TI-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 ÙS section of this guide.
About the Teacher Guide How the Teacher Guide is Organized Things to Keep in Mind 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.
Table of Contents How to Use the TI-30X ÚS (continued) About the Authors ii About the Teacher Guide iii 14 Notation 88 About the TI-30X ÖS iv 15 Logarithms and Antilogarithms 91 16 Angle Settings and Conversions 94 Activities 17 Polar and Rectangular Conversions 98 The Better Batter — Using the FIX Key 2 18 Hyperbolics Star Voyage — Using Scientific Notation Appendix A Quick Reference to Keys A-1 6 Appendix B Display Indicators B-1 Appendix C Error Messages C-1 Appendix D Support a
Activities © 1999 TEXAS INSTRUMENTS INCORPORATED The Better Batter — The FIX Key 2 Star Voyage — Scientific Notation 6 Trig Functions 10 What’s My Score? — 1-Variable Statistics 14 Heart Rates — 1-Variable Statistics 17 WNBA Stats — 2-Variable Statistics 23 TI-30X ÙS: A Guide for Teachers 1
The Better Batter — The FIX Key Math Concepts Overview Students use % ‚ on the TI-30X ÙS to change numbers to different place values. Students calculate batting averages using the TI-30X ÙS and then round their answers to three decimal places. Materials • rounding • TI-30X ÙS • place value • pencil • division • student activity • comparing and ordering decimals Introduction 1. Have students practice rounding the following numbers to 3 decimal places using pencil and paper. a. 2.35647 b. 15.3633 c.
The Better Batter — The FIX Key Player (Continued) Number of Hits Number of Times at Bat Batting Average C. Ripken 122 368 0.332 Puckett 119 363 0.328 Molitor 119 364 0.327 Greenwell 104 334 0.311 Tartabull 103 311 0.331 Palmeiro 120 366 0.328 Franco 109 344 0.317 Joyner 105 338 0.311 Boggs 106 329 0.322 Baines 91 290 0.314 113 388 0.291 Williams 20 74 0.270 Sheridan 15 63 0.238 Barfield 64 284 0.225 109 367 0.297 87 280 0.
The Better Batter — The FIX Key Name ___________________________ Date ___________________________ Problems 1. Round the following numbers to 3 decimal places. a. 2.35647 _________________ b. 15.3633 _________________ c. 0.02698 _________________ 2. Using the TI-30X ÙS, round the following numbers to 4 decimal places. a. 4.39865 _________________ b. 72.965912 _________________ c. 0.29516 _________________ d. 0.
The Better Batter — The FIX Key Name ___________________________ Date ___________________________ Problem You are going to play Virtual Baseball. You need to select 9 players from the list to be on your team. Choose the players with the best batting averages. Procedure 1. Find the batting averages (number of hits ¾ number of times at bat) rounded to 3 decimal places for each player. Player Number of Hits Number of Times at Bat C.
Star Voyage — Scientific Notation Math Concepts Overview Students investigate scientific notation by changing numbers into scientific notation, and then using them in calculations. Materials • scientific notation • TI-30X ÙS • addition • student activity • pencil • division Introduction Set up the activity by telling your students: The standard form for scientific notation is a Q 10 n, where a is greater than or equal to 1 and less than 10, and n is an integer. 1.
Star Voyage — Scientific Notation (Continued) Activity Present the following problem to students: You are a captain of a starship. You have been assigned to go to Alpha Centauri and you have 5 years to get there. The distance from the sun to Alpha Centauri is 2.5 x 10 13 miles. The distance from the earth to the sun is approximately 9.3 x 10 7 miles. Your ship can travel at the speed of light. You know that light can travel a distance of 6 x 10 12 miles in 1 light year.
Star Voyage — Scientific Notation Name ___________________________ Date ___________________________ Problems 1. Write the following numbers in scientific notation. Standard Notation Scientific Notation a. 93 000 000 _________________________ b. 384 000 000 000 _________________________ c. 0.00000000000234 _________________________ d. 0.0000000157 _________________________ 2. Using the TI-30X ÖS, change the following numbers into scientific notation. Standard Notation Scientific Notation a.
Star Voyage — Scientific Notation Name ___________________________ Date ___________________________ Problem You are a captain of a starship. You have been assigned to go to Alpha Centauri and you have 5 years to get there. The distance from the Sun to Alpha Centauri is 2.5 x 10 13 miles. The distance from the Earth to the Sun is approximately 9.3 x 10 7 miles. Your ship can travel at the speed of light. You know that light can travel a distance of 6 x 10 12 miles in 1 light year.
Trig Functions Students practice solving sine, cosine, and tangent ratios, and solve problems involving trigonometric ratios. Introduction Introduce the trigonometric ratios to students. • division • pencil • trigonometric ratios • student activity A 5 4 C ³ To set 2 decimal places: 1. Press % ‚. F0123456789 2. Press 2 to select 2 decimal places. 3 ¾ 5 = 0.60 4 ¾ 5 = 0.80 3 ¾ 4 = 0.75 4 ¾ 5 = 0.80 3 ¾ 5 = 0.60 4 ¾ 3 = 1.33 2. Have students find the value of each ratio using the TI-30X ÙS.
Trig Functions (Continued) Activity Present the following problem to students: You need to build a ramp to your front door. The distance from the ground to the bottom of the door is 1.5 feet. You dont want the angle of incline to be more than 6 degrees. The distance from the street to the door is 20 feet. Is there enough room to build the ramp? Procedure ³ 1. Press % \. 1. Make a drawing of the problem. tan-1( 2. Enter 1.5 W 20 and press E <. 1.5 ft. tan-1(1.5/20) 4.3 A 20 ft. 2.
Trig Functions Name ___________________________ Date ___________________________ Problems 1. Find the trigonometric ratios for the triangle. Round to the nearest hundredth. (Use % ‚ for rounding.) a. sin C _______________________ b. cos C _______________________ A c. tan C _______________________ 3 d. sin A _______________________ e. cos A _______________________ f. tan A _______________________ B 5 4 C 2. Using the TI-30X ÙS, find the value of each ratio.
Trig Functions Name ___________________________ Date ___________________________ Problem You need to build a ramp to your front door. The distance from the ground to the bottom of the door is 1.5 feet. You dont want the angle of incline to be more than 6 degrees. The distance from the street to the door is 20 feet. Is there enough room to build the ramp? Procedure 1. Make a drawing of the problem. 2. Use the trig ratio tan = opposite leg ¾ adjacent leg to find angle A.
What’s My Score? — 1-Variable Statistics Math Concepts Overview Students use the given test scores to find averages. • averages Materials • TI-30X ÙS • pencil • student activity Introduction Discuss finding averages with your students. Activity Present the following problem to students: You and your friend are having a contest. The one gets the highest average on their math tests for one quarter wins. Your scores are 98, 89, 78, 98, and 100. Your friends scores are 89, 89, 97, 90, and 100.
What’s My Score? — 1-Variable Statistics (Cont.) 2. Now find the average of your friends scores. Remember to put 2 as the frequency for 89 and 1 for all others. ³ 1. Press % t " " to select CLRDATA. Press <. 2. Press v and enter the friend’s first score. 3. Who won? X1 = 89 Your friend: 93 (You had 92.6.) 3. Continue entering the friend’s scores and frequencies, following steps 3 and 4 on the previous page. 4. When finished, press u " to select v, the average. Write it down. n v Sx sx ¹ 93.
What’s My Score? — 1-Variable Statistics Name ___________________________ Date ___________________________ Problems 1. You and your friend are having a contest. Whoever gets the highest average on their math tests for one quarter wins. Your scores are 98, 89, 78, 98, and 100. Your friend's scores are 89, 89, 97, 90, and 100. Who is the winner? Your average _______________________ Your friends average _______________________ 2. Your friend took a test on the day you were absent and scored 95.
Heart Rates — 1-Variable Statistics Math Concepts Overview Students use the statistics functions of the TI-30XÙS calculator to investigate the effect of exercise on heart rate. • mean, minimum, maximum, and range Materials • TI-30X ÙS • stopwatch or a watch with a second hand • student activity Introduction Students may be placed in smaller groups for this activity to minimize the amount of data to be entered.
Heart Rates — 1-Variable Statistics 4. Check the statistics calculations. After students display Òx (Sigma x), explain that Òx is the sum of all the heart rates. Ask students: • • How many heartbeats were there in one minute? Is the average heart rate higher or lower than you expected? 5. Now we will see the effect of some exercise on heart rate. Tell students: If at any point during this portion of the activity you experience pain, weakness, or shortness of breath, stop immediately. 6.
Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ Problem What do you think the average heart rate is for someone your age? What about after exercising? Procedure 1. Use this table to record your class or group data (resting). Heartbeats per minute (resting) Frequency 2. What is the class (group) average? ___________________________________ 3.
Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ 4. 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 ___________________________ 7. Use this table to record your class or group data (jumping). Heartbeats per minute (jumping) Frequency 8. What is the class (group) average? __________________________________ 9. What is the total number of heartbeats for the minute? _________________ 10.
Heart Rates — 1-Variable Statistics Name ___________________________ Date ___________________________ 11. Now make a histogram for each of the 3 sets of data you collected. Resting Running Jumping 12. How are the histograms the same? How are they different? _____________ _________________________________________________________________ _________________________________________________________________ 13.
WNBA Stats — 2-Variable Statistics Overview Students use WNBA statistics to explore the relationship between 2 variables. They use the TI-30X ÙS to compute the regression equation and evaluate some values.
WNBA Stats — 2-Variable Statistics Continued) ( 3. Calculate the statistical data. 1. Press % ‚. You may want to fix the decimal to 2 places before doing the statistical calculations. Ask students: • F0123456789 2. Press 2. 1. Press u. 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? n Ï Sx Îx Ð 12.00 2. Press " to Ï.
WNBA Stats — 2-Variable Statistics Continued) ( 7. Now calculate how many points you would expect a player to score if she plays 35 minutes a game. 8. Discuss the correlation as a class. Ask students: • • Are there other factors affecting the players minutes per game besides points scored? What about defense, rebounding, etc.? 1. Press u. n Ï Sx Îx Ð 12.00 2. Press ! ! to x¢. x¢ y¢ 3. Press <. 4. Type 35 E and press <. x¢(35) 17.
WNBA Stats — 2-Variable Statistics Name ___________________________ Date ___________________________ Problem 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 players field goal percentage? Procedure Use the following table of data to explore the relationships of different pairs of data.
WNBA Stats — 2-Variable Statistics Name ___________________________ Date ___________________________ Extension 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, or rebounds per game to minutes per game. (Remember, since you have already entered the minutes per game in Y, you only need to enter the new data in X.) 1. What is the average field-goal percentage? 2. Write the equation for the line of best fit. 3.
How to Use the TI-30X ÚS TI-30X ÚS Basic Operations Clear, Insert, and Delete Basic Math Order of Operations and Parentheses Constant Decimals and Decimal Places Memory Fractions Pi Powers, Roots, and Reciprocals Probability Statistics Trigonometry Notation Logarithms and Antilogarithms Angle Settings and Conversions Polar and Rectangular Conversions Hyperbolics © 1999 TEXAS INSTRUMENTS INCORPORATED 29 33 36 40 43 45 47 52 58 61 68 75 81 88 91 94 98 100 TI-30X ÙS: A Guide for Teachers 28
TI-30X Ú S Basic Operations 1 Keys 1. & turns on the calculator. 2. % turns on the 2nd indicator and accesses the function shown above the next key you press. 7. % displays the RESET menu. RESET: N Y • Press < when N (no) is underlined to return to the previous screen without resetting the calculator. • Press < when Y (yes) is underlined to reset the calculator. The message MEM CLEARED is displayed. 3. % ' turns off the calculator and clears the display. 4.
%¥ ! " #$< Second, Off, Arrows, Equals Enter 46 N 23. Change 46 to 41. Change 23 to 26 and complete the operation. Enter 81 + 57 and complete the operation. Scroll to see your previous entries. Press 46 U 23 Display 46-23 DEG !!!!1 ""6< 41-26 81 T 57 < 81+57 ' 15. DEG ' 138.
%¨ Reset Reset the calculator. Press % Display ¨ RESET: N Y DEG " RESET: N Y DEG < MEM CLEARED DEG - ~ DEG Pressing & and - at the same time also resets the calculator immediately. No menu or message is displayed. ¨ Using % or & and returns all settings to their defaults and clears the memory.
Last Answer (Ans) %ª Use Last Answer (Ans) to calculate (2+2)2. Press 2T2< Display 2+2 4. DEG ª % F < © 1999 TEXAS INSTRUMENTS INCORPORATED ' Ans 2 16.
Clear, Insert, and Delete 2 Keys Notes 1. - clears characters and error messages. Once the display is clear, it moves the cursor to the most recent entry. • The examples on the transparency masters assume all default settings. • Pressing - does not affect the memories, statistical registers, angle units, or numeric notation. 2. % f lets you insert a character at the cursor. 3. J deletes the character at the cursor. Hold J down to delete all characters to the right.
J %‘ Delete, Insert Enter 4569 + 285, and then change it to 459 + 2865. Complete the problem. Press 4569 T 285 Display 4569+285 DEG !!!!! !J 459+285 DEG """" 459+2865 ‘6 % < DEG ' 459+2865 3324.
- Clear Enter 21595. Clear the 95. Clear the entry.
3 Basic Math Keys Notes 1. T adds. • The examples on the transparency masters assume all default settings. • The TI-30X ÙS allows implied multiplication. Example: 3 (4+3) = 21 • Do not confuse M with U. U allows subtraction. • Results of percent calculations display according to the decimal notation mode setting. 2. U subtracts. 3. V multiplies. 4. W divides. 5. < completes the operation or executes the command. 6. M lets you enter a negative number. 7. % _ changes a real number to a percent.
TUVW < Add, Subtract, Multiply, Divide, Equals Find: 2 + 54 ½ 6 = 16 x 21 = 78 P 2 = 12 x (5 + 6) = Press Display 2 T 54 U 6 < 2+54-6 16 V 21 < 16*21 ' 50. DEG ' 336. DEG 78 W 2 < ' 78/2 39. DEG 12 V D 5 T 6E< © 1999 TEXAS INSTRUMENTS INCORPORATED ' 12*(5+6) 132.
M Negative Numbers The temperature in Utah was L3¡ C at 6:00 a.m. By 10:00 a.m. the temperature had risen 12¡ C. What was the temperature at 10:00 a.m.? Press M 3 T 12 < © 1999 TEXAS INSTRUMENTS INCORPORATED Display ' -3+12 9.
%£ Percent Mike makes $80 per week. He saves 15% of his earnings. How much does Mike save per week? Press 15 Display 15 DEG £ % V 80 < © 1999 TEXAS INSTRUMENTS INCORPORATED ' 15%*80 12.
Order of Operations and Parentheses 4 Keys Notes 1. D opens a parenthetical expression. • The examples on the transparency masters assume all default settings. • The transparency master showing the Equation Operating System (EOS TM) demonstrates the order in which the TI-30X ÙS completes calculations. • Operations inside parentheses are performed first. Use D E to change the order of operations and, therefore, change the result. Example: 1 + 2 x 3 = 7 (1 + 2) x 3 = 9 2.
Equation Operating System EOS 1 (first) Expressions inside D E. 2 Functions that need a E and precede the expression, such as the >, A, or %’ menu items. 3 Functions entered after the expression, such as F and angle unit modifiers (¡, ¢, £, r, g). 4 Fractions. 5 Exponentiation (G) and roots (% 6 Negation (M). 7 Permutations (nPr), and combinations (nCr). 8 Multiplication, implied multiplication, and division. 9 Addition and subtraction. 10 Conversions (% ¡). š, %“, and 8DMS).
TVDE Order of Operations 1+2x3= Press 1T2V3 < Display ' 1+2*3 7. DEG (1 + 2) x 3 = Press D1T2EV 3< © 1999 TEXAS INSTRUMENTS INCORPORATED Display ' (1+2)*3 9.
5 Constant Keys Notes 1. % l turns on the constant mode and lets you define a constant. A K displays when the constant mode is on. • The examples on the transparency masters assume all default settings. • All functions, except statistics, work in constant mode. • To enter a constant: 2. < places the contents of K at the end of the expression in the display. 1. Press % l. If a constant is already stored, press - to clear it. 2. Enter your constant (any set of operations, functions, and values). 3.
%™ 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= DEG V 3.25 < K = *3.25 DEG K DEG K 16 < ' 16*3.25 52. DEG 12 < K ' 12*3.25 39. DEG 17 < K ' 17*3.25 55.25 DEG % ™ (Constant mode is off.
Decimals and Decimal Places 6 Keys Notes 1. 8 enters a decimal point. • 2. % ‚ displays the following menu that lets you set the number of decimal places. 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.
8 %© Decimal, FIX Round 12.345 to the hundredths place, to the tenths place, and then cancel the FIX setting. Press 12 8 345 Display 12.345 DEG % © F _0123456789 DEG """ F01_ 23456789 DEG < 12.345 FIX < DEG ' 12.345 12.35 FIX % ©1 ©8 ' 12.345 12.3 FIX % DEG DEG ' 12.345 12.
7 Memory Keys 1. L displays the following menu of variables. A B C D E Lets you select a variable in which to store the displayed value. The new variable replaces any previously stored value. rand Lets you set a seed value for random integers. 2. z displays the following menu of variables. A B C D E Lets you view the stored value before pasting it in variable form to the display. 3. % { clears all variables. 4. % h displays the following menu of variables.
Lz Store, Memory Variable, Clear Variable %¦ Test scores: 96, 76, 85. Weekly scores: 92, 83, 97, and 86. Find the average of test and weekly scores. Find the final average. Press 96 T 76 T 85 < Display 96+76+85 257. DEG W3< ' Ans/3 85.66666667 DEG L< ' Ans¹A 85.66666667 DEG 92 T 83 T 97 T 86 < ' 92+83+97+86 358. DEG W4< ' Ans/4 89.5 DEG Tz << Ans+A 175.1666667 ' DEG W2< Ans/2 87.
L Store, Recall %§ Which would be the better buy: 3 cassette tapes for $7.98, or 4 cassette tapes for $9.48? Press Display 7 8 98 W 3 < 7.98/3 L< Ans¹A 2.66 DEG ' 2.66 DEG 9 848 W 4 < 9.48 / 4 L"< A n s ¹B ' 2.37 DEG ' 2.37 DEG View the first price again. % § A _ B C D E 2.66 ' DEG View the second price again. " A _ B C D E 2.
L Store, Recall %§ Shop A B C Purchases Qty Cost shirts 2 $13.98 ea. ties 3 $7.98 ea. belt 1 $6.98 suspenders 1 $9.98 How much did you spend at each shop, and how much did you spend altogether? Press 2 V 13 8 98 < Display 2*13.98 27.96 DEG L A B C D E ¹ 27.96 ' DEG < ' Ans¹A 27.96 DEG 3 V 7 8 98 < ' 3*7.98 23.
Store, Recall L (Continued) %§ Press L"< Display ' Ans¹B 23.94 DEG 6 8 98 T 9 8 98 < 6.98+9.98 16.96 ' DEG L"" < ' Ans¹C 16.96 DEG § %
8 Fractions Keys Notes 1. N lets you enter mixed numbers and fractions. • The examples on the transparency masters assume all default settings. 2. % O converts a simple fraction to a mixed number or a mixed number to a simple fraction. • To enter a mixed number or a fraction, press N between the whole number and the numerator and between the numerator and the denominator. 3. % j converts a fraction to its decimal • equivalent or changes a decimal to its fractional equivalent, if possible.
N Fractions At the party, you ate 5/6 of the pepperoni pizza and 1/10 of the sausage pizza.
N Mixed Numbers A baby weighed 4 3/8 kilograms at birth. In the next 6 months, she gained 2 3/4 kilograms.
Mixed Number to Fraction, Fraction to Mixed Number %š Sam is making his birthday cake. The recipe calls for 3 1/2 cups of flour. He has only a 1/2-cup measuring cup. To find out how many times Sam must use his measuring cup, change the mixed number to a fraction. 3 1/2 ¾ 1/2 = 7 Press 3N1N2 Display 3®1®2 DEG % š b d 3®1®2' A /c , ' /e DEG < b ' d 3®1®2' A /c , ' /e 7 DEG /2 Show the mixed number again.
%“ Fraction to Decimal Juan swims 20 laps in 5.72 minutes. Mary swims 20 laps in 5 3/4 minutes. Change Mary’s time to a decimal to determine who swims faster. Press Display 5N3N 4% < “ © 1999 TEXAS INSTRUMENTS INCORPORATED 5®3®4.F, 'D DEG 5®3®4.F, 'D 5.
%“ Decimal to Fraction Change 2.25 to its fractional equivalent. Press 2 8 25 % “< © 1999 TEXAS INSTRUMENTS INCORPORATED Display 2.25.
9 Pi Keys Notes 1. g displays the value of pi rounded to 10 digits (3.141592654). • The examples on the transparency masters assume all default settings. • Internally, pi is stored to 13 digits (3. 141592653590). • 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. The transparency masters show both ways.
g 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. C = 2pr = 2 x p x 1.5m Press 2 V g V 1.5 < © 1999 TEXAS INSTRUMENTS INCORPORATED Display 2*p*1.5 9.
g Area Use this formula to find how much of a lawn would be covered by the sprinkler. Round your answer to the nearest whole number, and then return to Floating Decimal mode. A = pr2 = p x 42 Press gV4F < % ©" Display p*42 50.26548246 DEG F0 _123456789 DEG < ' p*42 FIX % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED 50. DEG p*42 ' 50.
Powers, Roots, and Reciprocals 10 Keys Notes 1. F squares the value. • The examples on the transparency masters assume all default settings. • To use G, enter the base, press G, and then enter the exponent. • The base (or mantissa) and the exponent may be either positive or negative. Refer to Domain under Error Messages in Appendix C for restrictions. • The result of calculations with G must be within the range of the TI-30X ÙS. • A sign change takes precedence over exponents.
FG Squares Use this formula to find the size of the tarp needed to cover the entire baseball infield. A = x2 = 27.42 Press Display 27.4 F < or 27.42 27.4 G 2 < 90^2 © 1999 TEXAS INSTRUMENTS INCORPORATED ' 750.76 DEG ' 750.
%œ Square Roots Use this formula to find the length of the side of a square clubhouse if 3m2 of carpet would cover the floor. Round your answer to 0 decimal places. L = x = 3 of carpet Press Display œ (3) © (3) % 3E < % " < © 1999 TEXAS INSTRUMENTS INCORPORATED 1.732050808 DEG 2.
Cubes G Use this formula to find the volume of a cube with sides 2.3 meters long. Change your answer to a fraction. V = L3 = 2.33 Press 283G3 < “ % < © 1999 TEXAS INSTRUMENTS INCORPORATED Display ' 2.3^3 12.167 DEG ' Ans.F, .
Powers G Fold a piece of paper in half, in half again, and so on until you cannot physically fold it in half again. How many sections would there be after 10 folds? After 15 folds? Press 2 G 10 < Display ' 2^10 1024. DEG 2 G 15 < ' 2^15 32768.
Roots % ¡ If the volume of a cube is 125 cm3, what is the length of each side? Press 3% < Display ¡ 125 © 1999 TEXAS INSTRUMENTS INCORPORATED 3 xÑ125. 5.
a Reciprocals The chart below shows the amount of time spent building model ships. Time Portion Spent Completed Ships Building Per Hour Sailing 10 hrs. ? Steam 5 hrs. ? Luxury 5 1/3 hrs. ? How much of each model was completed per hour? Press Sailing ship: Display “ 10 a % < ' 10 -1.F, .D 1 DEG / 10 Steam ship: “ 5a% < ' 5-1.F, .
11 Probability Keys Notes 1. H displays the following menu of functions. • The examples on the transparency masters assume all default settings. • A combination is an arrangement of objects in which the order is not important, as in a hand of cards. • A permutation is an arrangement of objects in which the order is important, as in a race. nPr Calculates the number of possible permutations. nCr Calculates the number of possible combinations. ! Calculates the factorial.
H Combination (nCr) You have space for 2 books on your bookshelf. 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 A B AB and BA count as only 1 combination. Press 4H" C D AB BA CA DA AC BC CB DB AD BD CD DC Display nPr ! ¹ nCr --DEG 2< ' 4 nCr 2 6.
H 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. 4 nPr 2 = x A B AB and BA count as 2 permutations. Press 4H C D AB BA CA DA AC BC CB DB AD BD CD DC Display nPr --- ! ¹ nCr DEG 2< ' 4 nPr 2 12.
H Factorial (!) Using the digits 1, 3, 7, and 9 only one time each, how many 4-digit numbers can you form? 4! = x ABCD BACD CABD DABC 1 3 7 9 A B C ABDC BADC CADB DACB ACBD BCAD CBAD DBAC Press 4H"" D ADCB BDAC CDBA DCBA ADBC BDCA CDAB DCAB ACDB BCDA CBDA DBCA Display nPr ! ¹ - nCr DEG << ' 4! 24.
H Random (RAND) Generate a sequence of random numbers. Press H""" Display ¸ RAND -___ RANDI DEG << RAND 0.839588694 DEG ' << RAND 0.482688185 DEG ' Results will vary.
H Random (RAND) Set 1 as the current seed and generate a sequence of random numbers. Press 1L! Display ¸ rand ---1083958869. DEG << ' 1¹rand 1. DEG H""" << RAND 0.000018633 DEG ' < RAND 0.
H Random Integer (RAND I ) Generate a random integer from 2 through 10. Press Display H! ¸ RAND RANDI ---__ DEG <2% 10 E ¤ < ¸ ' ANDI( 2, 10) DEG RANDI( 2, 10) ¹ 3. DEG ' Results will vary.
12 Statistics Keys 1. % t displays a menu from which you can select 1-VAR, 2-VAR or CLRDATA. 1-VAR 2-VAR CLRDATA Analyzes data from 1 set of data with 1 measured variable—x. Analyzes paired data from 2 sets of data with 2 measured variables—x, the independent variable, and y, the dependent variable. Clears data values without exiting STAT mode. 3. % w displays the following menu that lets you clear data values and exit STAT mode.
%” v Entering 1-VAR Stat Data Five students took a math test. Using their scores, enter the data points—85, 85, 97, 53, 77. Press % ” Display 1-VAR- 2-VAR ¹ ----DEG
Viewing the Data u (Cont.) Find the number of data points (n), the mean (v), the sample standard deviation (Sx), the population standard deviation (sx), the sum of the scores (Gx), and the sum of the squares (Gx2). Press Display u n v Sx sx 5. STAT DEG ¹ " n v Sx sx 79.4 STAT DEG ¹ " n v Sx sx --- ¹ 16.39512123 STAT DEG " n v Sx sx --- ¹ 14.66424222 STAT DEG " ¸Gx --- Gx 2 397. DEG STAT " ¸Gx Gx --2 STAT 32597.
Removing Data Points (Cont.) %˜ Return to the first data point. Display the lowest score, drop it, and then find the new mean (v). Clear all data by exiting STAT mode. Press Display v X 1=85 STAT $$$$ DEG S X 3=53 STAT $0< S DEG S FRQ=0 0. STAT DEG u" n v Sx sx 86.
%” v 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. Month April May Press % Total No.(x) Brand A (y) 58 (x1) 35 (y1) 47 (x2) 28 (y2) Display ”" 1-VAR 2-VAR& ----DEG
Viewing the Data u (Cont.) %˜ If the store sells 32 pairs of shoes in June, predict the June sales of Brand A. When finished, exit STAT mode and clear all data points. Press u! Display % x’ y’ t DEG < 32 E < y’ (32) 18.
13 Trigonometry Keys Notes 1. @ calculates the tangent. • The examples on the transparency masters assume all default settings. • Before starting a trigonometric calculation, be sure to select the appropriate angle mode setting (degree, radian, or gradient—See Chapter 16, Angle Settings and Conversions). The calculator interprets values according to the current angle-unit mode setting. • E ends a trig function. 2. % \ calculates the inverse tangent. 3. ? calculates the cosine. 4.
@ 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 78 W @ 27 E < % ©" Display ' 78/tan (27) 153.0836194 DEG F0123456789 DEG < % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED 78/tan (27) 153. FIX DEG ' ' 78/tan (27) 153.
%Ÿ Inverse Tangent Use this formula to find the angle of depression. Round your answer to the nearest tenth, and then return to floating decimal mode. TAN x = 600/2500 Press %Ÿ 600 W 2500 E < % ©"" Display tan -1 (600/25 ¹ 13.49573328 DEG F0123456789 DEG < % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED ' tan -1 (600/25 ¹ 13.5 FIX DEG ' tan -1 (600/25 ¹ 13.
? 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, and then return to floating decimal mode. D = 5 x COS 75 Press 5V? 75 E < % ©" Display ' 5*cos (75) 1.294095226 DEG F0123456789 FIX < ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED ' 5*cos (75) FIX % DEG 1. DEG ' 5*cos (75) 1.
% Inverse Cosine Use this formula to find the angle of the ski jump. Round your answer to the nearest tenth, and then return to floating decimal mode. COS x = 453/500 Press % 453 W 500 E < % ©"" Display cos-1 (453/50¹ 25.04169519 DEG F0123456789 DEG < % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED cos-1 (453/50¹ 25.0 FIX DEG ' ' cos-1 (453/50¹ 25.
> Sine Use this formula to find the length of the ramp. Round your answer to the nearest whole number, and then return to floating decimal mode. D = 1.5/SIN 12 Press Display 185W> 12 E < 1.5/sin (12) ¹ 7.214601517 DEG ©" F0123456789 - % ' DEG < % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED 1.5/sin (12) ¹ 7. FIX DEG ' ' 1.5/sin (12) ¹ 7.
% Inverse Sine Use this formula to find the angle of the conveyor belt. Round your answer to the nearest tenth, and then return to floating decimal mode. SIN x = 13/20 Press sin-1 (13/20) ¹ 40.54160187 DEG ©"" F0123456789 - % 13 W 20 E < % Display ' DEG < % ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED sin-1 (13/20) ¹ 40.5 FIX DEG ' sin-1 (13/20) ¹ 40.
14 Notation Keys 1. % d displays the following numeric notation mode menu. Restores standard mode FLO (floating decimal). Turns on scientific mode SCI and displays results as a number from 1 to 10 (1 n < 10) times 10 to an integer power. Turns on engineering mode ENG and displays results as a number from 1 to 1000 (1 n < 1000) times 10 to an integer power. The integer power is always a multiple of 3. 2. % C lets you enter and calculate the exponent.
% Engineering, Scientific, Floating Decimal Enter 12543, which will be in floating decimal notation (default), and alternate between scientific and engineering notations. Press 12543 Display FLO % " << % " SCI ENG --DEG 12543 04 x10 1.2543 SCI DEG FLO SCI SCI < % " SCI ENG < ENG --DEG 12543 03 x10 12.543 ENG DEG FLO --- ' ' ENG DEG ' 12543 12543.
%¢ Exponent The Earth is 1.496 x 108 kilometers from the Sun. Jupiter is 7.783 x 108 kilometers from the Sun. Enter the numbers in Scientific notation and determine how far away the Earth is from Jupiter. Press 7 8 783 % ¢8 Display 7.783E 8-1.4 ¹ 628700000.
Logarithms and Antilogarithms 15 Keys Note 1. A calculates the common logarithm (base 10). • The examples on the transparency masters assume all default settings. 2. B calculates the natural logarithm (base e, where e = 2.718281828459). • E ends a logarithmic function. 3. % ] calculates the common antilogarithm (10 raised to the power of the value). 4. % ^ calculates the natural antilogarithm (e raised to the power of the value).
AB Common Logarithm, Natural Logarithm Find log 23 rounded to 4 decimal places. Then find ln 23 rounded to 4 decimal places and return to Floating Decimal notation. Press A 23 E < % © Display log (23) 1.361727836 DEG ' F0123456789 DEG 4 FIX B 23 E < % ' log (23) ©8 © 1999 TEXAS INSTRUMENTS INCORPORATED 1.3617 DEG ' ln (23) FIX 3.1355 DEG ln (23) 3.
% Common Antilogarithm, Natural Antilogarithm % Find antilog 3.9824 rounded to 4 decimal places. Then find antiln 3.9824 rounded to 4 decimal places. When finished, return to Floating Decimal notation. Press 10^ (3.9824) 9602.846792 DEG © F0123456789 - % 38 9824 E < % Display ' DEG 10^ (3.9824) 9602.8468 FIX DEG ' e^ (3.9824) 53.6456 FIX DEG ' ©8 e^ (3.9824) 53.
Angle Settings and Conversions 16 Keys 1. I displays the following menu that lets you change the angle mode setting to DEG, RAD, and GRD without affecting the value in the display. 2. = displays a menu that lets you specify the unit of an angle. º Specifies degrees. r Specifies radians. DEG Sets degree mode. g Specifies gradients. RAD Sets radian mode. DMS GRD Sets gradient mode. Specifies degrees (º), minutes (´), and seconds (´´).
= Degrees, Minutes, 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. How long did you watch videos? Press 2= Display ¡- Å Æ ¹ r g DEG < ' 2¡ DEG 5=" ¡ -Å Æ ¹ r g DEG PAGE 100= Fraction to Degrees, Minutes, and Seconds How much is 2/3 of an hour in hours, minutes, and seconds? Press 2N3 Display ' 2®3 DEG =! % 'DMS ---DEG << 2®3 ' DMS 0¡ 40Å 0Æ ' DEG © 1999 TEXAS INSTRUMENTS INCORPORATED TI-30X ÙS: A Guide For Teachers 96
I Degrees, Radians, Gradients Calculate the sine of 30 in degrees, radians, and gradients, and then return to degrees. Press Display > 30 E < sin(30) I" DEG ' 0.5 DEG RAD GRD --DEG << sin(30) -0.988O31624 RAD I" DEG ' RAD GRD --RAD << sin(30) 0.4539905GRAD ' I"< < sin(30) ' © 1999 TEXAS INSTRUMENTS INCORPORATED 0.
Polar and Rectangular Conversions 17 Keys 1. % k displays the following menu that lets you convert rectangular coordinates (c,y) to polar coordinates (r,q) or vice versa. R4Pr Converts rectangular coordinate to polar coordinate r. R4Pq Converts rectangular coordinate to polar coordinate q. P4Rc Converts polar coordinate to rectangular coordinate c. P4Ry Converts polar coordinate to rectangular coordinate y. 2. % ` enters a comma.
%’ Polar to Rectangular Convert the polar ordered pair (7,30) to rectangular using the DEG (¡) angle unit. y (x = ?, y = ?) 4 3 2 r=7 1 30° 1 2 3 4 5 6 7 Press x Display %’ " " ¸ P' Rx ---- P' R y DEG ¤ <7% 30 E < %’ ! ' P' Rx(7,30) 6.062177826 DEG ¸ P' Rx P' R y ---DEG ¤ <7% 30 E < ' P' Ry(7,30) 3.5 DEG The rectangular ordered pair is 6.062177826,3.5.
18 Hyperbolics Keys Notes 1. % Y accesses the hyperbolic (sinh, cosh, tanh) function of the next trig key that you press. • The example on the transparency master assumes all default settings. • Hyperbolic calculations are not affected by the angle mode setting—whether or not the calculator is in RAD (radian), GRD (gradient), or DEG (degree) modes.
%› Sine, Cosine, Tangent Find the hyperbolic sine (sinh), cosine (cosh), and tangent (tanh) of 5. Press › % >5 E< › % ?5 E< › % @5 E< © 1999 TEXAS INSTRUMENTS INCORPORATED Display ' sinh(5) 74.20321058 DEG ' cosh(5) 74.20994852 DEG ' tanh(5) 0.
Quick Reference to Keys A Key Function !" Moves the cursor left and right so you can scroll the entry line. Press % ! or % " to scroll to the beginning or end of the entry line. #$ Moves the cursor up and down so you can see previous entries. Press % # or % $ to scroll to the beginning or end of the history. TUVW Adds, subtracts, multiplies, and divides. 7–6 Enters the digits 0 through 9. D Opens a parenthetical expression. E Closes a parenthetical expression. a Calculates the reciprocal.
Quick Reference to Keys ( C o n t i n u e d ) A Key Function N Lets you enter mixed numbers and fractions. %O Converts a simple fraction to a mixed number or a mixed number to a simple fraction. %i Recalls the most recently calculated result, displaying it as Ans. - Clears characters and error messages on the entry line. Once the display is clear, it moves the cursor to the last entry in history. %{ Clears all memory variables. ? Calculates the cosine. %[ Calculates the inverse cosine.
Quick Reference to Keys ( C o n t i n u e d ) A Key Function %j Converts a fraction to its decimal equivalent or converts a decimal to its fractional equivalent, if possible. %‚ Displays the following menu that lets you set the number of decimal places. F0123456789 F Sets floating decimal (standard) notation. 0-9 Sets number of decimal places. %Y Accesses the hyperbolic (sinh, cosh, tanh) function of the next trig key that you press. %f Lets you insert a character at the cursor.
Quick Reference to Keys ( C o n t i n u e d ) Key Function % Displays the RESET menu. RESET: N Y A Press < when N (no) is underlined to return to the previous screen without resetting the calculator. Press < when Y (yes) is underlined to reset the calculator. The message MEM CLEARED is displayed. Also, press & and - simultaneously to reset the calculator immediately. No menu or message is displayed.
Quick Reference to Keys ( C o n t i n u e d ) A Key Function u Displays the following menu of stat variables with their current values. n Number of x (or x,y) data points. v or w Mean of all x or y values. Sx or Sy Sample standard deviation of x or y. sx or sy Population standard deviation of x or y. Gx or Gy Sum of all x values or y values. Gx2 or Gy2 Sum of all x 2 values or y 2 values. L Gxy Sum of (x Q y) for all xy pairs in 2 lists. a Linear regression slope.
B Display Indicators Indicator Meaning 2nd 2nd function. HYP Hyperbolic function. FIX Fixed-decimal setting. SCI, ENG Scientific or engineering notation. STAT Statistical mode. DEG, RAD, GRAD Angle mode (degrees, radians, or gradients). K Constant mode. x10 Precedes the exponent in scientific or engineering notation. º» An entry is stored in history before and/or after the active screen. Press # and $ to scroll. ¸¹ An entry or menu displays beyond 11 digits. Press ! or " to scroll.
C Error Messages Message Meaning ARGUMENT A function does not have the correct number of arguments. DIVIDE BY 0 • You attempted to divide by 0. • In statistics, n = 1. DOMAIN You specified an argument to a function outside the valid range. For example: • • • • • • • • For x : x = 0 or y < 0 and x is not an odd integer. For y x: y and x = 0; y < 0 and x is not an integer. For x: x < 0. For LOG or LN: x 0. For TAN: x = 90¡, M90¡, 270¡, M270¡, 450¡, etc. For SIN -1 or COS -1: |x | > 1.
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