# Math Insight

### Overview of: Differentiation exam

The differentiation module exam for Math 1241 is based on part 3 from the Math 1241 thread, with the knowledge from part 1 also assumed.

#### Material for the exam

1. Introduction to the derivative (See section from the Math 1241 thread)

1. The slope of the secant line as average rate of the change, and the slope of the tangent line as instantaneous rate of change.
2. The tangent line as the limit of a secant line with the two points approaching each other.
3. The derivative is the slope of the tangent line, which we also call the slope of the function itself.
4. The limit as the idea of getting as close as possible with actually going all the way.
2. Derivatives of polynomials (See section from the Math 1241 thread)

Be able to calculate the derivative of polynomials or the derivative of powers with other exponents.

3. Derivatives of exponential and logarithmic functions (See section from the Math 1241 thread)

Be able to calculate the derivative of the exponential function and the logarithm.

4. Differentiation rules (See section from the Math 1241 thread)

1. Be able to calculate the derivative of the product and quotient of two functions.
2. Be able to calculate the derivative of simple compositions using the chain rule, especially those of the form $f(x)=e^{p(x)}$, $f(x)=\ln(p(x))$, or $(p(x))^n$, where $p(x)$ is a polynomial.
3. Be able to combine product and chain rule to differential functions of the form $f(x)=p(x)e^{q(x)}$, where $p(x)$ and $q(x)$ are polynomials.
4. Be able to differentiate functions that include parameters, such as $f(x) = ax^2 + b e^{cx} + d$, where $a$, $b$, $c$, and $d$ are constant parameters.

#### Study aids

1. Sample problems

All questions that may appear in the differentiation exam are available so that you can practice them, as outlined below. In both these problems and on the actual exam, the set of problems as well as values of numbers, variables, parameters, and other quantities are selected randomly. You will want to generate multiple versions of the problems to see the larger array of problems. Given the random nature, we cannot guarantee that you will actually see all the problems that will appear on the exam. But the more problems you work on, the greater the chance you will work on problems that will show up on the test.

1. Free form questions

Review questions: Elementary derivative problems contains short answer versions of problems that could appear on the exam.

2. Computer-scored problems

Review questions: Derivative intuition practice, matching and Review questions: Basic derivative practice contain problems where the computer will the score your answer for you, so you can see how well you did. These computer generated scores do not count toward your grade. These problems are in a similar format to what you will see on the computer-graded exam, though on the exam, it won't tell you if you got the answer correct.

3. Quiz problems

Online quiz: Quiz 4 contains additional computer-graded problems that could show up on the exam. Even after the due date of quizzes, you can still generate more attempts and check out how well you can answer those questions.

2. Problem sets

The problem sets from the Math 1241 thread are also good review.

#### Exam rules

When the exam is available, you can take the exam on your computer. Once you begin an attempt, you will have 50 minutes to complete it.

We ask that you take the computer graded exams with no aids other than one (double-sided) sheet of notes and a scientific calculator. (If you don't have a scientific calculator, then we ask that you don't use the graphing or derivative/integral functions of your graphing calculator.)

The exam format will be similar to the Gateway Exam. The exam will not tell you if you got the problems correct or incorrect, but will simply say that the answer was received and show you how it interpreted your response.

When you are finished with an exam attempt, you can go to your gradebook to see your score.

#### Exam times

You can take the exam as many times as you like between 11:00 AM on Thursday, October 22 and 2:30 PM on Thursday, October 29. Click the “Generate new assessment attempt” at the bottom of the exam to get a new exam. If you take the exam more than once, your exam score will be the maximum of your scores from the attempts.

#### Points and due date summary

Total points: 20
Assigned: Oct. 19, 2020, 11 a.m.
Due: Oct. 29, 2020, 11:59 p.m.
Time limit: 50 minutes