The courses I am taking are very challenging. There is not a single day where I do not go home and study, review, work on problems, or think about calculus for a good amount of time. I am just not very good at timed math tests, it takes me longer to do math. I can do very long and hard problems in mathematics, but just not at a high speed. It has also been a while since I have seen most of the problems on the act, and not to mention the way those questions are being taught have changed quite a lot.
To put it into perspective, at the academy I go to, a lot of people have got a 31-33 on their act. I performed much better than they are performing in Calc 1 this year, because I am methodical with my work. I am not in any way fast.
They may have got a higher ACT score, but I am still better at mathematics, especially calculus. I do not see the virtue in retaking a test which predicts my performance on a course that I have already taken.
It was also predicted by the PSAT that I could not handle a college level course in Mathematics, but I performed much better than those around me who scored higher on the ACT portion. Maybe it is because I struggle with timed tests in general, get anxiety about Math Tests, and am tired from the other test portions.
I guess I would want to know your perspective on what a hard math problem is. This is an example of an average homework problem given to us to be completed for the next class with proper notation and explanation using vectors.
“Water traveling along a straight portion of a river normally flows fastest in the middle, and the speed slows
almost to zero at the banks. Consider a long stretch of river flowing north, with parallel banks 40 meters
apart. If the maximum water speed is 3 m/s the flow rate from the bank can be modeled with f(x) = 3sin x
40
If a boater would like to cross from A to B with a constant heading and has a constant boat speed of 5
m/s, determine the angle at which the boat should head.”
Or
“Given the vector valued function r(t) = <cost, sin=”" t,="" ln(cost)="">, -
π
2 < t < π
2.
a) Find the vectors T, N, and B at the point (1, 0, 0). (6 points)
b) Find the curvature function k(t) and determine the value(s) of t for which the curvature is largest. (4 points)
c ) Find the curvature k(t) at the value of t determine in part b.
Plot the function on the Calc3DPlot and print out a good graph that confirms your t value. (2 points)
d) You are at the point (1, 0, 0), approximately where will you be 5 units down the curve? "</cost,>