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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?
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.
Full Transcript
- 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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