Manual / Guide · 2011–2026
Texas Instruments' guidebook for the TI-36X Pro: modes, MathPrint, memories, calculus, statistics and distributions, tables, matrices, vectors, solvers, number bases, constants, conversions, complex numbers and battery replacement, with worked examples.
i} Texas INSTRUMENTS TI-36X Pro education.ti.com vip Texas INSTRUMENTS TI-36X Pro Calculator Important information 3 Examples wees tee 4 Switching the calculator on and off vettttvetttteerrereee 4 Display contrast ............... . we 4 Home screen 0... tte 4 2nd functions 6 Modes ....... 6 Multi-tap keys 9 Menus .......... . vO Scrolling expressions and history tecttttttteereeeeeees 10 Answer toggle 1 Last answer .... 1 Order of operations. . ve. 12 Clearing and correcting oo... 0.0... cece. 13 Fractions . . cece 4 Percentages 0.00.0... eee eee eee eee eee 16 EE key . . . . 1 17 Powers, roots and inverses . 18 Number functions Svcs veivestttvetrtetiesee 21 Angles ................ 22 Rectangular to polar 24 Trigonometry ... . 5 Hyperbolics .. 27 Logarithm and exponential functions Numeric derivative Numericintegral .... Stored operations . Memory and stored variables Data editor andlist formulas 2.2.02. .... eee Statistics, regressions, and distributions Probability ... Function table Matrices ... Vectors . : : : : SOWErS oo. cece rete teeteeeee eect eee Number bases Expression evaluation Constants Conversions ....... Complex numbers . Errors see Battery information In case of difficulty ... Texas Instruments Support and Service ................. 81 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 and EOS are trademarks of Texas Instruments Incorporated. Copyright © 2010-2026 Texas Instruments Incorporated Examples Each section is followed by instructions for keystroke examples that demonstrate the TI-36X Pro 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-36X Pro 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 *, Vy, e*, 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. The calculator is performing an operation. av Anentry is stored in memory before and/or after the active screen. Press © and © to scroll. 0 Anentry or menu displays beyond 16 digits. Press © or @® to scroll. | | Normal cursor. Shows where the next item you type will appear. # Entry-limit cursor. No additional Indicator Definition characters can be entered. 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, [v-] 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 selectit. Press or [2nd] [quit] to return to the Home screen and perform your work using the chosen mode settings. Default settings are highlighted in these sample screens. oe ee ERE fas * Sifhiceres 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. NORNM 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 1.2345678E5 (which is the same as 1.2345678%10°). ENG displays results as a number from 1 to 999 times 10 to an integer power. The integer power is always a multiple of 3. 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 012345678 9—Sets the decimal notation mode. FLOAT (floating decimal point) displays up to 10 digits, plus the sign and decimal. 012345678 9 (fixed decimal point) specifies the number of digits (0 through 9) to display to the right of the decimal. REAL atbi 120 —Sets the format of complex number results. REAL real results atbi rectangular results 26 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 [A], 2a] [B], and so on.) BIN binary OCT octal CLASSIC = MATHPRINT CLASSIC mode displays inputs and outputs in a single line. MATHPRINT mode displays most inputs and outputs in textbook format. Examples of Classic and MathPrint™ modes Classic mode MathPrint™ mode Sci Sci 12345 1. 2345e4 12345” 1.234564 Float mode and answer Float mode and answer toggle key. toggle key. 1a. 0. 168 & 2 “ . Ly 0,125 : Fix2 Fix 2 and answer toggle key. an” 6.28 an ” an 2ne 6.28 Unid Unid 4.5/9 4179 4a * aa Ss 3 Exponent example Exponent example 25 "32 2 "32 Square root example Square root example 12) _ E . B 1.414213562 Tde 1.414213562 Cube root example Cube root example 3ié4 “4 ia “4 Multi-tap keys A multi-tap key is one that cycles through multiple functions when you press it. For example, the (&&:] 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 65, &3, [integ), , and (25). 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 a recall], display a single menu. Others, such as isplay 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 [clear]. To exit a menu and return to the Home screen, press [quit]. [recall] (key with a single menu): RECALL VAR (with values set to default of 0) (key with multiple menus): MATH NUM DMS RoP 4:bnid«> Unid 1: abs( 1:° 1: PPRx( 2: lem( 2: round( 2" 2:P>Ry( 3: gcd( 3: iPart( 3:” 3: R> Pri 4:pPfactor 4: fPart( 4:r 4:R>PO( 5: sum( 5: int( 5:g 6: prod( 6: min( 6:>DMS 7: max( 8: mod( Scrolling expressions and history ODOO Press © or ® to move the cursor within an expression that you are entering or editing. Press © or 2nd] © 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 PF-4c3c1) 37 7431) 37 Tama iF 3] Fine (219 CET Rama Ge U3Pe_6,.08276253 Answer toggle fe] 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 [J 8 enter] rar toggle & a 2{2e ” 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 393 345 “3 3 33 a) ans#3 2r 3 [v] 33 “3 Order of operations The TI-36X Pro 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 Reb P menu items. 3rd Fractions. 4th Functions that are entered after the argument, such as x’ and angle unit modifiers. 5th Exponentiation (A) and roots (*V). Note: In Classic mode, exponentiation using the [x5] key is evaluated from left to right. The expression 2342 is evaluated as (2°32, with aresult of 64. 2032 ” 64 In MathPrint™ mode, exponentiation using the key is evaluated from right to left. The expression 2342 is evaluated as 2(342), with aresult of 512. 2 512 The calculator evaluates expressions entered with (<2) and [3] from left to right in both Classic and MathPrint™ modes. Pressing 3 12 calculated as (3°) = 81. 6th Negation (-). 7th Permutations (nPr) and combinations (nCr). 8th Multiplication, implied multiplication, division. 9th Addition and subtraction. 10th | Conversions (n/d«> Un/d, F«> D, »DMS). 11th completes all operations and closes all open parentheses. Examples tear etS¥-12 0 () 164) (©) 8G) 12 enter} |] .-c412 3 [-] 9G) 16 — “3 0) 2030) aaa 20 4(0 2H)3 40243) "20 andy -] 3B] 20 [eaea 5 4) 2 ented) Clearing and correcting (sui) Returns to the Home screen. 13 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, andd to their default value of 0. [reset] 2 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. Fractions Gna] [G8] [math] 1 [and) [Fd] In the MathPrint™ mode, fractions with [E] can include real and complex numbers, operation keys ((4], [x], etc.), and most function keys [%], etc.). In Classic mode, fractions with [2] 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 (Q and Oo. The calculator defaults output to improper fractions. Results are automatically simplified. . enters a simple fraction. Pressing [E] 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 [E] 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 [2nd] © 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 22nd] © 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 (bn/d¢> Un/d). . [fd] converts results between fractions and decimals. Examples Classic mode nid, Unid | 3(8) 4 Gna) [03] Be4elurel2 "7/3 7) 12 (enter) nide> Unid | 9(§) 2 [math] 1 [enter] S/2MiWUR dui? FaD 4 Gna) [105] 1(E) 22nd) |] auiporred “a5 [Ferd] Examples MathPrint™ mode n/d, Un/d 30401 ea => atlas 3 [ag] 7© 12 nid@Unid |9)2@ 1 Syooun “hh aw ze FoD — /4GR [98]1©20 |Tiaseg yg [fr] Examples | (2) 1.264) 1304 seed 9,625 + (MathPrint™ mode only) (MathPrint™ | (2) (2) 54) Baa) [] |, = a mode only) a4 pect cerIeerr} 2 e20 Percentages [x] To perform a calculation involving a percentage, press [2] after entering the value of the percentage. Example 2 [2nd) [%] [x] 150 [enter] 2h 50 "3 Problem Amining 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? 3 Gna) [%] Be) 5000 fenter) 3%45000 “150 2.3 [2nd] [%] [x] 7300 [enter] yue5009 “150 Rnst2. 7500 [) 280 325000, 150 Fns#2, Sx#7300 Ans#280 9012 The two extractions represent a total of 317.9 tons of metal for a total value of 89012 dollars. EE key =) [EE] is a shortcut key to enter a number in scientific notation format. Example 2 (Ee) 5 285 200000 eo rap ceo wg OR 265 Powers, roots and inverses Calculates the square of a value. The TI-36X Pro calculator evaluates expressions entered with [x2] and [3] from left to right in both Classic and MathPrint™ modes. Raises a value to the power indicated. Use ® to move the cursor out of the power. [|__| Calculates the square root of a non-negative value. [ex] | 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] from left to right in both Classic and MathPrint™ modes. Examples © wut gy 5 4 10 Pra (49 = 7 [3 ae) [TSS Gna) [7] 64 ene a 2rd) [3] n y Pi multi-tap key) m= 3.141592653590 for calculations. m= 3.141592654 for display. Example ud 2 2h "an cz) Zin "on 2me 6, 283185307 Problem Whats the area of a circle if the radius is 12 cm? Reminder: A = mxr” G2) 125) ee = tne [oe] Mane 3893421 The area of the circle is 144 m square cm. The area of the circle is approximately 452.4 square cm when rounded to one decimal place. Math 4:pn/d«> Un/d Converts between simple fractions and mixed-number form. 2: Iem( Least common multiple 3: ged( Greatest common divisor 4:»Pfactor Prime factors 5: sum( Summation 6: prod( Product Examples nidé>Unid_ | 9(§) 2@ [math] 1 3 “4 Sour 4 Iom( 2 1ems99 1B 6 Gna) [>] 9 ged( 3 scd18.33> 3 18 Gnd] [>] 330) pPfactor | 253 [math] 4 [enter] 255r Factor, - * sum( 5 4 “ 1040 PAC) 20 20 prod( 6 ea, 10501 LG) Fe ®® Number functions NUM © displays the NUM menu: 1: abs( Absolute value 2: round( Rounded value 3: iPart( Integer part of anumber 4: fPart( Fractional part of a number 5: int( Greatest integer that is < the number 6: min( Minimum of two numbers 7: max( Maximum of two numbers 8: mod( Modulo (remainder of first number + second number) Examples abs o1 lB (2) Baa) [7] 5 fenter] round( @2 round¢L. 245.1) 1.245 2nd) [.] 10) round 1.2585 13°! [oXC) @OOOOOS iPart( a Ox (3) lentes) int( @5 inko-3.6) "6 (©) 5.60) min( ® 6 min¢4, -5) “ 5 max( 4 Bnd) [.] (50) maxG.Br.7? Oe? @7 6 2nd) [;] .70) moa o8 idC1 7-123 . ‘5 17 nd] [,] 120) mod¢1?, 16) 7 [XS) OO6 © © displays the DMS menu: Specifies the angle unit modifier as degrees (°). 2" Specifies the angle unit modifier as minutes ('). 3.” Specifies the angle unit modifier as seconds ("). 4ur Specifies a radian angle. 5g Specifies a gradian angle. 6:>DMS 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. 22 Examples RAD ® DEG [dg GRAD gp Sc ENG GLgsHES7 ES fates a8 4 MATH NUN WE! RoP 30 [math] ® ® on 10) sint30*> ae 3 DEG neo, see 4 sin¢30°> 4 OO4 ant 365 »DMS 1.5 [math] ® © 6 enter] || i ncsoe ant 36 T.5DMS _1°30"O! Sram Problem 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. DOOD O enter] cao, agen Ber ENS, laa ote ZEO7°? 12 [math] © © NATH NUM Wilt RP Sp" 1 12°31 “45"426850 34 OO2 . 45 [math] ® ® 3 23 (4) 26 [math] © © 1 54 [math] © © 2 38 [math] © © 3 [enter] [math] ® © 6 fenter] 12851 '45"426°54b anshDMS, 39°26 '25" The result is 39 degrees, 26 minutes and 23 seconds. Problem Itis known that 30° = 2/6 radians. In the default mode, degrees, find the sine of 30°. Then set the calculator to radian mode and calculate the sine of 2/6 radians. Note: Press to clear the screen between problems. 300 anu ® sint30) “4 2 6® sin(Z) i Retain radian mode on the calculator and calculate the sine of 30°. Change the calculator to degree of x/6 radians. mode and find the sine © 0 Gre] 1) Esl sint30*) sin(Z") raps tome ” © displays the R¢> P menu, which has functions for converting coordinates between rectangular (x,y) and polar 24 (r,8) 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>P@( Converts rectangular to polar and displays 0. Example Convert polar coordinates (r, 8)=(5, 30) into rectangular coordinates. Then convert rectangular coordinates (x, y) = (3, 4) into polar coordinates. Round the results to one decimal place. RoP TO) CE... ® ea OB 57° [,] 30) [enter] . [math] © 2 5 Gnd] [+] 30 0) enter) @ 3 PrRx(5, 30) “4.3 3 Gnd) [,] 40) Repeessay 88 @4 R>PACS,4) 1 3 Gnd [,] 40] Converting (r, 8) = (5, 30) gives (x, y) = (4.3, 2.5) and (x, y) = (3, 4) gives (r, @) = (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. 25 Example Degree Mode tan XC) tan(asy) 45 -1 roy tan taniL> 45 cos Becos(60) 3 50d Ge] 600) Example Radian Mode tan = tan) 1 -1 we tan tan 1) 0, 785398163 3] 0, 785598165 0. 78559816559750 4 cos = secos($) SE 5G, 2 3, 535533906 Problem 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: 26 tanA=therefore 3mZA=tan \3 mZA+mZB + 90° = 180° A therefore mZB =90°-mZA 2 2 caV3 +7 c ; XOXOXO) eae Waa arbi rn cé 7H30 tam(Z) 66.8 90 (=) [anal [answer] ag) = 66.8 90-ans 23.2 []3 7 90-sns 23.2 ped 2 eI s0-ans 22 32472 458 SEE. 7.6 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 (GI (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. 27 Example Set floating (XC) . decimal HYP sinha Zoszi0se 502 Se © sinks Zpszi0se sinh" So Basasai 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. aises e to the power you specify. 10°} raises 10 to the power you specify. Examples LOG 1 waa 0 LN (intog] 50) E) 2fente] |] roger) 12 19975825 a] = 10 ieee? “9 login) 5 28 er 1.648721271 5 [enter] Numeric derivative [Yet] [“%xU] calculates an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and e (if not specified, the default is 1E -3). This function is valid only for real numbers. Example in MathPrint™ mode [Mex] [“axa] HOF) pena 5 © (]) 1 lenter) Example in Classic mode Classic: nDeriv(expression, variable, value, €]) [Mix nberivn24Sie tsb [“axa] 5 L D]f1 nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points. jl (2) _ flero ot (e-9 As ¢ becomes smaller, the approximation usually becomes more accurate. In MathPrint™ mode, the default ¢ is 1E -3. You can switch to Classic mode to change ¢ for investigations. 29 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. Problem Find the slope of the tangent line to the curve f(x) = x? — 4x at 2 x=v5, What do you notice? (Fix 3 decimal places.) {mode] © © © D © © lenter] Gnd] [Yast] AGF -40)] ge 2 (5) Bad] [] 3 The slope of the tangent line at x =¥3 is zero. Amaximum or minimum of the function might be at this point. Numeric integral [igoax] [Igcax] 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 ® a “= [igoax] [ecu] [Esasingao ode 0 Problem Find the area under the curve f(x) = -x°+4 from -2 to 0 and then from 0 to 2. What do you notice? What could you say about the graph? 30 Gand) [[sax] [2] 2® 0® Oe ay ey 40 bal ice +4 )dne Jt “244)dou . oxo) “2 © © O[detete} [er Crteadaee 2 |5¢ Pia) Notice that both areas are equal. Since this is a parabola with the vertex at (4,0) and zeros at (~2,0) and (2,0) you see that the symmetric areas are equal. Stored operations [or] [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. Ifyou apply [op] directly toa [op] result, the n=1 iteration counter is incremented. 31 Examples Clear op [set op] ors “ Ifastored op is present, click [clear] to clear it. Setop Gd 2) Samed) or=#243 Recallop | 2nd] [quit] 4243 nee Ii 4 Bnd [op] [or] 4i2e3 net 114243 nee 25 6 2nd) [op] 44243 net 1h 114243, nz 25 #243 net 15 Redefine [set op] ors® oP Recallop | 5 (2nd) [op] =e te os 20 [2nd] [op] 207 nei 400 Problem Given the linear function y = 5x — 2, calculate y for the following values of x: -5; -1. [set op] op=45+2 J 5E)2 f)5 [or] 545-2 1 [or] “145-2 32 Memory and stored variables [recall] [clear var] The TI-36X Pro 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 to store a variable, and press [x25..] to 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 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. [recall] recalls the values of variables. Press [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. [clear var] clears variable values. Press [clear var] and select 1: Yes to clear all variable values. Examples Start with [quit] clear screen Clear Var [clear var] “ “ 33 Store 1 (Selects Yes) 15 159%, 1535, 15 Recall [recall] 153%, 1 152 225 153%, 15 15? 225 ans? 153 me 5* 225 ans? 255 Lark “ 12 a 225 ans3y 225 2 (=) 4 (enter) 15° "O95 anssy 225 255 ans/4 96.25 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. {mode] © ® © [enter] [clear] JoDHSEOe, 1963 340] 6105 350sSe00n | 156e5 S40861059 207.483 150 [recall] 150¥196000,." 29.486 210%) [recall] 2upe1z600, 6 : 16e 2104196009, 41.1666 150%) 3111186 2104196000, 41.1686 150") 31,11e6 iDky 43, 55466 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 ofa list, and © to go to the bottom ofa list. List formulas accept all calculator functions and real numbers. 35 Numeric notation, decimal notation, and angle modes affect the display of an element (except fractional elements). Example ul axa] 1) 40 “uP 2840 po 340 a 4 (5) 4 [enter] Formula |@ (0) [Ford] ‘sCe=Livreae 14 _ i em BA la3e Le) = 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 Ona November day, a weather report on the Internet listed the following temperatures. Paris, France 8°C Moscow, Russia -1°C. Montreal, Canada 4°C Convert these temperatures from degrees Celsius to degrees Fahrenheit. (See also the section on Conversions.) 9 Reminder: F = 5 C + 32 36 (data) [data] 4 [data] © 5 FORMULA ear LZ Sitlear C3 CLEAR last cs ear roa dicieer CS Fala LwBClear ALL | 8O()10400 [data] @ 1 9 =) 5 [&) [data] 4 [+] 32 If Sydney, Australia is 21°C, find the te Fahrenheit. © OO O21 [enter] Statistics, regressions, and distributions [stat-reg/distr] lets you enter and edit the data lists. [stat-reg/distr] displays the STAT-1 the following options. REG menu, which has Note: Regressions store the regression information, along with the 2-Var statistics for the data, in StatVars (menu item 1). 1: StatVars Displays a secondary menu of statistical result variables. Use © and © to locate 37 2: 1-Var Stats 3: 2-Var Stats 4: LinReg ax+b 5: QuadraticReg 6: CubicReg 7: LnReg atbinx 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. 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 R?. For three data points, the equation is a polynomial fit; for four or more, itis 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 R’. 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 38 8: PwrReg ax“b 9: ExpReg ab’x 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; italso 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 andr. [stat-reg/distr] ® displays the DISTR menu, which has the following distribution functions: 1: Normalpdf 2: Normaledf 3: invNorm 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: -(@=py e 2 >0 1 A206 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 = ~1£99 and UPPERbnd = 1£99. Note: -1£99 to 1E99 represents infinity to infinity. Ax) = 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 39 4: Binompdf 5: Binomedf 6: Poissonpdf 7: Poissoncdf 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 atx 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 mustbe true. The probability density function (pdf) is: fo) = (")p\A—py" x = Olan Computes a cumulative probability at.x for the discrete binomial distribution with the specified numtrials and probability of success () 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.) 0 < p <1 must be true. Computes a probability atx for the discrete Poisson distribution with the specified mean mu (11), which must be a real number > 0. x can be an non-negative integer (SINGLE) or alist of integers (LIST). The probability density function (pdf) is: fx) = e "u/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 alist of integers (LIST). 40 Note: The default value for mu (1) 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. Xory Mean ofall x or y values. Sxor Sy Sample standard deviation of x or y. Ox OF oy Population standard deviation of x or y. =x or Ly Sum of all x or y values. =x’ or xy’ Sum of all ¥ ory’ values. xy 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 inputa y value. y’ (2-Var) Uses a and b to calculate predicted y value when you input an x value. 4 MinX Minimum of x values. Q1 (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 (enter). . SelectL1, L2, or L3, and the frequency. 4. Press to display the menu of variables. . To clear data, press (data) , select a list to clear, and press [enter] . 1-Var Example Find the mean of {45, 55, 55, 55} wo a Clear all e©oo FORMULA data ear LZ SiClear L3. Data gf 45@ 55© 55O@ 55 || eee 42 Stat 342-Var a iver “Shats j DISTR 2 (Selects 1-Var Stats) (XO) fee | Peer aiid Ci CB 3 Le = Stat Var — | 2 (enter) x 525 2 [enter) x 52.9 ans#2 105 2-Var Example Data: (45,30); (55,25). Find: x’ (45) Clear all (OXOXS) FORMULA data steteh LS Data 4550 5500 30 BO Stat [stat-reg/distr] | O15 aes i-t er Eats Si2-Var Stat: 3 (Selects 2-Var Stats) [auit] ; [stat-reg/distr] 4 SSSES08 43 450) x45) “15 Problem For his last four tests, Anthony obtained the following scores. Tests 2 and 4 were given a weight of 0.5, and tests 1 and3 were given a weight of 1. Test No. 1 2 3 4 Score 12 13 10 11 Coefficient 1 0.5 1 05 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 Xx given by the calculator represent? Reminder: The weighed average is n 140541405 3. The teacher gave Anthony 4 more points on test 4 due toa grading error. Find Anthony's new average grade. eror) roman aulesr Ls CLEAR anu (OKOKOXOO) dicieer CS Fala | wHClear ALL | 129 139 109 119 aa lead O19 5O1© 5lenter] a [stat-reg/distr] aneee Distr ei-Gar Stats Sb2-Var Stats 2 (Selects 1-Var Stats) A-VAR STATS © OO enter] PRA OME CE i oe pepe . BRESESEX) S5xsError Anthony has an average (x) of 11.33 (to the nearest hundredth). On the calculator, n represents the total sum of the weights. n=14+0.5+1+0.5. =x 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] te [stat-reg/distr] 2 O00 If the teacher adds 4 points to Test 4, Anthony's average grade is 12. Problem The table below gives the results of a braking test. Test No. 1 2 3 4 Speed 33 49 65 79 (kph) Braking §.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. 45 Ahand-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, /=ax'+b , for data entered in lists. [data] [data] © © © mea oe SiClear LS BOMOHOIOGDS3 || *_ lec © 14.45 © 20.21 © 38.45 enter] |“ [auit] DISTR [stat-reg/distr] Zier stats 3 (Selects 2-Var Stats) ™ INC) Pons. ee Lil 3U5x215. 89137166 Press © as necessary to view a eee | and b. 1500, 2775251896 Peete This line of best fit, /=0.67732519x'— 18.66637321 models the linear trend of the data. Press © until y'is highlighted. (enter) 55 (55) 18. 58651222 The linear model gives an estimated braking distance of 18.59 meters for a vehicle traveling at 55 kph. 46 Regression example 1 Calculate an axtb linear regression for {1,2,3,4,5}; (5,8,11,14,17}. the following data: Clear all data (XOXO) FORMULA aieleer LS Data Boo 1©2©304©@ |) i bie 500 TateTE §5©8O N10 14 e117 Regression [quit] [stat-reg/distr] LIAS) BuIA. tie eatee GOoe : Press © to examine all the result variables. | 'S4"?=1 Regression example 2 Calculate the exponential regression for the following data: L4={0, 1,2, 3,4} L2=(10, 14, 23, 35, 48} Find the average value of the data in L2. Compare the exponential regression val lues to L2. Clear all data 4 Data 191920304 © ONS 140 BOSE 35 © 48 [enter] 47 Regression [stat-reg/distr] DISTR © opaiage atbine % Save the Oooo wore wake tet regression equation to f (x) in the menu. Regression a Equation Find the [stat-reg/distr] average 1 (Selects StatVars) value (¥) of Jo@e the data in L2using ORO) Notice that the title StatVars. LIAS) bar reminds you of your last statistical or regression calculation. Examine the 2 7 “ table of Fea=ab values of the regression equation. 0 1 ee 5 me Fo TEE 2 babii’ i= Warning: If you now calculate 2-Var Stats on your data, the variables a and b (along with rand r’) will be calculated as a linear regression. Do not recalculate 2-Var Stats after any 48 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 listL1, and store the results in L2. Clear all [IOXS) FORMULA data ear LZ 3:Clear LS Data a 3@ 6© 9 enter] - DISTR [stat-reg/distr] ® STAT-REG Mei INS) Stinohiorn es) © a . = 20© 06 Tee \ (XS) = Probability [rendon] is a multi-tap key that cycles through the following options: 49 A factorial is the product of the positive