Manual / Guide · c. 2010

TI-30X Pro MultiView Guidebook

Texas Instruments' guidebook for the TI-30X Pro MultiView, the European twin of the TI-36X Pro.

Author: Texas Instruments
Year: c. 2010
Type: Manual / Guide
Credit: Texas Instruments; via education.ti.com.

4 Texas INSTRUMENTS TI-30X Pro MultiView™ Calculator Important informatio! Examples......... Switching the calculator on and off Display contrast Home screen . 2nd functions . Modes Multi-tap keys. Menus Scrolling expressions and history Answer toggle... Last answer... Order of operations. . Clearing and correcting 13 Fractions. 13 Powers, roots and inverses 17 Pi. 18 Math.. 19 Number functions... 20 Angles..... 2 Rectangular to pola 23 Trigonometry... 24 Hyperbolics 26 Logarithm and exponential functions 27 Numeric derivative Numeric integral Stored operations Memory and stored variables Data editor and list formulas... Statistics, regressions, and distributions. Probability....... Function table Matrices Vectors. Solvers Number bases Expression evaluation Constants. Conversions...... Complex numbers ENMOFS .sscsssseseee Battery information. In case of difficulty...... Texas Instruments Support and Service Important information Texas Instruments makes no warranty, either express 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 product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. MathPrint, APD, Automatic Power Down, EOS, and MultiView are trademarks of Texas Instruments Incorporated. Copyright © 2017 Texas Instruments Incorporated Examples Each section is followed by instructions for keystroke examples that demonstrate the TI-30X Pro MultiView™ functions Examples assume all default settings, as shown in the Modes section. Some screen elements may differ from those shown in this document. Switching the calculator on and off turns on the calculator. off] turns it off. The display is cleared, but the history, settings, and memory are retained. The APD™ (Automatic Power Down™) feature turns off the calculator automatically if no key is pressed for about 5 minutes. Press after APD. The display, pending operations, settings, and memory are retained. Display contrast The brightness and contrast of the display can depend on room lighting, battery freshness, and viewing angle. To adjust the contrast: 1. Press and release the key. 2. Press [4] (to darken the screen) or [=] (to lighten the screen). Home screen On the Home screen, you can enter mathematical expressions and functions, along with other instructions. The answers are displayed on the Home screen. The TI-30X Pro MultiView™ screen can display a maximum of four lines with a maximum of 16 characters per line. For entries and expressions of more than 16 characters, you can scroll left and right (© and @®) to view the entire entry or expression. In the MathPrint™ mode, you can enter up to four levels of consecutive nested functions and expressions, which include fractions, square roots, exponents with *, «, eX, and 10%. When you calculate an entry on the Home screen, depending upon space, the answer is displayed either directly to the right of the entry or on the right side of the next line. Special indicators and cursors may display on the screen to provide additional information concerning functions or results. Indicator Definition 2ND 2nd function. FIX Fixed-decimal setting. (See Mode section.) SCI, ENG ‘Scientific or engineering notation. (See Mode section.) DEG, RAD, [Angle mode (degrees, radians, or GRAD gradians). (See Mode section.) L1, L2, L3 Displays above the lists in data editor. H, B, O Indicates HEX, BIN, or OCT number-base mode. No indicator displayed for default DEC mode. x The calculator is performing an operation. 56 |An entry is stored in memory before and/or after the active screen. Press (© and © to scroll. [poly-solv] An entry or menu displays beyond 16 digits. Press © or ® to scroll. | Normal cursor. Shows where the next item you type will appear. Es Entry-limit cursor. No additional characters can be entered. Indicator Definition Placeholder box for empty MathPrint™ element. Use arrow keys to move into the box. ] MathPrint™ cursor. Continue entering the current MathPrint™ element, or press an arrow key to exit the element. 2nd functions Most keys can perform more than one function. The primary function is indicated on the key and the secondary function is displayed above it. Press to activate the secondary function of a given key. Notice that 2ND appears as an indicator on the screen. To cancel it before entering data, press again. For example, [7] 25 [enter] calculates the square root of 25 and returns the result, 5. Modes Use to choose modes. Press © © © © to choose a mode, and to select it. Press or [quit] to return to the Home screen and perform your work using the chosen mode settings. Default settings are highlighted in these sample screens. Bifhceres 4 DEG RAD GRAD Sets the angle mode to degrees, radians, or gradians. NORM SCI ENG Sets the numeric notation mode. Numeric notation modes affect only the display of results, and not the accuracy of the values stored in the unit, which remain maximal NORM displays results with digits to the left and right of the decimal, as in 123456.78. SCI expresses numbers with one digit to the left of the decimal and the appropriate power of 10, as in 1.2345678B5 (which is the same as 1.2345678x10°). ENG displays results as a number from 1 to 999 times 10 to an integer power. The integer power is always a multiple of3 Note: [EE] is a shortcut key to enter a number in scientific Notation format. The result displays in the numeric notation format selected in the mode menu. FLOAT 0123456789 Sets the decimal notation mode. FLOAT (floating decimal point) displays up to 10 digits, plus the sign and decimal. 0123456789 (fixed decimal point) specifies the number of digits (0 through 9) to display to the right of the decimal. REAL atbi r+ q Sets the format of complex number results. REAL real results atbi rectangular results rt q polar results DEC HEX BIN OCT Sets the number base used for calculations. DEC decimal HEX hexadecimal (To enter hex digits A through F, use : , and so on.) BIN binary OCT octal CLASSIC }MATHPRINT FLASSIC mode displays inputs and outputs in a single ine. MATHPRINT mode displays most inputs and outputs in textbook format. Examples of Classic and MathPrint™ modes Classic mode MathPrint™ mode Sci Sci 12549 1.23454 12545 1.23454 Float mode and answer toggle key. Float mode and answer toggle key. . Ay 0.125 2 Fix 2 Fix 2 and answer toggle key. an” 6.28 an ” an ane 6.28 Unid Unid 40509 41d 4 Exponent example Exponent example 25 ™ 2 25 “ 2 Square root example Square root example 4629 1.414213562 Bg Iz Jae 16414213562 Cube root example Cube root example 364 4 3 [ea 4 Multi-tap keys A multi-tap key is one that cycles through multiple functions when you press it. For example, the (i) key contains the trigonometry functions sin and sin/ as well as the hyperbolic functions sinh and sinh/ . Press the key repeatedly to display the function that you want to enter. Multi-tap keys include (x2é:.) , GJ (438), and (3). Applicable sections of this guidebook describe how to use the keys. Menus Menus give you access to a large number of calculator functions. Some menu keys, such as [recall], display a single menu. Others, such as [math], display multiple menus. Press ® and © to scroll and select a menu item, or press the corresponding number next to the item. To return to the previous screen without selecting the item, press To exit a menu and return to the Home screen, press 2nd] [quit] [recall] (key with a single menu): RECALL VAR (with values set to default of 0) (key with multiple menus): MATH NUM DMs R [poly-solv] P 1:4") 1: abs( 1° 1:P RX d[poly-solv] U"/d 2: Iem( 2: round( 2:¢ 2:P Ry 3: gcd( 3: iPart( Bf 3:R Pr( 4: 4Pfactor 4: fPart( ar 4:R Pq( 5: sum( 5: int( 5g 6: prod( 6: min( 6: DMS 7: max( 8: mod( Scrolling expressions and history (OROKCKS) Press © or ® to move the cursor within an expression that you are entering or editing. Press @or ® to move the cursor directly to the beginning or end of the expression. After you evaluate an expression, the expression and its result are added automatically to the history. Use © and © to scroll through the history. You can reuse a previous entry by pressing to paste it on the bottom line, where you can edit it and evaluate a new expression. Example Scroll M10 PP-4CICLY BF exe) leon S| Via: L919 OTS Rana i (i) Via: L919 OTS Teapa [SP 6. 08276253. Answer toggle 4] Press the [+=] key to toggle the display result (when possible) between fraction and decimal answers, exact square root and decimal, and exact pi and decimal. Pressing [«*=] displays the last result in the full precision of its stored value, which may not match the rounded value. Example Answer fv] 8 7 toggle fe 22 fal ic 28 2120 2, 828427125 Last answer [answer] The last entry performed on the home screen is stored to the variable ans. This variable is retained in memory, even after the calculator is turned off. To recall the value of ans: * Press [answer] (ans displays on the screen), or + Press any operations key ((+], =], and so forth) as the first part of an entry. ans and the operator are both displayed. Examples ans 3 [enter] ET lente) Rad 9 3 [ented] cad “3 Bnet3 2 10 [7] Baal [answer] J . yas 2% Order of operations The TI-30X Pro MultiView™ calculator uses Equation Operating System (EOS™) to evaluate expressions. Within a priority level, EOS evaluates functions from left to right and in the following order. 1st Expressions inside parentheses 2nd Functions that need a) and precede the argument, such as sin, log, and all R[poly-solv] P menu items 3rd Fractions. 4th Functions that are entered after the argument, such as x? and angle unit modifiers. 5th Exponentiation (4) and roots (*4). Note: In Classic mode, exponentiation using the key is evaluated from left to right. The expression 2°32 is evaluated as (2”3)*2, with fa result of 64. v2 64 In MathPrint™ mode, exponentiation using the key is evaluated from right to left. The expression 2432 is evaluated as 2*(3"2), with fa result of 512. pt 512 The calculator evaluates expressions entered with (x?) and [3] from left to right in both Classic land MathPrint™ modes. Pressing 3 i calculated as (342 =81. i 6th Negation (M. 7th Permutations (nPr) and combinations (nCr). 8th Multiplication, implied multiplication, division. 9th Addition and subtraction. 10th Conversions (n/d[poly-solv] Unid, F[poly-solv] D, 4DMS). 11th completes all operations and closes all lopen parentheses. Examples QP 5G (o)2 2 lente oo oaaz Q ©) 8 [4] 12 [enter 1+-gH12 “5 fv] 9) 16 css 0 anze 20 40243) "20 Nanda - [x44 3 12 Clearing and correcting [quit] Returns to the Home screen. Clears an error message. Clears characters on entry line. Moves the cursor to last entry in history once display is clear. Deletes the character at the cursor. insert] Inserts a character at the cursor. clear var] Clears variables x, y, Z, t, a, b, c, and d to their default value of 0. Resets the calculator. Returns unit to default settings; clears memory variables, pending operations, all entries in history, and statistical data; clears any stored operation, and ans. ny Fractions Gnd] [Og] [math] 1 In the MathPrint™ mode, fractions with (2) can include real and complex numbers, operation keys (( etc.), and most function keys (2), [%], etc.). In Classic mode, fractions with (E] do not allow operation keys, functions, or complex fractions in the numerator or denominator. Note: In Classic mode, only number entries are supported when using [8]. Fractions in Classic mode are shown with a double-thick fraction bar (for example, 89). The numerator must be an integer, and the denominator must be a positive integer. To compute more complex expressions (functions, variables, complex numbers, etc.), use [] along with ( and The calculator defaults output to improper fractions. Results are automatically simplified. 13 . enters a simple fraction. Pressing (&] before or after a number can result in different behavior. Entering a number before pressing (&] makes that number the numerator. To enter fractions with operators or radicals, press before you enter a number (in MathPrint™ mode only). + In MathPrint™ mode, press © between the entry of the numerator and the denominator. + In Classic mode, press [§] between the entry of the numerator and the denominator. The fraction bar will appear thicker than the division bar. + Pressing © from any MathPrint™ level, including the denominator or a lower limit, places the cursor in the history. Pressing enter will then paste the expression back to that MathPrint™ level. — To paste a previous entry in the denominator, place the cursor in the denominator, press © to scroll to the desired entry, and then press to paste the entry to the denominator. — To paste a previous entry in the numerator or unit, place the cursor in the numerator or unit, press © or iS) to scroll to the desired entry, and then press to paste the entry to the numerator or unit. . [cg] enters a mixed number. Press the arrow keys to cycle through the unit, numerator, and denominator. . 1 converts between simple fractions and mixed- number form (4"/dpoly-solv] U"/d). . converts results between fractions and decimals. Examples Classic mode "g,U% = 8B) 4 1 2nd) [08] 7 12 Se4d41urel2 P73 I 9 2 [math] enter BZ dul eZ [poly-solv] U "Id 14 F[poly-solv] [4 [2nd] [203] 1[8) 2 4ul/2rfed 4.5 D Examples MathPrint™ mode nid, U nid urs” Ma 9 [5] 2 [math] 1 [enter] [poly-solv] U" Ig F[poly-solv] D [foA]102Q0 |S 4g rted 4.5 Examples = [8)1.2(4] 13© 4 12.3 0,605 + (MathPrint™ mode only) (MathPrint™ oo mode only) Boerne Percentages [%] To perform a calculation involving a percentage, press [] after entering the value of the percentage. Example 2 Gaal 150 [enter] BFS 3 1 §Problem A mining company extracts 5000 tons of ore with a concentration of metal of 3% and 7300 tons with a concentration of 2.3%. On the basis of these two extraction figures, what is the total quantity of metal obtained? If one ton of metal is worth 280 dollars, what is the total value of the metal extracted? *] ba) 5000 3445000 150 23 [x] f) 7300 yerso00, "150 Ainst2. Sa7500. | 280 [enter] 5009 Finst2. Se? 300. , 317.9 | fins#k280 85012 — The two extractions represent a total of 317.9 tons of metal for a total value of 89012 dollars. EE key (3) (EE) is a shortcut key to enter a number in scientific notation format. Example 2 (EE) 5 [enter] — Ee) lente] 29 200000 XO) —-* ma gee le 2e5 16 Powers, roots and inverses Calculates the square of a value. The TI-30X Pro MultiView™ calculator evaluates expressions entered with [<3] and [3] from left {to right in both Classic and MathPrint™ modes. Raises a value to the power indicated. Use ® Ito move the cursor out of the power. [] {Calculates the square root of a non-negative value. [°-] |Calculates the nth root of any non-negative value and any odd integer root of a negative value. [a] Gives the inverse of a value: 1/x. The calculator evaluates expressions entered with [x3] and [3] ifrom left to right in both Classic and MathPrint™ modes Examples © [au 5 4 410 SP+qett a3 a 2 = 10 Ford Baal] 49 ——= Ta 7 [and][v-] 3 a Ix=424 S 6 2] 64 [enter] “> {2nd][*] 64 [enter] _ _ v7 2 [and) [8] [enter] OO np nh Pi (multi-tap key) p = 3.141592653590 for calculations. p =3.141592654 for display. Example 2h 2a p Zen 2m 2ne 6, 283185307 §Problem What is the area of a circle if the radius is 12 cm? Reminder: A = p xr2 12 (x?) [enter] The area of the circle is 144 p square cm. The area of the circle is approximately 452.4 square cm when rounded to one decimal place. 18 Math MATH displays the MATH menu: 44") Converts between simple fractions and dlpoly-solv] UNjy Mixed-number form 2: Iem( Least common multiple 3: gcd( Greatest common divisor 4: 4Pfactor Prime factors 5: sum( Summation 6: prod( Product Examples ny EJEEXO) Lfente > efpoly-solv] ere Ud Icm( 2 lengée9> 1B 6 f2na) [.] 9) (enter) gon 3 i... 5] 18 [2nd] L] 330) 9cd¢18, 33) 3 4Pfactor 253 4 [enter] ZS5HPPactor, 11423 sum( 5 = 104 2 Co¥2) 20 prod 5 = = 1050 LG) os O® 19 Number functions NUM © displays the NUM menu: 1: abs( Absolute value 2: round( Rounded value 3: iPart( Integer part of a number 4: fPart( Fractional part of a number 5: int( Greatest integer that is Athe number 6: min( Minimum of two numbers 7: max( Maximum of two numbers 8: mod( Modulo (remainder of first number P second number) Examples abs( 151 round( c round¢1. 245. 1.2 round¢1. 255.1)" iPart( = fPart( Pee heo G fPartorieS 2.7 int( int<-3.6) min( aa max( makes ae 7 -6 na] [.] .7 20 mod( Angles DMs ® © displays the DMS menu: 1° 2:¢ BE ar 5:g 6: DMS Specifies the angle unit modifier as degrees (°). Specifies the angle unit modifier as minutes (’). Specifies the angle unit modifier as seconds ("). Specifies a radian angle. Specifies a gradian angle. Converts angle from decimal degrees to degrees, minutes, and seconds You can also convert between rectangular coordinate form (R) and polar coordinate form (P). (See Rectangular to polar for more information.) Choose an angle mode from the mode screen. You can choose from DEG (default), RAD, or GRAD. Entries are interpreted and results displayed according to the angle mode setting without needing to enter an angle unit modifier. Examples RAD [mode] [enter] 30 (0X0) a sintsge> 21 DEG singsoey OO4 owe ec TMS (LS [math] © © Cee) sint30") 2 ant 360 1.5DMS _1°30"0" 5Problem Two adjacent angles measure 12° 31¢ 45£ and 26°54¢ 38£ respectively. Add the two angles and display the result in DMS format. Round the results to two decimal places. [dear]{modJOOOOOEn] | arao cam “Gmsage 789 (clear) 12 [math] ® © YesTH HUM WY Re? 12°31 '45"+26254> 39.44 12°31 '45"+26254> Sor44 ans+DMS The result is 39 degrees, 26 minutes and 23 seconds. 5Problem Itis known that 30°= p / 6 radians. In the default mode, degrees, find the sine of 30°. Then set the calculator to radian mode and calculate the sine of p / 6 radians. 22 Note: Press [clear] to clear the screen between problems. (clear) (J 30 (1) fenter) sint30) 2 2 sint30) sin(Z] 3 rs 2 Retain radian mode on the calculator and calculate the sine of 30°. Change the calculator to degree mode and find the sine ofp / 6 radians. sint30") (EJ 30 [math] ® © [enter] rap tome ” Rectangular to polar R[poly-solv] P @ displays the R[poly-solv] P menu, which has functions for converting coordinates between rectangular (x,y) and polar (r,q) format. Set Angle mode, as necessary, before starting calculations. 1:P Rx( Converts polar to rectangular and displays x. 2:P Ry( Converts polar to rectangular and displays y. 3:R Pr( Converts rectangular to polar and displays r. 4:R Pq( Converts rectangular to polar and displays q. Example Convert polar coordinates (r, q)=(5, 30) into rectangular coordinates. Then convert rectangular coordinates (x, y) = (3, 4) into polar coordinates. Round the results to one decimal place. R[poly-solv] RAD. GRAD jf eer ENG, SMesNge7a9 Lash ashe a8 23 {math} © 1 i100) eee [,] 300) (enter) nN @3 1] 4D) [enter] @4 [] 4D) enter) Converting (r, q) = (5, 30) gives (x, y) = (4.3, 2.5) and (r (x, y) = (3, 4) gives (1, q) = (5.0, 53.1). Trigonometry (multi-tap keys) Enter trigonometric functions (sin, cos, tan, sin", cos“, tan’), just as you would write them. Set the desired Angle mode before starting trigonometric calculations. Example Degree Mode 45 tan tan) 45 cos — 600) Secos(60) 2 Example Radian Mode tan ® l= 4] 4 tan(¥) 1 24 2 fear} ne tan tan) 0. 785398163 les) o. 785398165 0, 7ESSSB1ESS97 50 a cos = 5 400) | sreos(t) sz ® es) sz, 2 _* _s.sssss3e06_ 5Problem Find angle A of the right triangle below. Then calculate angle B and the length of the hypotenuse c. Lengths are in meters. Round results to one decimal place. Reminder: tan A= Z therefore m: A= tan‘ (2) mt A+mt B+ 90°= 180° A therefore mt B= 90°-mt A c 3 c= 3° 477 c 7 8 mode] [enter] © © © © fenter] RAD. GRAD jf eer ENG, SMesNge7a9 esas BE ae” 66.8 25 90 ©) Bad) [answer] 7 [x3] [enter] To one decimal place, the measure of angle A is 66.8°, the measure of angle B is 23.2°, and the length of the hypotenuse is 7.6 meters. Hyperbolics (multi-tap keys) Pressing one of these multi-tap keys repeatedly lets you access the corresponding hyperbolic or inverse hyperbolic function. Angle modes do not affect hyperbolic calculations. Example Set floating decimal [mode] © © [enter] HYP sinh(g}+Z 76. 20321058 sinh(g}+Z 76, 20321058 sinh 5342 26 Logarithm and exponential functions (multi-tap keys) yields the logarithm of a number to the base e (e = 2.718281828459). yields the common logarithm of a number. raises e to the power you specify. raises 10 to the power you specify. Examples LOG {Intog}1 1031? Q LN 50) 2 10901) "o [nea] fener 3 Tres d42 216875825 6 10 pheste? 2 loam) 5 e To] .s eS 1649721271 Numeric derivative [Mixa] [xq] calculates an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1E\B). This function is valid only for real numbers. 27 Example in MathPrint™ mode [Yet] hlvF450) | x, Example in Classic mode Classic: nDeriv(expression,variable,value[,H]) [“axO] dix] nDerivGnt +S tb e100 nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points. F(x +8) - f(x fro) = (+8) -fx- 8) ie) Te As H becomes smaller, the approximation usually becomes More accurate. In MathPrint™ mode, the default H is 1EV8. You can switch to Classic mode to change Hfor investigations. You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the calculator can return a false derivative value at a nondifferentiable point. 5Problem Find the slope of the tangent line to the curve f(x) = x? - 4x at 2 AB What do you notice? (Fix 3 decimal places.) GO OOOO = = i] Hel) | 2 = 0.000 28 Numeric integral [geuax] [sax] calculates the numeric function integral of an expression with respect to a variable x, given a lower limit and an upper limit. Example in RAD angle mode [gous] [2nd] ne [Reasintwnods 5Problem Find the area under the curve f(x) = Mk2+4 from N2 to 0 and then from 0 to 2. What do you notice? What could you say about the graph? Puc eee Oa JL CoP etd Notice that both areas are equal. Since this is a parabola with the vertex at (4,0) and zeros at (NR, 0) and (2, 0) you see that the symmetric areas are equal. 29 Stored operations op] dl [set op] set op] lets you store a sequence of operations. op] plays back the operation. To set an operation and then recall it: 1. Press [2nd] [set op]. 2. Enter any combination of numbers, operators, and/or values, up to 44 characters. 3. Press to store the operation. 4. Press [op] to recall the stored operation and apply it to the last answer or the current entry. If you apply [op] directly toa [op] result, the n=1 iteration counter is incremented. Examples Clear op [set op] OO oP= If a stored op is present, click to clear it. Set op 3 ors*2+3 Recall op 4e2t3 4t2t3. 118243 6 [er] 44243, 11#2+3 eHZ+3 Redefine op = op=* 30 Recallop —_ 5 [2nd] [op] Oo 20 {and} [oP] fot ona 4d §Problem Given the linear function y = 5x - 2, calculate y for the following values of x: -5; -1. Gad] [set op] = = 5 (2 op=45-2 (© 5 Gd or] Ses fo)1 [op] Ta5-2 Memory and stored variables Gard][recall] [nd] [clear var] The TI-30X Pro MultiView™ calculator has 8 memory variables—x, y, Z, t, a, b,c, and d. You can store a real or complex number or an expression result to a memory variable. Features of the calculator that use variables (such as the solvers) will use the values that you store. lets you store values to variables. Press [sto] to store a variable, and press o select the variable to store. Press to store the value in the selected variable. If this variable already has a value, that value is replaced by the new one. is a multi-tap key that cycles through the variable names x, y, Z, t, a, b, c, and d. You can also use recall the stored values for these variables. The name of the variable is inserted into the current entry, but the value assigned to the variable is used to evaluate the expression. To enter two or more variables in succession, press ® after each. 31 2nd] [recall] recalls the values of variables. Press [2nd][recall] to display a menu of variables and their stored values. Select the variable you want to recall and press [enter]. The value assigned to the variable is inserted into the current entry and used to evaluate the expression. [2nd][clear var] clears variable values. Press [2nd]| select 1: Yes to clear all variable values. Examples [clear var] and Start with clear screen [quit] Clear Var —_|[2nd) [clear var] oe Store 1 (Selects Yes) _ 154% 154% ™ ts Recall [recall] Oo Lita 15 15? 225 Lita 15 15 225 Lita 15 = 225 Srs39 225, 32 fered “1 ia 225 ans 225 Lie 4G) i] 15¢ 225 ans? 325 a 225 §Problem In a gravel quarry, two new excavations have been opened The first one measures 350 meters by 560 meters, the second one measures 340 meters by 610 meters. What volume of gravel does the company need to extract from each excavation to reach a depth of 150 meters? To reach 210 meters? Display the results in engineering notation. S50560%% 19663 3505E0%n 19663 Sate 109 207.483 fener enter 1508196000,” 23.486 [recall 2104196009, 150 2104196001 1509 33 210 2104196001 7 = 41.1626 150vy 31. 11e6 For the first excavation: The company needs to extract 29.4 million cubic meters to reach a depth of 150 meters, and to extract 41.16 million cubic meters to reach a depth of 210 meters. For the second excavation: The company needs to extract 31.11 million cubic meters to reach a depth of 150 meters, and to extract 43.554 million cubic meters to reach a depth of 210 meters. Data editor and list formulas lets you enter data in up to 3 lists. Each list can contain up to 42 items. Press © to go to the top of a list, and © to go to the bottom of a list. List formulas accept all calculator functions and real numbers. Numeric notation, decimal notation, and angle modes affect the display of an element (except fractional elements). Example Lt [data] 1[E] 4© a 2840 ad 3E}40 tren 4 (E) 4 [enter] Formula oO 0) nS ae ined Ba reas Clear Lt Ernla _ditlear 12 Frmla 34 Notice L2 is calculated using the formula you entered, and L2(1)= in the author line is highlighted to indicate the list is the result of a formula. §Problem On a November day, a weather report on the Internet listed the following temperatures. Paris, France 8°C Moscow, Russia ML°C Montreal, Canada 4c Convert these temperatures from degrees Celsius to degrees Fahrenheit. (See also the section on Conversions.) Reminder: F = 2 C+32 a ——> 5 FORMULA (ex) © zieteer Le Sere Sm 4:Clear L3 Frula | wAClear ALL 8O (FJ 10400 a o1 == 9) 50) ata) 1[5) 32 ——— 35 If Sydney, Australia is 21°C, find the temperature in degrees Fahrenheit. © OO © Al enter] = Statistics, regressions, and distributions [stat-reg/distr] lets you enter and edit the data lists. [stat-reg/distr] displays the STAT-REG menu, which has the following options. Note: Regressions store the regression information, along with the 2-Var statistics for the data, in StatVars (menu item 1). 1: StatVars 2: 1-Var Stats 3: 2-Var Stats Displays a secondary menu of statistical result variables. Use © and © to locate the desired variable, and press to select it. If you select this option before calculating 1-Var stats, 2-Var stats, or any of the regressions, a reminder appears. Analyzes statistical data from 1 data set with 1 measured variable, x. Frequency data may be included. Analyzes paired data from 2 data sets with 2 measured variables—x, the independent variable, and y, the dependent variable. Frequency data may be included. Note: 2-Var Stats also computes a linear regression and populates the linear regression results. 36 4: LinReg ax+b 5: QuadraticReg 6: CubicReg 7: LnReg atbinx 8: PwrReg ax”b 9: ExpReg ab’x Fits the model equation y=ax+b to the data using a least-squares fit. It displays values for a (slope) and b (y-intercept); it also displays values for r? and r. Fits the second-degree polynomial y=ax?+bx+c to the data. It displays values for a, b, and ¢; it also displays a value for R2. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required. Fits the third-degree polynomial y=ax*+bx?+cx+d to the data. It displays values for a, b, c, and d; it also displays a value for R2, For four points, the equation is a polynomial fit; for five or more, itis a polynomial regression. At least four points are required. Fits the model equation y=a+b In(x) to the data using a least squares fit and transformed values In(x) and y. It displays values for a and b; it also displays values for rand r. Fits the model equation y=ax® to the data using a least-squares fit and transformed values In(x) and In(y). It displays values for aand b; it also displays values for r? and r. Fits the model equation y=ab* to the data using a least-squares fit and transformed values x and In(y). It displays values for a and b; it also displays values for r? and r. [stat-reg/distr] ® displays the DISTR menu, which has the following distribution functions: 37 1: Normalpdf 2: Normaledf 3: invNorm 4: Binompdf Computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean mu=0 and standard deviation sigma=1. The probability density function (pdf) is: (x=) e 2 >0 Sx) = 1 Computes the normal distribution probability between LOWERbnd and UPPERbnd for the specified mean mu and standard deviation sigma. The defaults are mu=0; sigma=1; with LOWERbnd = MLE99 and UPPERbnd = 199. Note: MLE99 to 1£99 represents Mnfinity to infinity. Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean mu and standard deviation sigma. It calculates the x value associated with an area to the left of the x value. 0{ area{ 1 must be true. The defaults are area=1, mu=0 and sigma=1. Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x is a non-negative integer and can be entered with options of SINGLE entry, LIST of entries or ALL (list of probabilities from 0 to numtrials is returned). 0{ p{ 1 must be true. The probability density function (pdf) is: fos) = (")p"-p)" x x = 0,1... 38 5: Binomcdf 6: Poissonpdf 7: Poissoncdf Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be non- negative integer and can be entered with options of SINGLE, LIST or ALL (a list of cumulative probabilities is returned.) O{ p{ 1 must be true. Computes a probability at x for the discrete Poisson distribution with the specified mean mu (m), which must be a real number > 0. x can be an non-negative integer (SINGLE) or a list of integers (LIST). The probability density function (pdf) is: Ax) = e My /xtx = 01,2... Computes a cumulative probability at x for the discrete Poisson distribution with the specified mean mu, which must be a real number > 0. x can be an non-negative integer (SINGLE) or a list of integers (LIST). Note: The default value for mu (m) is 0. For Poissonpdf and Poissoncdf, you must change it to a value > 0. 1-Var Stats and 2-Var Stats results Important note about results: Many of the regression equations share the same variables a, b, c, and d. If you perform any regression calculation, the regression calculation and the 2-Var statistics for that data are stored in the StatVars menu until the next statistics or regression calculation. The results must be interpreted based on which type of statistics or regression calculation was last performed. To help you interpret correctly, the title bar reminds you of which calculation was last performed. Variables Definition n Number of x or (x,y) data points. Vv orw Mean of all x or y values Sx or Sy Sample standard deviation of x or y. 39 sxorsy Population standard deviation of x or y. Gx or Gy Sum of all x or y values. Gx? or Gy? Sum of all x2 or y2 values. Gxy Sum of (x...Y) for all xy pairs a (2-Var) Linear regression slope. b (2-Var) Linear regression y-intercept. r (2-Var) (Correlation coefficient. x¢ (2-Var) Uses a and b to calculate predicted x value when you input a y value. y¢ (2-Var) Uses a and b to calculate predicted y value when you input an x value. Minx Minimum of x values. Qi (1-Var) Median of the elements between MinX and Med (1st quartile). Med Median of all data points (1-Var stats only). Q3 (1-Var) Median of the elements between Med and MaxX (3rd quartile). MaxX Maximum of x values. To define statistical data points: 1. Enter data in L1, L2, or L3. (See Data editor.) Note: Non-integer frequency elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, the sample standard deviation, Sx, is undefined for non-integer frequencies, and Sx = Error is displayed for that value. All other statistics are displayed. 2. Press [stat-reg/distr]. Select 1-Var or 2-Var and press 3. Select L1, L2, or L3, and the frequency. 4. Press to display the menu of variables. 5. To clear data, press [data], select a list to clear, and press 40 1-Var Example Find the mean of {45, 55, 55, 55} Clear all OXOXS) “mesg roma St Clear tg Data = = BOsOSO5S | E rat Stat [auit] bist -reg/di [stat-reg/distr] eee 2 (Selects 1-Var Stats) exo) re Stat Var 2 x 52.3 ansa2 105 2-Var Example Data: (45,30); (55,25). Find: x¢(45) Clear all OXOXS) “mesg roma St Clear tg Data lenter] 45 © 55 © © 30 OBO 41 Stat [stat-reg/distr] 3 (Selects 2-Var Stats) XS) (ai tat-reg/distr] 1 SOSeeoe [enter] 45 (1) fenter] 5Problem For his last four tests, Anthony obtained the following scores. Tests 2 and 4 were given a weight of 0.5, and tests 1 and 3 were given a weight of 1. Test No. 1 2 3 4 Score 12 13 10 1 Coefficient 1 05 1 0.5 1. Find Anthony's average grade (weighted average). 2. What does the value of n given by the calculator represent? What does the value of Gx given by the calculator represent? Reminder: The weighed average is =x _ (12)() + (13)(0.5) + (10)(1) + 11)(0.5) ni 140541405 3. The teacher gave Anthony 4 more points on test 4 due to a grading error. Find Anthony's new average grade. [data] [data] © © © ‘ORMULA L2 ig 42 CLERR il DOOCO Sree Ee 1 4:Clear LS Frnla | wHClear ALL 129 BO WOUS O1© 5O1© 5 fencer] [stat-reg/distr] 2 (Selects 1-Var Stats) Vee sare.” © © O lente] PaaS ORE Ci ia 3 ER=11, 33333333 | SoSxSErrop Anthony has an average (V ) of 11.33 (to the nearest hundredth). On the calculator, n represents the total sum of the weights. n=1+05+1+0.5, Gx represents the weighted sum of his scores. (12)(1) + (13)(0.5) + (10)(1) + (11)(0.5) = 34. Change Anthony's last score from 11 to 15. [data] © © © 15 [enter] 7 [stat-reg/distr] 2 XOXO) If the teacher adds 4 points to Test 4, Anthony's average grade is 12. 43 5Problem The table below gives the results of a braking test. Test No. 1 2 3 4 Speed 33 49 65 79 (kph) Braking 5.30 14.45 20.21 38.45 distance (m) Use the relationship between speed and braking distance to estimate the braking distance required for a vehicle traveling at 55 kph. A hand-drawn scatter plot of these data points suggest a linear relationship. The calculator uses the least squares method to find the line of best fit, y=ax'+b, for data entered in lists. XOXO) [ors roemeh St Clear tg 33© 49© 65 © 799© © 53 se zeal © 14.45 © 20.21 © 38.45 CtE3= [sui] ——= [stat-reg/distr] ae a 3 (Selects 2-Var Stats) om. / IAS) vm ot ia to fie a PAY ee Press © as necessary to view = aand b. ee ta=0, 6775251996 we 8 cee ehes 44 This line of best fit, Y=0.67732519x'N 18.66637321 models the linear trend of the data. Press © until y’ is highlighted = pass Bios tet bm 58 0) v5) : 18.58651222 The linear model gives an estimated braking distance of 18.59 meters for a vehicle traveling at 55 kph Regression example 1 Calculate an ax+b linear regression for the following data: {1,2,3,4,5}; {5,8,11,14,17}. Clear all data QoOe ce SiClear LS Data 7 = co 19203040 : |B 5O® Peres 5O8sOQOUSCUO 17 [enter] Regression [quit] [stat-reg/distr] XS) DAKO Press © to examine all {the result variables. Regression example 2 Calculate the exponential regression for the following data: 45 L1={0,1, 2, 3, 4}; L2={10, 14, 23, 35, 48} Find the average value of the data in L2. Compare the exponential regression values to L2. Clear all data [data] (data) 4 Data 0516203040 OS 140 23 35 © 48 [enter] Regression [stat-reg/distr] =] LEBEXeRea ab“ regression Spare CT A LE equation to Soo? BS f(x) in the menu. Regression Equation Find the [stat-reg/distr] average 1 (Selects StatVars) value (y) of |}OO@ thedatain |JOO©@ L2using |OOO Notice that the title StatVars. bar reminds you of lyour last statistical lor regression \calculation. Examine the 2 = table of FCadeab™ values of the regression equation 46 0 a 2 ez. 21432038 Warning: If you now calculate 2-Var Stats on your data, the variables a and b (along with r and r2) will be calculated as a linear regression. Do not recalculate 2-Var Stats after any other regression calculation if you want to preserve your regression coefficients (a, b, c, d) and r values for your particular problem in the StatVars menu. Distribution example Compute the binomial pdf distribution at x values {3,6,9} with 20 trials and a success probability of 0.6. Enter the x values in list L1, and store the results in L2. Clear all data [SXSXS) "mega Fo St Clear tg Data = 3O6O9 i Tene DISTR [stat-reg/distr] INO) 3 Nornsie St invlorm ® PRE le au 4 = 20 © 0.6 4 eed © 7 ae ee oe 47 Probability options: is a multi-tap key that cycles through the following (A factorial is the product of the positive integers from 1 to n.n must be a positive whole number { 69. ncr Calculates the number of possible combinations of n items taken rat a time, given n and r. The order lof objects is not important, as in a hand of cards nPr Calculates the number of possible permutations of in items taken rat atime, given n and r. The order of objects is important, as in a race. displays a menu with the following options: rand Generates a random real number between 0 and 1. To control a sequence of random numbers, store an integer (seed value) | 0 to rand. The seed value changes randomly every time a random number is generated. randint( Generates a random integer between 2 integers, Aand B, where A{ randint{ B. Separate the 2 integers with a comma. Examples 4 24 nCr oT 4) 24 52 ntr 5 2598960, 48 ar oC Cd Ce) Send | = 52 ntr 5 2598960, STO 4rand [5 [sto] (2 vee iran frandint¢ 1 (Selects rand) wns nr 2598960, 8 nPr 3 336 = Rand 1 [enter] BonFr 3 Strand rand Randint( 2 corand == [ 1 O rant 0, 000093165 §Problem Anice cream store adve