TEXTBOOK: Blitzer, Algebra and Trigonometry (UB custom 4th ed., or regular
4th ed.) , Prentice Hall
Calculator: TI-30Xa Texas Instruments. This
non-programmable calculator is a required purchase for the
students. Its use must be al lowed and encouraged throughout the course. Its use
on examinations
should be allowed, while the use of any other calculator should not be allowed.
Should students
complain about not being able to use the calculator they already have (most
likely a programmable
graphing calculator), they should be reminded that this course is about learning
how to do precalculus
mathematics, not about how to get a machine to do precalculus mathematics.
Description: This is a precalculus course and
covers topics from the NYS Regents Math B
curriculum : order, absolute value, inequalities, exponents, radicals,
polynomials, rational
expressions, solving systems of linear equations , quadratic equations and
inequalities, functions
(rational, logarithmic, exponential, trigonometric), graphing, trigonometric
identities, and
application problems throughout. This fast paced course is designed to review
Math B and prepare
students for further courses in mathematics. Persons with three years of high
school math, but with
weak algebra skills should take ULC 147 before MTH 115. Persons who have had
only two years of
high school mathematics may take MTH 115 or may prefer to take a two semester
sequence covering
this material more thoroughly and at a more moderate pace: ULC 147 and ULC 148.
Syllabus: The course should cover Chapters 1
through 6, (omitting Sections 3.6 -3.7, 4.5 and 6.4), and
include also Sections 7.1, 7.2, 8.1, and 8.4. Please note that this constitutes
more than 600 pages
from the text. Instructors should take care in their presentation in order to be
able to cover the
entire body of material. There should be at least two (2) in-class tests and a
final examination.
One possible arrangement to achieve this is as follows: (based on a 13-week
semester; in the summer
this would, of course, have to be pro-rated.)
| Week |
Section |
Topic |
| 1 |
P.1–P.6 |
Fundamental Concepts: Algebraic Expressions and
Real Numbers , Exponents and
Scientific Notation, Radicals and Rational Exponents, Polynomials,
Factoring
Polynomials, Rational Expressions . |
| 2 |
1.2-1.5 |
Linear Equations and Rational Equations
Models and Applications
Complex Numbers
Quadratic Equations |
| 3 |
1.6-1.7, 2.1-2.3 |
Other Types of Equations
Linear Inequalities and Absolute Value Inequalities
Basics of Functions and Their Graphs
More on Functions and Their Graphs
Linear Functions and Slope |
| 4 |
2.4–2.8 |
Transformations of Functions
Combinations of Functions : Composite Functions
Inverse Functions
Distance and Midpoint Formulas; Circles |
| 5 |
* * * * * * * * * |
* * * * * * * * * Review and Test * * * *
* * * * * * |
| 6 |
3.1–3.5 |
Quadratic Functions
Polynomial Functions and Their Graphs
Dividing Polynomials [Note: synthetic division may be omitted]
Zeros of Polynomial Functions, Rational Functions and Their Graphs |
| 7 |
4.1 - 4.4 |
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations |
| 8 |
5.1–5.4 |
Angles and Radian Measure
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Trigonometric Functions of Real Numbers: Periodic Functions |
| 9 |
* * * * * * * * * |
* * * * * * * * * * Review and Test * * *
* * * * * * * |
| 10 |
5.5–5.8 |
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Applications of Trigonometric Functions |
| 11 |
6.1–6.3, 6.5 |
Verifying Trigonometric Identities
Sum and Difference Formulas
Double-Angle, Power - Reducing , and Half-Angle Formulas
Trigonometric Equations |
| 12 |
7.1–7.2 |
The Law of Sines
The Law of Cosines |
| 13 |
8.1, 8.4 |
Systems of Linear Equations in Two Variables
Systems of Nonlinear Equations in Two Variables |
NOTE 1: It might be necessary to spend more time on
the preliminary material (including such things as
exponents and radicals) than is provided here. It would be a good idea to start
the course with a
diagnostic test in order to see what portions of the preliminary material (which
one hopes is review)
need to be covered in greater depth. It is possible to create such a diagnostic
test to be taken online
using the publisher’s material.
Also, note that students can test themselves on their
readiness for this course using the self diagnostic
tests on the Department’s home page. There are two versions of tests
referenced there, one from the University of New Brunswick and another from the
University of Arizona.
NOTE 2: Instructors should tell students early
about the Department Help Center in Room 107, Math Bldg.
