What are some examples of students making ridiculous math mistakes?

[micromass]

Here's a HORRIBLE math mistake that I've seen (and somebody actually wrote this on a test)

$$\int_0^{2\pi}{\cos xdx}=\left[\frac{\sin x}{x}\right]_0^{2\pi}=\frac{\sin 2\pi}{2\pi}-\frac{\sin 0}{0}=\sin - \sin = 0$$

The sad thing is that the answer is actually correct. And afterwarts that person claimed that you should have gotten partial credit for getting the correct answers...

Here's another one: somebody claimed that

$$2(\log x)=(2\log) x$$

because of associativity of the multiplication. I was sad all day after seeing this...

What are some of the most horrible math mistakes you've seen? It could also be instructive to students to see which mistakes not to make!

 

[Caramon]

Haha, that 2pi and 0 one canceling is absolutely hilarious!

 

[chiro]

Here's a HORRIBLE math mistake that I've seen (and somebody actually wrote this on a test)

$$\int_0^{2\pi}{\cos xdx}=\left[\frac{\sin x}{x}\right]_0^{2\pi}=\frac{\sin 2\pi}{2\pi}-\frac{\sin 0}{0}=\sin - \sin = 0$$

The sad thing is that the answer is actually correct. And afterwarts that person claimed that you should have gotten partial credit for getting the correct answers...

Here's another one: somebody claimed that

$$2(\log x)=(2\log) x$$

because of associativity of the multiplication. I was sad all day after seeing this...

What are some of the most horrible math mistakes you've seen? It could also be instructive to students to see which mistakes not to make!

I think yours (1st one) takes the cake

 

[AlephZero]

I don't feel sad about these at all. I would be much more worried if the next generation of students could do my job better than I can

 

[Mark44]

I'm with micromass. In a course that is dealing with definite integrals, an instructor should be able to expect a certain level of expertise from the students, such as understanding that the notation sin x does not mean sin times x, nor can (sin x)/x be simplified to sin.

Some years ago I had a student in an intermediate algebra class, who came to see me to question why she had gotten no credit for the correct answer on a homework problem, and her friend had gotten half credit for an incorrect answer on the same problem. I explained to her that 1) the answer was in the back of the book, and 2) none of her work led in any way to the answer she wrote down. In contrast, her friend's work made sense most of the way through her work, but there was a mistake in the last step or so.

The integral problem in the first post in this thread is like the work of the student who came into complain - almost none of it makes any sense at all.