Download Course Syllabus

MOUNT PLEASANT AREA
COURSE SYLLABUS
Title: PreCalculus
Department: Mathematics
Grades Taught: 11th, 12th
Course Description:
PreCalculus is a course with emphasis on the study of functions. The 12 basic functions will be
covered with an emphasis on polynomial (linear, quadratic, cubic and quartic), rational, exponential,
logarithmic and trigonometric functions. The conic sections are also covered in this course. Students
who take this course will use graphing calculators on a daily basis. This course will prepare students
for calculus as seniors or college mathematics for those who are graduating.
Prerequisites: Algebra 2 - C, Geometry – C
Length of Course: Year
Credit: 1
Course Standards:
Numbers, Number Systems and Number Relationships
Computation and Estimation
Measurement and Estimation
Mathematical Reasoning and Connections
Mathematical Problem Solving and Communication
Algebra and Functions
Geometry
Trigonometry
Learning Objectives:
Students will be able to:
I.
Unit 1
A. Determine whether a given relation is a function.
B. Identify the domain and range of a relation or function.
C. Evaluate Functions.
D. Perform operations with functions.
E. Find composite functions.
F. Iterate functions using real numbers.
G. Graph linear equations.
H. Find the x- and y-intercepts of a line.
I. Find the slope of a line through 2 points.
J. Find zeros of linear functions.
K. Write linear equations.
L. Write equations of parallel and perpendicular lines.
M. Draw and analyze scatter plots.
N. Write a prediction equation and draw best-fit lines.
O. Use a graphing calculator to compute correlation coefficients to determine goodness of
fit.
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COURSE SYLLABUS
II.
III.
IV.
V.
P. Solve problems using prediction equation models.
Q. Identify and graph piecewise functions.
R. Graph linear inequalities.
Unit 2
A. Solve systems of equations graphically and algebraically.
B. Solve systems of equations involving 3 variables algebraically.
C. Find reduced row-echelon form of an augmented matrix to solve systems of equations.
D. Model data using matrices.
E. Add, subtract, and multiply matrices.
F. Evaluate determinants.
Unit 3
A. Use algebraic tests to determine whether the graph of a relation is symmetrical.
B. Classify functions as even or odd.
C. Identify transformations of simple graphs.
D. Sketch graphs of related functions.
E. Graph polynomial, absolute value, and radical inequalities in two variables.
F. Solve absolute value inequalities.
G. Determine inverses of relations and functions.
H. Graph functions and their inverses.
I. Determine whether a function is continuous or discontinuous.
J. Identify the end behavior of functions.
K. Determine whether a function is increasing or decreasing on an interval.
L. Find the extrema of a function.
M. Graph rational functions.
N. Determine vertical, horizontal and slant asymptotes.
Unit 4
A. Determine roots of polynomial equations.
B. Apply the Fundamental Theorem of Algebra.
C. Solve quadratic equations.
D. Find the factors of polynomials using the Remainder and Factor Theorems.
E. Identify all possible rational roots of a polynomial equation by using the rational root
theorem.
F. Approximate the real zeros of a polynomial function.
G. Solve rational equations.
H. Decompose a fraction into partial fractions.
I. Solve radical equations.
J. Write polynomial functions to model real world data.
K. Use polynomial functions to interpret real world data.
Unit 5
A. Convert decimal degree measures to degree, minute and seconds and vice versa.
B. Find the number of degrees in a given number of rotations.
C. Identify angles that are coterminal with a given angle.
D. Find the values of trigonometric ratios for acute angles of right triangles.
E. Find the values of six trigonometric functions using the unit circle.
F. Find the values of six trigonometric functions of an angle in standard position given a
point on its terminal side.
G. Use trigonometry to find the measures of the sides of right triangles.
H. Evaluate inverse trigonometric functions.
I. Find missing angle measurements.
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COURSE SYLLABUS
J. Solve right triangles.
VI.
VII.
VIII.
IX.
K. Solve triangles by using the Law of Sines if the measures of two angles and a side are
given.
L. Find the area of a triangle if the measures of 2 sides and the included angle or the
measures of 2 angles and a side are given.
M. Solve triangles by using the Law of Sines.
N. Solve triangles by using the Law of Cosines.
O. Find the area of triangles if the measures of the 3 sides are given.
Unit 6
A. Change from radian measure to degree measure and vice versa.
B. Find the length of an arc given the measure of the central angle.
C. Find the area of a sector.
D. Graph the sine and cosine functions from -360 to 360 degrees.
E. Find the amplitude and period for the sine and cosine functions.
F. Write equations of sine and cosine functions given the amplitude and period.
G. Find the phase shift and the vertical translation for sine and cosine.
H. Write the equations of sine and cosine functions given the amplitude, period, phase shift
and vertical translation.
I. Model real world data using sine and cosine functions.
J. Use sinusoidal functions to solve problems.
K. Graph tangent, cotangent, secant and cosecant functions.
L. Graph inverse trigonometric functions.
Unit 7
A. Identify and use reciprocal identities, quotient identities, Pythagorean identities,
symmetry identities and opposite angle identities.
B. Use the basic trigonometric identities to verify other identities.
Unit 8
A. Use and determine the standard and general forms of the equation of a circle.
B. Graph circles.
C. Use and determine the standard and general forms of the equation of an ellipse.
D. Graph ellipses.
E. Use and determine the standard and general forms of the equation of a hyperbola.
F. Graph hyperbolas.
G. Build a parabolic reflector using the properties of the parabola.
Unit 9
A. Use the properties of exponents.
B. Evaluate and simplify expressions containing rational exponents.
C. Solve equations containing rational exponents.
D. Graph exponential functions.
E. Solve problems involving exponential growth and decay.
F. Use the exponential function y = e^x.
G. Evaluate expressions involving logarithms.
H. Solve equations involving logarithms.
I. Graph logarithmic functions.
J. Find common logarithms and antilogarithms of numbers.
K. Solve equations using common logarithms.
L. Solve real world applications with common logarithmic functions.
M. Find natural logarithms of numbers.
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COURSE SYLLABUS
N. Solve equations using natural logarithms.
O. Solve real world applications with natural logarithmic functions.
Expectations:
Students will:
1. Be on time for class.
2. Be prepared for class (have book, notebook, pencil).
3. Be quite and listen while the teacher is teaching.
Texts:
Advanced Mathematical Concepts: Precalculus with Applications (Glencoe, McGraw-Hill)
Resources:
Anything you want to use.
Websites:
Click on the following link to access my class webpage:
http://mtpasd.schoolwires.com/667970920152931/site/default.asp
Course Outline/Activities/Assessments:
The following are the assessments for this PreCalculus Course. They must be completed in the order
listed below.
 1.1-1.4 Test
 1.5-1.8 Test
 Chapter 2 Test (2.1, 2.2, 2.5B, 2.3, 2.5)
 3.1-3.4 Test
 3.5-3.7 Test
 4.1-4.3 Test
 4.4-4.8 Test
 Partial Fraction Decomposition Quiz
 Special Triangle Quiz
 Midterm Exam
 5.1-5.4 Test
 5.6-5.8 Test
 Chapter 6 Test (6.1, 6.4, 6.5, 6.6)
 6 Trig Graph Quiz
 Inverse Trig Graph Quiz
 7.1-7.2 Test
 15 Trig Identities Quiz
 Log Properties and Graphs Quiz
 Chapter 10 Test (10.2, 10.3, 10.4, 10.5)
 Chapter 11 Test (11.1, 11.2, 11.3, 11.4, 11.5, 11.6)
 Final Exam
Materials Used:
Graphing Calculator, Smartboard, Chalkboard, Chalk, PreCalculus Text (listed above)
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COURSE SYLLABUS
Classroom Expectations (attendance & behavior):
Students should:
1. Be prepared
2. Be prompt
3. Be on task
4. Complete all assignments
5. Treat others with respect
Homework Procedure:
Homework is assigned daily. Homework is checked and graded on a daily basis. Homework can be
found on the internet by clicking on the following link.
http://mtpasd.schoolwires.com/667970920152931/icalsw/calendar.asp?Cal=em&calendar_ID=6696
Grading Scale:
A 93 - 100
B 84 - 92
C 75 - 83
D 65 - 74
F 0 - 64
Extra Help:
Available by appointment.
Contact Information:
Email: [email protected]
Phone: 724-547-4100 ext: 1120
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