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Math S-Xab -
Introduction to Functions and Calculus
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See the Course Information page for general information about gateway exams.
Click here to take a gateway exam.
Gateway 1 will be first administered at the start of class on Friday, July 2nd. Note that we will meet in B-11C, one of the computer labs in the basement of the Science Center from 10 to 10:30 that day in order to take the online gateway.
The gateway will test your ability to perform certain important algebraic computations. Calculators are not permitted on this or any other gateway. The gateway will have eight multiple-choice questions. In order to pass the gateway, you must get at least seven questions correct. If you fail the gateway, see Dr. Bruff or Dr. Judson for a retake. You may continue retaking the gateway until you pass.
The first gateway will include questions on the following skills.
| Skill | Practice Problems |
| Laws of Exponents | Problems on Exponents |
| Expanding Expressions | Problems on Expanding |
| Factoring Expressions | Problems on Factoring |
| The Quadratic Formula | Problems on the Quadratic Formula |
| Working with Fractions | Problems on Fractions |
| Solving Equations | Problems on Equations |
| Solving Systems of Equations | Problems on Systems of Equations |
| Working with Inequalities | Problems on Inequalities |
Gateway 2 will be first administered at the start of class on Tuesday, July 20th. Note that we will meet in B-11C, one of the computer labs in the basement of the Science Center from 10 to 10:30 that day in order to take the online gateway.
The gateway will test your ability to perform calculate derivatives using the basic differentiation formulas. See the Gateway 2 Practice handout for a list of formulas tested as well as 80 practice problems.
Calculators are not permitted on this or any other gateway. The gateway will have eight multiple-choice questions. In order to pass the gateway, you must get at least seven questions correct. If you fail the gateway, see Dr. Bruff or Dr. Judson for a retake. You may continue retaking the gateway until you pass.
Gateway 3 will be first administered at the start of class on Tuesday, July 27th. We will meet in B-11C, one of the computer labs in the basement of the Science Center from 10 to 10:30 that day in order to take the online gateway.
This gateway exam will test your ability to work with exponential and logarithmic functions. These questions are divided into five categories (see table below).
| 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 logarihmic exponential equations |
| Graphs of exponential and logarithmic functions | Problems on the graphs of exponential and logarithmic functions |
Calculators are not permitted on this or any other gateway. The gateway will have eight multiple-choice questions. In order to pass the gateway, you must get at least seven questions correct. If you fail the gateway, see Dr. Bruff or Dr. Judson for a retake. You may continue retaking the gateway until you pass.
Gateway 4 will be first administered at the start of class on Monday, August 9th. We will meet in B-11C, one of the computer labs in the basement of the Science Center from 10 to 10:30 that day in order to take the online gateway.
This gateway exam will test your ability to work with trigonometry and trigonometric functions. These questions are divided into six categories (see table below).
| 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 |
Calculators are not permitted on this or any other gateway. The gateway will have eight multiple-choice questions. In order to pass the gateway, you must get at least seven questions correct. If you fail the gateway, see Dr. Bruff or Dr. Judson for a retake. You may continue retaking the gateway until you pass.
Page maintained by Derek Bruff
(bruff@fas.harvard.edu).
Last updated on July 15, 2004.
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