CAHSEE Practice: Problems 28-31 CAHSEE Practice: Problems 28-31
CAHSEE Practice: Problems 28-31
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- 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.
- 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.
- The graph below compares the weight of an object on Earth
- to its weight on the Moon.
- 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.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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