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 24th, lab meetings.

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, from either Dr. Judson or Dr. Bruff 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

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, from either Dr. Judson or Dr. Bruff 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 22nd, lab meetings.

Page maintained by Derek Bruff (bruff@fas.harvard.edu).
Last updated on April 3, 2004.
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