APPLIED TECHNICAL MATHEMATICS
I. COURSE DESCRIPTION
This course presents a review of arithmetic , elements of algebra, statistics,
geometry, and
trigonometry. It emphasizes manipulative skills to prepare students for work in
specialized
areas of technology.
II. PREREQUISITES
MTH 2 or the equivalent by placement test.
III. INTRODUCTION
This course is designed to provide the student with a solid foundation in the
mathematical skills
needed to work on a day-to-day basis in a variety of technical disciplines.
IV. INSTRUCTIONAL MATERIALS
Textbook: Elementary Technical Mathematics 9th edition by Dale Ewen and C. Robert
Nelson
ISBN 13: 9780495012740; Thomson Brooks/Cole, 2007 REQUIRED
Scientific or graphing calculator REQUIRED
Protractor and ruler with metric and US units REQUIRED
1pass Instant Access to ThomsonNow, vMentor, and Book Companion Website
OPTIONAL
ISBN 10: 0-495-18970-7 (included with new text)
See Section IX for additional resources .
V. MATERIAL TO BE COVERED
| Unit I |
Chapters 1 – 4; Omit 2.7, 4.8 and 4.9
|
4 weeks |
| Unit II |
Chapters 5 – 7; Omit 5.3, 5.4, 5.5, 5.6
and 5.7; 6.9 optional |
4 weeks |
| Unit III |
Chapters 8, 12, 13 and 14; Omit 8.4,
12.7, 12.8, 12.9, 12.10 and 14.2 |
5 weeks |
| Unit IV |
Chapter 15; Omit 15.4, 15.7,
15.9 – 15.13 |
2 weeks |
VI. BASIC CONCEPTS
The student must master the following concepts.
Chapter 1: Basic Concepts
This is mainly review.
1.1 Review of Basic Operations
1.2 Order of Operations
1.3 Area and Volume Emphasize
1.4 Formulas Emphasize
1.5 Prime Factorization Divisibility
1.6 Introduction to Fractions
1.7 Addition and Subtraction of Fractions
1.8 Multiplication and Division of Fractions
1.9 The U. S. System of Weights and Measures Emphasize
1.10 Addition and Subtraction of Decimal Fractions
1.11 Rounding Numbers
1.12 Multiplication and Division of Decimal Fractions
1.13 Percent
1.14 Part (Amount), Base, and Rate
1.15 Powers and Roots Omit cube roots
Chapter 2: Signed Numbers and Powers of 10
The first 4 sections are review.
2.1 Addition of Signed Numbers
2.2 Subtraction of Signed Numbers
2.3 Multiplication and Division of Signed Numbers
2.4 Signed Fractions
2.5 Powers of 10
2.6 Scientific Notation Use of calculator in scientific mode is
optional.
2.7 OMIT
Chapter 3: The Metric System
3.1 Introduction to the Metric System
3.2 Length
3.3 Mass and Weight
3.4 Volume and Area
3.5 Time, Current, and Other Units
3.6 Temperature
3.7 Metric and U. S. Conversion
Chapter 4: Measurement
4.1 Approximate Numbers and Accuracy
4.2 Precision and Greatest Possible Error
4.3 The Vernier Caliper
4.4 The Micrometer Caliper
4.5 Addition and Subtraction of Measurements
4.6 Multiplication and Division of Measurements
4.7 Relative Error and Percent of Error
4.8 OMIT
4.9 OMIT
Chapter 5: Polynomials: An Introduction to Algebra
5.1 Fundamental Operations
5.2 Simplifying Algebraic Expressions
5.3 OMIT
5.4 OMIT
5.5 OMIT
5.6 OMIT
5.7 OMIT
Chapter 6: Equations and Formulas
6.1 Equations
6.2 Equations with Variables in Both Members
6.3 Equations with Parentheses
6.4 Equations with Fractions
6.5 Translating Words into Algebraic Symbols
6.6 Applications Involving Equations
6.7 Formulas
6.8 Substituting Data into Formulas
6.9 Reciprocal Formulas Using a Calculator Optional
Chapter 7: Ratio and Proportion
7.1 Ratio
7.2 Proportion
7.3 Direct Variation
7.4 Inverse Variation
Chapter 8: Graphing Linear Equations
8.1 Linear Equations with Two Variables
8.2 Graphing Linear Equations
8.3 The Slope of a Line Omit parallel and perpendicular lines.
8.4 OMIT
(OMIT Chapters 9 – 11)
Chapter 12: Geometry
12.1 Angles and Polygons
12.2 Quadrilaterals
12.3 Triangles
12.4 Similar Polygons
12.5 Circles
12.6 Radian Measure
12.7 OMIT
12.8 OMIT
12.9 OMIT
12.10 OMIT
Chapter 13: Right Triangle Trigonometry
13.1 Trigonometric Ratios
13.2 Using Trigonometric Ratios to Find Angles
13.3 Using Trigonometric Ratios to Find Sides
13.4 Solving Right Triangles
13.5 Applications Involving Trigonometric Ratios
Chapter 14: Trigonometry with Any Angle
14.1 Sine and Cosine Graphs
14.2 Omit
14.3 Solving Oblique Triangles: Law of Sines
14.4 Law of Sines: The Ambiguous Case
14.5 Solving Oblique Triangles: Law of Cosines
Chapter 15: Basic Statistics
15.1 Bar Graphs
15.2 Circle Graphs
15.3 Line Graphs
15.4 OMIT
15.5 Mean Measurement
15.6 Other Average Measurements and Percentiles
15.7 OMIT
15.8 Range and Standard Deviation
15.9 – 15:13 OMIT
VII. SUGGESTED WEEKLY SCHEDULE – 16 WEEK SEMESTER
Week 1: Chapter 1 Emphasize 1.3, 1.4, 1.9 and Unit Reviews. Omit cube
roots in 1.15.
Week 2: 2.1 – 2.6, omit 2.7
Week 3: 3.1 – 3.7
Week 4: 4.1 – 4.7, omit 4.8 and 4.9
Week 5: Test 1, 5.1, 5.2, omit the rest of Chapter 5
Week 6: 6.1 – 6.4
Week 7: 6.5 – 6.8, (6.9 optional if time permits.)
Week 8: 7.1 – 7.4, Test 2
Week 9: 8.1 – 8.3, omit 8.4
Week 10: 12.1 -12.4
Week 11: 12.5, 12.6, omit 12.7 – 12.10, 13.1 – 13.3
Week 12: 13.4, 13.5, 14.1
Week 13: 14.3 – 14.5, Test 3
Week 14: 15.1 – 15.3, omit 15.4, 15.5
Week 15: 15.6, omit 15.7, 15.8
Give Final Exam during the scheduled exam period
VIII. SUGGESTED WEEKLY SCHEDULE – 10 WEEK SEMESTER
Week 1: Chapters 1 and 2, (Omit 2.7)
Week 2: Chapter 3, 4.1 - 4.4
Week 3: 4.5 – 4.7, (Omit 4.8, 4.9), Test 1, 5.1, 5.2 (Omit 5.3 – 5.7)
Week 4: 6.1 – 6.5
Week 5: 6.6 – 6.8, 7.1 – 7.4, Test 2
Week 6: 8.1 – 8.3, (Omit 8.4), 12.1 – 12.3
Week 7: 12.4 – 12.6, (Omit 12.7 – 12.10), 13.1, 13.2
Week 8: 13.3 – 13.5, 14.1, 14.3, 14.4
Week 9: 14.5, Test III, 15.1 – 15.3
Week 10: 15.5, 15.6, 15.8, EXAM
X. NOTES TO THE INSTRUCTOR
1. Chapter 1 is mainly review. You might give the suggested Chapter Review
exercises to
cover all but sections 1.3, 1.4, 1.9, and 1.15. Note that some students may not
have had
geometry and the prerequisite course does not use calculators. In section 1.3,
note the
measurement conventions before problem 7 in the exercise set.
2. Chapter 2 is also mainly review. Students will use these skills in solving
linear equations.
Calculators may be used. In section 2.4, you may wish to illustrate converting
mixed
numbers to improper fractions to perform operations. There is no example of
multiplying or
dividing mixed numbers. In 2.5, negative and zero exponents are probably new to
some
students. Section 2.6 is also probably new material. The main use of scientific
notation in
this course is recognizing if a calculator switches to scientific notation as it
does
computations. Performing operations in scientific mode is optional.
3. In Chapter 3, emphasize 3.1 and 3.2 using 3.3 – 3.6 to reinforce the basic
ideas. Section 3.7
should be covered, but not emphasized. Note the conversions are covered on the
reference
card in the front of the text.
4. In Section 4.2, the text discusses precision for fractions of an inch but
gives no examples.
Do not include any exercises after 21 unless you illustrate one in class.
Emphasize 4.5 and
4.6.
5. In Section 5.2, the suggested homework list includes all odd problems
since this is new and
most students will need the practice.
6. Note that rules for precision and accuracy are not used in this chapter.
There are no
examples with decimals in 6.1 – 6.4. Only a few exercises include decimals. None
are
included in the suggested homework problems for these sections. Section 6.4
includes some
simple rational equations and reminds students that the denominator may not be
zero, but
there are no exercises or examples with a possible solution that would make the
denominator zero. Be sure you do not include any on a test. Emphasize
applications,
Section 6.6. In Section 6.8, the text notes that you may substitute values first
and that this is
usually preferred if a calculator is used. (Students do not have to solve for
the desired
variable first.)
7. Note that rules for precision and accuracy are not used in this chapter.
In Section 7.1, omit
medical examples (9 and 10). Ratio and proportion should be a review for the
students.
8. In Section 8.3, you may omit parallel and perpendicular lines.
9. Chapter 12. Remember that geometry may be new for some students. Students
should be
able to use the formulas, you do not have to require them to memorize the
formulas.
Memorizing a few basic formulas, including the Pythagorean Theorem, is probably
good.
10. In Chapters 13 and 14, all angles are in degrees. Students should
memorize at least the
definitions of sine, cosine and tangent.
11. We are interested in descriptive statistics and will not deal with
inferential statistics in this
course. They may use standard deviation later in quality control issues. In
Section 15.6, the
text illustrates the mode but does not include any exercises. You should not
test on modes.
XI. SUGGESTED HOMEWORK
Elementary Technical Mathematics 9th ed by Ewen and Nelson
If you wish to assign more problems, make sure they are similar or appropriate
for the class.
| Section |
Page |
Problems |
| CR |
91 |
1, 3, 5, 7, 13 – 33 (odd), 39 – 63 (odd) |
| 1.3 |
15 |
5, 7, 11, 13, 17, 19, 21, 27, 31, 35 |
| 1.4 |
20 |
1, 5, 9, 15, 19, 23, 25, 29 |
| 1.9 |
50 |
3, 9, 13, 17, 23, 29, 35, 37, 41, 49, 53 |
| 1.15 |
86 |
1, 7, 13, 15, 17 |
| 2.1 |
98 |
11, 15, 21, 27, 33, 39, 45, 49, 55, 61, 67 |
| Section |
Page |
Problems |
| 2.2 |
100 |
1, 7, 11, 17, 23, 31, 37, 41, 45, 49, 51, 55, 59 |
| 2.3 |
102 |
7, 9, 11, 13, 23, 31, 37, 43, 53, 59, 65, 71, 75,
79 |
| 2.4 |
106 |
1, 5, 9, 13, 17, 21, 27, 31, 33, 37, 41, 43, 45 |
| 2.5 |
110 |
1, 3, 5, 7, 13, 19, 23, 27 |
| 2.6 |
115 |
1, 5, 9, 17, 19, 23, 29, 31, 43, 47, 55 |
| 3.1 |
127 |
1 – 23 (odd), 35, 37, 39 |
| 3.2 |
129 |
7 – 27 (odd), 49 – 61 (odd) |
| 3.3 |
132 |
7 – 23 (odd), 35, 39, 43, 47 |
| 3.4 |
135 |
7 – 25 (odd), 39, 43, 47, 49 |
| 3.5 |
138 |
7 – 31 (odd) |
| 3.6 |
140 |
1 – 19 (odd) |
| 3.7 |
143 |
1, 5, 9, 13, 15, 23, 31, 51 |
| 4.1 |
151 |
1, 5, 9, 13, 19, 23, 27, 31, 35 |
| 4.2 |
155 |
1, 5, 9, 13, 17, 21 |
| 4.3 |
158 |
1, 5, 9 |
| |
161 |
1, 5, 9 |
| 4.4 |
164 |
1, 5, 9, 13, 15 |
| |
167 |
1, 5, 9, 13, 15 |
| 4.5 |
172 |
1, 5, 9, 13, 17, 21, 25, 29, 35, 39, 43, 49, 51,
53 |
| 4.6 |
175 |
1, 5, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 45 |
| 4.7 |
178 |
1, 5, 9 13, 17, 25, 29, 33, 37, 39 |
| 5.1 |
203 |
1, 5, 9, 11, 15, 17, 21, 25, 29, 33, 37, 41 |
| 5.2 |
207 |
1 – 77 (odd) |
| 6.1 |
228 |
1 – 59 (odd) |
| 6.2 |
230 |
1 – 29 (odd) |
| 6.3 |
232 |
1, 5, 9, 13, 17, 21, 25, 31, 35, 39, 45 |
| 6.4 |
237 |
1, 5, 9, 13, 17, 21, 27, 31, 35, 39 |
| 6.5 |
238 |
1 – 25 (odd) |
| 6.6 |
242 |
1, 3, 5, 9, 11, 13, 15, 17, 21, 23 |
| 6.7 |
246 |
1, 5, 9, 15, 19, 23, 27, 29, 33 |
| 6.8 |
248 |
1, 5, 9, 13, 17, 21 – 29 (odd) |
| 7.1 |
259 |
1, 5, 9, 13, 17, 21, 25, 29, 35, 37, 41, 45, 49 |
| 7.2 |
264 |
13, 17, 21, 25, 27, 31, 35, 41, 45, 55, 59, 69,
73, 77 |
| 7.3 |
270 |
3, 9, 17, 21, 23, 25, 33, 35, 39, 43, 47 |
| 7.4 |
274 |
1, 5, 7, 11, 15, 17, 19, 21, 25, 29, 31, 35, 39 |
| 8.1 |
283 |
1, 5, 9, 13, 17, 21, 25, 29, 35, 37 – 65 (odd) |
| 8.2 |
290 |
1 – 29 (odd), 43, 45 |
| 8.3 |
296 |
1- 25 (odd) |
| 12.1 |
373 |
1 – 35 (odd) |
| 12.2 |
377 |
1 – 11 (odd), 15, 23, 25, 29, 35, 41 |
| 12.3 |
384 |
1 – 15 (odd), 19, 23, 27, 33, 35, 39, 43, 45 |
| 12.4 |
389 |
7, 9, 11, 17, 19 |
| 12.5 |
394 |
1 – 11 (odd), 15, 17, 21, 25, 29, 33, 35 |
| 12.6 |
402 |
1 – 29 (odd) |
| Section |
Page |
Problems |
| 13.1 |
435 |
1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49,
53, 57, 61, 65, 69 |
| 13.2 |
438 |
1, 5, 9, 13, 17, 21 |
| 13.3 |
440 |
1, 5, 9, 13, 17, 21 |
| 13.4 |
442 |
1, 5, 9, 13, 17, 21 |
| 13.5 |
445 |
1, 5, 9, 13, 17, 21, 23, 25, 29, |
| 14.1 |
459 |
1, 5, 7, 13 – 35 (odd) |
| 14.3 |
465 |
1, 5, 9, 13, 17, 19 |
| 14.4 |
471 |
1, 3, 5, 9, 13, 15, 19 |
| 14.5 |
474 |
1, 5, 11, 13, 23, 25, 29 |
| 15.1 |
483 |
1 – 23 (odd) |
| 15.2 |
487 |
1, 5, 9, 13, 15 |
| 15.3 |
488 |
1, 9, 11, 13 |
| 15.5 |
493 |
1, 5, 9, 13, 15, 19 |
| 15.6 |
495 |
1, 5, 9, 13, 15, 19, 21, 25 |
| 15.8 |
505 |
1, 5, 9, 13, 15, 19 |
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