There is no information in the question about grades, so the best we can do is to determine the most likely number of correctly answered test questions. I'll assume that the $25$ questions are randomly drawn with uniform distribution without replacement from $87$ possible questions about the $87$ facts, and the student answers a question correctly if and only if she remembered the corresponding fact. (It would have been preferable if you had stated such assumptions in the question rather than leaving them to our fancy.)
The student learns $47$ out of $87$ facts. The number of ways in which $25$ questions can be chosen from $87$ is $\binom{87}{25}$, and the number of ways they can be chosen such that the student knows the answers to $n$ of them is $\binom{47}{n}\binom{40}{25-n}$. Since $\binom{87}{25}$ doesn't depend on $n$, the most likely number of correct questions is the one that maximizes $\binom{47}{n}\binom{40}{25-n}$, which is
$\frac{47!}{n!(47-n)!}\frac{40!}{(25-n)!(15+n)!}\;.$
The ratio between the values for $n$ and $n+1$ is
$\frac{(n+1)(15+n+1)}{(47-n)(25-n)}\;.$
The most likely value occurs where this crosses $1$:
$\frac{(n+1)(15+n+1)}{(47-n)(25-n)}=1\;,$
$(n+1)(15+n+1)=(47-n)(25-n)\;,$
$17n+16=-72n+1175\;,$
$89n=1159\;,$
$n=13.02\dots\;.$
Since the ratio is $1$ for $n=13.02\dots$, it is less than $1$ for $n=13$ and greater than $1$ for $n=14$, so the maximum occurs at $n=14$. This is confirmed by a table of the ratios. Thus, the most likely number of questions for the student to get right is $14$.
[Edit:]
Several comments have argued that the question might be intended to ask for the expected value. (I think asking what grade we can "most likely expect" would be a terrible way to ask for the expected value.) For this interpretation, Brian has given the direct solution in a comment on discipulus' answer. The reason the answer is so straightforward in this case is linearity of expectation. The chance of getting a question right is the same for all questions, so the expected number of correctly answered questions is simply the number of questions times the chance of getting one of them right. The latter is $47/87$, since the student knows the answer to $47$ out of the $87$ questions, so the result is $25\cdot47/87=1175/87\approx13.5$.