Description
Topics include: vectors; trigonometric functions and their
graphs; identities; exponential and
logarithmic functions and equations; radical equations; equations with rational
exponents;
dimension of a circle; velocity; sine and cosine graphs; complex numbers in
polar and rectangular
form; trigonometric equations; conic sections ; and analysis of statistical data.
Emphasis will be on
the application of skills to technical problems. CrLf
Types of Instruction
| Instruction Type |
Contact Hours |
Credits |
| Classroom Presentation |
72 |
4 |
Prerequisites
Satisfactory completion of College Technical Mathematics 1
(10-804-115) with a grade of C or
better
OR College Technical Mathematics 1B (10-804-114) with a grade of C or better
OR appropriate placement score
Exit Learning Outcomes
External Standards
AMERICAN MATHEMATICAL ASSOCIATION OF TWO YEAR COLLEGES
STANDARDS
STANDARDS FOR CONTENT
Standard C-2: Symbolism and Algebra CrLfStudents will translate problem
situations into their
symbolic representations and use those representations to solve problems. CrLf
Standard C-1: Number Sense CrLfStudents will perform arithmetic operations,
as well as reason
and draw conclusions from numerical information . CrLf
Standard C-4: Function CrLfStudents will demonstrate understanding of the
concept of function
by several means (verbally, numerically, graphically, and symbolically) and
incorporate it as a
central theme into their use of mathematics. CrLf
Standard C-3: Geometry CrLfStudents will develop a spatial and measurement
sense. CrLf
STANDARDS FOR INTELLECTUAL DEVELOPMENT
Standard I-1: Problem Solving Students will engage in substantial
mathematical problem solving.
Standard I-2: Modeling Students will learn
mathematics through modeling real-world situations.
Standard I-3: Reasoning CrLfStudents will expand their mathematical
reasoning skills as they
develop convincing mathematical arguments. CrLf
Standard I-4: Connecting With Other Disciplines CrLfStudents will develop
the view that
mathematics is a growing discipline, interrelated with human culture, and
understand its
connections to other disciplines. CrLf
Standard I-5: Communicating CrLfStudents will acquire the ability to read,
write, listen to, and
speak mathematics. CrLf
Standard I-6: Using Technology CrLfStudents will use appropriate technology
to enhance their
mathematical thinking and understanding and to solve mathematical problems and
judge the
reasonableness of their results. CrLf
Standard I-7: Developing Mathematical Power CrLfStudents will engage in rich
experiences that
encourage independent, nontrivial exploration in mathematics, develop and
reinforce tenacity and
confidence in their abilities to use mathematics, and inspire them to pursue the
study of
mathematics and related disciplines. CrLf
Competencies
A. Graph exponential and logarithmic functions You will
demonstrate your competence:
A.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
A.1. graph exponential functions
A.2. graph logarithmic functions
A.3. relate logarithmic functions to its inverse function
A.4. graph functions on logarithmic or semi-logarithmic scales
A.5. apply skill to technical problems
A.6. utilize appropriate technology
A.7. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
B. Solve exponential and logarithmic equations
You will demonstrate your competence:
B.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
B.1. solve exponential equations
B.2. solve logarithmic equations
B.3. solve applied problems involving exponential or logarithmic
equations, such as growth and decay
B.4. utilize appropriate technology
B.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
C. Perform operations with exponents and radicals
You will demonstrate your competence:
C.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
C.1. evaluate an expression containing rational powers on numbers with
rational roots
C.2. convert between rational powers and radical notation
C.3. simplify radical expressions
D. Solve equations with radicals and rational exponents
You will demonstrate your competence:
D.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
D.1. convert between radical and fractional exponent form
D.2. solve radical equations involving one variable
D.3. solve equations with fractional exponents
D.4. verify solutions by substitution into the original equation
D.5. apply skill to technical problems
D.6. utilize appropriate technology
D.7. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
E. Use formulas involving radicals and exponents
You will demonstrate your competence:
E.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
E.1. choose formula when appropriate
E.2. identify unknown value(s)
E.3. relate the given values to the variables in the formula formed after
given values
are substituted into a formula that includes radical expressions
E.4. transform a formula by isolating a variable which is contained in a
radical expression
E.5. solve equations formed after given values are substituted into a
formula that includes radical expressions
E.6. apply skill to technical problems
E.7. utilize appropriate technology
E.8. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
F. Calculate unknown dimensions as related to a circle
You will demonstrate your competence:
F.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
F.1. calculate the length of a circular arc, given the radius and central
angle
F.2. calculate the central angle and the chord depth, given the radius and
chord length of a circle
F.3. calculate the area of a sector of a circle, given the radius and
central angle
F.4. calculate the area of a segment of a circle, given the radius,
central angle, and area of sector to which the segment belongs
F.5. calculate the length of a chord, given the radius and the angle
between the chord and a tangent at one end of the chord
F.6. calculate the angle between two tangents, given the radius of a
circle and the length of the segments attached to the circle
F.7. apply skill to technical problems
F.8. utilize appropriate technology
F.9. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
G. Solve rotational, linear, and angular velocity
problems
You will demonstrate your competence:
G.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
G.1. calculate the linear velocity of a point on the circumference of a
wheel, given
either the diameter or radius and the angular velocity
G.2. calculate the angular velocity of a point on the circumference of a
wheel when
given either the diameter or radius and the linear velocity
G.3. convert between radians over time and revolutions over time
G.4. apply skill to technical problems
G.5. utilize appropriate technology
G.6. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution, solution is within stated range and reflects appropriate accuracy or
precision,
solution is labeled with appropriate units)
H. Perform operations with vectors
You will demonstrate your competence:
H.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
H.1. determine the resultant of two or more vectors
H.2. resolve vectors by components
H.3. apply skill to technical problems
H.4. utilize appropriate technology
H.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
I. Perform arithmetic operations using complex numbers
in both polar and rectangular forms
You will demonstrate your competence:
I.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
I.1. add , subtract, multiply, and divide in rectangular form
I.2. multiply and divide in polar form
I.3. apply skill to technical problems
I.4. utilize appropriate technology
I.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
J. Relate complex (rectangular) notation to polar
notation
You will demonstrate your competence:
J.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
J.1. convert between polar and rectangular form
J.2. use the quadratic equation to find non-real solutions
J.3. apply skill to technical problems
J.4. utilize appropriate technology
J.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
J. Relate complex (rectangular) notation to polar
notation
You will demonstrate your competence:
J.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
J.1. convert between polar and rectangular form
J.2. use the quadratic equation to find non-real solutions
J.3. apply skill to technical problems
J.4. utilize appropriate technology
J.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
L. Graph sine/cosine waves
You will demonstrate your competence:
L.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
L.1. plot a graph of sine/cosine wave from an equation
L.2. plot a graph of sine/cosine wave given the amplitude, frequency, and
phase shift
L.3. apply skill to technical problems
L.4. utilize appropriate technology
L.5. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
M. Solve trigonometric equations
You will demonstrate your competence:
M.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
M.1. manipulate identities
M.2. factor trigonometric expressions
M.3. write a trigonometric expression in terms of sine and cosine
M.4. solve trigonometric equations with multiple solutions
M.5. apply skill to technical problems
M.6. utilize appropriate technology
M.7. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution, solution is within stated range and reflects appropriate accuracy or
precision,
solution is labeled with appropriate units)
N. Analyze the equations of conic sections and their
graphs
You will demonstrate your competence:
N.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
N.1. determine, by inspection, whether a given second-degree equation
represents a
circle, ellipse, parabola , or hyperbola
N.2. write the equation of a circle, ellipse, parabola, or hyperbola from
given information
N.3. construct a graph of any of the conic sections from equation(s)
N.4. apply skill to technical problems
N.5. utilize appropriate technology
N.6. apply the process for solving technical problems according to the
problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution,
solution is within stated range and reflects appropriate accuracy or precision,
solution
is labeled with appropriate units)
O. Analyze data statistically
You will demonstrate your competence:
O.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
O.1. calculate measures of central tendency
O.2. calculate measures of dispersion
O.3. construct a graph that describes data
O.4. interpret data in terms of statistics
O.5. apply skill to technical problems
O.6. utilize appropriate technology
O.7. apply the process for solving technical problems according to the
problemsolving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution, solution is within stated range and reflects appropriate accuracy or
precision,
solution is labeled with appropriate units)
