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jedishrfu

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I had a geometry teacher who once scolded us for our poor performance on his tests. He told us that it took him 5 minutes to work out and write down the answers in full to any of his tests and from that he would give us 45 minutes to complete the test. He showed us how we answered his questions in frivolous roundabout ways that wasted precious time because we didn't know exactly how or in what manner we could present our answer to him.

The big takeaway for me was its okay to plot a line solution to y=mx+b by simply drawing and labeling the axes x,y with tick marks to y-intercept (no numbered labels for each tick mark) and similarly for the other point using tick marks on the x-axis for the x-value and a vertical bar with more tick marks for the y-value and then simply labeling the point.

We students had been trying to reproduce the books plots in gory detail with 10 numbered tick marks in each direction on each axis before we even started the problem. We didn't realize that we could've used the same notational shortcuts that the teacher used when drawing answers on the black board. Duh...

The second thing I learned was how to reduce trig notation to brief cryptic diagrams that I would write at the top of my paper so I didn't have to keep remembering it during the test. It was a kind of visual cue that allowed me to speed through the test with confidence.

Some example mnemonic devices I used were:

Code:

```
s2+c2=1 // for sin^2(a) + cos^2(a) = 1
1+t2=s2 // for 1 + tan^2(a) = sec^2(a)
sab=sacb+casb // for sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
cab=cacb-sasb // cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
```

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f95toli

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Whereas I agree with the bit I put in bold I don't think the part it italics follows. You can be very good a "standard" math without being great at the type of math you sometimes find in the types of tests the OP is referring to; the reason is simply that these tests do not necessarily testWhile I can't answer your question, I realize it would probably depend on the math lecturer and what he taught regularly. As we progress in our math studies, the math we learn in grade school is child's play to us now. Following that extension if your job is to teach higher level math then that math will be child's play to you andyou should easily be able to do the problems you routinely assign to your students.I'm sure this would be true of the Putnam.

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jedishrfu

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Here's a writeup from Bruce Reznick who wrote and chaired the Putnam exam in the 1980's:

https://faculty.math.illinois.edu/~reznick/putnam.pdf