CAHSEE practice: Problems 35-37

WEBVTT
Kind: captions
Language: en

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Problem 35.

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In the figure below, every
angle is a right angle.

00:00:04.940 --> 00:00:06.940
So they're just saying that's a
right angle, that's a right

00:00:06.940 --> 00:00:09.330
angle, these are all
right angles.

00:00:09.330 --> 00:00:10.610
You get the idea.

00:00:10.610 --> 00:00:16.140
What is the area, in square
units, of the figure?

00:00:16.140 --> 00:00:16.850
So the area.

00:00:16.850 --> 00:00:18.520
How can we figure this out?

00:00:18.520 --> 00:00:21.670
We can divide this up into a
bunch of rectangles and figure

00:00:21.670 --> 00:00:23.520
out their respective areas.

00:00:23.520 --> 00:00:29.390
So if we drew a rectangle right
here, that rectangle,

00:00:29.390 --> 00:00:29.880
what's its area?

00:00:29.880 --> 00:00:33.770
It's going to be 6 times
8, which is 48.

00:00:33.770 --> 00:00:38.190
That's that rectangle right
there, is 48 square units.

00:00:38.190 --> 00:00:39.840
Let's see what else we can do.

00:00:39.840 --> 00:00:42.390
We can do this rectangle
right here.

00:00:42.390 --> 00:00:45.730
That rectangle right there is
also 6 by 8, so this is also

00:00:45.730 --> 00:00:49.620
going to be 48 square
units right there.

00:00:49.620 --> 00:00:52.510
And then we have-- we'll
do it in another color.

00:00:52.510 --> 00:00:55.640
We have this rectangle-- that
rectangle right there is

00:00:55.640 --> 00:00:58.390
divided right there-- we have
this rectangle right here,

00:00:58.390 --> 00:00:59.960
which is 3 by 4.

00:00:59.960 --> 00:01:02.190
So 3 times 4 is 12 units.

00:01:02.190 --> 00:01:05.880
And then you have this
rectangle right here,

00:01:05.880 --> 00:01:07.320
which is 3 by 4.

00:01:07.320 --> 00:01:09.320
So it's also 12 square units.

00:01:09.320 --> 00:01:13.190
So the whole area of the entire
thing is 12 plus 48,

00:01:13.190 --> 00:01:14.450
which is 60.

00:01:14.450 --> 00:01:14.700
Right?

00:01:14.700 --> 00:01:16.980
2 plus 48 is 50, right,
that's 60.

00:01:16.980 --> 00:01:20.550
So you have 60 there, and then
you have another 48, gives you

00:01:20.550 --> 00:01:23.120
108, plus 12, which is 120.

00:01:23.120 --> 00:01:28.690
So the area in square units
of the figure is 120.

00:01:28.690 --> 00:01:30.890
Problem 36.

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A rectangular field is 363 feet
long and 240 feet wide.

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How many acres is the field?

00:01:41.380 --> 00:01:42.460
So let me draw this field.

00:01:42.460 --> 00:01:45.730
I'll do it in green because
we're talking about a field.

00:01:45.730 --> 00:01:54.940
So it is 363 feet long
and 240 feet wide.

00:01:54.940 --> 00:01:56.760
That's the dimensions
of the field.

00:01:56.760 --> 00:01:59.430
So if we wanted to do it in
square feet, we would multiply

00:01:59.430 --> 00:02:00.750
these two numbers.

00:02:00.750 --> 00:02:02.260
So how many square feet is it?

00:02:02.260 --> 00:02:03.170
Well, I'll do it out here.

00:02:03.170 --> 00:02:04.060
I'll do it on the left.

00:02:04.060 --> 00:02:05.480
So let me multiply it out.

00:02:05.480 --> 00:02:12.930
We have 240 times 363.

00:02:12.930 --> 00:02:16.060
Actually, I want to do it with
a little bit more space.

00:02:16.060 --> 00:02:19.840
So we're going to
do it in blue.

00:02:19.840 --> 00:02:21.820
Maybe I should do it here.

00:02:21.820 --> 00:02:23.180
I don't think it will
confuse you.

00:02:23.180 --> 00:02:29.550
So I have 240 times 363.

00:02:29.550 --> 00:02:31.080
3 times 0 is 0.

00:02:31.080 --> 00:02:33.120
3 times 4 is 12.

00:02:33.120 --> 00:02:34.390
Carry the 1.

00:02:34.390 --> 00:02:37.260
3 times 2 is 6, plus 1 is 7.

00:02:37.260 --> 00:02:39.240
So it's 720.

00:02:39.240 --> 00:02:41.750
We can ignore that
for a little bit.

00:02:41.750 --> 00:02:43.710
Throw a 0 down here.

00:02:43.710 --> 00:02:45.980
6 times 0 is 0.

00:02:45.980 --> 00:02:50.020
6 times 4 is 24.

00:02:50.020 --> 00:02:55.890
6 times 2 is 12, plus
this 2 is 14.

00:02:55.890 --> 00:02:59.520
And then we have our last
row to deal with.

00:02:59.520 --> 00:03:01.690
So we're going to add two 0's
because we're dealing with the

00:03:01.690 --> 00:03:02.900
hundreds place.

00:03:02.900 --> 00:03:04.830
3 times 0 is 0.

00:03:04.830 --> 00:03:08.990
3 times 4 is 12.

00:03:08.990 --> 00:03:11.000
This was 4, carry the 1.

00:03:11.000 --> 00:03:14.240
3 times 2 is 6, plus 1 is 7.

00:03:14.240 --> 00:03:17.280
And now we can just
add everything up.

00:03:17.280 --> 00:03:18.750
0.

00:03:18.750 --> 00:03:19.430
2.

00:03:19.430 --> 00:03:23.130
7 plus 4 is 11.

00:03:23.130 --> 00:03:24.260
Carry the 1.

00:03:24.260 --> 00:03:26.140
1 plus 4 is 5.

00:03:26.140 --> 00:03:28.610
5 plus 2 is 7.

00:03:28.610 --> 00:03:31.280
And then we have
1 plus 7 is 8.

00:03:31.280 --> 00:03:41.010
So the field is 87,120
square feet.

00:03:41.010 --> 00:03:43.540
Now, they want to know how
many acres is the field?

00:03:43.540 --> 00:03:47.280
And they say an acre
is 43,560.

00:03:47.280 --> 00:03:49.160
And you see all your choices
are whole numbers.

00:03:49.160 --> 00:03:52.540
And you can just eyeball this,
that 87,000 whatever is

00:03:52.540 --> 00:03:56.150
roughly twice 43,560.

00:03:56.150 --> 00:03:56.400
Right?

00:03:56.400 --> 00:03:59.550
80,000 is roughly
twice 40,000.

00:03:59.550 --> 00:04:01.260
If you wanted to just hand-wave
it, you could just

00:04:01.260 --> 00:04:03.870
say, well, that's just
choice number A, or

00:04:03.870 --> 00:04:05.080
that's just 2, right?

00:04:05.080 --> 00:04:07.020
This looks like 2 times that.

00:04:07.020 --> 00:04:11.100
And if you wanted to verify it,
2 times-- let's verify it.

00:04:11.100 --> 00:04:14.010
Let me do it in a color that
you can actually see.

00:04:14.010 --> 00:04:17.279
So 43,560-- you wouldn't
actually have to do this on

00:04:17.279 --> 00:04:18.750
the test, but I want to
show you that our

00:04:18.750 --> 00:04:20.329
approximation works.

00:04:20.329 --> 00:04:21.459
2 times 0 is 0.

00:04:21.459 --> 00:04:23.320
2 times 6 is 12.

00:04:23.320 --> 00:04:27.270
2 times 5 is 10, plus
the 1 is 11.

00:04:27.270 --> 00:04:31.080
2 times 3 is 6, plus 1 is 7.

00:04:31.080 --> 00:04:32.810
2 times 4 is 8.

00:04:32.810 --> 00:04:35.080
And we've got the exact number
which was the square footage

00:04:35.080 --> 00:04:35.595
of the field.

00:04:35.595 --> 00:04:36.770
So it's 2 acres.

00:04:36.770 --> 00:04:38.630
So if you do it like
that, it's 2 acres.

00:04:38.630 --> 00:04:41.640
1 acre and 2 acres,
just like that.

00:04:41.640 --> 00:04:42.940
37.

00:04:42.940 --> 00:04:47.070
The object below is made of 10
rectangular prisms-- that just

00:04:47.070 --> 00:04:50.020
means these three-dimensional
rectangular things-- each with

00:04:50.020 --> 00:04:59.540
dimensions of 5 centimeters
by 3 centimeters by 2

00:04:59.540 --> 00:05:00.550
centimeters.

00:05:00.550 --> 00:05:03.500
What is the volume, in cubic
centimeters, of the object?

00:05:03.500 --> 00:05:05.390
So it's kind of this
plus sign, or this

00:05:05.390 --> 00:05:07.480
cross looking thing.

00:05:07.480 --> 00:05:10.020
And they do this-- I mean, these
things are really just

00:05:10.020 --> 00:05:10.910
to throw you off.

00:05:10.910 --> 00:05:13.490
So what is the volume
of each of these

00:05:13.490 --> 00:05:16.260
little cubes right there?

00:05:16.260 --> 00:05:19.950
So its volume is 5
times 2 times 3.

00:05:19.950 --> 00:05:22.650
So each cube has a volume
of, what's 5 times 2?

00:05:22.650 --> 00:05:25.220
Is 10, times 3 is 30.

00:05:25.220 --> 00:05:28.310
So each has 30 cubic
centimeters.

00:05:28.310 --> 00:05:29.630
Do it in a darker color.

00:05:29.630 --> 00:05:31.840
Each of these is 30
cubic centimeters.

00:05:31.840 --> 00:05:34.670
And how many of these are
there in this structure?

00:05:34.670 --> 00:05:37.390
Well, we have 2 layers.

00:05:37.390 --> 00:05:42.990
The top layer has 1 box here,
that's 1, 2-- this is the

00:05:42.990 --> 00:05:50.630
second box-- 2, 3,
4, and then 5.

00:05:50.630 --> 00:05:53.320
So the top layer has 5
in this plus sign.

00:05:53.320 --> 00:05:54.570
I could draw it like this.

00:05:57.980 --> 00:05:59.980
1, 2, 3, 4, 5.

00:05:59.980 --> 00:06:03.240
So if we have 5 in the top
layer, and we have 2 layers.

00:06:03.240 --> 00:06:05.620
So we have 10 of these
boxes, right?

00:06:05.620 --> 00:06:09.040
So 10 boxes, or rectangular
prisms if you want to call it

00:06:09.040 --> 00:06:15.140
that, times 30 cubic centimeters
per box.

00:06:18.620 --> 00:06:23.060
The boxes cancel out, you get 10
times 30 cubic centimeters,

00:06:23.060 --> 00:06:27.370
and you get 300 cubic
centimeters is the volume of

00:06:27.370 --> 00:06:29.150
this entire structure.

00:06:29.150 --> 00:06:31.640
And that is choice D.

00:06:31.640 --> 00:06:34.140
I literally think they drew
these little diagonals just to

00:06:34.140 --> 00:06:35.845
confuse you, just to maybe make
you think that you have

00:06:35.845 --> 00:06:37.250
to do something with
triangles.

00:06:37.250 --> 00:06:39.370
But no, you just have to count
the number of boxes and figure

00:06:39.370 --> 00:06:41.310
out the volume of
each of them.

00:06:41.310 --> 00:06:44.940
We had 10 boxes, each of them
has a volume of 30 cubic

00:06:44.940 --> 00:06:49.210
centimeters, so 300 cubic
centimeters total.


CAHSEE practice: Problems 23-27

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.160
Problem 23.

00:00:02.160 --> 00:00:06.700
Mario drives 1,500 miles
every month.

00:00:06.700 --> 00:00:10.930
Which line plot correctly
represents Mario's total miles

00:00:10.930 --> 00:00:13.590
driven over a period
of 6 months?

00:00:13.590 --> 00:00:15.810
So it's 1,500 miles
every month.

00:00:15.810 --> 00:00:17.660
So this is per month.

00:00:17.660 --> 00:00:20.880
So every month-- after 1 month
he should drive 1,500 hundred

00:00:20.880 --> 00:00:22.630
miles, and that looks
pretty good there.

00:00:22.630 --> 00:00:25.120
So after another month, it
should be another 1,500.

00:00:25.120 --> 00:00:26.680
Which goes to 3,000.

00:00:26.680 --> 00:00:26.880
Right?

00:00:26.880 --> 00:00:29.000
After 2 months, he should
drive 3,000 miles.

00:00:29.000 --> 00:00:30.670
So far, choice A looks
pretty good.

00:00:30.670 --> 00:00:32.170
So I'm just going
to circle that.

00:00:32.170 --> 00:00:33.760
Now let's just verify
that the other ones

00:00:33.760 --> 00:00:35.890
aren't describing this.

00:00:35.890 --> 00:00:40.500
So in choice C, it takes him
6 months to go 1,500 miles.

00:00:40.500 --> 00:00:41.380
That's not what they
said, they said

00:00:41.380 --> 00:00:42.940
1,500 miles every month.

00:00:42.940 --> 00:00:45.200
After 1 month here, he only
went-- I don't know.

00:00:45.200 --> 00:00:49.570
He only went 250 miles
or 5-- so this is

00:00:49.570 --> 00:00:51.210
definitely not the case.

00:00:51.210 --> 00:00:55.860
Choice B shows he started off
having traveled 1,500 miles

00:00:55.860 --> 00:00:56.710
and it never changes.

00:00:56.710 --> 00:00:57.940
So he doesn't travel anymore.

00:00:57.940 --> 00:00:59.840
So it's definitely
not choice B.

00:00:59.840 --> 00:01:03.660
And then choice D, after 1 month
he travels 9,000 miles.

00:01:03.660 --> 00:01:04.980
Which is completely wrong.

00:01:04.980 --> 00:01:07.730
They set it up per month
he travels 1,500 miles.

00:01:07.730 --> 00:01:08.920
Definitely not choice D.

00:01:08.920 --> 00:01:12.840
So choice A we can
feel good about.

00:01:12.840 --> 00:01:14.090
Let's go to the next page.

00:01:16.900 --> 00:01:18.470
All right.

00:01:18.470 --> 00:01:21.600
We have problem 24.

00:01:21.600 --> 00:01:26.990
The temperature on a mountain
peak was 7 degrees Fahrenheit

00:01:26.990 --> 00:01:29.660
at 6:00 PM.

00:01:29.660 --> 00:01:33.700
By 8:00 PM, so 2 hours later,
the temperature had dropped to

00:01:33.700 --> 00:01:36.800
0 degrees Fahrenheit.

00:01:36.800 --> 00:01:40.290
If the temperature continued
to drop at the same rate,

00:01:40.290 --> 00:01:44.400
which is the best estimate of
the temperature at 11:00 PM?

00:01:44.400 --> 00:01:45.030
So what happened?

00:01:45.030 --> 00:01:50.230
We went from 6:00
PM to 8:00 PM.

00:01:50.230 --> 00:01:52.650
That was 2 hours, right?

00:01:52.650 --> 00:01:58.080
And our temperature went from
7 degrees to 0 degrees

00:01:58.080 --> 00:01:59.230
Fahrenheit.

00:01:59.230 --> 00:02:02.750
So over 2 hours, we
dropped 7 degrees.

00:02:02.750 --> 00:02:05.870
Or you could say the rate of
droppage of our temperature,

00:02:05.870 --> 00:02:09.270
if you want to say it that
way, so you could say 7

00:02:09.270 --> 00:02:11.700
degrees-- let me write
it this way.

00:02:11.700 --> 00:02:18.110
7 degrees for every 2 hours.

00:02:18.110 --> 00:02:20.070
Or you could say minus 7 degrees
for every 2 hours,

00:02:20.070 --> 00:02:21.030
we're dropping.

00:02:21.030 --> 00:02:24.170
Or that's the same thing as
saying we're going minus 3.5

00:02:24.170 --> 00:02:28.710
degrees per hour.

00:02:28.710 --> 00:02:30.590
That's the rate at which
it dropped from

00:02:30.590 --> 00:02:32.090
6:00 PM to 8:00 PM.

00:02:32.090 --> 00:02:34.720
Minus 3.5 degrees per hour.

00:02:34.720 --> 00:02:36.120
So they say, what is the
best estimate of the

00:02:36.120 --> 00:02:38.030
temperature at 11:00 PM?

00:02:38.030 --> 00:02:43.930
Well, 11:00 PM is going to be
another 3 hours after 8:00 PM.

00:02:43.930 --> 00:02:47.220
And if we're dropping at minus
3.5 degrees per hour, and

00:02:47.220 --> 00:02:49.180
we're going to do that
for 3 hours, we just

00:02:49.180 --> 00:02:50.830
multiply the two.

00:02:50.830 --> 00:02:53.270
So you have-- do it over here.

00:02:53.270 --> 00:03:02.950
You have minus 3.5 degrees per
hour, and then times 3 hours.

00:03:02.950 --> 00:03:03.210
Right?

00:03:03.210 --> 00:03:06.880
That's how long we're going to
go from 8:00 PM to 11:00 PM.

00:03:06.880 --> 00:03:09.170
The hours cancel out, if
you want to make sure

00:03:09.170 --> 00:03:10.120
your units work out.

00:03:10.120 --> 00:03:16.970
But what's minus 3.5 times 3?

00:03:16.970 --> 00:03:18.360
Well, let's just write it out.

00:03:18.360 --> 00:03:21.570
So 3.5 times 3.

00:03:21.570 --> 00:03:22.560
I could put a minus there.

00:03:22.560 --> 00:03:24.000
We'll worry about
it in a second.

00:03:24.000 --> 00:03:26.460
5 times 3 is 15.

00:03:26.460 --> 00:03:30.160
3 times 3 is 9, plus 1 is 10.

00:03:30.160 --> 00:03:33.510
We have exactly 1 number behind
the decimal point.

00:03:33.510 --> 00:03:34.680
We have no decimals here.

00:03:34.680 --> 00:03:37.570
We have 1 number behind the
decimal point in our answer,

00:03:37.570 --> 00:03:39.330
and then we have a negative
times a positive, which is

00:03:39.330 --> 00:03:40.890
going to be a negative.

00:03:40.890 --> 00:03:43.610
So from 8:00 PM to 11:00
PM, we're going to

00:03:43.610 --> 00:03:46.070
drop by 10.5 degrees.

00:03:46.070 --> 00:03:48.410
Now, they say that the
temperature was 0 at 8:00 PM.

00:03:48.410 --> 00:03:52.870
So if we drop 10.5 degrees from
that, we're going to be

00:03:52.870 --> 00:03:57.610
approximately at minus 10
degrees Fahrenheit.

00:03:57.610 --> 00:04:00.010
They say, what is the
best estimate?

00:04:00.010 --> 00:04:03.270
If they said exactly, we would
say, oh, minus 10.5 degrees.

00:04:03.270 --> 00:04:06.060
If you wanted to do this-- you
could have done this in your

00:04:06.060 --> 00:04:08.020
head if you like, but I think
it's nice to say, oh, we're

00:04:08.020 --> 00:04:11.180
dropping 3.5 degrees per hour, 3
hours later it's going to be

00:04:11.180 --> 00:04:14.650
a little over 10 degrees, or
10.5 degrees, that we dropped

00:04:14.650 --> 00:04:18.560
from the 0 degrees at 8:00 PM.

00:04:18.560 --> 00:04:20.839
Problem 25.

00:04:20.839 --> 00:04:22.860
Do it in-- maybe orange.

00:04:22.860 --> 00:04:26.900
Brad bought a $6 binder and
several packs of paper that

00:04:26.900 --> 00:04:28.760
cost $0.60 each.

00:04:28.760 --> 00:04:32.790
If his total was $13.20,
how many packs of

00:04:32.790 --> 00:04:34.830
paper did Brad buy?

00:04:34.830 --> 00:04:35.150
All right.

00:04:35.150 --> 00:04:39.160
Let's say he bought
p packs of paper.

00:04:39.160 --> 00:04:40.170
So how much did he spend?

00:04:40.170 --> 00:04:46.740
He bought a $6 binder, so he
spent $6, plus $0.60 per pack

00:04:46.740 --> 00:04:49.050
times the number of
packs he bought.

00:04:49.050 --> 00:04:49.410
Right?

00:04:49.410 --> 00:04:53.490
So this is the total. $6 for the
binder plus $0.60 for each

00:04:53.490 --> 00:04:54.130
of the packs.

00:04:54.130 --> 00:04:57.660
If you bought 10 packs, we can
do 10 times $0.60 per pack,

00:04:57.660 --> 00:05:00.040
but we don't know what it is,
so we just leave it as p.

00:05:00.040 --> 00:05:06.090
And the total cost was $13.20.

00:05:06.090 --> 00:05:07.750
So we just have to
solve for p.

00:05:07.750 --> 00:05:10.382
How many packs of paper
did Brad buy?

00:05:10.382 --> 00:05:14.590
So if we subtract 6 from both
sides of this equation-- do it

00:05:14.590 --> 00:05:18.210
in blue-- just subtract this
6 from both sides.

00:05:18.210 --> 00:05:22.740
You get 0.6p-- maybe I'll
write it like this.

00:05:22.740 --> 00:05:25.880
Minus 6, plus there, and then
minus 6 right there.

00:05:25.880 --> 00:05:27.806
Just to show you I'm doing the
same thing to both sides of

00:05:27.806 --> 00:05:28.840
this equation.

00:05:28.840 --> 00:05:32.150
This minus 6 and that positive
6 cancel out, and so you're

00:05:32.150 --> 00:05:34.660
just left with a 0.6p on
the left-hand side.

00:05:34.660 --> 00:05:41.060
Is going to be equal to 13.2,
or $13.20 minus $6.

00:05:41.060 --> 00:05:43.000
You can write that
way if you like.

00:05:43.000 --> 00:05:45.390
13 minus 6 is 7.

00:05:45.390 --> 00:05:49.860
So it's going to be
$7.20, or 7.2.

00:05:49.860 --> 00:05:54.560
And then to solve for p, we just
divide both sides by 0.6.

00:05:54.560 --> 00:06:01.590
So if we divide both sides by
0.6, the 0.6's is cancel out

00:06:01.590 --> 00:06:04.270
on the left-hand side, so you're
just left with a p.

00:06:04.270 --> 00:06:06.440
So you're left with--
do it over here.

00:06:06.440 --> 00:06:14.920
p is equal to 7.2
divided by 0.6.

00:06:14.920 --> 00:06:16.010
So let's work this out.

00:06:16.010 --> 00:06:23.890
0.6 goes into 7.2-- I'll throw
in some trailing 0's.

00:06:23.890 --> 00:06:25.570
Now, division by decimals.

00:06:25.570 --> 00:06:27.860
This is sometimes a little bit
confusing, but you just have

00:06:27.860 --> 00:06:30.280
to remember, you take the number
that we're dividing

00:06:30.280 --> 00:06:32.920
into the other number, and you
make it into a whole number.

00:06:32.920 --> 00:06:34.740
So you shift its decimal
point, in this

00:06:34.740 --> 00:06:35.930
case 1 to the right.

00:06:35.930 --> 00:06:37.550
So it just becomes a 6.

00:06:37.550 --> 00:06:40.380
Since you shifted its decimal
point 1 to the right, you have

00:06:40.380 --> 00:06:43.700
to shift this guy's decimal
point 1 to the right.

00:06:43.700 --> 00:06:45.680
So it'll go right there.

00:06:45.680 --> 00:06:51.790
So 0.6 into 7.2 is the same
thing as 6 into 72.

00:06:51.790 --> 00:06:53.810
Or you could just do
this as a fraction.

00:06:53.810 --> 00:06:56.730
You multiply the top and the
bottom by 10, is the same

00:06:56.730 --> 00:06:58.640
thing as 72 divided by 6.

00:06:58.640 --> 00:07:00.630
And that's just exactly
what we did here.

00:07:00.630 --> 00:07:04.110
So 6 goes into 72-- well,
actually, even better, 6 goes

00:07:04.110 --> 00:07:05.640
into 7 one time.

00:07:05.640 --> 00:07:07.770
1 times 6 is 6.

00:07:07.770 --> 00:07:09.850
And then 7 minus 6 is 1.

00:07:09.850 --> 00:07:11.140
Bring down the 2.

00:07:11.140 --> 00:07:13.150
6 goes into 12 two times.

00:07:13.150 --> 00:07:14.930
2 times 6 is 12.

00:07:14.930 --> 00:07:16.140
You get a 0.

00:07:16.140 --> 00:07:17.050
All 0's left.

00:07:17.050 --> 00:07:18.710
So you get exactly 12 times.

00:07:18.710 --> 00:07:21.020
And if you know your 6 times
tables, you knew that.

00:07:21.020 --> 00:07:23.390
72 divided by 6 is 12.

00:07:23.390 --> 00:07:25.930
So p is equal to 12.

00:07:25.930 --> 00:07:30.740
He bought 12 packs of paper.

00:07:30.740 --> 00:07:32.130
Next problem.

00:07:32.130 --> 00:07:35.300
What is the value of this
thing, 3 plus 5 squared,

00:07:35.300 --> 00:07:39.820
divided by 4 minus x plus
1, when x is equal to 7?

00:07:39.820 --> 00:07:43.890
So let's write it down
when x is equal to 7.

00:07:43.890 --> 00:07:48.760
So this becomes 3 plus
5 squared-- so let me

00:07:48.760 --> 00:07:49.630
just write it out.

00:07:49.630 --> 00:07:51.860
5 squared is 25.

00:07:51.860 --> 00:07:54.750
Divided by-- and so they want us
to do a little bit of order

00:07:54.750 --> 00:07:55.990
of operations here.

00:07:55.990 --> 00:07:59.590
So parentheses are the
dominant role here.

00:07:59.590 --> 00:08:03.700
So this thing, 3 plus 25,
this is going to be 28.

00:08:03.700 --> 00:08:06.160
So parentheses take the dominant
role here, so this is

00:08:06.160 --> 00:08:10.050
going to be a 28 right there.

00:08:10.050 --> 00:08:11.120
So let me write it down.

00:08:11.120 --> 00:08:14.090
Parentheses are the most
important, then exponents,

00:08:14.090 --> 00:08:17.560
then multiplication and
division, and if there's a tie

00:08:17.560 --> 00:08:21.530
you go left to right, and
then you do addition and

00:08:21.530 --> 00:08:22.400
subtraction.

00:08:22.400 --> 00:08:24.890
So they're clearly trying to
make sure that we understand

00:08:24.890 --> 00:08:26.100
our order of operations.

00:08:26.100 --> 00:08:28.350
So let's do the things
in parentheses first.

00:08:28.350 --> 00:08:31.610
So it's 3 plus 5 squared is
3 plus 25, that's a 28.

00:08:31.610 --> 00:08:32.929
Then you have an x plus 1.

00:08:32.929 --> 00:08:35.030
They're telling us
that x is 7.

00:08:35.030 --> 00:08:38.789
This is a 7 plus 1, so that's
going to be an 8.

00:08:38.789 --> 00:08:42.289
And then we do the division
before we do the subtraction.

00:08:42.289 --> 00:08:45.260
So this becomes 28--
let me rewrite it.

00:08:45.260 --> 00:08:51.790
28 divided by 4, minus 8.

00:08:51.790 --> 00:08:56.560
And so order of operations,
we do this first. So 28

00:08:56.560 --> 00:08:58.660
divided by 4 is 7.

00:08:58.660 --> 00:09:03.340
And then we have the 7 minus
that 8 right there, which is

00:09:03.340 --> 00:09:05.280
equal to minus 1.

00:09:05.280 --> 00:09:08.900
So that is choice B.

00:09:08.900 --> 00:09:10.980
Next problem.

00:09:10.980 --> 00:09:14.080
Problem 27.

00:09:14.080 --> 00:09:16.680
What is the equation of
the graph shown below?

00:09:16.680 --> 00:09:19.500
So we just have to figure out
its slope and its y-intercept.

00:09:19.500 --> 00:09:21.530
In general, these are
all in kind of the

00:09:21.530 --> 00:09:23.930
classic mx plus b form.

00:09:23.930 --> 00:09:29.010
y is equal to mx plus b, where
m is the slope, b is the

00:09:29.010 --> 00:09:30.320
y-intercept.

00:09:30.320 --> 00:09:33.300
The slope here, our
rise over run.

00:09:33.300 --> 00:09:37.750
For every 1 we run,
we rise up 1.

00:09:37.750 --> 00:09:40.850
For a change in x of 1, we
have a change in y of 1.

00:09:40.850 --> 00:09:45.580
So slope is equal to change
in y over change in x,

00:09:45.580 --> 00:09:47.660
or rise over run.

00:09:47.660 --> 00:09:50.560
We rise by 1 when we run by 1.

00:09:50.560 --> 00:09:53.780
So it's equal to 1/1 which
is equal to 1.

00:09:53.780 --> 00:09:57.440
So m is equal to 1, and in
every situation here

00:09:57.440 --> 00:09:58.500
our slope is 1.

00:09:58.500 --> 00:10:00.250
So that didn't help us so far.

00:10:00.250 --> 00:10:04.150
But then b is the y-intercept,
where we intersect the y-axis.

00:10:04.150 --> 00:10:07.690
And you could see, just from
inspection, that's it.

00:10:07.690 --> 00:10:09.190
y is equal to 3.

00:10:09.190 --> 00:10:11.540
So we look for b is 3.

00:10:11.540 --> 00:10:16.300
So our equation is going to be y
is equal to 1 times x, which

00:10:16.300 --> 00:10:19.250
is just x, plus the
y-intercept of 3.

00:10:19.250 --> 00:10:25.640
So y is equal to x plus 3,
which is right there.

00:10:25.640 --> 00:10:28.050
No more problems on that page.


CAHSEE practice: Problems 32-34

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:01.930
Problem number 32.

00:00:01.930 --> 00:00:05.160
A scale drawing of a horse
is shown below.

00:00:05.160 --> 00:00:07.460
That's the horse.

00:00:07.460 --> 00:00:09.490
I'm probably not helping
you much at this point.

00:00:09.490 --> 00:00:12.340
What is the actual height of the
horse in inches, from the

00:00:12.340 --> 00:00:15.590
hoof to the top of the head?

00:00:15.590 --> 00:00:17.170
Well, they made a little
scale for us.

00:00:17.170 --> 00:00:20.080
This distance right
here is 8 inches.

00:00:20.080 --> 00:00:22.720
And then they measure this
scale multiple times.

00:00:22.720 --> 00:00:24.660
So how many times are we
going this distance?

00:00:24.660 --> 00:00:32.280
We go 1, 2, 3, 4,
5, 6, 7, 8, 9.

00:00:32.280 --> 00:00:36.990
So the horse is 9 times this
distance, which is 8 inches.

00:00:36.990 --> 00:00:39.700
Which is equal to 72 inches.

00:00:39.700 --> 00:00:43.150
So that's how tall the
horse is in reality.

00:00:43.150 --> 00:00:43.870
Which is what?

00:00:43.870 --> 00:00:46.250
It's like 6 feet tall.

00:00:46.250 --> 00:00:47.540
33.

00:00:47.540 --> 00:00:51.690
A shipping company has 25
offices that shipped 60,000

00:00:51.690 --> 00:00:54.000
packages last week.

00:00:54.000 --> 00:00:59.830
The offices were open 6 days and
used 80,000 kilowatt-hours

00:00:59.830 --> 00:01:00.910
of electricity.

00:01:00.910 --> 00:01:04.440
Which pieces of information
given above are necessary to

00:01:04.440 --> 00:01:08.850
find the average number
of packages shipped

00:01:08.850 --> 00:01:12.510
per day last week?

00:01:12.510 --> 00:01:13.360
So let's think about it.

00:01:13.360 --> 00:01:18.040
They didn't ask us anything
about electricity.

00:01:18.040 --> 00:01:20.870
So we definitely don't need
that information.

00:01:20.870 --> 00:01:23.640
And they're saying the average
number of packages shipped per

00:01:23.640 --> 00:01:24.460
day last week.

00:01:24.460 --> 00:01:27.590
They're not saying per day
per office last week.

00:01:27.590 --> 00:01:29.260
So we don't need to know
how many offices.

00:01:29.260 --> 00:01:33.440
We just need to know that 60,000
packages were shipped

00:01:33.440 --> 00:01:36.950
last week, and the offices
were open 6 days.

00:01:36.950 --> 00:01:39.840
So they operated for 6 days.

00:01:39.840 --> 00:01:41.690
So we could figure
out the answer.

00:01:41.690 --> 00:01:43.170
The answer is obviously
10,000.

00:01:43.170 --> 00:01:44.100
But they're not asking
us that.

00:01:44.100 --> 00:01:46.120
They're asking us, what
information do we need?

00:01:46.120 --> 00:01:50.000
We need the total number of
packages shipped last week,

00:01:50.000 --> 00:01:53.490
and we need the number of days
that the office was open.

00:01:53.490 --> 00:01:54.460
So what choices are that?

00:01:54.460 --> 00:01:56.280
The number of offices-- no, we
don't need the number of

00:01:56.280 --> 00:01:59.260
offices, because they didn't
ask us per office.

00:01:59.260 --> 00:02:01.070
The number of packages and the
amount of electricity?

00:02:01.070 --> 00:02:01.240
No.

00:02:01.240 --> 00:02:02.970
This has nothing to do
with electricity.

00:02:02.970 --> 00:02:05.270
The number of packages and
the number of days

00:02:05.270 --> 00:02:07.100
open during the week?

00:02:07.100 --> 00:02:07.970
Yeah, that's what we used.

00:02:07.970 --> 00:02:09.780
The number of packages and
the number of days

00:02:09.780 --> 00:02:11.970
open during the week.

00:02:11.970 --> 00:02:13.850
The number of days open during
the week and the amount of

00:02:13.850 --> 00:02:14.330
electricity?

00:02:14.330 --> 00:02:16.760
No, this had nothing to do
with the electricity.

00:02:16.760 --> 00:02:19.370
So our choice is C.

00:02:19.370 --> 00:02:22.600
Problem 34.

00:02:22.600 --> 00:02:26.790
A landscaper estimates that
landscaping a new park will

00:02:26.790 --> 00:02:30.280
take 1 person 48 hours.

00:02:30.280 --> 00:02:34.730
If 4 people work on the job,
and they each work 6-hour

00:02:34.730 --> 00:02:41.430
days, how many days are needed
to complete the job?

00:02:41.430 --> 00:02:44.745
If 1 person takes 48 hours,
4 people are going

00:02:44.745 --> 00:02:46.630
to take 1/4 as long.

00:02:46.630 --> 00:02:55.070
So 48 divided by 4 is going
to be equal to 12 hours.

00:02:55.070 --> 00:02:57.990
If 4 people are each working
12 hours, that's the same

00:02:57.990 --> 00:03:00.900
thing as 1 person working 48
hours, assuming that you could

00:03:00.900 --> 00:03:02.730
divide the job up in that way.

00:03:02.730 --> 00:03:05.960
So these 4 people are going to
take 12 hours, all working

00:03:05.960 --> 00:03:09.560
simultaneously, and they each
worked 6-hour days.

00:03:09.560 --> 00:03:12.300
So they're going to work a total
of 12 hours, because

00:03:12.300 --> 00:03:16.130
there's 4 of them, so they can
take 1/4 of the time, but they

00:03:16.130 --> 00:03:17.520
can only do 6 hours per day.

00:03:17.520 --> 00:03:20.070
So it's going to take them 2
days to work their 12 hours.

00:03:20.070 --> 00:03:25.600
It's going to take 2 days
to complete the job.

00:03:25.600 --> 00:03:28.250
And that's all we have
on that page.


CAHSEE practice: Problems 20-22

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.170
Problem number 20.

00:00:03.170 --> 00:00:07.970
At a local bookstore, books that
normally cost b dollars

00:00:07.970 --> 00:00:12.270
are on sale for $10 off
the normal price.

00:00:12.270 --> 00:00:16.930
So not just $10, it's $10
off the normal price.

00:00:16.930 --> 00:00:18.990
So if the normal price is b.

00:00:18.990 --> 00:00:21.810
So b is the normal price.

00:00:21.810 --> 00:00:27.010
The sale price is $10 off the
normal price, or b minus 10 is

00:00:27.010 --> 00:00:28.920
the sale price.

00:00:28.920 --> 00:00:32.920
How many dollars does it cost
to buy 3 books on sale?

00:00:32.920 --> 00:00:37.100
So each book on sale is going
to be b minus $10.

00:00:37.100 --> 00:00:39.430
So if you buy 3 of them, you
just multiply that times 3.

00:00:39.430 --> 00:00:43.720
So it's going to be 3
times b minus 10.

00:00:43.720 --> 00:00:46.710
And you see that choice
right there.

00:00:46.710 --> 00:00:48.790
Now if they didn't write like
this, if they multiplied it

00:00:48.790 --> 00:00:50.690
out, you would just
distribute the 3.

00:00:50.690 --> 00:00:54.170
So it would be 3 times
b, which is 3b, minus

00:00:54.170 --> 00:00:56.020
3 times 10 or 30.

00:00:56.020 --> 00:00:57.860
But that's not one of the
choices right there.

00:00:57.860 --> 00:00:59.710
And then lucky for us,
this choice is there.

00:00:59.710 --> 00:01:04.590
3 times b minus 10. b minus 10
is the cost of each book on

00:01:04.590 --> 00:01:08.320
sale, $10 off the
normal price.

00:01:08.320 --> 00:01:12.570
Problem 21.

00:01:12.570 --> 00:01:16.260
If a line passes through the
points A and B shown below--

00:01:16.260 --> 00:01:21.100
so this is A and this is B--
approximately where does the

00:01:21.100 --> 00:01:22.690
line cross the x-axis?

00:01:22.690 --> 00:01:25.010
Approximately.

00:01:25.010 --> 00:01:27.110
So they just want us
to get a sense.

00:01:27.110 --> 00:01:28.600
So they're talking
about this line.

00:01:28.600 --> 00:01:30.990
Let me draw it here.

00:01:30.990 --> 00:01:34.200
This line right there, and I
just keep going like that.

00:01:34.200 --> 00:01:36.100
Do my best to draw
it straight.

00:01:36.100 --> 00:01:37.220
If you had another
pencil, you could

00:01:37.220 --> 00:01:38.525
actually draw it perfectly.

00:01:38.525 --> 00:01:41.550
And so where does it
cross the x-axis?

00:01:41.550 --> 00:01:44.040
The way I drew it, it does cross
the x-axis right there.

00:01:44.040 --> 00:01:46.380
So let's see which of
these say that.

00:01:46.380 --> 00:01:48.300
So between minus
3 and minus 2.

00:01:48.300 --> 00:01:50.330
Well, yeah, I mean just the
way I drew it, this wasn't

00:01:50.330 --> 00:01:52.690
exact, but that looks
pretty good.

00:01:52.690 --> 00:01:54.900
So I'll underline this.

00:01:54.900 --> 00:01:56.640
If there were some other choices
that were close to

00:01:56.640 --> 00:01:58.670
that, I'd have to be a little
bit more exact.

00:01:58.670 --> 00:02:01.020
But let's see what the
other choices say.

00:02:01.020 --> 00:02:02.660
Between 0 and minus 1.

00:02:02.660 --> 00:02:04.240
Well, that means here.

00:02:04.240 --> 00:02:06.800
And clearly the line didn't
cross anywhere near there, so

00:02:06.800 --> 00:02:08.449
that's definitely
not our answer.

00:02:08.449 --> 00:02:10.050
Between 0 and 1.

00:02:10.050 --> 00:02:12.440
The line was nowhere near there,
so it's not there.

00:02:12.440 --> 00:02:13.610
Between 1 and 2.

00:02:13.610 --> 00:02:14.650
Clearly not there.

00:02:14.650 --> 00:02:17.910
So we can be very confident
that our choice is A.

00:02:17.910 --> 00:02:19.970
Out of all of the choices,
that's the one that even gets

00:02:19.970 --> 00:02:23.400
close to where even my rough
drawing crossed the x-axis.

00:02:23.400 --> 00:02:26.190
Actually, even my rough drawing
did go right between

00:02:26.190 --> 00:02:29.580
minus 3 and minus 2.

00:02:29.580 --> 00:02:31.490
Problem 22.

00:02:31.490 --> 00:02:35.630
Which expression is equivalent
to this thing right here?

00:02:35.630 --> 00:02:37.450
Let me rewrite it.

00:02:37.450 --> 00:02:44.200
So we have 7 times a squared
times b, times 7

00:02:44.200 --> 00:02:47.750
times b times c squared.

00:02:47.750 --> 00:02:49.530
So when you have multiplication,
it's actually

00:02:49.530 --> 00:02:50.110
commutative.

00:02:50.110 --> 00:02:52.550
You can switch the order
of multiplication.

00:02:52.550 --> 00:02:54.750
So if we just switch the order
of this, we could say that

00:02:54.750 --> 00:02:59.210
this is the same thing
as 7 times 7

00:02:59.210 --> 00:03:01.580
times a squared, right?

00:03:01.580 --> 00:03:02.940
7 times 7.

00:03:02.940 --> 00:03:04.610
That's that right there.

00:03:04.610 --> 00:03:06.710
And then you have times
an a squared.

00:03:06.710 --> 00:03:08.100
That's that right there.

00:03:08.100 --> 00:03:11.970
And then you're left with these
two b's, so you could

00:03:11.970 --> 00:03:16.470
say times b times bc
squared, right?

00:03:16.470 --> 00:03:18.750
That is that right there.

00:03:18.750 --> 00:03:20.650
And so we can just
rewrite this.

00:03:20.650 --> 00:03:23.920
7 times 7 is 49.

00:03:23.920 --> 00:03:26.710
a squared is just a squared.

00:03:26.710 --> 00:03:31.630
b times b is b squared, and
then you have a c squared.

00:03:31.630 --> 00:03:35.200
So it's 49a squared, b
squared, c squared.

00:03:35.200 --> 00:03:38.350
Which is choice C.

00:03:38.350 --> 00:03:41.620
49a squared, b squared,
c squared.


CAHSEE practice: Problems 17-19

WEBVTT
Kind: captions
Language: en

00:00:00.780 --> 00:00:05.410
Problem 17: Michelle read a book
review and predicted that

00:00:05.410 --> 00:00:09.790
the number of girls who will
like the book will be more

00:00:09.790 --> 00:00:13.930
than twice the number of boys
who will like the book.

00:00:13.930 --> 00:00:17.065
So, she predicted that the girls
would be more than twice

00:00:17.065 --> 00:00:21.580
-- let me box it out -- more
than twice the number of boys

00:00:21.580 --> 00:00:23.070
who will like the book.

00:00:23.070 --> 00:00:26.230
Which table shows data that
supports her prediction?

00:00:26.230 --> 00:00:28.670
So essentially, we just need
to find one of the tables

00:00:28.670 --> 00:00:32.090
where the number of girls who
like the book, that's just

00:00:32.090 --> 00:00:34.390
this column right here -- the
number who like the book --

00:00:34.390 --> 00:00:37.480
should be more than twice
the number of boys.

00:00:37.480 --> 00:00:41.090
Let's see the girls here is
40, the boys here are 35,

00:00:41.090 --> 00:00:44.130
there are more girls than boys,
but it's not more than

00:00:44.130 --> 00:00:45.300
twice the boys.

00:00:45.300 --> 00:00:46.520
The boys are 35.

00:00:46.520 --> 00:00:50.130
Twice the boys would be 70, and
girls is definitely not

00:00:50.130 --> 00:00:53.200
more than 70, so that's
not our answer.

00:00:53.200 --> 00:00:56.740
Let's just go here, well, here
the boys are more than the

00:00:56.740 --> 00:00:58.540
girls, which definitely isn't
going to be the case.

00:00:58.540 --> 00:01:01.810
We need a situation where the
girls are more than twice the

00:01:01.810 --> 00:01:02.540
number of boys.

00:01:02.540 --> 00:01:04.629
So that's not our situation,
because the girls are actually

00:01:04.629 --> 00:01:06.830
smaller than the boys here.

00:01:06.830 --> 00:01:11.320
Here we have 35 boys, if you
multiply that by 2, you would

00:01:11.320 --> 00:01:12.580
get 70 boys.

00:01:12.580 --> 00:01:14.660
So twice the boys is 70.

00:01:14.660 --> 00:01:18.230
And we see that the girls, at
80, are more than twice the

00:01:18.230 --> 00:01:19.490
boys at 70.

00:01:19.490 --> 00:01:21.580
So that is our choice.

00:01:21.580 --> 00:01:24.100
The girls are more than
twice the boys.

00:01:24.100 --> 00:01:26.200
And if you look here, the boys
and girls are even, so the

00:01:26.200 --> 00:01:28.440
girls are definitely not more
than twice the boys.

00:01:28.440 --> 00:01:32.410
So we know definitely,
that B is our answer.

00:01:32.410 --> 00:01:40.440
Go to the next page, Problem 18:
Anna has the letter tiles

00:01:40.440 --> 00:01:41.690
below in a bag.

00:01:41.690 --> 00:01:43.780
It's very interesting, it just
happens to spell out

00:01:43.780 --> 00:01:45.250
statistics.

00:01:45.250 --> 00:01:48.780
She reached in the bag,
and pulled out an S.

00:01:48.780 --> 00:01:51.090
She then put the tile
back in the bag.

00:01:51.090 --> 00:01:53.680
OK, so all of them are
still in the bag.

00:01:53.680 --> 00:01:57.830
If Anna randomly selects a tile
from the bag, what is the

00:01:57.830 --> 00:02:01.070
probability she will
select an S again?

00:02:01.070 --> 00:02:05.170
So this is a trick question on
some level, because this first

00:02:05.170 --> 00:02:10.050
part, that she reached in the
bag and pulled out an S and

00:02:10.050 --> 00:02:12.720
she then put the tile
back in the bag.

00:02:12.720 --> 00:02:13.930
That doesn't do anything!

00:02:13.930 --> 00:02:15.990
The fact that she pulled out an
S, and then put it back in

00:02:15.990 --> 00:02:18.520
the bag, that shouldn't change
what happens afterward.

00:02:18.520 --> 00:02:21.340
If she took out the S and kept
the S out, then this would be

00:02:21.340 --> 00:02:22.780
a different type of problem.

00:02:22.780 --> 00:02:25.700
But since she took out the S
and put it back in, this is

00:02:25.700 --> 00:02:27.060
almost useless information.

00:02:27.060 --> 00:02:30.450
We still have all of these
letters in the bag.

00:02:30.450 --> 00:02:35.300
It says if Anna randomly selects
a tile from the bag,

00:02:35.300 --> 00:02:37.580
what is the probability
she'll select an S?

00:02:37.580 --> 00:02:40.210
So all we have to say is, all
of these are in the bag, so

00:02:40.210 --> 00:02:42.480
what are the possible
outcomes?

00:02:42.480 --> 00:02:50.700
So there's 1, 2, 3, 4, 5, 6, 7,
8, 9, 10 possible outcomes.

00:02:50.700 --> 00:02:52.630
10 possible outcomes, so
that's going to be the

00:02:52.630 --> 00:02:54.870
denominator for our
probability.

00:02:54.870 --> 00:02:57.760
And then, what are the outcomes
that satisfy our

00:02:57.760 --> 00:02:58.280
conditions?

00:02:58.280 --> 00:03:01.330
Or, what are the outcomes
where she selects an S?

00:03:01.330 --> 00:03:06.170
She selects an S, so there's
1 S, 2 S, and 3 S's.

00:03:06.170 --> 00:03:09.310
There's 3 out of the 10
situations involve selecting

00:03:09.310 --> 00:03:12.130
an S, so the answer is 3/10.

00:03:12.130 --> 00:03:13.700
And the reason why I said it's
a trick question, is because

00:03:13.700 --> 00:03:16.550
they write statement which
really doesn't change the

00:03:16.550 --> 00:03:17.230
problem it all.

00:03:17.230 --> 00:03:19.190
She took out an S,
she put it back.

00:03:19.190 --> 00:03:23.050
If she said that she took out an
S, and then she did not put

00:03:23.050 --> 00:03:25.690
it back in the bag, then you
would say, oh gee, then

00:03:25.690 --> 00:03:30.300
there's only 9 tiles left; and
only two of them are S's, and

00:03:30.300 --> 00:03:31.730
then you would have said 2/9.

00:03:31.730 --> 00:03:34.080
But since she did put the S back
in the bag, we could say,

00:03:34.080 --> 00:03:38.120
oh, there's 10 letters in the
bag, 3 of them are S's, so the

00:03:38.120 --> 00:03:40.340
answer is 3/10.

00:03:40.340 --> 00:03:45.780
Problem 19: The scatterplot
below shows the ages of some

00:03:45.780 --> 00:03:49.350
children and the distance
each lives from school.

00:03:49.350 --> 00:03:51.670
So this is the ages, and
then this is the

00:03:51.670 --> 00:03:55.090
distance in that axis.

00:03:55.090 --> 00:03:59.520
Which statement best describes
the relation between age and

00:03:59.520 --> 00:04:02.780
distance from the school?

00:04:02.780 --> 00:04:04.890
Just looking at this, I really
don't see any relation, it

00:04:04.890 --> 00:04:06.370
seems to be fairly random.

00:04:06.370 --> 00:04:08.725
Let's see what the statements
tell us.

00:04:11.750 --> 00:04:13.220
As age and increases, the

00:04:13.220 --> 00:04:15.750
distance from school increases.

00:04:15.750 --> 00:04:18.649
No, not really, I mean,
that would look

00:04:18.649 --> 00:04:19.899
something like this.

00:04:23.400 --> 00:04:28.330
So this is our age axis, this
is our distance axis, what A

00:04:28.330 --> 00:04:30.830
is describing is as age
increases, the distance from

00:04:30.830 --> 00:04:32.000
school increases.

00:04:32.000 --> 00:04:34.890
The data points should look
something like this.

00:04:34.890 --> 00:04:37.160
They should generally increase
-- distance should generally

00:04:37.160 --> 00:04:38.870
increase as age increases.

00:04:38.870 --> 00:04:40.890
That's not what we see here,
I mean this really

00:04:40.890 --> 00:04:42.180
kind of seems arbitrary.

00:04:42.180 --> 00:04:44.970
It's not like this nice
upward trend.

00:04:44.970 --> 00:04:46.380
B, as age increases the

00:04:46.380 --> 00:04:47.820
distance from school decreases.

00:04:47.820 --> 00:04:50.430
Well I don't even see a downward
trend either, what B

00:04:50.430 --> 00:04:53.960
is describing, the data
would look like this.

00:04:53.960 --> 00:04:55.700
Where we have this
downward trend.

00:04:55.700 --> 00:04:57.810
I don't see that here, either.

00:04:57.810 --> 00:04:59.830
C, as age increases,
the distance from

00:04:59.830 --> 00:05:03.020
school remains constant.

00:05:03.020 --> 00:05:05.590
What C is describing
would have data

00:05:05.590 --> 00:05:07.090
that looks like this.

00:05:07.090 --> 00:05:09.250
That regardless of age, the
distance from school

00:05:09.250 --> 00:05:10.800
is about the same.

00:05:10.800 --> 00:05:12.770
I don't really see
that either.

00:05:12.770 --> 00:05:15.190
There's still a huge spread
of distances.

00:05:15.190 --> 00:05:18.840
And then D, there is no
relationship between the age

00:05:18.840 --> 00:05:20.230
and distance from school.

00:05:20.230 --> 00:05:23.350
I'll go with that one because,
you could imagine, if I tried

00:05:23.350 --> 00:05:25.530
to draw trend line, I could
draw something like that,

00:05:25.530 --> 00:05:27.630
maybe that makes it look
like there's a trend.

00:05:27.630 --> 00:05:29.460
But I just as easily could
have drawn that.

00:05:29.460 --> 00:05:31.350
And looks just is good to me.

00:05:31.350 --> 00:05:33.130
Or I just as easily could
have drawn that.

00:05:33.130 --> 00:05:36.170
None of these look like it
fits the data any better.

00:05:36.170 --> 00:05:41.360
So, at least the answer that I
feel comfortable with is D.


CAHSEE practice: Problems 15-16

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:02.270
Problem 15.

00:00:02.270 --> 00:00:07.270
A restaurant is advertising
3-item combination specials

00:00:07.270 --> 00:00:11.490
that must include a main dish,
a vegetable, and a drink.

00:00:11.490 --> 00:00:14.440
OK, so you have to have
at least one of these.

00:00:14.440 --> 00:00:16.100
So what are they going
to ask us?

00:00:16.100 --> 00:00:20.010
How many 3-item combinations
include a

00:00:20.010 --> 00:00:22.675
soft drink and a corn?

00:00:28.800 --> 00:00:31.150
So let's reread what
the conditions are.

00:00:31.150 --> 00:00:33.370
A restaurant is advertising
3-item combination specials

00:00:33.370 --> 00:00:38.350
that must include a main dish,
a vegetable, and a drink.

00:00:38.350 --> 00:00:41.190
So you pick one from each
of these buckets.

00:00:41.190 --> 00:00:43.066
So they're already picking two
of the buckets for us.

00:00:43.066 --> 00:00:50.860
It includes a soft drink, and
it has to include a corn.

00:00:50.860 --> 00:00:53.610
So they've essentially already
picked our choices from this

00:00:53.610 --> 00:00:56.040
bucket and that bucket
right there.

00:00:56.040 --> 00:00:58.420
And they're saying, how many
combinations are left?

00:00:58.420 --> 00:01:01.430
Well, we only have
two choices.

00:01:01.430 --> 00:01:02.990
We only have freedom
when it comes to

00:01:02.990 --> 00:01:03.920
picking the main dish.

00:01:03.920 --> 00:01:05.760
Because the problem has already
picked for us our

00:01:05.760 --> 00:01:09.090
vegetable and our drink, the
corn and the soft drink.

00:01:09.090 --> 00:01:12.060
And so there's only two possible
main dishes, so those

00:01:12.060 --> 00:01:14.880
are the 3-item combinations
that include a

00:01:14.880 --> 00:01:16.230
soft drink and a corn.

00:01:16.230 --> 00:01:19.240
There's two possible ones,
chicken and beef.

00:01:19.240 --> 00:01:20.470
So it's two.

00:01:20.470 --> 00:01:21.880
Just to make sure you understand
that, what are the

00:01:21.880 --> 00:01:24.260
two combinations, just
to make it explicit?

00:01:24.260 --> 00:01:28.720
Well, one combination is
chicken, corn, and soft drink.

00:01:28.720 --> 00:01:28.980
Right?

00:01:28.980 --> 00:01:31.440
They're forcing the corn and
the soft drink on us.

00:01:31.440 --> 00:01:35.880
And then the other combination
is beef, corn, and soft drink.

00:01:35.880 --> 00:01:37.930
That's the second combination,
because they're forcing the

00:01:37.930 --> 00:01:39.300
corn and the soft drink on us.

00:01:39.300 --> 00:01:41.150
So there's two combinations.

00:01:41.150 --> 00:01:43.480
But the way I just thought about
that is this thing has

00:01:43.480 --> 00:01:45.800
been constrained for us, the
vegetable and the drink, so

00:01:45.800 --> 00:01:46.780
you can ignore it.

00:01:46.780 --> 00:01:49.060
And so how many combinations
of main dishes are there?

00:01:49.060 --> 00:01:49.640
Well, there's two.

00:01:49.640 --> 00:01:50.530
I just counted them.

00:01:50.530 --> 00:01:52.300
Chicken and beef.

00:01:52.300 --> 00:01:54.270
Problem 16.

00:01:54.270 --> 00:01:59.290
Donald priced six personal
Compact Disc players.

00:01:59.290 --> 00:02:01.990
And they wrote the
CD right there.

00:02:01.990 --> 00:02:03.970
The prices are shown below.

00:02:03.970 --> 00:02:06.450
OK, so these are
six CD players.

00:02:06.450 --> 00:02:09.080
What is the median price?

00:02:09.080 --> 00:02:10.710
So the trick of this
problem is just

00:02:10.710 --> 00:02:12.350
knowing what median means.

00:02:12.350 --> 00:02:14.980
Median literally means
the middle price.

00:02:14.980 --> 00:02:18.190
So if I were to put all of these
numbers in order, which

00:02:18.190 --> 00:02:20.720
I'm going to do right now, the
median is going to be the

00:02:20.720 --> 00:02:21.450
middle number.

00:02:21.450 --> 00:02:22.260
So let's put them in order.

00:02:22.260 --> 00:02:24.100
What's the smallest
number here?

00:02:24.100 --> 00:02:25.770
21.

00:02:25.770 --> 00:02:27.130
Cross that out.

00:02:27.130 --> 00:02:28.760
And then we have another 21.

00:02:28.760 --> 00:02:30.820
So let me write that down.

00:02:30.820 --> 00:02:33.300
I'll cross that out, make
sure I know I used it.

00:02:33.300 --> 00:02:37.150
The next largest number is 23.

00:02:37.150 --> 00:02:39.100
So let me cross that out.

00:02:39.100 --> 00:02:43.370
The next largest number is 25.

00:02:43.370 --> 00:02:44.930
Cross that out.

00:02:44.930 --> 00:02:47.640
Next largest number is 31.

00:02:47.640 --> 00:02:48.910
Cross that out.

00:02:48.910 --> 00:02:52.380
And then the next
number is 39.

00:02:52.380 --> 00:02:54.910
So what is the middle
number here?

00:02:54.910 --> 00:02:57.400
Well, you see we have six
numbers, and, actually, there

00:02:57.400 --> 00:02:58.540
is no middle number.

00:02:58.540 --> 00:03:00.780
If we have an even number of
numbers, there's no single

00:03:00.780 --> 00:03:01.490
middle number.

00:03:01.490 --> 00:03:02.970
There's two numbers
that we can kind

00:03:02.970 --> 00:03:04.900
of view as the middle.

00:03:04.900 --> 00:03:06.610
These two numbers here
are the middle.

00:03:06.610 --> 00:03:06.900
Right?

00:03:06.900 --> 00:03:10.360
I can't say 23 by itself is the
middle, because there's

00:03:10.360 --> 00:03:12.670
two above it and
three below it.

00:03:12.670 --> 00:03:15.430
And I can't say 25 is the
middle, because there's two

00:03:15.430 --> 00:03:17.130
below it and three above it.

00:03:17.130 --> 00:03:21.050
So when you have an even number
of, I guess, data, like

00:03:21.050 --> 00:03:24.220
you have right here, you
pick the middle two.

00:03:24.220 --> 00:03:27.210
If I had the numbers 1,
2, and 3, then I could

00:03:27.210 --> 00:03:29.780
just pick the 2.

00:03:29.780 --> 00:03:32.950
But if I have 1, 2, 3,
and 4, I have to pick

00:03:32.950 --> 00:03:34.650
the middle two numbers.

00:03:34.650 --> 00:03:38.350
So here I pick the middle two
numbers, and I need a median.

00:03:38.350 --> 00:03:41.070
And so what I do is I average
these middle two numbers.

00:03:41.070 --> 00:03:43.360
I take the mean, or I go
right in between them.

00:03:43.360 --> 00:03:46.520
So what's exactly in
between 23 and 25?

00:03:46.520 --> 00:03:47.390
Well, you can do that
in your head.

00:03:47.390 --> 00:03:49.460
It's going to be 24.

00:03:49.460 --> 00:03:51.670
But if you can't do it in your
head, you literally would just

00:03:51.670 --> 00:03:56.750
add those two numbers, 23 plus
25, and then divide by 2.

00:03:56.750 --> 00:03:59.920
So this is going to be
equal to 48 divided

00:03:59.920 --> 00:04:02.690
by 2, which is $24.

00:04:02.690 --> 00:04:04.760
And I just explained that to
you, and just in case you got

00:04:04.760 --> 00:04:07.740
the situation where these are
some weird decimal numbers, or

00:04:07.740 --> 00:04:09.310
these were much larger numbers,
where you couldn't

00:04:09.310 --> 00:04:11.700
just say, hey, 24 is right
in between those

00:04:11.700 --> 00:04:14.170
two guys right there.


CAHSEE practice: Problems 10-12

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.029
Problem 10.

00:00:02.029 --> 00:00:09.390
John uses 2/3 of a cup of oats
per serving to make oatmeal.

00:00:09.390 --> 00:00:15.180
How many cups of oats does he
need to make 6 servings?

00:00:15.180 --> 00:00:17.050
So he uses 2/3 per
serving, and he's

00:00:17.050 --> 00:00:18.820
going to have 6 servings.

00:00:18.820 --> 00:00:22.170
So it's going to be 6 times--
for every serving there's 2/3,

00:00:22.170 --> 00:00:24.140
so it's going to be
6 times that.

00:00:24.140 --> 00:00:28.100
So it's going to be 2/3 per
serving, and we can even put

00:00:28.100 --> 00:00:28.650
units there.

00:00:28.650 --> 00:00:32.240
We could say 1 over servings.

00:00:32.240 --> 00:00:33.360
Well, that just confuses it.

00:00:33.360 --> 00:00:37.280
2/3 per serving times
6 servings.

00:00:37.280 --> 00:00:39.920
So that's just 6 times 2/3.

00:00:39.920 --> 00:00:44.400
And that is equal to-- maybe
it's easier to visualize in

00:00:44.400 --> 00:00:46.190
your head as multiplying
two fractions.

00:00:46.190 --> 00:00:52.410
We can write that as 2/3 times
6/1, and that's equal to-- we

00:00:52.410 --> 00:00:54.230
could simplify it
ahead of time.

00:00:54.230 --> 00:00:57.160
Or we can just write that as 2
times 6 in the numerator--

00:00:57.160 --> 00:01:01.220
which is 12-- and the
denominator is 3 times 1--

00:01:01.220 --> 00:01:01.730
which is 3.

00:01:01.730 --> 00:01:06.430
Multiplying fractions is far
easier than adding or

00:01:06.430 --> 00:01:07.030
subtracting.

00:01:07.030 --> 00:01:10.440
Because literally the new
numerator of the product is

00:01:10.440 --> 00:01:14.990
just the product of the
numerators, and then the

00:01:14.990 --> 00:01:17.310
denominator of the product is
just the product of the

00:01:17.310 --> 00:01:17.980
denominators.

00:01:17.980 --> 00:01:19.760
2 times 6 is 12.

00:01:19.760 --> 00:01:21.600
3 times 1 is 3.

00:01:21.600 --> 00:01:25.400
And 12/3-- that's the same thing
as 12 divided by 3--

00:01:25.400 --> 00:01:28.600
that just equals 4.

00:01:28.600 --> 00:01:31.120
Which is choice B right there.

00:01:31.120 --> 00:01:33.680
Another way you could have
done it is you could have

00:01:33.680 --> 00:01:34.860
simplified it right here.

00:01:34.860 --> 00:01:38.030
You could have divided the
6 and the 3 both by 3.

00:01:38.030 --> 00:01:44.430
So if you had 2/3 times 6/1,
you could divide the 6 by 3

00:01:44.430 --> 00:01:46.270
and the 3 by 3.

00:01:46.270 --> 00:01:50.170
So you get 1, and then you just
get 2 times-- sorry, 6

00:01:50.170 --> 00:01:52.160
divided by 3 is 2.

00:01:52.160 --> 00:01:56.870
So you have 2 times 2 is equal
to 4, over 1 times 1.

00:01:56.870 --> 00:01:59.360
And the whole reason why you
could do that is this thing

00:01:59.360 --> 00:02:01.270
right here, instead of solving
it up here, I could have

00:02:01.270 --> 00:02:08.580
rewritten it as 2 times
6 over 3 times 1.

00:02:08.580 --> 00:02:12.180
And then you could simplify it
before getting to this stage.

00:02:12.180 --> 00:02:14.620
You could just divide the
6 by the 3, and you

00:02:14.620 --> 00:02:16.450
get a 1 and a 2.

00:02:16.450 --> 00:02:19.070
6 divided by 3 is
2, you get 4.

00:02:19.070 --> 00:02:22.660
I'm probably beating a dead
horse, but just in case you

00:02:22.660 --> 00:02:26.990
need a review multiplying
fractions, you just got it.

00:02:26.990 --> 00:02:34.560
Which expression represents
0.0000007

00:02:34.560 --> 00:02:38.320
in scientific notation?

00:02:38.320 --> 00:02:41.030
So the easy way to convert
scientific notation,

00:02:41.030 --> 00:02:43.080
especially when you have a
number behind the decimal

00:02:43.080 --> 00:02:46.730
point like this, is you
literally just count the

00:02:46.730 --> 00:02:48.560
digits behind the
decimal point.

00:02:48.560 --> 00:02:56.770
And we have 1, 2, 3,
4, 5, 6, 7 numbers

00:02:56.770 --> 00:02:59.020
behind the decimal point.

00:02:59.020 --> 00:03:02.390
So our answer is
going to be 7.

00:03:02.390 --> 00:03:08.700
This 7, right here, 7 times 10
to the-- it's going to be a

00:03:08.700 --> 00:03:11.190
negative exponent because
we're going less than 1.

00:03:11.190 --> 00:03:13.450
We're going behind the
decimal point.

00:03:13.450 --> 00:03:17.510
10 to the minus-- and
I just counted.

00:03:17.510 --> 00:03:20.850
1, 2, 3, 4, 5, 6, 7.

00:03:20.850 --> 00:03:23.670
10 to the minus 7.

00:03:23.670 --> 00:03:25.140
Right there.

00:03:25.140 --> 00:03:27.930
And if you find this problem a
little bit daunting, I have

00:03:27.930 --> 00:03:29.890
actually two videos where
I go into depth

00:03:29.890 --> 00:03:31.380
about scientific notation.

00:03:31.380 --> 00:03:34.520
So you might want to watch
those, just in case you run

00:03:34.520 --> 00:03:35.750
into the opposite situation.

00:03:35.750 --> 00:03:39.450
If you had 7,000, and you
want to write that

00:03:39.450 --> 00:03:40.640
in scientific notation.

00:03:40.640 --> 00:03:44.490
So in this case we're going
above, we're going into the

00:03:44.490 --> 00:03:46.130
positive domain.

00:03:46.130 --> 00:03:49.940
Then, instead of just counting--
when we had a

00:03:49.940 --> 00:03:51.980
decimal, you counted
the actual digits.

00:03:51.980 --> 00:03:54.370
You included the 7, right?

00:03:54.370 --> 00:03:56.220
That's where you got
10 to the minus 7.

00:03:56.220 --> 00:03:59.430
When you have something like
this, you just count the 0's.

00:03:59.430 --> 00:04:04.230
So 7,000 would be 7 times
10 to the third.

00:04:04.230 --> 00:04:06.600
If you want more of the
rationale of why that works, I

00:04:06.600 --> 00:04:09.210
definitely recommend that you
watch the two videos that I

00:04:09.210 --> 00:04:11.920
have on scientific notation.

00:04:11.920 --> 00:04:13.820
Next problem.

00:04:13.820 --> 00:04:17.930
The Venn diagram below shows
the number of girls on the

00:04:17.930 --> 00:04:21.160
soccer and track team
at a high school.

00:04:21.160 --> 00:04:23.790
So this is the soccer team,
this is the track team.

00:04:23.790 --> 00:04:26.820
And right here, this is the
girls who are on both the

00:04:26.820 --> 00:04:28.670
soccer and the track team.

00:04:32.500 --> 00:04:35.520
How many girls are on both the
soccer and the track teams?

00:04:35.520 --> 00:04:37.250
So I kind of jumped the gun.

00:04:37.250 --> 00:04:39.880
They're telling us the
answer right there.

00:04:39.880 --> 00:04:41.630
There are 6 girls.

00:04:41.630 --> 00:04:43.550
This overlap region-- right?

00:04:43.550 --> 00:04:46.180
If some girl is, let's say that
some girl right there,

00:04:46.180 --> 00:04:49.030
she's in the soccer circle,
and she's also

00:04:49.030 --> 00:04:50.050
in the track circle.

00:04:50.050 --> 00:04:53.050
And this number tells us that
there's 6 of these girls.

00:04:53.050 --> 00:04:57.800
So there are 6 girls that are
on both the soccer and the

00:04:57.800 --> 00:04:59.450
track teams.


CAHSEE practice: Problems 4-9

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.420
We're on problem 4.

00:00:02.420 --> 00:00:05.840
Traditions Clothing Store
is having a sale.

00:00:05.840 --> 00:00:09.590
Shirts that were regularly
priced at $20

00:00:09.590 --> 00:00:12.840
are on sale for $17.

00:00:12.840 --> 00:00:15.540
What is the percentage of
the decrease in the

00:00:15.540 --> 00:00:17.110
price of the shirts?

00:00:17.110 --> 00:00:19.680
So what is just the decrease
in the price of the shirts?

00:00:19.680 --> 00:00:23.180
Well, they've gone
from $20 to $17.

00:00:23.180 --> 00:00:26.140
So the decrease is $3.

00:00:26.140 --> 00:00:30.440
We have a $3 decrease in the
price of the shirts.

00:00:30.440 --> 00:00:32.840
So what is the percentage
of decrease?

00:00:32.840 --> 00:00:36.980
Well, we're starting at $20,
and we're decreasing by $3.

00:00:36.980 --> 00:00:40.360
So the percentage of the
decrease-- let me write it in

00:00:40.360 --> 00:00:41.620
a darker color.

00:00:41.620 --> 00:00:46.280
We're starting at $20 and we're
decreasing it by $3, or

00:00:46.280 --> 00:00:48.560
decreasing it by 3/20.

00:00:48.560 --> 00:00:52.100
This is the percent decrease,
or the fraction

00:00:52.100 --> 00:00:53.120
decrease right there.

00:00:53.120 --> 00:00:54.960
And this is going to
be equal to what?

00:00:54.960 --> 00:00:56.210
This is the same thing.

00:00:56.210 --> 00:00:59.350
We can divide it out.

00:00:59.350 --> 00:01:00.590
You might be able to do
that in your head.

00:01:00.590 --> 00:01:03.050
But just in case you
can't, let me just

00:01:03.050 --> 00:01:04.110
write it out like this.

00:01:04.110 --> 00:01:08.650
If I divide 20 into 3, 20
does not go into 3.

00:01:08.650 --> 00:01:11.700
Or you could say 20 goes
into 3 zero times.

00:01:11.700 --> 00:01:14.800
0 times 20 is zero.

00:01:14.800 --> 00:01:17.150
And then I put a decimal
point right there.

00:01:17.150 --> 00:01:20.690
20 goes into 30-- maybe I should
have done this-- let me

00:01:20.690 --> 00:01:21.420
do it over here.

00:01:21.420 --> 00:01:26.060
20 goes into 3 zero times.

00:01:26.060 --> 00:01:28.820
0 times 20 is 0.

00:01:28.820 --> 00:01:33.230
And then let me put a decimal
point like that.

00:01:33.230 --> 00:01:36.390
And then I'll do
3 minus that 0.

00:01:36.390 --> 00:01:39.270
So I'll just say you have
3.0, just like that.

00:01:39.270 --> 00:01:40.640
Maybe I shouldn't even
write the decimal.

00:01:40.640 --> 00:01:42.040
Maybe I'll write
a 30 like that.

00:01:42.040 --> 00:01:43.660
We have the decimal up here.

00:01:43.660 --> 00:01:46.310
20 goes into 30 one time.

00:01:46.310 --> 00:01:48.740
1 times 20 is 20.

00:01:48.740 --> 00:01:51.280
30 minus 20 is 10.

00:01:51.280 --> 00:01:54.360
And then bring down another
0, this 0 right there.

00:01:54.360 --> 00:01:57.360
And 20 goes into
100 five times.

00:01:57.360 --> 00:02:00.400
5 times 20 is 100.

00:02:00.400 --> 00:02:03.520
100 minus 100 is 0.

00:02:03.520 --> 00:02:09.720
So 3/20 can be rewritten
as 0.15.

00:02:09.720 --> 00:02:12.800
And another way you could think
about this is 3/20, is

00:02:12.800 --> 00:02:14.840
the same thing-- if you multiply
the numerator and the

00:02:14.840 --> 00:02:18.960
denominator by 5-- is the
same thing as 15/100.

00:02:18.960 --> 00:02:19.180
Right?

00:02:19.180 --> 00:02:21.980
If I multiply the top and the
bottom by 5, which we can

00:02:21.980 --> 00:02:25.180
always do, this is the
same thing as 15/100.

00:02:25.180 --> 00:02:26.880
So that's the way you could have
done that in your head,

00:02:26.880 --> 00:02:29.960
saying, oh, that's the
same thing as 0.15.

00:02:29.960 --> 00:02:35.360
And 0.15 expressed as
a percentage is 15%.

00:02:35.360 --> 00:02:38.360
So the correct answer is B.

00:02:38.360 --> 00:02:38.950
All right.

00:02:38.950 --> 00:02:41.050
Problem number 5.

00:02:41.050 --> 00:02:45.890
Which number equals 2 to
the minus fourth power?

00:02:45.890 --> 00:02:48.290
So this is a little bit of
review of exponents.

00:02:48.290 --> 00:02:54.760
2 to the minus 4 is the same
thing as 1 over 2 to the

00:02:54.760 --> 00:02:55.500
fourth power.

00:02:55.500 --> 00:02:57.780
That's all a negative
exponent does.

00:02:57.780 --> 00:03:00.630
It means 1 over essentially
the base to

00:03:00.630 --> 00:03:02.210
the positive exponent.

00:03:02.210 --> 00:03:06.320
And this is just going to
be 1 over 2 times 2

00:03:06.320 --> 00:03:08.550
times 2 times 2.

00:03:08.550 --> 00:03:09.210
And that's what?

00:03:09.210 --> 00:03:13.110
2 times 2 is 4, times 2
is 8, times 2 is 16.

00:03:13.110 --> 00:03:16.660
So it's equal to 1/16.

00:03:16.660 --> 00:03:20.120
So that is choice C.

00:03:20.120 --> 00:03:23.110
Problem 6.

00:03:23.110 --> 00:03:27.130
What is 3/4 minus 1/6?

00:03:27.130 --> 00:03:29.550
So whenever you add or subtract
fractions, you have

00:03:29.550 --> 00:03:33.400
to find a common denominator.

00:03:33.400 --> 00:03:36.620
And a good common denominator
is the least common multiple

00:03:36.620 --> 00:03:39.480
of these two guys, or the
smallest number that both of

00:03:39.480 --> 00:03:41.600
these denominators go into.

00:03:41.600 --> 00:03:43.880
So the smallest number that both
of these denominators go

00:03:43.880 --> 00:03:46.440
into is 12, right?

00:03:46.440 --> 00:03:50.580
4 goes into 12 three times, and
6 goes into 12 two times.

00:03:50.580 --> 00:03:53.130
So let's rewrite these fractions
with 12 as a

00:03:53.130 --> 00:03:54.910
denominator.

00:03:54.910 --> 00:03:59.730
So something over 12 minus
something over 12.

00:03:59.730 --> 00:04:03.940
So how do we rewrite 3/4
as something over 12?

00:04:03.940 --> 00:04:07.520
Well, 4 goes into
12 three times.

00:04:07.520 --> 00:04:10.250
Or we could say 3
times 4 is 12.

00:04:10.250 --> 00:04:12.670
So 3 times 3 will be the
other numerator.

00:04:12.670 --> 00:04:14.550
You get 9/12.

00:04:14.550 --> 00:04:17.870
3/4 and 9/12 are the exact
same fraction.

00:04:17.870 --> 00:04:20.660
This is in kind of its simplest
form, when you

00:04:20.660 --> 00:04:22.250
reduced the numerator
and denominator

00:04:22.250 --> 00:04:23.260
as much as you can.

00:04:23.260 --> 00:04:25.680
But this is a completely
equivalent fraction.

00:04:25.680 --> 00:04:28.430
To go from there to there, you
just multiply the numerator

00:04:28.430 --> 00:04:30.500
and the denominator by 3.

00:04:30.500 --> 00:04:33.970
3 times 3 is 9, 3
times 4 is 12.

00:04:33.970 --> 00:04:35.260
And the way you can think
about it, 4 goes

00:04:35.260 --> 00:04:36.720
into 12 three times.

00:04:36.720 --> 00:04:39.410
So just multiply 3 times
that numerator.

00:04:39.410 --> 00:04:41.890
Let's do the same
thing with 1/6.

00:04:41.890 --> 00:04:44.540
6 goes into 12 two times.

00:04:44.540 --> 00:04:46.490
So to go from there to
there, we have to

00:04:46.490 --> 00:04:48.310
multiply the 6 by 2.

00:04:48.310 --> 00:04:50.860
So to go from there to whatever
this numerator is, we

00:04:50.860 --> 00:04:53.250
have to multiply that
numerator by 2.

00:04:53.250 --> 00:04:55.210
So you stick a 2 right there.

00:04:55.210 --> 00:04:58.800
And now that we have a common
denominator, this becomes a

00:04:58.800 --> 00:05:00.700
simple problem to work out.

00:05:00.700 --> 00:05:05.550
It is equal to-- we have 9 out
of 12 pieces, minus 2 out of

00:05:05.550 --> 00:05:07.890
12 pieces, or whatever
we're talking about.

00:05:07.890 --> 00:05:08.990
Or slices of pie.

00:05:08.990 --> 00:05:13.240
So that's going to
be equal to 7/12.

00:05:13.240 --> 00:05:16.680
And that is choice C.

00:05:16.680 --> 00:05:19.060
Next problem.

00:05:19.060 --> 00:05:20.563
Problem 7.

00:05:23.420 --> 00:05:24.830
Do it in blue again.

00:05:24.830 --> 00:05:28.360
A salesperson at a clothing
store earns a 2%

00:05:28.360 --> 00:05:32.020
commission on all sales.

00:05:32.020 --> 00:05:34.260
How much commission does
the salesperson

00:05:34.260 --> 00:05:36.780
earn on a $300 sale?

00:05:36.780 --> 00:05:39.630
Well, they earn 2% on that.

00:05:39.630 --> 00:05:42.070
Or you could say 0.02
of the sale.

00:05:42.070 --> 00:05:47.650
So you could just multiply
300 times 0.02.

00:05:47.650 --> 00:05:49.220
This is kind of the
way to just do it.

00:05:49.220 --> 00:05:51.090
And I'll maybe give you a little
intuition on how you

00:05:51.090 --> 00:05:53.970
could do this in your head if
you're constrained for time.

00:05:53.970 --> 00:05:55.600
But the easiest way to think
about it is just

00:05:55.600 --> 00:05:57.590
multiply 2 times 300.

00:05:57.590 --> 00:06:00.330
Or 2 times 0 is 0.

00:06:00.330 --> 00:06:04.920
2 times 0 is 0, and
2 times 3 is 6.

00:06:04.920 --> 00:06:05.960
You could have done
that in your head.

00:06:05.960 --> 00:06:08.290
2 times 300 is 600.

00:06:08.290 --> 00:06:10.510
And then you worry about
the decimals.

00:06:10.510 --> 00:06:13.290
So we have two spaces behind
the decimal right here.

00:06:13.290 --> 00:06:13.570
Right?

00:06:13.570 --> 00:06:15.160
We have one, two.

00:06:15.160 --> 00:06:17.420
So we're going to have to have
two spaces behind the decimal

00:06:17.420 --> 00:06:18.670
in our answer.

00:06:21.830 --> 00:06:24.870
So the answer right
here is $6.

00:06:24.870 --> 00:06:27.490
And that is choice A.

00:06:27.490 --> 00:06:29.110
Now, a way you could have done
this in your head, you could

00:06:29.110 --> 00:06:32.350
have said, look, he makes
a 2% commission.

00:06:32.350 --> 00:06:36.220
So for every $100,
he makes $2.

00:06:36.220 --> 00:06:36.700
Right?

00:06:36.700 --> 00:06:39.650
2% is the same thing
as 2 out of 100.

00:06:39.650 --> 00:06:41.670
So every $100, he makes $2.

00:06:41.670 --> 00:06:47.030
He sold $300, so that would
also be 3 times

00:06:47.030 --> 00:06:49.460
$2 per 100, or $6.

00:06:49.460 --> 00:06:53.010
Whatever is easier for you
to understand, that's

00:06:53.010 --> 00:06:54.420
what you should do.

00:06:54.420 --> 00:06:56.140
Problem number 8.

00:06:56.140 --> 00:06:58.420
I'll do this in green.

00:06:58.420 --> 00:07:05.740
Some students attend school 180
of the 365 days in a year.

00:07:05.740 --> 00:07:09.920
About what part of the year
do they attend school?

00:07:09.920 --> 00:07:12.870
And so the keyword here is
about, which tells me that

00:07:12.870 --> 00:07:14.630
they don't want an
exact answer.

00:07:14.630 --> 00:07:17.040
They don't want me to sit
there-- I mean, if I wanted

00:07:17.040 --> 00:07:21.500
to, they attend 180
out of 365 days.

00:07:21.500 --> 00:07:23.650
If I wanted the exact
percentage, I would have to

00:07:23.650 --> 00:07:29.590
take 365 and divide it into 180,
with some decimals, and

00:07:29.590 --> 00:07:32.970
I'll get some-- I could work
it out, just like I did the

00:07:32.970 --> 00:07:36.200
decimal division in the past,
but it would take some time,

00:07:36.200 --> 00:07:38.020
and they just want
to know about.

00:07:38.020 --> 00:07:41.550
So what's 180/365 roughly?

00:07:41.550 --> 00:07:43.840
Well, what's 180 times 2?

00:07:43.840 --> 00:07:49.190
You could say 180/360, and I
picked 360 because that's 180

00:07:49.190 --> 00:07:53.880
times 2, that's equal to 50%.

00:07:53.880 --> 00:07:55.930
This is not that different
than this.

00:07:55.930 --> 00:07:58.610
We just have a small change
of the denominator, small

00:07:58.610 --> 00:08:01.310
relative to how large
that denominator is.

00:08:01.310 --> 00:08:05.060
So the answer here is 50%.

00:08:05.060 --> 00:08:09.630
If they had a couple of other
choices here like 49% or 51%,

00:08:09.630 --> 00:08:10.960
then you would have to
work this out in a

00:08:10.960 --> 00:08:12.310
little bit more detail.

00:08:12.310 --> 00:08:17.510
But it's pretty clear
that 180/365 is

00:08:17.510 --> 00:08:19.130
pretty close to 50%.

00:08:19.130 --> 00:08:23.100
It's nowhere near 18% or 75%,
so you can feel pretty good

00:08:23.100 --> 00:08:23.790
about this answer.

00:08:23.790 --> 00:08:26.520
If 49% were one of the choices,
then I would have to

00:08:26.520 --> 00:08:28.520
do a little bit more
arithmetic right

00:08:28.520 --> 00:08:30.330
here with the division.

00:08:30.330 --> 00:08:33.250
Problem number 9.

00:08:33.250 --> 00:08:37.539
What is the value of 2 to the
sixth times 2 to the fourth,

00:08:37.539 --> 00:08:39.750
divided by 2 to the fifth?

00:08:39.750 --> 00:08:42.360
Now, you could solve each
of these powers.

00:08:42.360 --> 00:08:43.580
2 to the sixth is what?

00:08:43.580 --> 00:08:48.430
It's 64.

00:08:48.430 --> 00:08:51.650
You could work out each of
these exponents, and then

00:08:51.650 --> 00:08:54.240
multiply them and then divide,
but it would take you forever.

00:08:54.240 --> 00:08:56.830
So what they really want you
to do here is use your

00:08:56.830 --> 00:08:58.230
exponent rules.

00:08:58.230 --> 00:09:00.460
So when you multiply two
exponents and they have the

00:09:00.460 --> 00:09:02.620
same base-- let me write
it this way.

00:09:02.620 --> 00:09:06.210
2 to the sixth times 2 to
the fourth, all of that

00:09:06.210 --> 00:09:07.740
over 2 to the fifth.

00:09:07.740 --> 00:09:08.890
What's that equal to?

00:09:08.890 --> 00:09:11.490
So let's just simplify the
numerator first. So I'll keep

00:09:11.490 --> 00:09:13.300
the denominator the same.

00:09:13.300 --> 00:09:19.610
When you multiply two exponents
with the same base,

00:09:19.610 --> 00:09:22.420
you essentially can just
add the exponents.

00:09:22.420 --> 00:09:23.920
So the same base is 2.

00:09:23.920 --> 00:09:29.270
So this is going to be equal to
2 to the 6 plus 4, or 2 to

00:09:29.270 --> 00:09:30.810
the 10th power.

00:09:30.810 --> 00:09:34.840
Now, when you divide exponents
that have the same base, you

00:09:34.840 --> 00:09:36.060
subtract the exponents.

00:09:36.060 --> 00:09:41.290
So this is going to be equal to
2 to the 10 minus 5 power,

00:09:41.290 --> 00:09:45.140
which is equal to
2 to the fifth.

00:09:45.140 --> 00:09:46.040
And that's our answer.

00:09:46.040 --> 00:09:48.620
And we look at our choices, we
don't see 2 to the fifth.

00:09:48.620 --> 00:09:50.970
So we're actually going to
have to multiply it out.

00:09:50.970 --> 00:09:54.250
And so 2 to the fifth
is 2 times 2 times 2

00:09:54.250 --> 00:09:56.880
times 2 times 2.

00:09:56.880 --> 00:09:58.670
2 times itself five times.

00:09:58.670 --> 00:10:00.560
That's what 2 to the
fifth means.

00:10:00.560 --> 00:10:01.140
So what is this?

00:10:01.140 --> 00:10:02.780
2 times 2 is 4.

00:10:02.780 --> 00:10:04.720
4 times 2 is 8.

00:10:04.720 --> 00:10:06.650
8 times 2 is 16.

00:10:06.650 --> 00:10:08.830
16 times 2 is 32.

00:10:08.830 --> 00:10:10.930
So that is our answer.

00:10:10.930 --> 00:10:12.180
D.


CAHSEE practice: Problems 13-14

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:02.310
Problem 13.

00:00:02.310 --> 00:00:05.390
These eight cards are placed
face down and shuffled.

00:00:05.390 --> 00:00:07.200
So these are the eight cards.

00:00:07.200 --> 00:00:11.090
If Beatrice turns over only
one card, what is the

00:00:11.090 --> 00:00:13.450
probability that she will
get a card with a

00:00:13.450 --> 00:00:17.310
number less than four?

00:00:17.310 --> 00:00:20.240
So all of these cards right here
are potential outcomes.

00:00:20.240 --> 00:00:21.710
She's going to flip
them all over.

00:00:21.710 --> 00:00:24.190
And then she wants to know the
probability that she gets a

00:00:24.190 --> 00:00:25.940
card less than four.

00:00:25.940 --> 00:00:28.050
So what are the cards
that satisfy that?

00:00:28.050 --> 00:00:32.549
Well, there's three cards
that are less than four.

00:00:32.549 --> 00:00:35.630
They didn't say less than
or equal to four.

00:00:35.630 --> 00:00:39.810
So it could be that card,
that card, or that card.

00:00:39.810 --> 00:00:42.720
Those are the cards that she
can pick, out of the eight

00:00:42.720 --> 00:00:45.170
cards, that would satisfy
this constraint.

00:00:45.170 --> 00:00:48.590
Or those would be the three
outcomes, out of the eight

00:00:48.590 --> 00:00:52.290
possible outcomes, that would
satisfy these conditions.

00:00:52.290 --> 00:00:57.550
So the probability is just three
cards that satisfy your

00:00:57.550 --> 00:01:01.190
condition divided by the total
number of outcomes.

00:01:01.190 --> 00:01:04.519
So the probability of her
picking a card that is less

00:01:04.519 --> 00:01:07.210
than four-- there's three cards
that are less than four

00:01:07.210 --> 00:01:08.900
out of eight cards.

00:01:08.900 --> 00:01:11.440
The probability is 3/8.

00:01:11.440 --> 00:01:13.820
And that is choice B.

00:01:13.820 --> 00:01:16.980
Always nice when our answer
is actually there.

00:01:16.980 --> 00:01:17.520
OK.

00:01:17.520 --> 00:01:20.280
Problem-- what's the
next problem?

00:01:20.280 --> 00:01:22.430
Problem 14.

00:01:22.430 --> 00:01:26.810
The Smithburg town library
wanted to see what types of

00:01:26.810 --> 00:01:29.390
books were borrowed
most often.

00:01:29.390 --> 00:01:30.510
All right, there we go.

00:01:30.510 --> 00:01:33.250
They drew a little
pie diagram.

00:01:33.250 --> 00:01:38.720
According to the circle graph
shown above-- OK, let's see

00:01:38.720 --> 00:01:40.360
which of these statements
are true.

00:01:40.360 --> 00:01:43.380
The first statement says, "more
Children's books were

00:01:43.380 --> 00:01:46.850
borrowed than Romance and
Science Fiction combined."

00:01:46.850 --> 00:01:48.170
Let's see if that's true.

00:01:48.170 --> 00:01:52.070
Children's is 26%, and
then Romance and

00:01:52.070 --> 00:01:54.210
Science Fiction combined.

00:01:54.210 --> 00:01:58.960
Romance is 13, and Science
Fiction is 18.

00:01:58.960 --> 00:02:04.750
So what's 13 plus 18?

00:02:04.750 --> 00:02:07.390
3 plus 8 is 11.

00:02:07.390 --> 00:02:10.740
And then we have 1
plus 1 plus 1.

00:02:10.740 --> 00:02:13.450
And so then we get 31.

00:02:13.450 --> 00:02:16.750
So if you take Romance and
Science Fiction combined,

00:02:16.750 --> 00:02:21.150
that's 31% of the books,
while the Children's

00:02:21.150 --> 00:02:22.670
books were only 26%.

00:02:22.670 --> 00:02:25.880
So that is definitely
not correct.

00:02:25.880 --> 00:02:29.490
More than half of the books
borrowed were Children's,

00:02:29.490 --> 00:02:31.440
Mysteries, and Art combined.

00:02:31.440 --> 00:02:34.360
So more than half would mean
it has to be more than 50%.

00:02:34.360 --> 00:02:36.920
So they think Children's,
Mysteries, and Art combined.

00:02:36.920 --> 00:02:38.610
So let's see what that gets.

00:02:38.610 --> 00:02:41.230
Children's-- I'll do it
in a different color.

00:02:41.230 --> 00:02:45.800
Children's, Mysteries,
and Art.

00:02:45.800 --> 00:02:50.870
So Children's and Mysteries, if
you add those together, 26

00:02:50.870 --> 00:02:54.420
plus 20, that gives you 46%.

00:02:54.420 --> 00:02:57.000
And then you add another
4% to that.

00:02:57.000 --> 00:02:58.640
We're combining with Art.

00:02:58.640 --> 00:03:00.640
That gets us to 50%.

00:03:00.640 --> 00:03:03.960
So exactly half the books
borrowed were Children's,

00:03:03.960 --> 00:03:05.270
Mysteries, and Art.

00:03:05.270 --> 00:03:07.140
But they're saying
more than half.

00:03:07.140 --> 00:03:08.580
This is exactly half.

00:03:08.580 --> 00:03:10.650
So this doesn't seem
right either.

00:03:10.650 --> 00:03:13.400
If they said half or
more, then we would

00:03:13.400 --> 00:03:14.170
have picked this choice.

00:03:14.170 --> 00:03:17.540
But they said definitely more
than 50%, so that can't be it.

00:03:17.540 --> 00:03:21.270
Although it's kind of a tricky
one, because it's exactly 50%.

00:03:21.270 --> 00:03:25.230
C, more Mysteries were borrowed
than Art and Science

00:03:25.230 --> 00:03:27.870
Fiction combined.

00:03:27.870 --> 00:03:33.720
Mysteries was 20%, and then
Art and Science Fiction

00:03:33.720 --> 00:03:36.270
combined is 4 plus 18.

00:03:36.270 --> 00:03:40.700
If you combine these two, you
get 4 plus 18 is 22%.

00:03:40.700 --> 00:03:43.230
So the Mysteries are definitely
not more than the

00:03:43.230 --> 00:03:45.060
Art and Science Fiction
combined.

00:03:45.060 --> 00:03:49.290
So that's not the
correct answer.

00:03:49.290 --> 00:03:51.820
And then finally, more than half
of the books-- this is

00:03:51.820 --> 00:03:54.730
probably going to be our answer,
if we haven't made any

00:03:54.730 --> 00:03:56.070
silly mistakes.

00:03:56.070 --> 00:03:58.740
This says more than half of
the books borrowed were

00:03:58.740 --> 00:04:01.880
Romance, Mysteries, and Science
Fiction combined.

00:04:01.880 --> 00:04:03.620
Let's see that.

00:04:03.620 --> 00:04:08.485
Romance, Mysteries, and
Science Fiction.

00:04:11.820 --> 00:04:15.130
We already know Romance plus
Science Fiction, that was 13

00:04:15.130 --> 00:04:18.980
plus 18, which we already
figured out was 31%.

00:04:18.980 --> 00:04:22.700
These two could combine at 31%,
and then you add that 31%

00:04:22.700 --> 00:04:23.930
to the Mysteries.

00:04:23.930 --> 00:04:25.850
So it becomes 51%.

00:04:25.850 --> 00:04:28.330
So that's right.

00:04:28.330 --> 00:04:31.020
This is 51% of the
books borrowed.

00:04:31.020 --> 00:04:34.370
So that's definitely more than
half of the books, so the

00:04:34.370 --> 00:04:37.820
correct choice here is D.


CAHSEE practice: Problems 1-3

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.380
Problem number 1.

00:00:02.380 --> 00:00:05.890
Which number has the greatest
absolute value?

00:00:05.890 --> 00:00:08.630
Absolute value is just the
distance that the number is

00:00:08.630 --> 00:00:13.060
from 0, or how large the number
is, regardless of its

00:00:13.060 --> 00:00:14.890
sign or its direction.

00:00:14.890 --> 00:00:18.060
So if you kind of visualize it
on a number line, the absolute

00:00:18.060 --> 00:00:20.220
value of minus 17.

00:00:20.220 --> 00:00:23.640
Minus 17 is 17 to
the left of 0.

00:00:23.640 --> 00:00:26.700
So its absolute value
is just 17.

00:00:26.700 --> 00:00:29.340
The absolute value
of minus 13?

00:00:29.340 --> 00:00:32.290
Well, it's 13 to the left of
0, if you imagine it on a

00:00:32.290 --> 00:00:33.360
number line.

00:00:33.360 --> 00:00:35.490
So it's just going to be 13.

00:00:35.490 --> 00:00:37.730
Absolute value of 15?

00:00:37.730 --> 00:00:39.330
Well, that's just
going to be 15.

00:00:39.330 --> 00:00:42.010
It's 15 to the right of
0 on the number line.

00:00:42.010 --> 00:00:43.620
I think you see a
pattern here.

00:00:43.620 --> 00:00:45.690
When you take the absolute
value of a number, you

00:00:45.690 --> 00:00:47.530
essentially just disregard
the sign.

00:00:47.530 --> 00:00:50.120
The absolute value of a negative
number is going to be

00:00:50.120 --> 00:00:53.000
positive, and the absolute value
of a positive number is

00:00:53.000 --> 00:00:53.870
going to be positive.

00:00:53.870 --> 00:00:56.300
The absolute value is always
going to be positive, because

00:00:56.300 --> 00:00:59.210
you're just measuring how far
you are away from 0 on the

00:00:59.210 --> 00:01:00.320
number line.

00:01:00.320 --> 00:01:04.430
And then finally, the absolute
value of 19 is going to be

00:01:04.430 --> 00:01:06.470
equal to 19.

00:01:06.470 --> 00:01:08.780
So the number that has the
greatest absolute value?

00:01:08.780 --> 00:01:11.850
Well, the greatest absolute
value is right there, it's 19.

00:01:11.850 --> 00:01:14.540
So 19 has the greatest
absolute value.

00:01:14.540 --> 00:01:17.890
So it also happens to be the
largest number here.

00:01:17.890 --> 00:01:19.430
Just like that.

00:01:19.430 --> 00:01:21.250
Problem number 2.

00:01:21.250 --> 00:01:24.160
Maybe I'll do this in gray.

00:01:24.160 --> 00:01:26.740
Between which two integers
is the value of the

00:01:26.740 --> 00:01:29.940
square root of 61?

00:01:29.940 --> 00:01:31.940
So the way you think about this
is that you know there's

00:01:31.940 --> 00:01:34.870
some number-- the square root
of 61 is going to be some

00:01:34.870 --> 00:01:37.650
decimal number, I don't know
what it is-- but there's going

00:01:37.650 --> 00:01:41.630
to be some number that if I
square it, is going to be a

00:01:41.630 --> 00:01:43.230
little bit lower than 61.

00:01:43.230 --> 00:01:45.170
And then some other integer,
if I square it, should be a

00:01:45.170 --> 00:01:46.940
little bit greater than 61.

00:01:46.940 --> 00:01:49.630
So let's see if we can
figure this out.

00:01:49.630 --> 00:01:54.080
So 6 squared is going
to be 36.

00:01:54.080 --> 00:01:57.310
And then 7 squared is
going to be 49.

00:01:57.310 --> 00:01:59.610
That number is not
dark enough.

00:01:59.610 --> 00:02:00.820
Do a darker color.

00:02:00.820 --> 00:02:03.060
So this isn't going to
be the case, right?

00:02:03.060 --> 00:02:08.610
Because the square of 61-- or 61
is greater than 49-- so the

00:02:08.610 --> 00:02:12.360
square root of 61 is going to
be greater than the square

00:02:12.360 --> 00:02:13.740
root of 49.

00:02:13.740 --> 00:02:14.790
Or actually let me write
it this way.

00:02:14.790 --> 00:02:18.770
I could rewrite 6 and 7 as the
square root of 36 and the

00:02:18.770 --> 00:02:21.880
square root of 49.

00:02:21.880 --> 00:02:27.010
I can rewrite 7 and 8 as the
square root of 49 and the

00:02:27.010 --> 00:02:31.250
square root of 64, right?

00:02:31.250 --> 00:02:34.850
7 squared is 49, so the square
root of 49 is 7.

00:02:34.850 --> 00:02:40.030
8 squared is 64, so the square
root of 64 is going to be 8.

00:02:40.030 --> 00:02:45.480
So I just rewrote 7 and 8 as the
square root of 49 and the

00:02:45.480 --> 00:02:47.280
square root of 64.

00:02:47.280 --> 00:02:50.650
Well, the square root of 61 is
clearly going to be between

00:02:50.650 --> 00:02:52.410
these two numbers, right?

00:02:52.410 --> 00:02:54.560
It's going to be between the
square root of 49 and the

00:02:54.560 --> 00:02:55.460
square root of 64.

00:02:55.460 --> 00:02:58.750
The 61 is between 49 and 64.

00:02:58.750 --> 00:03:00.940
So our answer is B.

00:03:00.940 --> 00:03:04.260
Square root of 61 is between
these two numbers, but these

00:03:04.260 --> 00:03:07.670
two numbers are the same
thing as 7 and 8.

00:03:07.670 --> 00:03:10.240
Next problem, number 3.

00:03:10.240 --> 00:03:14.130
Use the addition problems below
to answer the question.

00:03:14.130 --> 00:03:17.000
All right, so they wrote some
addition problems right there.

00:03:17.000 --> 00:03:18.070
We're dealing with fractions.

00:03:18.070 --> 00:03:19.560
Let's see where this goes.

00:03:19.560 --> 00:03:26.360
Based on this pattern, what is
the sum of 1/2 plus 1/4 plus

00:03:26.360 --> 00:03:33.590
1/8 plus 1/16, all the
way to 1/1024?

00:03:33.590 --> 00:03:37.070
So let's see if we can discern
some type of a pattern here.

00:03:37.070 --> 00:03:40.260
Maybe I'll do this in red just
to keep things interesting.

00:03:40.260 --> 00:03:46.480
So when I took the first
two terms, I got 3/4.

00:03:46.480 --> 00:03:50.500
When I took the next two terms,
or not the next two

00:03:50.500 --> 00:03:52.180
terms. When I add another
term to it.

00:03:52.180 --> 00:03:57.200
When I add the 1/8 term to this
over here, I got 7/8.

00:03:57.200 --> 00:04:01.590
Then when I add a 1/16 to
7/8, I get a 15/16.

00:04:01.590 --> 00:04:06.610
So the general pattern here is
that whenever I add it up, my

00:04:06.610 --> 00:04:10.150
denominator and my sum-- I guess
you could call it that

00:04:10.150 --> 00:04:13.390
way-- my denominator is going
to be the same denominator

00:04:13.390 --> 00:04:15.670
that I have right there.

00:04:15.670 --> 00:04:18.190
And then my numerator, if I
just look at all of the

00:04:18.190 --> 00:04:23.140
pattern here, just turns out to
be 1 less than that, right?

00:04:23.140 --> 00:04:27.270
So when I added 1/2 plus 1/4, I
got 4 in the denominator and

00:04:27.270 --> 00:04:28.150
3 in the numerator.

00:04:28.150 --> 00:04:33.690
When I had 1/2 plus 1/4 plus
1/8, 8 in the denominator and

00:04:33.690 --> 00:04:35.260
1 less than that in
the numerator.

00:04:35.260 --> 00:04:39.680
When I added it all the way
to 1/16, I got 16 in the

00:04:39.680 --> 00:04:42.770
denominator and 1 less
in the numerator.

00:04:42.770 --> 00:04:45.720
When I added it all the way
to 32, I got 32 in the

00:04:45.720 --> 00:04:48.540
denominator and 1 less
in the numerator.

00:04:48.540 --> 00:04:52.280
And this only worked when I'm
adding successive powers of, I

00:04:52.280 --> 00:04:53.720
guess you could call
it 1/2, right?

00:04:53.720 --> 00:04:55.980
This is 1/2, 1/2 squared,
1/2 to the

00:04:55.980 --> 00:04:57.880
third, 1/2 to the fourth.

00:04:57.880 --> 00:05:00.960
So based on this pattern, what
is the sum if I were to go all

00:05:00.960 --> 00:05:06.910
the way to 1/1024?

00:05:06.910 --> 00:05:10.410
Well, based on this pattern, my
denominator is going to be

00:05:10.410 --> 00:05:15.580
1,024, and my numerator is going
to be 1 less than 1,024.

00:05:15.580 --> 00:05:18.740
So it's going to be 1,023.

00:05:18.740 --> 00:05:23.790
And that is choice
C right there.