# Tutor profile: Kristen P.

## Questions

### Subject: Chemistry

Let's say you were given a mechanism, A + B ⇄ C (fast, in equilibrium) C→ D + E (slow, not in equilibrium) Assuming the above are elementary steps, what expression would denote the formation of E?

The formation of products is dependent on the rate of the reactants. Given: - A + B ⇄ C (fast) Equilibrium constant K1 (Note equilibrium constant is the rate of the forward reaction divided by the rate of the backwards reaction) - C → D + E (slow) Rate constant - k2 (a singular rate, no backwards reaction) The formation of E is dependent on the rate at which C dissociates, so the rate of the formation of of E could be denoted by k2[C}. However, the formation of C is a dependent on A and B, whose rate can be expressed by K1[A][B]. Knowing this, C can be substituted to express the formation of E as K1k2[A][B]

### Subject: Psychology

Explain how social or cultural factors affect one cognitive process.

Questions like these have a particular choice of words for a reason. If this were given as an IB psychology prompt, answering the question takes priority above all else, as this program is so particular with their grading system. The first thing you should do is look at what command terms were given. In this case, the prompt is asking you to explain, which is to give a detailed explanation including reasons or causes. Note that the prompt asks you to look at either social or cultural factors, meaning you must select one. If you chose to write about social factors and chose to discuss Bartlett, this would not add to your answer as Bartlett evaluated schema development as it pertains to Native American and white culture. The prompt then asks you to look at one cognitive process. I recommend evaluating memory as there's so much accessible research to discuss, and can be easily explained in a cultural context with underlying reasons being the way our cultures shape our schema development. If you choose to explain memory, you also need to be specific - what about memory? The process of creating memories? Encoding memories? Memory loss? Likely you mean the process of encoding memories into our long-term, but be specific because IB is particular. In an AP context, you do not need to be nearly this specific, and it may be better to generalize the processes of memory and blend social and cultural factors, so long as when used they are explicitly stated. Good luck!

### Subject: Calculus

Say your friendly town farmer Dan is attempting to build a new fence around his land to keep his herd of sheep and he needs your help. To paint the scene, Dan wants to make a rectangular enclosure with one of the longest sides adjacent to a river, which the sheep cannot cross. The thing is, Dan only has 300 feet of wire fencing to work with. What is the largest area that Dan can enclose?

Based on the wording of this problem, you might be able to tell this is an optimization problem (we're optimizing the area given parameters for the perimeter of a region). We know that we need to make a rectangular region with side lengths equivalent to at most 300 feet, because that's all the fencing we have. This makes the perimeter our constraint. We know that the perimeter of a rectangle, P, equals the length of its two shorter sides and its two longer sides, so P=2x+2y. We also know that the area of a rectangle is equivalent to A=xy. If two parallel sides are denoted by x, and the perpendicular sides are denoted by y, then 2x+2y=300. We also know that Dan lives by a river that the sheep cannot cross. In other words, Dan needs enough fencing to enclose a rectangular region on three of its sides. We'll assume that the side the rectangle is adjacent to is y, so the actual perimeter we need to enclose is y+2x=300. Our goal is to maximize A=xy using the constraint P=2x+y. If we set 2x+y equal to 300, we can isolate one of the variables. For simplicity let's isolate y, so now we have y=300-2x. We can then take this expression and replace y in the area equation, so now A=x(300-2x), or A=300x-2x^2. We're trying to find the maximum value x can take in this expression on [0,300]. Based on the extreme value theorem, this would occur on either endpoints or critical points, but endpoints here would not make sense, because any extreme would leave the next side at a value of zero. So now we know we're looking for critical points, which can be found by taking the derivative of the expression and setting it equal to zero. fi we do this with A=300x-2x^2, we get A=300-4x, so x=75. Plugging this into the original perimeter equation lets us find the dimension of the next variable y, which should equal 150.

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