Notes on Midterm 2023 grading

1.1
If there is any derivation rule that is correctly used (e.g quotient rule), but the answer is otherwise wrong -> 1p
If it is realized that the question is about differentiating a composite function -> +1p
If one of the derivatives in the chain rule goes wrong (e.g. wx+b) but otherwise correct -> 4p
Typical mistake, wrong sign of the derivative -> one point penalty (-1p)

1.2
If there is something correct in the limit argument but wrong answer (e.g. realization that e to power infinity is there)-> +1p
Correct answer without any arguments -> 1p
Typical mistake: arguing limit to be 0 as is the case when z goes to minus inf -> 1p

2.1 
Correct A -> 2p
if A is 2 x 3 matrix or something else that makes some (but little) sense-> +1p
if in A there is a in place of a^2 -> -1p.
Correct vector b -> 2p
- wrong sign for c or 2d -> -1p
If some manipulating the system and forming the matrix for the manipulated system -> then half of the max points

2.2
Correct determinant 1p, Forming detA=0 -> 1p and solving it -> 1p
Arguing that invertibility requires non-zero determinant -> 1p
Pointing out that there is unique solution if det \neq 0 -> 1p

Mentioning that determinant should be non-zero for invertibility (but otherwise incorrect) -> 1p
Correct answer with a wrong matrix -> 3p (-1p if uniqueness of the solution is not mentioned)

3.
If sensible row operations but wrong answers -> 4p
If some row operations but no answer (incomplete answer) -> 2p
No Gauss-Jordan but otherwise correct -> 4p

4.1. 
There has to be sensible argument, if argument is in the style "just by looking" -> 1p
if there is argument that is half correct +1p
correct argument with a mistake/something missing -> -1p 
Correct answer with wrong argument -> +2p

4.2 There are multiple ways determine linear indepence: determinant, solving a pair of equations, verbal argumentation (like they are not scalar multiples of each other), all are acceptable
if the linear independence is correctly argued but the answer is still incorrect (answer: do not form a basis) -> 1p
if it is only said that the vectors are linearly independent but the argument is missing -> 1p
Just computing determinant -> 1p

4.3. There has to be some argument that the third compenent is nonzero and other two are zero.
Correct definition of inner product (and some understanding that it should be used) -> +1p
If otherwise correct answer but no arguments -> 2p (quite common)
if partial argument (no inner product and not sufficient explanation) -> +1p
If the answer is found by using the cross product -> full points (goes beyond the course material but is correct)