

00:10:07.276 --> 00:10:09.344
they could think of in order to try to

00:10:09.344 --> 00:10:11.341
improve the economy.

00:10:11.341 --> 00:10:13.013
But I think the question is

00:10:13.013 --> 00:10:15.171
if we think about the basic assumptions

00:10:15.171 --> 00:10:16.890
of the New Deal itself,

00:10:16.890 --> 00:10:19.443
were those radical or
were they conservative?

00:10:19.443 --> 00:10:21.534
Okay, let's pause here to think about that

00:10:21.534 --> 00:10:23.902
a little bit more and in the next video

00:10:23.902 --> 00:10:25.691
we'll decide which way we want to lean

00:10:25.691 --> 00:10:28.778
and think about how to write that essay.


AP Chemistry multiple choice sample: Boiling points

WEBVTT
Kind: captions
Language: en

00:00:01.767 --> 00:00:03.741
- [Voiceover] Consider the
molecules represented above

00:00:03.741 --> 00:00:05.924
and the data in the table below.

00:00:05.924 --> 00:00:08.118
We have the structure up here for nonane,

00:00:08.118 --> 00:00:12.678
the structure for 2,3,4-trifluoropentane,

00:00:12.678 --> 00:00:13.795
which is really hard to say

00:00:13.795 --> 00:00:17.296
so I'm gonna abbreviate that, TFP.

00:00:19.194 --> 00:00:21.493
And we have this data in the table.

00:00:21.493 --> 00:00:25.672
So nonane, and 2,3,4-trifluoropentane

00:00:25.672 --> 00:00:28.331
have almost identical molar masses,

00:00:28.331 --> 00:00:32.127
so 128 versus 126 grams per mole,

00:00:32.127 --> 00:00:36.272
but nonane has a significantly
higher boiling point.

00:00:36.272 --> 00:00:40.125
So we can see that nonane
has a boiling point of 151,

00:00:41.046 --> 00:00:44.279
versus 89 Celsius for our TFP.

00:00:45.447 --> 00:00:47.292
Which of the following statements

00:00:47.292 --> 00:00:50.956
best helps explain this observation?

00:00:52.946 --> 00:00:54.874
Before we look at our answer choices,

00:00:54.874 --> 00:00:56.977
let's think really fast
about what it means

00:00:56.977 --> 00:01:00.087
to have a higher or lower boiling point.

00:01:00.087 --> 00:01:04.290
The boiling point tells us how much energy

00:01:04.290 --> 00:01:09.290
we have to add to break
the intermolecular bonds

00:01:09.295 --> 00:01:11.765
between all of our molecules.

00:01:11.765 --> 00:01:16.505
So a higher boiling point means that

00:01:16.505 --> 00:01:21.459
you have more intermolecular forces

00:01:22.518 --> 00:01:24.115
to overcome.

00:01:26.640 --> 00:01:28.904
So what we're really asking here is,

00:01:28.904 --> 00:01:31.957
which of these answer choices explains

00:01:31.957 --> 00:01:36.415
why nonane has more intermolecular forces

00:01:36.415 --> 00:01:40.346
amongst the molecules, compared to TFP?

00:01:42.174 --> 00:01:46.631
So, answer choice A says,
the carbon-fluorine bond

00:01:46.631 --> 00:01:50.318
is easier to break than
the carbon-hydrogen bond.

00:01:50.318 --> 00:01:52.298
And we know this is a wrong answer,

00:01:52.298 --> 00:01:54.236
because this has nothing to do

00:01:54.236 --> 00:01:56.535
with intermolecular forces.

00:01:56.535 --> 00:01:58.334
When something boils, you're not actually

00:01:58.334 --> 00:02:01.423
breaking any of the covalent bonds,

00:02:01.423 --> 00:02:04.749
so that doesn't explain anything
about the boiling point.

00:02:05.974 --> 00:02:09.573
Answer choice B says that
the carbon-fluorine bond

00:02:09.573 --> 00:02:13.892
is more polar than the
carbon-hydrogen bond.

00:02:13.892 --> 00:02:15.982
So we can see that TFP does have

00:02:15.982 --> 00:02:18.362
these carbon-fluorine bonds,

00:02:18.362 --> 00:02:22.821
and we know that a
carbon-hydrogen bond isn't

00:02:22.821 --> 00:02:26.059
all that polar, and fluorine
is pretty electronegative,

00:02:26.059 --> 00:02:26.918
so this is true.

00:02:26.918 --> 00:02:29.084
This statement by itself is true.

00:02:30.134 --> 00:02:32.392
So this is true,

00:02:33.698 --> 00:02:37.716
but does it explain the
boiling point trend?

00:02:37.716 --> 00:02:41.443
And the answer there
is, it actually doesn't.

00:02:41.443 --> 00:02:45.262
So we're saying that if
the carbon-fluorine bond

00:02:45.262 --> 00:02:48.106
is more polar than these bonds here,

00:02:48.106 --> 00:02:51.663
we're saying that

00:02:51.663 --> 00:02:53.888
if TFP

00:02:54.799 --> 00:02:59.565
has more polar bonds,

00:03:04.540 --> 00:03:08.540
that would normally suggest it has

00:03:09.892 --> 00:03:14.740
stronger intermolecular forces,

00:03:16.498 --> 00:03:18.333
which would mean you would predict it

00:03:18.333 --> 00:03:21.119
to have a higher boiling point.

00:03:21.119 --> 00:03:22.651
And so, that's the opposite of what

00:03:22.651 --> 00:03:24.753
we're actually seeing here.

00:03:24.753 --> 00:03:28.086
Even though our TFP has

00:03:28.086 --> 00:03:30.223
more polar C-F bonds,

00:03:30.223 --> 00:03:32.128
it actually has a lower boiling point,

00:03:32.128 --> 00:03:35.528
so this observation, which is true,

00:03:35.528 --> 00:03:38.109
still doesn't explain

00:03:38.109 --> 00:03:42.284
what we're trying to explain. (laughs)

00:03:43.609 --> 00:03:47.023
So choice C says, the
carbon chains are longer

00:03:47.023 --> 00:03:51.568
in nonane than they are
in 2,3,4-trifluoropentane.

00:03:53.199 --> 00:03:54.849
So if we just look at the pictures here

00:03:54.849 --> 00:03:57.071
of the structures, this is also true.

00:03:58.622 --> 00:04:01.024
In nonane we have these
one, two, three, four, five,

00:04:01.024 --> 00:04:04.124
six, seven, eight, nine carbons.

00:04:04.124 --> 00:04:07.239
We have nine carbons
versus one, two, three,

00:04:07.239 --> 00:04:09.450
four, five carbons.

00:04:11.836 --> 00:04:16.027
So, how could we link
this to the boiling point?

00:04:16.027 --> 00:04:19.429
We know that even though
the molar mass here

00:04:19.429 --> 00:04:24.429
is the same, the length of the chain

00:04:26.060 --> 00:04:29.028
is actually related to

00:04:29.028 --> 00:04:32.070
the London dispersion forces.

00:04:32.070 --> 00:04:35.994
So as the length of the chain goes up,

00:04:35.994 --> 00:04:40.681
that actually means that the
London dispersion forces,

00:04:42.231 --> 00:04:46.880
so the intermolecular forces that happen

00:04:46.880 --> 00:04:50.472
when you get these tiny
instantaneous dipoles,

00:04:52.405 --> 00:04:54.570
those forces also go up.

00:04:59.579 --> 00:05:03.202
So, we're saying, okay,
this has a longer chain.

00:05:03.202 --> 00:05:07.544
Therefore, it will have more
London dispersion forces

00:05:07.544 --> 00:05:10.835
because these molecules
are better able to interact

00:05:10.835 --> 00:05:13.749
with each other with their
instantaneous dipoles,

00:05:13.749 --> 00:05:16.767
and that means these forces go up

00:05:16.767 --> 00:05:18.508
and the boiling point should go up,

00:05:18.508 --> 00:05:20.274
and that's what we're trying to explain.

00:05:20.274 --> 00:05:23.990
So C is the correct answer,
but lets' look at D anyway,

00:05:23.990 --> 00:05:28.181
just to make sure we didn't
make any bad decisions.

00:05:28.181 --> 00:05:29.481
So, just checking.

00:05:29.481 --> 00:05:31.815
D says the carbon chains are further apart

00:05:31.815 --> 00:05:33.858
in that sample of nonane than they are

00:05:33.858 --> 00:05:36.714
in 2,3,4-trifluoropentane.

00:05:36.714 --> 00:05:39.187
Well, we don't actually
know if this is true or not,

00:05:39.187 --> 00:05:41.520
but let's see, if this
statement were true,

00:05:41.520 --> 00:05:45.197
would it lead to the boiling
point trend we're seeing?

00:05:45.197 --> 00:05:48.413
If the carbon chains are
further apart in nonane,

00:05:48.413 --> 00:05:51.849
further apart would mean,
the further apart they are,

00:05:51.849 --> 00:05:54.550
the weaker the intermolecular forces.

00:05:55.391 --> 00:05:58.654
So this would mean, nonane has weaker

00:05:58.654 --> 00:06:02.439
intermolecular forces,
and that would suggest

00:06:02.439 --> 00:06:05.022
it would have a lower boiling point.

00:06:06.293 --> 00:06:08.940
So a lower boiling point.

00:06:08.940 --> 00:06:10.740
And again, this is not what
we're trying to explain.

00:06:10.740 --> 00:06:12.400
We know it has a higher boiling point,

00:06:12.400 --> 00:06:14.532
so this also doesn't explain,

00:06:16.197 --> 00:06:17.918
that doesn't explain the boiling points.

00:06:17.918 --> 00:06:18.927
So the answer is C.


2015 AP Chemistry free response 5a: Finding order of reaction

WEBVTT
Kind: captions
Language: en

00:00:00.224 --> 00:00:02.406
- [Voiceover] Blue food
coloring can be oxidized

00:00:02.406 --> 00:00:06.450
by household bleach, which
contains hypochlorite ion,

00:00:06.450 --> 00:00:09.882
or OCI-, to form colorless products,

00:00:09.882 --> 00:00:12.242
as represented by the equation above.

00:00:12.242 --> 00:00:16.649
So we have this equation where
we have blue food coloring,

00:00:16.649 --> 00:00:18.693
which has this chemical formula,

00:00:18.693 --> 00:00:23.569
and it's reacting with
bleach, or hypochlorite,

00:00:23.569 --> 00:00:25.694
and it's making colorless products.

00:00:25.694 --> 00:00:28.579
So we're getting this color
change from blue to colorless.

00:00:29.572 --> 00:00:32.625
A student used a spectrophotometer

00:00:32.625 --> 00:00:36.189
set at a wavelength of 625 nanometers

00:00:36.189 --> 00:00:38.546
to study the absorbance
of the food coloring

00:00:38.546 --> 00:00:41.363
over time during the bleaching process.

00:00:42.366 --> 00:00:45.791
In the study, bleach is
present in large excess,

00:00:45.791 --> 00:00:49.494
and I will underline that
'cause that's important.

00:00:49.494 --> 00:00:52.548
It's present in large excess
so that the concentration

00:00:52.548 --> 00:00:54.951
of hypochlorite is essentially constant

00:00:54.951 --> 00:00:57.255
throughout the reaction.

00:00:57.255 --> 00:00:58.962
The student used data from the study

00:00:58.962 --> 00:01:01.365
to generate the graphs below.

00:01:01.365 --> 00:01:04.919
So we'd like to answer, in part a,

00:01:04.919 --> 00:01:07.762
based on the graphs
above, what is the order

00:01:07.762 --> 00:01:11.617
of the reaction with respect
to the blue food coloring?

00:01:11.617 --> 00:01:13.416
So we have a lot of information here.

00:01:13.416 --> 00:01:15.278
We have these three graphs.

00:01:17.087 --> 00:01:20.001
If we write absorbance as A, we're looking

00:01:20.001 --> 00:01:23.043
at the concentration of A over time.

00:01:23.043 --> 00:01:26.867
We're looking at the ln of A over time,

00:01:27.779 --> 00:01:30.879
the natural log, and we are also, lastly,

00:01:30.879 --> 00:01:34.414
looking at one over the
concentration A over time.

00:01:36.811 --> 00:01:39.834
So, we would like to
know, what is the order

00:01:39.834 --> 00:01:42.581
of the reaction with respect to our blue?

00:01:43.989 --> 00:01:46.254
My first instinct when I see this problem,

00:01:46.254 --> 00:01:51.064
is actually to be a little bit panicky

00:01:51.064 --> 00:01:53.781
because, hey we have a
lot of information here,

00:01:53.781 --> 00:01:55.522
so how do we deal with it?

00:01:55.522 --> 00:01:57.891
We also have a little bit more information

00:01:57.891 --> 00:01:58.866
for this problem.

00:01:58.866 --> 00:02:02.186
We also have the equation sheet.

00:02:02.186 --> 00:02:03.870
So this is the part of the equation sheet

00:02:03.870 --> 00:02:05.789
that's relevant for this problem.

00:02:05.789 --> 00:02:09.316
So it's all of the equations
that have to do with kinetics,

00:02:09.316 --> 00:02:12.045
which is looking at reaction rates,

00:02:12.045 --> 00:02:14.621
so that is what we're looking at here.

00:02:14.621 --> 00:02:16.316
So we have three possible things

00:02:16.316 --> 00:02:17.999
that might be helpful for this problem.

00:02:17.999 --> 00:02:18.999
Maybe not, right?

00:02:18.999 --> 00:02:21.878
So we have this first
equation which gives us

00:02:21.878 --> 00:02:25.402
the first order integrated rate law.

00:02:26.336 --> 00:02:28.721
We have the second
equation, which gives us

00:02:28.721 --> 00:02:31.298
the second order integrated rate law,

00:02:31.298 --> 00:02:33.178
and we have this third equation

00:02:33.178 --> 00:02:35.708
which is actually an
equation for the half-life.

00:02:35.708 --> 00:02:38.270
So it's saying half-life is .693

00:02:38.270 --> 00:02:41.665
divided by k, and that is the half-life

00:02:43.969 --> 00:02:48.283
for a first order reaction.

00:02:51.353 --> 00:02:53.513
And the important thing to remember here,

00:02:53.513 --> 00:02:55.451
which will come up again in a second,

00:02:55.451 --> 00:02:58.295
is that this is a constant,
because k is a constant,

00:02:58.295 --> 00:03:00.119
so our half-life is also a constant

00:03:00.119 --> 00:03:01.948
for a first order reaction.

00:03:03.299 --> 00:03:05.970
So that's the information we have.

00:03:05.970 --> 00:03:08.292
Let's look back at our graphs.

00:03:08.292 --> 00:03:10.591
We're gonna start by looking
at just the first graph.

00:03:10.591 --> 00:03:12.716
It turns out we can get
a lot of information

00:03:12.716 --> 00:03:16.227
just by looking at the
concentration of A over time.

00:03:17.278 --> 00:03:18.591
So if we look at this first graph,

00:03:18.591 --> 00:03:19.670
and we look at the concentration

00:03:19.670 --> 00:03:21.689
of our blue stuff going down over time,

00:03:21.689 --> 00:03:25.184
we can see immediately
that this is not linear.

00:03:25.184 --> 00:03:26.753
So the fact that it's not linear

00:03:26.753 --> 00:03:29.991
immediately tells us it's not zero order.

00:03:29.991 --> 00:03:32.720
If it was zero order, we would expect

00:03:32.720 --> 00:03:36.986
to see a straight line,
which I will draw in pink,

00:03:36.986 --> 00:03:38.288
with a dotted line because that's not

00:03:38.288 --> 00:03:39.964
actually what we're seeing.

00:03:39.964 --> 00:03:41.869
So it's not zero order.

00:03:43.035 --> 00:03:44.904
We can also get some more information

00:03:44.904 --> 00:03:46.041
by looking at this one graph.

00:03:46.041 --> 00:03:47.202
We know it's not zero order.

00:03:47.202 --> 00:03:50.245
Can we tell from this first
graph if it's first order?

00:03:50.245 --> 00:03:53.240
And the answer is, we actually can.

00:03:53.240 --> 00:03:55.963
If you remember from looking
at the equations sheet,

00:03:55.963 --> 00:03:58.878
we said that first order reactions,

00:03:59.988 --> 00:04:03.224
so for first order reactions, we know,

00:04:03.224 --> 00:04:04.412
and I'd say this is maybe one of

00:04:04.412 --> 00:04:07.226
the most important things
about first order reactions,

00:04:07.226 --> 00:04:10.924
is that half-life is constant.

00:04:12.694 --> 00:04:15.898
So that means that the time it takes

00:04:15.898 --> 00:04:17.431
for the concentration to go down

00:04:17.431 --> 00:04:21.610
to half of what it was,
is the same no matter what

00:04:21.610 --> 00:04:23.131
your initial concentration is, no matter

00:04:23.131 --> 00:04:27.224
what point in your reaction you're at.

00:04:28.495 --> 00:04:30.109
So that's something we
can actually investigate

00:04:30.109 --> 00:04:31.932
just by looking at this first graph.

00:04:31.932 --> 00:04:33.871
We can see how much time it takes

00:04:33.871 --> 00:04:37.156
to get to half the concentration,

00:04:37.156 --> 00:04:39.420
and see if that's something
that changes over time.

00:04:39.420 --> 00:04:43.053
So for example, if we
start with .8 right here,

00:04:44.152 --> 00:04:48.308
half of .8 is .4,

00:04:48.308 --> 00:04:50.094
so we can see how much time it takes

00:04:50.094 --> 00:04:53.699
to get from .8 to .4, which is right here,

00:04:54.749 --> 00:04:58.712
and if we go down we can
see it takes 20 seconds

00:05:03.044 --> 00:05:06.733
to have the concentration

00:05:06.733 --> 00:05:10.142
starting at .8 absorbance units.

00:05:11.609 --> 00:05:16.044
We can look at the half-life
now to go from .4 to .2.

00:05:16.044 --> 00:05:20.131
So if we go from .4 to .2,
and I will change colors

00:05:20.131 --> 00:05:22.913
to make this look more obvious.

00:05:22.913 --> 00:05:25.397
We'll do this in orange.

00:05:25.397 --> 00:05:30.081
So going from .4 to .2
takes another 20 seconds.

00:05:31.434 --> 00:05:33.536
And so we can do this again and again.

00:05:33.536 --> 00:05:35.952
We could go from .2 to .1.

00:05:35.952 --> 00:05:38.006
We'll just see the
continuation of a pattern here,

00:05:38.006 --> 00:05:41.443
which is that, we can see that
it always takes 20 seconds

00:05:41.443 --> 00:05:43.413
to halve the concentration.

00:05:44.266 --> 00:05:47.239
And so the fact that half-life is constant

00:05:47.239 --> 00:05:50.687
based on Graph I, immediately tells us

00:05:50.687 --> 00:05:53.415
that our reaction is first order

00:05:53.415 --> 00:05:55.389
because our half-life is constant.

00:05:55.389 --> 00:05:57.863
We don't even have to look
at any of the other graphs.

00:05:57.863 --> 00:06:00.265
There is another way you
could do this problem.

00:06:00.265 --> 00:06:03.597
You might remember, based on
the equations that we have,

00:06:03.597 --> 00:06:06.131
or based on just equations you know

00:06:06.131 --> 00:06:08.244
off the top of your head.

00:06:08.244 --> 00:06:11.391
So one reason we know, and
one reason we could say

00:06:11.391 --> 00:06:14.760
this is first order, is
because t 1/2 is constant.

00:06:14.760 --> 00:06:18.453
The other reason why we
know this is first order is,

00:06:18.453 --> 00:06:22.713
when a reaction is first
order in your reactant,

00:06:22.713 --> 00:06:27.651
you know that graphing ln of your reaction

00:06:27.651 --> 00:06:31.971
versus time, gives you a straight line,

00:06:31.971 --> 00:06:34.435
and we can see from Graph II

00:06:36.483 --> 00:06:38.149
that this is the case.

00:06:39.502 --> 00:06:42.114
So we have these two pieces of evidence,

00:06:42.114 --> 00:06:44.621
from Graph I and Graph II, that tell us

00:06:44.621 --> 00:06:49.103
that this particular reaction
is actually first order

00:06:49.103 --> 00:06:51.040
with respect to the blue food coloring.


2015 AP Calculus AB 6b

WEBVTT
Kind: captions
Language: en

00:00:00.440 --> 00:00:02.540
- [Voiceover] "Find the
coordinates of all points

00:00:02.540 --> 00:00:05.370
"on the curve at which the line tangent

00:00:05.370 --> 00:00:08.400
"to the curve at that point is vertical."

00:00:08.400 --> 00:00:11.020
So we wanna figure out
the points on that curve

00:00:11.020 --> 00:00:13.962
where the tangent line is vertical.

00:00:13.962 --> 00:00:16.930
So let's just remind
ourselves what the slope

00:00:16.930 --> 00:00:19.320
of a tangent line is, or what it isn't.

00:00:19.320 --> 00:00:21.360
I guess this may be a better
way to think about it.

00:00:21.360 --> 00:00:23.260
If you have a horizontal line,

00:00:23.260 --> 00:00:25.340
so let me draw a horizontal line.

00:00:25.340 --> 00:00:28.014
If you have a horizontal line like that,

00:00:28.014 --> 00:00:29.610
well then your slope is zero.

00:00:29.610 --> 00:00:31.850
Or you can say your rate of change of y

00:00:31.850 --> 00:00:35.106
with respect to x is equal to zero.

00:00:35.106 --> 00:00:36.580
What about a vertical line?

00:00:36.580 --> 00:00:39.383
If you have a vertical line like that,

00:00:39.383 --> 00:00:44.162
what is your rate of change
of y with respect to x?

00:00:44.162 --> 00:00:46.880
Well, some people might say it's infinity,

00:00:46.880 --> 00:00:49.091
or you could say it's undefined.

00:00:49.091 --> 00:00:52.130
It's undefined in some way

00:00:52.130 --> 00:00:53.560
because at some point your rate,

00:00:53.560 --> 00:00:56.130
or one way to think about it,
you're gonna try to divide

00:00:56.130 --> 00:00:59.680
by zero because you
have a huge change in y

00:00:59.680 --> 00:01:01.950
over no change in x.

00:01:01.950 --> 00:01:03.500
Or another way to think about it

00:01:03.500 --> 00:01:04.980
that's a little bit more in line with that

00:01:04.980 --> 00:01:08.370
is you could say that your
change in x with respect

00:01:08.370 --> 00:01:11.000
to change in y, notice I
took took the reciprocal,

00:01:11.000 --> 00:01:12.960
so now we're talking about
a change at the derivative

00:01:12.960 --> 00:01:16.670
of x with respect to y is equal to zero

00:01:16.670 --> 00:01:19.540
because your y can change,
but as your y changes,

00:01:19.540 --> 00:01:21.629
your x does not change.

00:01:21.629 --> 00:01:26.340
So can we use this little
insight here on vertical lines

00:01:26.340 --> 00:01:29.280
to think about the coordinates
of all points in the curve

00:01:29.280 --> 00:01:30.920
at which the line tangent to the curve

00:01:30.920 --> 00:01:32.856
at that point is vertical.

00:01:32.856 --> 00:01:35.190
Well before, they told us,

00:01:35.190 --> 00:01:37.200
they gave us the curve of the equation,

00:01:37.200 --> 00:01:40.780
and they also told us what dy, dx is.

00:01:40.780 --> 00:01:43.200
Let me just rewrite 'em again
just so we have 'em there.

00:01:43.200 --> 00:01:45.520
So we know that y to the third

00:01:45.520 --> 00:01:48.460
minus xy is equal to two.

00:01:48.460 --> 00:01:50.870
This is the equation of our curve.

00:01:50.870 --> 00:01:54.160
And we know that dy, dx

00:01:54.160 --> 00:01:55.940
is equal to y

00:01:55.940 --> 00:02:00.740
over 3y squared minus x.

00:02:00.740 --> 00:02:03.400
So one thing we could do is, well,

00:02:03.400 --> 00:02:05.570
let's just figure out
what the derivative of x

00:02:05.570 --> 00:02:08.900
with respect to y is and set
that to be equal to zero.

00:02:08.900 --> 00:02:10.880
So this is the derivative
of y with respect to x.

00:02:10.880 --> 00:02:12.140
If we take the reciprocal of that,

00:02:12.140 --> 00:02:15.220
the derivative of x with respect to y,

00:02:15.220 --> 00:02:16.300
it's just the reciprocal of this,

00:02:16.300 --> 00:02:19.020
is going to be the reciprocal
of what we have here.

00:02:19.950 --> 00:02:24.520
So it's going to be 3y squared

00:02:24.520 --> 00:02:27.375
minus x over y.

00:02:27.375 --> 00:02:29.680
And if we want this to be equal to zero,

00:02:29.680 --> 00:02:31.150
like we said right over here,

00:02:31.150 --> 00:02:32.600
well then that's only going to happen

00:02:32.600 --> 00:02:34.856
if the numerator is equal to zero.

00:02:34.856 --> 00:02:36.830
So we could say, okay, at what x, y pair

00:02:36.830 --> 00:02:38.680
does this numerator equal to zero?

00:02:38.680 --> 00:02:41.950
3y squared minus x is equal to zero.

00:02:41.950 --> 00:02:45.980
Can add x to both sides
and you get 3y squared

00:02:45.980 --> 00:02:47.580
is equal to x.

00:02:47.580 --> 00:02:49.460
Now, another way you could
have thought about it is,

00:02:49.460 --> 00:02:52.720
well, at what x and y
values does the derivative

00:02:52.720 --> 00:02:55.100
of y with respect to x become undefined?

00:02:55.100 --> 00:02:56.560
Well, that's gonna become undefined

00:02:56.560 --> 00:02:59.220
if the denominator here is zero.

00:02:59.220 --> 00:03:01.300
But when you're dealing
with things like undefined,

00:03:01.300 --> 00:03:04.480
it gets a little bit more hand-wavy.

00:03:04.480 --> 00:03:06.480
I like to just think of
this as the rate at which x

00:03:06.480 --> 00:03:09.480
is changing with respect to y is zero.

00:03:09.480 --> 00:03:11.760
And so that got us to the same conclusion.

00:03:11.760 --> 00:03:14.140
Well, for that to be true,

00:03:14.140 --> 00:03:16.300
x has to be equal to 3y squared.

00:03:16.300 --> 00:03:20.700
And of course, the x, y
pair has to also satisfy

00:03:20.700 --> 00:03:23.085
the equation for the curve.

00:03:23.085 --> 00:03:25.750
So why don't we use both
of these constraints,

00:03:25.750 --> 00:03:27.874
and then we can solve for x and y?

00:03:27.874 --> 00:03:30.200
And so the easiest thing
I can think of doing

00:03:30.200 --> 00:03:32.460
is let's substitute x

00:03:32.460 --> 00:03:35.140
with 3y squared because they are the same,

00:03:35.140 --> 00:03:36.560
that's the second constraint.

00:03:36.560 --> 00:03:38.860
So if we take our original
equation of the curve,

00:03:38.860 --> 00:03:41.210
we get y to the third minus,

00:03:41.210 --> 00:03:44.546
instead of writing x, I could 3y squared.

00:03:44.546 --> 00:03:48.360
3y squared times y

00:03:48.360 --> 00:03:50.088
is equal to two.

00:03:50.088 --> 00:03:52.980
And so we get y to the third

00:03:52.980 --> 00:03:56.809
minus 3y to the third is equal to two.

00:03:56.809 --> 00:04:00.050
This is negative 2y to the third

00:04:00.050 --> 00:04:01.320
is equal to two.

00:04:01.320 --> 00:04:04.830
Can divide both sides by negative two

00:04:04.830 --> 00:04:08.180
and we get y to the third

00:04:08.180 --> 00:04:09.790
is equal to negative one,

00:04:09.790 --> 00:04:12.540
or y is equal to negative one.

00:04:12.540 --> 00:04:15.430
Negative one to the third
power is negative one.

00:04:15.430 --> 00:04:17.780
Now if y is negative one, what is x?

00:04:17.780 --> 00:04:20.614
Well, x is going to be equal to three

00:04:20.614 --> 00:04:24.566
times negative one squared.

00:04:24.566 --> 00:04:26.540
So negative one squared is just one,

00:04:26.540 --> 00:04:28.660
so x is going to be equal to three.

00:04:28.660 --> 00:04:31.760
So the point on that curve
at which the tangent line

00:04:31.760 --> 00:04:34.840
is vertical is going to be the point

00:04:34.840 --> 00:04:37.884
three, comma, negative one.

00:04:37.884 --> 00:04:39.680
And we are all done.