TI-30X IITI-30X ÚS: A Guide for Teachers Developed by Texas Instruments Incorporated Activities developed by Gary Hanson and Aletha Paskett Illustrated by Jay Garrison About the Authors Gary Hanson and Aletha Paskett are math teachers in the Jordan Independent School District in Sandy, Utah. They developed the Activities section and assisted in evaluating the appropriateness of the examples in the How to Use the TI-30X ÖS section of this guide. Important Notice Regarding Book Materials Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this book. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. Note: Using calculators other than the TI-30X IIS may produce results different from those described in these materials. Permission To Reprint or Photocopy Permission is hereby granted to teachers to reprint or photocopy in classroom, workshop, or seminar quantities, the pages or sheets in this book that carry a Texas Instruments copyright notice. These pages are designed to be reproduced by teachers for use in classes, workshops, or seminars, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except as authorized above, prior written permission must be obtained from Texas Instruments Incorporated to reproduce or transmit this work or portions thereof in any other form or by any other electronic or mechanical means, including any information storage or retrieval system, unless expressly permitted by federal copyright law. Send inquiries to this address: Texas Instruments Incorporated 7800 Banner Drive, M/S 3918 Dallas, TX 75251 Attention: Manager, Business Services Note: If you request photocopies of all or portions of this book from others, you must include this page (with the permission statement above) to the supplier of the photocopying services. www.ti.com/calc
[email protected] Copyright © 1999 Texas Instruments Incorporated. Except for the specific rights granted herein, all rights are reserved. Printed in the United States of America. Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers ii About the Teacher Guide How the Teacher Guide is Organized This guide consists of two sections: Activities and How to Use the TI-30X ÙS. The Activities section is a collection of activities for integrating the TI-30X ÙS into mathematics instruction. The How To Use the TI-30X ÙS section is designed to help you teach students how to use the calculator. Things to Keep in Mind • While many of the examples on the transparency masters may be used to develop mathematical concepts, they were not designed specifically for that purpose. For maximum flexibility, each example and activity is independent of the others. Select the transparency master appropriate for the key you are teaching, or select the activity appropriate for the mathematical concept you are teaching. If an example does not seem appropriate for your curriculum or grade level, use it to teach the function of a key (or keys), and then provide relevant examples of your own. To ensure that everyone starts at the same point, have students reset the calculator by pressing & and simultaneously or by pressing % and then selecting Y (yes). • Activities The activities are designed to be teacherdirected. They are intended to help develop mathematical concepts while incorporating the TI-30X ÙS as a teaching tool. Each activity is self-contained and includes the following: • • • • • An overview of the mathematical purpose of the activity. The mathematical concepts being developed. The materials needed to perform the activity. The detailed procedure, including step-bystep TI-30X ÙS key presses. A student activity sheet. • • Conventions Used in the Teacher Guide • In the text, brackets [ ] around a key’s symbol/name indicate that the key is a second, or alternate, function. For example: Z On the transparency masters, second functions are shown just as they appear on the keyboard. For example: How to Use the TI-30X ÚS This section contains examples on transparency masters. Chapters are numbered • and include the following. • An introductory page describing the calculator keys presented in the example, the location of those keys on the TI-30X ÙS, and any pertinent notes about their functions. Transparency masters following the introductory page provide examples of practical applications of the key(s) being discussed. The key(s) being discussed are circled on the TI-30X ÙS keyboard. How to Order Additional Teacher Guides To place an order or to request information about Texas Instruments (TI) calculators, use our e-mail address:
[email protected] visit our TI calculator home page: www.ti.com/calc or, call our toll-free number: 1-800-TI-CARES (1-800-842-2737) • © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X IIS: A Guide for Teachers iii About the TI -30XÚ S Two-Line Display The first line (entry line) displays an entry of up to 88 digits (47 digits for the stat and constant entry lines). Entries begin on the left; those with more than 11 digits scroll to the right. Press ! and " to scroll the entry line. Press % ! or % " to move the cursor immediately to the beginning or end of the entry. The second line (result line) displays a result of up to 10 digits, plus a decimal point, negative sign, x10 indicator, and 2-digit positive or negative exponent. Results that exceed the digit limit are displayed in scientific notation. Menus Certain TI-30X ÙS keys display menus: z, % h, L, % t, u, % w, H, I, % k, = % d, % ‚ and % . Press ! or " to move the cursor and underline a menu item. To return to the previous screen without selecting the item, press -. To select a menu item: • • Press < while the item is underlined, or For menu items followed by an argument value (for example, nPr), enter the value while the item is underlined. The item and the argument value are displayed on the previous screen. Display Indicators Refer to Appendix B for a list of the display indicators. Previous Entries # $ After an expression is evaluated, use # and $ to scroll through previous entries, which are stored in the TI-30X ÙS history. You cannot retrieve previous entries while in STAT mode. Order of Operations The TI-30X ÙS uses the Equation Operating System (EOS TM) to evaluate expressions. The operation priorities are listed on the transparency master in Chapter 4, Order of Operations and Parentheses (page 41). Because operations inside parentheses are performed first, you can use D E to change the order of operations and, therefore, change the result. Error Messages Refer to Appendix C for a listing of the error messages. Last Answer (Ans) The most recently calculated result is stored to the variable Ans. Ans is retained in memory, even after the TI-30X ÙS is turned off. To recall the value of Ans: • Press % i (Ans displays on the screen), or • Press any operation key (T, U, etc.) as the first part of an entry. Ans and the operator are both displayed. 2nd Functions Pressing % displays the 2nd indicator, and then accesses the function printed above the next key pressed. For example, % b 25 E < calculates the square root of 25 and returns the result, 5. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers iv About the TI -30XÚ S (Continued) Resetting the TI-30X ÚS Pressing & and - simultaneously or pressing % and then selecting Y (yes) resets the calculator. Resetting the calculator: • Returns settings to their defaults— standard notation (floating decimal) and degree (DEG) mode. Clears memory variables, pending operations, entries in history, statistical data, constants, and Ans (Last Answer). • Note: The examples on the transparency masters assume all default settings. Automatic Power Downé(APDé) If the TI-30X ÙS remains inactive for about 5 minutes, APD turns it off automatically. Press & after APD. The display, pending operations, settings, and memory are retained. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers v and Delete Basic Math Order of Operations and Parentheses Constant Decimals and Decimal Places Memory Fractions Pi 29 33 36 40 43 45 47 52 58 Appendix C Error Messages Appendix D D-1 Support and Service Information Appendix E Warranty Information E-1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers vi . Roots. and Reciprocals 61 11 Probability 68 75 81 88 Activities The Better Batter — The FIX Key Star Voyage — Scientific Notation Trig Functions What’s My Score — 1-Variable Statistics Heart Rates — 1-Variable Statistics WNBA Stats — 2-Variable Statistics 2 6 10 14 17 23 12 Statistics 13 Trigonometry 14 Notation 15 Logarithms and Antilogarithms 91 16 Angle Settings and Conversions 94 17 Polar and Rectangular Conversions 18 Hyperbolics Appendix A Quick Reference to Keys Appendix B Display Indicators 98 100 A-1 B-1 C-1 How to Use the TI-30X ÚS 1 2 3 4 5 6 7 8 9 TI-30X ÖS Basic Operations Clear.Table of Contents About the Authors About the Teacher Guide About the TI-30X ÖS ii iii iv How to Use the TI-30X ÚS (Continued) 10 Powers. Insert. Activities The Better Batter — The FIX Key Star Voyage — Scientific Notation Trig Functions What’s My Score? — 1-Variable Statistics Heart Rates — 1-Variable Statistics WNBA Stats — 2-Variable Statistics 2 6 10 14 17 23 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 1 . 2952 0.39865 4. 72. Enter the first number. 4. Have students round the following numbers to 4 decimal places using the TI-30X ÖS. Choose the players with the best batting averages.9659 0. 0.39865 4. 2. See the table on page 3 for solutions. You need to select 9 players from the list to be on your team.The Better Batter — The FIX Key Overview Students use % ‚ on the TI-30X ÙS to change numbers to different place values.356 15. 4. F0123456789 Activity Present the following problem to students: You are going to play Virtual Baseball.3987 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 2 .3987 72.02698 2. 4. 15. a.29516 d. Have students practice rounding the following numbers to 3 decimal places using pencil and paper. 0. Find the batting averages (number of hits ¾ number of times at bat) rounded to 3 decimal places for each player. Math Concepts • • • • rounding place value division comparing and ordering decimals Materials • TI-30X ÙS • pencil • student activity Introduction 1. from highest to lowest.0040 2.3633 c. Press 4 to select 4 decimal places.965912 c. Make a list of your players in order.39865 b.00395 4. Press % ‚ to display the menu that lets you set the number of decimal places. 0. a. Press <.027 ³ 1. 3.39865 2.363 0. 4.35647 b. Students calculate batting averages using the TI-30X ÙS and then round their answers to 3 decimal places. 328 0.327 0.311 0.314 0.225 0.322 0.328 0.The Better Batter — The FIX Key Player C.332 0.270 0.238 0.311 0.311 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 3 .317 0.297 0. Ripken Puckett Molitor Greenwell Tartabull Palmeiro Franco Joyner Boggs Baines Sax Williams Sheridan Barfield Mattingly Hall (Continued) Number of Hits 122 119 119 104 103 120 109 105 106 91 113 20 15 64 109 87 Number of Times at Bat 368 363 364 334 311 366 344 338 329 290 388 74 63 284 367 280 Batting Average 0.331 0.291 0. 0. a. 0.00395 _________________ _________________ _________________ _________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 4 . 72. 4. Round the following numbers to 3 decimal places.39865 b.The Better Batter — The FIX Key Problems Name ___________________________ Date ___________________________ 1. 15. Using the TI-30X ÖS.29516 d. round the following numbers to 4 decimal places.35647 b.02698 _________________ _________________ _________________ 2. 0.3633 c. 2.965912 c. a. Ripken Puckett Molitor Greenwell Tartabull Palmeiro Franco Joyner Boggs Baines Sax Williams Sheridan Barfield Mattingly Hall Number of Hits 122 119 119 104 103 120 109 105 106 91 113 20 15 64 109 87 Number of Times at Bat 368 363 364 334 311 366 344 338 329 290 388 74 63 284 367 280 Batting Average (rounded to 3 decimal places) 2. Find the batting averages (number of hits ¾ number of times at bat) rounded to 3 decimal places for each player. You need to select 9 players from the list to be on your team. Make a list of your players in order.The Better Batter — The FIX Key Problem Name ___________________________ Date ___________________________ You are going to play Virtual Baseball. Player 1 Player 2 Player 3 Player 4 Player 5 ____________________ ____________________ ____________________ ____________________ ____________________ TI-30X ÙS: A Guide for Teachers Player 6 Player 7 Player 8 Player 9 ____________________ ____________________ ____________________ ____________________ © 1999 TEXAS INSTRUMENTS INCORPORATED 5 . Player C. Choose the players with the best batting averages. from highest to lowest. Procedure 1. FLO SCI ENG 3. Enter the first number.00000003 2. 5. a. Press % d.Star Voyage — Scientific Notation Overview Students investigate scientific notation by changing numbers into scientific notation.8¯ 3. FLO SCI ENG 9. 12 000 000 b. 384 000 000 000 c. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 6 . where a is greater than or equal to 1 and less than 10. press % C. Press " < <. 0. and n is an integer. 5. 12000000 2. a. Press !.2 Q 10 7 2. 974 000 000 c.32 Q 105 c. 0.000000004 Note: 1. 1.34 Q 10 -12 1. Have students change the following numbers into floating decimal (standard notation). 0. 6. 93 000 000 b. Have students practice writing the following numbers in scientific notation using pencil and paper. 3 Q 10-8 Note: a.84 Q 10 11 1. ³ 1.4 Q 10 -6 4 Q 10 -9 3. 5.0000062 0. and then using them in calculations.57 Q 10 -8 2. 7. To enter a negative number. press % d. press M and then enter the number. Have students change the following numbers into scientific notation using the TI-30X ÖS. Enter 7. Enter 5.74 Q 10 8 3. 12000000 1.00000000000234 d.3 Q 10 7 3.0000034 d.2x1007 Answers assume the default floating decimal setting.8. Press < <. Math Concepts • scientific notation • addition • division Materials • TI-30X ÙS • pencil • student activity Introduction Set up the activity by telling your students: The standard form for scientific notation is a Q 10 n. FLO SCI ENG 4.2 Q 10-6 d. b.8¯7 58000000. 0.8 Q 10 7 58 000 000 732 000 0.0000000157 9. 5000093 Q 10 13 P 6 Q 10 12 = 4. (distance traveled P 1 light year) 2.5 x 10 13 miles. 2.3 x 10 7 miles. You have been assigned to go to Alpha Centauri and you have 5 years to get there. How long will it take you to get there from Earth? Hint: The Earth is approximately 9.5000093 Q 10 13 miles 2.3 x 107 miles from the Sun. find the total distance you need to travel. Your ship can travel at the speed of light. Extension Now that you have been successful. The distance from the Sun to Delta Centauri is 9 x 10 13 miles. Using the TI-30X ÖS.166682167 years 3. You know that light can travel a distance of 6 x 10 12 miles in 1 light year.5 Q 10 13 + 9. The distance from the earth to the sun is approximately 9. you have been asked to make another trip.3 Q 10 7 = 2. Next. ≈15 years © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 7 . Will you be able to get to Alpha Centauri on time? (Continued) Procedure 1. The distance from the sun to Alpha Centauri is 2.Star Voyage — Scientific Notation Activity Present the following problem to students: You are a captain of a starship. Can you make the trip in the given time? Yes Hint: Make sure your calculator is in scientific notation mode before beginning addition. find out how long it will take you to travel the distance. 974 000 000 c. Standard Notation Scientific Notation a.32 Q 105 c. change the following numbers into scientific notation. 93 000 000 b. Using the TI-30X ÖS.Star Voyage — Scientific Notation Problems Name ___________________________ Date ___________________________ 1. 7. 0. Using the TI-30X ÖS. Standard Notation Scientific Notation a. 6.0000034 d. 0.8 Q 10 7 b. 12 000 000 b. change the following numbers into floating decimal notation (standard). Write the following numbers in scientific notation.000000004 _________________________ _________________________ _________________________ _________________________ 3. 3 Q 10-8 _________________________ _________________________ _________________________ _________________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 8 . 0.2 Q 10-6 d. 5. 0. 384 000 000 000 c. Scientific Notation Standard Notation a.0000000157 _________________________ _________________________ _________________________ _________________________ 2.00000000000234 d. The distance from the Sun to Alpha Centauri is 2. Next. Your ship can travel at the speed of light. (distance traveled P 1 light year) ________________________________________________________ _______________________________________________________________________________ 3. You have been assigned to go to Alpha Centauri. and you have 5 years to get there. you have been asked to make another trip. 2. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 9 .3 Q 10 7 miles from the Sun. Can you make the trip in the given time? _____________________________ Extension Now that you have been successful. You know that light can travel a distance of 6 x 10 12 miles in 1 light year.5 x 10 13 miles. The distance from the Earth to the Sun is approximately 9. Using the TI-30X ÖS. find the total distance that you need to travel. The distance from the Sun to Delta Centauri is 9 x 10 13 miles. How long will it take you to get there from Earth? Hint: The Earth is approximately 9. _________________________________________________________________ Hint: Make sure your calculator is in scientific notation mode before you begin addition. find out how long it will take you to travel the distance.Star Voyage — Scientific Notation Problem Name ___________________________ Date ___________________________ You are a captain of a starship.3 x 10 7 miles. Will you be able to get to Alpha Centauri on time? Procedure 1. sin A e. Press % ‚.4567) 27. cos C c. sin C b. Round to the nearest 10 thousandth. Have students find the value of each ratio using the TI-30X ÖS. tan C = 5.9063 ³ To find sin 71°: 1. press E <.4567 b. Round to the nearest hundredth if necessary.9455 3. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 10 . sin( 2. a.4567: 1. Press 2 to select 2 decimal places. cos A f. Press % Z.6009 0. cos 25° 0.83 27 degrees 47 degrees 80 degrees ³ To find B when sin B=0. sin -1(.60 4 ¾ 5 = 0. Press % ‚ 4.1744 3.75 4 ¾ 5 = 0.80 3 ¾ 5 = 0. Round to the nearest degree. tan A 3 ¾ 5 = 0. Have students find the trigonometric ratios for the triangle using the above definitions. and solve problems involving trigonometric ratios. sin 71° b. Press >.60 4 ¾ 3 = 1. cos A = 0.80 3 ¾ 4 = 0. Enter . (Use % ‚ for rounding. cosine.Trig Functions Overview Students practice solving sine. Enter 71.4567) 27. sin(71) 0.6758 c.) a. F0123456789 2. and tangent ratios. tan 31° c.33 A 3 5 4 B C ³ To set 2 decimal places: 1.9455 0. sin -1(.4567. sin = opposite leg ¾ hypotenuse cos = adjacent leg ¾ hypotenuse tan = opposite leg ¾ adjacent leg 1.945518576 3. Have students find the measure of each angle using the TI-30X ÖS. sin(71) 0. press E <. Press % ‚ 0. tan C d. 2. sin -1( 2. Math Concepts • multiplication • division • trigonometric ratios Materials • TI-30X ÙS • pencil • student activity Introduction Introduce the trigonometric ratios to students. a. sin B = 0. Enter 1. angle A is 5.5 ft.3 Extension Present the following problem to students: You want to start the ramp 15 feet away from the door.7º. tan-1(1. Press % \. there is enough room to build the ramp.5 ¾ 15 and press <. ³ 1. Press % \. Use the trigonometric ratio tan = opposite leg ¾ adjacent leg to find angle A. Yes.5/15 5. Can you do that and still have the angle of incline be less than 6 degrees? Yes. tan-1( 2.7 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 11 . 1. A 20 ft. Enter 1. ³ 1. The distance from the ground to the bottom of the door is 1. The distance from the street to the door is 20 feet. tan-1(1.5/20) 4. Is there enough room to build the ramp? Procedure 1.Trig Functions (Continued) Activity Present the following problem to students: You need to build a ramp to your front door. tan-1( 2. You don’t want the angle of incline to be more than 6 degrees.3 degrees (rounded to the nearest tenth). Angle A is 4.5 W 20 and press E <.5 feet. Make a drawing of the problem. 2. sin B = 0.) a. find the measure of each angle. Using the TI-30X ÖS. cos C c. tan 31º c. cos A f. tan C = 5. sin 71º b. Round to the nearest hundredth. a. cos 25º _______________________ _______________________ _______________________ 3. a.83 _______________________ _______________________ _______________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 12 . (Use % ‚ for rounding. cos A =0. Round to the nearest degree. Find the trigonometric ratios for the triangle.6758 c. sin A e.4567 b. find the value of each ratio.Trig Functions Problems Name ___________________________ Date ___________________________ 1. tan A _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ A 3 5 4 B C 2. Using the TI-30X ÖS. tan C d. sin C b. Round to the nearest ten thousandth. 5 feet. The distance from the street to the door is 20 feet.Trig Functions Problem Name ___________________________ Date ___________________________ You need to build a ramp to your front door. You don’t want the angle of incline to be more than 6 degrees. Can you do that and still have the angle of incline be less than 6 degrees? © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 13 .) _________________________ _________________________________________________________________ 3. Make a drawing of the problem. Use the trigonometric ratio tan = opposite leg ¾ adjacent leg to find angle A. 2. (Round your answer to the nearest tenth. Is there room to build the ramp? ____________________________________ Extension You want to start the ramp 15 feet away from the door. The distance from the ground to the bottom of the door is 1. Is there enough room to build the ramp? Procedure 1. Press $ and enter 2 as the frequency for 98. FRQ = 2 4. Your friend’s scores are 89. ³ 1. pressing $ after each score and frequency. 5. Press v and enter your first score. X1 = 98 3. 89. The one who gets the highest average on their math tests for one quarter wins. 78. Have students find the average of their scores using the TI-30X ÖS.What’s My Score? — 1-Variable Statistics Overview Students use the given test scores to find averages. When finished. Continue entering your scores and frequencies. 90. and 100. the average. press u " to select v. Activity Present the following problem to students: You and your friend are having a contest. 2. Remember to enter 2 as the frequency for 98 and 1 for all others. Press $. Write it down. Math Concepts • averages Materials • TI-30X ÙS • pencil • student activity Introduction Discuss finding averages with your students. n v Sx sx 92. 98. Who is the winner? Procedure 1.6 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 14 . Press % t < to select 1-VAR mode. Your scores are 98. and 100. 89. 97. ) ³ 1. Remember to put 2 as the frequency for 89 and 1 for all others. To exit STAT mode. Press % t and " " to CLRDATA. 2. Write it down. 2. Press % t " " < to select CLRDATA. 4. Recalculate your friend’s average. press u " to select v. Now find the average of your friend’s scores. Continue entering the friend’s scores and frequencies. X1 = 89 3. Press <. What score do you need to get so that you are the winner? The score you need: 98 Note: Make sure you exit the STAT mode before going on to another problem. Press v and enter the friend’s first score.What’s My Score? — 1-Variable Statistics (Continued) 2. Who won? Your friend: 93 (You had 92. ³ 1. When finished. the average. Use guess and check to figure out what score you need to get. following steps 3 and 4 on the previous page. making sure to include the new score. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 15 . n v Sx sx 93. 3. 4. press % w <.0 Extension Present the following problem to students: Your friend took a test on the day you were absent and scored 95.6. 3. 78. Your friend’s scores are 89. Your friend took a test on the day you were absent and scored 95. What score do you need to get so that you are the winner? Your friend’s new average _______________________ The score you need _______________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 16 . Who is the winner? Your average Your friend’s average _______________________ _______________________ 2. Whoever gets the highest average on their math tests for one quarter wins. Your scores are 98. and 100.What’s My Score? — 1-Variable Statistics Problems Name ___________________________ Date ___________________________ 1. 89. 98. 90. and 100. 89. You and your friend are having a contest. 97. Press % t <. Enter first heart rate and press $. Ask students: • • What do you think the average heart rate is for someone your age? What about after exercising? Activity Have students complete the following investigation to check their estimations. FRQ= 4. 60 61 62 3 5 6 63 64 65 3 1 4 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 17 . b. (You could have them time for 10 seconds and then multiply by 6. Have students check their resting heart rate by timing their pulse for 1 minute. and then press $. Enter the first frequency and press $. add another tally mark in the frequency column. maximum. Press v to enter the heart rates and frequencies. and the number of tallies for that heart rate as the frequency. Math Concepts • Materials • TI-30X ÙS • stopwatch or a watch with a second hand • student activity mean. For example. Continue entering until you have entered all the heart rates and frequencies. You must press $ between entries. and then press $. assume a class of 22 students: Rate Students Rate Students ³ 1. enter the first heart rate. and range Introduction Students may be placed in smaller groups for this activity to minimize the amount of data to be entered. As other students have the same heart rate.Heart Rates — 1-Variable Statistics Overview Students use the statistics functions of the TI-30X ÙS calculator to investigate the effect of exercise on heart rate. Enter each student’s heart rate and a mark in the frequency column. Enter the first heart rate on the chart as the first X value. 2. Enter the first frequency. minimum. 1. a. 3. 5. For example. Collect data on the chart. X1= 3. Enter the heart rate data into the TI-30X ÚS. but this could be the quietest minute of your day!) 2. Tell students: If at any point during this portion of the activity you experience pain. n Ï Sx Îx 22. c. explain that Òx is the sum of all the heart rates. 7. Enter the data into the calculator. • • • How are the histograms the same? How are they different? Is the data grouped the same. 6. 5. d. then you are in great shape. or is it more spread out in one graph compared to another? © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 18 . Press " " " to Òx. b. Press u. 2. Instruct them to time their pulse for 1 minute again and record as before. 3. Have the students run in place for 2 minutes and then give them these instructions: a. Compare to the other 2 averages. Record your heart rate as before. weakness. Have them enter the data into the calculator again and calculate the average heart rate after jumping jacks. After students display Òx (Sigma x). Now we will see the effect of some exercise on heart rate. If it is higher than 125. Check the statistics calculations. Instruct students to make a histogram of the 3 sets of data they collected. Compare the average heart rate after running with the resting heart rate. • • How many heartbeats were there in one minute? Is the average heart rate higher or lower than you expected? n should equal the total number of student sampled. stop immediately. then you are in poor shape. Your students’ results will vary depending on the size of group and the heart rate readings. Note: The numbers show the results for the example described above. or shortness of breath. Now have the students do jumping jacks for 2 minutes. Ask students: 1. Press " to Ï to see the average heart rate. Ask students: 9. Òx Òx 2 1370. Time your pulse for 1 minute. 8 How fit is the class? If the class (or individual) heart rate after jumping jacks is less than 90. n Ï Sx Îx 62.Heart Rates — 1-Variable Statistics (Continued) 4. Heart Rates — 1-Variable Statistics Problem Name ___________________________ Date ___________________________ What do you think the average heart rate is for someone your age? What about after exercising? Procedure 1. What is the class (group) average? ___________________________________ 3. Heartbeats per minute (resting) Frequency 2. Use this table to record your class or group data (resting). What is the total number of heartbeats for the minute? _________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 19 . What is the total number of heartbeats for the minute? _________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 20 . Use this table to record your class or group data (running). Heartbeats per minute (running) Frequency 5. What is the class (group) average?___________________________________ 6.Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ 4. then you are in poor shape. Use this table to record your class or group data (jumping). If it is higher than 125. What is the class (group) average? __________________________________ 9. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 21 . What is the total number of heartbeats for the minute? _________________ 10. then you are in great shape. How fit is the class? _______________________________________________ _________________________________________________________________ Note: If the class (or individual) heart rate after jumping jacks is less than 90. Heartbeats per minute (jumping) Frequency 8.Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ 7. Now make a histogram for each of the 3 sets of data you collected. How are the histograms the same? How are they different? _____________ _________________________________________________________________ _________________________________________________________________ 13.Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ 11. Is the data grouped the same or is it more spread out in one graph compared to another? _____________________________________________ _________________________________________________________________ _________________________________________________________________ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 22 . Resting Running Jumping 12. Enter 10. Enter data for each player in the table. 1-VAR 2-VAR 2. enter the data. Press v. X1=10. Y1=1 4.1 (points per game for the first player. X1= 2. Press $ and enter data for the second player.WNBA Stats — 2-Variable Statistics Overview Students use WNBA statistics to explore the relationship between 2 variables. Press $. 2. 1. ` © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 23 . 6. Rhonda Mapp). Put the calculator in STAT mode and choose 2-VAR statistics. 1.7 5. Press $ after entering each data point. Enter 21. Using the table in the activity (page 26). Press % t and then ". Math Concepts • 2-variable statistics Materials • TI-30X ÙS • pencils • student activity Activity Present the following problem to students: Do you think WNBA (Women’s National Basketball Association) playing time (in minutes per game) is related to how many points a player scores? Do you think it is related to how many rebounds a player gets? Or is it related to the player’s field goal percentage? Procedure 1. They use the TI-30X ÙS to compute the regression equation and evaluate some values.7 (minutes per game for Rhonda Mapp). Enter points per game as the X-variable and minutes per game (playing time) as the Y-variable. Press < to select 2-VAR.1 3. Y1=21. WNBA Stats — 2-Variable Statistics (Continued) 3.00 4. the better the correlation between the two variables. Press % ‚. Press 2. Ask students: 1. The form of the equation is y = ax + b. Now calculate how many minutes you would expect a player to play if she averages 15 points per game. Write the equation for the line of best fit (round to the nearest hundredth). This is the slope of the line of best fit.02 5. n Ï Sx Îx Ð 12. Write the correlation coefficient.91 6. You may want to fix the decimal to 2 places before doing the statistical calculations. ÒXY a b r 1. F0123456789 2. Ò XY a b r 7. Press " " to y¢.00 • • • What is the average points scored for the players shown? What is the average playing time? What is the total number of points scored per game for all the given players? 2. Calculate the statistical data.44 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 24 . 3. Press " to r. Press " until you get to a. 1. y¢(15) 30. 3. Press " " " to Ð. n Ï Sx Îx Ð 9. Press " " " to Òx. This is the y-intercept of the line. 1. n Ï Sx Îx Ð 21. 1.02 r = .56 2. ÒXY a b r 0. x¢ y¢ 2. Type 15 E and press <.91 3.59 4. Press <.33 You may want to discuss the other statistical variables and what they mean.56x + 7. Sy Îy Òx 112. Press " to Ï. Press " to b. 1. This is the correlation coefficient. Press u. The closer the correlation coefficient value is to 1 (or –1). 4. which have the correlation coefficient closest to 1 or –1?) © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 25 . Now calculate how many points you would expect a player to score if she plays 35 minutes a game.) Ask students: Which 2 variables have the closest correlations? (That is. Discuss the correlation as a class. x¢(35) 17. Press <. n Ï Sx Îx Ð 12. you only need to enter the new data in X. Ask students: 1. Press ! ! to x¢.92 Extension Now have students use the calculator to investigate the correlation of the other data in the chart such as the relation of field goal percentage to minutes per game.00 2.WNBA Stats — 2-Variable Statistics (Continued) 7. (Remember. 8. x¢ y¢ • • Are there other factors affecting the players’ minutes per game besides points scored? What about defense. Type 35 E and press <. rebounding. or rebounds per game to minutes per game.? 3. etc. since you have already entered the minutes in Y. Press u. Rebecca Lobo 10. Begin by entering the points per game as the X-variable and the minutes per game as the Y-variable.420 .3 .7 31.1 13.9 . Malgozata Dydek 7. Cynthia Cooper 5.467 .6 28 16.426 . Player 1.294 . Maria Stepanova Field Goal Percentage .9 12.3 Rebounds per Game 4.9 35 33.6 6. Keri Chaconas 9.7 9.6 3. Coquese Washington 11.7 4.9 Minutes per Game 21. Rhonda Mapp 2.441 .3 6.3 6.297 .8 6.6 3.8 22.9 1.6 21. Toni Foster 12.7 13.8 11. Elena Baranova 6. Janeth Arcain 4.9 4.446 . Heidi Burge 8.7 12.5 3.9 3. Vicky Bullet 3.9 6.9 1.482 .426 Points per Game 10.WNBA Stats — 2-Variable Statistics Problem Name ___________________________ Date ___________________________ Do you think WNBA playing time (in minutes per game) is related to how many points a player scores? Do you think it is related to how many rebounds a player gets? Or is it related to the player’s field goal percentage? Procedure Use the following table of data to explore the relationships of different pairs of data.506 .484 .5 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 26 .2 8.2 29.509 .1 13.3 7.7 1. or rebounds per game to minutes per game. Write the correlation coefficient. you only need to enter the new data in X. which have the correlation coefficient closest to 1 or –1?) © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 27 .) 1. 3. What is the average field goal percentage? 2. What is the average number of rebounds per game? 5. 6. Write the equation for the line of best fit. Write the equation for the line of best fit. Which 2 variables have the closest correlation? (That is. 9. Write the equation for the line of best fit. 8. 4. (Remember. Write the correlation coefficient.WNBA Stats — 2-Variable Statistics Extension Name ___________________________ Date ___________________________ Use the calculator to investigate the correlation of the other data in the table such as the relation of field goal percentage to minutes per game. What is the total number of rebounds per game for all the given players? 7. since you have already entered the minutes per game in Y. and Reciprocals Probability Statistics Trigonometry Notation Logarithms and Antilogarithms Angle Settings and Conversions Polar and Rectangular Conversions Hyperbolics 29 33 36 40 43 45 47 52 58 61 68 75 81 88 91 94 98 100 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 28 . and Delete Basic Math Order of Operations and Parentheses Constant Decimals and Decimal Places Memory Fractions Pi Powers. Insert. Roots.How to Use the TI-30X ÚS TI-30X ÚS Basic Operations Clear. No menu or message is displayed. more characters are located above or below the entry line. 4. 2 6 3 1 7 • 4 5 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 29 . Press < when Y (yes) is underlined to reset the calculator. statistical data. settings. entries in history. and Ans (Last Answer). 5. • Note: Pressing & and simultaneously resets the calculator immediately. % # or % $ scroll to the beginning or end of history. & turns on the calculator. pending operations. pending operations. The display. ! and " move the cursor left and right to scroll the entry line. constants. Notes The examples on the transparency masters assume all default settings. Resetting the calculator: Returns settings to their defaults: floating decimal (standard) notation and degree (DEG) mode. 6. % ' turns off the calculator and clears the display. Press % ! or % " to scroll to the beginning or end of the entry line. % i recalls the most recently calculated result and displays it as Ans. • The entry line can contain up to 88 characters. < completes the operation or executes the command. 3. • • 7. the entry line contains more characters to the left or right. and memory are retained.TI-30X ÚS Basic Operations Keys 1. Press & after Automatic Power Downé (APDé). RESET: N Y • 1 Press < when N (no) is underlined to return to the previous screen without resetting the calculator. When ¸ or ¹ appear in the display. 2. # and $ move the cursor up and down through previous entries. % displays the RESET menu. Clears memory variables. When º or » appear. The message MEM CLEARED is displayed. % turns on the 2nd indicator and accesses the function shown above the next key you press. Change 23 to 26 and complete the operation. Arrows. Equals Enter 46 N 23.Second. Off. Press Display 46-23 DEG %¥ ! " #$< 46 U 23 !!!!1 ""6< 81 T 57 < %¥ & ##$ 41-26 81+57 ~ 81+57 ' 15. Enter 81 + 57 and complete the operation. Scroll to see your previous entries. DEG ' DEG ' DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 30 . Change 46 to 41. DEG ' 138. No menu or message is displayed.at the same time also resets the calculator immediately. Press Display RESET: RESET: N Y N Y - %¨ %¨ " < - DEG DEG MEM CLEARED DEG ~ DEG Pressing & and .Reset Reset the calculator. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 31 . Using %¨ or & and returns all settings to their defaults and clears the memory. ' 16.Last Answer (Ans) Use Last Answer (Ans) to calculate (2+2)2. Press Display 2+2 Ans Ans2 ' %ª 2T2< %ª F < DEG 4. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 32 . statistical registers.Clear. Insert. 2. 2 Notes • • The examples on the transparency masters assume all default settings. Pressing . each time you press J. it moves the cursor to the most recent entry. Once the display is clear. Then. or numeric notation.clears characters and error messages. 3. 2 3 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 33 . it deletes 1 character to the left of the cursor. Hold J down to delete all characters to the right. J deletes the character at the cursor. angle units.does not affect the memory. and Delete Keys 1. . % f lets you insert a character at the cursor. and then change it to 459 + 2865.Delete and Insert Enter 4569 + 285. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 34 . Complete the problem. Press Display 4569+285 DEG J %‘ 4569 T 285 !!!!! !J """" % < 459+285 DEG ‘6 459+2865 DEG 459+2865 ' 3324. Clear Enter 21595. Press Display 21595 DEG - 21595 !!(Clear to right) 215 DEG (Clear entry) ~ DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 35 . Clear the entry. Clear the 95. Basic Math Keys 1. 5. 3. T adds. Example: 3 (4+3) = 21 Do not confuse M with U. 4 7 3 2 1 5 6 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 36 . W divides. 6. 3 Notes • • • • The examples on the transparency masters assume all default settings. < completes the operation or executes the command. 7. 2. The TI-30X ÙS allows implied multiplication. 4. V multiplies. % _ changes a real number to a percent. Results of percent calculations display according to the decimal notation mode setting. M lets you enter a negative number. U subtracts. U allows subtraction. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 37 . Subtract.Add. Divide. DEG ' 39. DEG ' 132. DEG ' 336. Equals Find: 2 + 54 ½ 6 = 16 x 21 = 78 P 2 = 12 x (5 + 6) = Display 2+54-6 16*21 78/2 12*(5+6) ' TUVW < Press 2 T 54 U 6 < 16 V 21 < 78 W 2 < 12 V D 5 T 6E< 50. Multiply. ? Press Display L3+12 ' M M 3 T 12 < DEG 9. the temperature had risen 12¡ C.Negative Numbers The temperature in Utah was L3¡ C at 6:00 a. By 10:00 a. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 38 .m. What was the temperature at 10:00 a.m.m. He saves 15% of his earnings. How much does Mike save per week? Press Display 15 15%*80 DEG %£ 15 %£ V 80 < ' 12.Percent Mike makes $80 per week. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 39 . Operations inside parentheses are performed first. 2. E closes a parenthetical expression. therefore. 4 Notes • • The examples on the transparency masters assume all default settings. Use D E to change the order of operations and. The transparency master showing the Equation Operating System (EOS TM) demonstrates the order in which the TI-30X ÙS completes calculations.Order of Operations and Parentheses Keys 1. Example: 1 + 2 x 3 = 7 (1 + 2) x 3 = 9 • 1 2 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 40 . change the result. D opens a parenthetical expression. or %’ menu items Functions entered after the expression. such as the >. %“. and 8DMS) 3 4 5 6 7 8 9 10 11 (last) < completes all operations and closes all open parentheses. implied multiplication. ¢. such as F and angle unit modifiers (¡. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 41 . £. and division Addition and subtraction Conversions (%š. g) Fractions Exponentiation (G) and roots (%¡) Negation (M) Permutations (nPr) and combinations (nCr) Multiplication. A. r.Equation Operating System 1 (first) 2 Expressions inside D E EOSé Functions that need a E and precede the expression. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 42 .Order of Operations 1+2x3= Press Display 1+2*3 ' TVDE 7. 1T2V3 < (1 + 2) x 3 = Press DEG Display ( 1+2 ) *3 1+2) ' D1T2EV 3< DEG 9. < places the contents of K at the end of the expression in the display. A K displays when the constant mode is on. Press < to place the contents of K at the end of the expression and evaluate it. K appears in the display.to clear the display. 3. and values). Press . press . Enter an initial value. except statistics. If you do not enter a value. To enter a constant: 1. % l turns on the constant mode and lets you define a constant. 5 Notes • • • The examples on the transparency masters assume all default settings. 2. Press % l. Continue pressing < to repeat the constant. and the constant is used to evaluate the new expression. 7. If a constant is already stored. Press < to turn on the constant mode. 4. All functions. 0 is assumed. The result is stored in Ans.Constant Keys 1. 6. 5. 1 2 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 43 .to clear it. functions. Enter your constant (any set of operations. and Ans will appear in the display. 2. which is displayed. work in constant mode. Constant Three people babysit for $3.25 each per hour. First person works 16 hours. Second person works 12 hours. Third person works 17 hours. How much did each person earn? Press Display K= %™ %™ V 3.25 < 16 < 12 < 17 < %™ (Constant mode is off.) © 1999 TEXAS INSTRUMENTS INCORPORATED K = *3.25 ~ 16*3. 16*3 . 25 12*3. 12*3 . 25 17*3. 17*3 . 25 ~ DEG DEG K ' DEG K ' DEG 52. K ' DEG 39. K ' 55.25 DEG K ' DEG K TI-30X ÙS: A Guide for Teachers 44 Decimals and Decimal Places Keys 1. 8 enters a decimal point. 2. % ‚ displays the following menu, which lets you set the number of decimal places. F0123456789 F 0-9 Sets floating decimal (standard) notation. Sets the number of decimal places. • 6 Notes • • The examples on the transparency masters assume all default settings. % ‚ 8 removes the setting and returns to standard notation (floating decimal). The FIX setting affects all decimal results and the mantissa of scientific and engineering notation results. The TI-30X ÙS automatically rounds the result to the number of decimal places selected. For example, when the decimal is set to 2 places, 0.147 becomes 0.15 when you press <. The TI-30X ÙS also rounds or pads resulting values with trailing zeros to fit the selected setting. For example, when the decimal is set to 5 places, 0.147 becomes 0.14700 when you press <. All results are displayed to the FIX setting until you clear the setting by either pressing % ‚ 8 or selecting F(floating) on the decimal notation menu. Resetting the calculator also clears the FIX setting. After pressing % ‚, you can select the number of decimal places in 2 ways: Press ! or " to move to the number of decimal places you want, and then press <, or Press the number key that corresponds to the number of decimal places you want. • 1 2 FIX affects only the results, not the entry. • • • © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 45 Decimal, FIX Round 12.345 to the hundredths place, to the tenths place, and then cancel the FIX setting. Press Display 12.345 DEG 8 %© 12 8 345 %© """ < < F0123456789 _ DEG F01_3456789 2 DEG 12.345 FIX DEG 12.345 FIX ' 12.35 DEG %© 1 %© 8 © 1999 TEXAS INSTRUMENTS INCORPORATED 12.345 FIX ' 12.3 DEG 12.345 ' 12.345 DEG TI-30X ÙS: A Guide for Teachers 46 A B C D E Lets you view the stored value before pasting it in variable form to the display. The new variable replaces any previously stored value. the variable name (A. 3. A B C D E Lets you view the stored value before pasting it to the display. z displays the following menu of variables. see Chapter 11. Probability (page 68). • • Resetting the calculator clears all memory variables. • 3 2 4 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 47 . rand Lets you set a seed value for random integers. % h displays the following menu of variables. You can store a real number or an expression that results in a real number to a memory variable. or E) is displayed on the entry line. C. When you select a variable using z. 2. the value of the stored variable is displayed on the entry line. A B C D E Lets you select a variable in which to store the displayed value. B. 7 4. Notes • • The examples on the transparency masters assume all default settings. D.Memory Keys 1. % { clears all variables. L displays the following menu of variables. For more about rand. When you select a variable using % h. 83.58333333 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 48 .66666667 DEG Ans¹A Ans A DEG ' 92+83+97+86 Ans/4 Ans+A Ans/2 DEG ' 358. Memory Variable.66666667 85. and 86.1666667 DEG ' 87. Press Display Lz %¦ 96 T 76 T 85 < W3< L< 92 T 83 T 97 T 86 < W4< Tz << W2< 96+76+85 Ans/3 ' 257. ' 89. 97. Clear Variable Test scores: 96.5 DEG ' 175. 76. DEG ' 85. Find the average of test and weekly scores. Weekly scores: 92. Find the final average. 85.Store. Store. Recall Which would be the better buy: 3 cassette tapes for $7.37 DEG ' 2.98. %§ A B C D E - 2.66 DEG ' 2.48? Press Display 7.48 / 4 Ans ¹ B ' L %§ 7 8 98 W 3 < L< 9 848 W 4 < L"< 2.37 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 49 . " A B C D E - 2.66 DEG ' 2.98/3 Ans¹A Ans A 9. or 4 cassette tapes for $9.66 DEG View the second price again.37 DEG View the first price again. 98 ' 27. belt 1 $6. 2*13 .Store. ties 3 $7. Recall Shop A B C Purchases Qty Cost shirts 2 $13.98 L %§ How much did you spend at each shop. and how much did you spend altogether? Press Display 2*13.98 ea.98 ea.96 DEG ' 23. 3*7 .96 DEG & Ans¹A 3*7. 98 ' 2 V 13 8 98 < L < 3 V 7 8 98 < ¹A B C D E DEG 27.98 suspenders 1 $9.94 DEG Continued © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 50 . 96+23.Store. 96+23 .96 DEG ' DEG % . DEG ' 27.86 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 51 . Recall (Continued) L Press Display Ans¹B ' %§ 23. 27 . 94 &' 68.96 DEG ' 16.94 DEG L"< 6 8 98 T 9 8 98 < L"" < %§ <T %§ " <T %§ " " << 6 . 98+9 . 98 98+9. 96 + ' 16. 96+23 . 94+ 96+23. 96+ 27 . Ans¹C 27. 8 Notes • • The examples on the transparency masters assume all default settings. 3. the whole number can be up to 3 digits. the numerator can be up to 3 digits. N lets you enter mixed numbers and fractions. You can use fractions and decimals together in a calculation. When possible. the numerator can be up to 6 digits and the denominator can be any number through 1000. Fractional calculations can show fractional or decimal results. To enter a mixed number or a fraction.Fractions Keys 1. Fractional results and entries are automatically reduced to their lowest terms. • • • 3 2 1 • Calculations involving a fraction and a decimal will always display results as decimals. and the denominator can be any number through 1000. You can enter a fraction or mixed number anywhere you can enter a decimal value. For a simple fraction. For a mixed number. % O converts a simple fraction to a mixed number or a mixed number to a simple fraction. • © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 52 . 2. press N between the whole number and the numerator and between the numerator and the denominator. calculations involving 2 fractions or a fraction and any integer will display fractional results. % j converts a fraction to its decimal • equivalent or changes a decimal to its fractional equivalent. if possible. Fractions At the party. How much pizza did you eat? N Press Display 5®6+1 10 6+1®10 ' 5N6T1 N 10 < 14 / 15 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 53 . you ate 5/6 of the pepperoni pizza and 1/10 of the sausage pizza. she gained 2 3/4 pounds. In the next 6 months. How much does she weigh? N Press Display 4®3®8+2 3®4 3 8+2®3 4 DEG 4N3N 8T2N3 N4< ' 7− 1/8 \ © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 54 .Mixed Numbers A baby weighed 4 3/8 pounds at birth. To find out how many times Sam must use his measuring cup. The recipe calls for 3 1/2 cups of flour. He has only a 1/2-cup measuring cup. Fraction to Mixed Number Sam is making his birthday cake. %š < Ans ¾ A b/c ½ ¾ d/e ' 3− 1/2 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 55 . change the mixed number to a fraction.Mixed Number to Fraction. 3 1/ 2 ¾ 1/ 2 = 7 %š Press Display 3®1®2 1 2 3®1®2 ¾ A b/c ½ ¾ d/e 1 2 3®1®2 ¾ A b/c ½ ¾ d/e 1 2 DEG DEG 3N1N2 %š < ' 7/2 DEG Show the mixed number again. Press Display 5®3®4 ¾ F ½ ¾ D 3 4 DEG %“ 5N3N 4 %“ < 5®3®4 ¾ F ½ ¾ D 3 4 ' 5. Change Mary’s time to a decimal to determine who swims faster.72 minutes. Mary swims 20 laps in 5 3/4 minutes.75 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 56 .Fraction to Decimal Juan swims 20 laps in 5. Press Display 2.25 to its fractional equivalent.25 ¾ F ½ ¾ D ' %“ 2 8 25 %“ < 2−1/4 1/4 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 57 .Decimal to Fraction Change 2. The transparency masters show both ways. 141592653590).141592654). 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 58 . you can select the number of decimal places in 2 ways: Press ! or " to move to the number of decimal places you want. Internally. and then press <. After pressing % ‚.Pi Keys 1. 9 Notes • • • The examples on the transparency masters assume all default settings. pi is stored to 13 digits (3. or Press the number key that corresponds to the number of decimal places you want. g displays the value of pi rounded to 10 digits (3. C = 2pr = 2 x p x 1.5 ' 9.5 < * 2*p*1.Circumference Use this formula to find the amount of border you need if you want to put a circular border all the way around the tree.424777961 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 59 .5m g Press Display 2 V g V 1. and then return to floating decimal mode.26548246 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 60 .26548246 DEG ©" F0123456789 DEG < p*42 * p*42 FIX ' 50. Round your answer to the nearest whole number.Area Use this formula to find how much of a lawn would be covered by the sprinkler. A = pr2 = p x 42 g Press Display p*42 * ' gV4F < % 50. DEG % ©8 ' 50. The result of calculations with G must be within the range of the TI-30X ÙS. press G. % c calculates the specified root (x) of the value. 3. and Reciprocals Keys 1. A sign change takes precedence over exponents.Powers. The base (or mantissa) and the exponent may be either positive or negative. F squares the value. G raises a value to a specified power. 2. 4. Example: L5 2 = L25 (L5) 2 = 25 4 3 5 2 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 61 . enter the base. and then enter the exponent. % b calculates the square root. Roots. To use G. Refer to Domain under Error Messages in Appendix C (page C-1) for restrictions. • • 10 Notes • • • The examples on the transparency masters assume all default settings. 5. a calculates the reciprocal. Squares Use this formula to find the size of the tarpaulin needed to cover the entire baseball infield.4^2 ' 27.42 FG Press Display 27.76 DEG ' 750.4 G 2 < 750.76 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 62 .4 F < or 27.42 27. A = x2 = 27. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 63 .Square Roots Use this formula to find the length of the side of a square clubhouse if 3m2 of carpet would cover the floor.732050808 DEG © ' FIX DEG 2. L= x = 3 %œ 3m2 of carpet Press Display ‹(3) ‹(3) ' %œ 3 E < % " < 1. Round your answer to 0 decimal places. Change your answer to a fraction.167 DEG ' 12−167/1000 12 167/1000 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 64 .Cubes Use this formula to find the volume of a cube with sides 2. V = L3 = 2.3^3 ' 283G3 < % < “ Ans¾ Ans¾F½ ¾ D 12.3 meters long.33 G Press Display 2. and so on until you cannot physically fold it in half again. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 65 . DEG ' 32768.Powers Fold a piece of paper in half. in half again. How many sections would there be after 10 folds? After 15 folds? Press Display 2^10 2^15 ' G 2 G 10 < 2 G 15 < 1024. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 66 . what is the length of each side? Press Display 3 x‹125 %¡ 3 %¡ 125 < DEG 5.Roots If the volume of a cube is 125 cm3. ? Luxury 5 1/3 hrs. ? Steam 5 hrs. Time Portion Spent Completed Per Hour Ships Building Sailing 10 hrs. ? How much of each model was completed per hour? Press Sailing ship: Display a 10 a % < “ 10-1¾F½ ¾ D ' 1 / 10 DEG Steam ship: 5a% < “ 5-1¾F½ ¾ D ' 1/5 DEG Luxury liner: 5N1N3 a< 5®1®3 -1 1 3 ' 3 / 16 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 67 .Reciprocals The chart below shows the amount of time spent building model ships. nPr nCr ! RAND Calculates the number of possible permutations. A combination is an arrangement of objects in which the order is not important. H displays the following menu of functions. Calculates the factorial. as in a hand of cards. where n is a positive whole number 69. Generates a random integer between 2 numbers that you specify. use a comma to separate the 2 numbers that you specify. • 11 Notes • • The examples on the transparency masters assume all default settings. • RANDI • • 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 68 . The seed value changes randomly when a random number is generated. To control a sequence of random numbers. as in a race. Generates a random 10-digit real number between 0 and 1. For RANDI. Calculates the number of possible combinations. A factorial is the product of all the positive integers from 1 to n.Probability Keys 1. you can store (L) an integer to RAND just as you would store values to memory variables. A permutation is an arrangement of objects in which the order is important. Combination (nCr) You have space for 2 books on your bookshelf. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 69 . Press B C AB BA CA DA Display nPr D AC BC CB DB AD BD CD DC ! DEG 4H" 2< nCr --- & 4 nCr 2 ' 6. You have 4 books to put on the shelf. Use this formula to find how many ways you could place the 4 books in the 2 spaces. 4 nCr 2 = x H A AB and BA count as only 1 combination. Press AD BD CD DC ! & Display nPr --- 4H 2< 4 nPr 2 ' 12. 4 nPr 2 = x H A B C AB BA CA DA D AC BC CB DB nCr DEG AB and BA count as 2 permutations. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 70 .Permutation (nPr) Four different people are running in a race. Use this formula to find how many different ways they can place 1st and 2nd. 7. 3. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 71 . how many 4-digit numbers can you form? 4! = x H 1 A ABCD BACD CABD DABC Press ABDC BADC CADB DACB 3 B ACBD BCAD CBAD DBAC 7 9 C ACDB BCDA CBDA DBCA Display nPr 4! nCr DEG D ADBC BDCA CDAB DCAB ADCB BDAC CDBA DCBA ! - 4H"" << & ' 24. and 9 only one time each.Factorial (!) Using the digits 1. Press Display % H H""" << < Results will vary. RAND -___ RANDI DEG 0.839588694 DEG RAND RAND ' ' 0.Random (RAND) Generate a sequence of random numbers.482688185 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 72 . 000018633 DEG ' 0. Press Display % H 1L! < H""" << < rand ---- 1¹rand RAND RAND 310000. DEG ' DEG 1.Random (RAND) Set 1 as the current seed and generate a sequence of random numbers.745579721 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 73 . ' 0. RAND RANDI ---__ DEG ¤ % ANDI( 2. 10) &' 3. 10) DEG RANDI( 2.Random Integer (RAND) Generate a random integer from 2 through 10. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 74 . Press Display % H H! <2% 10 E < Results will vary. 2-VAR CLRDATA 2 sets of data with 2 measured variables—x. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 75 . the independent variable. % w displays the following menu that lets you clear data values and exit STAT mode. Analyzes paired data from 3. 1 3 4 2 a b r Number of x (or x. Sum of all x values or y values. You can change data points once they are entered. Sample standard deviation of x or y. u displays the menu of variables with their current values.y) data points. % t displays a menu from which you can select 1-VAR. • 4. Population standard deviation of x or y. Press < when N (no) is underlined to return to the previous screen without exiting STAT mode. EXIT ST: Y N • Press < when Y (yes) is underlined to clear data values and exit STAT mode. Mean of all x or y values. Sum of all x 2 values or y 2 values. Sum of (x Q y) for all xy pairs in 2 lists. and y. the dependent variable. Linear regression slope.Statistics Keys 1. x and y for 2-VAR stats). Notes • • • The examples on the transparency masters assume all default settings. To save the last data point or frequency value entered. you must press < or $. Clears data values without exiting STAT mode. n v or w Sx or Sy sx or sy Gx or Gy Gx2 or Gy2 Gxy 2. 2-VAR or CLRDATA. Linear regression y-intercept. Correlation coefficient. v lets you enter data points (x for 1-VAR stats. 1-VAR 12 Analyzes data from 1 set of data with 1 measured variable—x. 85. 53.Entering 1-VAR Stat Data Five students took a math test. 77. Press Display 1-VAR ----X 1= X1=85 STAT %” v %” <v 85 $ 2 $ 97 $ $ 53 $ $ 77 < Continued © 1999 TEXAS INSTRUMENTS INCORPORATED 2-VAR DEG & S DEG S FRQ=1 FRQ=1 FRQ=2 FRQ=2 X2=97 X3=53 X4=77 STAT DEG S STAT DEG S STAT DEG S STAT DEG S STAT DEG STAT 77. Using their scores. DEG S TI-30X ÙS: A Guide for Teachers 76 . 97. enter the data points—85. 39512123 STAT DEG --- & n v Sx sx STAT 14.66424222 DEG --- & % --- Gx Gx STAT 2 397. the population standard deviation (sx). DEG % Gx STAT --- Gx 2 32597. and the sum of the squares (Gx2). & n v Sx sx STAT 79. the sum of the scores (Gx).Viewing the Data (Continued) Find the number of data points (n). the mean (v). Press Display n v Sx sx STAT u u " " " " " Continued & DEG 5. the sample standard deviation (sx).4 DEG n v Sx sx 16. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 77 . Display the lowest score. and then find the new mean (v). STAT DEG DEG ~ DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 78 . drop it. Press Display X1=85 STAT DEG %˜ v $$$$ $0< u" %˜ < S X3=53 STAT DEG S FRQ=0 FRQ=0 STAT S DEG 0. & n EXIT ST: Y N STAT v Sx sx 86.Removing Data Points (Continued) Return to the first data point. Clear all data by exiting STAT mode. Month April May Press %” v Total No.(x) 58 (x1) 47 (x2) Brand A (y) 35 (y1) 28 (y2) 2-VAR ----DEG Display 1-VAR X 1= X1=58 STAT %” " <v 58 $ 35 $ 47 $ 28 < Continued © 1999 TEXAS INSTRUMENTS INCORPORATED & S DEG S Y1 =35 X2 =47 Y2 =28 Y2 =28 STAT DEG S STAT DEG S STAT DEG S STAT DEG STAT 28.Entering 2-VAR Stat Data The table below shows the number of pairs of athletic shoes sold by a small shoe store. Enter this data as the data points. DEG S TI-30X ÙS: A Guide for Teachers 79 . Press Display % u %˜ u! < 32 E < %˜ < x' STAT y' - DEG 18.45454545 STAT DEG y' (32) EXIT ST: Y N STAT DEG ~ DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 80 . predict the June sales of Brand A. When finished.Viewing the Data (Continued) If the store sells 32 pairs of shoes in June. exit STAT mode and clear all data points. ? calculates the cosine. 6. be sure to select the appropriate angle mode setting (degree. 2. • 13 Notes • • The examples on the transparency masters assume all default settings. or gradient—See Chapter 16. E ends a trig function. @ calculates the tangent. > calculates the sine. % Z calculates the inverse sine. The calculator interprets values according to the current angle-unit mode setting. Before starting a trigonometric calculation. 5. 3.Trigonometry Keys 1. radian. % \ calculates the inverse tangent. % [ calculates the inverse cosine. Angle Settings and Conversions). 4. 6 5 2 1 4 3 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 81 . 0836194 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 82 . DEG ' 153.0836194 DEG 78/tan (27) FIX ' 78/tan (27) 153.Tangent Use this formula to find the distance from the lighthouse to the boat. Round your answer to the nearest whole number. and then return to floating decimal mode. D = 78/TAN 27 @ Press Display 78/tan (27) ' 78 W @ 27 E < %© " < %© 8 F0123456789 DEG 153. 49573328 2500 E < DEG %© " " < %© 8 F0123456789 DEG tan tan -1 (600/25 FIX &' 13. TAN x = 600/2500 %Ÿ Press Display tan tan -1 (600/25 &' %Ÿ 600 W 13. and then return to floating decimal mode.49573328 tan tan -1 (600/25 DEG 13. Round your answer to the nearest tenth.Inverse Tangent Use this formula to find the angle of depression.5 DEG &' © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 83 . and then return to floating decimal mode. ' TI-30X ÙS: A Guide for Teachers 84 .294095226 DEG 5*cos (75) ' F0123456789 DEG 5*cos (75) FIX ' DEG 1.Cosine Use this formula to find how far the base of the ladder is from the house. Round your answer to the nearest whole number.294095226 DEG 5*cos (75) 1. D = 5 x COS 75 ? Press Display 5V? 75 E < %© " < %© 8 © 1999 TEXAS INSTRUMENTS INCORPORATED 1. 04169519 DEG cos-1 (453/50 cos-1 (453/50 &' 25. Round your answer to the nearest tenth.Inverse Cosine Use this formula to find the angle of the ski jump. and then return to floating decimal mode. COS x = 453/500 % Press Display cos-1 (453/50 &' % 453 W 500 E < %© " " < %© 8 F0123456789 DEG 25.04169519 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 85 .0 DEG &' 25. 214601517 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 86 .214601517 1.5/sin (12) 7. and then return to floating decimal mode. Round your answer to the nearest whole number. D = 1.5/SIN 12 > Press Display 185W> 12 E < % ©" F 0123456789 DEG 7. DEG &' 7.Sine Use this formula to find the length of the ramp.5/sin (12) FIX &' % ©8 1.5/sin (12) &' DEG < 1. and then return to floating decimal mode.54160187 sin-1 (13/20) 40.Inverse Sine Use this formula to find the angle of the conveyor belt.5 DEG &' DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 87 .54160187 sin-1 (13/20) &' DEG F0123456789 DEG sin-1 (13/20) FIX &' 40. Round your answer to the nearest tenth. SIN x = 13/20 % Press Display % 13 W 20 E < %© " " < %© 8 40. Restores standard mode FLO (floating decimal).Notation Keys 1. Turns on engineering mode ENG and displays results as a number from 1 to 1000 (1 n < 1000) times 10 to an integer power. Turns on scientific mode SCI and displays results as a number from 1 to 10 (1 n < 10) times 10 to an integer power. For a negative exponent. Results requiring more than 10 digits are automatically displayed in scientific notation. Notes • • The examples on the transparency masters assume all default settings. and ENG) affect only the display of results. These modes (FLO. % d displays the following numeric notation mode menu. For the decimal notation mode. You can enter a value in scientific notation regardless of the numeric notation mode setting. press M before entering it. • • • 1 2 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 88 . 14 2. refer to % ‚ in Chapter 6. The integer power is always a multiple of 3. SCI. Decimals and Decimal Places. % C lets you enter and calculate the exponent. Engineering. Press Display FLO SCI ENG --DEG % 12543 % " << % " < % " < 12543 FLO ' 1.2543x1004 x10 SCI DEG SCI SCI ENG --DEG 12543 FLO --- ' 12. Scientific.543x1003 x10 ENG DEG SCI ENG DEG ENG 12543 ' 12543. which will be in floating decimal notation (default). Floating Decimal Enter 12543. and alternate between scientific and engineering notations. DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 89 . DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 90 .4 8-1.783 x 108 kilometers from the Sun. Press Display 7.783E 8-1.496 x 108 kilometers from the Sun. &' %¢ %¢ 8 7 8 783 U 1 8 496 %¢ 8 < 628700000.Exponent The Earth is 1. Jupiter is 7. Enter the numbers in scientific notation and determine how far away the Earth is from Jupiter. 718281828459). B calculates the natural logarithm (base e. % ] calculates the common antilogarithm (10 raised to the power of the value). E ends a logarithmic function. 15 Notes • • The examples on the transparency masters assume all default settings. where e = 2. % ^ calculates the natural antilogarithm (e raised to the power of the value). 2. A calculates the common logarithm (base 10). 4. 3 1 4 2 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 91 . 3.Logarithms and Antilogarithms Keys 1. 361727836 DEG log (23) FIX ' ln (23) FIX 1. Natural Logarithm Find log 23 rounded to 4 decimal places.3617 DEG ' ln (23) 3. Then find ln 23 rounded to 4 decimal places and return to floating decimal notation. Press Display log (23) ' AB A 23 E < %© 4 B 23 E < %© 8 F0123456789 DEG 1.135494216 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 92 .1355 DEG ' 3.Common Logarithm. return to floating decimal notation.Common Antilogarithm. Then find antiln 3. When finished.64562936 DEG e^ (3.9824) 53.9824 rounded to 4 decimal places.9824 rounded to 4 decimal places. Press Display 10^ (3.9824) ' % % % 3 8 9602.9824) FIX 9602.6456 DEG ' © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 93 .9824) FIX ' e^ (3. Natural Antilogarithm Find antilog 3.846792 9824 E < DEG %© 4 % 3 8 9824 E < %© 8 F0123456789 DEG 10^ (3.8468 DEG ' 53. Specifies gradients. • 1 2 • • © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 94 . 16 2. the calculator interprets all values as degrees. Notes • • The examples on the transparency masters assume all default settings. and GRD without affecting the value in the display. DMS angles are entered as º (degrees). ´ (minutes). Otherwise.Angle Settings and Conversions Keys 1. Sets radian mode. DEG RAD GRD Sets degree mode. The default setting is DEG. angles (without a trig function) are converted and displayed according to the angle mode setting. º Å Æ r g DMS Specifies degrees. Angles with a trig function ignore the angle mode setting and display results in the original unit. RAD. For decimal/DMS conversions. Specifies seconds. and ´´ (seconds). Specifies radians. = displays a menu that lets you specify the unit of an angle. Sets gradient mode. regardless of the angle-unit setting. I displays the following menu that lets you change the angle mode setting to DEG. Specifies minutes. Lets you convert an angle from decimal degrees to DMS notation. You enter decimal-degree angles the same as you would any other number. 85 DEG DEG Ans ¾ DMS ' 3¡ 51 0 51Å 0Æ DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 95 .Æ r g DEG & 2¡ 5Å + 1¡ DEG 2¡ 5Å + 1¡ 46Å % ' ¾DMS ---- 3. How long did you watch videos? Press Display ¡ Å 2¡ DEG = 2= < 5=" <T1= < 46 = " << =! << Æ r g DEG & Å ¡ . Minutes.Degrees. and Seconds to Decimal You watched 2 videos that were 2:05 (2 hours and 5 minutes) and 1:46 (1 hour and 46 minutes) in length. Minutes. and Seconds How much is 2/3 of an hour in hours. minutes.Fraction to Degrees. and seconds? Press Display 2®3 DEG = 2N3 =! << % ¾DMS ---- DEG 2®3 ¾ DMS 0¡ 40Å 0Æ DEG ' © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 96 . 5 DEG -0. and gradients. Radians. radians.4539905 GRAD © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 97 .Degrees. Gradients Calculate the sine of 30 in degrees.988O31624 RAD sin(30) DEG ' RAD GRD --RAD sin(30) ' 0. Press Display sin(30) DEG ' I > 30 E < I" << I" << RAD GRD --DEG 0. 1 2 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 98 . Converts polar coordinate to rectangular coordinate c. set angle mode as necessary. R4Pr R4Pq P4Rc P4Ry Converts rectangular coordinate to polar coordinate r. 2.Polar and Rectangular Conversions Keys 1.q) or vice versa. Converts polar coordinate to rectangular coordinate y. Converts rectangular coordinate to polar coordinate q. % ` enters a comma. Before starting calculations. % k displays the following menu that lets you convert rectangular coordinates (c. 17 Notes • • The example on the transparency master assumes all default settings.y) to polar coordinates (r. 30) ' 3.5 DEG The rectangular ordered pair is 6.5.Polar to Rectangular Convert the polar ordered pair (7. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 99 .30) Rx(7.30) P¾Rx ' DEG P¾R y ---- DEG P¾Ry (7.062177826 % P¾Rx (7. y 4 3 2 1 1 (x = ?.30) to rectangular using the DEG (¡) angle unit.062177826.30) Ry(7.3. y = ?) %’ r=7 30° 1 1 2 3 4 5 6 7 x P¾R y DEG Press Display % %’ " " < 7 %¤ 30 E < %’ ! < 7 %¤ 30 E < P¾Rx ---- 6. % Y accesses the hyperbolic (sinh. tanh) function of the next trig key that you press. GRD (gradient). 18 Notes • • The example on the transparency master assumes all default settings.Hyperbolics Keys 1. cosh. 1 © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 100 . Hyperbolic calculations are not affected by the angle mode setting—whether or not the calculator is in RAD (radian). or DEG (degree) modes. and tangent (tanh) of 5. cosine (cosh).999909204 DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers 101 . Cosine.20321058 DEG sinh(5) ' 74.20994852 DEG cosh(5) tanh(5) ' ' 0. Tangent Find the hyperbolic sine (sinh).Sine. Press Display %› %› > 5 E< %› ? 5 E< %› @ 5 E< 74. Specifies minutes. subtracts. Specifies gradients. Calculates the square root. Closes a parenthetical expression. Enters a decimal point. Opens a parenthetical expression. º Å Æ r g 4DMS Specifies degrees. TUVW 7–6 D E a F g 8 M G = Adds. Displays the following menu that lets you specify the unit of an angle. Moves the cursor up and down so you can see previous entries. multiplies.Quick Reference to Keys KEY !" #$ A FUNCTION Moves the cursor left and right so you can scroll the entry line. Lets you convert an angle from decimal degrees to DMS notation. % %] %b Turns on the 2nd indicator and accesses the function shown above the next key that you press. Enters the value of pi rounded to 10 digits (3. Enters the digits 0 through 9. Indicates the value is negative.141592654). Specifies radians. Press % # or % $ to scroll to the beginning or end of the history. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers A-1 . Press % ! or % " to scroll to the beginning or end of the entry line. Calculates the reciprocal. and divides. Specifies seconds. Calculates the common antilogarithm (10 raised to the power of the value). Squares the value. Raises a value to a specified power. it deletes all characters to the right.Quick Reference to Keys KEY %_ % [. Sets gradient mode. radians (r). it is always in the DEG mode. Displays the following menu that lets you change the Angle mode to degrees (º). displaying it as Ans. I When you turn on the TI30X ÙS. Calculates the specified root (x) of the value. Converts a simple fraction to a mixed number or a mixed number to a simple fraction. Deletes the character at the cursor. Lets you enter mixed numbers and fractions. Results display according to the decimal notation mode setting. If you hold J down. DEG RAD GRD Sets degree mode. Clears all memory variables. Calculates the cosine. Calculates the inverse cosine. Once the display is clear. it deletes 1 character to the left of the cursor. or gradients (g). © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers A-2 . Enters a comma. Lets you enter the statistical data points (x for 1-VAR stats. Completes the operation or executes the command. %^ %C < Calculates the natural antilogarithm (e raised to the power of the value). it moves the cursor to the last entry in history.] %c N %O %i %{ ? %[ v J (Continued) A FUNCTION Changes a real number to percent. Recalls the most recently calculated result. Sets radian mode. Lets you enter and calculate the exponent. x and y for 2-VAR stats). Then each time you press J. Clears characters and error messages on the entry line. and then back to degrees without affecting the value in the display. Lets you insert a character at the cursor. Press < when N (no) is underlined to return to the previous screen without exiting STAT mode. Turns on the constant mode and lets you define a constant. Displays the following menu that lets you set the number of decimal places. Sets number of decimal places. Turns on the calculator. Displays the following menu of variables. %Y %f %l B A z Accesses the hyperbolic (sinh. Calculates the natural logarithm (base e. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers A-3 . ABCDE Lets you view the stored value before pasting it to the display. %' & Turns off the calculator and clears the display.718281828459). tanh) function of the next trig key that you press.Quick Reference to Keys KEY %w (Continued) A FUNCTION Displays the following menu that lets you clear data values and exit STAT mode. where e = 2. if possible. %j %‚ Converts a fraction to its decimal equivalent or converts a decimal to its fractional equivalent. F0123456789 F 0-9 Sets floating decimal (standard) notation. EXIT ST: Y N Press < when Y (yes) is underlined to clear data values and exit STAT mode. cosh. Calculates the common logarithm (base 10). RANDI Generates a random integer between 2 numbers that you specify. R4Pr R4Pq P4Rc P4Ry Converts rectangular coordinate to polar coordinate r. nPr nCr ! Calculates the number of possible permutations. Converts rectangular coordinate to polar coordinate q. No menu or message is displayed. Also. FLO SCI ENG Restores standard mode (floating decimal). %d Displays the following numeric notation mode menu. press & and .q) or vice versa. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers A-4 . Calculates the number of possible combinations.Quick Reference to Keys KEY H (Continued) A FUNCTION Displays the following menu of functions. RESET: N Y Press < when N (no) is underlined to return to the previous screen without resetting the calculator.y) to polar coordinates (r. Converts polar coordinate to rectangular coordinate y. Calculates the factorial. Turns on engineering mode and displays results as a number from 1 to 1000 (1 n < 1000) times 10 to an integer power. The message MEM CLEARED is displayed. RAND Generates a random 10-digit real number between 0 and 1. %k Displays the following menu that lets you convert rectangular coordinates (c. Turns on scientific mode and displays results as a number from 1 to 10 (1 n < 10) times 10 to an integer power. %h % Recalls the stored values to the display. Converts polar coordinate to rectangular coordinate c. Displays the RESET menu. Separate the 2 numbers with a comma. Press < when Y (yes) is underlined to reset the calculator.simultaneously to reset the calculator immediately. The integer power is always a multiple of 3. Correlation coefficient. ABCDE Lets you select a variable in which to store the displayed value. Displays the following menu from which you can select 1-VAR. Lets you set a seed value for random integers. Clears data values without exiting STAT mode. The new variable replaces any previously stored value. and y. the dependent variable. Population standard deviation of x or y.Quick Reference to Keys KEY > %Z %t (Continued) A FUNCTION Calculates the sine. Sample standard deviation of x or y. CLRDATA u Displays the following menu of stat variables with their current values. the independent variable. Linear regression y-intercept. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers A-5 . n v or w Sx or Sy sx or sy Gx or Gy Number of x (or x.y) data points. Analyzes paired data from 2 sets of data with 2 measured variables—x. Gx2 or Gy2 Sum of all x 2 values or y 2 values. or CLRDATA. Calculates the inverse tangent. Calculates the inverse sine. 2-VAR. Sum of all x values or y values. Linear regression slope. L Displays the following menu of variables. Gxy a b r Sum of (x Q y) for all xy pairs in 2 lists. rand @ %\ Calculates the tangent. 1-VAR 2-VAR Analyzes data from 1 set of data with 1 measured variable−x. Mean of all x or y values. RAD. or gradients). Press ! or " to scroll. An entry is stored in history before and/or after the active screen. Scientific or engineering notation. radians. Precedes the exponent in scientific or engineering notation. Statistical mode. Press # and $ to scroll. x10 '( %& © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers B-1 . Hyperbolic function.Display Indicators INDICATOR 2nd HYP FIX SCI. GRAD K B MEANING 2nd function. ENG STAT DEG. An entry or menu displays beyond 11 digits. Angle mode (degrees. Constant mode. Fixed-decimal setting. or having misplaced functions. etc. For y x y and x = 0. |q | ‚ 1¯10. or commas. In statistics. or R4Pr function. 8 pending values. n = 1. hyperbolic. For example: For x ‡ x = 0 or y < 0 and x is not an odd integer. SYNTAX The command contains a syntax error—entering more than 23 pending operations. For LOG or LN x 0. For x ! x is not an integer between 0 and 69. M90¡. or not an integer. You attempted to divide by 0. u. • • • You pressed u with no defined data points. FRQ value (in 1-variable statistics) < 0 or >99. or % w when not in STAT mode. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide for Teachers C-1 . For nCr or nPr n or r are not integers ‚ 0. where q is an angle in a trig. For ‡x x < 0. DOMAIN You specified an argument to a function outside the valid range. EQUATION LENGTH ERROR FRQ DOMAIN OVERFLOW STAT An entry exceeds the digit limits (88 for entry line and 47 for statistics or constant entry lines). arguments. You pressed v. for example. For SIN -1 or COS -1 |x | > 1. combining an entry with a constant that exceeds the limit. For TAN x = 90¡. Statistical analyses do not have at least 2 data points (n > 1). parentheses. 450¡. M270¡.Error Messages MESSAGE ARGUMENT DIVIDE BY 0 C MEANING A function does not have the correct number of arguments. y < 0 and x is not an integer. 270¡. and the Virgin Islands For general questions. and the Virgin Islands Contact TI by e-mail or visit the TI calculator home page on the World Wide Web. Puerto Rico.com/calc © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X IIS: A Guide For Teachers D-1 . Customers outside the U. Puerto Rico. contact Texas Instruments Customer Support: phone: e-mail: 1-80-T-CARES (1-800-842-2737) ti-cares@ti. and Canada Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor..ti. e-mail: ti-cares@ti. Other TI Products and Services Visit the TI calculator home page on the World Wide Web.S.S. Canada.Support and Service Information Product Support D Customers in the U.com For technical questions. and Canada Only Always contact Texas Instruments Customer Support before returning a product for service. call the Programming Assistance Group of Customer Support: phone: 1-972-917-8324 Customers outside the U.com internet: www. www.com/calc Product Service Customers in the U.ti.S. Canada.S.. Warranty Disclaimers. This TI electronic product is warranted against defective materials and construction. Legal Remedies. Warranty Performance. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. The software and any documentation supplied with this product are protected by copyright. or contact your local Texas Instruments retailer/distributor. This warranty gives you specific legal rights. Software is licensed. NEGLECT. TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS. EXPENSES. whichever is longer. All Customers outside the U. TI strongly recommends that you insure the product for value prior to mailing. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE.S. postage prepaid. to Texas Instruments Service Facility. INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. 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IMPROPER SERVICE. and Canada Only One-Year Limited Warranty for Electronic Product E This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product. and you may also have other rights that vary from state to state or province to province. so the above limitations or exclusions may not apply to you. refer to your package and/or to the warranty statement enclosed with this product. © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X IIS: A Guide For Teachers E-1 . THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE. ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER. OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR CONSTRUCTION. The Netherlands Printed By:
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