What is a differentiation gateway?

It tests differentiation skills (basically, use of formulas). The bonus to having a gateway is that there are no plain differentiation problems on the exams, and no hard differentiation as part of questions on the exams... you've proven your skills on the gateway. On the other hand, the gateway is pretty tough to pass. The basic reason for giving the gateway is to make sure that students who complete a calculus course can take derivatives accurately and efficiently.

Rules:

• You are allowed 20 minutes in which to take the gateway.
• It has 7 questions.
• You must give perfect answers for 6 of the 7 questions.
• "Perfect" means no incorrect signs, all parentheses present, accounted for, and matching... you get the drift.
• "Perfect" also means that you use equals signs (=) appropriately. In particular, if a problem is given as y = x², then writing = 2x will be counted as wrong because it will appear that you are claiming that y = x² = 2x, which is not the case.
• You may not use calculators, notes, books, etc. on the gateway.
• The penalty for not passing the gateway by one week before the end of classes is one letter-grade for the course.
• You may take only one gateway exam per day.
• There is no limit to the number of times you can take the gateway (except the number of days available on which to take it).

The gateways are randomly generated from a database of problems, in such a way that essentially the same skills are tested in each gateway... so it's quite rare that there's a "hard gateway" or an "easy gateway." Almost everyone has to study seriously and do lots of practice problems to pass the gateway. We'll take the gateway once, together, during class time.

Resources for practice:

• Here is a sample gateway (.pdf).
• Good practice problems can be found in the chapter on differentiation formulas of our text.
• More practice problems can be found in any other calculus text.

Here's an incentive for you to pass the gateway sooner rather than later... You'll receive

• full credit if you pass the gateway on the first or second attempt
• 80% credit if you pass within 2 weeks of the first gateway exam
• 40% credit if you pass during the last possible week
• (and 60% credit if you pass between those last two times)

Here are some tips on how to pass the gateway, modified slightly from Bob Megginson's page on the topic (and he is the Gateway Master!):

Each time a graded copy of the test is returned to you, study the errors you have made and correct any misunderstanding you have. Remember that since there is no partial credit, there are no "sloppy" errors or "little stupid" errors or "just-got-in-a-hurry" errors on this test; there are only errors. Think about why you made each error and how you can avoid it on the next attempt.

Make it your goal to pass the test within two weeks of the first gateway exam. Though the test is offered after that, it is generally assumed that students who do not pass it by the second week after the test is first offered are struggling with this material, so do not take it amiss if your instructor starts asking you about difficulties you are having with derivatives if you have not passed it by then.

Under no circumstances should you wait until the last week the test is offered before you get serious about passing it. This is a recipe for disaster (well, at least a recipe for losing one letter from your course grade). Since the time during which the test is offered is quite generous, there can be no waiving of the rule about only one attempt per day because a student has thought that he or she was too busy to take the test until near the deadline. To net it out, none of the rules or policies will change during the last week the test is offered just because the deadline is approaching. There is a sign that one often sees posted on secretaries' desks that says PROCRASTINATION ON YOUR PART DOES NOT CONSTITUTE AN EMERGENCY ON OUR PART. That is, and must be, the policy for gateway tests.

For further information on gateway exams in general, here's my favorite source. (Yes, you guessed it! It's a page of Bob Megginson's!)