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# CAHSEE practice: Problems 28-31

Video transcript

Problem 28. Which equation best represents
the part of the graph shown below? So we have a bunch of
equations here. Let's see. This one is just a linear
equation, so this is just some number times x. So that graph in general would
be a straight line. This one and this one
are straight lines. This one would be a straight
line with a positive slope, maybe look something
like that. This choice C right here would
be a straight line with a negative slope, like that. They would both go through the
origin, because they don't have any y-intercept
right there. So neither of these
are the answer. So let's look at these two--
I guess we could call them quadratics. So here we have 1.75x squared. So the graph of x squared--
let me do it in a better color-- the graph of x squared
looks like this. It's a parabola. You've seen that before. And they're drawing it in the
first quadrant right there, and that looks about right. And you're like, hey, but
what about the 1.75? Well, that's just a
scaling factor. If you throw a larger number
there, it'll curve up a little bit faster. If you throw a smaller number
there, it'll curve up a little bit slower. But the general idea is that
they all have the general shape of a parabola. So this one looks pretty good. It's an upward opening
parabola. It's kind of an upright U. So this looks like a pretty
good solution. If we were to draw the whole
graph, it would continue on this side like that. Then choice D, it's just like
choice B, except they have a minus here. And the reason why I know that's
not going to work is that the graph of minus x
squared, or minus anything times x squared is going
to look like this. It's going to be downward
opening. So this is the graph of minus x
squared, the graph of minus 1.75x squared, might
open up or go down a little bit faster. So it's going to have the
same general shape. So we know that this is also
not the right answer. So our choice is B. Next question. 29. Lisa typed a 1,000-word essay
at the average rate of 20 words per minute. If she started typing at 6:20
PM and did not take any breaks, at what time did Lisa
finish typing the essay? So she had a 1,000-word essay
and she was typing at 20 words per minute. So let me write that down. So she had 1,000 words
and she's typing at 20 words per minute. So if you're writing 1,000 words
and you're doing 20 per minute, how many minutes
is it going to take? Well, what's 1,000
divided by 20? You could do this
in your head. You say 100 divided
by 20 is 5. 1,000 is 10 hundreds. So it's going to be 50. But if you don't want to do it
in your head, you can just say 20 goes into 1,000-- 20 goes
into 10 zero times. 20 goes into 100 five times. 5 times 20 is 100, and then
you bring down the 0. 20 goes into 0 zero times, and
then 0 times 20 is 0, and then you are done. 20 goes into 1,000
fifty times. Or you could say 2 goes
into 100 five times. All the same thing. Just 20-- and then--
sorry, 50. Want to be careful. So it'll take her 50 minutes,
and actually the units work out. You have words divided by words
per minute, or that's the same thing as words times
minutes per word. They cancel out, and you
end up with 50 minutes. If that confuses you, don't
worry about it too much. The intuition is what's
important. You had a 1,000-word essay, you
did 20 words per minute. So it was going to take
you 50 minutes. 50 minutes times 20 words
per minute is equal to 1,000 words. So you're going to
have 50 minutes. So she starts at 6:20 PM. So at 7:00 PM, she's worked
for 40 minutes. Because there's 60 minutes
in an hour. But she works for 50
minutes, so she does another 10 minutes. So that gets her to 7:10. So the choice is D. Problem 30. What does-- let me
do it in red. What does x to the fifth equal
when x is equal to minus 2? So it's minus 2 times minus 2
times minus 2 times minus 2 times minus 2. Now we can just multiply
it all out. Let's just do that,
just for fun. Minus 2 times minus
2 is positive 4. Then positive 4 times
minus 2 is minus 8. Minus 8 times minus
2 is positive 16. Positive 16 times minus
2 is minus 32. So our answer is A. Now, if you wanted to do that
really fast, you might recognize, well, 2 to
the fifth is 32. So it's either going to be that
choice or that choice. And then we have
a odd exponent. So we're going to be multiplying
a negative times itself an even time, and
then one more negative. So you're going to get
a negative number. When you have an odd exponent,
you're going to end up with a negative. You have an even exponent,
you'll end up with a positive. So that would have been the fast
way to do it, but even if you didn't do that, you could
have just multiplied it straight out like we just did. And just remember a negative
times a negative is a positive, and then a
positive times the negative is a negative. It's minus 32. 31. The graph below compares the
weight of an object on Earth to its weight on the Moon. Interesting. An object's weight on the Moon,
OK, so this is the Moon weight, this is the
Earth weight. So something that-- let's say--
well, I actually do weigh 150 pounds. So I weigh 150 pounds on Earth,
and according to this chart, I would weigh 25
pounds on the Moon. Or I would weigh essentially
1/6 my weight that I am on Earth. What is it asking me? What is the approximate weight
on the Moon of an astronaut who weighs 120 pounds
on Earth? Well, I just said, essentially
this thing is just taking 1/6. You can look at any point. When you weigh 10 pounds on
the Moon, you're weighing roughly 60 pounds on Earth,
or vice versa. So you just take 1/6,
or we could actually just look at the chart. 120 pounds-- so if we go
halfway, that's about 125, between 100 and 150. 120 pounds would
be right there. You go up the graph,
just like that. And you go there, and it looks
like 18 or 19 pounds. And they say, what is the
approximate weight? So the closest thing we are
here, let's see, the choice of 15 and 20. We're definitely closer to
20 than we are to 15. So I will go with
20 right here. And you know, if we really
wanted to look at it, this is actually the point that we
should have looked at, this point right here would
have been 120 pounds. But you just approximate where
120 is, you read the graph, you say, oh, it's closer
to 20 than any of these other choices. So that'll be our answer.