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Welcome to Calculus Skills Rules Page

Academic Integrity Policies

  • All Calculus-Skills-No-Partial-Credit Problems will be photocopied after grading and before return to the class.

  • Any appeal of a grade on a Calculus-Skills-No-Partial-Credit Problem must be made within one week of the return date of the quiz or exam.

  • Any student that submits a changed answer of Calculus-Skills-No-Partial-Credit Problem for re-grading will have violated an academic integrity standard. The uniform penalty will be failure in the course. If students submit an appeal they are responsible, regardless of whether they knew the answer was changed.

  • Remember that there are no calculators or other computational devices allowed on exams or quizzes in Calculus.

Forms of Answers

For the Calculus-Skills-No-Partial-Credit Problems, answers that are not in the appropriate form will get zero credit. Below we describe the appropriate forms for answers as precisely as we can so grading by different graders will be done uniformly. Please read these instructions carefully and review them before you take an exam or quiz.

Simplified Form of Numerical Answers: If the answer is a number and you are asked to write it in simplified form, you should use the following rules:

1.
If the answer can be written as an integer, you must write it as an integer. (This means 3 is right, but 6/2 will get zero credit.)
2.
Otherwise, if the answer is a rational number, but not an integer, the easiest way to guarantee credit is to write it in the form p/q or $\frac{p}{q}$ where p and q are integers with no common factors other than $\pm 1.$ By convention, we will also accept $p \cdot \frac{1}{q}$ in place of $\frac{p}{q}$ and $ - \frac{p}{q}$ in place of $\frac{-p}{q}$ or $\frac{p}{-q}.$ The use of ``mixed'' fractions is strongly discouraged, but they will be accepted if they are written correctly and are not used as part of another formula. In case fractions are written in other forms, here are some examples.
(a)
If the answer is 8/3 then the following will be marked correct: $8/3, \frac{8}{3}, 8 \cdot \frac{1}{3} $ (and $2 \frac{2}{3}$ as a mixed fraction meaning 2 plus $\frac{2}{3}$).
(b)
If the answer is 8/3 then the following will be marked incorrect: $16/6, 2 + \frac{2}{3}, 4\cdot \frac{2}{3}.$
(c)
If the answer is $\frac{5}{6}$ then $\frac{1}{3} + \frac{1}{2}$ will get zero credit.
(d)
If the answer is $\frac{10}{21}$ then $\frac{2}{3} \cdot \frac{5}{7}$ will get zero credit.

3.
Exponentials must be evaluated at 0 and 1 (a0 = 1 and a1=a for $a\neq 0$) and natural logarithms must be evaluated at 1 and powers of e, $\ln(1)=0$ and, in general $\ln(e^k) = k$ (e.g. $\ln(e)=1, \ln(e^2)=2$ and similarly for all real k...) and eln(k) = k for k > 0.
4.
All trigonometric functions must be evaluated at arguments that can be expressed in the form
$k\pi, k\pi/2, k\pi/3, k\pi/4, k\pi/6$ where k is an integer (possibly negative or zero).

5.
In general, if a numerical answer or any part of a numerical answer can be written as a rational number, then the rational number should be in simplified form as described by 1 and 2 above.

Elementary Functions If the instructions ask for the answer in terms of elementary functions, this means the answer should be written as

1.
Polynomials.
2.
Trigonometric functions and inverse trigonometric functions.
3.
Exponential functions and logarithmic functions.
4.
The absolute value function.
5.
Sums, differences, products and quotients of other elementary functions.
6.
Compositions of other elementary functions.

In other words, Elementary Functions are the smallest class of functions that contain the functions that include the functions in 1-4 and is closed under sums, differences, products, quotients and compositions.


Grading Policies

Please keep the following policies in mind as you answer the Calculus-Skills-No-Partial-Credit problems.

1.
Failure to follow instructions regarding simplification or the final form of the answer will always result in zero credit.

2.
All answers must appear within a single rectangular box. Anything outside the box, will be ignored. Any ambiguity, no matter how slight, as to what is intended as a final answer will result in zero credit for the problem.

3.
Unreadable answers will get zero credit. Write neatly.

4.
Missing or incorrect parenthesis will result in zero credit.

5.
Usage of the incorrect variable is wrong and will result in zero credit.

6.
Switching upper case letters and lower case letters is wrong and will result in zero credit.

7.
To guarantee full credit it is recommended that arguments of all trigonometric and logarithmic functions be enclosed in parenthesis. Otherwise, your answer may be ambiguous and get zero credit. Failure to use parenthesis may mean the interpretation of what is written may depend on how much space is left between characters and since this cannot always be reliably interpreted in handwritten text it may result in zero credit.

8.
Missing or incorrect usage of constants of integration, will render the answer incorrect and will be assigned zero credit.

9.
Note that unless the problem asks for a specific form for the answer, or gives other instructions, it is not necessary to do any simplification.

10.
Decimals will be accepted only if they are exactly equal to the answer.

Technical Notes

1.
When asked to differentiate or find the derivative, it is not necessary to state the domain of the derivative. That is, it is correct to state a function (in the specified form) that matches the derivative of the given function at all values where the given function is differentiable. (e.g. If $f(x)=\ln(x)$ we will accept f'(x) = 1/x as correct even though it would be better to write f'(x) = 1/x,   x>0.
2.
When asked for an indefinite integral, the answer should be such that for any connected component of the domain of the integrand, the answer represents all anti-derivatives on that component through the use of an arbitrary constant (+C). (e.g Credit will give given to

\begin{displaymath}\int \frac{1}{x} dx = \ln(\vert x\vert) + C\end{displaymath}

even though it would be better to write something like

\begin{displaymath}\int \frac{1}{x} dx = \ln(\vert x\vert) + \cases{ C_1 & if $x>0$ \cr C_2 & if $x<0$ }.\end{displaymath}

But,

\begin{displaymath}\int \frac{1}{x} dx = \ln(x) + C\end{displaymath}

will be marked incorrect.