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CAHSEE Math 2.5 Number Sense 304 Views


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Description:

Number Sense: Drill Set 2, Problem 5. By what percent did his percentage grade increase from one test to the other?

Language:
English Language

Transcript

00:04

And here's your shmoop du jour.

00:06

Kyle's father, a general in the army, has promised to buy his son a tank for his 16th birthday...

00:11

but only if he steps up his academic performance.

00:14

On his first math test of the school year, Kyle had a score of 80 out of 100.

00:19

On his second test, after spending some time on Shmoop, he received a score of 45 out of 50.

00:24

By what percent did his percentage grade increase from one test to the other?

00:30

And will it be enough to get him into a shiny new tank that will be the envy of all his friends?

00:34

Here are our potential answers...

00:44

First of all... decreased? After taking Shmoop?

00:47

Get real. Just cross out answer D angrily and let's get serious.

00:51

OK, this question is really a 2-parter.

00:53

First, we have to convert his second score to a percentage...

00:57

...and then we have to figure out the % INCREASE from the first test to the second.

01:02

In the first test, Kyle got an 80%.

01:04

The question gives us the percentage, more or less, because it's just out of 100.

01:09

So now we have to convert the second test to a percentage score...

01:13

and we get that a familiar-looking percentage equation.

01:17

That is, 45 is to 50 as whatever-percent is to 100.

01:22

And a quick way to solve this one is to just multiply top and bottom by 2...

01:26

...50 times 2 is 100 and 45 times 2 is 90

01:30

so the answer is 90 percent. But now comes the tricky part.

01:33

It's asking for the percent IMPROVEMENT.

01:36

And there's a total curveball here that they give us in answer A, which is totally wrong.

01:43

Yes, Kyle improved from 80 to 90 percent on the 2 exams.

01:47

But his PERCENTAGE improvement was meaningfully bigger.

01:51

If he'd gone from 100 to 110 percent ...if that were even possible...

01:55

then he'd have improved 10 percent.

01:57

But here he is growing from a smaller base in 80 percent.

02:00

So hopefully it makes sense that if his percentage goes up the same amount -- 10 percent here...

02:06

...then the RATE of growth will be higher.

02:08

And here is one of the golden formulas of our math we should tattoo onto our leg:

02:15

NEW MINUS OLD OVER OLD. Or NMOOO, if we ever get stuck.

02:20

The formula gives us the RATE OF GROWTH for these kinds of problems and here the "new"

02:25

score is 90; the old score is 80. So new minus old is 90 minus 80... or 10 in

02:31

the numerator... and we put it over old, or 80, which goes in the denominator.

02:35

So we have 10 over 80, or 1 over 8 or, converting to a percentage...

02:40

...we divide 8 into 1... ...and we get 12.5%.

02:44

And it's answer B.

02:48

Looks like Kyle is going to be Big Man on Campus... ...tooling around town in his fancy new tank.

02:52

Just check out those guns.

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