Problems and Review Materials for Math Xb Gateway 2

The first gateway will test your facility with the concepts and calculations of antiderivatives, integral notation and areas under curves.

The gateway test will have eight questions on it. These questions are divided into eight categories (see table below). Each gateway test will feature one question drawn from each of the eight categories.

The first time that the gateway will be given will be during lab on Tuesday March 19.
Each test will feature eight questions. A passing grade is seven or eight perfectly correct.
The questions that appear on each test will be drawn from the categories shown in the table below.
If you don't pass the test on the first attempt, you will be able to retake the test from Xa lab leaders through the Math Question Center or else from section leaders during office hours.
Remember that you are not allowed to use a calculator or a page of notes on gateway tetsts.
Remember: You have to pass all of the gateway tests by 5p.m. on Friday May 3. For every gateway test that you have not passed by that time, your final grade in the course will be lowered by one complete letter.

Category	Review Problems and Answers
Antiderivatives of Power Functions	Problems on calculating the antiderivatives of power functions.
Antiderivatives of Polynomial Functions	Problems on calculating the antiderivatives of polynomial functions.
Antiderivatives of Exponential Functions	Problems on calculating the antiderivatives of exponential functions.
Antiderivatives that Involve Natural Logarithms	Antiderivative calculations that involve the natural logarithm function in some way.
Integral Notation	Problems on writing areas under curves using integral notation.
The Idea of an Antiderivative	Problems in which you have to verify that a given F(x) is an antiderivative of a function f(x).
Calculating the values of area under curves that are expressed using Integral Notation	Problems on calculating the value of an area under a curve.
The Technique of u-Substitution	Problems on calculating antiderivatives using the technique of u-substitution.