Summer Review Calculus

The importance of a solid foundation in algebra cannot be over-emphasized. Algebra is used throughout Math 110 and Math 140 as it is in all subsequent courses. The student cannot be expected to grasp the new concepts encountered if s/he is deficient in this important basic tool. The following are some of the skills with which a student should be very familiar. 

1. Manipulate algebraic expressions involving exponents and radicals
2. Manipulate algebraic fractions
3. Factor algebraic expressions
4. Solve equations through quadratics; complete the square in a quadratic expression
5. Solve simultaneous equations
6. Solve "word problems", i.e., translate words into algebraic expressions
7. Functions and graphs (rectangular coordinates)
8. Solve inequalities
9. Find roots of polynomials using synthetic division
10. Use the binomial theorem
11. Manipulate complex numbers
12. Manipulate logarithmic expressions, graph logarithmic functions and solve logarithmic equations
13. Graph exponential functions and solve exponential equations
14. Find equations of straight lines and conic sections
15. Determine inverse functions

Trigonometry also plays an important role in calculus and is used throughout Math 140. The student must know trigonometry in order to be successful in the course. In particular the student should be familiar with the following: 

1. Fundamental definitions
2. Basic identities
3. Application of basic identities to the solution of trigonometric equations and proving identities
4. Graphing of trigonometric functions
5. Radian measure
6. Graphing of the inverse trigonometric functions

The most appropriate texts for review of these fundamentals are those high school texts with which the student is already familiar.

Those students who plan to take Math 110 or 140 and whose Profile of Academic Abilities indicate that they should take at least one of the courses from Math 4, 21, 22, 26, 40 and 41 have a serious deficiency in algebra an/or trigonometry. Its is required that students show proficiency in these areas before scheduling Math 110 or 140. Passing one or more of the courses from Math 4, 21, 22, 26, 40 and 41 demonstrates that the student has acquired the necessary skills in algebra and/or trigonometry.

Enrollment in similar courses offered by other colleges and universities is equally satisfactory. Successful completion of these courses can demonstrate that the student has the necessary proficiencies in algebra and/or trigonometry.

If a student scores remedially in algebra and/or trigonometry and is unable to take courses during the summer, or if the student is unable to study the material on his/her own, it is required that s/he take the algebra and trigonometry courses noted on the Profile before scheduling Math 110 and 140.

The following are some texts that are appropriate for learning algebra and trigonometry:

College Algebra, 4^th Edition
David Cohen
West Publishing

College Trigonometry, 3^rd Edition
Aufmann, Barker and Nation
Houghton Mifflin Company

A Primer for Calculus, 6^th Edition
Leonard Holder
Wadsworth Publishing

Precalculus, 5^th Edition
David Cohen
West Publishing

Approved by the Mathematics Department, June 2007

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