**SYLLABUS **

Fall Semester, 2001

**Course:** M1030-9, Introduction to Quantitative Reasoning

(meets MWF, 2:00pm - 2:50 pm, ST 205)

**Instructor:** Dr. A.D.Roberts, JWB 312, 581-6710;

e-mail: aroberts@math.utah.edu

webpage: http://www.math.utah.edu/~aroberts/schedule.html

**Office Hours: **MWF,1:00pm -1:50pm; also at other times by appointment

**Text: ** __Using and Understanding Mathematics: A Quantitative Reasoning __ __Approach,__ Bennett and Briggs (second edition)

**Prerequisite:** Math 1010 (Intermediate Algebra)

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**Course Description**

In this course we will consider how mathematics is used to examine problems and questions that arise in such areas as the Social and Behavioral Sciences, Business, and the Liberal Arts. In particular we will focus on the correct use of numbers, measurements, and percentages in the real world and we will examine models to describe patterns of growth and change. The course material will be drawn from chapters 1-4 and 8-10 as indicated in the tentative schedule below.

**Attention: **The M1030 course is primarily intended for students who seek only to satisfy the QA (quantitative reasoning - course A) requirement for the bachelor's degree and whose further study of mathematics will be limited to statistics. This course does NOT satisfy either a M1090, or a M1050-M1060 prerequisite for other courses.

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**Grading **

Quizzes (lowest two scores dropped) 30%

Group Projects (2) 30%

Midterm 15%

Final Examination __ 25%__

Total 100%

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Notes

1. **Prerequisite, M1010: **To be successful in M1030 you need to have a working knowledge of the algebra and geometry concepts covered in M1010 (Intermediate Algebra). Basically this means you should able to manipulate variable expressions, solve simple equations, work with fractions and exponents, and know the basic properties of simple geometric shapes.

A short diagnostic test covering this material is attached to help you evaluate your background knowledge. I strongly advise you to give yourself this test and then check your answers with the solutions that will be given out in class during the first week. In the first week of class we will review *some* of the basic concepts of algebra and geometry. This is *a review only and* *cannot provide* the level of knowledge of Intermediate Algebra that students' require for Math 1030.

2. **Quizzes/Midterm: ** There will be about 6 twenty-minute quizzes. Generally these quizzes will be given on Fridays, although the first and last quiz are on Wednesdays. These quizzes will be based on class discussions and homework assigned. The lowest two quiz scores will be dropped to make reasonable accomodations for sickness, family emergencies, et cetera. Since the two lowest quiz grades will be dropped, no makeups will given for missed quizzes. A fifty minute midterm covering Chapters 1-4 will be given on Monday. October 15, 2001.

3. **Group Projects:** Working in groups of 2-3, students are required to submit two projects during the semester - projects are to be selected from an approved list that will be handed out in class. The first project is due on Monday, October 22nd (10th week); the second project is due on Wednesday, December 5th (16th week). Projects must be typewritten on 81/2 x 11 paper - but math formulas, equations, or diagrams can be written in by hand if done neatly. The analysis of the problem, organization of work, grammar, and spelling will all be considered in the project grade. We will discuss project expectations and the list of topics for the first project during the second week of class.

4. The **Final Examination** is comprehensive and is scheduled for Monday, December 10, 2001, from 8:00am to 10:00am.

5. The **Americans with Disabilities Act **requires that reasonable accommodations be made for students with physical, sensory, cognitive, systemic, learning, and psychiatric disabilities. Please contact me *at the beginning of the semester *to discuss any such accomodations for the course.

6. **Withdrawals: **Please note that the last day to withdraw from the class is Friday, March 3, 2000. Check the Fall Class Schedule for details.

7. **Helpful Hints: **

• Form a study group. Explaining your ideas on homework or examining another student's solution develops a stronger grasp of the mathematics involved.

• Study *regularly *throughout the week, reading ahead before the next class.

• On homework, don't simply jump back and forth between the assigned problems and examples done out in the text. Remember, you won't have the text as a guide when you take a quiz or test! Do your own work first. If your answer doesn't agree with that in the text, examine your work for mistakes before comparing your work with examples from the text.

• Don't underestimate the study time required outside of class - *6 to 9 hours each week - *and read pages 9 - 10, "How to succeed in Mathematics", in the text.

• Make good use of office hours! If you are having difficulty with a concept be sure to get help - earlier rather than later.

__Tentative Schedule__

__Week__ __Topic__

**1 ** (8/22) __Introduction and Algebra Review__

**2** (8/27) __Ch1: Critical Thinking__

Quiz 1 on 8/29; Project 1 topics given out in class

**3 ** (9/3) Ch1 (Continued; Ch 2: Problem Solving Tools

Project 1 groups determined

**Monday Holiday** (Labor Day)

**4 ** (9/10) __Ch2 (Continued)__

Quiz #2

**5 ** (9/17) Ch2 (Continued); Ch3: Numbers in the Real World

**6** (9/24) __Ch3 (Continued)__

Quiz #3 Project 1 discussion

**7 ** (10/1) __Ch4 (Financial Management)__

**Fall Break** (Thursday,10/4 - Friday,10/5)

**8 ** (10/8) __Ch4 (Continued)__

**9 ** (10/15) __Ch4 (Continued); Ch8: Exponential Astonishment__

Midterm 10/15; Project 1 Discussion

**10 **(10/22) __Ch8: (Continued) __

Project 1 due 10/22; Project 2 topics given out in class

**11 **(10/29) __Ch8 (Continued); Ch9 (Modeling Our World__)

** **Quiz #4; Project 2 groups determined

**12** (11/5) __Ch9 (Continued)__

**13** (11/12) __Ch 9 (Continued)__** **

Project 2 Discussion; Quiz #5

**14** (11/19) __Ch 9 (Continued); Ch 10, SecA (Fundamentals of Geometry)__

**Thanksgiving Holiday** (Thursday 11/22-Friday 11/23)

**15 **(11/26) __Ch 10(Continued)__

Quiz #6

**16 ** (4/24) __Ch 10(Continued)__

Project 2 due 12/5 ** **

**Homework **(Please note that changes may be made in this list as the course progresses.)

Ch 1

Sec C: odd problems 1-40; 43,45,51,53; Sec. D: 3,5,7,11,13,15,17,19,23,27,31,33

Ch 2

Sec A: odd problems 1-30; 35,37,40; Sec. B: 1.3.5.7.9.; odd problems 13-23; 31,33,35,37,41,43,45,47,49; Sec. C: 9.10.11.13.15.17.21

Ch 3

Sec A: 1,3,5,7,9,11,15,19,21,23,25,29,31,33,35,41,43,45,47,49,51,53,55,59,61,63;

Sec B: 1,3,5,9,11,15,21,23,29,35,45,47,49; Sec. C: 17,19,25,29,31

Ch 4

Sec A: 1,3,5,7,11,13,15,19,21,23,25,27,28,29,35,37,39,41,43,45; Sec B1,3,5,7,9,11,13,15,19,21,25,31,39,41; Sec C: 1,3,5,7,13,17,21,25,27,33,37,39

Ch 8

Sec A: 1,3,5,13,15; Sec B: 1,3,5,7,11,13,17,19,21,23,25,27,31,33,35,37; Sec C: 3, 5,11,15,17

Ch 9

Sec A: 11,15,17,21,27; Sec. B: odd problems 1-33; Sec. C: 1,3,5,7,9,15,17,19,21,23,25

Ch 10

Sec. A: 9,11,13,15,17,19,21,23,25,27,29,31,33

Diagnostic Test

M1010 is a prerequisite for M1030. This means that you should have a working knowledge of intermediate algebra. This diagnostic test covers some of this background material. You should give yourself this test and then check your answers with the solution sheet provided in class. The first quiz in the class will be based on the material covered in this test. If you have any difficulty with this material please see me before the quiz.

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1. Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from basket to be sure of getting two apples of one kind?

2. There are 150 people in a class. If 80% of them are registered, how many are not registered?

3. Express "three-fifths" as a fractions, a decimal, and as a percentage.

4. Evaluate each of the following if a = 4, b = , c = - 6:

a(b+c) ab + c - c 5b - 3c2

5. Evaluate the following expressions on your calculator:

(250 / (34 + 56))x 27 23 + 6.3 (45 ) 3-

6. Simplify:

a) b) (x-2 y3 )2 c) (x-5 y4 )2 (x0 y-2 )2

7. If there are 0.76 US dollars in one Canadian dollar, which is smaller, one US dollar, or one Canadian dollar?

8. One number is 4 times a second number. Find the numbers if their difference is 39.

9. If you drive at an average speed of 65 miles per hour, how long will it take you to drive 530 miles? If you can bike a distance of 45 miles in three hours and 15 minutes, what is your average biking speed in miles per hour?

10. The length of a rectangle is 5 inches more than its width. If the area is 50 square inches, find the length and width of the rectangle.

11. Suppose that three-quarters of the freshmen live in a dorm. If two-thirds of the freshmen dorm residents are women, what percentage of the freshman class are women who live in the dorm?

12. Solve for x in the following equations:

3x - 5 = 9 + 7x x2 - 5 = 31 x2 - x - 12 = 0

= | x+3| = 10

13. Solve for x and y in the two simultaneous equations: 3x - 2y = 5 and x + y = 7.

14. Graph the line 5x - 2y = 6. What is the y-intercept?

15. A warehouse contains bicycles, tricycles, and cars. Altogether there are 18 wheels in the warehouse. How many bicycles, tricycles, and cars are there? Give as many answers as possible.

16. A playground is in the shape of a rectangle with a semicircle attached at the shorter end so that the diameter lies along the shorter side of the rectangle. Suppose that the longer side of the rectangle is twice the length of the shorter side and that the radius of the semicircle is 12 feet. What is the perimeter and the area of the playground?

17. Suppose that the ratio of undergraduate students to graduate students in an institution

is 18:7. What percentage of the student body are graduate students?

18. Suppose that your annual tuition as a freshmen was $1856. Each year tuition has increased 5%. Now you are in your senior year. What is your annual tuition this year?

19. The company you work for was doing poorly two years ago and as a result everyone took a 10% cut in pay for the last year. The company is doing better now and the CEO has just promised to raise everyone's salary 10% for next year. Does this mean that your salary next year will be same as it was two years ago? Explain.

20. Determine any errors made in the work shown below. Then explain the mistake made.

a) = 1

-5 + 3x = 1

3x = 6

x = 3

b) 2( ) = x

= x + -3

2x = 5x - 15

x = 5x - 17

-4x = - 17

x = -21

c) 5(x2 y3 ) = 5x2 5y3 = 25x2 y3