Here’s a challenge for the board. Are we smarter than an 8th grader from 1911?
Each doper needs to pick three questions to participate. There’s no answer key so feel free to check other peoples answers.
No cheating with Google. But you can use a calculator.
I’ll start.
Arithmetic #7 barn 40ft high, rope is tied from the top to the ground and extends out 30 ft. How much rope is needed?
a²+b²=c²
1600+900=c²
2500= c²
c=50 ft of rope
#5 sold watch for $180 and lost 16 2/3% what was the cost of the watch?
I’ll treat this like a discount and we need the original price.
sale price = (100% - discount) * original cost
x= original cost
sale price = 180
180 = (100%-16.667%) x
180 = (99 3/3% - 16 2/3%) x
180 = 83 1/3% x
180 = .83333 x
180/.83333 = x
x = $216
#4 man bought farm $2400 and sold it for $2700 what is % profit?
%= part/whole
%= 300/2400
% = .125
12.5% profit
x = 216
I may play later, but for now, I just wanted to comment on one thing. Geography question #8 - naming, in order, the three largest states. Apart from maybe giving you an answer on Jeopardy, why would that matter? Just knowing a certain city/state/country occupies a certain area really doesn’t tell you much, does it? Area doesn’t necessarily correlate to population, wealth, resources, or anything else for that matter, so why is it something you’d need to know? Knowing physical features, like elevation or bodies of water or average temperature, can tell you something of value about a region. Knowing the Rhode Island is the smallest state really doesn’t tell you anything about RI, does it?
Knowing how to multiply is a valuable skill. Knowing pi to 100 places is a party trick.
Maybe I’m just bitter because so much of my education was based on memorization rather than analytical thinking…
Geez those fractions bring back memories. We had to work everything out by hand all the way through high school. Complex fractions are a major PITA. We had to keep our fractions right up to the last step. Even then it had to be reduced to the lowest common denominator. 7 8/64 got points taken off. you better reduce it to 7 1/8
They don’t even teach this stuff anymore do they? Do modern kids even know to factor out 10 for 180 * 3/250 to 18 * 3/25 before multiplying? Those kinds of tricks helped us stay sane before calculators hit the market.
This answer isn’t right. 50 ft of rope would make the trip, but there would be no rope left for which to make the knot. So it is 50ft + however many inches it takes to make a knot
Is the question asking for the interest earned on $50.30 over that time period, or how much principal would be required to generate that much interest over that time? Is the interest calculated as simple (easy enough to figure) or compound? If compound, how often is the earned interest credited? Is a leap year involved? Too many variables…
For 8% simple interest on $50.30 over 3 yr., 3mo., 3 days with no leap year the answer is $13.11:
$50.30*.08 = $4.024 annual interest earned
4.024/365 days per year = 0.011 interest earned per day
365 days/12 months = 30.416 days per month
30.416 days per month * 3 = 91.25 days in 3 months
365 days * 3 years = 1095 days in 3 years
3 yr (1095 days)+ 3 months (91.25 days) + 3 days = 1189.25 days
1189.25 days * $0.011 interest earned per day = $13.11
Okay, maybe I’m going to really embarrass myself here but wouldn’t the answer be 70 ft plus the inches to tie the knot? No fancy math involved, just that you need 40 ft to go from the top of the roof to the ground and 30 ft more to extend out:
What you are missing is that the rope is assumed to be taut and stretched into a single straight line.
The barn is 40 feet tall – this, together with that fact (that the rope touches the ground 30 feet away from the barn) tells us that what we have here is a right triangle (we are assuming that the barn wall is perfectly vertical and the ground is perfectly level and horizontal). We know the two shortest sides (30 and 40 feet), so finding the hypotenuse (the length of the rope) is trivial. Little diagram:
|
|
|
|
|
| <– Barn wall
| (40 ft)
|
|
|
| Point where the rope touches the ground
|_______________V (this is 30 ft. away from the wall)
It becomes instantly obvious that this is a right triangle, and that we have to find the hypotenuse. The assumption is that the rope is taut and goes in a straight line
I was also going to comment similarly on this question, and add that the answer now would be different than in 1911 because Alaska wasn’t a state then.
I was surprised at the difficulty of the test. There are some that I’d have to research to answer. Arithmetic 10- I have no idea how big a cord of wood is. #3 calculating paint. I know you figure the wall area minus the windows/door. But that one would be tricky. I normally don’t subtract out the windows/doors. I don’t want to run short.
One like history #7 frustrated me. I remembered – assassinated (as of 1911) Lincoln, William McKinley
died of illness in office - William Henry Harrison, Zachary Taylor
I racked my brain for awhile and just couldn’t dredge up James A. Garfield. :smack: I just had a brain fart on this one.
I was hoping the Dopers would take this test challenge. Theres some interesting questions on many subjects in that test
Your answer using ratios/proportions is probably what the teacher expected. I had to use simple algebra and I’m not certain those 1911 kids knew algebra in 8th grade.
I tended to struggle with word problems in school. Taking the hard approach instead of an easier one. It hurt my grade in a few junior high math classes.
I understand. I was completely stymied by algebra in HS. Blew through Euclidean geometry w/o a care though. It’s amazing how selective certain types of brain damage can be. But years later I took matrix algebra and a couple semesters of analytical calc and geometry just to prove I could do it. Between the exposure I’d been forced into at college and grad school, everything fell into place and it seemed completely intuitive. The proofs were something else, but the ideas finally made sense.
Lets say the 40 ft barn’s rope extended to a sloped ground 30 ft out. The ground slopes approx. 14 degrees away.
Thats a more real world problem. Law of CoSines is needed.
c² = a²+b² - 2ab cos(angle of ab)
I loved trig because there’s so many real world applications. Like a power pole and guy wire. The ground probably slopes and you have to consider it when buying your cable.
Now trig functions and calculus weren’t fun. The theorems in Cal II made it a tough class. integral (cos x)^2 dx that gives me indigestion thinking about it. I was glad to finish those classes and never look back.
It hurt my grade in a few junior high math classes.