Math Xb - Introduction to Functions and Calculus II
Gateway Exams

See the Course Information page for general information about gateway exams.

Gateway 1: Exponential and Logarithmic Functions

Gateway 1 will be first administered in the Tuesday, February 15th, lab meetings. The deadline for passing is Friday, March 18th.

This gateway exam will test your ability to work with exponential and logarithmic functions. Calculators are not permitted on any gateway test, including this one. You will not be required to simplify your answers or perform complicated arithmetical calculations. You will be required to perform derivative calculations, straight-forward manipulations and simple arithmetic (usually involving integer quantities) correctly. The gateway test will have eight questions on it. These questions are divided into six categories (see table below).

This test will feature eight questions. A passing grade is seven or eight perfectly correct.

If you do not pass the test on the first attempt, you can take it from either Dr. Judson or Dr. Vierling-Claassen during office hours or by appointment.

Category	Review Problems
Properties of exponents	Problems on the properites of exponents
Properties of logarithms	Problems on the properites of logarithms
Solving exponential equations	Problems on solving exponential equations
Solving logarithmic equations	Problems on solving logarithmic exponential equations
Graphs of exponential and logarithmic functions	Problems on the graphs of exponential and logarithmic functions

Gateway 2 will be first administered in the Thursday, March 3rd, lab meetings. The deadline for passing is Friday, April 8th.

This gateway exam will test your ability to work with trigonometry and trigonometric functions. Calculators are not permitted on any gateway test, including this one. You will not be required to simplify your answers or perform complicated arithmetical calculations. You will be required to perform derivative calculations, straight-forward manipulations and simple arithmetic (usually involving integer quantities) correctly. The gateway test will have eight questions on it. These questions are divided into six categories (see table below).

This test will feature eight questions. A passing grade is seven or eight perfectly correct.

If you do not pass the test on the first attempt, you can take it from either Dr. Judson or Dr. Vierling-Claassen during office hours or by appointment.

Category	Review Problems
Unit circle definitions of sine and cosine	Problems on Unit circle definitions of sine and cosine
Right angle triangle definitions of sine, cosine and tangent	Problems on the right angle triangle definitions of sine, cosine and tangent
Inverse trigonometric functions using the unit circle definitions	Problems on inverse trigonometric functions from the unit circle definitions of sine and cosine
Inverse trigonometric functions using the right angle triangle definitions	Problems on the inverse trigonometric functions using the right angle triangle definitions of sine, cosine and tangent
The sine, cosine, and tangent of standard angles	Problems on the sine, cosine, and tangent of standard angles
Graphs of sine, cosine, and tangent	Problems on the graphs of sine, cosine, and tangent

Gateway 3 will be first administered in the Thursday, April 7 lab meetings. Gateways will be given online. You will be able to take the first two versions online.
- 9-10 AM in SC 229 (Wendy Widman).
- 3-4 PM in SC 229 (Ashley Hinerman-Mulroy).
- 6-7 PM in SC 229 (Connie Zong).
- 8-9 PM in SC 229 (Shayak Sarkar).

This gateway exam will test your ability to all of the methods we have used in Math X to differentiate functions. Calculators are not permitted on any gateway test, including this one. The questions are divided into six categories (see table below).

This test will feature eight questions. A passing grade is seven or eight perfectly correct.

If you do not pass the test on the first attempt, you can take it from either Dr. Judson or Dr. Vierling-Claassen during office hours or by appointment.

Category	Review Problems
Derivatives of algebraic functions	Problems on derivatives of algebraic functions
Using the product and quotient rules	Problems on product and quotient rules
Derivatives of functions involving logarithms and exponentials	Problems on derivatives of logs and exponentials
Using the chain rule	Problems on the chain rule
Derivatives of trigonometric and inverse trigonometric functions	Problems on trig and inverse trig derivatives

Page maintained by Angela Vierling-Claassen (angelavc@fas.harvard.edu).
Last updated on Wednesday, March 27, 2005 .
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