Math 251 (Phillips) Midterm 1

Information and material covered

• Sections 2.1 through 2.4, omitting infinite limits and limits at infinity.
• Differentiation rules: Sections 3.1, 3.2 3.3, 3.5, 3.6, and 3.9. (But no higher derivatives will appear.)
• Maximums and minimums (Section 4.3).
• The early part of Section 4.5 (significance of the first derivative for the shape of the graph of a function).
• Maximizing and minimizing in word problems, in Section 4.7, but so far only those for which the closed bounded interval method applies. (You need the chain rule, not yet covered, for some of the examples there.)

Review session

Sample Problems

There are six primary sources for sample problems for Midterm 1:

• Written homework for Weeks 2, 3, and 4:
  • Week 2.
  • Week 3 part 1.
  • Week 3 part 2.
  • Week 4.
• Sample Midterm 1 (pdf). (This is a corrected version, with corrections to the interval and function name in Problem 9.)
• WeBWorK homework due through Wednesday 29 January 2025.
• Quiz 1.
• In class worksheets. Warning: The hints on the worksheets won't be provided on the midterm. Links won't work for worksheets which don't yet exist.
  • Worksheet 1 (pdf).
  • Worksheet 2 (pdf).
  • Worksheet 3 (pdf).
  • Worksheet 4 (pdf).
  • Worksheet 5 (pdf).
  • Worksheet 6 (pdf).
  • Worksheet 7 (pdf).
  • Worksheet 8 (pdf).
• The worksheet used at the review session.

Of course, you should also know how to do all the Midterm 0 problems. Note, though, that the Midterm 1 problems will be in format much more like the problems in the first list above. Also, they will be graded by me rather than by a grader, and I will look at work and notation much more carefully than the grader does.

Solutions to items in the list above:

• Written homework for Weeks 2, 3, and 4:
  • Week 2 solutions.
  • Week 3 part 1 solutions.
  • Week 3 part 2 solutions.
  • Week 4 solutions.
• Sample Midterm 1 solutions (pdf).
• Answers to WeBWorK problems are available on WeBWorK after the due date of each assignment.
• Solutions to Quiz 1 will be provided after it is given.
• Solutions to in class worksheets. Links won't work for worksheets which don't yet exist.
  • Worksheet 1 solutions (pdf).
  • Worksheet 2 solutions (pdf).
  • Worksheet 3 solutions (pdf).
  • Worksheet 4 solutions (pdf).
  • Worksheet 5 solutions (pdf).
  • Worksheet 6 solutions (pdf).
  • Worksheet 7 solutions (pdf).
  • Worksheet 8 solutions (pdf).
• Solutions to the worksheet used at the review session.

Point recovery possibility (not done for Midterm 1)

(This won't be done for Midterm 1.)

Normally, I distribute solutions to the exam as you leave the classroom after taking it. This is a description of a possible "point recovery" option for Midterm 1 which could be used instead. I reserve the right to add to the conditions.

After Midterm 1 is handed back, you will have two or three days (depending on the day it is handed back) to write complete and fully correct solutions to problems you got wrong.

• It must be chosen for both sections or neither.
• You will be able to consult the book, your notes, and the course website, but not to consult with anybody else in the class, your instructor, any tutor, any other professor, any artificial intelligence, your grandmother, or any other human being or interactive resource. You will have to hand in a signed statement to the effect that you have gotten no help on the reworked problems.
• You can get at most half the lost credit back on any problem.
• Detailed work must be shown, including all intermediate steps! For example, if you are asked to find the limit as x goes to 3 of x^2 + 2 x - 7, you will need to show the intermediate step 3^2 + (2) (3) - 7.
• Grading will be much more severe than on the original. In particular, even minor mistakes in notation will lose substantial numbers of points.
• On the real Midterm 1, there will be more problems like "Let f be a function such that f' (x) = sin (x^3). Differentiate g (x) = x f (2 x)" and fewer like "Differentiate f (x) = sin (x^3)".
• There will be fewer comments on the returned exams than normal.
• Complete solutions (even just answers) will be posted only after the point recovery papers are turned in.
• Point recovery does not apply to extra credit problems.

Real Midterm 1

• Midterm 1, 9:00 am (pdf).
• Solutions to Midterm 1, 9:00 am (pdf), slightly corrected.
• Midterm 1, 11:00 am (pdf).
• Solutions to Midterm 1, 11:00 am (pdf), slightly corrected.

• Midterm 1 retake, 9:00 am (pdf).
• Solutions to Midterm 1 retake, 9:00 am (pdf), slightly corrected.
• Midterm 1 retake, 11:00 am (pdf).
• Solutions to Midterm 1 retake, 11:00 am (pdf), slightly corrected.

Reminder: Extra credit will be given for finding mistakes. You need to say what is wrong and how to fix it, you need to be one of the first two people to report the mistake to me, and you need to report it before a corrected version is posted. You can get extra credit for finding mistakes in the solutions to the other section's Midterm 1 as well as the solutions to your own.

Return to main Math 251 page.

This page maintained by N. Christopher Phillips, email.

Last significant change 25 January 2025.