1. course - Sinclair Community College

SINCLAIR COMMUNITY COLLEGE
DAYTON, OHIO
DEPARTMENT SYLLABUS FOR COURSE IN
MAT 1580 – PRE-CALCULUS
(5 SEMESTER HOURS)
1. COURSE DESCRIPTION:
Includes equations; properties, operations, and transformations of functions;
piecewise-defined, polynomial, radical, rational, exponential, and logarithmic
functions and their graphs; rational and polynomial inequalities; conic
sections; systems of linear equations; sequences and series; and applications.
Trigonometric functions of angles, solving right and oblique triangles,
identities, vectors, trigonometric equations, radian measure, graphs of
trigonometric functions, and inverse trigonometric functions.
2. COURSE OBJECTIVES:
To develop in the student the theories, skills, and techniques that form the
foundation of algebra and trigonometry, to provide the student with
opportunities to apply their knowledge of algebra and trigonometry in a
variety of contexts with an emphasis on elementary functions, to build within
the student the mathematical maturity necessary for the study of calculus.
3.
PREREQUISITE:
Satisfactory score on Mathematics Placement Test or a grade of "B" or better
in MAT 1370.
4.
ASSESSMENT:
In addition to required exams as specified on the syllabus, instructors are
encouraged to include other components in computing final course grades
such as homework, quizzes, and/or special projects. However, 80% of the
student’s course grade must be based on in-class proctored exams.
5.
TEXT:
Algebra and Trigonometry, Third Edition
Stewart/Redlin/Watson
Cengage
Adopted: Fall 2012
WebAssign is an optional component of this course. Please provide this
Enhanced WebAssign class key _________to your students. It will give them
access to the online version of the textbook, as well as an optional set of
homework assignments and quizzes that they can do for extra practice. If you
would like to make WebAssign required as part of the grade for your course,
please contact Kinga Oliver for help getting set-up
6.
CACULATOR:
A scientific calculator is required. The use of a graphing calculator is left up
to the discretion of the instructor.
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7.
2
PREPARED BY:
Kinga Oliver -point of contact, David Hare, Susan Harris, Craig
Birkemeier
Effective: Summer 2013
SINCLAIR COMMUNITY COLLEGE
DAYTON, OHIO
CLASS SCHEDULE FOR COURSE IN
MAT 1580 – PRE-CALCULUS
(5 SEMESTER HOURS)
CLASSES MEETING THREE TIMES A WEEK
Lecture
Sections
Topics
1
3.1/3.2
Introduction, What Is a Function**/ Graphs of Functions
2
3.3/3.5
Getting Information from the Graph of a Fun./ Transformations of Functions
3
3.5
4
3.6/3.7
Combining Functions/ One-to-One Functions and Their Inverses
5
3.7/4.1
One-to-One Functions and Their Inverses/ Quadratic Functions and Models
6
4.1
Quadratic Functions and Models
7
4.2
Polynomial Functions and Their Graphs
8
4.3/4.4
9
4.5
Complex Zeros and the Fund. Thm of Algebra
10
4.6
11
1.6
Rational Functions
Inequalities
Transformations of Functions
Dividing Polynomials/ Real Zeros of Polynomials
12
REVIEW FOR TEST 1
13
TEST 1 [1.6. Chap. 3, and Chap. 4]
14
5.1/5.2
Exponential Functions/ The Natural Exponential Function
15
5.3/5.4
Logarithmic Functions/ Laws of Logarithms
16
5.5
Exponential and Logarithmic Equations
17
5.6
Exponential and Log. Equations
18
Holiday/Catch-up
19
6.1/6.2
Angle Measure/Trigonometry of Right Triangles
20
6.3
Trigonometric Functions of Angles
21
6.5
The Law of Sines
22
6.6
The Law of Cosines
23
REVIEW FOR TEST 2
24
TEST 2 [Chap. 5, 6.1-6.3, 6.4, 6.5]
SPRING BREAK
**
Note to instructors regarding section 3.1: Please do not introduce or assign examples that require the use of
quadratic inequalities to find the domains of functions. Quadratic inequalities are introduced later in the
course.
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MAT 1580 – PRE-CALCULUS
THREE TIMES A WEEK SECTIONS CLASS SCHEDULE (continued)
Lecture
Sections
25
7.1
The Unit Circle
26
7.2
Trigonometric Functions of Real Numbers
27
7.3
Trigonometric Graphs
28
7.4
More Trigonometric Graphs
29
7.5
Inverse Trigonometric Functions and Their Graphs
30
Topics
Holiday/Catch-up
31
8.1/8.2
Trigonometric Identities /Addition and Subtraction Formulas
32
8.3
Double-Angle, Half-Angle, and Product-Sum Formulas
33
8.4
Basic Trigonometric Equations
34
8.5
More Trigonometric Equations
35
REVIEW FOR TEST 3
36
TEST 3 [7.1-7.5, Chap. 8]
37
10.1
Vectors in Two Dimensions
38
11.1/11.2
Systems of Linear Eqns in Two Var./ Syst. of Lin. Eqns in Several Var.
39
12.1, 12.2
Parabolas, Ellipses***
40
12.3
Hyperbolas
41
12.4
Shifted Conics
42
13.1
Sequences and Summation Notation
43
13.2/13.3
Arithmetic Sequences/ Geometric Sequences
44
REVIEW FOR TEST 4
45
TEST 4 [10.1, 11.1, 11.2, 12.1-12.4, 13.1-13.3]
Finals Week Review
COMPREHENSIVE FINAL EXAM
*** Note to instructors regarding section 12.2: Please mention that a circle is a special case of an ellipse where
a = b = r. Circles were introduced in section 2.2 and are not covered again in chapter 12.
Extra time may be available for some sections in the syllabus. If more time is needed (due to holidays, snow days,
etc) the catch-up days may need to be omitted.
A comprehensive final exam is to be administered in week 16. Extra time for review may be provided earlier in
the 16th week.
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MAT 1580 Course Formulas
Prerequisite Formulas
Formulas of special importance that students are expected to know upon entering this course.
- Pythagorean Theorem
The square of the length of the hypotenuse of a right triangle equals the sum
of the squares of the lengths of the other two sides of the triangle: c 2  a 2  b 2
- Distance Formula
d  ( x 2  x1 ) 2  ( y 2  y1 ) 2
- Midpoint Formula
 x1  x 2 y1  y 2 

M 
,
 2
2 
- Equation of a Circle
 x  h 2   y  k  2  r 2
- Sum of Angles
The sum of the measures of the three angles in any triangle is 180 o :
A  B  C  180 o
- Similar Triangles
Ratios of corresponding sides of similar triangles are equal.
- Geometric Formulas
Area
A
Triangle
1
bh
2
A   r2
Circle
- Slope of a Line
Perimeter
m
P  abc
C  2 r
y 2  y1
x 2  x1
- Forms of linear Equations
Slope-Intercept Form
y  mx  b
Point-Slope Form
y  y1  m x  x1 
Horizontal Line
yb
Vertical Line
xa
- Definition of i and i 2
i   1 , i 2  1
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ANGLE RELATIONSHIPS AND SIMILAR TRIANGLES
Vertical Angles: Vertical angles are opposite each other when two lines cross and have equal measures (AED=BEC and AEB=DEC)
AlternateInteriorAngles
For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below,
angle A and angle D are called alternate interior angles. Alternate interior angles have the same degree
measurement. Angle B and angle C are also alternate interior angles.
AlternateExteriorAngles
For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below,
angle A and angle D are called alternate exterior angles. Alternate exterior angles have the same degree
measurement. Angle B and angle C are also alternate exterior angles.
CorrespondingAngles
For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below,
angle A and angle C are called corresponding angles. Corresponding angles have the same degree measurement.
Angle B and angle D are also corresponding angles.
Angle Sum of a Triangle: The sum of the measures of the angles of any triangle is 180°.
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Types of Triangles:
a. Equilateral triangle: If the lengths of all three sides of the triangle are equal, then it is called an equilateral
triangle. Since the sum of all the angles of a triangle is 1800, it can be said that each angle of an equilateral
triangle is 600.
b. Isosceles triangle: If only two sides of a triangle are equal in length, it is called as an isosceles triangle.
c.
Scalene triangle : If all the sides of a triangle have different lengths it is called a scalene triangle
d. Acute triangle: A triangle in which all the angles are acute, (i.e. < 900) is called as an acute triangle.
e. Obtuse triangle: A triangle in which one of the angles is obtuse is called as an obtuse triangle.
f. Right Triangle: It is a triangle in which one of the angles is a right angle.
Congruent Triangles - Two triangles are said to be congruent, if all the corresponding parts are equal. The
symbol used for denoting congruence is  and  PQR  STU implies that corresponding angles and
corresponding sides are equal.
Similar Triangles - Two triangles are called similar if all their angles are equal, respectively. Note that it is
sufficient for two triangles to have two pairs of equal angles to be similar. Corresponding sides must be
proportional.
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Course Formulas - Formulas that students are required to memorize in this course:
Chapter 4
f  x  ax 2  bx  c;
- Quadratic Function
  b   b 

vertex 
, f
 2 a  2 a 
vertex  h, k 
f  x  a  x  h 2  k ;
If ax  bx  c  0, a  0
2
- Quadratic Formula
then
 b  b 2  4ac
x
2a
Chapter 5
- Definition of Logarithm
y  log a x if and only if a y  x
- Properties of Logarithms
log a a  1,
log a a x  x,
(with a > 0, a  1, x > 0)
log a 1  0,
a log a x  x
- Laws of Logarithms
log a  AB   log a A  log a B
 A
log a    log a A  log a B
B
log a  AC   c log a A
log a x
log a b
- Change of Base Formula
log b x 
- Exponential Growth and Decay
n  t   n0ert ,
- Compound Interest
 r
At   P1  
 n
r 0
nt
m  t   m0e rt , r  0
At   Pe rt
Chapter 6
-
Definition of Radian Measure, Page 408
Relationship between Degrees and Radians, Page 409
Length of a Circular Arc, Page 411
Area of a Circular Sector, Page 412
The Trigonometric Ratios (right triangle trigonometry), Page 417
Values of Trigonometric Ratios for Special Angles,
Page 419
Definitions of the Trigonometric Functions (x-y-r definitions), Page 426
Trigonometric Functions of Any Angle (use signs, reference angles), Page 428
Fundamental Identities, Page 431
Law of Sines, Page 443
Law of Cosines, Page 450
Chapter 7
- Definition of the Trigonometric Functions, Page 475
- Special Values of the Trigonometric Functions, Page 476
8
-
Signs of the Trigonometric Functions, Page 478
Fundamental Identities, Page 480
Sine and Cosine Curves, Page 488
Shifted Sine and Cosine Curves, Page 489
Tangent and Cotangent Curves, Page 500
Cosecant and Secant Curves, Page 501
Definition of the Inverse Sine Function, Page 505
Definition of the Inverse Cosine Function, Page 506
Definition of the Inverse Tangent Function, Page 507
Chapter 8
- Fundamental Trigonometric Identities,
*
- Addition and Subtraction Formulas ,
*
- Double Angle Formulas ,
*
- Half-Angle Formulas ,
Page 532
Page 538
Page 546
Page 548
Chapter 10
- Magnitude and Direction of a Vector, Pages 620 and 622
- Horizontal and Vertical Components of a Vector, Page 622
Chapter 12
- Equations of Conic Sections
Parabola
 x  h
Circle
 x  h 2   y  k  2  r 2
2
 y  k  2  4 p  x  h
 4 p y  k ,
Ellipse
Hyperbola
Chapter 13
- Arithmetic Sequence: an  a   n  1 d ; Geometric Sequence: a n  ar n1
- Partial sums of an Arithmetic Sequence
*
Sn 
 a  an 
S n  n

 2 
n
2a  n  1d 
2
- Partial sums of a Geometric Sequence
Sn  a
- Sum of an infinite Geometric Series
S
1 r n
1 r
a
if
1 r
r 1
memorization of tangent identities is at the discretion of the instructor
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