CAHSEE
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CAHSEE Practice: Problems 1-3
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CAHSEE Practice: Problems 4-9
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CAHSEE Practice: Problems 10-12
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CAHSEE Practice: Problems 13-14
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CAHSEE Practice: Problems 15-16
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CAHSEE Practice: Problems 17-19
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CAHSEE Practice: Problems 20-22
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CAHSEE Practice: Problems 23-27
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CAHSEE Practice: Problems 28-31
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CAHSEE Practice: Problems 32-34
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CAHSEE Practice: Problems 35-37
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CAHSEE Practice: Problems 38-42
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CAHSEE Practice: Problems 43-46
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CAHSEE Practice: Problems 47-51
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CAHSEE Practice: Problems 52-53
CAHSEE Practice: Problems 35-37 CAHSEE Practice: Problems 35-37
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- Problem 35.
- In the figure below, every angle is a right angle.
- So they're just saying that's a right angle,
- that's a right angle, these are all right angles.
- You get the idea.
- What is the area, in square units, of the figure?
- So the area. How can we figure this out?
- We can divide this up into a bunch of rectangles
- and figure out their respective areas.
- So if we drew a rectangle right here,
- that rectangle, what's its area?
- It's going to be 6 times 8, which is 48.
- That's that rectangle right there, is 48 square units.
- Let's see what else we can do.
- We can do this rectangle right here.
- That rectangle right there is also 6 by 8,
- so this is also going to be 48 square units right there.
- And then we have-- we'll do it in another color.
- We have this rectangle--
- that rectangle right there is divided right there--
- we have this rectangle right here, which is 3 by 4.
- So 3 times 4 is 12 units.
- And then you have this rectangle right here,
- which is 3 by 4.
- So it's also 12 square units.
- So the whole area of the entire thing is 12 plus 48,
- which is 60. Right?
- 2 plus 48 is 50, right, that's 60.
- So you have 60 there, and then you have another 48,
- gives you 108, plus 12, which is 120.
- So the area in square units of the figure is 120.
- Problem 36.
- A rectangular field is 363 feet long and 240 feet wide.
- How many acres is the field?
- So let me draw this field.
- I'll do it in green because we're talking about a field.
- So it is 363 feet long and 240 feet wide.
- That's the dimensions of the field.
- So if we wanted to do it in square feet,
- we would multiply these two numbers.
- So how many square feet is it?
- Well, I'll do it out here. I'll do it on the left.
- So let me multiply it out.
- We have 240 times 363.
- Actually, I want to do it with a little bit more space.
- So we're going to do it in blue.
- Maybe I should do it here.
- I don't think it will confuse you.
- So I have 240 times 363.
- 3 times 0 is 0.
- 3 times 4 is 12.
- Carry the 1.
- 3 times 2 is 6, plus 1 is 7.
- So it's 720.
- We can ignore that for a little bit.
- Throw a 0 down here.
- 6 times 0 is 0.
- 6 times 4 is 24.
- 6 times 2 is 12, plus this 2 is 14.
- And then we have our last row to deal with.
- So we're going to add two 0's
- because we're dealing with the hundreds place.
- 3 times 0 is 0.
- 3 times 4 is 12.
- This was 4, carry the 1.
- 3 times 2 is 6, plus 1 is 7.
- And now we can just add everything up.
- 0.
- 2.
- 7 plus 4 is 11.
- Carry the 1.
- 1 plus 4 is 5.
- 5 plus 2 is 7.
- And then we have 1 plus 7 is 8.
- So the field is 87,120 square feet.
- Now, they want to know how many acres is the field?
- And they say an acre is 43,560.
- And you see all your choices are whole numbers.
- And you can just eyeball this, that 87,000
- whatever is roughly twice 43,560. Right?
- 80,000 is roughly twice 40,000.
- If you wanted to just hand-wave it,
- you could just say, well, that's just choice number A,
- or that's just 2, right?
- This looks like 2 times that.
- And if you wanted to verify it,
- 2 times-- let's verify it.
- Let me do it in a color that you can actually see.
- So 43,560-- you wouldn't actually have to do
- this on the test,
- but I want to show you that our approximation works.
- 2 times 0 is 0.
- 2 times 6 is 12.
- 2 times 5 is 10, plus the 1 is 11.
- 2 times 3 is 6, plus 1 is 7.
- 2 times 4 is 8.
- And we've got the exact number
- which was the square footage of the field.
- So it's 2 acres.
- So if you do it like that, it's 2 acres.
- 1 acre and 2 acres, just like that.
- 37.
- The object below is made of 10 rectangular prisms--
- that just means these three-dimensional rectangular things--
- each with dimensions of 5 centimeters
- by 3 centimeters by 2 centimeters.
- What is the volume, in cubic centimeters, of the object?
- So it's kind of this plus sign,
- or this cross looking thing.
- And they do this-- I mean,
- these things are really just to throw you off.
- So what is the volume of each of these
- little cubes right there?
- So its volume is 5 times 2 times 3.
- So each cube has a volume of, what's 5 times 2?
- Is 10, times 3 is 30.
- So each has 30 cubic centimeters.
- Do it in a darker color.
- Each of these is 30 cubic centimeters.
- And how many of these are there in this structure?
- Well, we have 2 layers.
- The top layer has 1 box here, that's 1, 2--
- this is the second box-- 2, 3, 4, and then 5.
- So the top layer has 5 in this plus sign.
- I could draw it like this.
- 1, 2, 3, 4, 5.
- So if we have 5 in the top layer, and we have 2 layers.
- So we have 10 of these boxes, right?
- So 10 boxes,
- or rectangular prisms if you want to call it that,
- times 30 cubic centimeters per box.
- The boxes cancel out, you get 10 times 30 cubic centimeters,
- and you get 300 cubic centimeters is the volume of
- this entire structure.
- And that is choice D.
- I literally think they drew these little diagonals
- just to confuse you,
- just to maybe make you think that
- you have to do something with triangles.
- But no, you just have to count the number of boxes
- and figure out the volume of each of them.
- We had 10 boxes,
- each of them has a volume of 30 cubic centimeters,
- so 300 cubic centimeters total.
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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