Casio fx-9860G AU manuals
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1 User’s Guide5 Quick-Start24 Getting Acquainted— Read This FirstAbout this User’s Guide u!x() um EQUA EQUA uFunction Keys and Menus uMenu Titles [OPTN] [MAT] 25 Getting AcquainteduGraphs Left hand page Right hand page 3. Draw the graph 3 5(DRAW)(or w) uCommand List PRGM Example: The following operation displays Xfct: [VARS]-[FACT]-[Xfct] uPage Contents uSupplementary Information *indicates a note about a term that appears in the same page as the note 26 Basic Operation27 1-1Keys28 kKey Table29 1-1-3KeyskKey Markings Function Key Operation log The following describes the color coding used for key markings Color Orange Press ! and then the key to perform the marked function Red Press a and then the key to perform the marked function #Alpha Lock 30 1-2Display31 DisplayS • SHT (Spreadsheet) the calculator’s built-incommands and S • SHT mode in the STAT mode GRAPH Use this mode to store graph functions and to draw graphs using the functions DYNA (Dynamic Graph) versions of a graph by changing the values assigned to the variables in a function TABLE Use this mode to store functions, to generate a numeric table of different solutions as the values assigned to RECUR Use this mode to store recursion formulas, to generate a (Recursion) CONICS Use this mode to draw graphs of conic sections EQUA (Equation) unknowns, quadratic equations, and cubic equations PRGM (Program) run programs TVM (Financial) cash flow and other types of graphs LINK Use this mode to transfer memory contents or back-updata to another unit or PC MEMORY Use this mode to manage data stored in memory SYSTEM Use this mode to initialize memory, adjust contrast, and to make other system settings 32 kAbout the Function Menu• Next Menu Selecting displays a menu of hyperbolic functions • Command Input Selecting inputs the sinh command • Direct Command Execution Selecting executes the DRAW command kAbout Display Screens Text Screen 33 kNormal Displayu How to interpret exponential format 34 kSpecial Display FormatskCalculation Execution Indicator 35 1-3Inputting and Editing Calculations36 ddd!D(INS)(INS) To abort this operation, press !D(INS) again uTo delete a step Example To change 369 ⋅ ⋅ 2 to 369 ⋅ Adgj**c In the insert mode, the D key operates as a backspace key 37 uTo insert a stepuTo change the last step you input 38 kUsing Replay MemoryExample 1 To perform the following two calculations 4.12⋅ 6.4 4.12⋅ 7.1 Ae.bc*g.ew dddd !D(INS) h.b Abcd+efgw cde-fghw f(One calculation back) f(Two calculations back) 39 kMaking Corrections in the Original CalculationExample 14 ⎟ 0 ⋅ 2.3 entered by mistake for 14 ⎟ 10 ⋅ 2.3 Abe/a*c.d kUsing the Clipboard for Copy and Paste uTo specify the copy range Linear input mode 40 Math input modeu To cut the text 41 uPasting Text! j !j(PASTE) kCatalog Function uTo use the Catalog to input a command 1. Press !e(CATALOG) to display an alphabetic Catalog list of commands Example To use the Catalog to input the ClrGraph command A!e(CATALOG)I(C)c~cw Pressing J or !J(QUIT) closes the Catalog 42 kInput Operations in the Math Input Mode43 uMath Input Mode Functions and SymbolsFunction/Symbol Bytes Fraction (Improper) Mixed Fraction*1 Power Square Negative Power (Reciprocal) !)(x –1) !x Cube Root !((3 Power Root !M(x !I(ex) !l(10x) log(a,b) (Input from MATH menu*2) Abs (Absolute Value) Linear Differential*3 Quadratic Differential*3 Integral*3 Σ Calculation*4 Matrix 14*5 Parentheses (and ) Braces (Used during list input.) !*( { ) and !/( } ) Brackets (Used during matrix input.) !+( [ ) and !-( ] ) 44 uUsing the MATH Menulog dx2 uMath Input Mode Input Examples Example 1 To input 23 + 46 Example 4 To input 2 ⋅u When the calculation does not fit within the display window 47 uInserting a Function into an Existing Expressionu To insert a function into an existing expression To insert the function into the expression 1 + (2 + 3) + 4 so the parenthetical expression becomes the argument of the function 2.Press !D(INS) •This changes the cursor to an insert cursor (') 3.Press !x() to insert the function •This inserts the function and makes the parenthetical expression its argument u Function Insert Rules 48 u Functions that Support InsertionOriginal Expression After uEditing Calculations in the Math Input Mode 49 To do this:Move the cursor from the end of the calculation to the beginning Move the cursor from the beginning of the calculation to the end uMath Input Mode Calculation Result Display Sample Calculation Result Displays 50 uMath Input Mode Input Restrictions51 1-4Option (OPTN) Menu53 1-5Variable Data (VARS) Menu54 u STAT — Recalling statistical dataminX maxX minY maxY MSe •{Q1}/{Q3} •{Med}/{Mod} •{Strt}/{Pitch} PTS 55 u GRPH — Recalling Graph Functions•{Xt}/{Yt} ... parametric graph function {Xt}/{Yt} • {X} ... {X=constant graph function} (Press these keys before inputting a value to specify a storage memory.) u DYNA — Recalling Dynamic Graph Set Up Data •{Strt}/{End}/{Pitch} u TABL — Recalling Table Set Up and Content Data ... {table range start value}/{table range end value}/{table value increment} •{Reslt*1} ... {matrix of table contents} 56 u RECR — Recalling Recursion Formula*1, Table Range, and Table Content Data•{FORM} ... {recursion formula data menu} • {an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/{cn+1}/{cn+2} ... {an}/{an+1}/{an+2}/{bn}/{bn+1}/{bn+2}/{cn}/{cn+1}/{cn+2} expressions •{RANG} ... {table range data menu} •{Strt}/{End} ... table range {start value}/{end value} • {a0}/{a1}/{a2}/{b0}/{b1}/{b2}/{c0}/{c1}/{c2} ... {a0}/{a1}/{a2}/{b0}/{b1}/{b2}/{c0}/{c1}/{c2} value •{anSt}/{bnSt}/{cnSt} •{Reslt*2} ... {matrix of table contents*3} u EQUA — Recalling Equation Coefficients and Solutions*4 *5 •{S-Rlt}/{S-Cof} unknowns*6 •{P-Rlt}/{P-Cof} ... matrix of {solution}/{coefficients} for a quadratic or cubic equation u TVM — Recalling Financial Calculation Data • {n}/{I%}/{PV}/{PMT}/{FV} • {P/Y}/{C/Y} 57 1-6Program (PRGM) Menu58 1-7Using the Setup Screen59 uMode (calculation/binary, octal, decimal, hexadecimal mode)Comp •{Dec}/{Hex}/{Bin}/{Oct} uFrac Result (fraction result display format) d/c ab/c uFunc Type (graph function type) •{Y=}/{r=}/{Parm}/{X=c} •{Y>}/{Y<}/{Yt}/{Ys} uDraw Type (graph drawing method) •{Con}/{Plot} uDerivative (derivative value display) •{On}/{Off} uAngle (default angle unit) •{Deg}/{Rad}/{Gra} uComplex Mode Real •{a + bi}/{r ∠θ} uCoord (graph pointer coordinate display) uGrid (graph gridline display) 60 uAxes (graph axis display)uLabel (graph axis label display) uDisplay (display format) •{Fix}/{Sci}/{Norm}/{Eng} uStat Wind (statistical graph V-Windowsetting method) •{Auto}/{Man} ... {automatic}/{manual} uResid List (residual calculation) •{None}/{LIST} ... {no calculation}/{list specification for the calculated residual data} uList File (list file display settings) • {FILE} ... {settings of list file on the display} u Sub Name (list naming) uGraph Func (function display during graph drawing and trace) uDual Screen (dual screen mode status) •{G+G}/{GtoT}/{Off} uSimul Graph (simultaneous graphing mode) 61 uBackground (graph display background)•{None}/{PICT} u Sketch Line (overlaid line type) uDynamic Type (dynamic graph type) •{Cnt}/{Stop} uLocus (dynamic graph locus mode) uY=Draw Speed (dynamic graph draw speed) •{Norm}/{High} uVariable (table generation and graph draw settings) •{RANG}/{LIST} uΣ Display (Σ value display in recursion table) uPayment (payment period setting) •{BGN}/{END} 62 uDate Mode (number of days per year setting)•{365}/{360} ... interest calculations using {365}*1/{360} days per year uAuto Calc (spreadsheet auto calc) ... {execute}/{not execute} the formulas automatically uShow Cell (spreadsheet cell display mode) • {Form}/{Val} ... {formula}*2/{value} uMove (spreadsheet cell cursor direction)*3 • {Low}/{Right} ... {move down}/{move right} 63 1-8Using Screen Capture64 1-9When you keep having problems…66 Manual Calculations67 2-1Basic Calculations68 kNumber of Decimal Places, Number of Significant Digits, NormalDisplay Range [SET UP]- [Display] -[Fix] /[Sci] / [Norm] Condition 100/6w 4 decimal places !m(SET UP) f(or c12 times) 1(Fix)ewJw (Fix) 5 significant digits 2(Sci)fwJw (Sci) 1.6667E+01 Cancels specification 3(Norm)Jw 69 200 ⎟ 7 ⋅ 14200/7*14w 3 decimal places 1(Fix)dwJw Calculation continues using 200/7w display capacity of 10 digits Ans ⋅ 14w • If the same calculation is performed using the specified number of digits: The value stored internally K6(g)4(NUM)4(Rnd)w is rounded off to the number of decimal places specified on the Setup screen You can also specify the number of decimal places for 6(RndFi)!-(Ans),2) RndFix(Ans,2) rounding of internal values for a specific calculation.*1 (Example: To specify rounding to two decimal places) kCalculation Priority Sequence 1Type A functions Augment, Mat →List, P(, Q(, R(, t(, List, RndFix, log ab Composite functions*2 fn, Yn, rn, Xtn, Ytn, Xn 70 2Type B functions3Power/root ^(xy) 4Fractions ab/c Abbreviated multiplication format in front of 2π, 5A, etc 6Type C functions Abs, Int, Frac, Intg, Arg, Conjg, ReP, ImP 2 3, A log2, etc 8Permutation, combination nPr, nCr, ∠ 9⋅, ⎟ 0+, – ! Relational operators =, G, >, <, ≥, ≤ @And (logical operator), and (bitwise operator) #Or (logical operator), or, xor, xnor (bitwise operator) Example 2 + 3 ⋅ (log sin2π2 + 6.8) = 22.07101691 (angle unit = Rad) 71 kMultiplication Operations without a Multiplication SignYou can omit the multiplication sign (⋅) in any of the following operations Before Type A functions 2sin30, 10log1.2, 2 3, 2Pol(5, 12), etc • Before constants, variable names, memory names 2π, 2AB, 3Ans, 3Y1, etc • Before an open parenthesis 3(5 + 6), (A + 1)(B – 1), etc kOverflow and Errors •When any result, whether intermediate or final, or any value in memory exceeds ±9.999999999 ⋅ 1099 (Ma ERROR) 72 kMemory Capacity73 2-2Special Functions74 uTo display the contents of a variableTo display the contents of variable A uTo clear a variable To clear variable A uTo assign the same value to more than one variable uFunction Memory STO RCL SEE 75 uTo store a functionExample To store the function (A+B) (A–B)as function memory number (av(A)+al(B)) (B) (av(A)-al(B)) K6(g)6(g)3(FMEM) 1(STO)bw JJJ uTo recall a function Example To recall the contents of function memory number K6(g)6(g)3(FMEM) 2(RCL)bw uTo recall a function as a variable daav(A)w baal(B)w K6(g)6(g)3(FMEM)3(fn) b+cw uTo display a list of available functions 4(SEE) 76 uTo delete a functionExample To delete the contents of function memory number uTo use stored functions y = x3 + x2 + x + Xmin = – 4 Xmax = 4 Ymin = –10 Ymax = 10 77 kAnswer FunctionuTo use the contents of the answer memory in a calculation 123 + 456 789 – 579 Abcd+efgw hij-!-(Ans)w (Ans) kPerforming Continuous Calculations Ab/dw (Continuing)*dw 78 kHistory Function*cw To change “1+2” to “1+3” and recalculate Perform the following operation following the sample shown above ffffdDdw 79 kStacksstacks numeric value stack command stack program subroutine stack Numeric Value Stack Command Stack 80 kUsing Multistatements• Colon (:) • Display Result Command (^) Abcdaav(A) !J(PRGM)6(g)5(:)g.j *av(A)!J(PRGM)5(^) av(A)/d.cw 81 2-3Specifying the Angle Unit and Display Format82 uTo specify the number of significant digits (Sci)To specify three significant digits 2(Sci) dw uTo specify the normal display (Norm 1/Norm 2) Press 3(Norm) to switch between Norm 1 and Norm Norm 1: 10–2 (0.01)>|x|, |x| >1010 Norm 2: 10–9 (0.000000001)>|x|, |x| >1010 Ab/caaw (Norm 1) (Norm 2) uTo specify the engineering notation display (Eng mode) E (Exa) m (milli) ⋅ 10–3 P (Peta) T (Tera) n (nano) G (Giga) p (pico) M (Mega) f (femto) k (kilo) 83 2-4Function Calculations84 uAngle Units, Coordinate Conversion, Sexagesimal Operations (ANGL)[OPTN]-[ANGL] •{°}/{r}/{g} ... {degrees}/{radians}/{grads} for a specific input value •{° ’ ”} ... {converts decimal value to degrees/minutes/seconds value}*1 Pol Rec •{'DMS} ... {converts decimal value to sexagesimal value} uEngineering Symbol (ESYM) [OPTN]-[ESYM] ENG the {left}/{right} and {decreases}/{increases} the exponent by three.*2 85 kAngle Units• Be sure to specify Comp for Mode in the Setup screen !m(SET UP)cccccc1(Deg)J 4.25K6(g)5(ANGL)2(r)w 47.3° + 82.5rad = 4774.20181° 47.3+82.5K6(g)5(ANGL)2(r)w 2K6(g)5(ANGL)4(° ’ ”) 204(° ’ ”) 4(° ’ ”)+04(° ’ ”)394(° ’ ”)304(° ’ ”)w 5(° ’ ”) 2.255° = 2°1518 2.255K6(g)5(ANGL)6(g)3('DMS)w 86 kTrigonometric and Inverse Trigonometric Functions2*s45*c65w*1 1/s30w 87 kLogarithmic and Exponential Functionslog 1.23 (log101.23) l1.23w log2 8 K4(CALC)6(g)4(logab)2,8)w 4(MATH)2(logab) 2e8w In 90 (loge90) I90w 101.23 !l(10x)1.23w (To obtain the antilogarithm of common logarithm 1.23) e4.5 !I(ex)4.5w (To obtain the antilogarithm of natural logarithm 4.5) (–3)4 = (–3) ⋅ (–3) ⋅ (–3) ⋅ (–3) (-3)M4w –34 = –(3 ⋅ 3 ⋅ 3 ⋅ 3) = –81 -3M4w 7 123 (= 123 7 ) 7!M( )123w !M(x )7e123w 2 + 3 ⋅ 3 64 – 4 2+3*3!M(x )64-4w*1 2+3*!M(x )3e64e-4w 88 kHyperbolic and Inverse Hyperbolic Functions89 kOther Functions)(36*42*49)w )36*42*49w 90 kRandom Number Generation (Ran#)Ran# (Generates a random number.) K6(g)3(PROB)4(Ran#)w (Each press of w generates a new random number.) •Specifying an argument of 0 initializes the sequence.*1 Ran# (Generates the first random number in sequence 1.) K6(g)3(PROB) 4(Ran#)bw (Generates the second random number in sequence 1.) (Initializes the sequence.) 4(Ran#)aw 91 kCoordinate Conversion92 kPermutation and Combinationu Permutation items selected from among 10 items Formula that can be selected from among 10 items kFractions Improper Fraction 7 {3 2 {1 {3 93 $2c5e+!$(&)3e1c4 w––+ 3 ––= ––– 2$5+3$1$4w $1c2578e+$1c4572w 10 1$2578+1$4572w ⋅ 0.5 = 0.25*2 $1c2e*.5w 1$2*.5w Display: 1.5+2.3!a(i)w 1.5 + 2.3i = ––+ –– 3{2 +23{10i MM $1c$1c3e+$1c4w 1$(1$3+1$4)w 94 Switching between improper fraction and mixed fraction formatPressing the !M(<) key toggles the display fraction between mixed fraction and improper fraction format Switching between fraction and decimal format kEngineering Notation Calculations Input engineering symbols using the engineering notation menu !m(SET UP) f (or c 12 times) 4(Eng)J 999k (kilo) + 25k (kilo) 999K6(g)6(g)1(EYSM)6(g)1(k)+ = 1.024M (mega) 251(k)w 9 ⎟ 10 = 0.9 = 900m (milli) 9/10w K6(g)6(g)1(EYSM)6(g)6(g)3(ENG)*1 = 0.0009k (kilo) 3(ENG)*1 2(ENG)*2 = 900m 95 2-5Numerical Calculations96 kDifferential CalculationsUsing Differential Calculation in a Graph Function 97 To determine the derivative at point x = 3 for the functiony = x3 + 4x2 + x – 6, with a tolerance of “tol” = 1E – Input the function f(x) AK4(CALC)2(d/dx)vMd+evx+v-g (CALC) Input point x = a for which you want to determine the derivative Input the tolerance value bE-f) A4(MATH)4(d/dx)vMde +evx+v-ged 98 uApplications of Differential Calculations––– f (a) = f '(a) ––– g (a) = g'(a) Therefore: f'(a) + g'(a), f '(a) ⋅ g'(a), etc 2⋅ f '(a), log ( f '(a)), etc •Functions can be used in any of the terms ( f (x), a, tol) of a differential –––(sinx + cosx, sin0.5, 1E - 8), etc. dx 99 kQuadratic Differential Calculations[OPTN]-[CALC]-[d2/dx2] K4(CALC)3(d 2/dx2) f(x),a,tol) (a: differential coefficient point , tol: tolerance) –––(f (x), a) ––– f (a) dx2 dx2 a – f To determine the quadratic differential coefficient at the point where x = 3 for the function y = x3 + 4x2 + x – Here we will use a tolerance tol = 1E – AK4(CALC)3(d2/dx2) vMd+ evx+v-g Input 3 as point a, which is the differential coefficient point 100 A4(MATH)5(d2/dx2)vMde+evx+v-gedw uQuadratic Differential Applications • Arithmetic operations can be performed using two quadratic differentials ––– f (a) = f ''(a) ––– g (a) = g''(a) f ''(a) + g''(a), f ''(a) ⋅ g''(a), etc 2 ⋅ f ''(a), log ( f ''(a) ), etc f ––– (sin x + cos x, sin 0.5, 1E - 8), etc. dx2 101 ∫( f(x), a, b, tol) ⇒ ∫ab f(x)dx102 4(MATH)6(g)1(∫dx)cvx+dv+eebffw uApplication of Integration Calculation • Integrals can be used in addition, subtraction, multiplication or division ∫ab f(x) dx + ∫cd g(x) dx, etc 2 ⋅ ∫ab f(x) dx, etc. log (∫ab f(x) dx), etc • Functions can be used in any of the terms ( f(x), a, b, tol) of an integral (sin x + cos x) dx = ∫(sin x + cos x, sin 0.5, cos 0.5, 1E - 4) 103 f(x)dx +.....+ ∫b f(x)dx104 kΣ Calculations[OPTN]-[CALC]-[Σ ] K4(CALC)6(g)3(Σ( ) ak ,k ,α ,β ,n ) Σ(ak, k, α, β, n) = Σ ak = aα + aα +1 +........+ aβ (n: distance between partitions) Example To calculate the following: Σ6 (k2 – 3k + 5) Use n = 1 as the distance between partitions AK4(CALC)6(g)3(Σ( )a,(K) x-da,(K)+f,a,(K),c,g,b)w A4(MATH)6(g)2(Σ( )a,(K) x-da,(K)+fea,(K)ecfgw 105 Sn + Tn, Sn – Tn, etc2 ⋅ Sn, log (Sn), etc Σ (sink, k, 1, 5), etc 106 kMaximum/Minimum Value CalculationsuMinimum Value uMaximum Value 107 AK4(CALC)6(g)2(FMax) -vx+cv+c(FMax) 108 2-6Complex Number Calculations109 kArithmetic OperationsExample 1 (1 + 2i) + (2 + 3i) Example 2 (2 + i) ⋅ (2 – i) kReciprocals, Square Roots, and Squares (3 + i) kComplex Number Format Using Polar Form Example 2∠30 ⋅ 3∠45 = 6∠75 110 kAbsolute Value and Argument[OPTN]-[CPLX]-[Abs]/[Arg] and calculates absolute value Z and argument (arg) To calculate absolute value (r) and argument (θ) for the complex number 3 + 4i, with the angle unit set for degrees Imaginary axis Real axis AK3(CPLX)2(Abs) (d+e1(i))w (Calculation of absolute value) AK3(CPLX)3(Arg) (Calculation of argument) kConjugate Complex Numbers[OPTN]-[CPLX]-[Conj] [CPLX] [Conj] Example To calculate the conjugate complex number for the complex number 2 + AK3(CPLX)4(Conj) (c+e1(i))w 111 kExtraction of Real and Imaginary Parts[OPTN]-[CPLX]-[ReP]/[lmP] complex number of the form a + bi To extract the real and imaginary parts of the complex number 2 + AK3(CPLX)6(g)1(ReP) (c+f6(g)1(i))w (Real part extraction) AK3(CPLX)6(g)2(ImP) (Imaginary part extraction) 112 kPolar and Rectangular Form Transformation[OPTN]-[CPLX]-['r∠θ]/['a+bi] polar form 113 2-7Binary, Octal, Decimal, and Hexadecimal Calculations with Integers118 2-8Matrix Calculations119 kInputting and Editing Matricesm ⋅ n … m (row) ⋅ n (column) matrix None… no matrix preset •{DEL}/{DEL·A} ... deletes {a specific matrix}/{all matrices} •{DIM} ... {specifies the matrix dimensions (number of cells)} u Creating a Matrix u To specify the dimensions (size) of a matrix Example To create a 2-row ⋅ 3-columnmatrix in the area named Mat B Highlight Mat B 3(DIM) (This step can be omitted.) Specify the number of rows Specify the number of columns • All of the cells of a new matrix contain the value 120 uTo input cell valuesTo input the following data into Matrix B : bwcwdw ewfwgw To exit the Matrix input screen, press J 121 uDeleting Matricesu To delete a specific matrix u To delete all matrices 122 kMatrix Cell OperationsR-OP •{ROW} INS ADD •{COL} EDIT u Row Calculations Swap Rw+ u To swap two rows Matrix A 123 u To calculate the scalar multiplication of a row4 : 4, then add the result to row 3 : 124 u To add two rows togetheru Row Operations u To delete a row 125 u To insert a rowu To add a row 126 uColumn Operations•{DEL} ... {delete column} •{INS} ... {insert column} •{ADD} ... {add column} u To delete a column To delete column 2 of the following matrix : 3(COL)1(DEL) u To insert a column To insert a new column between columns 1 and 2 of the following 3(COL)2(INS) 127 u To add a columnExample To add a new column to the right of column 2 of the following kModifying Matrices Using Matrix Commands u To display the matrix commands Det Trn Aug Iden Dim Fill 128 u Matrix Data Input Format[OPTN]-[MAT]-[Mat] a1n a2n am1 am2 amn =[ [a11, a12, ..., a1n] [a21, a22, ..., a2n] .... [am1, am2, ..., amn] ] → Mat [letter A through Z] Example 1 To input the following data as Matrix A : !+( [ )!+( [ )b,d,f !-( ] )!+( [ )c,e,g !-( ] )!-( ] )aK2(MAT) 1(Mat)av(A) 129 u To input an identity matrixExample 2 To create a 3 ⋅ 3 identity matrix as Matrix A u To check the dimensions of a matrix Example 3 To check the dimensions of Matrix A, which was input in Example Example 4 To specify dimensions of 2 rows and 3 columns for Matrix B 130 uModifying Matrices Using Matrix Commandsu To assign values to and recall values from an existing matrix [OPTN]-[MAT]-[Mat] Example 1 Assign 10 to the cell at row 1, column 2 of the following matrix : 1 Matrix A = 3 131 uTo fill a matrix with identical values and to combine two matrices into asingle matrix [Fill]/[Aug] Example 1 To fill all of the cells of Matrix A with the value K2(MAT)6(g)3(Fill) d,6(g)1(Mat)av(A)w 1(Mat)av(A)w Example 2 To combine the following two matrices : A B K2(MAT)5(Aug) 1(Mat)av(A) 1(Mat)al(B)w 132 uTo assign the contents of a matrix column to a list[OPTN]-[MAT]-[M→L] 133 kMatrix CalculationsuTo display the matrix commands 134 uMatrix Arithmetic Operations[OPTN]-[MAT]-[Mat]/[Iden] Example 1 To add the following two matrices (Matrix A + Matrix B) : AK2(MAT)1(Mat)av(A)+ AfK2(MAT)1(Mat) av(A)w Example 3 To multiply the two matrices in Example 1 (Matrix A ⋅ Matrix B) AK2(MAT)1(Mat)av(A) Example 4 To multiply Matrix A (from Example 1) by a 2 ⋅ 2 identity matrix 6(g)1(Iden)cw Number of rows and columns 135 uDeterminant[OPTN]-[MAT]-[Det] Obtain the determinant for the following matrix : K2(MAT)3(Det)1(Mat) uMatrix Transposition [OPTN]-[MAT]-[Trn] To transpose the following matrix : K2(MAT)4(Trn)1(Mat) av(A)w 136 uMatrix Inversion[OPTN]-[MAT]-[x–1] To invert the following matrix : K2(MAT)1(Mat) av(A)!)(x–1) w uSquaring a Matrix [OPTN]-[MAT]-[x2] Example To square the following matrix : K2(MAT)1(Mat)av(A)xw 137 uRaising a Matrix to a Power[OPTN]-[MAT]-[] To raise the following matrix to the third power : K2(MAT)1(Mat)av(A) Mdw uDetermining the Absolute Value, Integer Part, Fraction Part, and Maximum Integer of a Matrix [OPTN]-[NUM]-[Abs]/[Frac]/[Int]/[Intg] To determine the absolute value of the following matrix : K6(g)4(NUM)1(Abs) K2(MAT)1(Mat)av(A)w 138 kPerforming Matrix Calculations Using Natural InputuTo specify the dimensions (size) of a matrix 139 uTo input cell valuesuTo assign a matrix created using natural input to a MAT mode matrix 140 List Function141 3-1Inputting and Editing a List149 3-2Manipulating List Data150 u To count the number of data items in a listTo count the number of values in List 1 (36, 16, 58, 46, 56) u To create a list or matrix by specifying the number of data items [OPTN]-[LIST]-[Dim] 151 contains 0) in Matrix Au To replace all data items with the same value[OPTN]-[LIST]-[Fill] [LIST] [Fill] Example To replace all data items in List 1 with the number u To generate a sequence of numbers f(x) = X2. Use a starting value of 1, an ending value of 11, and an increment of 152 u To find the minimum value in a list[OPTN]-[LIST]-[Min][Min] Example To find the minimum value in List 1 (36, 16, 58, 46, 56) u To find the maximum value in a list u To find which of two lists contains the smallest value contains the smallest value u To find which of two lists contains the greatest value 153 u To calculate the mean of data items[OPTN]-[LIST]-[Mean][Mean] Example To calculate the mean of data items in List 1 (36, 16, 58, 46, 56) u To calculate the mean of data items of specified frequency [OPTN]-[LIST]-[Mean] frequency is indicated by List 2 (75, 89, 98, 72, 67) u To calculate the median of data items in a list[OPTN]-[LIST]-[Med] [Med] Example To calculate the median of data items in List 1 (36, 16, 58, 46, 56) 154 u To calculate the median of data items of specified frequency[OPTN]-[LIST]-[Med] u To combine lists u To calculate the sum of data items in a list[OPTN]-[LIST]-[Sum] [Sum] Example To calculate the sum of data items in List 1 (36, 16, 58, 46, 56) 155 u To calculate the product of values in a list[OPTN]-[LIST]-[Prod][Prod] Example To calculate the product of values in List 1 (2, 3, 6, 5, 4) u To calculate the cumulative frequency of each data item [OPTN]-[LIST]-[Cuml] u To calculate the percentage represented by each data item [OPTN]-[LIST]-[%] 156 To calculate the percentage represented by each data item in ListAK1(LIST)6(g)6(g)4(%) u To calculate the differences between neighboring data inside a list [OPTN]-[LIST]-[A] K1(LIST)6(g)6(g)5(A)<list number 1-26>w • The result of this operation is stored in ListAns memory AK1(LIST)6(g)6(g)5(A) 157 3-3Arithmetic Calculations Using Lists162 3-4Switching Between List Files163 Equation Calculations171 Graphing172 5-1Sample Graphs180 5-2Controlling What Appears on a Graph Screen190 5-3Drawing a Graph191 u To store a polar coordinate function (r=) *1Example To store the following expression in memory area r2 : r = 5 sin3θ 3(TYPE)2(r=) (Specifies polar coordinate expression.) fsdv(Inputs expression.) w(Stores expression.) u To store a parametric function *2 To store the following functions in memory areas Xt3 and Yt3 : x = 3 sin T y = 3 cos T 3(TYPE)3(Parm) (Specifies parametric expression.) dsvw(Inputs and stores x expression.) dcvw(Inputs and stores y expression.) 192 u To store an X = constant expression *1Example To store the following expression in memory area X4 : X 3(TYPE)4(X=c) (Specifies X = constant expression.) d(Inputs expression.) u To store an inequality *1 Example To store the following inequality in memory area Y5 : y> x2 – 2x – 3(TYPE)6(g)1(Y>) (Specifies an inequality.) vx-cv-g(Inputsexpression.) u To create a composite function To use relations in Y1 and Y2 to create composite functions for Y3 and Y4 Y1= (X + 1), Y2 = X2 + Assign Y1°Y2 to Y3, and Y2°Y1 to Y4 (Y1°Y2 = ((x2 + 3) +1) = (x2 + 4) Y2°Y1 = ( (X + 1)) 2 + 3 = X + 4 (X ≧ –1)) Input relations into Y3 and Y4 3(TYPE)1(Y=)J4(GRPH) 1(Y)b(1(Y)c)w (Y) J4(GRPH)1(Y)c (1(Y)b)w • A composite function can consist of up to five functions 193 u To assign values to the coefficients and variables of a graph function194 Memory Area TypeDefault Variable Xtn Ytn Y1 (3) and Y1 (X = 3) are identical values 195 kEditing and Deleting Functionsu To edit a function in memory Example To change the expression in memory area Y1 from y = 2x2 – 5 to y= 2x2 – u To change the line style of a graph function “Broken” 196 u To change the type of a function*1Example To change the function in memory area Y1 from y = 2x2 – 3 to y< 2x2 – u To delete a function 197 k Selecting Functions for Graphingu To specify the draw/non-drawstatus of a graph Y1 = 2x2 – 5, r2 = 5 sin3θ Xmin = –5 Ymin = –5 Ymax = 5 Tθ min = 0 Tθ max = π Tθ ptch = 2π 198 kGraph MemoryA single save operation saves the following data in graph memory •All graph functions in the currently displayed Graph relation list (up to 20) •Graph types •Function graph line information •Draw/non-drawstatus •V-Windowsettings (1 set) u To store graph functions in graph memory 1.Press 5(GMEM)1(STO) to display the pop-upwindow • There are 20 graph memories numbered G-Mem1to G-Mem20 u To recall a graph function 1.Press 5(GMEM)2(RCL) to display the pop-upwindow 199 5-4Storing a Graph in Picture Memory200 5-5Drawing Two Graphs on the Same Screen206 5-6Manual Graphing214 5-7Using Tables215 u To generate a table using a list1.While the Table relation list is on the screen, display the Setup screen 2.Highlight Variable and then press 2(LIST) to display the pop-upwindow 3.Select the list whose values you want to assign for the x-variable To select List 6, for example, press After specifying the list you want to use, press uGenerating a Table To generate a table of values for the functions stored in memory areas Y1 and Y3 of the Table relation list Each cell can contain up to six digits, including negative sign 216 •To change x variable values by replacing values in columnPress 1(FORM) or J to return to the Table relation list u To generate a differential number table *1 uSpecifying the function type You can specify a function as being one of three types.*2 •Rectangular coordinate (Y=) •Polar coordinate (r=) •Parametric (Parm) 1.Press 3(TYPE) while the relation list is on the screen Press the number key that corresponds to the function type you want to specify 217 u To edit a functionExample To change the function in memory area Y1 from y = 3x2 – 2 to y= 3x2 – 218 kEditing TablesFORM G·CON G·PLT u To change variable values in a table 219 uRow Operations220 Example To add a new row below Row 7 in the table generated on pageuDeleting a Table 221 kCopying a Table Column to a Listu To copy a table to a list 222 kDrawing a Graph from a Number Table1.From the Main Menu, enter the TABLE mode 3.Store the functions 4.Specify the table range 5.Generate the table 6.Select the graph type and draw it 5(G • CON) ... line graph*1 6(G • PLT) ... plot type graph*1 Selecting 223 Store the two functions below, generate a number table, and then drawa line graph. Specify a range of –3to 3, and an increment of Y1 = 3x2 – 2, Y2 Xmin = 0 Xmax = 6 1m TABLE 2!3(V-WIN) awgwbwc -cwbawcwJ 33(TYPE)1(Y=)dvx-cwvxw 45(SET)-dwdwbwJ (SET) 56(TABL) 65(G • CON) 224 kSpecifying a Range for Number Table Generation225 Store the three functions shown below, and then generate a table forfunctions Y1 and Y3. Specify a range of –3to 3, and an increment of Y1 = 3x2 – 2, Y2 = x + 4, Y3 23(TYPE)1(Y=)dvx-cwv+ew vxw 35(SET)-dwdwbwJ 4ff1(SEL) 226 kSimultaneously Displaying a Number Table and Graph3.On the Setup screen, select T+G for Dual Screen 5.Specify the table range 6.The number table is displayed in the sub-screenon the right 7.Specify the graph type and draw the graph 5(G • CON) ... line graph 6(G • PLT) ... plot type graph 227 Store the function Y1 = 3x2 – 2 and simultaneously display its numbertable and line graph. Use a table range of –3to 3 with an increment of 3!m(SET UP)cc1(T+G)J 43(TYPE)1(Y=)dvx-cw 55(SET) -dwdwbwJ 66(TABL) 75(G • CON) 228 kUsing Graph-TableLinking2.Make the required V-Windowsettings 3.Input the function of the graph and make the required table range settings 5(G • CON) ... connect type graph 5.Press K2(GLINK) to enter the Graph-TableLinking mode Now when you use To exit the Graph-TableLinking mode, press J or !J(QUIT) 229 Xmin = –1Xmax = 10 Ymin = –1 Ymax = 4 2!3(V-WIN) -bwbawbwc -bwewbwJ !m(SET UP)cc1(T+G)J 33(TYPE)1(Y=)dlvw cwjwbwJ 46(TABL) 6(G • PLT) 5K2(GLINK) 6c ~ c, f ~ f 230 5-8Dynamic Graphing238 5-9Graphing a Recursion Formula239 Generate a number table from recursion between three terms asexpressed by an+2 = an+1 + an, with initial terms of a1 = 1, a2 (Fibonacci sequence), as n changes in value from 1 to 1m RECUR 23(TYPE)3(an+2) 34(n. an ··)3(an+1)+2(an)w 45(SET)2(a1)bwgwbwbwJ *The first two values correspond to a1 = 1 and a2 240 kGraphing a Recursion Formula (1)241 Generate a number table from recursion between two terms asexpressed by an+1 = 2an+1, with an initial term of a1 = 1, as n changes in value from 1 to 6. Use the table values to draw a line graph Ymin = –15 Ymax = 65 1mRECUR -bfwgfwfwJ 33(TYPE)2(an+1)c2(an)+bw 45(SET)2(a1)bwgwbwJ 51(SEL+S)f2()J 242 kGraphing a Recursion Formula (2)243 Graphing a Recursion FormulaGenerate a number table from recursion between two terms as in value from 1 to 6. Use the table values to draw a plot line graph with ordinate Σan, abscissa n 2!m(SET UP)1(On)J 3!3(V-WIN) awgwbwc 43(TYPE)2(an+1)c2(an)+bw 55(SET)2(a1)bwgwbwJ 61(SEL+S)f2()J 76(TABL) 86(G • PLT)6(Σan) 244 kWEB Graph (Convergence, Divergence)245 To draw the WEB graph for the recursion formula an+1 = –3(an)2 + 3anbn+1 = 3bn + 0.2, and check for divergence or convergence. Use the following table range and V-WindowSettings Table Range Start = 0, End = 6, a0 = 0.01, anStr = 0.01, b0 = 0.11, bnStr V-WindowSettings Xmax = 1 Ymin = 0 Ymax = 1 2!3(V-WIN) awbwbwc awbwbwJ 33(TYPE)2(an+1)-d2(an)x+d2(an)wd3(bn)+a.cw 45(SET)1(a0) awgwa.abwa.bbwc a.abwa.bbwJ 64(WEB) 7w~w(an is convergence) cw~w(bn is divergence) 246 kGraphing a Recursion Formula on Dual Screen4.Specify the recursion formula type and input the formula 247 3!m(SET UP)ccc1(T+G)J85(G • CON) 248 5-10Changing the Appearance of a Graph256 5-11Function Analysis257 Read coordinates along the graph of the function shown belowY1 = x2 – 2!3(V-WIN) -fwfwbwc 3(TYPE)1(Y=)vx-dw 3!1(TRCE) 4d~d 5-bw 258 kDisplaying the Derivative259 Read coordinates and derivatives along the graph of the functionshown below 2!m(SET UP)cccc1(On)J 4!1(TRCE) 5d~d 6-bw 260 kGraph to Table261 Save, in a table, the coordinates in the vicinity of the points ofintersection at X = 0 for the two graphs shown below, and store the table contents in List Y1 = x2 – 3, Y2 = – x + 2!m(SET UP)cc2(GtoT)J 43(TYPE)1(Y=) vx-dw -v+cw 5!1(TRCE) 6d~dwe~ew 7K1(CHNG) 8K2(LMEM)bw 262 kCoordinate Rounding264 kCalculating the Root265 Draw the graph shown below and calculate the root for Y1Y1 = x(x + 2)(x – 2) 3!5(G-SLV)1(ROOT) 5e e 266 kCalculating the Point of Intersection of Two Graphs267 Graph the two functions shown below, and determine the point ofintersection between Y1 and Y2 Y1 = x + 1, Y2 3(TYPE)1(Y=)v+bw vxw 2!5(G-SLV)5(ISCT) 268 kDetermining the Coordinates for Given Points269 Graph the two functions shown below and then determine the ycoordinate for x = 0.5 and the x-coordinatefor y = 2.2 on graph Y2 Y1 = x + 1, Y2 = x(x + 2)(x – 2) Xmin = –6.3,Xmax = 6.3, Xscale Ymin = –3.1,Ymax = 3.1, Yscale = 1 (initial defaults) !3(V-WIN)1(INIT)J 3(TYPE)1(Y=)v+bw v(v+c)(v-c)w 2 !5(G-SLV)6(g)1(Y-CAL) 2 !5(G-SLV)6(g)2(X-CAL) 3 cw 4 a.fw 4 c.cw 270 kCalculating the lntegral Value for a Given RangeUse the following procedure to obtain integration values for a given range 5.Use e to move the upper limit pointer to the location you want 6.Press w to calculate the integral value 271 value at (–2,0)Ymin = –4 272 kConic Section Graph Analysisu Parabolic Graph Analysis FOCS VTX LEN DIR SYM X-IN Y-IN u Circular Graph Analysis CNTR RADS u Elliptical Graph Analysis u Hyperbolic Graph Analysis ASYM 273 u To calculate the focus, vertex and length of latus rectumTo determine the focus, vertex and length of latus rectum for the parabola X = (Y – 2)2 + 274 u To calculate the center and radiusTo determine the center and radius for the circle (X + 2)2 + (Y + 1)2 275 u To calculate the x- and y-interceptsTo determine the x- and y-interceptsfor the hyperbola (X – 3)2 (Y – 1)2 276 u To draw and analyze the axis of symmetry and directrix277 uTo draw and analyze the asymptotes[G-SLV]-[ASYM] To draw the asymptotes for the hyperbola (X – 1)2 Ymin = –5,Ymax = 5, Yscale mCONICS cccccccw cwcwbwbw6(DRAW) 5(ASYM) (Draws the asymptotes.) uTo calculate eccentricity [G-SLV]-[e] To determine the eccentricity of the graph for ellipse (X – 2)2 (Y – 2)2 Xmax = 7 mCONICS ccccccw ewcwcwcw6(DRAW) !5(G-SLV) (G-SLV) 6(g)1(e) (Calculates eccentricity.) 278 Statistical Graphs and Calculations279 6-1Before Performing Statistical Calculations280 kChanging Graph Parameters•{GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3} drawing*1 SEL •{SET} ... {graph settings (graph type, list assignments)} 1. General graph settings [GRPH]-[SET] • Graph Type • Frequency 281 • Mark TypeThis setting lets you specify the shape of the plot points on the graph u To display the general graph settings screen Pressing 1(GRPH)6(SET) displays the general graph settings screen •StatGraph (statistical graph specification) •{GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3} •Graph Type (graph type specification) Scat NPP Hist Box N·Dis Brkn Med X^2 X^3 X^4 Log Exp Pwr Sin Lgst •XList (x-axisdata list) •{LIST} ... {List 1 to 26} •YList (y-axisdata list) •Frequency (number of times a value occurs) •{1} ... {1-to-1plot} •{LIST} ... frequency data in {List 1 to 26} •Mark Type (plot mark type) •{}/{⋅}/{•} ... scatter diagram plot points •Outliers (outliers specification) •{On}/{Off} ... {display}/{do not display} Med-Boxoutliers 282 2. Graph draw/non-drawstatus[GRPH]-[SEL] 1. Pressing 1(GRPH) 4(SEL) displays the graph On/Off screen •{On}/{Off} ... {On (draw)}/{Off (non-draw)} •{DRAW} ... {draws all On graphs} 3.To return to the graph menu, press J x/y 283 6-2Calculating and Graphing Single-VariableStatistical Data287 6-3Calculating and Graphing Paired-VariableStatistical Data288 Input the two sets of data shown below. Next, plot the data on ascatter diagram and connect the dots to produce an xy line graph 0.5 1.2 2.4 4.0 (xList) –2.1 0.3 1.5 2.0 (yList) 1m STAT 2a.fwb.cw c.ewewf.cw e -c.bwa.dwb.fwcwc.ew 3(Scatter diagram)1(GRPH)6(SET)c1(Scat)J 1(GPH1) 3(xy line graph)1(GRPH)6(SET)c2(xy)J 1(GPH1) (xy line graph) 289 kDrawing a Regression Graph290 Input the two sets of data shown below and plot the data on a scatterdiagram. Next, perform logarithmic regression on the data to display the regression parameters, and then draw the corresponding regression graph 0.5, 1.2, 2.4, 4.0 –2.1,0.3, 1.5, 2.0 2a.fwb.cw c.ewewf.cw e -c.bwa.dwb.fwcwc.ew 1(GRPH)6(SET)c1(Scat)J 1(GPH1) (GRPH) (Scat) (GPH1) 31(CALC)6(g)2(Log) 291 kSelecting the Regression Type•{2VAR} ... {paired-variablestatistical results} •{X}/{Med}/{X^2}/{X^3}/{X^4}/{Log}/{Exp}/{Pwr}/{Sin}/{Lgst} kDisplaying Regression Calculation Results kGraphing Statistical Calculation Results 292 kLinear Regression GraphThe graphic representation of this relationship is a linear regression graph 1(CALC)2(X) The following is the linear regression model formula y = ax + b regression coefficient (slope) regression constant term (y-intercept) r............. correlation coefficient MSe mean square error kMed-MedGraph 1(CALC)3(Med) The following is the Med-Medgraph model formula a............. Med-Medgraph slope b............. Med-Medgraph y-intercept 293 kQuadratic/Cubic/Quartic Regression GraphQuadratic regression Cubic regression Quartic regression 294 kLogarithmic Regression Graphy = a + b • ln kExponential Regression Graph y = a • ebx 295 k Power Regression Graphy = a • xb k Sinusoidal Regression Graph 296 kLogistic Regression GraphThe following is the logistic regression model formula y 1 + ae–bx 1(CALC)6(g)6(g)1(Lgst) kResidual Calculation Residual calculation can be performed and saved for all regression models 297 kDisplaying the Calculation Results of a Drawn Paired-VariableGrapho sum of data stored in xList sum of squares of data stored in xList population standard deviation of data stored in xList xσn-1 of data stored in xList number of data p sum of data stored in yList stored in yList yσn-1 ....sample standard deviation of data Σxy ..... sum of the product of data stored in xList and yList kCopying a Regression Graph Formula to the GRAPH Mode • This will display the GRAPH mode graph relation list.*1 298 kMultiple Graphs299 kOverlaying a Function Graph on a Statistical Graph300 scatter diagram and overlay a function graph y = 2ln–2.1,0.3 2a.fwb.cw c.ewewf.cw e -c.bwa.dwb.fwcwc.ew 1(GRPH)1(GPH1) 32(DefG) cIvw(Register Y1 = 2In x) 301 6-4Performing Statistical Calculations311 6-5Tests312 k Z Testsu Z Test Common Functions u 1-Sample Z Test Z = o – ∝0 315 u 2-Sample Z Test– o2 317 u 1-Prop Z Test– p0 Z 318 u 2-Prop Z Testp(1– p ) 320 k t Testsu t Test Common Functions 321 u 1-Sample t Testt 323 u 2-Sample t Test+ n2 – df C 326 u LinearReg t TestΣ( x – o)( y – p) b a = p – bo t = r 1 – r Σ(x – o)2 327 6-5-17Testsβ G0 & ρ G0 constant term coefficient standard error 328 6-5-18Testskχ2 Test Expected counts 3(CHI) Observed positive integers) Expected name of matrix (A to Z) that is for saving expected frequency 329 6-5-19Testsχ2 value degrees of freedom You can use the following graph analysis functions after drawing a graph • 1(CHI) ... Displays χ2 value Press J to clear the χ2 value 330 k2-Sample F Test331 6-5-21Testsσ1Gσ2 F value mean of sample 1 (Displayed only for Data: List setting.) mean of sample 2 (Displayed only for Data: List setting.) • 1(F) ... Displays F value Press J to clear the F value 332 6-5-22TestskANOVA One-WayANOVA is used when there is one independent variable and one dependent 5(ANOV) How Many selects One-WayANOVA or Two-WayANOVA (number of levels) Factor A category list (List 1 to 26) Dependnt list to be used for sample data (List 1 to 26) first list for storage of calculation results (None or List 1 to 22)*1 The following item appears in the case of Two-WayANOVA only Factor B category list (List 1 to 26) • 6(DRAW) ... Draws the graph (Two-WayANOVA only) 333 TestsOne-WayANOVA Line 1 (A) Factor A df value, SS value, MS value, F value, p-value Line 2 (ERR) Error df value, SS value, MS value Two-WayANOVA Line 2 (B) Factor B df value, SS value, MS value, F value, p-value Line 3 (AB) Factor A ⋅ Factor B df value, SS value, MS value, F value *Line 3 does not appear when there is only one observation in each cell Line 4 (ERR) mean squares You can use the following graph analysis function after drawing a graph • 1(Trace) or !1(TRCE) ... Trace function Press J to clear the pointer from the display 334 kANOVA (Two-Way)uDescription uSolution 336 6-6Confidence Interval347 6-7Distribution370 7-1Before Performing Financial Calculations371 kGraphing in the TVM ModeSFV •Zoom, Scroll, and Sketch cannot be used in the TVM mode Note that graphs should be used only for reference purposes when viewing 372 7-2Simple Interest374 7-3Compound Interestlog 375 FV = – (PMT ⋅ n + PV )PV + FV uConverting between the nominal interest rate and effective interest rate When calculating n, PV, PMT, FV i = I%'⎟100 When calculating I% I% 376 2(CMPD)number of compound periods of savings) PMT payment for each installment (payment in case of loan; deposit in case of savings) future value (unpaid balance in case of loan; principal plus interest in case of savings) P/Y installment periods per year C/Y compounding periods per year Inputting Values Precision 377 PMT378 7-4Cash Flow (Investment Appraisal)379 uPBPPBP n – NPVn NPVn+1 – NPVn CFk NPVn = Σ NPV IRR PBP NFV 381 7-5Amortization384 7-6Interest Rate Conversion385 7-7Cost, Selling Price, Margin386 7-8Day/Date Calculations387 PRDd1+D d1–D 360-dayDate Mode Calculations 388 Programming8389 8-1Basic Programming Steps391 8-2PRGM Mode Function Keys393 8-3Editing Program Contents394 kUsing an Existing Program to Create a New ProgramUse TETRA as the file name S = 3 A2, V = ––––A3 Use the following key operations when inputting the program Length of One Side A .. !J(PRGM)4(?)aav(A)6(g)5(:) )d*av(A)x6(g)5(^) Volume V )c/bc*av(A)Md c*!x( )d*av(A)x6(g)5(^) •Deleting c*(underlined using a wavy line above) •Changing dto bc(underlined using a solid line above) 396 k Searching for Data Inside a ProgramExample To search for the letter “A” inside the program named OCTA 1.Recall the program 2.Press 3(SRC) and input the data you want to find 3(SRC) av(A) Each press of 397 8-4File Management401 8-5Command Reference402 Boldface TextActual commands and other items that always must be input are shown in boldface {Curly Brackets} Curly brackets are used to enclose a number of items Do not input the curly brackets when inputting a com mand [Square Brackets] Square brackets are used to enclose items that are a command Alpha Characters kBasic Operation Commands ? (Input Command) Syntax: ? → <variable name>, ”<prompt>” ? → <variable name Example: ? → A Description: 403 ^(Output Command)Function: Displays an intermediate result during program execution : (Multi-statementCommand) Function: Connects two statements for sequential execution without stopping Unlike the output command You can also use a carriage return indicated by _ (Carriage Return) Operation of the carriage return is identical to that of the ’ (Comment Text Delimiter) Function: Indicates comment text inserted inside a program 404 kProgram Commands (COM)If~Then~(Else~)IfEnd Function: Then <statement <statement Else <statement IfEnd Parameters: condition, numeric expression (1)If ~ Then ~ IfEnd When the condition is true, execution proceeds with the •When the condition is false, execution jumps to the statement following IfEnd (2)If ~ Then ~ Else ~ IfEnd When the condition is false, execution jumps to the For~To~(Step~)Next For <starting value> → <control variable name> To <ending value Step <step value> : Next •control variable name: A to Z starting value: value or expression that produces a value (i.e. sin •ending value: value or expression that produces a value (i.e. sin x, A, etc.) •step value: numeric value (default: 1) 405 Do~LpWhileParameters: expression 406 While~WhileEndkProgram Control Commands (CTL) Break Syntax: Break 407 Prog408 ReturnSyntax: Return Stop Syntax: Stop 409 kJump Commands (JUMP)Dsz 410 Goto~Lbl411 Isz⇒(Jump Code) 412 kClear Commands (CLR)ClrGraph Syntax: ClrGraph ClrList ClrMat ClrText Syntax: ClrText 413 kDisplay Commands (DISP)DispF-Tbl, DispR-Tbl No parameters Function: These commands display numeric tables DispF-Tbl DrawDyna Function: This command executes a Dynamic Graph draw operation DrawFTG-Con, DrawFTG-Plt Function: This command uses values in a generated table to graph a function •This command draws a function graph in accordance with current conditions DrawFTG-Con DrawGraph Function: This command draws a graph Description: This command draws a graph in accordance with current conditions DrawR-Con, DrawR-Plt DrawR-Con 414 DrawRΣ-Con, DrawRΣ-PltΣan(Σbn or Σcn) as the vertical axis and n as the horizontal axis DrawR DrawStat Function: This draws a statistical graph Syntax: See “Using Statistical Calculations and Graphs in a Program” on page DrawWeb Syntax: DrawWeb <recursion type>, <number of lines Example: DrawWeb an+1 (bn+1 or cn+1) 415 kInput/Output Commands (I/O)Getkey Syntax: Getkey 416 LocateExample: Cls 417 Receive ( / SendOpenComport38k/CloseComport38k Receive38k/Send38k 418 kConditional Jump Relational Operators (REL)kOther RclCapt 419 8-6Using Calculator Functions in Programs431 8-7PRGM Mode Command List434 8-8Program Library444 Spreadsheet445 9-1Spreadsheet Overview446 kS • SHT Mode Function MenuOPEN RECAL EDIT CUT PASTE COPY CELL BOT 447 SEQFILL SRT ROW COL ALL CLR {GPH1}/{GPH2}/{GPH3}/{SEL}/{SET} {1VAR}/{2VAR}/{REG}/{SET} 448 •{STO} … {displays the STO submenu}•{VAR} … {assigns the contents of a cell to a variable} •{LIST} … {saves the contents of a range of cells as a list} •{FILE} … {saves the contents of a range of cells as a file} •{MAT} … {saves the contents of a range of cells as a matrix} •{RCL} … {displays the RCL submenu} •{LIST} … {imports data from a list into the spreadsheet} •{FILE} … {imports data from a file into the spreadsheet} •{MAT} … {imports data from a matrix into the spreadsheet} uData Input Function Menu • {GRAB} … {enters the Grab mode for inputting sell references} For details, see “To reference a particular cell” (page 9-4-6) •{$} … {inputs the absolute reference command ($) into a cell} •{:} … {inputs the cell range command (:) into a cell} •{If} … {inputs the “CellIf(” S • SHT mode command} CEL •{REL} … {displays a submenu for inputting the following relational operators} 449 9-2File Operations and Re-calculation450 u To open a fileu To delete a file 451 u To save a file under a new name (Save As)1.In the S • SHT mode, press 1(FILE)3(SV • AS) •This will display a dialog box for entering a file name 2.Enter up to eight characters for the file name, and then press w k About Auto Save k Recalculating a Formula Use the following procedure to recalculate the formulas in a spreadsheet u To re-executeall of the formulas in a spreadsheet While the spreadsheet is on the display, press 1(FILE)4(RECAL) This will 452 9-3Basic Spreadsheet Screen Operations453 u To move the cell cursor using the JUMP commandTo move the cell cursor to Do this: here: A particular cell Press 2(EDIT)4(JUMP)1(GO) On the “Go To Cell” dialog box that appears, enter the name of the destination cell (A1 to Z999) Press w Line 1 of current column Press 2(EDIT)4(JUMP)2(TOP↑) Column A of current line Press 2(EDIT)4(JUMP)3(TOP←) Bottom line of current column Press 2(EDIT)4(JUMP)4(BOT↓) Column Z of current line Press 2(EDIT)4(JUMP)5(BOT→) u Specifying Cell Cursor Movement when Inputting Cell Data kSelecting Cells u To select a single cell • See “Moving the Cell Cursor” (page 9-3-1)for more information 454 u To select an entire lineu To select an entire column u To select all of the cells in a spreadsheet 455 u To select a range of cells1.Move the cell cursor to the start cell of the range you want to select 2.Press !i(CLIP) This will cause the cell cursor to change from highlighting to a Selected cells are highlighted To cancel cell selection, press 456 9-4Inputting and Editing Cell Data457 u To replace a cell’s current contents with new input1.Move the cell cursor to the cell where you want to input data 2.Input the desired data 3.After everything is the way you want, press w If “Auto Calc” is turned on (page To cancel data input, press u To edit the current contents of a cell 1.Move the cell cursor to the cell where you want to edit data •This will display the contents of the cell, flush right, in the edit box 458 2.Press 2(EDIT)3(CELL)3.Edit the data in the edit box 4.After everything is the way you want, press w kInputting a Formula •Values •Mathematical expressions •Cell references •Calculator built-infunction commands (page 2-4-1) •S • SHT mode commands (page 9-5-1) 459 u Formula Input Exampleu To input formulas 460 kUsing Cell ReferencesRelative Cell References Absolute Cell References This cell reference: Does this: 461 kReferencing a Particular Cellu To reference a particular cell 1.Move the cell cursor to cell A2, and then input 2.Press 1(GRAB) To move the cell cursor to here: A specific cell 2(GO) 3(TOP↑) 4(TOP←) 5(BOT↓) 6(BOT→) 3.Press f to move the cell cursor to cell A1 4.Press 1(SET) •This inputs the reference to cell A1 462 kReferencing a Range of Cellsu To reference a range of cells 463 5.Press !i(CLIP)You can use the function menu keys 7.To register the range of cells, press 1(SET) •This will input the cell range (A6:B7) 8.Press w to store the formula Indicates the sum of the values in cells A6 through B7 464 kInputting the Absolute Reference Symbol ($)u To input the absolute reference symbol 465 kInputting a ConstantConstant Displayed Result 7+3 sin sin X+1 *1 AX *1*2 dim {1,2,3} 1=0 1>0 Syntax ERROR {1,2,3} 466 kInputting TextUp to six characters can be displayed by the cell kGenerating a Numeric Sequence in a Spreadsheet u To generate a numeric sequence in a spreadsheet To generate a numeric sequence starting from cell A1 using the following parameters Function: f (x) Variable: Starting Value: Ending Value: Increment: 2.Press 2(EDIT)5(SEQ) •This will display a dialog box like the one shown to the right This is the cell you selected in step 467 3.Enter the required items to generate the sequence• The following describes the required input items Item Expr Function f(x) for generating the sequence Var Name of the variable in the function f(x) Even if a function has only one variable, its name must be defined here The starting value (Start), ending value (End) and pitch (Incre) of the values assigned to the variable specified by Var Specifying Start: 1, End: 15, and Incre: 7, for example, will generate a Incre sequence by assigning the following values to the variable: 1, 8 4.After inputting data for all the items, press 6(EXE) or the w key 468 kFilling a Range of Cells with the Same Contentu To fill a range of cells with the same content 469 4. Press w5.Press 6(EXE) or the w key =A1+1 =B1+1 =A2+1 =B2+1 470 kCut and Pasteu How cut and paste affects cell references Let’s say we have a spreadsheet that contains the following data: A1: 4, B1: =A1+1, C1: =B1+2 Cut B1:C1 (left screen) and paste the data in B2:C2 (right screen) 471 A1: 4, B1: =A1+1, C1: = $B$1+2u To cut and paste spreadsheet data 1.Select the cell(s) you want to cut See “To select a single cell” (page 2.Press 2(EDIT)1(CUT) This selects the data and enters the paste mode, which causes the You can exit the paste mode at any time during the following steps by pressing 472 4.Press 1(PASTE)kCopy and Paste u To copy and paste spreadsheet data 1.Select the cell(s) you want to copy 2.Press 2(EDIT)2(COPY) 473 After you are finish pasting the data where you want, press474 kSorting Spreadsheet Datau To sort spreadsheet data Descending: 2(EDIT)6(g)3(SRT•D) •Selecting a sort type will sort the data kDeleting and Inserting Cells u To delete an entire line or column of cells 1. Select one or more cells inside the line(s) or column(s) you want to delete This cell selection can be used to delete lines 1 and 2 or columns A and B You could also select the entire line or column to be deleted 2. Press 3(DEL) to display the DEL submenu 475 u To delete the contents of all the cells in a spreadsheet476 u To insert lines or columns of blank cells2.Press 4(INS) to display the INS submenu 3.Use the INS submenu to perform the operation you want To exit the INS submenu without inserting anything, press kClearing Cell Contents u To clear cell contents 1.Select the cell(s) whose contents you want to clear 2.Press 5(CLR) •This will clear the contents of the currently selected cells 477 9-5S • SHT Mode Commands481 9-6Statistical Graphs482 kConfiguring Graph Parameter Settingsu XCellRange (range x-axisdata cells) Cell u YCellRange (range y-axisdata cells) u Frequency (number of times a value occurs) 483 kGraphing Statistical Datau To graph statistical data Example: Input the following data into a spreadsheet, and then draw a scatter diagram 485 kConfiguring Range Settings for Graph Data Cellsu To change the XCellRange and YCellRange settings manually 1.Press 6(SET) on the GRPH submenu to display the graph settings screen 2.Use the f and c cursor keys to move the highlighting to XCellRange 3.Press 1(CELL) or simply input something •The function menu will change to the colon (:) 4.Input or edit the cell range •To input the colon, press 1(:) 6.After all the settings are the way you want, press J Jc to move to the to configure its setting 486 kConfiguring the Frequency Settingu To specify the frequency of each data item 487 9-7Using the CALC Function488 k Configuring Statistical Calculation Data Settingsu 1Var XCell (x-variablecell range for single-variablestatistical calculations) u 1Var Freq (value frequency) u 2Var XCell (x-variablecell range for paired-variablestatistical calculations) u 2Var YCell (y-variablecell range for paired-variablestatistical calculations) u 2Var Freq (value frequency) 489 k Executing a Statistical Calculationu To execute a statistical calculation 490 9.Press J2(2VAR)10.Press J3(REG)1(X) •This will display the linear regression coefficients for the original data 11.Press J to return to the spreadsheet screen 491 9-8Using Memory in the S • SHT Mode492 k Saving Spreadsheet Data to List Memoryu To save the contents of a range of cells to List Memory 1.Select the range of cells whose data you want to save in List Memory 2.Press 6(g)3(STO)2(LIST) •The “Cell Range” setting will show the range of cells you selected in step 3.Press c to move the highlighting to “List [1~26]” 4.Enter a list number in the range of 1 to 26, and then press w 5.Press 6(EXE) or the w key to save the data in the List Memory k Saving Spreadsheet Data to File Memory The following shows how spreadsheet data in the range of A1:C3 is saved to File File6 List1 List2 List3 Spreadsheet File Memory 493 u To save the contents of a range of cells to File Memory1.Select the range of cells whose data you want to save in File Memory 2.Press 6(g)3(STO)3(FILE) 3.Press c to move the highlighting to “File [1~6]” 4.Enter a file number in the range of 1 to 6, and then press w 5.Press 6(EXE) or the w key to save the data in the File Memory k Saving Spreadsheet Data to Mat Memory u To save the contents of a range of cells to Mat Memory 1.Select the range of cells whose data you want to save in Mat Memory 2.Press 6(g)3(STO)4(MAT) 3.Press c to move the highlighting to “Mat Name” 4.Input the Mat Memory name (A to Z) where you want to save the data 5.Press 6(EXE) or the w key to save the data in the Mat Memory 494 k Recalling Data from MemoryThe above also applies when pasting data into a spreadsheet k Recalling Data from List Memory u To recall data from a List Memory to a spreadsheet •The “1st Cell” setting will show the name of the cell you selected in step 4.Press 6(EXE) or the w key to recall the data 495 u To recall data from a File Memory to a spreadsheetu To recall data from a Mat Memory to a spreadsheet u To use a variable in a spreadsheet 496 eActivity497 10-1eActivity Overview505 10-2Working with eActivity Files508 10-3Inputting and Editing eActivity File Data509 kNavigating around the eActivity Workspace ScreenuTo scroll the eActivity workspace screen vertically uTo jump to the top or the bottom of the eActivity workspace screen kUsing a Text Line uTo input into a text line 510 uTo change the current line into a text lineuTo insert a text line Perform this key operation: located here: 511 uInputting and Editing Text Line ContentsYou can input up to 255 bytes of text into a text line. Scroll arrows ) will appear on text that does not right cursor keys •The 5(A↔a) function key toggles between upper-caseand lower-caseinput. This You can input a carriage return into a text line by pressing kUsing Math Lines •You can input stop lines in an eActivity 512 u To input a calculation formula into an eActivity•“To change the current line into a math line” below •“To insert a math line” (page 10-3-6) 2.Input the expression Example: s$!E(π)cg •“Inputting and Editing Math Line Contents” (page10-3-6) 3.To obtain the result of the calculation and display it, press w u To change the current line into a math line 2.Press 3(TEXT) to change the text line to a math line This will cause the 3 key menu to change to “CALC” 513 uTo insert a math lineTo insert a math line while the cursor is 5(INS)2(CALC) 6(g)3(INS)2(CALC) 3(INS)2(CALC) uInputting and Editing Math Line Contents kUsing Stop Lines automatically uTo insert a stop line To insert a stop line while the cursor is 5(INS)3(STOP) 6(g)3(INS)3(STOP) 3(INS)3(STOP) 514 uStop Line Example1 and pressing w will produce a result of and then stop B:These math lines are not required to test various values for θ 515 kInserting a StripTitle Field Screen Name Field You can input a strip title up to 16 characters long that the strip contains 516 uTo insert a strip1.Move the cursor to the location where you want to insert the strip 2.Press 2(STRP) When you want to embed this type of data: Select this type of strip: RUN • MAT mode calculation screen Run (Math)*1 GRAPH mode Graph screen GRAPH mode Graph Editor screen Graph Editor (Graph relation list) TABLE mode Table Editor screen Table Editor (Table relation list) CONICS mode Conics Graph screen Conics Graph CONICS mode Conics Editor screen Conics Editor STAT mode Stat Graph screen Stat Graph STAT mode List Editor screen List Editor EQUA mode Solver screen Solver RECUR mode Recur Editor screen Recur Editor Notes screen*2 Notes RUN • MAT mode Matrix Editor screen Matrix Editor EQUA mode Simul Equation screen Simul Equation EQUA mode Poly Equation screen Poly Equation 517 DYNA mode Dynamic Graph screenDynamic Graph TVM mode Financial screen Financial S • SHT mode Spreadsheet screen SpreadSheet 4.Press w The text cursor will also appear if you start to input text without pressing 6.Press w to assign the title to the strip 518 uTo change the title of a strip519 uTo call up an application from a strip2.Press w •Also see “Practical Strip Examples” (page 10-3-13)for more information Press !a(') 520 Press !,(,)On the application list that appears, use kPractical Strip Examples uGraph Strip Example This example shows how to create a Graph strip to graph the function y Things to remember uTo create a Graph strip On the eActivity workspace screen, press •This will insert a Graph strip 2.Input the strip title, and then press w •Here we will input “Graph draw” 521 3.Press w to call up the graph screen4.Press !6(G↔T) to display the Graph Editor screen 5.Input the function you want to graph (Y1 = X2 in this example) 6.Press 6(DRAW) to graph the function 7.To return to the eActivity workspace screen, press !a(') 8.Press w again to call up the graph screen •This will re-graphthe function you input in step 522 uTable Editor Strip ExampleuTo create a Table Editor strip 523 8.Call up the List Editor screen (page 6-1-1)9.Input the values into List 10.Return to the Table Editor screen 11.When the Table Editor screen appears, press w This generates the number table for the function 12.To return to the eActivity workspace screen, press !a(') kUsing Copy and Paste to Draw a Graph 524 uTo use copy and paste to draw a graphPerform steps 1 through 7 under “To create a Graph strip” (page 2.Press 3(INS)1(TEXT) to input a text line 3.Enter the following expression into the text line: Y = X2 – See “To specify the copy range” (page •This will graph the function currently stored in “Graph draw ” strip memory 6.Press !j(PASTE) •This will graph the function that is on the clipboard (Y = X2 – 1) 7.To return to the eActivity workspace screen, press !a(') •This will re-graphthe function currently stored in “Graph draw” strip memory 525 kUsing NotesYou can perform the following operations on a Notes screen u Input and edit text u Copy and paste text uNotes Screen Function Menu The following describes the function menu of the Notes screen •{DEL • L} … {deletes the line where the cursor is located} MATH 526 kDeleting an eActivity Line or StripuTo delete a line or strip 2.Press 6(g)2(DEL • L) 527 k Saving an eActivity Fileu To replace the existing file with the new version On the eActivity workspace screen, press 1(FILE)1(SAVE) 1.Press 1(FILE)2(SV • AS) 2.Enter up to eight characters for the eActivity file name, and then press w 528 10-4Using Matrix Editor and List Editor529 k Calling Up List Editoru To call up List Editor To call up List Editor while the cursor is 6(g)6(g)2('LIST) 6(g)4('LIST) u To return to the eActivity workspace screen from List Editor u To use List Editor 530 10-5eActivity File Memory Usage Screen531 System Settings Menu539 Data Communications571 Appendix572 1 Error Message Table576 2 Input Ranges577 α-2-2Internal number solutions digits Pol (x, y) x2 + y2 < 1 ⋅ |r| < 1 ⋅ However, for tanθ : Rec | 90(2n+1): DEG (DEG) | (10 ) (RAD) | | < 5 /2(2n+1): RAD (GRA) |θ | < 1 ⋅ 1010grad |θ | ≠ 100(2n+1): GRA |a|, b, c < 1 ⋅ 0 < b, c Sexagesimal display: x > 0: –1 ⋅ 10100 < ylogx x = 0 : y x < 0 : y = n, –––– ^(x ) 2n+1 –1 ⋅ 10100 < ylog |x| y > 0 : x ≠ –– logy y = 0 : x y < 0 : x = 2n+1 (m ≠ 0; m, n are integers) –– log |y| Total of integer, numerator ab/c and denominator must be within 10 digits (includes division marks) 578 Input range579 3 Specifications580 Data Communications3-pinserial port Method: Transmission speed (BPS): <115200 bits/second Parity: EVEN Bit length: 8 bits Stop bit: X ON/X OFF Control: None <9600, 38400 bits/second Parity: None USB port 581 4 Key Index584 5 P Button (In case of hang up)585 6 Power Supply586 α-6-2k Replacing Batteries Precautions: Be sure that the positive (+) and negative • Never mix batteries of different types • Never mix old batteries and new ones • Never leave dead batteries in the battery compartment Remove the batteries if you do not plan to use the calculator for long periods uTo replace the main power supply batteries •Be sure to replace all four batteries with new ones 587 α-6-31.Press !o(OFF) to turn off the calculator Making sure that you do not accidently press the 4.Remove the four old batteries 6.Replace the back cover Turn the calculator front side up and slide off its case. Next, press 588 uTo replace the memory back up battery589 α-6-5(+) side is facing up Next, replace the back cover kAbout the Auto Power Off Function
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