Precalculus Video Manual - Abeka...Precalculus • T5 Both the video and the video manual will indicate when to give the quiz. The standard amount of time required to give, grade,

VIDEO PROGRAM

PrecalculusVideo Manual

P.O. BOX 17600, PENSACOLA, FL 32522-7750, U.S.A.

PENSACOLA CHRISTIAN COLLEGE

A ministry of

PrecalculusVideo Manual Two Semesters

Textbooks & MaterialsStudent Materials

1. Texts 115797 • Precalculus with Trigonometry and Analytical Geometry 147796 • Precalculus Practice Exercises

2. Quizzes / Tests 115827 • Precalculus Quizzes / Tests

3. Supplies (may be purchased from a local vendor) • Spiralnotebook(forclassnotesandhomework) • Assignmentnotebook • ScientificCalculator

Teacher Materials1. TeacherKeys 139289 • Precalculus SolutionKey 178519 • Precalculus TeacherQuiz/TestKey

2. Optional 115819 • Precalculus with Trigonometry and Analytical Geometry TeacherEdition

Precalculus Video ManualCopyright © mmxii, mmix Pensacola Christian College All rights reserved. Printed in U.S.A.This manual and the videos that are part of the course are protected by copyright law. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, or by license from any collective or licensing body, without permission in writing from the publisher. The curriculum (lesson manual) is leased only and remains the property of Pensacola Christian College. The agreement with Pensacola Christian College is that you will not sell, lend, share, or give away the curriculum since the right to use the curriculum is not transferable. The curriculum must be destroyed upon completion of the course.

ContentsIntroduction ....................................................................T4SubjectDescription .........................................................T4

Responsibilities of the Classroom Teacher ..............T4Class Schedule ..........................................................T5Additional Help for Students ...................................T6

Giving/GradingQuizzesandTests ................................T6AveragingGrades ............................................................T7

Daily Guides (Lessons 1–170) ........................................1

Appendix ......................................................................... A1

Mr. Eric Collins• M.S., Educational Administration

• 20 years teaching experience

Video Teacher

T4 • Precalculus

The purpose of this course in Precalculus is to teach the student how to select and apply vari-ous techniques to solve mathematical problems in a skillful, systematic, and logical manner. Students will learn the underlying principles of trigonometry and the interrelationships of lines and functions with graphical and analyti-cal problem-solving techniques from a study in analytic geometry. The study culminates with an introduction to selected calculus topics.

Each video lesson is about 45 minutes in length and will best fit into a 50-minute class period. Five minutes is allowed for you to check homework and for students to present homework problems. Plan to give quizzes and tests yourself.

Establish accountability on the part of each stu-dent. Let students know that you expect them

to listen, to learn, and to participate every day. You may wish to have a student be respon-sible to stop / start the video.

When a student has been absent, check the Daily Guide to see what homework he needs to make up. He may also need to watch video lessons he missed or be helped by another student or yourself in order to catch up with the class.

Note: Lessons have been videotaped for only 170 days, although most school years are longer. The extra days are allowed for the scheduling of field trips or special school events.

1. Checking Equipment. Check equipment each day to make sure it is running prop-erly. Be ready to start on the right lesson.

2. Following the Daily Guides. Check Daily Guides each day to determine specific responsibilities for that day.

3. Checking Homework. Check daily at the beginning of class to see that each student has completed his homework. Although students may not completely understand a problem, they should at-tempt every problem. Spot-check this homework quickly (using the Solution Key) to see whether students are completing the homework problems accurately. This check will help you to identify difficulties early. It is not necessary to grade the homework.

4. Giving Practice Exercises. You will be assigning and dictating answers for the Pre-

calculus Practice Exercises at the beginning of most lessons from the third week of school until the last month. These short exercises are designed for students to review and practice mathematical skills and concepts which have been studied in previous courses. Answers to the prac-tice exercises are found in the Appendix of this manual.

5. Giving Quizzes and Tests. You will be giving quizzes and tests as they occur in lessons. Plan to remain in the classroom during any quiz or test. Grade quizzes in class with students and grade tests after school. Tests and quizzes are found in Precalculus Quizzes / Tests. Further quizzing and testing information is provided in the Giving / Grading Quizzes and Tests section of this manual.

Introduction

Subject DescriptionResponsibilities of the Classroom Teacher

Precalculus • T5

Both the video and the video manual will indicate when to give the quiz. The standard amount of time required to give, grade, and collect a quiz is 10 minutes. If an unusual amount of time is required for a quiz, it will be indicated on the video and in the video manual. The quizzes are located in Precalculus Quizzes / Tests; quiz answers and suggested point values are located in the Precalculus Teacher Quiz / Test Key. Have students take the first quiz as they watch the video. View this first quiz with them to note the proce-dure used by the video teacher.

4. Review and Lesson. After homework has been discussed, the video teacher reviews important principles and presents new material. Have students follow the lesson as they are instructed on the video. It is vital that students pay close attention, use their books, and follow the question-and-answer exchange given on the video. Tell students to answer the teacher’s questions in their minds (or aloud) and to follow closely the answers given by the video students. Close attention to this portion of the video lesson will help them to learn and to retain the facts and principles they need to know.

5. Practice. Students will be assigned prob-lems to practice from the text. If students are not having difficulty with the work, assign an appropriate number of students to put their work on the chalkboard and present it to the class. Then, go directly to the explanation on video.

6. Homework Assignment. The video teacher gives the homework assignment at the conclusion of each lesson. Students should copy this assignment into their assignment notebook.

The following is a typical class schedule for Precalculus with suggested times for your students to participate.

1. Homework Check. Begin each day with homework check. Walk around the room and look at each student’s work; spot-check for accuracy. Assign practice exer-cises for students to do while you check homework. This check should be com-pleted within 5 minutes. Before turning on the video for homework discussion, go over the answers for the practice exercises. The manual lessons give more details concerning practice exercises. (See lesson 11.) Certain exercises which are noted in the Daily Guides are graded. Grade these practice exercises using the same proce-dures as for grading quizzes.

2. Homework Presentation. At the begin-ning of each video lesson, homework problems are discussed and answered. Video students write their homework problems on the chalkboard and present their work and the answers. Students should compare their work with the answers on video and make any correc-tions needed. (If your students are doing especially well, you may occasionally wish to have them explain the homework them-selves and then go directly to the lesson. If students are having difficulty, you may need to allow them to see the homework presentation on video first and then briefly explain the problems again themselves before going on to the lesson. Your goal, of course, is for students to really under-stand—not merely listen to—the video explanations.) At the end of the Home-work Presentation each day, have students write at the top of their homework the number of correct answers they had for that day.

3. Quizzes. Most quizzes are given before the homework presentation on video.

Class Schedule

T6 • Precalculus

If you have a student who needs additional help, consider assigning additional problems from the textbook. Have students who are having great difficulty with the assigned practice view

the explanations that are given on the video. You might also have a student who does well help other students, perhaps once each week as a help class.

Additional Help for Students

1. Have students clear their desks and take out one clean sheet of paper, a pen, pencil, and calculator. Students should take quizzes in pencil and grade them in pen.

2. Distribute quizzes. (The quizzes are located in Precalculus Quizzes / Tests.) Have stu-dents write their name and the date at the top of the quiz.

3. Have students use the sheet of paper as a cover sheet. They should move it down to cover their answers as they take the quiz.

4. When you have finished giving the quiz, instruct students to put their pencils away (off their desks) and to grade in pen. Have students exchange papers for grading. Tell them to sign the paper they will be grading.

5. Give instructions for grading—how many points to deduct for each wrong answer and how to mark the quiz. (Having students grade quizzes in a uniform manner saves you time when you go through them later.)

6. Give correct answers. (The answers and suggested point values are in the Precalculus Teacher Quiz / Test Key.)

7. Have students figure the final grade by subtracting from 100 the number of points missed.

8. If a student has a question about the paper that he is grading, have him place a question mark both by the number in question and by the grade at the top.

9. Collect quizzes. Instruct students to return the papers to their owners, who will check them briefly and pass them to the front. The quiz should take approximately 10 minutes.

10. Go through the quizzes later, checking them for question marks, adjusting the scores (if necessary), and writing the grade in red at the top. Record the grades.

Giving / Grading Quizzes and TestsProcedure for Giving / Grading Quizzes

Procedure for Giving / Grading Tests 1. Have students clear their desks of every-

thing except two clean sheets of paper (one for a cover sheet and one for a checksheet), two pencils, and a calculator.

2. Distribute the tests. (Tests are located in Precalculus Quizzes / Tests.)

3. Explain any special directions for the test. Also, tell students what they are to do when they finish the test (where to turn in their papers, what to study, etc.).

4. Have students take the test in pencil, writ-ing the answers directly on the test paper. Have them keep their answers covered at all times with the blank sheet of paper.

5. After students finish the test, they use the check sheet to rewrite problems and check their answers. Some problems can be checked by rereading the question and checking the answer for accuracy.

6. Always watch your students until all of the tests and check sheets have been turned in.

Precalculus • T7

grades in your grade book until after going over the test in class.

7. Have all tests graded and ready to return in the next lesson.

7. Check that all tests have been collected. Grade the tests yourself. Do not grade tests in class. Answers and suggested point values are given in the Precalculus Quiz / Test Key. It is best not to record

1. Have students clear their desks of every-thing except a pen. Distribute graded tests.

2. To go over the test, ask if a student in the class has all of the answers correct in the first section. Choose such a student to read the answers in that section. Continue this procedure until all of the answers have been given. Answer any questions students may have about a particular test question. Have someone work a problem on the chalk-board if needed.

3. Watch students carefully while you are going over a test. They should not have any pencils out while they have graded tests.

4. If students find a question that has been graded incorrectly, they should write (in pen) the number of the incorrectly graded question with a question mark at the top of the first page.

5. Collect tests, check any question marks, and record grades.

Procedure for Going over Graded Tests

Grades are averaged at the end of each nine-weeks period. In your grade book, record the grades of tests in red ink and the quiz grades in blue or black ink. At the end of the nine-weeks period, follow this procedure:

1. Average the quiz grades, including the practice exercises average. This is the quiz average and counts as one third of the nine-weeks grade.

2. Average together the tests that occurred during the nine weeks. This is the test average and counts as one third of the nine-weeks grade.

3. The cumulative exams (Nine-Weeks or Semester or Final Exam) count as the final one third of the nine-weeks grade for that quarter.

Example:

Quiz average: 96 Test average: 94 Cumulative test: + 92

282 ÷ 3 = 94% (Nine-weeks grade) 4. Figure a semester average by averaging the two nine-weeks grades for that semester.

Example:

First nine-weeks: 94 Second nine-weeks: + 86

180 ÷ 2 = 90% (Semester grade)

Averaging Grades

Precalculus

Daily G

uides

Daily Guides

It is IMPORTANT . . .

to train the student to respond along with the video class as they review, have class drill, and respond to class questions. This is most effective in student mastery of the subject content and emphasizes what the teacher considers important. Daily learning is reinforced here.

Student test scores will usually reflect this mental participation—either for good or for bad.

The classroom video teacher from time to time may mention things to enhance the class that your students may or may not be able to participate in. The video manual will not necessarily mention such activities.

Lesson 1Materials Needed:

Precalculus with Trigonometry and Analytical Geometry (optional—to show students)

Teacher Instructions: 1. Prepare seating chart. Assign seats before

starting the video. 2. Explain school procedures / rules for your

classroom. 3. Check to see that each student has a copy of

Precalculus with Trigonometry and Analytical Geometry (referred to as the text throughout).

4. Turn on the video. (You may wish to watch the first video lesson with your students to become familiar with classroom procedures.)

5. If time remains after each video lesson, allow students to begin their homework.

Homework:Pages 3–4: Problems 2–10 (even)


Precalculus with Trigonometry and Analytical Geometry Solution Key

Teacher Instructions: 1. Homework Check. Instruct students to have

homework on their desks for you to check when class begins. (Refer to the guidelines for checking homework in the front of this manual.) Check homework for complete-ness. It is not necessary for you to grade homework, but check to see that the work is neat. The video teacher goes over the answers on video. Occasionally spot-check your stu-dents’ answers for accuracy, using the Solu-tion Key.

(During HW check, students review terms, definitions, and facts from les. 1.)

2. Turn on the video.

Homework:Pages 8–9: Problems 2–6 (even)Pages 12–13: Problems 2–8 (even)


Solution KeyQuiz 1 (one for each student; located in the

Precalculus with Trigonometry and Analytical Geometry Quizzes / Tests)

Teacher Key for Quiz 1 (from Precalculus with Trigonometry and Analytical Geometry Teacher Quiz / Test Key)

Teacher Instructions: 1. Homework Check. Check for completeness.

Spot-check for accuracy using the Solution Key.

(During HW check, students review terms, definitions, and facts from les. 1–2.)

2. Turn on the video. 3. Students will take Quiz 1 with the video

class. Watch the video to see the teacher’s procedures. Distribute the quizzes to your students. Ten minutes is allowed for stu-dents to take and grade Quiz 1. You will be giving all future quizzes. (Refer to the front of this manual for instructions for Giving / Grading Quizzes and Tests.)

4. Collect quizzes and record grades. (See the Teacher Quiz / Test Key for answers and sug-gested point values; subtract from 100 the total points missed.) Note: Due to a grading scale change, please use the

point values given in the Teacher Quiz / Test Key rather than the point values given by the video teacher.

Homework:Pages 13–15: Problems 12–28 (every other

even problem)


Solution KeyQuiz 2 (one for each student; located in the

Precalculus with Trigonometry and Analytical Geometry Quizzes / Tests)

Teacher Key for Quiz 2 (from Precalculus with Trigonometry and Analytical Geometry Teacher Quiz / Test Key)

Lessons 1–4 • 3


Spot-check for accuracy, using the Solution Key.

(During HW check, students review the reciprocal and cofunction identities.)


Homework:Page 20: Complete the problems for finding

the six trigonometric function values of 60° and 90°.


Solution KeyQuiz 3 Teacher Key



(During HW check, students construct from memory the special angle chart.)

2. Students clear their desks and take out quiz materials (one clean sheet of paper for a cover sheet, a pen, and a pencil) before quizzes are distributed.

3. Students will take Quiz 3. (Refer to the front of this manual for instructions for Giving / Grading Quizzes and Tests.)

4. Collect quizzes and record grades. (See the Teacher Quiz / Test Key for answers and sug-gested point values; subtract from 100 the total points missed.)


Homework:Pages 22–23: Problems 2, 4, 12, 14 and 20–30

(even)


Solution Key




2. Students clear their desks and take out quiz materials (one clean sheet of paper for a cover sheet, a pen, and a pencil) before quizzes are distributed.




Homework:Page 17: Problems 14–34 (even)


Solution Key

Teacher Instructions: 1. Homework Check. Continue throughout

the year to check HW for completeness and spot-check for accuracy, using the Solution Key. This instruction will not be repeated daily unless something special is to be checked.





Solution Key

4 • Precalculus



(During HW check, students find the trigonometric function values of 30°, 45°, or 60° using a 30°-60°-90° or 45° -45°-90° triangle.)


Homework:Page 26: Problems 1, 4, and 6


Solution KeyQuiz 4 Teacher Key



(During HW check, students construct from memory the special angle chart.)

2. Students clear their desks and take out quiz materials (one clean sheet of paper for a cover sheet, a pen, and a pencil) before quiz-zes are distributed.






Solution Key



(During HW check, students review solving right triangles by reviewing the examples on pp. 24–25.)




Solution KeyAnswer Key for Precalculus Practice Exercises

(located in the back of this manual)

Teacher Instructions: 1. Homework Check. Today, students begin

completing Precalculus Practice Exercises for review and reinforcement (during HW check time—approximately 2–4 minutes).

Have students complete Practice Exercise 1 while homework is being checked for com-pleteness. After homework is checked, give the answers to the practice exercise before turning on the video. Students should write the number correct near the heading of that exercise. Tell students that sometimes the practice exercises will be graded. They will not know when they are graded until after they have completed the problems. These video lesson pages tell you when to grade the practice exercises.

(During HW check, students do Practice Exercise 1.)



Lessons 4–11 • 5


Test 1 (one for each student; located in Precal-culus with Trigonometry and Analytical Geometry Quizzes / Tests)

Teacher Key for Test 1 (from Precalculus with Trigonometry and Analytical Geometry Teacher Quiz / Test Key)

Teacher Instructions: 1. There is no homework to check. 2. Announce the homework assignment. 3. Turn on the video. 4. Students clear their desks and take out test

materials (two clean sheets of paper, one for a cover sheet and one for a check sheet, and two pencils) before tests are distributed.

5. After watching the video for test instruc-tions, give Test 1 over Ch. 1–2. You will be giving all future tests. (Refer to the front of this manual for Procedure for Giving / Grad-ing Tests.)

6. Collect and grade tests. (See the Teacher Quiz / Test Key for answers and suggested point values; subtract from 100 the total number of points missed.)

7. Plan to return graded tests in les. 15.

Homework:Read pp. 39 and 43.


Graded Test 1 (return to students)Teacher Key for Test 1

Teacher Instructions: 1. There is no written homework to check. 2. Hand back and go over graded Test 1. Refer

to the front of this manual for detailed procedures for going over tests. (Follow this procedure for the remainder of the course.) Collect tests and record grades.




Solution KeyAnswer Key for Precalculus Practice Exercises

(Since students do practice exercises every day except test days and the day after tests, these materials will not continue to be listed here. Have them available daily.)

Teacher Instructions: 1. Homework Check.



Homework:Pages 32–33: Problems 2, 6, and 8


Quiz 5Teacher Key



2. Students clear their desks and take out quiz materials (one clean sheet of paper for a cover sheet, a pen, and a pencil) before quiz-zes are distributed.

3. Students will take Quiz 5. (Refer to the front of this manual for instructions for Giving / Grading Quizzes and Tests.) Follow this procedure for the remainder of the year.



Homework:Study for Test 1 over Ch. 1–2.

6 • Precalculus

Lesson 16Teacher Instructions: 1. Homework Check.







Homework:Pages 40–41: Problems 34–62 (every other even)


(During HW check, students do Practice Exercise 6. Grade this as Practice Exercise Quiz 1. Suggested scale: 8 points off for each incorrect answer. Subtract from 100 the total number of points missed. After you have grades for Practice Exercise Quizzes 1–3, average the three grades and count as one regu-lar quiz grade.)




Quiz 6 Teacher Key



2. Give, grade, and collect Quiz 6. 3. Turn on the video.

Homework:Pages 47–48: Problems 18–38 and 46–68 (every

other even)




Homework:Pages 48–50: Problems 40, 42, 44, 72, and 74




Homework:Pages 54–55: Problems 2, 6, 12, and 20–38

(even)


Quiz 7Teacher Key




Homework:Page 55: Problems 40–60 every other even


points missed. After you have grades for Practice Exercise Quizzes 1–3, average the three grades and count as one regu-lar quiz grade.)


Homework:Pages 68–69: Problems 2–12 and 30–40 (even)






Quiz 9 Teacher Key






Test 2Teacher Key

Teacher Instructions: 1. There is no homework to check. 2. There will be no video today. 3. Announce the homework assignment.










Quiz 8Teacher Key




Homework:Pages 64–65: Problems 6, 7 (150° and 210°), 8,

16, 22, 26


(During HW check, students do Practice Exercise 14. Grade this as Practice Exercise Quiz 2. Suggested scale: 9 points off for each incorrect answer. Subtract from 100 the total number of

8 • Precalculus

4. Students clear their desks and take out test materials (two clean sheets of paper, one for a cover sheet and one for a check sheet, and two pencils) before tests are distributed.

5. Give Test 2 over Ch. 3–4. (Refer to the front of this manual for Procedure for Giving / Grading Tests.) Follow this proce-dure for the remainder of the year.

6. Collect and grade tests. (See the Teacher Quiz / Test Key for answers and suggested point values; subtract from 100 the total number of points missed.)


Homework:Read pp. 45–46.


Graded Test 2Teacher Key

Teacher Instructions: 1. There is no written homework to check. 2. Hand back and go over graded Test 2. Col-

lect tests and record grades. 3. Turn on the video.

Homework:Page 72: Problems 2, 4, 6, 12, 14, and 16




Homework:Page 75: Problems 6–9 all and 10–20 (even)




Homework:Page 75: Problems 28–33 all and 37–39 all




Homework:Pages 79–80: Problems 2, 4, 6, and 10


Quiz 10Teacher Key




Homework:Page 80: Problems 15 and 16 twice each











Quiz 12Teacher Key




Homework:Graph the cosecant and secant curves twice

each using sine and cosine as respective guides.






Quiz 13Teacher Key








Homework:Pages 88–89: Problems 2, 4, 6, 14, 16, 18, 26,

and 28


Quiz 11Teacher Key


(During HW check, students do Practice Exercise 24. Grade this as Practice Exercise Quiz 3. Suggested scale: 11 points off for each incorrect answer. Subtract from 100 the total number of points missed. Average the grades for Practice Exercise Quizzes 1–3 and count as one regular quiz grade.)


Homework:Pages 88–89: Problems 30, 32, 34, 40, and 42

10 • Precalculus




Homework:Page 26: Problem 11Page 60: Problems 16 and 17Graph each of the six trigonometric functions

once in [0,2π].






Test 3Teacher Key

Teacher Instructions: 1. There is no homework to check. 2. There is no video today. 3. Announce the homework assignment. 4. Students clear their desks and take out test


5. Give Test 3 over Ch. 1–5. Collect and grade tests.





Teacher Instructions: 1. There is no written homework to check. 2. Hand back and go over graded Test 3. Collect

tests and record grades. 3. Turn on the video.

Homework:Pages 107–108: Problems 4, 6, and 20–32 every

other even problem




Homework:Pages 107–108: Problems 10–34 every other

even problem




Homework:Page 111: Problems 2–12 even


Quiz 14Teacher Key

Lessons 36–48 • 11




Homework:Page 123: Problems 26, 30, 34, 38, and 40


Quiz 16Teacher Key






(During HW check, students do Practice Exercise 38. Grade this as Practice Exercise Quiz 4. Suggested scale: 14 points off for each incorrect answer. Subtract from 100 the total number of points missed. After you have grades for Practice Exercise Quizzes 4–6, average the three grades and count as one regular quiz grade.)














Homework:Pages 116–117: Problems 4a, 8, 14 (all), 16, and

18


Quiz 15Teacher Key





12 • Precalculus


Quiz 17Teacher Key




Homework:Page 129: Problems 19–24 letter b




Homework:Page 129: Problems 28, 30, 32, and 38. Write the

sum and difference, double angle, and half angle identities once each. Include all forms for identities with more than one form.


Quiz 18Teacher Key




Homework:Pages 132–133: Problems 2–12 (even) and

16–20 (even)


Quiz 19Teacher Key










Quiz 20Teacher Key




Homework:Study for Test 4 over Ch. 6.

Lessons 48–60 • 13








Homework:Pages 144–145: Problems 2, 4, 6, and 10


Quiz 21Teacher Key








Homework:Page 145: Problems 22, 24, 28, and 30


Test 4 Teacher Key



5. Give Test 4 over Ch. 6. Collect and grade tests. 6. Plan to return graded tests in les. 62.

Homework:Read pp. 174 and 179.










14 • Precalculus








Homework:Pages 149–150: Problems 16–24 (even), 25–28

all, and 30




Homework:Pages 158–159: Problems 2–34 every other even


Quiz 22Teacher Key




Homework:Page 159: Problems 40 and 44






Quiz 23Teacher Key






Test 5Teacher Key



5. Give Test 5 over Ch. 7. Collect and grade tests. 6. Plan to return graded tests in les. 75.


Lessons 61–74 • 15

16 points off for each incorrect answer. Subtract from 100 the total number of points missed. Average the three grades for Practice Exercise Quizzes 4–6 and count as one regular quiz grade.)









2. Turn on the video.Note: Students will take Test 6 (Semester Exam) in

les. 85. Plan to allow 20–30 extra minutes for this exam. Students should not have more than two major exams in one day.

Homework: Page 171: Problems 7–12


Quiz 25Teacher Key
















Homework:Pages 166–167: Problems 6 and 10–14 (even)


Quiz 24Teacher Key


(During HW check, students do Practice Exercise 58. Grade this as Practice Exercise Quiz 6. Suggested scale:

16 • Precalculus





Homework:Page 39: Problems 12 and 13Page 55: Problem 54Page 65: Problem 12


Quiz 26Teacher Key




Homework:Page 89: Problem 33Page 111: Problem 3Page 129: Problem 30List from memory the domain and range of

each inverse trigonometric function.






Test 6Teacher Key



5. Give Test 6 over Ch. 1–8. Collect and grade tests. Note: Student will take the Semester Exam. Plan

to allow 20–30 minutes extra for this exam. Students should not have more than two major exams in one day.


Homework:Read p. 200.





Homework:Page 180: Problems 2–16 (even), 22, 26, 28,

and 32




Lessons 75–87 • 17




Homework:Page 192: Problems 3b, d, f, 7b and d


Quiz 28Teacher Key




Homework:Page 192: Problem 7f, i, and l


Quiz 29Teacher Key


(During HW check, students do Prac-tice Exercise 71.)


Homework:Pages 195–196: Problems 2–14 every other even

Homework:Page 183: Problems 2–8 and 14–20 (even)


Quiz 27Teacher Key












Homework:Page 192: Letters b, d, and f on problems 1 and 2

18 • Precalculus






Quiz 30Teacher Key










Quiz 31Teacher Key






Test 7 Teacher Key





Homework:Read p. 244.


Graded Test 7 Teacher Key



Homework:Pages 203–204: Problems 1b, 2b, 8b, 12b, and 12e




Lessons 87–100 • 19




Homework:Pages 213–214: Problems 1 and 2 parts b, d, f,

and h




Homework:Pages 214–215: Problems 4–6 parts b, d, f, and h


Quiz 33Teacher Key




Homework:Page 217: Problems 1b, d, f, h, j, 2b, and d




Homework:Page 219: Letters b, d, f, and h on problems 1–3

Homework:Pages 207–208: Problems 1–3 parts b, d, f, and

h, and 4b




Homework:Page 208: Problems 5b, 7b, and 9




Homework:Page 210: Problems 1–3 parts b and d, 5, and 6b


Quiz 32Teacher Key




Homework:Page 210: Problems 8a and b and 10b

20 • Precalculus




Homework:Pages 219–220: Problems 4b, 5b, 7b, and 8b




Homework:Pages 223–224: Letters b, d, and f, on problems

1, 3, and 4


Quiz 34Teacher Key




Homework:Page 224: Problems 5b, 6a and b, 8, and 10b




Homework:Page 226: Problems 1b, 2b, 3b, and 5


(During HW check, students do Practice Exercise 88. Grade this as Practice Exercise Quiz 9. Suggested scale: 8 points off for each incorrect answer. Subtract from 100 the total number of points missed. Average the three grades for Practice Exercise Quizzes 7–9 and count as one regular quiz grade.)


Homework:Page 227: Letters b, d, f, h, and j on problems 1

and 2


Quiz 35 Teacher Key






Test 8 Teacher Key

Lessons 100–114 • 21




Homework:Page 232: Problems 4, 6, 8, and 9d




Homework:Page 237: Parts b and d on problems 1 and 2




Homework:Page 237: Problems 4b, 6, 8d, 9b, and d




Homework:Pages 237–238: Problems 9f, h, 10b, d, 11b, and d



5. Give Test 8 over Ch. 11. Collect and grade tests.







Homework:Page 230: Problems 1b and d, 5, 9, 11, 13a–c,

and 14




Homework:Page 232: Problems 1b, d, f, 2b, and d


Quiz 36Teacher Key

22 • Precalculus




Homework:Page 245: Problems 1 and 2 parts b, d, f, and h,

and 3b


Quiz 37Teacher Key




Homework:Page 245: Problems 4, 6, 8, and 10b




Homework:Page 245: Problems 10d, f, h, 11b, d, and f


(During HW check, students do Practice Exercise 98. Grade this as Practice Exercise Quiz 10. Suggested scale: 10 points off for each incorrect answer. Subtract from 100 the total number of

points missed. After you have grades for Practice Exercise Quizzes 10–12, average the three grades and count as one regular quiz grade.)


Homework:Page 251: Problems 2b, f, and h


Quiz 38Teacher Key




Homework:Page 252: Problems 4, 6, 8, and 10b




Homework:Page 252: Problems 10d, f, h, 11b, d, and f





Lessons 114–127 • 23

Homework:Page 192: Problem 7i (do not graph)Page 195: Problem 11 (do not graph)Given A(–2, 4), B(1, –3), and C(5, 3), find the

length and equation of AB and the size of angle A.






Test 9Teacher Key







Quiz 39Teacher Key




Homework:Page 257: Problem 12












24 • Precalculus





Homework:Page 261: Problems 6, 8a and b, 12, 14, and 16


Copies of polar coordinate graph paper (5 per student copied on both sides; duplicate from text Solution Key, p. 407).



2. Hand out polar coordinate graph sheets. 3. Turn on the video.

Note: Chapter 13 is an optional chapter; sections 13.2–13.4 are not taught in this video series. Quizzes 40–42 and Test 10 will not be used.

Homework:Pages 276–277: Problems 5, 6, and 8




Homework:Pages 278–279: Problems 1 and 2 b, d, f, 4, 6, 8,

16, 18, and 20




Homework:Pages 278–279: Problems 1 and 2 h, 10, 12, 14,

22, 24, and 26


Quiz 43Teacher Key












Lessons 128–140 • 25






(During HW check, students do Practice Exercise 117. Grade this as Practice Exercise Quiz 12. Suggested scale: 6 points off for each incorrect answer. Subtract from 100 the total number of points missed. Average the three grades for Practice Exercise Quizzes 10–12 and count as one regular quiz grade.)








Quiz 45Teacher Key

Homework:Pages 288–289: Problems 1b, d, 2, 4, and 6; also

graph each equation




Homework:Page 289: Problems 8, 10, and 12; also graph

each equation


Quiz 44Teacher Key






(During HW check, students do Prac-tice Exercise 115.)



26 • Precalculus






Test 11Teacher Key














Homework:Pages 296–297: Problems 6 and 8


Quiz 46Teacher Key


(During HW check, students read pp. 299–300 and study Examples 2 and 3.)




(During HW check, students read p. 299 and study Examples 2 and 3 on pp. 299–301.)




(During HW check, students begin working problems 7–9 on pp. 303–304.)


Lessons 140–153 • 27


Test 12Teacher Key










Homework:Page 310: Problems 2, 4, 8, 10, and 12


(During HW check, students read pp. 310–311.)


Homework:Page 314: Problems 1 and 2 parts b, d, f, and

problem 3

Homework:Page 304: Problems 10–12


(During HW check, students read p. 304 and study Example 1 on pp. 304–306.)




(During HW check, students read p. 306 and study Example 2.)


Homework:Using the last five data-pairs of problem 5 on

p. 307 and the equation forms y = ax + b , y = ax b, and y = ae bx, select and find the best-fit equation for the data.


Quiz 47Teacher Key


(During HW check, students begin reviewing pp. 292–307.)



28 • Precalculus






(During HW check, students read p. 317.)








Quiz 48Teacher Key


(During HW check, students review pp. 308–322.)


Homework:Page 323: Problems 8 and 10; then using the

same instructions complete problems 8, 10, and 12 on p. 318.




Homework:Page 328: Problems 1 and 2 parts b, d, and f



2. Turn on the video.Note: Students will take Test 13 (Semester Exam) in

les. 170. Plan to allow 20–30 minutes extra for this exam. Students should not have more than two major exams in one day.

Homework:Page 329: Problems 3 b, d, f, 4 b, and d


(During HW check, students review examples 2 and 3 on p. 326.)


Homework:Page 55: Problem 42Graph y 2 sin 3x in [0, 2].Solve cos 2θ sin θ for all angles in [0, 360].Review Ch. 1–8.

Lessons 153–166 • 29


(During HW check, students review Ch. 15–16.)


Homework:Study for Test 13 over Ch. 1–12 and 14–16.


Test 13 (Final Exam)Teacher Key

Teacher Instructions: 1. There is no homework to check. 2. There is no video today. 3. Students clear their desks and take out test


4. Give Test 13 over Ch. 1–12 and 14–16. Collect and grade tests. Note: Student will take the Final Exam. Plan

to allow 20–30 minutes extra for this exam. Students should not have more than two major exams in one day.


Quiz 49Teacher Key




Homework:Page 224: Problem 11bPage 252: Problem 10hReview Ch. 9–12 and 14.


(During HW check, students review Ch. 9–12 and 14.)


Homework:Given f(x) x24x 8, without graphing

(use derivatives) find the maximum or minimum point and determine if it is a maximum or minimum point.

Find the area under f(x) in [1, 3] along the x-axis.

Review Ch. 15–16.

30 • Precalculus

Precalculus

Appendix

Ap

pend

ix

Appendix • A3

Precalculus Practice Exercises Answer Key

Exercise 1 23 + 17 + 31 + 16 = 87 19 – 9 – 5 + 8 = 13 34 + 67 + 23 + 74 = 198

184 + 389 + 58 = 631 13 + _87 + 45 + 56 = 201 _318_ + 106 + 843 = 1,267

341 – 209 – 16 = 116 _152_ – 67 = 85 505 – _106_ = 399

Exercise 2 8 x 9 x 4 = 288 12 x 10 x 6 x 11 = 7,920 5 x _3 x 3 x 8 = 360

72 ÷ 8 ÷ 3 = 3 204 ÷ 2 ÷ 3 = 34 720 ÷ 10 ÷ 4 = 18

54 x 5 ÷ 9 ÷ 3 = 10 15 x 4 ÷ 5 x 9 = 108 207 ÷ 9 x _7 = 161

Exercise 3 (If the digit immediately to the right of the place being rounded is less than 5, leave the digit being rounded alone. If the digit to the right is 5 or more, add 1 to the digit being rounded. All digits to the right of the one being rounded become 0s.)Round off to the nearest tens’ place.593 590 4,899 4,900 505 510 6,836 6,840

Round off to the nearest thousands’ place.49,482 49,000 7,804 8,000 23,075 23,000 79,901 80,000

Round off the answer to the hundreds’ place.489 + 945 + 194 = 1,600 4,593 – 3,108 = 1,500 9,894 – 4,785 + 3,782 = 8,900

Exercise 4 (To find the average of several numbers, divide the sum by the number of addends.)Average. Round all answers to the nearest tenth except the money answer. Round off money to the nearest cent.43; 17; 34; 52; 78; 62 47.7 125; 316; 202; 278 230.3 78; 92; 91; 88; 73; 92; 84; 69; 75 82.4

$26.84; $56.88; $67.95 $50.56 258; 435; 99; 376; 510 335.6

23; 53; 9; 43; 57; 24; 36; 31; 62 37.6

A4 • Precalculus Practice Exercises Answer Key

Exercise 5 To make an A in a class, Colin must have at least an average of 94. On the first three tests he has an average of 91. What must he average on the last three tests to have at least an average of 94? 97

The average cost of six houses is $135,000. The costs of five of the houses are $128,000; $167,500; $105,400; $152,900; and $137,600. What is the cost of the sixth house? $118,600

The perimeter of a square is 2,268 feet. What is the length of each side? (The formula for perimeter of a square is P = 4s.) 567 ft.

Exercise 6 (quiz—8 each) 8(52) = 416 4_

9(18) = 8 287 = 4 6 • 29 = 174

= 10 3_8 • 132 = 491

2 28(15) = 420 (422)(613) = 258,686

Exercise 7

25025

2 x 2 x 3 x 5 x 7 = 420 2 x 2 x 2 x 3 x 3 = 72 5 x 5 x 7 x 11 = 1,925 13 x 17 x 19 = 4,199

24 = 16 22 x 32 = 36 2 x 3 x 5 = 30 23 x 7 = 56

Division by primes is a good method to find prime factors. The prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

Exercise 8 To find the greatest common factor ( gcf ) multiply the shared prime factors. The gcf is used to simplify fractions.

Write >, <, or = in each blank.14 _<_ 18 21

7 _=_ 1.5(2) 3(8) _<_ 11 + 14 91(5) _>_ 4 •106

List the prime factors.16 36 30 56 55 18 12 72 2 • 2 • 2 • 2 2 • 2 • 3 • 3 2 • 3 • 5 2 • 2 • 2 • 7 5 • 11 2 • 3 • 3 2 • 2 •3 2 • 2 • 2 • 3 • 3

Find the gcf for each group of numbers.24; 60; 84 12 45; 150; 175 5 15; 20 5 12; 36; 72 12

16; 30 2 18; 24; 36 6 50; 110; 210 10 9; 15; 27 3

Appendix • A5

Exercise 9 To reduce a fraction to lowest terms, divide both terms by the gcf.Reduce to lowest terms.

1824

34

2436

23

28144

736

81135

35

1640

25

3268

817

104136

1317

210360

712

Exercise 10 Meteorologists calculate that there are an average of 100 lightning strikes per second. Find the average number of lightning strikes per day. 8,640,000 per day

Sound travels at the rate of 1,130 feet per second. To the nearest tenth of a mile, how far away is the lightning strike if it is heard in 5 seconds? (Remember that 1 mile equals 5,280 feet.) 1.1 mi.

One tornado was tracked at moving 25 miles per hour. Another one was tracked at moving 150 miles per hour. How many times faster was the second tornado moving? 6 times faster

Exercise 11 To find the least common multiple (lcm) multiply all the different prime factors using a factor as often as it is found in any one number. The lcm is used to find the common denominator of two or more fractions.Find the lcm for each group of numbers.6; 8; 12 24 3; 4; 5 60 8; 12; 18 72 6; 9; 15 90

12; 15; 18 180 8; 24; 40 120 2; 3; 4 12 5; 10; 25 50

Exercise 12 Write the least common denominator for each group of fractions.215 ;

35;

23 15

724 ;

23;

316 48

910 ;

56 30

34;

58;

35 40

2742 ;

34;

67 84

14;

15;

16 60

25;

78;

13 120

14;

27 28

Exercise 13 Order the fractions from least to greatest.12;

15;

38;

13

15

13

38

12

16;

34;

19;

15

19

16

15

34

27;

57;

17;

87

17

27

57

87

14;

58;

23;

18

18

14

58

23

14;

18;

12;

16

18

16

14

12

35;

55;

14;

12

14

12

35

55

34;

78;

23;

56

23

34

56

78

58;

15;

19;

16

19

16

15

58


Exercise 14 (quiz—9 each) 458 + 428 + 893 = 1,779 23 x 17 x _5_ = 1,955 230 ÷ 10 x 6 = 138 23 x 5 = 40

Round off the answer to the nearest hundred.2,783 – 998 1,800 4,893 + 7,832 + 8,392 21,100 435 x 32 13,900

Reduce to lowest terms.46

23

1024

512

2832

78

140160

78

Exercise 15 Norris has 56 quarters, 32 dimes, 17 nickels, and 33 rolls of pennies with 50 pennies each. Round the amount that he has to the nearest five dollars. $35

The cost of a one-day pass to the amusement park is $27 for adults and $24 for children ages 1–10. Children under 1 are admitted free. What is the cost for Mr. and Mrs. Harrison to take their children aged 6 months, 3 years, 8 years, 12 years, and 15 years? $156

A machine in a factory can fill 180 cans in 15 minutes. At the same rate, how many cans can the machine fill in 40 minutes? 480 cans

Exercise 16 Fractions must have a common denominator to be added or subtracted.35 +

23 +

16 = 1 7

12 1112 –

715 = 9

20 9 38 + 3

29 – 10

59 = 2 1

24

2 59 +7

56 +3

13 = 1313

18 11 14 – 6

25 = 417

20 4 23 + 4

17 = 817

21

Exercise 17 51_

2 + 73_4 + 15_

6 = 15 112 32_

9 – = 3 118 93_

8 + 71_4 + 121_

2 = 2918

123_7 + 192_

5 – 241_4 = 7 81

140 11 – 62_9 = 47

9 10 + 124_9 – 63_

8 + 42_5 = 20 169

360

318

Appendix • A7

Exercise 18 To change a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.Change to improper fractions.

5 27

377 9

14

374 2

15

115 10

38

838 4

37

317 19

46

1186 21

310

21310

The reciprocal of a number is the number inverted. The numerator becomes the denominator, and the denominator becomes the numerator.Write the reciprocal of each.47

74 6 1

6 911

119

35

53

29

92

14 4 15 1

15

Exercise 19 Cancel common factors before multiplying when possible.

31_3 • 21_

2 = 813 13_

5 • 12_3 = 22

3 3_8 •

4_5 • 7_9 = 7

30

3_5 ÷ 9

10 = 23 7_

8 ÷ 21 = 124 51_

3 ÷ 8_9 = 6

Exercise 20 What is the sum of 3_8 and its reciprocal? 3 1

24

Because a hurricane is a possibility from June 1 through November 30, this period of time is called “hurricane season” in the Northern Hemisphere. How many days does “hurricane season” last? Does “hurricane season” last for less than one-half year, one-half year, or more than one-half year? (Base your answer on a year that is not a leap year.) 183 days; more than one-half year

Exercise 21 78 • 45

710 1

17

12 ÷ 4 •

23

110 3

23 X 5

12 20

Exercise 22 (Remember, only like place values may be added or subtracted. For instance, tenths can be added to tenths.) Round the answer to the nearest tenth.

32.583 + 6.8 = 39.4 53.829 + 0.37 – 1.574 = 52.6

2.005 + 5.892 – 1.9405 = 6.0 30.3 – 23.894 + 16.894 = 23.3

100.75 – 9.6743 – 78.9032 = 12.2 7.8943 + 89.673 – 1.1 + 7.8941 = 104.4

710

45

2318

458

16


Exercise 23 (The product has as many decimal places as the factors combined.)19.254 x 0.8 = 15.4032 9.465 x 10 = 94.65 3.1(45.983 – .796 + 457.8) = 1,559.2597

6.8932 x 0.1894 = 1.30557208 100 x .8943 = 89.43 (43.78 – 1.895)2.5 = 104.7125

(.965 + 1.895)1,000 = 2,860 1.1(2.3 – 0.895) = 1.5455 (56.8943 + 16.854)100 = 7,374.83

Exercise 24 (quiz—11 each) 9 x 8 x 3 x 2 = 432 6 x 5 x 9 x 0 x 3 = 0 7 x _6_ x 4 x 3 x 2 = 1,008

589 x 5 x 2 = 5,890 _76_ x 25 x 4 = 7,600 8 x 5 x 3 x 7 x 6 = 5,040

9.5 x 4 x 2 = 76 141_2 x 12 x 7.5 = 1,305 1_

2 x 1_4 x 36 = 41

2

Exercise 25 The city bus has 20 passengers. For the next 15 stops, the bus picks up 3 passengers and drops off 2. For stops 16–18, no passengers get off and 3 con-tinue to get on. How many passengers will be on the bus after the eighteenth stop? 44 passengers

The stride of a man is 214 ft. The stride of his wife is 11

8 feet. How many of the wife’s strides are needed to equal 50 of her husband’s strides? 100 strides

Three bean seeds laid side-by-side equal one inch. How many feet is 900 bean seeds? How many yards? 25 ft.; 81

3 yd.

Exercise 26 If the divisor has a decimal point, multiply both terms by the power of ten that eliminates the decimal point from the divisor.Find the answers.2.8 ÷ .05 = 56 45.63 ÷ 16.9 = 2.7 .0774 ÷ .0006 = 129

90.932 ÷ 35.8 = 2.54 5.3757 ÷ 0.99 = 5.43 9.1 ÷ 0.455 = 20

Appendix • A9

Exercise 27 Find the answers.5.78 + 9.9 – 0.785 = 14.895 12.21 – 4.893 + 7.9 = 15.217

45.894 + 0.93 + 7.8328 = 54.6568 8.9463 x .8 = 7.15704

.09685 x 3,000 = 290.55 69.896 x .001 = .069896

7 + 2 + 6 + _34_ + 8 = 57 _195_ + 724 + 631 = 1,550

65 + 72 + 15 + _69_ = 221

Exercise 28 Estimate the answer by rounding the terms to the nearest whole number. The answer should be rounded to the nearest whole number also.

Exercise 29 16 ÷ 5 = 3.2 _5_ x 7 = 35 450 ÷ 25 = 18 = 9

212 ÷ _4_ = 53 9 x _32_ = 288 12 ÷ 1_8 ÷ 1_2 = 192

Exercise 30 $60,000 is divided among a niece, a nephew, and a sister in the ratio 3:4:5. How much does the nephew receive? $20,000

Thomas Cann lived 1_5 of his life in Atlanta, Georgia, 1_

4 of his life in Rome, Italy, 1_3 of his life in Los Angeles, California, and the rest of his life in Miami, Florida. How many years did he live in Miami if he died at the age of 60? 13 years

Mr. Tucker has some cows and chickens. If there are 60 heads and 200 legs, how many chickens does he have? 20 chickens

Exercise 31 (Decimals must have the same name to be compared.)Arrange the decimals in each row in order from least to greatest..145 1.0002 .50 .1 .005 .234 .005 .1 .145 .234 .50 1.0002

.09 .38 .455 .9 .0001 .050 .0001 .050 .09 .38 .455 .9

637

13.23 x 5.9 = 78 $799.85 x 9.1 = $7,200 572.9 x 5.2 x 7.9 = 22,920

2,351.11 ÷ 9.9 = 235 $399.99 ÷ 0.87 = $400 24.91 ÷ 5.06 x 19.86 = 100

5.2 x 6.9 x 3.8 = 140 27.8 ÷ 3.9 = 7 631.2 x 9.999 ÷ 99.9 = 63

10 ÷ 14 = 40


Exercise 32 (To compare fractions, either get common denominators or write as decimals.)Arrange the fractions in each row in order from least to greatest.23

78

34

14

67

49

14

49

23

34

67

78

516

1423

58

12

37

2332

516 3

7 12 14

23 58 23

32

Exercise 33 Write the decimal equivalent of the fractions.1_4 .25 5_

8 .625 4_5 .8 2_

3 .–6 3_4 .75 1_

6 .1–6

Write each decimal as a percent..316 31.6% .2125 21.25% 3.01 301% 2.7 270% .08 8% .0097 .97%

Exercise 34 3.416 + 2.7 + 4.62 = 10.736 4 − .6135 = 3.3865 17.716 − 14.23 = 3.486

54.312 + 5.43 − 3.1456 = 56.5964 12.6 x 4.73 = 59.598 .6 x .0037 = .00222

111.714 ÷ 17.32 = 6.45 219.03 ÷ 6.258 = 35 6.1 x 0 x 3.2 x 5.1 = 0

Exercise 35 Seedless green grapes are selling for $1.68 per pound. There are an average of 84 grapes per pound. How many grapes could you buy for $14.28? 714 grapes

A student begins typing a 2,580 word research paper at 8:40 P.M. At what time will he finish if he averages 30 words per minute and the printer takes 5 minutes to print the paper? 10:11 p.m.

Ann, Bill, Cara, and Denis weighed in pairs. Ann and Bill weigh 180 pounds altogether. Bill and Cara weigh 190 pounds altogether, and Cara and Denis weigh 210 pounds altogether. How much do Ann and Denis weigh altogether? 200 pounds

Exercise 36 Convert each percent to a decimal by moving the decimal point two places to the left.

15% .15 5% .05 37.2% .372 912% .095

% .0075 134% 1.34

Convert the months to a fractional part of a year. If necessary, reduce to lowest terms.

7 mo. 712 8 mo. 2

3 4 mo. 13 10 mo. 5

6 6 mo. 12 2 mo. 1

6

34

Appendix • A11

Exercise 37 Find the percentage. (To find the percentage, multiply the base by the percent written as a decimal.)

6% of 210 12.6 25% of 300 75 4_5% of 500 4

Find the percent to the nearest whole percent. (To find the percent, divide the percentage by the base.)

Find the base. (To find the base, divide the percentage by the percent written as a decimal.)

16 is 8% of what number? 200 21 is 101_2% of what number? 200

Exercise 38 (quiz—14 each) Find the answers. Find the percents to the nearest whole percent.

91_4% of 50 4.625 19% of $650 $123.50 3_

8% of 4,000 15

11 is 5% of what number? 220 60 is 120% of what number? 50

43 is what percent of 78? 55% 22 is what percent of 80? 28%

Exercise 39 Find the simple interest (i = prt). Remember that rate (r) must be written as a decimal and that time (t) must be in years.p = $1,000 p = $5,000 p = $800 p = $10,000 p = $4,000r = 8% r = 12% r = 6.8% r = 123_

4% r = 91_2%

t = 1 yr. $80 t = 3 yr. $1,800 t = 6 mo. $27.20 t = 8 yr. $10,200 t = 8 mo. $253.33

Exercise 40 Find the travel time. Use hours and minutes for the first four problems. Use years, months, days, hours, and minutes for the last problem. (Time zone adjustments have already been made.)

The school bus left the school at 3:08 P.M. and dropped the last student off at 4:56 P.M. 1 hr. 48 min.

The Henry family left Tulsa, Oklahoma, at 7:35 A.M. and arrived in Pensacola, Florida, at 10:10 P.M. 14 hr. 35 min.

The plane took off at 10:25 A.M. and landed at 1:18 P.M. 2 hr. 53 min.

The boat pulled away from port on Monday at 1:30 P.M. and returned on Friday at 8:30 A.M. 91 hr.

The Orbital Space Station (O.S.S.) left on October 29, 2005, at 11:30 P.M. and returned on May 21, 2009, at 5:00 A.M. 3 yr. 6 mo. 21 da. 5 hr. 30 min.

12 is what % of 48? 25% 200 is what % of 450? 44% 15 is what % of 90? 17%


Exercise 41 (To convert from a larger unit to a smaller unit, multiply by the number ofsmaller units in one of the larger units. To convert from a smaller unit to a larger unit, divide by the number of smaller units in one of the larger units.)

12 ft. = _144_ in. 96 ft. = _32_ yd. 3.2 mi. = _16,896_ ft.

9,680 yd. = _5.5_ mi. 5 hr. = _300_ min. 128 oz. = _8_ lb.

15 mo. = 114 yr. 32 t. = _64,000_ lb. 1 mi. = _63,360_ in.

Exercise 42 Estimate the answer by rounding the terms to the nearest whole number. The answer should be rounded to the nearest whole number also..99732 x 9.9 = 10 499.978 x 9.1 x 1.98 = 9,000 .901 x 54.5 x 9.9 = 550

40.44 ÷ 5.4 ÷ 1.1 = 8 $299.95 x 10.31 ÷ 2.3 = $1,500 16.23 x 5.06 ÷ 79.81 = 1

4.2 x 4.9 x 3.8 = 80 55.2 ÷ 10.9 x 99.9 = 500 9.9 x 9.999 ÷ 99.9 = 1

Exercise 43 6 + 9 + 4 + 7 + 3 + 8 = 37 23 + 76 + 59 + 36 = 194 9 + 47 + 16 + 5 + 48 = 125

148 + 69 + 893 + 7 = 1,117 706 + 845 + 19 + 358 = 1,928 45 + 19 + 689 + 683 = 1,436

5 + 8 + _16_ + 9 + 3 = 41 84 + _18_ + 32 + 19 = 153 _75_ + 689 + 436 = 1,200

115 – 98 = 17 1,895 – 793 = 1,102 700 – 516 = 184

Exercise 44 (quiz—12 each) 5

38 + 7

512 = 1219

24 11 49 – 7

23 = 37

9 1 12 ÷ 34 = 2 .07 x .63 = .0441

6 25 x 15

16 = 6 4.78 + 2.64 + 7.995 = 15.415 34.6 ÷ 10 = 3.46 3.06 – 1.7328 = 1.3272

Appendix • A13

Exercise 45 A horse ran at a rate of 1,200 ft./min. At that rate, how many miles to the nearest whole mile did the horse run in 1 hour? 14 mi.

Evan feeds his horse 101_2 cups of oats per day. He feeds 31_

4 cups in the morning and 31_ cups at noon. How many cups of oats does he give his horse at night? 311

12 c.

Tucker farms has five horses that weigh a total of 2,521 kilograms. Four of the horses have an average weight of 483 kilograms. How much does the fifth horse weigh? 589 kg

A horse’s height is measured in hands. A hand is equal to 4 inches. How many hands tall is a horse that is 4 feet, 10 inches tall? 14.5 hands

Most male horses have 40 teeth, and most female horses have 36 teeth. What per-cent more teeth does a male have than a female? 10% more

Exercise 46 Use the formula d = st where t = time, d = distance, and s = speed.

45 mph for 3 hr. 135 mi. 630 mph for 11_2 hr. 945 mi. 12 mph for 11_

4 da. 360 mi.

54 mph for 11 hr. 594 mi. 128 mph for 30 min. 64 mi. 600 mph for 10 min. 100 mi.

Exercise 47 53_

8 + 5 18 = 101_

2 94_9 – 4

19 = 51_

3 3.89 + 3.95 = 7.84 _5.7_ x .63 = 3.591

_12_ x 34 = 9 15 ÷ = 45 5.8965 ÷ _100_ = .058965 _5_ ÷ 1_

6 = 30

Exercise 48 Find the missing term in each proportion using the cross multiplication method. Find the answer to the nearest tenth.

13

13

78 =

x23 20.1

2x = 58 3.2

x11 =

1225 5.3

910 =

33x 36.7

x12 =

1724 8.5

11x = 27 38.5

89 =

x15 13.3

56 =

12x 14.4


Exercise 49 Average. $1,140 $843 96 138$2,076 $925 87 410$1,293 $715 24 782$1,783 $683 32 654 $784 61

34; 62; 71; 55; 39 52.2 1,720; 1,652; 1,995 1,789 $410; $225; $536; $483 $413.50

Exercise 50 In a school election for president, Sara received 32% of the votes, Dan received 35%, and Joanna received the rest of the votes. If 580 students voted, how many votes did the winner receive? 203 votes

A large pizza with 2 toppings cost $12.95. Each additional topping is $.85. Find the cost of a large pizza with 5 toppings. Include an 8% sales tax. $16.74

Josh Wentworth’s trailer holds 7 cows. Find the minimum number of trips needed to take 38 cows to the market. 6 trips

The cost to fly round-trip to Seattle, Washington, was $280.80. The cost included an 8% tax. What was the cost of the ticket without the tax? $260

Exercise 51 Estimate the answers by rounding each term to the nearest tenth. Answers should also be to the nearest tenth.30.1 x .09 3.0 47.999 ÷ 1.183 40.0 155.21 x .11 x .09 1.6 .95 x .95 x .95 1.0

15.03 + 7.89 22.9 200.99 – 106.89 94.1 9.894 x 19.99 198.0 .95 ÷ .95 ÷ .95 1.0

Exercise 52 Use the formula d = st where t = time, d = distance, and s = speed.70 mph for 5 hr. 350 mi 514 mph for 21_

2 hr. 1,285 mi. 15 mph for 61_4 da. 2,250 mi.

63 mph for 11 hr. 693 mi. 254 mph for 30 min. 127 mi. 88 mph for 13 hr. 1,144 mi.

$1,573$790 60

496

Appendix • A15

Exercise 53 Find the simple interest using the formula i = prt (i = interest, p = principal, r = rate of interest, and t = number of years).

Exercise 54 Convert these measures.9 ft. = _108_ in. 11_

2 mi. = _7,920_ ft. 2.5 da. = _60_ hr.

54 oz. = 338 lb. 195 min. = 3

14 hr. 5 wk. = _35_ da.

72 in. = _2_ yd. 19 tsp. = 613 tbsp. 5 qt. = _20_ c.

Exercise 55 Mr. Thomas charges $45 to make a service charge and for the first hour of work. $45 is charged even if the repair takes less than one hour. He charges $30 per hour for each additional hour or part of an hour that is required to make the necessary repairs. On Friday, he made 4 house calls. The times required were

2 23 hours; 34 hour; 1.5 hours; and 3 hours, 15 minutes. Find his total charge. $360

The scale on a map is 3_4 inch equals 200 miles. How many inches are needed to represent 750 miles? Find the answer to the nearest quarter inch. 23

4

One of Alex Turk’s notebooks holds 276 baseball cards. What is the minimum number of notebooks needed to hold 2,632 cards? 10 notebooks

Exercise 56 5.784 x 16 x 2.2 = 203.5968

58 + 23 – 14 = 1 1

24 20 – (3.78 x 2.68) = 9.8696

12 x 15 x 12 x 5 = 450 3.14 x 2.68 x 14 = 2.1038

79 + 34 x 35 = 1 41

180

p = $5,000 p = $2,300 p = $25,000 p = $575r = 12% r = 4% r = 101_

2% r = 15%t = 1 yr. $600 t = 3 yr. $276 t = 10 yr. $26,250 t = 6 mo. $43.13p = $9,500 p = $12,000 p = $50,000 p = $13,600r = 83_

4% r = 18% r = 8% r = 91_4%

t = 4 yr. $3,325 t = 2.5 yr. $5,400 t = 25 yr. $100,000 t = 6 yr. $7,548

in.


Exercise 57 (The mean is the average of the statistics.)Find the mean to the nearest tenth.

Exercise 58 (quiz—16 each) Find the mean temperature to the nearest whole degree.

Exercise 59 2 da. = _48_ hr. 24 fl. oz. = _ 3 _ c. 3 gal. = _24_ pt.

8 fl. oz. = ____ pt. 210 min. = ____ hr. 8 in. = ____ ft.

15 hr. 7 min. 23 ft. 8 in. 8 lb. 9 oz.– 6 hr. 12 min. 8 hr. 55 min. + 16 ft. 9 in. 40 ft. 5 in. x 15 128 lb. 7 oz.

Exercise 60 Myles Gordon has an electric car that can travel up to 65 miles before recharging. If he wishes to travel 207 miles after recharging the battery, how many more recharges will be necessary? 3 more

Mrs. Owens paid $385.56 for a dishwasher after receiving a 15% discount off the list price and paying an 8% sales tax. What was the list price of the dish-washer? $420

An 8 x 10 photo is enlarged to a 10 x 13. What is the percent of increase in area? 62 1

2 % increase

68°; 67°; 73°; 65°; 57° 66° 93°; 81°; 88°; 81° 86° 20°; 18°; 19°; 23°; 20°; 17° 20°

84°; 91°; 77°; 65° 79° 16°; 21°; 17° 18° 12°; 23°; 12°; 19°; 17°; 19° 17°

12 3 1

223

56; 59; 51; 63; 68; 57; 53 58.1 146; 153; 115; 148 140.5 200; 141; 257; 318; 199 223

912; 738; 410 686.7 15; 9; 7; 6; 8; 11; 4; 9; 6; 7 8.2 19; 27; 34; 18; 23 24.2

Appendix • A17

Exercise 61 Complete this chart based upon a monthly net income of $5,000.

Exercise 62 Round these amounts to the nearest whole cent.$12.056 $0.2399 $8.003 $73.568 $0.80099$12.06 $0.24 $8.00 $73.57 $0.80

Write the cents by using a decimal point and dollar sign. Round to the nearest whole cent.23¢ 8¢ 13.5¢ 139¢ 8.56¢ 2¢$.23 $.08 $.14 $1.39 $.09 $.02

Write these dollar amounts in cents.$1.18 $0.45 $2.05 $55 $32.95118¢ 45¢ 205¢ 5,500¢ 3,295¢

How many quarters are needed to be equal to the sum of all the answers in this practice exercise? 753 quarters

Exercise 63 Use the formula t = d

s where t = time, d = distance, and s = speed.

560 mph for 4,760 mi. 40 mph for 20 mi. 180 mph for 45 mi.

437 mph for 1,748 mi. 17.5 mph for 665 mi. 63.5 mph for 825.5 mi.

Expense

Tithe

Housing

Food

Utilities

Transportation

Insurance

Medical

Clothing

Education

Savings

Percent

12%

23%

15%

8%

9%

7%

5%

6%

11%

4%

Amount

$600

$1,150

$750

$400

$450

$350

$250

$300

$550

$200

8.5 hr.

4 hr.

12 hr.

38 hr. 13 hr.

14 hr.


Exercise 64 Complete this chart based upon a monthly net income of $4,000.

Exercise 65 How many ounces of peppermints should Todd buy to have a total purchase in whole pounds, if he buys 1 pound 3 ounces of chocolate peanuts and 14 ounces of lemon drops? 15 oz.

Lemon drops cost $2.80 per pound. What is the cost of 14 ounces including a 9% sales tax? Round the answer to the nearest cent. $2.67

For the aerobic run in physical education class, Julie ran an 8-minute mile and Anna ran a 12-minute mile. They began at the same place on the mile track and both ran for 30 minutes. How many minutes passed before they were at the starting point together? 24 min.

Exercise 66 Just by looking, identify the calculations that are wrong.6.34 x 8.91 = 5.64894 wrong 25.09 x 2.8 = 70.252 5.8 x .45 = .261 wrong

14% of 980 = 13.72 wrong 78 is 20% of 390 12 is 75% of 48 wrong

15 is 30% of 50 991_2% of 6,000 is 597 wrong 30 is 67% of 20 wrong

Expense

Tithe

Housing

Food

Utilities

Transportation

Insurance

Medical

Clothing

Education

Savings

Percent Amount

$480

$920

$600

$320

$360

$280

$200

$240

$440

$160

12%

23%

15%

8%

9%

7%

5%

6%

11%

4%

Appendix • A19

Exercise 67 75_

9 + 62_3 – 41_

4 = 93536 101_

2 – 33_4 + 75_

6 = 14712 22

3 x 910 ÷ 11

2 = 1 35

1_2% of 10,500 = 52.5 11_

4% of 6,900 = 86.25 3_5% of 25,000 = 150

Exercise 68 Find what percent the numerator is of the denominator.Find the answer to the nearest whole percent.1220 60%

100250 40%

4303,200 13%

7805,600 14%

2104,830 4%

Exercise 69 (quiz—12 each) 29 456 372 9,387 432,605 37 493 943 2,563 784,528 16 108 415 8,904 784,528 48 934 869 1,987 406,783 72 275 132 3,659 199,417 65 806 516 4,016 932,540 + 57 + 528 + 839 + 7,992 + 629,508 324 3,600 4,086 38,508 4,169,909

87 + 56 + 29 + 34 = 206 19 + 25 + 48 + 97 = 189 132 + 667 + 894 + 125 = 1,818

Exercise 70 A parking garage charges $2 for the first hour, $1.25 for each additional hour or part of an hour, and $6 for half-day parking. Half-day parking allows a maximum of 4 12 hours. If a customer parked for 7 hours, what is the least amount that he would owe? $9.50

How many fluid ounces are needed to yield full quarts if 3 cups are added to 22 fluid ounces? 18 fl. oz.

Hot dog buns are sold in packages of 8, and hot dogs are sold in packages of 10. What is the least number of each that can be bought to have an equal number of buns and hot dogs? 40


Exercise 71 6,384 10,050 $18.39 $200.43 3.14 – 1,296 – 9,473 – 6.84 – 196.87 – 2.687

5,088 577 $11.55 $3.56 0.453

5.894 – 2.89543 = 2.99857 10.45 – 9.78432 = 0.66568 $200 – $18.87 = $181.13

Exercise 72 Use the formula C = 5_

9(F – 32) to convert these temperatures to the nearest tenth.

Exercise 73 (The sum of the three angles in a triangle is 180°.)Write the number of degrees in the third angle of a triangle.

Find the third angle of the triangle and classify the triangle as acute, obtuse, or right.

Exercise 74 (Two angles with a sum of 90° are complementary angles. Two angles with a sum of 180° are supplementary.) Find the number of degrees in the complements of these angles.

Find the number of degrees in the supplements of these angles.

Classify each angle as acute, obtuse, or right.51° acute 90° right 145° obtuse 10° acute 91° obtuse

48 °F. 8.9° 80 °F. 26.7° 105 °F. 40.6° –10 °F. –23.3° 22 °F. –5.6°

–86 °F. –65.6° 14 °F. –10.0° 64 °F. 17.8° 99 °F. 37.2° 32 °F. 0°

90°; 22° 68° 45°; 45° 90° 132°; 40° 8° 60°; 30° 90° 67°; 42° 71°

60°; 60° 60°acute 75°; 65° 40°acute 70°; 20° 90°right 12°; 20° 188°obtuse100°; 40° 40°obtuse

50° 40° 25° 65° 12° 78° 78° 12° 321_2° 57

12 °

122° 58° 150° 30° 23° 157° 503_4° 129

14 ° 100° 80°

Appendix • A21

Exercise 75 A rectangle has a length of 20 in. and a width of 10 in. If each dimension is increased by 20%, by what percent is the area increased? 44% increase

The perimeter of a rectangle is 220 feet. The ratio of length to width is 15:7. How many feet long is the rectangle? 75 ft.

What percent of the letters in the following sentence are e’s? Dee ate the whole pie before breakfast. Express your answer to the nearest whole percent. 28%

Exercise 76 (1 sq. yd. = 9 sq. ft.; 1 sq. ft. = 144 sq. in.; 1 cu. yd. = 27 cu. ft.; 1 cu. ft. = 1,728 cu. in.)Change each area to square inches.

Change each volume to cubic feet.

Exercise 77 Find the perimeter and area of a square with sides of 7 ft. P = 28 ft. A = 49 sq. ft.

Find the area of a rectangle with a length of 5 yd. and a width of 3 yd. A = 15 sq. yd.

Find the number of inches in 4 yards. In 6 feet. 144 in.; 72 in.

Find the average of 32 lb., 25 lb., and 27 lb. 28 lb.

Exercise 78 (quiz—10 each) 328 480 42,385 49,382 95,784 x 16 x 37 x 23 x 72 x 95,248 17,760 974,855 3,555,504 862,056

8 x 9 x 3 = 216 14 x 19 x 0 = 0 10 x 85 x 2 = 1,700 13 x 5 x 9 = 585 85 x 1 x 5 = 425

Exercise 79 (To write a negative power as a positive power, write it as a reciprocal. 10–2 can be written as 1___

10 .)Write as a positive power.

7–2 17 y–2 1

y2 a–3 1a3 x–5 1

x5 9–4 194 m–3 1

m3 4–4 144

17–3 73 1

x–2 x2 110–5 105 1

y–6 y6 18–2 82 1

b–9 b9 13–3 33

2

6 sq. ft. 864 sq. in. 3 sq. yd. 3,888 sq. in. .5 sq. yd. 648 sq. in. 3_4 sq. ft. 108 sq. in.

3 cu. yd. 81 cu. ft. 3,456 cu. in. 2 cu. ft. 864 cu. in. 12

cu. ft. 2_3 cu. yd. 18 cu. ft.

2


Exercise 80 What percent of the first 15 whole numbers have exactly 4 distinct whole number divisors? (1, 2, 3, and 6 are the four distinct divisors of 6.) 33

13 %

What is the tenth number in the sequence 8, x, 18? 53

What common fraction has a reciprocal of 3.2?

What percent of the digits in the following number is 5s?

Express your answer to the nearest whole percent. 46%

Exercise 81 Write a proportion and find each answer. Use this format for the proportion: = .

14% of 980 137.2 12 is 75% of what number? 16 150 is 120% of what number? 125

312 % of 50 1.75 15 is what % of 50? 30% 28 is what % of 140? 20%

150% of 80 120 30 is what % of 20? 150% 78 is 20% of what number? 390

Exercise 82 (Mathematical probability is a number expressed as a ratio that shows how likely it is that something will occur. Use this formula: Probability = .)

Answer the questions about a cube with the numbers 1–6 on the faces.What is the probability that the number 5 will land face up? 1

6

number of favorable outcomestotal number of possible outcomes

percent100%

percentagebase

516

4,575,035,659,554

What is the probability that an even number will land face up? 12

What is the probability that a prime number will land face up? 12

What is the probability that a number less than 5 will land face up? 23

What is the probability that a perfect square will land face up? 13

Appendix • A23

Exercise 83 (To write a number using scientific notation, write the number as a decimal between 1 and 10. Then multiply or divide by the correct power of ten. If you multiply, the exponent is positive. If you divide, the exponent is negative.)Write using scientific notation.

Exercise 84 Write the prime factors.

Write the greatest common factor (gcf) for each group of numbers.24; 18; 32 2 15; 12; 45 3 50; 450; 60 10 18; 72; 36 18

Exercise 85 What is the probability that two numbers chosen at random from this group (1, 2, 3, 4) have a product greater than 6? 1

3

What is the probability that two numbers chosen at random from this group (1, 2, 3, 4, 5) have a product greater than 12? 1

5

If all positive integers are possible outcomes, what is the probability that a number chosen at random will be divisible by 5 and 11? 1

55

Tim flipped two nickels until one of them had tails up. What is the probability that both of them had tails up? 1

3

4,870,000 489,308,000,000 .000675 6,4004.87 x 106 4.89308 x 1011 6.75 x 10–4 6.4 x 103

.0534 6,905,000 .00034 .00055.34 x 10–2 6.905 x 106 3.4 x 10–4 5.0 x 10–4

56,000 .0000473 567.9 .0031 5.6 x 104 4.73 x 10–5 5.679 x 102 3.1 x 10–3

36 44 27 842•2•3•3 2•2•11 3•3•3 2•2•3•7


Exercise 86 Find the median of these fractions.

15 1

2 38 2

3 34 4

9 17 5

12 710

49

Exercise 87 Find each mean.–8; 9; 6; –7; –3; 9 1 |–5|; |6|; |–12|; |–1| 6 √144 ; √81 ; √25 ; √1 ; √64 7

10% of 420; 5% of 800; 40% of 240; 12% of 150 49 1_2; 1_3; 1_

4; 1_5; 1_6 2960

Exercise 88 (quiz—8 each) Write using scientific notation.

Exercise 89 (Circumference is the distance around a circle. The formulas for finding circumference are C = πd and C = 2πr. 2 radii (r) are equal to 1 diameter (d).)Use π = 3.14.Find the circumference. If necessary, round to the nearest hundredth.

Exercise 90 The track at Pineview Christian School is an oval shape (a rectangle with a semicircle at each end). The radius of each semicircle is 14 yards, and the length of the rectangle is three times the diameter of the semicircle. How many yards will Jackson run if he goes around the track three times? (Use the approximate value of 31

7 for π.) 768 yd.

What is the area of a triangle that has a base of 4.75 x 102 ft. and a height of 2.04 x 102 ft.? Write your answer using scientific notation and with 2 significant digits. 4.8 x 104

6,789,000,000 .000785 8,900 .00056.789 x 109 7.85 x 10–4 8.9 x 103 5.0 x 10–4

.00031 5,000,000 .0008932 3,005,000,0003.1 x 10–4 5.0 x 106 8.932 x 10–4 3.005 x 109

3,400 + 7,800 = .0003 – .000025 = 5,000 – 120 = .0056 + .000543 =1.12 x 104 2.75 x 10–4 4.88 x 103 6.143 x 10–3

d = 10 ft. 31.4 ft. r = 5.5 ft. 34.54 ft. r = 12 ft. 75.36 ft. d = 6 m 18.84 m

r = 91_2 ft. 59.66 ft. d = 3.5 cm 10.99 cm r = 12.65 hm 79.44 hm d = 25 yd. 78.5 yd.

Appendix • A25

Exercise 91 Estimate the answer by rounding the terms to the nearest whole numbers. Answers should be rounded to nearest whole number also.39.576 x 8.042 320 5,267.3 ÷ 0.95 5,267 99.9 x 9.99 ÷ 0.99 1,000

$699.87 x 11.4 $7,700 $599.65 ÷ 9.5 $60 200.2 ÷ 49.6 x 25.3 100

0.984 x 9.84 x 98.4 980 34.3 ÷ 1.9 ÷ 0.91 17 53.7 ÷ 5.99 ÷ 3.06 3

Exercise 92 18% of $608 $109.44 51_

4% of $944 $49.56 335% of $75 $251.25

74.4 is 12% of what number? 620 57.6 is 120% of what number? 48

6.6 is 71_2% of what number? 88

Exercise 93 Write a proportion and find each answer. Use this format for the proportion: . If necessary, round to the nearest tenth.

31_2% of 1,800 63 140% of 68 95.2 85% of 650 552.5

110% of 140 154 60% of 170 102 11_2% of 400 6

Exercise 94 Write a proportion and find each answer. Use this format for the propor-tion: . Find the percent to the nearest whole percent.



Exercise 95 The hundreds and units digits of 5,893 are switched to form a new number. What is the sum of 5,893 and the new number? 11,291 What is the difference of 3 and its reciprocal? 22

3

What is the maximum number of $.79 greeting cards that Penny can buy with $9? 11 cards

=percent100%

percentagebase

percent100%

percentagebase

=


Exercise 96 (1 acre equals 43,560 square feet, and 1 square mile equals 640 acres.)4 sq. yd. = 36 sq. ft. 2.5 acres = 108,900 sq. ft. 18 sq. ft. = _ 2__ sq. yd.

720 sq. in. = 5 sq. ft. 81 sq. ft. = _9__ sq. yd. 3_4 acre = _32,670_ sq. ft.

Exercise 97 Use the formula F = 9_

5C + 32 to convert these temperatures to the nearest whole degree.25 °C 77° 80 °C 176° 105 °C 221° –10 °C 14° 22 °C 72°

–12 °C 10° 14 °C 57° 34 °C 93° 37 °C 99° 45 °C 113°

Exercise 98 (quiz—10 each) Complete this chart based upon a monthly net income of $2,800.

Expense

Tithe

Housing

Food

Utilities

Transportation

Insurance

Medical

Clothing

Education

Savings

Amount

$336

$644

$420

$224

$252

$196

$140

$168

$308

$112

Percent

12%

23%

15%

8%

9%

7%

5%

6%

11%

4%

Appendix • A27

Exercise 99 Find the simple interest using the formula i = prt (i = interest, p = principal, r = rate of interest, and t = number of years).p = $12,000 p = $7,900 p = $13,000 p = $8,575r = 15% r = 13.5% r = 81_

2% r = 21%t = 1 yr. $1,800 t = 3 yr. $3,199.50 t = 10 yr. $11,050 t = 6 mo. $900.38

p = $10,700 p = $52,000 p = $120,000 p = $6,800r = 53_

4% r = 9% r = 8% r = 91_4%

t = 2 yr. $1,230.50 t = 2 yr. $9,360 t = 25 yr. $240,000 t = 3 mo. $157.25

Exercise 100 The formulas C = 5_9(F+ 40) – 40 and F = 9_5(C+ 40) – 40 can be used to convert temperatures. If the outside temperature is 85 °F, what is the temperature on the Celsius scale to the whole degree? If the inside temperature is 21 °C, what is the temperature on the Fahrenheit scale to the nearest whole degree? 29 °C; 70 °F

The overnight low in one city was –12 °C. During the day, the temperature rose 17 degrees. What was the increased temperature? How many degrees above freezing was the warmer temperature on the Fahrenheit scale? 5 °C; 9 °F above freezing

Exercise 101 (To convert from one metric unit to another, write the metric units horizontally as illustrated below:

U stands for meter, liter, or gram. As a conversion is made to the right, multiply by the power of ten that corresponds with the number of spaces moved to the right. As a conversion is made to the left, divide by the power of ten that corresponds with the number of spaces moved to the left.)

23 km = _23,000_ m 1.5 hL = _.15 kL 1,500 cg = 15_ g

7.3 daL = _.73__ hL 9 kg = _900,000_ cg 32,000 mm = _320_ dm

57.34 hm = _573,400_ cm 6,700 mg = _.0067_ kg 18 m = _1.8_ dam

k h da u d c m


Exercise 102 (Some metric / English approximate relationships are given. 1 km = .62 mi.; 1 kg = 2.2 lb.; 1 g = .04 oz.; 1 liter = 1.06 qt.; 1 m = 1.09 yd.)

Exercise 103 (Some English / metric approximate relationships are given. 1 mi. = 1.61 km; 1 lb. = .45 kg; 1 oz. = 28.35 g; 1 qt. = .95 liters; 1 yd. = .91 m)Find the answers to the nearest tenth.15 mi. = _24.2_ km 250 lb. = _112.5_ kg 16 oz. = _453.6_ g

81_2 qt. = _8.1_ liters 44 yd. = _ 40.0__ m 500 lb. = _225.0_ kg

Exercise 104 73% – 14% = 59% 51_

2% of $2,500 = $137.50 14% of 980 = 137.2

78 is 200% of what number? 39 12 is 75% of what number? 16

15 is what % of 50? 30% 150 is 120% of what number? 125

28 is what % of 140? 20% 30 is what % of 20? 150%

Exercise 105 Answer the questions about the following statement. Express each an-swer as a common fraction.

The counting numbers from 1 to 20 are written separately on a sheet of paper and all 20 numbers are placed in a paper bag.

What is the probability that the number 15 will be drawn from the bag? 120

What is the probability that an even number will be drawn? 12

What is the probability that a perfect square will be drawn? 15

What is the probability that a prime number will be drawn? 25

What is the probability that a power of two will be drawn? 14

What is the probability that a multiple of four will be drawn? 14

What is the probability that an integer will be drawn? 11

Find the answers to the nearest tenth.5.5 km = _3.4_ mi. 16 kg = _35.2_ lb. 2,000 g = _80_ oz.

12.5 liters = _13.3_ qt. 25 m = _27.3_ yd. 110 kg = _242_ lb.

Appendix • A29

Exercise 106 (quiz—11 each) 9 ft. = 108_ in. 11_

2 mi. = _7,920_ ft. 2.3 liters = _2,300_ mL

54 oz. = 338 lb. 195 cg = _1.95_ g 15 mi. = _24.15_ km

72 in. = _2 _ yd. 19.5 liters = __20.67_ qt. 380 g = _15.2_ oz.

Exercise 107 27 lb. 8 oz. 23 yd. 8 in. 16 lb. 9 oz. – 10 yd. 31 in. 6 13 pk. 4 qt. + 12 lb. 4 oz. 56 lb. 5 oz.

12 yd. 13 in.

2 pk. 2 qt.

Exercise 108 Express using scientific notation.

Exercise 109 62_

3 + 54_7 – 31_

4 = 88384 133_

5 x 2534 + 13_

4 – 71_7 = 417

28 3_5 x 15 ÷ 3_5 = 15

4.35 + 0.784 – 7.8943 • 5.5 + .034 – 5.8 • 3 = –55.65065 1_2 x 1_3 x 1_4 x 1_5 x 1_6 x 1_7 = 1

5,040

5 kg 3 hg 9 dag 8 m 4 dm 13 ft. 6 in. x 7 = 94 ft. 6 in. x 8 – 2 m 9 dm 43 kg 1 hg 2 dag 5 m 5 dm

.00073 914,000 1,800,0007.3 x 10–4 9.14 x 105 1.8 x 106

196.3 .00173 .0151.963 x 102 1.73 x 10–3 1.5 x 10–2

234,000,000 .00000000032 843.62.34 x 108 3.2 x 10–10 8.436 x 102


Exercise 110 (To find the length of one side of a right triangle, use the Pythagorean rule— c2 = a2 + b2.)

A rabbit ran 40 ft. up a path and turned left and ran 30 ft. before stopping at the finish line. A turtle started at the same place but took a diagonal path to get to the finish line. How many feet did the turtle travel? 50 ft.

An 8-inch by 15-inch rectangle is inscribed (drawn inside) within a circle. The diagonal of the rectangle is the diameter of the circle. What is the circumference of the circle? 53.38 in.

How high up on a wall does a 12-foot ladder reach if the base of the ladder is 4

Exercise 111 (6! is read six factorial and means 6 x 5 x 4 x 3 x 2 x 1.)

Exercise 112 Find the value of x.

15% of (x + 5) = 24 155 31_2% of (x – 3) = 14 403 140% of 5x = 35 5

75% of √x = 60 6,400 25% of x5 = 8 2 15% of 2x = 30 100

Exercise 113 Write a proportion and find each answer. Use this format for the proportion: .

125% of 500 625 83 is 50% of what number? 166 7 is 1_2% of what number? 1,400

123_5% of 400 50.4 25 is what % of 100? 25% 9 is what % of 30? 30%

1_2% of 80 .4 11 is what % of 22? 50% 90 is 125% of what number? 72%

feet from the wall? (Find the answer to the nearest tenth of a foot.) 11.3 ft.

Find the value of each.4! 24 5!4! 2,880 6

3,024 7! 5,040 6!3! 4,3209!5!

6! 5!

percent100%

percentagebase

=

Appendix • A31

Exercise 114 Express as a common fraction or mixed number the difference between the mean and the median.12; 15; 23; 10; 13; 20; 17 5

7 8; 4; 4; 7; 5; 9; 3; 0; 2; 6 310 120; 115; 142; 137; 122 5 1

5

Exercise 115 A cube has a volume of 125 cubic inches. What is the sum of the lengths of all the edges? 60 in.

Two 10-inch diameters of a circle intersect to form four right angles. When the ends of the diameters are connected, four right triangles are formed. What is the area of one right triangle? 12.5 sq. in.

What is the height of an equilateral triangle which is 14 in. on each side? Find the height to the nearest whole inch. 12 in.

Exercise 116 Write the prime factors.81 24 48 963 • 3 • 3 • 3 2 • 2 • 2 • 3 2 • 2 • 2 • 2 • 3 2 • 2 • 2 • 2 • 2 • 3

Write the least common multiple (lcm) for each group of numbers.12; 9; 15 180 6; 8; 10 120 5; 8; 12 120 5; 25; 15 75

Exercise 117 (quiz—6 each) Find the number of degrees in the complements of these angles. 13° 77° 87° 3° 45° 45° 10° 80° 451_

2° 44 12

°

Find the number of degrees in the supplements of these angles.56° 124° 106° 74° 48° 132° 1103_

4° 69 14

° 135° 45°

Classify each angle as acute, obtuse, or right.103° obtuse 91° obtuse 31° acute 89° acute 90° right

Two angles of a triangle measure 56° and 38°. How many degrees are in the

Exercise 118 Find what percent the numerator is of the denominator. Find the answer to the nearest whole percent.

511 45% 7

9 78% 130800 16% 36

68 53%

3001,250 24%

supplement of the third angle of the triangle? 94°


Exercise 119 Use the formula d = st where t = time, d = distance, and s = speed.

135 mph for 3.4 hr. 459 mi. 63 mph for 91_2 hr. 598.5 mi. 45 mph for 11_

4 da. 1,350 mi.

68 mph for 11 hr. 748 mi. 538 mph for 30 min. 269 mi. 426 mph for 10 min. 71 mi.

Exercise 120 Dan Donaldson earned $494 last week. He worked 48 hours with 8 of the hours being paid at the overtime rate which is one and one-half times the regular rate. What is his pay per hour? $9.50

Ruth Gordon budgets 30 minutes of each day for devotions. What percent of her total day is budgeted for devotions? Find the answer to the nearest whole percent. 2%

Mrs. Bere had a food bill that totaled $87.29 before giving the clerk coupons for the following amounts: $.35; $1.10; $.60; $.25; $1.00; $1.80; $.75; $.65; $.15; and $.35. Coupons of fifty cents or less are doubled. What was her food bill after using the coupons? $79.19

Documents

Precalculus Video Manual - Abeka...Precalculus • T5 Both the video and the video manual will indicate when to give the quiz. The standard amount of time required to give, grade,