MATHEMATICS DEPARTMENT CURRICULUM
Syllabus – College Algebra / Trigonometry
INSTRUCTOR: __Mrs. Lisa Newman___
SCHOOL YEAR: __2011-12__ PERIOD: _4, 6, 8 COURSE NUMBER: 319
COURSE DESCRIPTION
This is the fourth course in the college preparatory mathematics sequence. Units of study include linear equations, polynomials,
rational functions, conics, exponential and logarithmic functions, trigonometric functions, linear programming, and sequences and
series.
Technological tools, such as the TI graphing calculator, will be used for both discovery and problem solving.
Classroom sets of graphing calculators will be provided.
Students will be expected to bring/purchase a _TI-30 XIIS or TI-83/84__ scientific/graphing calculator to class on a daily basis.
ENDURING UNDERSTANDINGS
1.
2.
3.
4.
5.
6.
There are various methods to determine the roots of polynomial functions, the graphs of which have specific shapes
Rational functions are ratios of polynomials, have points of discontinuity, and some solutions are extraneous
Exponential functions increase or decrease rapidly, and their inverse is logarithms
Creating a parabola, circle, ellipse or hyperbola requires specific technical components and exist in the real world.
The graphs of the sine and cosine functions are related to the unit circle
There are logical steps that are taken to solve problems involving trigonometric identities.
CREDIT:
1 credit
LEVEL:
11/12 – Regular/Honors
PREREQUISITES
This course is for students who have passed Algebra 2 with an A, B, or C, and students who passed Honors Algebra 2 with a C
or D.
AREAS OF STUDY
First Semester
P. Prerequisites: Fundamental Concepts of Algebra
1. Equations and Inequalities
2. Functions and Graphs
3. Polynomial and Rational Functions
Second Semester
5. Trigonometric Functions
6. Analytic Trigonometry
7. Laws of Sines and Cosines
4. Exponential and Logarithmic Functions
8/9. Linear Programming/Matrices
11. Sequences
1
TIMELINES
COURSE NAME - First Semester
Note: “Optional” sections may be taught at the teacher’s discretion, but will not be tested on the final exam.
Suggested Timelines
Chapter P Prerequisites: Fundamental Concepts of Algebra 10 days
P.1 Algebraic Expressions and Real Numbers
P.2 Exponents and Scientific Notation
A-SSE-3c
P.3 Radicals and Rational Exponents
N-RN-1/2
P.4 Polynomials
A-APR-1
P.5 Factoring Polynomials
A-SSE-2
P.6 Rational Expressions
A-APR-1/6
Suggested Timelines
Chapter 3 Polynomial and Rational Functions
17 Days
3.1 Quadratic Function
F-IF-7a
3.2 Polynomial Functions and Their Graphs
F-IF-7c/4
3.3 Dividing Polynomials; Remainder and Factor Theorms A-APR-2/6
3.4 Zeros of Polynomial Functions A-APR-2/3, A-REI-11, F-IF-7d
3.5 Rational Functions and Their Graphs
A-REI-12
3.6 Polynomial and Rational Inequalities
A-REI-12
3.7 Modeling Using Variation
F-LE-2
Chapter 1 Equations and Inequalities
15 days
1.1 Graphs and Graphing Utilities
A-CED-2, F-BF-1a
1.2 Linear Equations and Rational EquationsA-REI-2/3, A-CED-1
1.3 Models and Applications F-IF-6, A-CED-4, A-REI-6, F-BF1a
1.4 Complex Numbers
N-CN-1/2/3/4/7
1.5 Quadratic Equations
A-RIE-4a/b, A-SSE-3a/b
1.6 Other Types of Equations
A-REI-10
1.7 Linear Inequalities and Absolute Value Inequalities A-CED-3/7
Chapter 2 Functions and Graphs
19 days
2.1 Basics of Functions and Their Graphs
F-IF-1/2/5
2.2 More on Functions and Their Graphs
F-IF-1/5
2.3 Linear Functions and Slope
F-IF-1/5
2.4 More on Slope
2.5 Transformations of Functions
F-IF-7b, F-BF-3, F-IF-5
2.6 Combinations of Functions; Composite Functions F-BF-1b/c
2.7 Inverse Functions
F-BF-4a/b/c/d
2.8 Distance and Midpoint Formulas; Circles
G-GPE-1/7
Number of Teaching Days
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute, Stand. Testing
TOTAL DAYS: (82)
71 days
4 days
7 days
_______
82 days
2
TIMELINES
COURSE NAME - Second Semester
Note: “Optional” sections may be taught at the teacher’s discretion, but will not be tested on the final exam.
Suggested Timelines
Chapter 5 Trigonometric Functions
26 days
5.1 Angles and Radian Measure F-TF-1
5.2 Right Triangle Trigonometry G-SRT-7/8
5.3 Trigonometric Functions of Any Angle F-TF-2
5.4 Trigonometric Functions of Real Numbers; Periodic Functions
F-TF-3/4
5.5 Graphs of Sine and Cosine Functions F-TF-3
5.6 Graphs of Other Trigonometric Functions F-TF-3
5.7 Inverse Trigonometric Functions F-TF-6
5.8 Applications of Trigonometric Functions G-SRT-8
Chapter 6 Analytic Trigonometry
16 days
6.1 Verifying Trigonometric Identities
F-TF-8
6.2 Sum and Difference Formulas
F-TF-8
6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas (DoubleAngle Only)
F-TF-5
6.5 Trigonometric Equations
F-TF-5
Chapter 7 Additional Topics in Trigonometry
7.1 The Law of Sines (focus on ambiguous case)
7.2 The Law of Cosines
5 days
G-SRT-11
G-SRT-11
Suggested Timelines
Chapter 4 Exponential and Logarithmic Functions
12 days
4.1 Exponential Functions
F-IF-8b/7e
4.2 Logarithmic Function
F-IF-7e
4.3 Properties of Logarithms
F-BF-5
4.4 Exponential and Logarithmic Equations F-LE-4
4.5 Exponential Growth and Decay; Modeling Data F-LE-5
Chapter 8/9 Matrices and Determinants
Systems of Equations and Inequalities
9.1 Matrix Solutions to Linear Systems (TI-83)
8.6 Linear Programming (TI-83 and Matrices)
7 days
A-REI-8/9, N-VM-8
A-CED-3
Chapter 11 Sequences, Induction, and Probability
6 days
11.1 Sequences and Summation Notation F-IF-3
11.2 Arithmetic Sequences
F-IF-3, F-BF-2
11.3 Geometric Sequences and Series
A-SSE-4, F-BF-2, F-IF-3
Number of Teaching Days
Performance Assessment
Review for Semester Exam
Miscellaneous Days:
School Improvement, Assembly, Institute,
Stand. Testing Review, Stand. Testing
TOTAL DAYS: (84)
73 days
0 days
4 days
7 days
______
84
3