Create sample questions out of these given scenarios with solutions? 

1. There will be two derivatives and one limit to do. The two derivatives involve trigonometric and logarithmic function. Each needs chain rule, where one of them requires chain rule twice. The limit question is easy enough and can be done using L'Hospital rule. 2. This one involves implicit differentiation. You find slope or rate of change of a function and tangent line or points so that the tangent line is such & such. See lecture notes as we have done many of them. Note that if a point is on the curve, its coordinates (x,y) will satisfy the equation, meaning that you have to substitute x and y into the original equation and solve for either x or y. If you can't find any value of x or y after solving the original equation, you should just say there are no points. 3. A function f(x) and its first two derivatives f'(x) and f''(x) are given to you. Use them to answer questions related to critical points, increasing, decreasing, local max/min, concavities, and inflection points. Note please don't try to impress me much and find the first two derivatives on your own. You will not get more marks for doing that if it is correct. You will lose marks if it is wrong. So, it's a waste of time if you do that. Use the ones that I give you, and they will save your time. 4. There will be two complicated derivatives to do here. One needs logarithmic differentiation (or exponential alternative of that but use one of them meaning the one you are comfortable with). The other one involves finding a value of a derivative of an inverse function and leave the answer in the exact form not a decimal form. Note that you will see chain rule twice here as well. You must use radians, not degree, in term of units, for angles.2 5. This one is about a related rates problem. We will give you diagram and define all variables for you in the diagram of the problem, if needed. Any formula involving such as volume and surface area of complicated geometric shapes, if needed, will be given. You don't have to memorize. But, you will have to know simple trigonometric formulas involved in a right triangle, the Pythagorean formula, and areas of simple triangles or rectangles. Note that if the equation linking all the variables is given to you, use it and differentiate it to find the rate, i.e., the derivatives involved. All derivatives have to be done with respected to time, t. So, any derivatives of other variables must involve chain rule. 6. This one is about an easy a business related max/min problem in which an easy function is given. Use take derivative making it to zero to find critical number and hence point to answer all the questions asked. It could involve inflection point as well in which you will have find the second derivative. Note knowing how to find critical point, inflection point, and absolute max/min of a function will definitely help.