## Math 285 Test 1, Spring 2010

Test 1 Solutions. Median score: 61/75

Approximate grade ranges (out of 75 points):

• A: > 64
• B: 58-64
• C: 50-57
• D: 40-49
• F: <40
If you scored less than 40, then I recommend that you drop the course. The last drop date is March 12. You should talk to your academic adviser about your options.
One option might be Math 225 Sec. T1, which is a 2 credit course starting March 15. Matrix algebra is an important subject with terrific applications in many academic subjects, and I think most science and engineering students should take Math 225 (which will also make Math 415 easier, when you take it later).

Friday 19 February, in class, worth 15%. (Note no class on Monday 22 February - Furlough Day.)
You may not use books, notes, or electronic devices on the test.

Office hours (in 376 Altgeld Hall)
Tuesday 16 Feb, 1:30-2:30; Wednesday 17 Feb, 4:30-5:30pm; Thursday 18 Feb, 3:30-5:30; Friday 19 Feb, 12:30-1:30.

Material
Sections 1.1-1.6, 2.2, 2.4 (see the daily schedule), plus all quiz preparation problems, and all homework (including Iode Projects I and II).
You do not need to learn topics from the text that we did not cover (e.g. we did not cover "exact equations" in Section 1.6).

How to study
Make summary notes of the important ideas and methods, from the lecture notes on each section. Pay attention to all four types of work:

• modeling
• solving
• graphing
• interpreting
The test will cover all four activities (not just the solving part).

To help with "solving" DEs, make a checklist of the types of DE covered in Sections 1.2, 1.4, 1.5, 1.6, and the methods used to solve each type. Practice recognizing the different types by doing some Chapter 1 Review problems from the textbook.

Learn to look at the form of a DE and do not fixate on the variable letters e.g. dx/dt=kx is the same DE as dy/dx=ky.
Wherever possible, express the methods as algorithms or checklists: step 1, step 2, and so on, so that you have a plan of action for each type of problem.

Memorize the solutions of the two differential equations:

• dx/dt=ax (solution x=Ceat)
• dx/dt=ax+b where a and b are constants (solution x=Ceat-b/a)

Write paragraphs summarizing the main conceptual points learned in Iode Projects I and II. Those projects are examinable!

Re-work all homework problems, and quiz preparation problems. Ask for help at an office hour or tutoring room on every problem you are not sure of.
Then work new problems e.g. Chapter 1 Review problems.

Attempt the Practice Test (on website, with solutions).