Fall 2000 Math 74: Student’s Guidelines

Text: College Algebra and Trigonometry - Basics Through Pre calculus, 3rd Edition

By John J. Schiller and Mary A. Wurster

Prerequisites: Math placement or grade C or better in Math 73

Important Note:

1. A grade of C or better in Math 74 is required to register for Math 75 and Math 85

  1. Chapters P, 1 and 2 in the text contain materials you should have had before. Therefore these chapters will only be very briefly reviewed in the class. All topics from these chapters are frequently used in subsequent chapters. Therefore you should be very familiar with these chapters. If you have difficulty with these chapters, it indicates you do not have enough background to continue in Math 74, and may want to transfer to Math 45 or Math 73. You may want to refresh these chapters early enough in the course with help from the tutoring center.
  2. Math 74 satisfies only the first level Math core requirement.

TUTORING: Free one on one tutoring is available at Mathematics and Science Resource Center (MSRC), located at Room 18, Curtis Hall. Tutoring schedule is posted in Room 18. A few copies of the Student’s Solution Manual are available in Room 18 of MSRC and at the Mathematics Library, fourth floor, Wachman Hall. If you could not do a problem, or your answer does not match the answer in text, this is the book that will help you.

TESTS: There are four tests and a comprehensive final. There are no re-tests in this course.

Test 1. Test 1 is a departmental test. For MW class test 1 is on September 13 and for TTh class test 1 is on September 14. There are 15 questions in this test. There is no sample test for test 1.

Test 3. Test 3 is a departmental test given during the week of November 5. You will be given a sample test before test 3.

GRADING: Each test is worth 15% of your final grade and final is worth 25%. Homework, quizzes and attendance counts for 15% of your grade.

HOMEWORK: The instructor will collect homework on a regular basis and grade a few problems. Before you submit the homework, make sure you have i) done the homework in the same order as given in text ii) written neatly and legibly iii) stapled the papers and iv) written your name and ID # on top of first page.

FINAL: Math 74 has a comprehensive uniform final, given on Thursday December 14, 2:00 – 4.00 p.m. Room assignments for the final will be announced later.

Fall 2000 Math 74: Syllabus

 

Chapters P, 1 and 2 Basic Algebra etc 4 lecture hours

Briefly go over the review exercises in Chapter P and review exercises corresponding to sections 1.1, 1.2, 1.3, 1.4 and 1.5 in Chapter1; sections 2.1, 2.2, 2.4, 2.5 and 2.6 in Chapter 2.

Test 1. For T Th class this test is on September 12. For MW class this test is on September 13. There are 15 questions in this test. If you do not do well in this test you should seriously consider transferring to Math 45 or Math 73. September 18 is the last day for making this transfer.

Chapter 3 Algebra and Graphs of Quadratic Expressions 6 lecture hours

3.1 Quadratic Equations.

3.2 Complex Numbers
    1. Equations Reducible to Quadratic Form
    2. Quadratic Inequalities

3.5 Applications of Quadratic Equations and Inequalities

    1. Circles and Parabolas (Skip applications on page 219). Includes i) finding x and y intercepts of a parabola, vertex, axis of symmetry and drawing the graph. See supplementary exercises. ii) drawing graphs of circles given radius, center etc.

Chapter 4 Functions and Their Graphs 6 lecture hours

4.1 Functions. Includes i) finding f + g, f - g, f .g, f/g, f (B ) g and g (B ) f given functions f and g. ii) finding domain and range of these functions as well as evaluate them at a given point.

4.2 Polynomial Functions. Includes i) graphs of common functions like y = , y = , y = , y = 1/x , y 2 = x, y = 1/(x-2) etc. Do some examples in class to illustrate these graphs. ii) check for symmetry with respect to x - axis, y - axis and origin. iii) properties of odd and even functions and how to check if a given function is odd or even.

    1. Rational Functions (skip oblique asymptotes)
    2. Algebraic Functions. Includes graphing piecewise functions. See supplementary exercises.
    3. One to one and Inverse functions. Includes i) checking if f(x) is the inverse of g(x) ii) finding the inverse of f(x) iii) graphing f(x) and its inverse on the same graph. See supplementary exercises.

Test 2

Chapter 5 Exponential and Logarithmic Functions 7 lecture hours

5.1 The Exponential Function and its Graph

5.2 The Logarithmic Function and its Graph

5.3 Properties of the Logarithm (discuss using calculators instead of log tables)
    1. Applications and Exponential and Logarithmic Equations (do only compound interest and exponential growth and decay)

Chapter 6 Trigonometric Functions of Angles 6 lecture hours

6.1 Angles and Their Measurement (discuss using calculators, not tables). Includes i) converting 44" 12’30" to decimal degrees as 44.2083" and 44.235" as 44" 14’6" etc. ii) finding smallest positive angle co-terminal with a given angle. See supplementary exercises.
    1. The Trigonometric Function (use calculators, not tables). Includes finding, using a calculator, i) Sin (649)" , Cos (.236) etc.
    2. Solving Right Triangles. Includes i) applications problems using angle of elevation and depression ii) properties of Sin(-x), Cos(-x) and Tan(-x). See supplementary exercises.
    3. Law of Sines (Skip all derivations and ambiguous case on page 369)

6.5 The Law of Cosines (Skip applications on page 379 and all derivations on page 376)

Test 3. This test is during the week of November 5. Since this is a departmental test, you will receive a sample test before this test.

Chapter 7 Analytic Trigonometry 8 lecture hours

7.1 Trigonometric Functions with Real Domains

7.2 Graphs of the Trigonometric Functions (Skip graph of secant, cosecant and cotangent) Should know graphs of Sin(x), Cos(x) and Tan(x).
    1. Amplitude, Period, and Phase Shift (Skip phase shift and graphs of sums of trigonometric functions)

7.5 Inverse Trigonometric Functions (do only inverse sine, cosine and tangent. Use

calculator, not table). Includes i) finding exact value of Sin -1, Cos -1( -1),

Csc -1 ( 2) etc. without using a calculator. ii) finding, using a calculator, q if Sinq = .565, Cosq = .1903, Tanq = 5.675 etc. iii) finding, using a calculator, Sin -1(.2342),

Cos -1(-.0318), etc. See supplementary exercises.

Test 4

4 lecture hours

7.6 Basic Identities

    1. Sum and Difference Identities (Do only the four formulae for sine and cosine on page 438. Do not derive them). Includes use of sum and difference formula to find

i) Sin (15)° , Cos (105)° , Sin(15)° Cos(45)° + Cos(15)° Sin(45)° , Cos (x+p /2), Sin (x - p ) etc. See supplementary exercises.
    1. Multiple Angle Identities (Do only the double angle formula for sine and cosine)

 

The total number of scheduled lecture hours for Math 74 is 43 hours. The syllabus includes 41 hours of lecture hours. Please use recitation period to give tests, giving the test back, quizzes etc.

Final

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fall 2000 Math 74: Homework

 

The following exercises in Chapters 1-7 constitute a minimal assignment. Each exercise represents a typical type of problem you are expected to solve. If a certain type of problem gives you difficulty, you should get help at the tutoring center and try more exercises of that type till you understand it.

In addition to the exercises on the list, you should do the "true-false" and "fill-ins" that appear in most sections and the review exercises that appear at the end of each chapter. Answers to selected exercises are given in the back of the book.

Section Page Exercise number

Chapter P

Review 45 all 1 – 20

Chapter 1

Review 93 - 94 1-15, 19, 20, 21, 23, 24, 28, 31, 32

Chapter 2

Review 173 all 1 – 34

If you have difficulty with these review problems, you should do more problems from each section in Chapter P, 1 and 2.

Chapter 3

3.1 184 - 186 odd 11 - 19 and 23 - 31; 35, 37, 45, 47, 51, 53, 55, 61, 65, 67, 71, 73, 75, 77

3.2 192 - 194 odd 11 - 21 and 27 - 33; 39, 4 1,47,49

3.3 197 - 198 odd I 1 - 15, 21 - 29, and 31 - 3 5

3.4 202 21, 23, 25, 27, 37, 39, 41, 43

3.5 210 - 201 odd 1 – 31

3.6 221 - 223 odd 11 - 19, 21 - 27, 31 - 39, 41, 43, 45, 47, 49, (do 45, 47 and 49 by completing the square) 51, 53

Chapter 4

4.1 256 - 257 11, 13, 17, 21, 33, 35, 37, odd 45 - 55, 57, 59, 61, 63, 65, 69, 71,73, 75

4.2 265 - 266 odd 11 - 19, 20, 21, 22, 25

4.3 276 - 277 odd 11 - 17, 21, 22, 24, 29, 30, 31

4.4 284 odd 11 - 35

4.5 294 - 295 odd 11 – 19, 23, 25

 

Chapter 5

5.1 312 - 313 11, 13, 17, 25, 27, 34 - 37, 44, 45, 48

5.2 317 - 319 11, odd 15 - 31 and 49 - 53

5.3 325 - 326 odd 11 - 31 and 35 - 45

5.4 336 - 338 odd 1 - 17

Chapter 6

6.1 346 - 348 odd 11 - 23

6.2 359 - 360 odd 11 - 37 and 45 - 55

6.3 366 - 367 odd 11 – 23

6.4 381 odd 11 - 19

6.5 381 - 383 odd 11 – 19

Chapter 7

7.1 388 - 389 odd 11 - 27

7.2 399 - 400 odd 11 - 17 and 21 - 25

7.3 407 - 409 odd 11 - 25, 33, 37

7.5 426 - 427 odd 11 - 35

7.6 434 - 435 odd 11 - 33 and 43 - 47

7.7 441 - 442 odd 11 - 27 and 31 - 35; 39, 43, 44

7.8 448- 449 odd 11 – 25, 31, 33, 35, 37, 39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

From: K Raghunandanan September 1, 2000

To: All Math 74 Instructors

Subject: Changes for this semester. Please read carefully.

    1. On the first day of class students should receive a copy of the syllabus, students guidelines and list of homework and supplementary exercises. In order to finish Chapters P, 1 and 2 in time for test 1, you have to lecture at least for an hour on the first day of your class. There should be 4 lecture hours before giving the first test. In order to do that there is no recitation period (all lectures) till the first test. See 5 below.
    2. Now there are three lecture hours and one recitation period. If your section meets on MW it works out better if Monday first period is lecture and second period is recitation and Wednesday is all lecture (no recitation). For TTh sections, Tuesday first period is lecture and second period is recitation and Thursday is all lecture (no recitation). This will allow students enough time to try their homework before the recitation.

      3.  

    3. You will be assigned a CA or TA mostly to grade homework and therefore homework should be collected regularly and at least few problems graded which is counted towards the final grade. CA’s work 4 hours a week and TA’s 10 hours a week.
    4. This semester Test 1 and Test 3 are made from a test bank. There will a sample test for Test 3 and not for test 1. The other tests, Test 2 and 4 are made up by the instructor. For MW class, Test 1 must be given on September 13 and returned to the student before September 18.. TTh class test 1 must be given on September 14 and returned to the students before September 18. The reason for this is that September 18 is the last day for registration schedule revision. In case a student wants to switch to Math 73 or Math 45, this will give them a chance to do so. You can pick up test 1 on the day of the test from Trish in the Math. office.
    5. Test 3 is a departmental test and must be given during the week of November 5. A sample test will be given to you before that. You can pick up test 3 on the day of test from Trish in the Math. office.
    6. Chapters 4 through 7 is the core of Math 74. Please make every effort to cover all these chapters. Do not get bogged down with Chapters P, 1, 2 and 3. All the topics in these chapters are covered in detail in Math 73, which is a prerequisite for Math74. Just do review exercises in Chapters P, 1 and 2 as a review before giving the test 1. If a student is having trouble in these chapters please encourage that student to transfer to Math 73. Many of the calculus teachers complain that their students are very weak in algebra. The only place we can rectify this problem is Math 73 and Math 74. We need your help.

8. As before final is comprehensive and is given on Thursday December 14, 2:00 – 4:00 p.m.

This is the course that prepares a student to take any calculus course. Therefore it is very important that the syllabus is covered. To make all sections of Math 74 as uniform as possible, please follow the above guidelines very closely. Thank you for your co-operation.