* Lab and Q1,Q2,Q3

* 1 mark for the final answer and 1 mark for any reasonable explantion.

* If final answer is correct, this should be VERY fast to grade, just a quick glance at the work

* If final answer is incorrect, they will often get 1 out of 2 for a reasonable attempt.

* In Q3 give 0.5 marks for a final answer of DNE instead of $-\infty$

* if they use lhopiyaps rule flag it and I will look at it.

* Q4

* Take off 0.5 marks if the interval is “half correct”

* Be generous with part marks on the explanation! 0.5 marks for some reasonable steps is good.

* Q5a)

* 1 mark if they say "7" with ANY words/symbols written that explain about looking close to "x=1"

* 0 marks for “2” with any explanation

* 0 marks for most other answers (e.g. “7.003” will get 0) UNLESS they explain why that value AND NOT SOME OTHER VALUE should be the limit. Tag me on these ones and I can make final decision.

* Use “See solutions” comment for incorrect answers.

* Q5b)

* 2 marks for “No amount of numbers because you can never be sure that it gets arbitarily close”. Keywords: “no amount of numbers”, “never be sure”, “arbitarily close” (used correctly) Booklet 123 is a great example

* 2 marks if they explain that any finite amount of number is not good enough (They might say “\infty numbers is enough”, but focus on the explanation of why finitely many is not enough)

* 1 mark for “\infty amount of numbers” without discussing for finite amount of numbers. Booklet 103 and 118 are an example of this
* 0 marks for copying out “arbitrarily close” without an actual explanation of what this means or why its relevant. Booklet 122 is a good example of using “arbitrarily close” incorrectly1

* Q6a

* Any sequence of steps that looks like this gets 1 mark. $$\begin{align*}
|x-2| & <2\\
\iff-2<x-2 & <2\\
\iff0<x & <4\\
\iff1<2^{x} & <16\\
\iff-2<2^{x}-3 & <13\\
\implies-13<2^{x}-3 & <13\text{ }\\
\implies|2^{x}-3| & <13
\end{align*}$$
* (Booklet 125 is a good example)
* Let any minor errors that don't effect logic go (e.g. Booklet 132)

* Give 0.5 marks if its close or has some errors. (Booklet 121 is a good example of a generous 0.5)

* Q6b.

* First rule: Be generous! When in doubt, round up. Let very minor errors go with no penalty (e.g. Booklet 150 wrote 2^3=16; no penalty)4

* 1 mark: Statement of epsilon delta is correct OR written as “Given \ep>0, want to show....”

* 1 mark: $\delta=\min(2,\frac{\epsilon}{13}$) (or min of other stuff if they use a different lemma... $\delta=\min(1,\frac{\epsilon}{5})$ will be common)

* 1 mark: chain of logic connecting hypothesis to conclusion

* 1 mark: using a lemma to replace $|2^{x}-3|$ by 13 (or they could do a different assumption)

* Q7a

* Any mention that $\infty-\infty$ is indeterminant OR $\lim_{x\to\infty}x=\infty$ so limit rule does not apply. = 1mark

* Do not give any marks for “Its not correct”. We told them its not correct, they need to explain why. See Booklet 163 for an example.

* Q7b

* 1 mark multiply by conjugate

* 1 mark factor out largest part of numerator and denominator (See booklet 154)

* 1 mark invoke limit rule to compute final limit

* 1 mark final answer (This one is essentially a freebie if they get this far since you won't take off multiple marks if the made an algebra mistake along the way)

* Take marks off for algebra mistakes that change the final answer (e.g. Booklet 157), but do not take a second mark off for the final answer being different