MAT187 Pre-Calculus
Course Information Sheet
(Effective Fall 2015)
Textbook Information
Title:
Author:
Publisher:
ISBN-10:
Precalculus A Right Triangle Approach (5th Ed)
Beecher, Penna, Bittinger
Pearson
978-0-321-96955-2
Catalog Description: Pre-Calculus topics include: angles and their measures, properties and
graphs of trigonometric functions, trigonometric equations and identities, solutions of
triangles, applications, polar coordinates, quadratic equations, logarithmic and exponential
functions, systems of equations, partial fractions, conic sections, sequences and series.
Sections to Cover
Chapter
Sections
Topic
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
All
2.1-2.5
All
All
All
All
All
Graphs, Functions, and Models
More on Functions
Quadratic Functions and Equations, Inequalities
Polynomial Functions and Rational Functions
Exponential Functions and Logarithmic Functions
The Trigonometric Functions
Trigonometric Identities, Inverse Functions, and Equations
Chapter 8
All (8.3
optional)
All (9.5
optional)
All (10.5
optional)
11.1-11.3
Applications of Trigonometry
Chapter 9
Chapter 10
Chapter 11
Systems of Equations and Matrices
Conic Sections
Sequences, Series, and Combinatorics
MAT187
Learning Outcomes and Standards
Learning Outcome
1. Apply trigonometric concepts to solve
right and non-right triangle problems
Standard(s)
1a. Define the trigonometric functions as a
ratio of two sides of a right triangle.
1b. Model an application problem with a
right triangle to find the missing quantity
of the triangle.
1c. Apply the law of sines and law of
cosines to find the missing quantity of a
non-right triangle.
2. Solve problems involving circles and
angles
2a. Convert angle measures from degrees
to radians and vice versa.
2b. Determine the arc length and central
angle of a specified portion of a circle.
2c. Calculate the angular and linear speed
of an object moving along a circular path.
3a. Determine the period, amplitude, and
appropriate transformational shifts of a
trigonometric equation, and use the
information to graph.
3b. Convert from rectangular to polar
equation and vice versa.
3c. Formulate parametric equations for
curves defined by rectangular equations
and vice versa.
3d. Graph plane curves defined by
parametric and polar equations
4a. Apply trigonometric identities to find
the trigonometric value of an angle.
4b. Prove the validity of a trigonometric
statement by applying the appropriate
trigonometric identities.
4c. Solve a trigonometric equation by
applying the properties of equality and
trigonometric identities.
3. Identify and sketch the graphs of
trigonometric functions in rectangular,
polar and parametric forms.
4. Solve trigonometric equations using
trigonometric identities and inverse
functions
5. Apply concepts of trigonometry to solve
problems involving vectors
6. Develop multiple approaches to solving
systems of linear equations
5a. Express a vector in component form.
5b. Find the magnitude and direction of a
given vector.
5c. Apply the properties of vectors to solve
application problems involving forces and
equilibrium.
6. Solve a system of linear equations using
substitution, elimination, Gaussian
elimination, and Cramer’s Rule
7. Recognize the equations of conic sections 7a. Classify the graph of a given equation as
and sketch their graphs.
a circle, parabola, ellipse, or hyperbola.
7b. Sketch a given conic section while
clearly identifying all appropriate parts
including the center, radius, focal point(s),
vertex or vertices, minor axis, major axis,
transverse axis, and asymptotes
8. Decompose a rational expression into a
8. Decompose a rational expression where
sum of partial fractions.
the denominator can be factored into linear
and/or quadratic factors.
9. Solve and sketch polynomial, rational,
9a. Sketch the graphs of exponential and
logarithmic functions using the techniques
logarithmic and exponential equations
of transformation.
9b. Apply the properties of exponents and
logarithms to solve application problems
involving compound interest and
exponential growth and decay.
9c. Explain the conditions under which the
Rational Root Theorem can be used to find
the zeros of a polynomial
10. Distinguish the difference between
10a. Find the first term and common
difference of an arithmetic sequence.
arithmetic and geometric sequences.
10b. Find the first term and common ratio
of a geometric sequence.
10c. Establish an nth term formula for a
geometric or an arithmetic sequence.
11. Evaluate the sum of finite and infinite
11a. Evaluate the sum of an arithmetic
series.
series
11b. Evaluate the sum of a finite and
infinite geometric series.
11c. Evaluate the sum of a series written in
summation notation form.
12. Utilize technology to assist in solving
problems
13. Apply multiple techniques to solve
quadratic equations and other equations
reducible to quadratic form
14. Perform the basic operations on
matrices.
15. Determine the optimal solution to a
function, subject to constraints
16. Combine polynomial, rational, and
square root functions.
12. Use a graphing calculator or computer
software to model, solve and justify
answers to a problem
13a. Delineate the process by which an
equation can be rewritten in quadratic form.
13b. Evaluate the solution of a quadratic
equation by factoring, completing the
square, extracting square roots, and the
quadratic formula.
14a. Find the sum and difference of
matrices of the same dimensions.
14b. Find the product of a scalar and a
matrix.
14c. Find the product of two matrices
15. Maximize or minimize a function
within a certain region determined by
constraints in the form of linear inequalities
16a. Find the sum, difference, product, and
quotient of two functions.
16b. State the domain of a composite
function