PENNSYLVANIA COLLEGE OF TECHNOLOGY
Sciences, Humanities & Visual Communications
Mathematics Department Syllabus
Technical Algebra & Trigonometry I
MTH 124
Course Description:
Study of intermediate algebra and trigonometry, designed to prepare students for course
work in their technical majors. Topics include algebraic expressions, linear equations,
systems of equations, right triangle trigonometry, functions, graphs, geometry, ratio and
proportion, and variation. Emphasis on problem solving and technical application as well
as the use of technology. Not designed to prepare students for calculus.
3 Credits (3 lecture- 0 Lab)
Prerequisite(s): MTH 005 or Placement by Examination.
Required Student Outcomes:
Upon successful completion of the course, students should be able to demonstrate the
following competencies:
1. Use arithmetic computation, including the use of technology, to evaluate
mathematical expressions and to solve application problems.
2. Simplify algebraic expressions by applying algebraic laws and properties.
3. Simplify algebraic expressions involving exponents and radicals.
4. Solve linear equations and applications involving linear equations.
5. Graph functions by plotting points and by using appropriate technology.
6. Solve equations and practical problems graphically.
7. Use geometric methods, theorems, and formulas to solve practical problems involving
areas of circles and polygons as well as surface area and volume of solid figures.
8. Apply trigonometric principles to solve right triangle problems and applications.
9. Solve systems of equations and applications involving systems of equations using
graphing, algebraic techniques, and appropriate technology.
Required Student Outcomes (continued):
10. Solve applied ratio and proportion problems.
11. Solve variation problems and associated practical applications.
12. Apply basic principles of analytic geometry to straight lines and solve associated
applications.
13. Engage in substantial mathematical problem solving at an intermediate algebraic and
trigonometric level.
14. Model real-world situations within a technical environment.
15. Read, write, listen to, and speak mathematics.
16. Use appropriate technology to enhance their mathematical thinking and
understanding, to solve mathematical problems, and to judge the reasonableness of
their results.
Required Materials:
Technical Mathematics, Ewen, Gary & Trefzger, 2nd ed., Pearson Prentice Hall, 2005.
For success in college-level mathematics classes at Penn College, students must know
how to use a graphing calculator. All students are required to purchase the TI-84-Plus
calculator. The instructor in this course will use the TI-84 Plus calculator for class
demonstration.
Course Outline:
Unit 1
Unit 2
Unit 3
Sections 1.1 – 1.10
Sections 1.14, 2.1 – 2.5
Sections 3.1 – 3.4, 10.1 – 10.2
Unit 4
Unit 5
Sections 4.1 – 4.5
Sections 1.15, 6.1
Basic Algebraic Operations
Ratio, Proportion, and Review of Geometry
Right Triangle Trigonometry and
Trigonometric Functions
Equations and their Graphs
Variation and Systems of Linear Equations
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Course Competencies:
Calculator Competencies
Appropriately use the graphing calculator to support the course competencies.
Unit 1 Basic Algebraic Operations
a) Categorize real numbers using the subsets of natural numbers, whole numbers,
integers, rational numbers, and irrational numbers.
b) Evaluate numerical expressions utilizing the order of operations.
c) Perform operations and solve applied problems involving very large and very
small numbers by utilizing scientific notation.
d) Perform numerical operations with measurements using the rules for accuracy
and precision.
e) Evaluate and simplify algebraic expressions using the laws of exponents.
f) Evaluate and simplify radical expressions analytically, and approximate the
value of radicals with the graphing calculator.
g) Define the terminology associated with polynomials and be able to perform
the operations of addition, subtraction, multiplication, and division of
polynomials.
h) Solve linear equations algebraically.
Unit 2 Ratio, Proportion, and Review of Geometry
a) Simplify a ratio and set up and solve a proportion for a missing quantity.
b) Solve abstract and applied problems using proportions.
c) Find angles formed by intersecting straight lines and parallel lines, and solve
associated abstract and applied problems.
d) Solve problems that require finding the sides and angles of right triangles.
e) Solve problems in which the perimeter or the area of a triangle or a
quadrilateral must be found.
f) Solve problems involving the circumference, diameter, arc length, area of a
circle and tangent lines to a circle.
g) Compute surface areas and volumes of spheres, cylinders, cones, prisms and
pyramids, and solve associated applied problems.
Unit 3 Right Triangle Trigonometry and Trigonometric Functions
a)
b)
c)
d)
Convert angles between decimal degrees and degrees, minutes and seconds.
Find the trigonometric ratios: sin  , cos  , and tan  .
Evaluate trigonometric expressions containing sin  , cos  , and tan  .
Find the angle given the value of sin  , cos  , or tan  .
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Course Competencies Unit 3 (continued):
e) Find the missing sides and angles of a right triangle.
f) Solve abstract and applied problems involving the right triangle.
g) Identify the algebraic sign of sin  , cos  , and tan  for an angle in any
quadrant.
h) Evaluate sin  , cos  , and tan  given a point on the terminal side of  .
i) Determine the reference angle for a given angle.
j) Find all angles between 0 and 360 that have a given value of sin  , cos  ,
or tan  .
Unit 4 Equations and their Graphs
a)
b)
c)
d)
e)
Distinguish between relations and functions.
Find the domain and range with and without the graphing calculator.
Use function notation to evaluate functions.
Graph points in rectangular coordinates.
Graph a relation or function, including applications, with and without the
calculator.
f) Estimate the solutions of equations by graphing.
g) Determine the slope of a line, given two points on the line.
h) Write the equation of a line in slope-intercept form and point-slope form.
i) Determine the slope of a line parallel or perpendicular to a given line.
j) Calculate the midpoint of and distance between two points.
Unit 5 Variation and Systems of Linear Equations
a)
b)
c)
d)
e)
Solve direct, inverse, joint, and combined variation problems.
Solve a system of two linear equations by graphical methods.
Solve a system of two linear equations by the addition method.
Solve a system of two linear equations by the substitution method.
Classify systems of equations in terms of their graph, number of solutions,
equations, and type of system.
f) Use systems of linear equations to describe and solve application problems.
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GRADING
Pre-Final Exam Average Weights
20% classwork/homework/daily grades
(This work will be graded will be assigned and graded by Mrs. Miller)
20% Exam #1 graded by college professor
20% Exam #2 graded by college professor
20% Exam #3 graded by college professor
20% Exam #4 graded by college professor
Final Exam score (graded by college professor) may count as 20% or 50% of the final
grade whichever is best for each student’s overall average.
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