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checking test point sampling

checking test point sampling

by Joel Trussell -
Number of replies: 0
I recently has a case using a problem that asked the students to reconstruct an aliased sinusoid after sampling. the student's answer was
f1 = 9*cos(340*6*pi*t+1.5708)+10*cos(440*6*pi*t-1.0472);
the correct ansswer is
f2 = 9*cos(340*6*pi*t+1.5708)+10*cos(310*6*pi*t+1.0472);

The default answer checker counted the student's answer correct.
Note: the problems was written by a TA who was new to Webwork and didn't remember to set the test point limits.

The default limits seem to be either [-1,1]or [-2,2] with a granularity of 1000. Finding the sampling solution was difficult to find. I'd recommend updating the web page on test points

I changed the code to use limits of [-1/$Fmax,1/$Fmax], where Fmax is the maximum frequncy of the random frequencies in the problem. This works and showed the student's answer in error.

However, I wanted to check the effect of sampling with the default values, described above. I could not make a case for sampling that would give identical values. It would seem VERY unlikely to randomly obtain sampling points that all fell on the zeros of f1 - f2. It is "possible" but unlikely.

Any thoughts on why the default test points would fail?