AP US history DBQ example 4

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- [Voiceover] All right,
this is the fourth and final

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in a series of videos about how to tackle

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the DBQ or document-based question

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on the AP U.S. History exam.

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We started out by reading
all of the documents

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that are provided in the exam,

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from which we are to write an essay

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that analyzes the major changes

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and continuities in the social

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and economic experiences
of African Americans

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migrating from the rural South,

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to urban areas in the North
in the period 1910 to 1930.

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As we analyzed these primary documents,

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we kind of identified three major themes

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that we wanna talk about.

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And that was cultural differences

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between the South and the North,

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differences in the type of labor

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between the South and the North,

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and differences in patterns of segregation

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in the South and the North.

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And from these themes we
came up with a thesis,

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which was more or less

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that the more things change,

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the more things stay the same.

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So even though African Americans moved

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to a whole new city, a
whole new environment,

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a whole new system of labor,

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they couldn't escape persistent racism,

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which had similar effects
on their lives in the North

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as it did in the South.

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Now we're at the writing the essay part.

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And while obviously I can't sit here

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and write a whole essay on the screen,

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I do wanna outline things for you,

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and give you a general sense

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of what you could talk about where.

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For the DBQ we're gonna do

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a standard five-paragraph essay,

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which means introduction. . .

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with a thesis statement,

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paragraph 1,

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paragraph 2, paragraph 3.

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These will all be the body paragraphs

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where we'll give our evidence

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in support of our thesis.

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And then a conclusion,

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which wraps up what we've said before,

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and really drives home our point.

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In this essay, to get full credit,

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you should expect to use

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either all, or all but one

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of the primary documents
that are provided.

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And that means you need
to reference them all,

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although you don't necessarily
have to go into detail

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about every single one of them.

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And what I want to
caution you against doing

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is just talking about
each piece of evidence

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one after another

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without putting them into a
larger framework of ideas.

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So don't just say oh well
first their was a folk saying

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about the effect of the boll
weevil and sharecropping

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on black Southerner's lives

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and then some of them asked
for help moving North.

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They wrote to the Chicago defender,

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because you don't want
to just let this evidence

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lead you along.

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What you want to do instead is say

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that you have read these
pieces of evidence,

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you have analyzed them,

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and now you're going synthesize them

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into an argument of your own.

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This is where the themes come in handy,

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because we've taken the time to see

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what's going on in all of these documents

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and kind of bubble up to the surface

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what are the real important issues

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that people are talking about.

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And as we thought about
changes and continuities,

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in those things,

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the thesis that we came
up with was more or less

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that even though the form

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of each of these things changed,

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the form of the culture,
the form of the labor,

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the form of the segregation,

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the underlying problem of
racism kind of remained.

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So this thesis actually gives
us a really neat structure

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for the rest of the essay

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because we've said the forms changed,

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but the underlying
problem stayed the same.

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So for each of these body
paragraphs we'll talk

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first, about the change in form,

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but then we'll talk about
the underlying problems

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that stay the same.

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All right, are you ready to
take a stab at writing this?

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Let's kind of ease into
things with our introduction.

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I think a good thing for us to do

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might be to set the scene a little bit.

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And we talked about some
of the historical events

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that were going on at this time period.

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So you might say that sharecropping

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had really been an economic loss

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for African Americans.

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And so they were feeling the pressure,

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both from the system of sharecropping,

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where 50% of what they got
was sent back to landowners,

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and also from the boll weevil,

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which had killed off a
considerable amount of the crop.

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So they just weren't doing ok.

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You could also mention that in the 1890s,

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the Supreme Court case
Plessy versus Ferguson

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had made separate but equal accommodations

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legal for blacks and for whites,

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which basically put
racism as part of the law.

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So if there had been any hope remaining

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that the Civil War and reconstruction

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were going to result in
a society in the South

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that was not based on
racial discrimination,

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it was kind of destroyed
with Plessy versus Ferguson,

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at least for the time being.

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And then lastly you might
say that World War One,

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As the United States
mobilized for the war,

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led to many new factory jobs in the North,

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which gave African Americans in the South

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an opportunity to leave.

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At the end of your first
paragraph in the introduction,

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this is the time to bring out your thesis.

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Our thesis is even
though African Americans

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who moved from the South to the North

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in the period 1910 to 1930
experienced tremendous changes,

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in the culture surrounding them,

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the work that they did,

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and their living patterns,

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they still suffered from
many of the same problems

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that they had suffered from in the South

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due to the pervasive influence of racism.

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In a way what you're saying here is

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that racism was a national
problem in the United States.

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It didn't change from north to south.

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So even though the form that racism took

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might be different in
South Carolina and Chicago,

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there was no real qualitative difference

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in it's impact on the
lives of African Americans.

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This is where we break out our themes.

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Our first theme was about
cultural differences.

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Remember our structure.

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First we're gonna talk about
the things that were different,

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and then we're gonna talk about the things

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that stayed the same.

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One thing that was different would be

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that if sharecroppers moved to the city,

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they were moving from a rural
to an urban environment.

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Where many African Americans in the South

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had worked as sharecroppers

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and lived in a farming situation,

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now they were headed to
the heart of the city

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where they might be surrounded

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by other African Americans.

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Bring up the map from document 7 here.

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And they were also worried
about what it would be like

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to take a job in the city,

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somewhere that was completely
far away from home.

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And this would be a part

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where you might consider talking
about the newspaper letter

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in document 2,

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where a man writes to the Chicago defender

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asking for help because he's
afraid he might get hoodwinked.

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So what are some of the
things that stayed the same?

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Well I think we can definitely
say that some of their fears

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were justified about the move to the city,

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because many people
found that life there was

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just as hard as it was in the South

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and we see this in this document

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about the Cotton Belt Blues.

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We might even say on kind
of a larger cultural level,

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that white people in the North were

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no more kind to them than
white people in the South.

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And here you might consider
bringing up document number six,

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the one about the race riot in Chicago.

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That's a paragraph about
cultural differences.

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How about labor differences?

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In our second paragraph
we're gonna talk about

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how even though African Americans

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moved to a completely
different type of labor,

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from sharecropping to factory work,

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they still faced pervasive
racism in the factory system

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that led to whites rioting

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and also segregated facilities,

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even bathroom facilities
in these workplaces.

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The thing that changes
is the type of labor,

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and here you might wanna
bring up the first document

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where you're talking about sharecropping.

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So what kind of work they
were doing was different,

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but the same kind of problems they faced

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in the workplace were quite similar.

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They faced segregation in the workplace,

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and they faced

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stereotypes about the
kind of work they did

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and whether or not they were good workers.

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And here you might bring
up the third article,

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where the efficiency expert talks about

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how it's important to separate
white and black workers

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so that you don't have any kind

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of racial friction in your office.

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And you might also talk
about the sixth article,

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where they say that many people believe

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that African American workers
were used as scabs in strikes.

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So that's a kind of a way
of separating the races

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that's saying that white workers in unions

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might be undermined by black laborers

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willing to work for less.

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Lastly we're talking about
the experience of segregation.

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We've already mentioned this transition

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from a rural to an urban environment,

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but you might also talk about

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how living patterns changed.

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In the South, African Americans and whites

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usually lived in similar places,

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in the same town, in
the same parts of town,

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more or less,

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but the way that they used
space was slightly different.

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For example, African
Americans were often expected

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to use the servant's entrance,

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sit either at the back of a movie theater,

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or maybe not even go into the same places

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as a white person.

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But in Chicago,

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there is an entire African
American neighborhood,

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And for this you definitely wanna

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bring up document 7,

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which shows where African Americans

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were living in Chicago.

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And the thing that stays the same

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is really the system
of segregation itself.

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Northern segregation looks different,

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but it's still segregation,

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so you might talk about,

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I mean this is still segregation
is one thing you can say.

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And you can also say
that there's kind of a

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implicit promise of violence

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if African Americans step out of line

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in the system of segregation.

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And here you might talk
about document number four,

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which is this kind of
snearing newspaper article

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from a white newspaper in Mississippi,

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saying oh well in Mississippi

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we have lynching,

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in the North they have explosions.

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Their point was

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"Oh, well isn't lynching better?"

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But for the purposes of your essay

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what you can really say is

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"What's the difference?"

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They're both forms of death

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for getting out of line
in a system of racism.

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So there's nothing that's really

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all that different there anyway.

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And now we're at the conclusion.

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Generally I would advise you

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against bringing up any new information

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in a conclusion because
you want your reader

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to come away saying

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"Oh yea, that was right!"

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not "Wait a minute, the author didn't talk

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about that in the essay at all,

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why are they mentioning
it in the conclusion?"

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So I would advise you
to just kind of restate

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what you've been talking about

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throughout the essay saying

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that even though there is
this vast transformation,

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in the culture, the living situations,

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the work of African
Americans who are moving

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from the South to the North,

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the substantive problem
of racism stayed the same.

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All right, well that's it for the DBQ.

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Taking the time to do your due diligence

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and understanding these documents,

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and coming up with an
idea and a structure,

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and even an outline,

00:12:36.690 --> 00:12:38.513
will really pay off in the long run,

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because it will help you to write an essay

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that is really strong and really clear.


AP US history DBQ example 3

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Kind: captions
Language: en

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- [Voiceover] This is the
third in a series of videos

00:00:03.189 --> 00:00:06.269
about answering the
document based question,

00:00:06.269 --> 00:00:10.709
or DBQ on the AP U.S. History Exam.

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In the last video, we
started taking a look

00:00:12.629 --> 00:00:15.219
at and analyzing some of the primary

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documents provided for this exam.

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So the first one was a folk saying about

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how the boll weevil and sharecropping

00:00:23.352 --> 00:00:25.212
had taken away African-American's

00:00:25.212 --> 00:00:27.592
crops and homes in the South.

00:00:27.592 --> 00:00:29.432
The second was a letter from a black man

00:00:29.432 --> 00:00:33.252
living in New Orleans
asking the black newspaper

00:00:33.252 --> 00:00:36.572
The Chicago Defender, to
help in finding him a house

00:00:36.572 --> 00:00:38.512
and a job in Chicago.

00:00:38.512 --> 00:00:42.732
The third was an article
in an industrial journal

00:00:42.732 --> 00:00:45.672
counseling white factory
owners in the North

00:00:45.672 --> 00:00:49.572
to segregate black workers
from white workers.

00:00:49.572 --> 00:00:51.792
And the fourth, was an article

00:00:51.792 --> 00:00:55.012
in a white owned newspaper talking

00:00:55.012 --> 00:00:58.232
about race riots in Chicago, and how

00:00:58.232 --> 00:01:00.232
African-Americans were better off

00:01:00.232 --> 00:01:02.192
in the South, because they felt

00:01:02.192 --> 00:01:04.562
that lynch law was better than

00:01:04.562 --> 00:01:06.378
being killed in a race riot.

00:01:06.378 --> 00:01:08.278
So there are three more documents

00:01:08.278 --> 00:01:10.118
that we'll go through pretty quickly

00:01:10.118 --> 00:01:11.418
and then we can get started on

00:01:11.418 --> 00:01:13.338
writing a thesis statement.

00:01:15.098 --> 00:01:19.058
Okay, this is a song
by an African-American

00:01:19.058 --> 00:01:22.078
singer named Lizzie Miles, and the

00:01:22.078 --> 00:01:26.278
song is called Cotton
Belt Blues from 1923.

00:01:26.278 --> 00:01:27.998
Now I'm not going to attempt to sing this,

00:01:27.998 --> 00:01:29.458
'cause you do not want to hear that,

00:01:29.458 --> 00:01:32.906
but let's get a gist of what it's about.

00:01:32.906 --> 00:01:36.006
Look at me, look at me, and you see a gal

00:01:36.006 --> 00:01:38.686
with a heart bogged down with woe

00:01:38.686 --> 00:01:42.106
because I'm all alone,
far from my Southern home.

00:01:42.106 --> 00:01:44.566
Dixie Dan, that's the man, took me from

00:01:44.566 --> 00:01:48.966
the Land of Cotton to that
cold, cold minded North.

00:01:48.966 --> 00:01:50.706
Threw me down, hit the town,and I've

00:01:50.706 --> 00:01:52.886
never seen him henceforth.

00:01:52.886 --> 00:01:55.306
Just 'cause I trusted,
I'm broke and disgusted

00:01:55.306 --> 00:01:59.046
I got the Cotton Belt Blues.

00:01:59.046 --> 00:02:01.506
Well, it definitely seems like she has

00:02:01.506 --> 00:02:05.506
experienced the kind of con man behavior

00:02:05.506 --> 00:02:08.866
that the man in document
two was worried about.

00:02:08.866 --> 00:02:12.666
So, she's saying that she was fooled into

00:02:12.666 --> 00:02:15.966
coming up North for a man who has

00:02:15.966 --> 00:02:18.366
now left her alone.

00:02:18.366 --> 00:02:21.766
And she misses her home in the South.

00:02:26.126 --> 00:02:31.126
But you could also think about
the fact that she herself

00:02:31.256 --> 00:02:32.238
if we've got the lyrics to this song,

00:02:32.238 --> 00:02:35.498
and this recording,
probably did pretty well.

00:02:35.498 --> 00:02:38.538
So, this is more maybe of
an expression of popular

00:02:38.538 --> 00:02:43.198
culture, and less of a particular story

00:02:43.198 --> 00:02:45.845
about this person Lizzie Miles.

00:02:45.845 --> 00:02:49.105
So we could talk about
the influence of Jazz

00:02:49.105 --> 00:02:52.705
the fact that African-American's
came to the North

00:02:52.705 --> 00:02:56.425
and influenced popular culture.

00:02:59.825 --> 00:03:01.785
Alright, we're getting
down to the end of these.

00:03:01.785 --> 00:03:04.305
Let's look at document six.

00:03:04.305 --> 00:03:06.245
Alright, this document is from an

00:03:06.245 --> 00:03:10.305
African-American journalist
named George Schuyler

00:03:10.305 --> 00:03:13.605
whose writing in a magazine
called The Messenger

00:03:13.605 --> 00:03:16.105
which was a political
and literary magazine

00:03:16.105 --> 00:03:17.785
for African-Americans.

00:03:17.785 --> 00:03:21.365
So, he's writing for a
sympathetic audience.

00:03:21.365 --> 00:03:25.185
This is in August of 1925.

00:03:25.185 --> 00:03:27.645
Schuyler says "It is generally thought by

00:03:27.645 --> 00:03:30.245
both Negroes and whites
that Negroes are the

00:03:30.245 --> 00:03:33.865
chief strikebreakers in
the United States. This is

00:03:33.865 --> 00:03:37.265
far from the truth. The Negroe
workers' part in strikes

00:03:37.265 --> 00:03:41.265
has been dramatized by virtue
of the striking contrast

00:03:41.265 --> 00:03:45.145
of race which invariably
provoked race riots.

00:03:45.145 --> 00:03:48.425
But the fact is, there are many more scabs

00:03:48.425 --> 00:03:51.325
among the white than black workers.

00:03:51.325 --> 00:03:53.065
Partially because there are numerous

00:03:53.065 --> 00:03:56.045
industries in which Negroes
are not permitted to work.

00:03:56.045 --> 00:04:00.745
Which too, are by no means 100% organized.

00:04:00.745 --> 00:04:02.645
Out of 20 or more millions of workers in

00:04:02.645 --> 00:04:06.605
the United States, less than
five million are organized.

00:04:06.605 --> 00:04:08.965
Note the potential for scabs."

00:04:08.965 --> 00:04:10.705
So one thing you definitely
have to know here

00:04:10.705 --> 00:04:13.625
is what the word "scab" means.

00:04:13.625 --> 00:04:17.605
So "scab", I think you can
kind of tell from the context

00:04:17.605 --> 00:04:22.045
means strikebreaker, so
if a union goes on strike

00:04:22.045 --> 00:04:26.765
a factory owner might hire
scabs or replacement workers

00:04:26.765 --> 00:04:28.505
to try to break the strike.

00:04:28.505 --> 00:04:31.725
So Schuyler is saying
there is a perception

00:04:31.725 --> 00:04:34.445
that black workers are often used to break

00:04:34.445 --> 00:04:39.325
strikes or that when a white labor union

00:04:39.325 --> 00:04:41.945
would go on strike, the factory owner

00:04:41.945 --> 00:04:45.245
might then hire black
workers, who of course

00:04:45.245 --> 00:04:47.625
are going to have difficulty finding jobs

00:04:47.625 --> 00:04:49.825
in a segregated economy, and therefore

00:04:49.825 --> 00:04:54.825
they don't have to pay
the white workers more.

00:04:54.885 --> 00:04:57.445
And Schuyler says that this is not true

00:04:57.445 --> 00:05:00.425
it's actually just that
African-Americans are

00:05:00.425 --> 00:05:03.905
so frequently barred from
industries, that they

00:05:03.905 --> 00:05:06.805
can't be represented in
strikes because they're

00:05:06.805 --> 00:05:09.145
not represented in
unions, or the places that

00:05:09.145 --> 00:05:11.625
employ unionized workers.

00:05:11.625 --> 00:05:13.225
Okay, last one.

00:05:13.225 --> 00:05:14.625
This one is a map, and
I'm just going to put

00:05:14.625 --> 00:05:16.525
it right here in front of everything,

00:05:16.525 --> 00:05:18.545
because it's pretty large and if

00:05:18.545 --> 00:05:19.965
we made it any smaller it would be

00:05:19.965 --> 00:05:21.445
really hard to see.

00:05:21.445 --> 00:05:23.445
So when you're looking at maps like this,

00:05:23.445 --> 00:05:26.145
the first thing you want
to do is read the title.

00:05:26.145 --> 00:05:28.285
Because that way you know what this map

00:05:28.285 --> 00:05:30.245
is actually trying to show you, and you're

00:05:30.245 --> 00:05:32.105
not just making assumptions
of what it could

00:05:32.105 --> 00:05:33.725
be trying to show you.

00:05:33.725 --> 00:05:35.565
So this map is about the distribution of

00:05:35.565 --> 00:05:40.265
the African-American
population in Chicago in 1930.

00:05:40.265 --> 00:05:42.225
What you can see here,
are that the sections

00:05:42.225 --> 00:05:45.285
that are not shaded at
all, or shaded white

00:05:45.285 --> 00:05:49.205
are less than one percent
African-American population.

00:05:49.205 --> 00:05:51.445
The light grey is one to ten percent.

00:05:51.445 --> 00:05:53.805
The medium grey is 10 - 50%

00:05:53.805 --> 00:05:57.925
and then this dark grey is
more than 15% African-American.

00:05:57.925 --> 00:05:59.605
And now what you can see here is that

00:05:59.605 --> 00:06:03.325
it looks like there is a very,
definite African-American

00:06:03.325 --> 00:06:06.185
neighborhood on the South side of Chicago.

00:06:06.185 --> 00:06:09.430
Which, I think goes to show that

00:06:09.430 --> 00:06:13.969
there's some real segregation
happening in Chicago.

00:06:15.089 --> 00:06:16.669
And you can see here at the bottom,

00:06:16.669 --> 00:06:20.289
it tells you, how many
African-Americans were

00:06:20.289 --> 00:06:24.829
living in Chicago over
the 1910 - 1930 period.

00:06:24.829 --> 00:06:28.869
And even though the
share of the population

00:06:28.869 --> 00:06:31.469
more than triples in that time period,

00:06:31.469 --> 00:06:36.469
everyone is set in this one small area.

00:06:36.809 --> 00:06:38.749
So I think that goes to show that

00:06:38.749 --> 00:06:43.249
even if you were a Southerner
who moved to Chicago

00:06:43.249 --> 00:06:46.629
looking for a better life
as an African-American

00:06:46.629 --> 00:06:50.569
you might still be subject
to this system of segregation

00:06:50.569 --> 00:06:53.569
that would only allow you
to live in one neighborhood.

00:06:53.569 --> 00:06:56.489
But there might also be a
positive flip side to that.

00:06:56.489 --> 00:07:00.729
Which would be that this was
a thriving black community.

00:07:00.729 --> 00:07:03.569
If you were a Southerner who had lived

00:07:03.569 --> 00:07:06.569
in a relatively rural
place, you may not have

00:07:06.569 --> 00:07:08.909
been able to spend that much time

00:07:08.909 --> 00:07:11.749
with other African-Americans
as a young person.

00:07:11.749 --> 00:07:14.489
So that's a possible
positive interpretation,

00:07:14.489 --> 00:07:16.689
but we'll keep that one
the table just in case

00:07:16.689 --> 00:07:18.609
it might help us with
part of our argument.

00:07:27.249 --> 00:07:29.709
Alright, now we've read
all of the documents

00:07:29.709 --> 00:07:31.809
and as we get started
on our thesis statement

00:07:31.809 --> 00:07:34.069
I think one of the most
useful things you can do

00:07:34.069 --> 00:07:36.949
is just take a moment and brain-storm some

00:07:36.949 --> 00:07:40.349
of the themes have arisen
in these documents.

00:07:41.969 --> 00:07:43.649
So what themes do we see here?

00:07:44.989 --> 00:07:48.049
Well, I think that there's definitely

00:07:48.049 --> 00:07:52.419
a theme about labor in general

00:07:52.419 --> 00:07:55.849
not being able to do well under a

00:07:55.849 --> 00:07:58.669
sharecropping system of labor

00:07:58.669 --> 00:08:02.189
and looking for a good job.

00:08:02.189 --> 00:08:04.269
And several things about factory work

00:08:04.269 --> 00:08:08.419
whether factories should be segregated

00:08:08.419 --> 00:08:10.139
or whether African-Americans play

00:08:10.139 --> 00:08:12.839
a part in the labor movement in general

00:08:12.839 --> 00:08:17.379
or if they work against
unions by being scabs.

00:08:17.379 --> 00:08:22.359
I think there's definitely
a theme of segregation

00:08:22.359 --> 00:08:26.379
or living patterns.

00:08:26.379 --> 00:08:29.279
We saw that in the map,
and we also saw that

00:08:29.279 --> 00:08:32.549
in some of the documents

00:08:32.549 --> 00:08:36.019
about segregated work places.

00:08:36.019 --> 00:08:39.663
And there might also be just
kind of a cultural theme here

00:08:39.663 --> 00:08:42.303
about the differences between life

00:08:42.303 --> 00:08:45.183
in the North and in the South.

00:08:45.183 --> 00:08:48.903
We see that when our
newspaper letter writer

00:08:48.903 --> 00:08:51.783
says he's worried about being hoodwinked,

00:08:51.783 --> 00:08:55.543
and we see that when our Jazz singer

00:08:55.543 --> 00:08:59.904
talks about she was
fooled and left behind.

00:08:59.904 --> 00:09:02.523
We might even see that
with our perceptions

00:09:02.523 --> 00:09:06.583
of black neighborhood life,
that African-Americans

00:09:06.583 --> 00:09:10.283
may have gone from a system
of living very separately

00:09:10.283 --> 00:09:13.143
in the South, to living in a very dense,

00:09:13.143 --> 00:09:14.923
urban cultural area.

00:09:14.923 --> 00:09:16.623
Where they may have met many different

00:09:16.623 --> 00:09:19.663
African-Americans from all
different parts of the country.

00:09:19.663 --> 00:09:22.323
I think another useful thing for us to do

00:09:22.323 --> 00:09:25.063
is to think about some of
the major historical events

00:09:25.063 --> 00:09:27.163
going on at that time period, that

00:09:27.163 --> 00:09:30.243
we can connect to these documents.

00:09:30.243 --> 00:09:34.183
A big one that comes to
mind is the great migration,

00:09:34.183 --> 00:09:37.224
which we mentioned before.

00:09:37.224 --> 00:09:42.223
Which was a period in
the early 20th century

00:09:42.223 --> 00:09:44.703
when many Southern African-American's

00:09:44.703 --> 00:09:47.443
pretty much had had it
with life in the South.

00:09:47.443 --> 00:09:49.203
It was a combination of Jim Crow

00:09:49.203 --> 00:09:51.543
segregation being legalized.

00:09:51.543 --> 00:09:55.443
And also sharply declining
economic opportunities

00:09:55.443 --> 00:09:58.824
that led thousands of
African-Americans to pack up

00:09:58.824 --> 00:10:01.403
and head for Northern cities.

00:10:01.403 --> 00:10:03.463
Now on of the reasons
that they could do this,

00:10:03.463 --> 00:10:06.683
is because World War I was creating many

00:10:06.683 --> 00:10:08.904
new factory jobs, just the way that

00:10:08.904 --> 00:10:11.083
World War II would do later on.

00:10:11.083 --> 00:10:14.163
And so there were many new
opportunities in the North

00:10:14.163 --> 00:10:17.293
to draw African-Americans away to new

00:10:17.293 --> 00:10:19.404
and even better paying jobs.

00:10:19.404 --> 00:10:21.224
What else happened in this time period?

00:10:21.224 --> 00:10:24.024
Well, there was the Supreme Court ruling

00:10:24.024 --> 00:10:26.473
Plessy v. Ferguson,

00:10:26.473 --> 00:10:31.473
which legalized segregation in 1896.

00:10:31.493 --> 00:10:34.453
Which said that separate but equal

00:10:34.453 --> 00:10:37.793
accommodations were constitutional.

00:10:37.793 --> 00:10:42.133
The 1910s and 1920s
were times of increasing

00:10:42.133 --> 00:10:47.133
modernity, but also a time of
cultural and racial backlash

00:10:47.453 --> 00:10:50.073
as many new immigrants
streamed into the cities

00:10:50.073 --> 00:10:52.353
along with African-Americans
from the South.

00:10:52.353 --> 00:10:55.493
So there was also a
resurgence in the Ku Klux Klan

00:10:55.493 --> 00:10:58.593
at this time period, which
President Woodrow Wilson

00:10:58.593 --> 00:11:01.833
even kind of tacitly
approved of by watching

00:11:01.833 --> 00:11:05.433
the film Birth of a
Nation in the White House.

00:11:05.433 --> 00:11:07.093
And we might even talk about the

00:11:07.093 --> 00:11:10.713
Chicago race riot of 1919

00:11:10.713 --> 00:11:14.773
which is the race riot
mentioned in document four

00:11:14.773 --> 00:11:17.713
when and you might even
mention the Chicago

00:11:17.713 --> 00:11:22.433
race riot of 1919 which
was one of the deadliest

00:11:22.433 --> 00:11:26.013
race riots in American history.

00:11:26.013 --> 00:11:29.313
And this is the race riot that's
mentioned in document four

00:11:29.313 --> 00:11:31.333
kind of gloatingly.

00:11:31.333 --> 00:11:34.353
Alright, so we've identified
these three themes

00:11:34.353 --> 00:11:36.333
that we might discuss in our essay.

00:11:36.333 --> 00:11:41.233
Now the essay itself is about
changes and continuities.

00:11:41.233 --> 00:11:42.693
So for each of these three things,

00:11:42.693 --> 00:11:44.793
was there change over this time period

00:11:44.793 --> 00:11:46.853
or was there continuity?

00:11:46.853 --> 00:11:48.933
Well in labor you could say there's maybe

00:11:48.933 --> 00:11:52.773
a change in type of labor.

00:11:52.773 --> 00:11:55.884
But maybe many of the same problems

00:11:55.884 --> 00:11:57.824
of race around labor.

00:12:01.364 --> 00:12:02.944
Alright what about segregation?

00:12:02.944 --> 00:12:05.344
Well I think there's both
segregation in the North

00:12:05.344 --> 00:12:09.504
and in the South, but
again, it's kind of a

00:12:09.504 --> 00:12:12.024
difference of type and degree.

00:12:12.024 --> 00:12:15.944
So, segregation still exists in the North

00:12:15.944 --> 00:12:19.066
but now it's taken on this urban form

00:12:19.066 --> 00:12:20.986
where there are majority
black neighborhoods

00:12:20.986 --> 00:12:22.195
and then other neighborhoods where

00:12:22.195 --> 00:12:24.495
there are no African-Americans at all.

00:12:24.495 --> 00:12:25.815
So a different type.

00:12:28.395 --> 00:12:30.755
Alright, what about cultural changes?

00:12:30.755 --> 00:12:33.115
We could see that in some cases,

00:12:33.115 --> 00:12:35.595
African-Americans who moved North

00:12:35.595 --> 00:12:38.890
missed their old society.

00:12:41.350 --> 00:12:43.250
But then again, they certainly had

00:12:43.250 --> 00:12:46.230
many problems when they were in the South.

00:12:46.230 --> 00:12:48.870
Singing songs about how the boll weevil

00:12:48.870 --> 00:12:51.530
and sharecropping had caused feelings

00:12:51.530 --> 00:12:53.790
of dislocation and poverty.

00:12:59.990 --> 00:13:02.370
So I think if there is a thesis statement

00:13:02.370 --> 00:13:05.390
to be gotten out of this, it's that moving

00:13:05.390 --> 00:13:08.110
from the South to the North,

00:13:08.110 --> 00:13:10.335
African-Americans in the period from

00:13:10.335 --> 00:13:14.875
1910 to 1930, experience pretty much

00:13:14.875 --> 00:13:16.855
the same problems, but they

00:13:16.855 --> 00:13:18.055
took different forms.

00:13:23.199 --> 00:13:25.959
In the next video, I'll
talk about how we can turn

00:13:25.959 --> 00:13:29.399
that into a really beautiful
and robust thesis statement

00:13:29.399 --> 00:13:31.079
And then we'll go through the process

00:13:31.079 --> 00:13:33.329
of outlining this essay.


AP US history DBQ example 2

WEBVTT
Kind: captions
Language: en

00:00:00.886 --> 00:00:02.581
- [Voiceover] In this video
we're talking some more

00:00:02.581 --> 00:00:06.249
about the DBQ or
document-based question section

00:00:06.249 --> 00:00:09.733
of the AP U.S. history exam.

00:00:09.733 --> 00:00:11.984
In our first video we just
went through some general

00:00:11.984 --> 00:00:15.120
strategy about how to
approach the question,

00:00:15.120 --> 00:00:17.766
which asks you to write an essay

00:00:17.766 --> 00:00:21.622
with a thesis statement
addressing this question

00:00:21.622 --> 00:00:25.244
about the social and economic experiences

00:00:25.244 --> 00:00:28.541
of African Americans moving from the South

00:00:28.541 --> 00:00:32.512
to the North in the period 1910 to 1930

00:00:32.512 --> 00:00:36.250
using a series of primary
documents which are provided

00:00:36.250 --> 00:00:38.107
in the exam.

00:00:38.107 --> 00:00:40.174
In this video we're
gonna start taking a look

00:00:40.174 --> 00:00:43.100
at these documents and it's going to seem

00:00:43.100 --> 00:00:45.376
like this might take forever because

00:00:45.376 --> 00:00:48.719
I'm going through them really
slowly and methodically,

00:00:48.719 --> 00:00:51.274
but actually on the exam
itself you'll be able

00:00:51.274 --> 00:00:52.828
to look at these and get a sense

00:00:52.828 --> 00:00:54.919
of what's going on pretty quickly.

00:00:54.919 --> 00:00:56.938
So let's go through these
documents one by one

00:00:56.938 --> 00:00:58.889
and I'm gonna put them up on the screen

00:00:58.889 --> 00:01:01.723
and go through them and
take a few notes on them

00:01:01.723 --> 00:01:04.740
so that we can see all of
them before we go about

00:01:04.740 --> 00:01:07.620
the process of writing a thesis statement.

00:01:07.620 --> 00:01:09.548
So the first document we have here is

00:01:09.548 --> 00:01:13.425
an African American folk
saying from the South

00:01:13.425 --> 00:01:16.305
in the 1910s.

00:01:16.305 --> 00:01:18.069
And the folk saying says the white man

00:01:18.069 --> 00:01:21.042
got half the crop,
boll-weevil took the rest,

00:01:21.042 --> 00:01:22.712
and I ain't got no home.

00:01:22.712 --> 00:01:24.455
So what does this remind you of?

00:01:24.455 --> 00:01:29.144
Well, it's definitely a
reference here to sharecropping

00:01:30.014 --> 00:01:33.788
which was a system of agricultural labor

00:01:33.788 --> 00:01:37.248
devised after the Civil
War where white men

00:01:37.248 --> 00:01:40.196
would own a bunch of land and then rent

00:01:40.196 --> 00:01:43.355
portions of it to African American farmers

00:01:43.355 --> 00:01:45.909
and in return those farmers had to give

00:01:45.909 --> 00:01:48.789
portions of their crops
back to the landowners.

00:01:48.789 --> 00:01:51.458
So this really ended
in a never-ending cycle

00:01:51.458 --> 00:01:53.315
of debt for sharecroppers who could

00:01:53.315 --> 00:01:54.710
never get ahead.

00:01:54.710 --> 00:01:58.470
It also mentions the boll
weevil which was a pest

00:01:58.470 --> 00:02:00.189
that got into the cotton crop,

00:02:00.189 --> 00:02:03.372
which really reduced the amount of cotton

00:02:03.372 --> 00:02:05.020
produced in the South and led to

00:02:05.020 --> 00:02:08.636
a major economic crisis.

00:02:09.873 --> 00:02:12.891
And lastly it talks about a kind of sense

00:02:12.891 --> 00:02:14.655
of dislocation, right?

00:02:14.655 --> 00:02:16.420
You don't have a home because you're in

00:02:16.420 --> 00:02:19.759
serious economic trouble.

00:02:20.739 --> 00:02:21.946
All right, not bad.

00:02:21.946 --> 00:02:26.614
Let's move on to a second document.

00:02:26.614 --> 00:02:28.425
All right, well this one
is a lot longer so I'm

00:02:28.425 --> 00:02:31.212
gonna try to squeeze it in here.

00:02:31.212 --> 00:02:34.183
It says it is a letter from a prospective

00:02:34.183 --> 00:02:37.713
African American migrant in 1917

00:02:37.713 --> 00:02:39.571
who lives in New Orleans.

00:02:39.571 --> 00:02:41.684
He writes, "Dear Sirs,

00:02:41.684 --> 00:02:44.053
"being desirous of leaving the South for

00:02:44.053 --> 00:02:46.374
"the betterment of my condition generally

00:02:46.374 --> 00:02:48.580
"and seeking a home somewhere in Illinois

00:02:48.580 --> 00:02:51.437
"Chicago or some other prosperous town

00:02:51.437 --> 00:02:54.177
"I am at sea about the
best place to locate

00:02:54.177 --> 00:02:57.310
"having a family dependent
upon me for support.

00:02:57.310 --> 00:02:59.796
"I am informed by the Chicago Defender,

00:02:59.796 --> 00:03:02.373
"a very valuable paper
which has for its purpose

00:03:02.373 --> 00:03:04.301
"the uplifting of my race,

00:03:04.301 --> 00:03:07.597
"and of which I am a constant
reader and real lover,

00:03:07.597 --> 00:03:10.036
"that you were in a
position to show some light

00:03:10.036 --> 00:03:12.403
"to one in my condition.

00:03:12.403 --> 00:03:14.609
"Seeking a Northern home.

00:03:14.609 --> 00:03:17.837
"If this is true kindly
inform me by next mail

00:03:17.837 --> 00:03:20.555
"the next best thing
to do being a poor man

00:03:20.555 --> 00:03:22.482
"with a family to care for.

00:03:22.482 --> 00:03:25.895
"I am not coming to live
on flowery beds of ease

00:03:25.895 --> 00:03:28.937
"for I am a man who works and wish to make

00:03:28.937 --> 00:03:31.097
"the best I can out of life.

00:03:31.097 --> 00:03:33.232
"I do not wish to come there hoodwinked

00:03:33.232 --> 00:03:35.903
"and not know where to go or what to do.

00:03:35.903 --> 00:03:38.202
"so I solicit your help in this matter

00:03:38.202 --> 00:03:40.547
"and thanking you in
advance for what advice

00:03:40.547 --> 00:03:42.172
"you may be pleased to give.

00:03:42.172 --> 00:03:44.377
"I am yours for success."

00:03:44.377 --> 00:03:47.885
So in this document it's a man

00:03:47.885 --> 00:03:51.901
who is trying to relocate to the North

00:03:54.291 --> 00:03:56.800
and he's drawing on the assistance

00:03:56.800 --> 00:03:58.449
of the Chicago Defender,

00:03:58.449 --> 00:04:02.158
which was a major black newspaper.

00:04:07.436 --> 00:04:10.221
And he's also saying
that he is maybe afraid

00:04:10.221 --> 00:04:11.730
of being hoodwinked,

00:04:11.730 --> 00:04:13.659
so you could see that perhaps he's heard

00:04:13.659 --> 00:04:15.678
some rumors that Southerners moving

00:04:15.678 --> 00:04:17.605
to the North might get into trouble

00:04:17.605 --> 00:04:22.040
or be conned some how.

00:04:22.040 --> 00:04:25.198
And he's also very eager to say that

00:04:25.198 --> 00:04:28.821
he doesn't want to live
on flowery beds of ease.

00:04:28.821 --> 00:04:30.562
He's a working man.

00:04:30.562 --> 00:04:33.419
So he is coming expecting
to do a good job.

00:04:33.419 --> 00:04:35.345
He's looking for work
and he's trying to put

00:04:35.345 --> 00:04:39.776
to rest any stereotypes
that he could be a lazy man.

00:04:46.074 --> 00:04:48.280
Okay, here's our third document.

00:04:48.280 --> 00:04:53.201
It is an article in the
magazine Industrial Management

00:04:53.201 --> 00:04:55.710
from 1918,

00:04:55.710 --> 00:04:59.239
and it's written by
Dwight Thompson Farnham.

00:04:59.239 --> 00:05:01.816
That's not anyone we've
ever heard of before,

00:05:01.816 --> 00:05:04.621
but says he's a efficiency expert,

00:05:04.621 --> 00:05:06.897
so someone whose job it is to make sure

00:05:06.897 --> 00:05:09.242
that businesses are run efficiently.

00:05:09.242 --> 00:05:11.517
And his article is called
Negroes as a Source

00:05:11.517 --> 00:05:13.397
of Industrial Labor.

00:05:13.397 --> 00:05:14.861
Here's what he says.

00:05:14.861 --> 00:05:17.925
"A certain amount of
segregation is necessary

00:05:17.925 --> 00:05:20.666
"at times to preserve the peace.

00:05:20.666 --> 00:05:23.476
"This is especially true
when negroes are first

00:05:23.476 --> 00:05:25.588
"introduced into a plant.

00:05:25.588 --> 00:05:28.235
"It is a question if it is not always best

00:05:28.235 --> 00:05:31.253
"to have separate washrooms and the like.

00:05:31.253 --> 00:05:33.994
"In places where different
races necessarily come

00:05:33.994 --> 00:05:36.687
"into close contact and
in places where inherited

00:05:36.687 --> 00:05:39.822
"characteristics are
especially accentuated,

00:05:39.822 --> 00:05:42.399
"it is better to keep
their respective folkways

00:05:42.399 --> 00:05:45.210
"from clashing wherever possible."

00:05:45.210 --> 00:05:48.251
So in this document it seems like he is

00:05:48.251 --> 00:05:51.409
advising people who own factories

00:05:51.409 --> 00:05:54.775
to segregate workers.

00:05:54.775 --> 00:05:58.120
So if they're going to
hire black laborers,

00:05:58.120 --> 00:06:00.303
that they have to keep
them separate from whites,

00:06:00.303 --> 00:06:03.344
especially in bathrooms or places where

00:06:03.344 --> 00:06:06.339
inherited characteristics
are especially accentuated,

00:06:06.339 --> 00:06:07.803
whatever that means.

00:06:07.803 --> 00:06:10.867
To me it sounds like a
sort of racist biology

00:06:10.867 --> 00:06:14.228
that he's quoting here.

00:06:23.939 --> 00:06:26.077
I think another thing that he's saying

00:06:26.077 --> 00:06:29.583
is he's giving a clue that
white workers in the North

00:06:29.583 --> 00:06:31.766
are not necessarily going to be friendly

00:06:31.766 --> 00:06:33.391
to black workers,

00:06:33.391 --> 00:06:36.851
so I think it's fair to
say that it shows that

00:06:36.851 --> 00:06:39.312
African Americans moving to the North

00:06:39.312 --> 00:06:42.553
are going to face racism

00:06:42.553 --> 00:06:44.989
and various forms

00:06:44.989 --> 00:06:47.893
of violence or maybe even strikes

00:06:47.893 --> 00:06:51.928
from white people who don't
want to work with them.

00:06:57.623 --> 00:06:59.643
All right, let's do one more.

00:06:59.643 --> 00:07:01.824
This is another long one.

00:07:01.824 --> 00:07:05.377
A article from a white-owned newspaper,

00:07:05.377 --> 00:07:07.746
seems like that's important,

00:07:07.746 --> 00:07:10.254
from Jackson, Mississippi

00:07:10.254 --> 00:07:14.285
about a race riot in Chicago in 1919.

00:07:14.285 --> 00:07:17.978
The article says, "The
only surprising feature

00:07:17.978 --> 00:07:20.579
"about the race riot in Chicago yesterday

00:07:20.579 --> 00:07:24.014
"is that it did not
assume larger proportions.

00:07:24.014 --> 00:07:25.779
"Trouble has been brewing in that city

00:07:25.779 --> 00:07:27.545
"for several months and nothing short of

00:07:27.545 --> 00:07:30.099
"exceptionally good work
by the police department

00:07:30.099 --> 00:07:32.909
"can prevent further clashes.

00:07:32.909 --> 00:07:34.974
"The native white population of Chicago

00:07:34.974 --> 00:07:37.854
"bitterly resents the
influx of negro labor

00:07:37.854 --> 00:07:39.711
"and especially the housing of blacks

00:07:39.711 --> 00:07:41.244
"in white neighborhoods.

00:07:41.244 --> 00:07:44.587
"The decent, hard-working,
law-abiding Mississippi

00:07:44.587 --> 00:07:47.745
"negroes who were lured
to Chicago by the bait

00:07:47.745 --> 00:07:51.043
"of higher wages only to lose their jobs

00:07:51.043 --> 00:07:54.386
"or forced to accept lower
pay after the labor shortage

00:07:54.386 --> 00:07:58.265
"became less acute are hereby
notified that they will be

00:07:58.265 --> 00:08:01.677
"welcomed back home and
find their old positions

00:08:01.677 --> 00:08:03.211
"waiting for them.

00:08:03.211 --> 00:08:05.439
"Mississippi may lynch
a negro when he commits

00:08:05.439 --> 00:08:07.971
"the most heinous of all crimes,

00:08:07.971 --> 00:08:10.804
"but we do not blow up
the innocent with bombs

00:08:10.804 --> 00:08:13.613
"or explode sticks of
dynamite on their doorsteps."

00:08:13.613 --> 00:08:15.192
Well, youch.

00:08:15.192 --> 00:08:17.050
There's a lot going on here.

00:08:17.050 --> 00:08:21.810
First, you can see that this
is a white-owned newspaper

00:08:21.810 --> 00:08:23.714
and it seems like maybe they're trying

00:08:23.714 --> 00:08:26.848
to spread the word to African Americans

00:08:26.848 --> 00:08:29.333
who maybe have not yet left the South

00:08:29.333 --> 00:08:32.375
that things are not that
great in the North, right?

00:08:32.375 --> 00:08:33.675
'Cause they don't want
to lose their source

00:08:33.675 --> 00:08:35.417
of labor to the North.

00:08:35.417 --> 00:08:38.412
So basically they're saying
that if African Americans

00:08:38.412 --> 00:08:41.152
stay in the South they might get lynched,

00:08:41.152 --> 00:08:45.441
but that's better than
being killed in a race riot.

00:08:48.698 --> 00:08:52.740
I think what we can take away from this

00:08:52.740 --> 00:08:56.361
is in general there
weren't many good options

00:08:56.361 --> 00:08:59.146
for African Americans in this time period

00:08:59.146 --> 00:09:01.493
because in the South you have lynch law

00:09:01.493 --> 00:09:03.722
and in the North you have race riots.

00:09:03.722 --> 00:09:07.482
So the question is was
one better than the other?

00:09:07.482 --> 00:09:09.132
Now there are still three more documents

00:09:09.132 --> 00:09:11.059
for us to look at and we'll get to those

00:09:11.059 --> 00:09:12.475
in the next video,

00:09:12.475 --> 00:09:14.333
but I think if we have to kind of theorize

00:09:14.333 --> 00:09:16.538
right now about what's going on,

00:09:16.538 --> 00:09:19.883
it seems like there are
many African Americans

00:09:19.883 --> 00:09:23.645
who have been seriously hurt economically

00:09:23.645 --> 00:09:27.614
by sharecropping and the
boll weevil infestation

00:09:27.614 --> 00:09:30.076
who are looking to go North,

00:09:30.076 --> 00:09:32.305
but they're finding
that when they go North

00:09:32.305 --> 00:09:35.161
they may face segregation and violence

00:09:35.161 --> 00:09:37.738
that may or may not be
better than the lynch law

00:09:37.738 --> 00:09:39.295
of the South.

00:09:39.295 --> 00:09:41.360
In the next video we'll
take a look at the last

00:09:41.360 --> 00:09:44.518
three documents and then we'll take a stab

00:09:44.518 --> 00:09:46.654
at writing a strong thesis statement

00:09:46.654 --> 00:09:49.230
based on this evidence.


AP US history DBQ example 1

WEBVTT
Kind: captions
Language: en

00:00:00.328 --> 00:00:01.779
- [Voiceover] Alright, in
this video, we're talking

00:00:01.779 --> 00:00:06.144
about the document-based question, or DBQ,

00:00:06.144 --> 00:00:09.863
section on the AP US History exam.

00:00:09.863 --> 00:00:11.942
Now, this is one of two
main essays that are

00:00:11.942 --> 00:00:13.498
on the exam.

00:00:13.498 --> 00:00:16.840
One is based on documents
that are provided to

00:00:16.840 --> 00:00:19.743
you and the other is based
on your own knowledge

00:00:19.743 --> 00:00:21.323
of the subject.

00:00:21.323 --> 00:00:24.956
So you'll get 55 minutes
to do this portion of

00:00:24.956 --> 00:00:27.998
the exam and it's
generally recommended that

00:00:27.998 --> 00:00:30.936
you spend about 15 of
those minutes planning

00:00:30.936 --> 00:00:35.936
your answer and about 40 of those minutes

00:00:36.926 --> 00:00:38.911
actually writing your answer.

00:00:38.911 --> 00:00:41.408
Now your mileage might
differ, you might find that

00:00:41.408 --> 00:00:43.514
you're someone who wants
to spend a little bit more

00:00:43.514 --> 00:00:46.022
time planning or your
somebody who can plan

00:00:46.022 --> 00:00:48.076
really fast and write well.

00:00:48.076 --> 00:00:50.841
In any event, you want to
go in with a plan about

00:00:50.841 --> 00:00:53.417
how much time you're going to spend on

00:00:53.417 --> 00:00:56.239
each part so that you
don't get surprised at the

00:00:56.239 --> 00:00:58.560
end of the period that
you still have a couple

00:00:58.560 --> 00:01:01.653
paragraphs left to write
but you're out of time.

00:01:01.653 --> 00:01:04.222
So for the DBQ section,
you're going to get a

00:01:04.222 --> 00:01:09.122
question that asks you
to analyze changes or

00:01:09.122 --> 00:01:13.058
continuities over time,
something that really gets

00:01:13.058 --> 00:01:17.702
at the heart of how things
in history change over time.

00:01:17.702 --> 00:01:19.547
So unlike the short answer
questions, which are very

00:01:19.547 --> 00:01:23.867
specific about one period
in time, this is asking you

00:01:23.867 --> 00:01:28.047
to take a broader look at
US history and write an

00:01:28.047 --> 00:01:30.983
essay about one of its major themes.

00:01:30.983 --> 00:01:33.039
Let's take a look at this question.

00:01:33.039 --> 00:01:37.346
Analyze major changes and
continuities in the social

00:01:37.346 --> 00:01:42.346
and economic experiences
of African Americans who

00:01:43.070 --> 00:01:46.999
migrated from the South
to urban areas in the

00:01:46.999 --> 00:01:51.429
North in the period 1910 to 1930.

00:01:52.340 --> 00:01:54.720
Well that gives us a lot
of information about the

00:01:54.720 --> 00:01:56.994
kinds of things we should concentrate on.

00:01:56.994 --> 00:02:00.872
First, we're looking at
social history and economic

00:02:00.872 --> 00:02:05.872
history, we're looking
at African Americans, and

00:02:08.989 --> 00:02:11.799
we're looking at this migration pattern.

00:02:11.799 --> 00:02:15.571
This is the period of the
Great Migration, as they would

00:02:15.571 --> 00:02:19.670
say, when many African
Americans who lived in

00:02:19.670 --> 00:02:23.931
the South moved to the
North for new factory jobs

00:02:23.931 --> 00:02:26.856
in this time period
which certainly included

00:02:26.856 --> 00:02:28.361
World War I.

00:02:29.771 --> 00:02:32.452
And you can see from the
time frame that we're

00:02:32.452 --> 00:02:36.238
talking about a fairly early
20th century time period

00:02:36.238 --> 00:02:39.998
ending in 1930, so you don't
want to be talking about

00:02:39.998 --> 00:02:42.053
the experiences of African
Americans in the Great

00:02:42.053 --> 00:02:44.980
Depression or in World War
II, or in the Civil Rights

00:02:44.980 --> 00:02:47.417
Movement because that's much later.

00:02:47.417 --> 00:02:50.216
Now you might be able to
end on a note that shows

00:02:50.216 --> 00:02:52.978
your knowledge of what's
to come, but really for the

00:02:52.978 --> 00:02:56.578
meat of this essay, you
want to stick to the time

00:02:56.578 --> 00:02:58.458
period in question.

00:02:58.458 --> 00:03:00.839
To answer this, we're
going to want to write an

00:03:00.839 --> 00:03:05.839
essay and, at the very
least, I would go for your

00:03:07.016 --> 00:03:12.016
standard five paragraph
essay where you have an

00:03:12.112 --> 00:03:17.112
introductory statement,
introduction, which includes

00:03:18.648 --> 00:03:22.213
a strong thesis statement
and we'll get to how to

00:03:22.213 --> 00:03:24.790
write one of those soon.

00:03:24.790 --> 00:03:29.790
And then, three paragraphs
of body text, each that

00:03:30.677 --> 00:03:34.577
is trying to prove a point
brought up in its topic

00:03:34.577 --> 00:03:38.873
sentence, and a conclusion,
which wraps up what

00:03:38.873 --> 00:03:41.608
you've said and ties it up with a bow.

00:03:43.332 --> 00:03:45.073
Now to do this, you're going to have to

00:03:45.073 --> 00:03:49.798
consider and analyze about seven to nine

00:03:49.798 --> 00:03:53.733
primary documents, which
are provided for you

00:03:53.733 --> 00:03:55.452
by the exam.

00:03:55.452 --> 00:03:59.573
You should include all,
or maybe all but one, of

00:03:59.573 --> 00:04:02.395
those primary documents in your answer.

00:04:02.395 --> 00:04:04.369
Now you don't have to
go into detail about all

00:04:04.369 --> 00:04:08.630
of them, but you should
include analysis of some

00:04:08.630 --> 00:04:12.309
of the arguments, some of
the biases, and some of

00:04:12.309 --> 00:04:17.291
the larger ideas behind
some of those documents.

00:04:17.291 --> 00:04:19.635
You should also be prepared to give some

00:04:19.635 --> 00:04:23.769
outside information that
shows that you really know

00:04:23.769 --> 00:04:26.989
the material and can give context to it.

00:04:32.174 --> 00:04:34.867
So that's what these questions are about

00:04:34.867 --> 00:04:37.178
and how you should go
about answering them.

00:04:37.178 --> 00:04:39.268
In the next video, we'll
start looking at primary

00:04:39.268 --> 00:04:42.703
documents and getting ready
to make a thesis statement.


LIVE Office Hours with Sal (Monday, May 2nd)

WEBVTT
Kind: captions
Language: en

00:00:00.220 --> 00:00:02.220
- Hello AP Calculus students.

00:00:02.220 --> 00:00:04.980
This is Sal Khan of the Khan Academy.

00:00:04.980 --> 00:00:06.330
And as well all know,

00:00:06.330 --> 00:00:10.970
the AP Calculus exams,
both the AB and BC exams

00:00:10.970 --> 00:00:14.430
are coming up this Thursday, May 5th.

00:00:14.430 --> 00:00:16.050
And I'm sure you are buzzing

00:00:16.050 --> 00:00:18.400
with as much excitement as I am.

00:00:18.400 --> 00:00:20.010
And in case you didn't already realize it,

00:00:20.010 --> 00:00:23.240
Khan Academy has a lot of
resources for you in calculus.

00:00:23.240 --> 00:00:24.780
You could either jump
in and learn the things

00:00:24.780 --> 00:00:27.930
that you wanna learn, or we
have what we call our missions,

00:00:27.930 --> 00:00:30.290
where it'll guide you
through all the calculus

00:00:30.290 --> 00:00:34.470
that you need to learn for
either the AB or the BC exams.

00:00:34.470 --> 00:00:36.270
But on top of that,

00:00:36.270 --> 00:00:39.830
in preparation for this
super exciting exam,

00:00:39.830 --> 00:00:44.500
on Monday, May 2nd, we are
going to have live office hours.

00:00:44.500 --> 00:00:48.470
And so from 4 to 5 PM
Pacific Standard Time,

00:00:48.470 --> 00:00:52.100
it will be myself and Grant,
who is our calculus fellow,

00:00:52.100 --> 00:00:55.240
and we will be answering your
questions about calculus.

00:00:55.240 --> 00:00:56.680
It could be reviewing things.

00:00:56.680 --> 00:00:58.670
It will be going through example problems.

00:00:58.670 --> 00:01:00.760
Or we might point you
to the right resources

00:01:00.760 --> 00:01:02.220
on Khan Academy itself.

00:01:02.220 --> 00:01:03.600
And so, show up.

00:01:03.600 --> 00:01:05.290
It's going to be a lot of fun.

00:01:05.290 --> 00:01:07.860
You do not want to miss out on this.

00:01:07.860 --> 00:01:10.240
And anything that you want us to cover,

00:01:10.240 --> 00:01:13.420
go to the Facebook post
about this live stream

00:01:13.420 --> 00:01:16.030
that we're gonna have on
Facebook on Monday, May 2nd

00:01:16.030 --> 00:01:19.360
and put your questions, tell
us what you want us to cover,

00:01:19.360 --> 00:01:21.810
what you're confused about,
or any example problems

00:01:21.810 --> 00:01:23.150
that you wanna see.


2015 AP Calculus AB 6c

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:03.441
- [Voiceover] Part C, evaluate
the second derivative of y

00:00:03.441 --> 00:00:05.132
with respect to x squared

00:00:05.132 --> 00:00:08.879
at the point on the curve
where x equals negative one

00:00:08.879 --> 00:00:12.343
and y is equal to one.

00:00:12.343 --> 00:00:14.604
Alright, so let's just go to the beginning

00:00:14.604 --> 00:00:15.816
where they tell us

00:00:15.816 --> 00:00:18.652
that dy dx is equal to

00:00:18.652 --> 00:00:21.442
y over three y squared

00:00:21.442 --> 00:00:23.282
minus x.

00:00:23.282 --> 00:00:25.183
So let me write that down.

00:00:25.183 --> 00:00:27.169
So dy

00:00:28.039 --> 00:00:31.699
dy dx is equal to

00:00:31.699 --> 00:00:34.959
y over three y squared

00:00:34.959 --> 00:00:36.099
minus x.

00:00:36.099 --> 00:00:39.225
Three y squared minus x.

00:00:39.225 --> 00:00:41.118
And now what I wanna do is essentially,

00:00:41.118 --> 00:00:43.913
take the derivative of both sides again.

00:00:43.913 --> 00:00:46.670
Now, there's a bunch of ways
that we could try to tackle it,

00:00:46.670 --> 00:00:48.113
but the way it's written right now,

00:00:48.113 --> 00:00:50.299
if I take the derivative
of the right-hand side,

00:00:50.299 --> 00:00:53.061
I'm gonna have to apply the quotient rule,

00:00:53.061 --> 00:00:54.965
which is really just comes
from the product rule,

00:00:54.965 --> 00:00:56.901
but it gets pretty hairy.

00:00:56.901 --> 00:00:59.985
So, let's see if I can
simplify my task a little bit.

00:00:59.985 --> 00:01:01.752
I'm going to have to do
implicit differentiation

00:01:01.752 --> 00:01:02.824
one way or the other,

00:01:02.824 --> 00:01:04.270
so what if I multiply both sides

00:01:04.270 --> 00:01:06.376
of this times three y squared minus x?

00:01:06.376 --> 00:01:10.778
Then I get three y squared minus x

00:01:10.778 --> 00:01:14.400
times dy dx

00:01:14.400 --> 00:01:16.391
is equal to,

00:01:16.391 --> 00:01:19.267
is equal to y.

00:01:19.267 --> 00:01:21.728
And so now, taking the
derivative of both sides of this

00:01:21.728 --> 00:01:25.295
is going to be a little
bit more straightforward.

00:01:25.295 --> 00:01:26.685
In fact, if I want,

00:01:26.685 --> 00:01:27.575
I could,

00:01:27.575 --> 00:01:30.161
well actually, let me
just do it like this.

00:01:30.161 --> 00:01:31.362
And so, let's,

00:01:31.362 --> 00:01:34.428
let's apply our derivative
operator to both sides.

00:01:34.428 --> 00:01:36.286
Let's give ourselves some space.

00:01:36.286 --> 00:01:39.442
So I'm gonna apply my derivative
operator to both sides.

00:01:39.442 --> 00:01:42.149
We take the derivative
of the left-hand side

00:01:42.149 --> 00:01:43.633
with respect to x,

00:01:43.633 --> 00:01:46.234
and the derivative of the right-hand side

00:01:46.234 --> 00:01:48.436
with respect to x.

00:01:48.436 --> 00:01:50.916
And so, here I'll apply the product rule.

00:01:50.916 --> 00:01:53.518
First, I'll take the
derivative of this expression

00:01:53.518 --> 00:01:55.449
and then multiply that times dy dx,

00:01:55.449 --> 00:01:57.193
and then I'll take the
derivative of this expression

00:01:57.193 --> 00:01:58.323
and multiply it times this.

00:01:58.323 --> 00:02:01.178
So, the derivative of
three y squared minus x

00:02:01.178 --> 00:02:02.764
with respect to x,

00:02:02.764 --> 00:02:04.615
well, that is going to be,

00:02:05.455 --> 00:02:07.425
so if I take the derivative
of three y squared

00:02:07.425 --> 00:02:08.656
with respect to y,

00:02:08.656 --> 00:02:10.680
it's going to be six y,

00:02:10.680 --> 00:02:12.557
and then I have to take
the derivative of y

00:02:12.557 --> 00:02:13.601
with respect to x,

00:02:13.601 --> 00:02:16.249
so times dy dx.

00:02:16.249 --> 00:02:17.138
As we say,

00:02:17.138 --> 00:02:19.035
and this is completely unfamiliar to you

00:02:19.035 --> 00:02:21.108
and I encourage you to
watch the several videos

00:02:21.108 --> 00:02:23.463
on Khan Academy on
implicit differentiation,

00:02:23.463 --> 00:02:25.637
which is really just an
extension of the chain rule.

00:02:25.637 --> 00:02:27.714
I took the derivative of three y squared

00:02:27.714 --> 00:02:29.238
with respect to y,

00:02:29.238 --> 00:02:30.617
and took the derivative of y

00:02:30.617 --> 00:02:32.035
with respect to x.

00:02:32.035 --> 00:02:33.728
Now, if I take the
derivative of negative x

00:02:33.728 --> 00:02:34.936
with respect to x,

00:02:34.936 --> 00:02:36.167
that's going to be negative one.

00:02:37.227 --> 00:02:38.397
Fair enough.

00:02:38.397 --> 00:02:39.696
And so, I took the derivative of this,

00:02:39.696 --> 00:02:40.891
I'm gonna multiply it times that.

00:02:40.891 --> 00:02:44.310
So times dy dx

00:02:44.310 --> 00:02:45.222
and then to that,

00:02:45.222 --> 00:02:47.800
I'm going to add the derivative of this

00:02:47.800 --> 00:02:48.752
with respect to x.

00:02:48.752 --> 00:02:50.763
Well, that's just going to
be the second derivative

00:02:50.763 --> 00:02:53.184
of y with respect to x

00:02:53.184 --> 00:02:54.208
times this.

00:02:54.208 --> 00:02:56.388
And all I do is apply the product rule.

00:02:56.388 --> 00:02:59.154
Three y squared minus x.

00:02:59.154 --> 00:03:00.795
Once again, I'll say it a third time,

00:03:00.795 --> 00:03:03.243
derivative of this times this

00:03:03.243 --> 00:03:05.366
plus the derivative of this

00:03:05.366 --> 00:03:06.603
times that.

00:03:06.603 --> 00:03:07.317
Alright.

00:03:07.317 --> 00:03:08.431
That's going to be equal to,

00:03:08.431 --> 00:03:09.543
on the right-hand side,

00:03:09.543 --> 00:03:11.752
derivative of y with respect to x

00:03:11.752 --> 00:03:15.154
is just dy dx.

00:03:15.154 --> 00:03:15.954
Now, if I want to,

00:03:15.954 --> 00:03:19.553
I could solve for the
second derivative of y

00:03:19.553 --> 00:03:20.912
with respect to x,

00:03:20.912 --> 00:03:22.317
but what could be even better than that

00:03:22.317 --> 00:03:25.901
is if I substitute
everything else with numbers

00:03:25.901 --> 00:03:27.464
because then it's just going to be a nice,

00:03:27.464 --> 00:03:30.637
easy numerical equation to solve.

00:03:30.637 --> 00:03:31.571
So, we know that,

00:03:31.571 --> 00:03:33.260
what we wanna figure out,

00:03:33.260 --> 00:03:34.072
our second derivative,

00:03:34.072 --> 00:03:36.375
when y is equal to one.

00:03:36.375 --> 00:03:38.297
So y is equal to one.

00:03:38.297 --> 00:03:40.160
So that's going to be equal to one

00:03:40.160 --> 00:03:43.474
and this is going to be equal to one.

00:03:43.474 --> 00:03:46.245
X is equal to negative one.

00:03:46.245 --> 00:03:48.106
So, let me underline that.

00:03:48.106 --> 00:03:50.075
X is equal to negative one.

00:03:50.075 --> 00:03:52.424
So x is negative one.

00:03:52.424 --> 00:03:53.908
Are there any other xs here?

00:03:53.908 --> 00:03:55.884
And what's dy dx?

00:03:55.884 --> 00:03:57.058
Well, dy dx,

00:03:58.088 --> 00:03:59.832
dy dx

00:03:59.832 --> 00:04:01.712
is going to be equal to

00:04:01.712 --> 00:04:05.682
one over three times one,

00:04:05.682 --> 00:04:07.564
which is three,

00:04:07.564 --> 00:04:11.767
minus negative one.

00:04:11.767 --> 00:04:13.300
So, this is equal to one fourth.

00:04:13.300 --> 00:04:16.120
In fact, that's I think where
we evaluated in the beginning.

00:04:16.120 --> 00:04:18.480
Yep, at the point negative one comma one.

00:04:18.480 --> 00:04:21.130
At the point negative one comma one.

00:04:21.130 --> 00:04:24.070
So that's dy dx is one fourth.

00:04:24.070 --> 00:04:26.936
So this is one fourth,

00:04:26.936 --> 00:04:28.982
this is one fourth,

00:04:28.982 --> 00:04:31.468
and this is one fourth.

00:04:31.468 --> 00:04:33.943
And now, we can solve for the second

00:04:33.943 --> 00:04:36.163
can solve for the second derivative.

00:04:36.163 --> 00:04:38.343
Just gonna make sure I don't
make any careless mistakes.

00:04:38.343 --> 00:04:41.683
So if six times one times one fourth

00:04:41.683 --> 00:04:44.684
is going to be one point five,

00:04:44.684 --> 00:04:45.573
or six,

00:04:45.573 --> 00:04:47.810
well, six times one times
one fourth is six fourths,

00:04:47.810 --> 00:04:50.479
minus one is going to be,

00:04:50.479 --> 00:04:52.498
so six fourths minus four
fourths is two fourths,

00:04:52.498 --> 00:04:54.370
so this is going to be one half

00:04:54.370 --> 00:04:56.339
times one fourth,

00:04:56.339 --> 00:04:57.627
times one fourth,

00:04:57.627 --> 00:04:59.270
that's this over here,

00:04:59.270 --> 00:05:02.007
plus the second derivative of y

00:05:02.007 --> 00:05:03.844
with respect to x,

00:05:03.844 --> 00:05:06.752
and here I have one minus negative one,

00:05:06.752 --> 00:05:07.681
so it's one plus one,

00:05:07.681 --> 00:05:08.956
so times two.

00:05:08.956 --> 00:05:10.615
So maybe I'll write it this way.

00:05:10.615 --> 00:05:13.670
Plus two times

00:05:13.670 --> 00:05:15.820
the second derivative of y

00:05:15.820 --> 00:05:17.262
with respect to x

00:05:17.262 --> 00:05:21.244
is equal to one fourth.

00:05:21.244 --> 00:05:22.596
And so let's see,

00:05:22.596 --> 00:05:25.492
I have one eighth

00:05:25.492 --> 00:05:29.422
plus two times the second derivative

00:05:29.422 --> 00:05:32.089
is equal to one fourth.

00:05:32.089 --> 00:05:33.138
And let's see,

00:05:33.138 --> 00:05:35.637
I could subtract one
eighth from both sides.

00:05:35.637 --> 00:05:37.552
So let's subtract one eighth.

00:05:37.552 --> 00:05:39.612
Subtract one eighth.

00:05:39.612 --> 00:05:40.406
These cancel.

00:05:40.406 --> 00:05:42.927
I get two times the second derivative of y

00:05:42.927 --> 00:05:44.441
with respect to x

00:05:44.441 --> 00:05:45.249
is equal to,

00:05:45.249 --> 00:05:46.851
one fourth is the same
thing as two eighths,

00:05:46.851 --> 00:05:48.995
so two eighths minus one
eighth is one eighth.

00:05:48.995 --> 00:05:50.915
And then I can divide both sides by two,

00:05:50.915 --> 00:05:52.772
and we get a little bit
of a drum roll here,

00:05:52.772 --> 00:05:54.235
we divide both sides by two,

00:05:54.235 --> 00:05:57.195
or you could say multiple
both sides times one half,

00:05:58.095 --> 00:06:00.323
and you are going to get,

00:06:00.323 --> 00:06:01.713
you are going to get

00:06:01.713 --> 00:06:04.523
the second derivative of y

00:06:04.523 --> 00:06:06.500
with respect to x

00:06:06.500 --> 00:06:08.283
when x is negative one

00:06:08.283 --> 00:06:09.761
and y is equal to one,

00:06:09.761 --> 00:06:13.401
is one over 16.

00:06:13.401 --> 00:06:14.924
And we're done.


2015 AP Calculus AB 6a

WEBVTT
Kind: captions
Language: en

00:00:00.281 --> 00:00:02.719
- [Voiceover] Consider the
curve given by the equation

00:00:02.719 --> 00:00:06.040
Y to the third minus XY is equal to two.

00:00:06.040 --> 00:00:08.501
It can be shown that the derivative of Y

00:00:08.501 --> 00:00:13.501
with respect to X is equal
to Y over three Y squared

00:00:13.527 --> 00:00:15.304
minus X.

00:00:15.304 --> 00:00:16.384
All right?

00:00:16.384 --> 00:00:19.403
Write an equation for the
line tangent to the curve

00:00:19.403 --> 00:00:22.967
at the point negative one comma one.

00:00:22.967 --> 00:00:25.602
All right, so we can figure
out the equation for the line

00:00:25.602 --> 00:00:27.599
if we know the slope of the line

00:00:27.599 --> 00:00:29.248
and we know a point that it goes through

00:00:29.248 --> 00:00:30.502
so that should be enough to figure out

00:00:30.502 --> 00:00:32.359
the equation of the line.

00:00:32.359 --> 00:00:34.519
So the line's going to have a form

00:00:34.519 --> 00:00:38.164
Y is equal to MX plus B.

00:00:38.164 --> 00:00:43.164
M is the slope and is
going to be equal to DY/DX

00:00:44.538 --> 00:00:45.980
at that point,

00:00:45.980 --> 00:00:48.292
and we know that that's
going to be equal to.

00:00:48.292 --> 00:00:50.557
We'll see Y is, when X is negative one,

00:00:50.557 --> 00:00:53.134
Y is one, that sits on this curve.

00:00:53.134 --> 00:00:54.991
So Y is one.

00:00:54.991 --> 00:00:58.300
So one over three Y squared.

00:00:58.300 --> 00:01:00.936
So three times one squared which is three,

00:01:00.936 --> 00:01:04.198
minus X, when Y is one,

00:01:04.198 --> 00:01:07.938
X is negative one, or when
X is negative one, Y is one.

00:01:07.938 --> 00:01:09.808
So X is negative one here.

00:01:10.800 --> 00:01:11.767
And so this is the same thing as

00:01:11.767 --> 00:01:13.812
three plus positive one,

00:01:13.812 --> 00:01:16.470
and so this is equal to one fourth

00:01:16.470 --> 00:01:17.854
and so the equation of our line

00:01:17.854 --> 00:01:22.854
is going to be Y is equal
to one fourth X plus B.

00:01:23.287 --> 00:01:24.887
Now we need to solve for B

00:01:24.887 --> 00:01:26.605
and we know that point negative one

00:01:26.605 --> 00:01:27.929
comma one is on the line,

00:01:27.929 --> 00:01:30.530
so we can use that
information to solve for B.

00:01:30.530 --> 00:01:32.225
This line is tangent to the curve.

00:01:32.225 --> 00:01:34.732
So includes this point
and only that point.

00:01:34.732 --> 00:01:36.672
That's what it has in
common with the curve

00:01:36.672 --> 00:01:39.445
and so why is equal to one

00:01:39.445 --> 00:01:42.732
when X is equal to negative one,

00:01:42.732 --> 00:01:46.763
plus B and so we have one is equal to

00:01:46.763 --> 00:01:50.048
negative one fourth plus B.

00:01:50.048 --> 00:01:52.660
You add one fourth to both sides,

00:01:52.660 --> 00:01:55.307
you get B is equal to,

00:01:55.307 --> 00:01:57.507
we could either write it
as one and one fourth,

00:01:57.507 --> 00:01:59.783
which is equal to five fourths,

00:01:59.783 --> 00:02:02.825
which is equal to 1.25.

00:02:02.825 --> 00:02:04.566
We could write it any of those ways,

00:02:04.566 --> 00:02:06.842
so the equation for the
line tangent to the curve

00:02:06.842 --> 00:02:10.243
at this point is Y is equal to

00:02:10.243 --> 00:02:14.469
our slope is one fourth X plus

00:02:14.469 --> 00:02:16.722
and I could write it in any of these ways.

00:02:16.722 --> 00:02:21.722
I'll write it as plus five over four

00:02:21.970 --> 00:02:25.796
and we're done at least with
that part of the problem.


2015 AP Calculus AB/BC 1c

WEBVTT
Kind: captions
Language: en

00:00:00.259 --> 00:00:01.606
- [Voiceover] All right, part c.

00:00:01.606 --> 00:00:04.924
What time t, where zero
is less than or equal to t

00:00:04.924 --> 00:00:06.248
is less than or equal to eight,

00:00:06.248 --> 00:00:09.267
is the amount of water
in the pipe at a minimum?

00:00:09.267 --> 00:00:12.041
Justify your answer.

00:00:12.041 --> 00:00:14.059
All right, well, let's define a function w

00:00:14.059 --> 00:00:16.242
that represents the amount
of water in the pipe

00:00:16.242 --> 00:00:18.349
at anytime, t, and then
we could figure out how

00:00:18.349 --> 00:00:21.665
to figure out the minimum
value for w over that interval.

00:00:21.665 --> 00:00:24.454
So let's just say w of t.

00:00:24.454 --> 00:00:26.254
So that's the amount of water in the pipe

00:00:26.254 --> 00:00:28.487
at any given time, t.

00:00:28.487 --> 00:00:33.363
It's going to be equal to, well,
we start with 30 cubic feet

00:00:33.363 --> 00:00:35.152
of water in the pipe that t equals zero

00:00:35.152 --> 00:00:37.091
that tells us that right up here.

00:00:37.091 --> 00:00:38.837
So we start with that much.

00:00:38.837 --> 00:00:42.333
And then we are going to add
or take away some amount.

00:00:42.333 --> 00:00:44.795
So then it's going to be plus.

00:00:44.795 --> 00:00:48.614
We're going to sum up
from time zero to time t.

00:00:48.614 --> 00:00:50.217
Remember this is the function of t.

00:00:50.217 --> 00:00:53.711
Well, let's sum up our net inflow

00:00:53.711 --> 00:00:56.718
times little small changes in time.

00:00:56.718 --> 00:00:58.692
We will sum up all those
small changes in time

00:00:58.692 --> 00:01:02.094
from zero to t and that will
give us our aggregate inflow

00:01:02.094 --> 00:01:03.858
or aggregate net inflow.

00:01:03.858 --> 00:01:05.879
So what is our net inflow?

00:01:05.879 --> 00:01:08.456
Well, you have the function R which says

00:01:08.456 --> 00:01:10.894
the rate which the water is
entering and your function d

00:01:10.894 --> 00:01:13.274
which is the rate which water is exiting.

00:01:13.274 --> 00:01:15.429
Instead of using t as our variable,

00:01:15.429 --> 00:01:19.421
I'm going to use x since t is
already one of our variable,

00:01:19.421 --> 00:01:22.186
is one of our boundaries of integration.

00:01:22.186 --> 00:01:23.487
We can use any variable we want.

00:01:23.487 --> 00:01:25.519
It's really just a bit
of a placeholder variable

00:01:25.519 --> 00:01:26.761
for the integration.

00:01:26.761 --> 00:01:30.059
So our net inflow is

00:01:30.059 --> 00:01:32.013
R, I'll say R of x

00:01:32.013 --> 00:01:35.055
minus D of x

00:01:35.055 --> 00:01:36.478
and then dx.

00:01:36.478 --> 00:01:38.777
Once again, this is
our net rate of inflow.

00:01:38.777 --> 00:01:40.390
This is our inflow minus our outflow

00:01:40.390 --> 00:01:43.641
so our net rate of inflow
times small changes,

00:01:43.641 --> 00:01:46.230
we could view this as
time although it's x,

00:01:46.230 --> 00:01:48.761
and then we sum up from zero to time

00:01:48.761 --> 00:01:50.444
is equal to t.

00:01:50.444 --> 00:01:53.359
So this is how much water
we are going to have

00:01:53.359 --> 00:01:58.316
in the pipe at any time t.

00:01:58.316 --> 00:02:01.880
So let's now think about at what point

00:02:01.880 --> 00:02:04.887
does w hit a minimum in the central.

00:02:04.887 --> 00:02:06.141
And there's three possibilities

00:02:06.141 --> 00:02:08.928
where w could hit a minimum point.

00:02:08.928 --> 00:02:10.983
It could hit a minimum
at right at the beginning

00:02:10.983 --> 00:02:13.548
at each at w of zero.

00:02:13.548 --> 00:02:15.162
It could hit it at the end of our interval

00:02:15.162 --> 00:02:17.681
at w of eight at t equals eight

00:02:17.681 --> 00:02:19.469
or it could be some place in between

00:02:19.469 --> 00:02:22.407
where w is at a local maximum point.

00:02:22.407 --> 00:02:25.483
In which case, the derivative
of w will be equal to zero.

00:02:25.483 --> 00:02:28.363
So let's first evaluate
w at the end points.

00:02:28.363 --> 00:02:30.986
So w of zero.

00:02:30.986 --> 00:02:31.729
Oh, we know that.

00:02:31.729 --> 00:02:33.668
That's the boundary of a zero to zero

00:02:33.668 --> 00:02:35.422
that they gave it to us in the problem

00:02:35.422 --> 00:02:38.730
is the initial state is
we have 30 cubic feet

00:02:38.730 --> 00:02:41.363
of water in the pipe already.

00:02:41.363 --> 00:02:44.405
And now, what is w of eight?

00:02:44.405 --> 00:02:46.390
Well, this is going to be 30

00:02:46.390 --> 00:02:49.409
plus the definite integral
from zero to eight

00:02:49.409 --> 00:02:53.948
of R of x minus D of x,

00:02:53.948 --> 00:02:56.793
minus D of x, dx.

00:02:56.793 --> 00:02:58.825
And lucky for us, we're
allowed to use a calculator

00:02:58.825 --> 00:03:01.924
so let's use a calculator
to evaluate this.

00:03:01.924 --> 00:03:04.270
And so, let me get my calculator out.

00:03:04.270 --> 00:03:07.247
Let me go see the
definition of R of x, D of x

00:03:07.247 --> 00:03:10.115
right over here so I can type them in.

00:03:10.115 --> 00:03:11.032
And what I'm gonna do

00:03:11.032 --> 00:03:13.324
and there's a bunch of ways
of more advance you get

00:03:13.324 --> 00:03:15.973
with a calculator that
might save you some time

00:03:15.973 --> 00:03:17.299
in front of the AP test.

00:03:17.299 --> 00:03:19.103
I'm actually gonna define a function

00:03:19.103 --> 00:03:23.619
that is R of x minus D of x.

00:03:23.619 --> 00:03:25.326
So everywhere I see t,
I'm gonna substitute it.

00:03:25.326 --> 00:03:26.708
I'm gonna use x instead.

00:03:26.708 --> 00:03:28.493
And then I could use that later on

00:03:28.493 --> 00:03:31.883
to integrate it or to
solve it in some way.

00:03:31.883 --> 00:03:32.719
So let's do that.

00:03:32.719 --> 00:03:34.913
So y1 is gonna be 20

00:03:34.913 --> 00:03:37.641
times sine

00:03:37.641 --> 00:03:40.938
of x squared

00:03:40.938 --> 00:03:43.794
divided by 35,

00:03:43.794 --> 00:03:45.501
close parenthesis,

00:03:45.501 --> 00:03:47.603
minus open parenthesis.

00:03:47.603 --> 00:03:51.759
You have negative 0.04

00:03:51.759 --> 00:03:54.534
times t to the third power

00:03:54.534 --> 00:03:57.819
or sorry, so I'll write times x,

00:03:57.819 --> 00:04:02.301
x to the third power

00:04:02.301 --> 00:04:05.923
plus 0.4

00:04:05.923 --> 00:04:10.660
times x squared

00:04:10.660 --> 00:04:15.235
plus 0.96

00:04:15.235 --> 00:04:19.414
times x.

00:04:19.414 --> 00:04:22.607
And then I can close these parentheses.

00:04:22.607 --> 00:04:24.290
So does that make sense?

00:04:24.290 --> 00:04:26.125
20 times sine of x squared

00:04:26.125 --> 00:04:28.667
divided by 35 minus negative 0.04

00:04:28.667 --> 00:04:30.885
x to the third plus 0.4

00:04:30.885 --> 00:04:35.250
x squared plus 0.96 times x.

00:04:35.250 --> 00:04:36.248
All right, there you go.

00:04:36.248 --> 00:04:38.733
I have defined y1.

00:04:38.733 --> 00:04:42.193
And now I can use that to
evaluate different things.

00:04:42.193 --> 00:04:45.653
So let me now go back here.

00:04:45.653 --> 00:04:47.278
And so let me evaluate
what this is going to be.

00:04:47.278 --> 00:04:51.353
This is going to be 30
plus the definitive role

00:04:51.353 --> 00:04:52.874
of the math functions.

00:04:52.874 --> 00:04:54.313
You scroll down a little bit.

00:04:54.313 --> 00:04:56.855
You have, this is the function
for definite integral,

00:04:56.855 --> 00:04:58.678
function integral.

00:04:59.588 --> 00:05:01.592
The function is y1

00:05:01.592 --> 00:05:03.183
and I can go to vars.

00:05:03.183 --> 00:05:04.217
I'm gonna get my y vars.

00:05:04.217 --> 00:05:05.784
It's gonna be a function variable.

00:05:05.784 --> 00:05:08.385
So y1 is what I select.

00:05:08.385 --> 00:05:10.695
I could have typed it in but
this will hopefully save time

00:05:10.695 --> 00:05:12.286
and I can reuse y1.

00:05:12.286 --> 00:05:16.280
And my variable integration is x.

00:05:16.280 --> 00:05:18.475
I'm going from zero to eight.

00:05:18.475 --> 00:05:20.459
From my lower bound is zero.

00:05:20.459 --> 00:05:23.582
My upper bound is eight.

00:05:23.582 --> 00:05:25.475
Let's see, did I type everything in?

00:05:25.475 --> 00:05:26.578
All right.

00:05:26.578 --> 00:05:28.458
And I'm gonna munch a little bit.

00:05:28.458 --> 00:05:29.236
And there you have it.

00:05:29.236 --> 00:05:33.764
It's approximately 48.544

00:05:33.764 --> 00:05:37.154
cubic feet of water at t equals eight.

00:05:37.154 --> 00:05:38.060
So let me write that,

00:05:38.060 --> 00:05:40.858
48.544.

00:05:40.858 --> 00:05:43.122
So this is

00:05:43.122 --> 00:05:45.389
approximately

00:05:45.389 --> 00:05:49.839
48.544 cubic feet.

00:05:49.839 --> 00:05:52.178
And now let's see if
there's any point in between

00:05:52.178 --> 00:05:55.185
where w hits a local maximum point

00:05:55.185 --> 00:05:56.879
or a local minimum point I should say.

00:05:56.879 --> 00:05:59.259
I think I said a local maximum earlier on.

00:05:59.259 --> 00:06:01.198
I should say a local minimum point.

00:06:01.198 --> 00:06:04.042
And so if it's at a local
or maximum point really,

00:06:04.042 --> 00:06:06.422
the derivative of w is going to be zero.

00:06:06.422 --> 00:06:10.602
So let's see, at what t do
we get a zero derivative?

00:06:10.602 --> 00:06:13.458
So w prime of t.

00:06:13.458 --> 00:06:16.434
Well, the derivative or a
constant with respect to t is zero

00:06:16.434 --> 00:06:18.892
and the derivative of
this with respect to t

00:06:18.892 --> 00:06:22.189
and this comes from the
fundamental theorem of calculus,

00:06:22.189 --> 00:06:25.928
this is going to be R of t

00:06:25.928 --> 00:06:28.122
minus D of t.

00:06:28.122 --> 00:06:29.527
Well, once again, this is a function.

00:06:29.527 --> 00:06:31.013
We have t as the upper bound.

00:06:31.013 --> 00:06:33.045
And so we have whatever
here that we are integrating

00:06:33.045 --> 00:06:35.727
but it is now going to be a function of t.

00:06:35.727 --> 00:06:38.443
And so in order for this
to be equal to zero,

00:06:38.443 --> 00:06:39.790
we have to figure out when does

00:06:39.790 --> 00:06:42.809
R of t minus D of t equals zero.

00:06:42.809 --> 00:06:44.469
And lucky for us, we've already typed in

00:06:44.469 --> 00:06:46.017
R of t minus D of t.

00:06:46.017 --> 00:06:50.417
We defined that as y sub
one on our calculator.

00:06:50.417 --> 00:06:52.437
So let's go back here.

00:06:52.437 --> 00:06:54.620
And now I can use the Solver.

00:06:54.620 --> 00:06:55.932
So go to math

00:06:55.932 --> 00:06:57.507
and then let's see if I scroll up.

00:06:57.507 --> 00:06:59.655
Let's see or this is, I get to the Solver.

00:06:59.655 --> 00:07:00.714
I could have scrolled down as well.

00:07:00.714 --> 00:07:02.476
It's right below definite integral.

00:07:02.476 --> 00:07:03.897
So I go to the Solver.

00:07:03.897 --> 00:07:06.521
And I say the equation zero equals,

00:07:06.521 --> 00:07:08.312
and I could just go to y1.

00:07:08.312 --> 00:07:10.727
So go to my y variables, function.

00:07:10.727 --> 00:07:12.689
I select y1.

00:07:12.689 --> 00:07:15.684
So in my equation is equal to y1.

00:07:15.684 --> 00:07:18.355
And I press Enter.

00:07:18.355 --> 00:07:20.735
And now I could put an initial guess

00:07:20.735 --> 00:07:24.334
for what x value is going
to solve that equation.

00:07:24.334 --> 00:07:27.526
Usually a t value but I'm
using x as a variable here.

00:07:27.526 --> 00:07:30.626
And now I do alpha and
I quickly solve here.

00:07:30.626 --> 00:07:33.285
So a little blue you see
right above the Enter.

00:07:33.285 --> 00:07:36.986
And it gets to,

00:07:36.986 --> 00:07:38.386
well, zero is one of them.

00:07:38.386 --> 00:07:41.692
Let's see if I can get another one.

00:07:41.692 --> 00:07:43.318
So let's see if I can get,

00:07:43.318 --> 00:07:46.812
let's see if I started two, alpha,

00:07:46.812 --> 00:07:50.018
solve, what it munch on that a little bit.

00:07:50.018 --> 00:07:52.932
Okay, so this is actually
within the interval.

00:07:52.932 --> 00:07:55.646
So approximately

00:07:55.646 --> 00:08:00.646
3.272.

00:08:01.436 --> 00:08:04.099
So t is approximately

00:08:04.099 --> 00:08:07.829
3.272.

00:08:07.829 --> 00:08:09.952
That's where we have a local minimum point

00:08:09.952 --> 00:08:12.142
but now we have to evaluate w there.

00:08:12.142 --> 00:08:13.692
So we have to evaluate w

00:08:13.692 --> 00:08:17.753
at 3.272

00:08:17.753 --> 00:08:20.036
to figure out if it's truly lower

00:08:20.036 --> 00:08:21.801
than w zero.

00:08:21.801 --> 00:08:24.262
W of eight is higher than w of zero.

00:08:24.262 --> 00:08:26.085
So, how do we do that?

00:08:26.085 --> 00:08:28.918
Well, luckily, we can go back.

00:08:28.918 --> 00:08:31.728
So second quit.

00:08:31.728 --> 00:08:34.386
And that should be stored
into the variable x.

00:08:34.386 --> 00:08:35.594
Yep, it's right there.

00:08:35.594 --> 00:08:38.276
So then we can say, well, let's calculate.

00:08:38.276 --> 00:08:40.412
We wanna calculate the function evaluated

00:08:40.412 --> 00:08:43.013
when t is 3.272.

00:08:43.013 --> 00:08:47.843
So our function is 30

00:08:47.843 --> 00:08:49.990
plus the definite integral.

00:08:49.990 --> 00:08:51.808
Go to the math.

00:08:51.808 --> 00:08:54.503
So definite integral.

00:08:54.503 --> 00:08:56.887
Once again, we have y1.

00:08:56.887 --> 00:09:00.701
So let me go to my y
variables, function, y1.

00:09:00.701 --> 00:09:04.625
We already defined that
as R of x minus D of x.

00:09:04.625 --> 00:09:08.212
Our variable of integration is x.

00:09:08.212 --> 00:09:11.743
Our lower bound is zero

00:09:11.743 --> 00:09:13.793
and our upper bound

00:09:13.793 --> 00:09:18.011
is 3.272

00:09:18.011 --> 00:09:20.263
we've restored in the variable x.

00:09:20.263 --> 00:09:21.703
So we can actually,
it's a little confusing.

00:09:21.703 --> 00:09:23.352
This is saying what's
our variable integration.

00:09:23.352 --> 00:09:24.733
This is the actual variable.

00:09:24.733 --> 00:09:27.195
This is actual value for upper bound.

00:09:27.195 --> 00:09:31.538
And so let's munch on it a little bit

00:09:31.538 --> 00:09:35.318
and we get 27.965.

00:09:35.318 --> 00:09:39.382
So this is approximately equal to

00:09:39.382 --> 00:09:43.236
27.965.

00:09:43.236 --> 00:09:45.082
So now we're ready to answer.

00:09:45.082 --> 00:09:47.277
At what time t is the amount of water

00:09:47.277 --> 00:09:48.914
in the pipe at a minimum?

00:09:48.914 --> 00:09:51.792
We can see that at time

00:09:51.792 --> 00:09:53.871
3.272,

00:09:53.871 --> 00:09:55.424
we have less water in the pipe

00:09:55.424 --> 00:09:57.201
than either right when we started

00:09:57.201 --> 00:09:59.267
or right at the end of our interval

00:09:59.267 --> 00:10:00.625
at t equals eight.

00:10:00.625 --> 00:10:02.239
So, at what time t?

00:10:02.239 --> 00:10:06.349
We say t is equal to 3.272.

00:10:06.349 --> 00:10:10.668
We could write w of 3.272

00:10:10.668 --> 00:10:13.327
is less than w of zero

00:10:13.327 --> 00:10:15.992
which is less than w of eight.

00:10:15.992 --> 00:10:19.126
So this indeed just by knowing
the derivative of the zero,

00:10:19.126 --> 00:10:20.670
it could be a minimum or maximum.

00:10:20.670 --> 00:10:22.853
But the fact that it's lower
than both of the end points,

00:10:22.853 --> 00:10:26.620
this tells us that,
hey, this is a minimum,

00:10:26.620 --> 00:10:30.493
minimum point

00:10:30.493 --> 00:10:31.944
right over there

00:10:31.944 --> 00:10:34.995
or we could say that t equals 3.272

00:10:34.995 --> 00:10:38.757
is where we hit out minimum value.