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Casio FX-9860G −21, Example, Example, Matrix A, Matrix A, 1(Mat)av(A)w, uRow Echelon Form, K2(MAT)6(g)4(Ref), [OPTN]-[MAT]-[Ref], [OPTN]-[MAT]-[Rref]

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Matrix Calculations

uRow Echelon Form

[OPTN]-[MAT]-[Ref]

This command uses the Gaussian elimination algorithm to ﬁnd the row echelon form of a matrix.

Example

To ﬁnd the row echelon form of the following matrix:

1 2 3

Matrix A =

4 5 6

K2(MAT)6(g)4(Ref)

1(Mat)av(A)w

uReduced Row Echelon Form

[OPTN]-[MAT]-[Rref]

This command ﬁnds the reduced row echelon form of a matrix.

Example	To ﬁnd the reduced row echelon form of the following matrix:
	Matrix A =		2	−1	3	19
			2	−1	3	19
		1		1	−5	−21
			0	4	3	0

K2(MAT)6(g)5(Rref) 1(Mat)av(A)w

#The row echelon form and reduced row echelon form operation may not produce accurate results due to dropped digits.

200870201

Contents

User’s Guide Quick-Start TURNING POWER ON AND OFF USING MODES To select the RUN • MAT mode BASIC CALCULATIONS Parentheses Calculations Built-InFunctions REPLAY FEATURE FRACTION CALCULATIONS Converting an Improper Fraction to a Mixed Fraction Converting a Fraction to Its Decimal Equivalent EXPONENTS ONBOARD FUNCTION MANUAL GRAPH FUNCTIONS Page DUAL GRAPH Box Zoom DYNAMIC GRAPH Page TABLE FUNCTION Precautions when Using this Product MEMORY Page Contents Getting Acquainted — Read This First Chapter Basic Operation Manual Calculations Graphing Chapter 6 Statistical Graphs and Calculations Chapter 7 Financial Calculation (TVM) Programming Spreadsheet eActivity Chapter 11 System Settings Menu Data Communications Appendix Getting Acquainted — Read This First About this User’s Guide u m EQUA EQUA Getting Acquainted uGraphs Left hand page Right hand page 3. Draw the graph Basic Operation 1-1Keys the e • ACT or RUN • MAT e • ACT or RUN • MAT Page Page 1-1-5Keys kKey Markings Function Key Operation log 1-2Display S • SHT Use this mode to perform spreadsheet calculations. Each (Spreadsheet) to the calculator’s built-incommands and S • SHT mode in the STAT mode kAbout the Function Menu • Next Menu Selecting displays a menu of hyperbolic functions • Command Input Selecting inputs the sinh command kNormal Display uHow to interpret exponential format kSpecial Display Formats kCalculation Execution Indicator 1-3Inputting and Editing Calculations ddd!D(INS) To abort this operation, press !D(INS) again uTo delete a step Example To change 369 ⋅ ⋅ 2 to 369 ⋅ Adgj**c uTo insert a step uTo change the last step you input kUsing Replay Memory Example 1 To perform the following two calculations 4.12⋅ 6.4 4.12⋅ 7.1 Ae.bc*g.ew kMaking Corrections in the Original Calculation Example 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 Math input mode uTo cut the text uPasting Text !j(PASTE) kCatalog Function You can use either of the following two methods to input a command To do this: uTo input a command with uOnboard Function Manual kInput Operations in the Math Input Mode uMath Input Mode Functions and Symbols Function/Symbol Bytes Fraction (Improper) Mixed Fraction*1 uUsing the MATH Menu log uMath Input Mode Input Examples Example 1 To input 23 + Page Example 4 To input 2 ⋅ u When the calculation does not ﬁt within the display window uInserting a Function into an Existing Expression u 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) u Functions that Support Insertion Original Expression After uEditing Calculations in the Math Input Mode 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 uMath Input Mode Input Restrictions 1-4Option (OPTN) Menu •{LIST}/{CPLX}/{CALC}/{HYP}/{PROB}/{NUM}/{ANGL}/{ESYM}/{FMEM}/{LOGIC} •{List}/{CALC}/{HYP}/{PROB}/{NUM}/{FMEM}/{LOGIC} uOption menu when a number table value is displayed in the TABLE or RECUR mode LMEM 1-5Variable Data (VARS) Menu u STAT — Recalling statistical data minX maxX minY maxY 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 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} 1-6Program (PRGM) Menu 1-7Syntax Help 1-8Using the Setup Screen uFrac Result (fraction result display format) d/c ab/c uFunc Type (graph function type) •{Y=}/{r=}/{Parm}/{X=c} uLabel (graph axis label display) uSyntax Help (syntax help display setting) uDisplay (display format) •{Fix}/{Sci}/{Norm}/{Eng} uStat Wind (statistical graph V-Windowsetting method) uBackground (graph display background) •{None}/{PICT} u Sketch Line (overlaid line type) uDynamic Type (dynamic graph type) •{Cnt}/{Stop} 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 1-9Using Screen Capture 1-10When you keep having problems… kLow Battery Message Manual Calculations 2-1Basic Calculations kNumber of Decimal Places, Number of Signiﬁcant Digits, Normal Display Range [SET UP] - [Display] - [Fix] / [Sci] / [Norm] Condition 100/6w 200 ⎟ 7 ⋅ 14 200/7*14w 3 decimal places 1(Fix)dwJw Calculation continues using 2Type B functions x 3Power/root ^(xy), x 4Fractions a b/c Abbreviated multiplication format in front of kMultiplication Operations without a Multiplication Sign 2π, 2AB, 3Ans, 3Y1, etc 3(5 + 6), (A + 1)(B – 1), etc kOverﬂow and Errors kMemory Capacity 2-2Special Functions uTo display the contents of a variable To display the contents of variable A uTo clear a variable To clear variable A uTo assign the same value to more than one variable uTo store a function Example To store the function (A+B) (A–B)as function memory number (av(A)+al(B)) (av(A)-al(B)) K6(g)6(g)3(FMEM) uTo delete a function Example To delete the contents of function memory number uTo use stored functions y = x3 + x2 + x + Xmin = – 4 kAnswer Function uTo use the contents of the answer memory in a calculation Example 123 + 456 = 579789 – 579 Abcd+efgw hij-!-(Ans)w (Ans) kHistory Function *cw To change “1+2” to “1+3” and recalculate Perform the following operation following the sample shown above ffffdDdw kStacks stacks numeric value stack command stack program subroutine stack kUsing Multistatements • Colon (:) • Display Result Command (^) Abcdaav(A) !J(PRGM)6(g)5(:)g.j 2-3Specifying the Angle Unit and Display Format 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 2-4Function Calculations 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 kAngle Units • Be sure to specify Comp for Mode in the Setup screen Operation cccccc 47.3° + 82.5rad = 4774.20181° 47.3+82.5K6(g)5(ANGL)2(r)w kTrigonometric and Inverse Trigonometric Functions 2*s45*c65w*1 1/s30w kLogarithmic and Exponential Functions log 1.23 (log101.23) l1.23w log28 K4(CALC)6(g)4(logab)2,8)w kHyperbolic and Inverse Hyperbolic Functions kOther Functions $1c$1c3e-$1c4w !((3')36*42*49w 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.) kCoordinate Conversion → 24.98979792 (r) 255.928 → 55.92839019 (θ) K6(g)5(ANGL)6(g)1(Pol() 14,20.7)wJ kPermutation and Combination u Permutation u Combination Formula kFractions ––+ 3 ––= ––– $2c5e+!$(&)3e1c4w 2$5+3$1$4w $1c2578e+$1c4572w 1$2578+1$4572w Switching between improper fraction and mixed fraction format Switching between fraction and decimal format kEngineering Notation Calculations 9/10w kLogical Operators (AND, OR, NOT) And What is the logical AND of A and B when A = 3 and B = 2 A AND B What is the logical OR of A and B when A = 5 and B = 1 uAbout Logical Operations 2-5Numerical Calculations kDifferential Calculations [OPTN]-[CALC]-[d/dx] K4(CALC)2(d/dx) f(x),a,tol) (a: point for which you want to determine the derivative, tol: tolerance) To determine the derivative at point x = 3 for the function y = 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) uApplications of Differential Calculations ––– f (a) = f '(a) ––– g (a) = g'(a) Therefore: f '(a) + g'(a), f '(a) ⋅ g'(a), etc kQuadratic Differential Calculations [OPTN]-[CALC]-[d2/dx2] K4(CALC)3(d2/dx2) f(x),a,tol) (a: differential coefﬁcient point, tol: tolerance) –––( f (x), a) 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) ∫( f(x), a, b, tol) ⇒ ∫ab f(x)dx 4(MATH)6(g)1(∫dx)cvx+ dv+eebffw uApplication of Integration Calculation • Integrals can be used in addition, subtraction, multiplication or division f (x) dx + ∫c ∫ab f (x)dx = ∫ac f (x)dx + (–∫cb f (x)dx) ∫ab f (x)dx = ∫ax1 f (x)dx + ∫xx1 2 f (x)dx +.....+ ∫xb4 f (x)dx 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) Sn + Tn, Sn – Tn, etc kMaximum/Minimum Value Calculations uMinimum Value uMaximum Value AK4(CALC)6(g)2(FMax) -vx+cv+c 2-6Complex Number Calculations kArithmetic Operations Example 1 (1 + 2i) + (2 + 3i) Example 2 (2 + i) ⋅ (2 – i) kReciprocals, Square Roots, and Squares kComplex Number Format Using Polar Form kAbsolute Value and Argument [OPTN]-[CPLX]-[Abs]/[Arg] To calculate absolute value (r) and argument (Ƨ) for the complex number 3 + 4i, with the angle unit set for degrees Imaginary axis kExtraction of Real and Imaginary Parts [OPTN]-[CPLX]-[ReP]/[lmP] To extract the real and imaginary parts of the complex number 2 + AK3(CPLX)6(g)1(ReP) (c+f6(g)1(i))w kPolar and Rectangular Form Transformation [OPTN]-[CPLX]-['r∠Ƨ]/['a+bi] 2-7Binary, Octal, Decimal, and Hexadecimal Calculations with Integers uTo perform a binary, octal, decimal, or hexadecimal calculation [SET UP]-[Mode]-[Dec]/[Hex]/[Bin]/[Oct] d~o LOG kSelecting a Number System uTo specify a number system for an input value uTo input values of mixed number systems Example To input 12310 or 10102, when the default number system is hexadecimal Example 1 To calculate 101112 + !m(SET UP)c2(Dec)J A1(d~o)4(o)bcd 2(h)ABC*1w J3(DISP)2('Hex)w kNegative Values and Bitwise Operations Example 2 To display the result of “368 or 11102” as an octal value Example 3 To negate 2FFFED16 u Number System Transformation Dec Hex 2-8Matrix Calculations kInputting and Editing Matrices DEL DEL·A DIM u Creating a Matrix uTo input cell values To input the following data into Matrix B : bwcwdw ewfwgw To exit the Matrix input screen, press J uDeleting Matrices uTo delete a speciﬁc matrix uTo delete all matrices kMatrix Cell Operations R-OP •{ROW} INS ADD uTo calculate the scalar multiplication of a row 4 : 4, then add the result to row 3 : uTo add two rows together Matrix A = 3 u Row Operations uTo delete a row uTo insert a row 2(ROW)2(INS) uTo add a row 2(ROW)3(ADD) uColumn Operations uTo delete a column uTo insert a column uTo add a column matrix: kModifying Matrices Using Matrix Commands uTo display the matrix commands Det u Matrix Data Input Format [OPTN]-[MAT]-[Mat] ... a1n ... a2n am1 uTo input an identity matrix Example 2 To create a 3 ⋅ 3 identity matrix as Matrix A uTo 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 uModifying Matrices Using Matrix Commands uTo 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 : uTo ﬁll a matrix with identical values and to combine two matrices into a single matrix [OPTN]-[MAT]-[Fill]/[Aug] Example 1 To ﬁll all of the cells of Matrix A with the value K2(MAT)6(g)3(Fill) uTo assign the contents of a matrix column to a list [OPTN]-[MAT]-[M→L] kMatrix Calculations 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) uDeterminant [OPTN]-[MAT]-[Det] Obtain the determinant for the following matrix : −1 −2 K2(MAT)3(Det)1(Mat) uRow Echelon Form [OPTN]-[MAT]-[Ref] To ﬁnd the row echelon form of the following matrix: K2(MAT)6(g)4(Ref) uReduced Row Echelon Form Matrix Calculations uMatrix Inversion [x–1] To invert the following matrix: K2(MAT)1(Mat) uRaising a Matrix to a Power 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 kPerforming Matrix Calculations Using Natural Input To perform the calculation shown below uTo assign a matrix created using natural input to a MAT mode matrix List Function 3-1Inputting and Editing a List uTo batch input a series of values 1.Use the cursor keys to move the highlighting to another list !*( { )g,h,i!/( } ) 3.Press w to store all of the values in your list. w 2.Press K and input the expression kEditing List Values uTo change a cell value uTo edit the contents of a cell uTo delete a cell uTo delete all cells in a list uTo insert a new cell kNaming a List uTo name a list kSorting List Values uTo sort a single list Ascending order Descending order uTo sort multiple lists Page 3-2Manipulating List Data uTo count the number of data items in a list To count the number of values in List 1 (36, 16, 58, 46, 56) uTo create a list or matrix by specifying the number of data items [OPTN]-[LIST]-[Dim] Matrix A uTo replace all data items with the same value uTo generate a sequence of numbers contains the smallest value (Min) (List) To ﬁnd which of two lists contains the greatest value [LIST] uTo calculate the mean of data items Example To calculate the mean of data items in List 1 (36, 16, 58, 46 56) uTo calculate the mean of data items of speciﬁed frequency [OPTN]-[LIST]-[Mean] uTo calculate the median of data items of speciﬁed frequency [OPTN]-[LIST]-[Med] uTo combine lists uTo calculate the sum of data items in a list[OPTN]-[LIST]-[Sum] [Sum] uTo calculate the product of values in a list To calculate the product of values in List 1 (2, 3, 6, 5, 4) uTo calculate the cumulative frequency of each data item [OPTN]-[LIST]-[Cuml] (2, 3, 6, 5, 4) To calculate the percentage represented by each data item in List AK1(LIST)6(g)6(g)4(%) uTo 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 3-3Arithmetic Calculations Using Lists uTo directly input a list of values uTo assign the contents of one list to another list Example 1 To assign the contents of List 3 to List Example 2 To assign the list in ListAns Memory to List uTo recall the value in a speciﬁc list cell uTo input a value into a speciﬁc list cell kRecalling List Contents uTo use list contents in ListAns Memory in a calculation Example To multiply the list contents in ListAns Memory by kGraphing a Function Using a List kInputting Scientiﬁc Calculations into a List Example To use the TABLE mode to create a number table for the formula (Y1 x2 –1),and then copy the table to List 1 in the STAT mode kPerforming Scientiﬁc Function Calculations Using a List To use List 3 and List 3-4Switching Between List Files Equation Calculations 4-1Simultaneous Linear Equations To solve the following simultaneous linear equations for x, y, and z 4x + y – 2z = – x + 6y + – 5x + 4y + 4-2Quadratic and Cubic Equations x3 – 2x2 – x + 2 4-3Solve Calculations 9.8 (m/s2) H = VT – 1/2 GT2 23(SOLV) aM(H)!.(=)ac(V)a/(T)-(b/c) a$(G)a/(T)xw 4-4What to Do When an Error Occurs Graphing 5-1Sample Graphs To graph y 1m GRAPH 2dvxw 36(DRAW) (or w) kHow to draw a simple graph (2) Y1 = 2x2 – 3, r2 = 3sin2θ kHow to draw a simple graph (3) Graph Type Graph the circle (X–1)2 + (Y–1)2 1m CONICS 2ccccw 3 bwbwcw 46(DRAW) kHow to draw a simple graph (4) Page 5-2Controlling What Appears on a Graph Screen uV-WindowSetting Precautions kInitializing and Standardizing the V-Window uTo initialize the V-Window uTo initialize the V-Windowin accordance with an angle unit uTo standardize the V-Window kV-WindowMemory uTo store V-Windowsettings 3.Press 4(STO) to display the pop-upwindow Press a number key to specify the uTo recall V-Windowmemory settings kSpecifying the Graph Range Graph y = x2 + 3x – 2 within the range – 2 < x Xmin = –3 Xmax = 5 Ymax = 30 2!3(V-WIN)-dwfwbwc kZoom Graph y = (x + 5)(x + 4)(x + 3), and then perform a box zoom Xmin = –8 Xmax = 8 Ymin = –4 Ymax = 2 kFactor Zoom Controlling What Appears on a Graph Screen Enlarge the graphs of the two expressions shown below ﬁve times on both the x- and y-axisto see if they are tangent Y1 = (x + 4)(x + 1)(x – 3), Y2 = 3x + Ymin = –30 5-3Drawing a Graph uTo store a polar coordinate function (r=) *1 Example 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.) uTo store an X = constant expression *1 Example To store the following expression in memory area X4 : X 3(TYPE)4(X=c) (Speciﬁes X = constant expression.) d(Inputs expression.) uTo store an inequality *1 Example To store the following inequality in memory area Y5 : y > x2 − 2x − uTo assign values to the coefﬁcients and variables of a graph function Memory Area Type Default Variable Xtn Ytn Y1 (3) and Y1 (X = 3) are identical values kEditing and Deleting Functions uTo edit a function in memory uTo change the line style of a graph function “Broken” uTo change the type of a function *1 Example To change the function in memory area Y1 from y = 2x2 – 3 to y < 2x2 – kSelecting Functions for Graphing uTo specify the draw/non-drawstatus of a graph Y1 = 2x2 – 5, r2 = 5 sin3θ Xmin = –5 Ymin = –5 kGraph Memory A 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 5-4Storing a Graph in Picture Memory 5-5Drawing Two Graphs on the Same Screen Graph y = x(x + 1)(x – 1) in the main screen and sub-screen (Main Screen) Xmin = –2 Xmax = 2 Ymin = –2 kGraphing Two Different Functions screen kUsing Zoom to Enlarge the Sub-screen Box Zoom to enlarge it 5-6Manual Graphing Graph y = 2x2 + 3x – kIntegration Graph Ymin = –8 Ymax = 12 kDrawing Multiple Graphs on the Same Screen To graph y = Ax2 – 3 as the value of A changes in the sequence 3, 1 –1 2!m(SET UP)cc3(Off)J 3!3(V-WIN) -fwfwbwc -bawbawcwJ kUsing Copy and Paste to Graph a Function There are two types of functions you can paste into the graph screen Type 1 (Y= expression) Example: To paste Y=X and graph it • Any spaces to the left of Y are ignored previously copied function Y=X from the clipboard 5-7Using Tables uTo generate a table using a list 1.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 To scroll the display and view parts of the table that do not ﬁt in the display •To change x variable values by replacing values in column Press 1(FORM) or J to return to the Table relation list uTo generate a differential number table *1 uSpecifying the function type uTo edit a function Example To change the function in memory area Y1 from y = 3x2 – 2 to y = 3x2 – kEditing Tables G·CON G·PLT uTo change variable values in a table uRow Operations Example To add a new row below Row 7 in the table generated on page uDeleting a Table kCopying a Table Column to a List uTo copy a table to a list kDrawing a Graph from a Number Table 1.From the Main Menu, enter the TABLE mode 3.Store the functions 4.Specify the table range 5.Generate the table Store the two functions below, generate a number table, and then draw a line graph. Specify a range of –3to 3, and an increment of Y1 = 3x2 – 2, Y2 Xmin = 0 Xmax = 6 kSpecifying a Range for Number Table Generation Store the three functions shown below, and then generate a table for functions 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 35(SET)-dwdwbwJ kSimultaneously Displaying a Number Table and Graph 3.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 Store the function Y1 = 3x2 – 2 and simultaneously display its number table 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) kUsing Graph-TableLinking 2.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 increment of Xmin = –1 Xmax = 10 Ymin = –1 Ymax = 4 5-8Dynamic Graphing Dynamic Graphing Use Dynamic Graph to graph y = A (x – 1)2 – 1, in which the value of coefﬁcient A changes from 2 through 5 in increments of 1. The Graph is drawn 10 times Xmin = –6.3 kDrawing a Dynamic Graph Locus times kDynamic Graph Application Examples The path over time T of a ball thrown in the air at initial velocity V and an angle of θ degrees from horizontal can be calculated as follows X = (Vcos θ)T, Y = (Vsin θ)T – (1/2)gT2 (g = 9.8m/s2) Use Dynamic Graph to plot the path of a ball thrown at an initial velocity of 20 meters per second, at horizontal angles of 30, 45, and kAdjusting the Dynamic Graph Speed kGraph Calculation DOT Switching Function kUsing Dynamic Graph Memory The following is all of the data that makes up a set •Graph functions (up to 20) •Dynamic Graph conditions •Setup screen settings 5-9Graphing a Recursion Formula Generate a number table from recursion between three terms as expressed 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) kGraphing a Recursion Formula (1) Graphing a Recursion Formula Generate a number table from recursion between two terms as expressed 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 kGraphing a Recursion Formula (2) Generate 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 kWEB Graph (Convergence, Divergence) To draw the WEB graph for the recursion formula an+1 = –3(an)2 + 3an bn+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 kGraphing a Recursion Formula on Dual Screen 4.Specify the recursion formula type and input the formula 3!m(SET UP)ccc1(T+G)J 85(G • CON) 5-10Changing the Appearance of a Graph Draw a line that is tangent to point (2, 0) on the graph for y = x (x + 2)(x – 2) 3!m(SET UP)cccccc1()J 43(TYPE)1(Y=)v(v+c)(v-c)w 6!4(SKTCH)2(Tang) kInserting Comments You can insert comments anywhere you want in a graph 1.Draw the graph Insert text into the graph y = x (x + 2)(x – 2) !3(V-WIN) -fwfwbwc -fwfwbwJ 3(TYPE)1(Y=)v(v+c)(v-c)w 2!4(SKTCH)6(g)6(g)2(Text) 3 f~f d~d a-(Y)!.(=)v(v+c)(v-c) kFreehand Drawing Page kChanging the Graph Background 5-11Function Analysis Read coordinates along the graph of the function shown below Y1 = x2 – 2!3(V-WIN) -fwfwbwc 3(TYPE)1(Y=)vx-dw 3!1(TRCE) kDisplaying the Derivative Page kGraph to Table Function Analysis Save, in a table, the coordinates in the vicinity of the points of intersection at X = 0 for the two graphs shown below, and store the table contents in List Y1 = x2 – 3, Y2 = – x + kCoordinate Rounding 3(TYPE)1(Y=) vx-dw 3!2(ZOOM)6(g)3(RND) 4!1(TRCE) d~d kCalculating the Root Draw the graph shown below and calculate the root for Y1 Y1 = x(x + 2)(x – 2) 3(TYPE)1(Y=)v(v+c)(v-c)w6(DRAW) (DRAW) 3!5(G-SLV)1(ROOT) kCalculating the Point of Intersection of Two Graphs Graph the two functions shown below, and determine the point of intersection between Y1 and Y2 Y1 = x + 1, Y2 !3(V-WIN) -fwfwbwc -fwfwbwJ 3(TYPE)1(Y=) v+bw kDetermining the Coordinates for Given Points Graph the two functions shown below and then determine the y coordinate for x = 0.5 and the x-coordinatefor y = 2.2 on graph Y2 Y1 = x + 1, Y2 = x(x + 2)(x – 2) Xmax = 6.3, Xscale Ymax = 3.1, Yscale = 1 (initial defaults) kCalculating the lntegral Value for a Given Range at (–2,0) kConic Section Graph Analysis uParabolic Graph Analysis FOCS VTX LEN uTo calculate the focus, vertex and length of latus rectum To determine the focus, vertex and length of latus rectum for the parabola X = (Y – 2)2 + uTo calculate the center and radius To determine the center and radius for the circle (X + 2)2 + (Y + 1)2 uTo calculate the x- and y-intercepts To determine the x- and y-interceptsfor the hyperbola (X – 3)2 (Y – 1)2 uTo draw and analyze the axis of symmetry and directrix [G-SLV]-[SYM]/[DIR] X = 2(Y – 1)2 + uTo draw and analyze the asymptotes [G-SLV]-[ASYM] To draw the asymptotes for the hyperbola (X – 1)2 cwcwbwbw6(DRAW) Statistical Graphs and Calculations 6-1Before Performing Statistical Calculations kChanging Graph Parameters •{GPH1}/{GPH2}/{GPH3} ... graph {1}/{2}/{3} drawing*1 SEL •{SET} ... {graph settings (graph type, list assignments)} 1. General graph settings • Mark Type This setting lets you specify the shape of the plot points on the graph uTo display the general graph settings screen Pressing 1(GRPH)6(SET) displays the general graph settings screen •StatGraph (statistical graph speciﬁcation) 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} 6-2Calculating and Graphing Single-VariableStatistical Data kMed-boxGraph (MedBox) kNormal Distribution Curve (N • Dis) π) xσn kBroken Line Graph (Brkn) kDisplaying the Calculation Results of a Drawn Single-VariableGraph 6-3Calculating and Graphing Paired-VariableStatistical Data Input the two sets of data shown below. Next, plot the data on a scatter diagram and connect the dots to produce an xy line graph 0.5 1.2 2.4 k Drawing a Regression Graph Input the two sets of data shown below and plot the data on a scatter diagram. 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 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 kLinear Regression Graph The 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 kQuadratic/Cubic/Quartic Regression Graph Quadratic regression y = ax2 + bx + c y = ax3 + bx2 + cx + d Quartic regression kLogarithmic Regression Graph kExponential Regression Graph y = a·ebx kPower Regression Graph y = a·xb kSinusoidal Regression Graph kLogistic Regression Graph The following is the logistic regression model formula 1 + ae–bx 1(CALC)6(g)6(g)1(Lgst) kResidual Calculation kDisplaying the Calculation Results of a Drawn Paired-VariableGraph kCopying a Regression Graph Formula to the GRAPH Mode kMultiple Graphs k Overlaying a Function Graph on a Statistical Graph Input the two sets of data shown below. Next, plot the data on a scatter diagram and overlay a function graph y = 2ln -c.bwa.dw b.fwcwc.ew 1(GRPH)1(GPH1) (GRPH) (GPH1) 6-4Performing Statistical Calculations kSingle-VariableStatistical Calculations kPaired-VariableStatistical Calculations kRegression Calculation You can directly determine the same expression from the data input screen To display single-variableregression parameters 2(CALC)3(REG)1(X) u Calculation of the Coefﬁcient of Determination (r2) and MSe sin 2. Input the value you want for x and then press w This causes the coordinates for After you are ﬁnished, press •The Y-CALfunction can also be used with a graph drawn by using DefG feature uRegression Formula Copy Function from a Regression Calculation Result kEstimated Value Calculation ( , ) yi kNormal Probability Distribution Calculation Standard Normal Distribution 175.5 cm tall student fall 2.Input the height data into List 1 and the frequency data into List 3.Perform the single-variablestatistical calculations.*1 2(CALC)6(SET) 1(LIST)bw c2(LIST)cw!J(QUIT) k Drawing a Normal Probability Distribution Graph Page 6-5Tests kZ Tests uZ Test Common Functions u1-Sample Z Test Z o – μ0 Page Page u2-Sample Z Test Page u1-Prop Z Test – p0 Z p0 (1– p0) u2-Prop Z Test p(1– p ) Page 6-5-10Tests kt Tests ut Test Common Functions • 1(T) ... Displays t score Press J to clear the t score u 1-Sample t Test Page u 2-Sample t Test n1 + n2 – df = n1 + n2 – t df Page Page u LinearReg t Test Σ(x – o)( y – p) 1 – r Σ(x – o)2 6-5-17Tests β G 0 & ρ G 0 constant term coefﬁcient standard error 6-5-18Tests kχ2 Test Expected counts 3(CHI) Observed 6-5-19Tests χ2 value degrees of freedom You can use the following graph analysis functions after drawing a graph • 1(CHI) ... Displays χ2 value k 2-Sample F Test 6-5-21Tests σ1Gσ2 F value mean of sample 1 (Displayed only for Data: List setting.) mean of sample 2 (Displayed only for Data: List setting.) 6-5-22Tests kANOVA 5(ANOV) How Many selects One-WayANOVA or Two-WayANOVA (number of 6-5-23Tests One-WayANOVA Line 1 (A) Factor A df value, SS value, MS value, F value, p-value Line 2 (ERR) k ANOVA (Two-Way) uDescription uSolution Page 6-6Conﬁdence Interval u General Conﬁdence Interval Precautions kZ Interval u 1-Sample Z Interval The following is the conﬁdence interval Left = o – Z Right = o + Z Left conﬁdence interval lower limit (left edge) Right u 2-Sample Z Interval Left = (o1 – o2) – Z Page u 1-Prop Z Interval n : Left n n 1– n x : u 2-Prop Z Interval Left = x1 – x2 – Z α Right = x1 – x2 +Z α x1 α xσn–1 u 2-Sample t Interval Left = (o α x1σn–12 Page 6-7Distribution u Common Distribution Functions The following is the general procedure for using the P-CALfunction After drawing a distribution graph, press 2.Input the value you want for x and then press w This causes the k Normal Distribution u Normal Probability Density f(x) 2πσ u Normal Distribution Probability p u Inverse Cumulative Normal Distribution ∫−∞ f (x)dx = p ∫ f (x)dx = p f (x)dx = p Page k Student-t Distribution u Student-t Probability Density f (x) 1(tpd) degrees of freedom (df > 0) Γ 2 π df k χ2 Distribution u χ2 Probability Density f(x) χ2 probability density u χ2 Distribution Probability kF Distribution uF Probability Density 1 + nx F probability density uF Distribution Probability 1 + Page k Binomial Distribution u Binomial Probability f (x) = nCxpx(1–p)n – (x = 0, 1, ·······, n) p : success probability u Binomial Cumulative Density Page k Poisson Distribution u Poisson Probability u Poisson Cumulative Density k Geometric Distribution u Geometric Probability u Geometric Cumulative Density 2(Gcd) TVM 7-1Before Performing Financial Calculations 7-2Simple Interest 7-3Compound Interest 7-4Cash Flow (Investment Appraisal) 7-1Before Performing Financial Calculations kGraphing in the TVM Mode SFV •Zoom, Scroll, and Sketch cannot be used in the TVM mode Note that graphs should be used only for reference purposes when viewing 7-2Simple Interest ⋅ PV ⋅ REPT 7-3Compound Interest PMT = – uConverting between the nominal interest rate and effective interest rate ) –1 100 ⋅ [C / Y ] When calculating n, PV, PMT, FV 2(CMPD) number of compound periods of savings) PMT payment for each installment (payment in case of loan; PMT 7-4Cash Flow (Investment Appraisal) PBP n – NPVn NPVn+1 – NPVn NPV PBP NFV Page 7-5Amortization sign BAL INT PRN 7-6Interest Rate Conversion 7-7Cost, Selling Price, Margin 7-8Day/Date Calculations PRD d1+D d1–D 360-dayDate Mode Calculations Programming8 8-1Basic Programming Steps Store the calculation formula under the ﬁle name OCTA S = 2'3 A2, V = ––––A3 1m PRGM 23(NEW)OCTAw*1 3!J(PRGM)4(?)aav(A)6(g)5(:)*2 c*!x(')d*av(A)x6(g)5(^) 8-2PRGM Mode Function Keys uWhen you are inputting a program —— 2(BASE)*1 •{TOP}/{BTM}/{SRC} •{MENU} •{A↔a}/{CHAR} •{JUMP}/{?}/{^} 8-3Editing Program Contents kUsing an Existing Program to Create a New Program Page kSearching for Data Inside a Program Example 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) 8-4File Management kEditing a ﬁle name Example To change the name of a ﬁle from TRIANGLE to ANGLE While the program list is on the display, use 2.Make any changes you want DDD uTo delete all programs kRegistering a password After inputting the program, press kRecalling a Password Protected Program Example To recall the ﬁle named AREA which is protected by the password CASIO In the program list, use 8-5Command Reference kBasic Operation Commands ? (Input Command) Syntax: Example: ? → A Description: ^(Output Command) : (Multi-statementCommand) _(Carriage Return) ’ (Comment Text Delimiter) kProgram Commands (COM) If~Then~(Else~)IfEnd Function: <condition : Then <statement Do~LpWhile Parameters: expression While~WhileEnd kProgram Control Commands (CTL) Break Syntax: Break Prog Return Syntax: Return Stop Syntax: Stop kJump Commands (JUMP) Dsz Goto~Lbl Isz ⇒(Jump Code) kClear Commands (CLR) ClrGraph Syntax: ClrGraph ClrList ClrMat kDisplay Commands (DISP) DispF-Tbl, DispR-Tbl DrawDyna DrawFTG-Con, DrawFTG-Plt DrawGraph DrawR DrawStat DrawWeb kInput/Output Commands (I/O) Getkey Syntax: Getkey Code Locate Example: Cls Receive ( / Send OpenComport38k/CloseComport38k Receive38k/Send38k kConditional Jump Relational Operators (REL) kOther RclCapt 8-6Using Calculator Functions in Programs uTo calculate a scalar multiplication (`Row) uTo add two rows (Row+) Example 4 To add Row 2 to Row 3 of the matrix in Example kUsing Graph Functions in a Program Example Program uSyntax of other graphing functions kUsing Dynamic Graph Functions in a Program •Dynamic Graph range 1 → D Start kUsing Table & Graph Functions in a Program kUsing Recursion Table & Graph Functions in a Program kUsing List Sort Functions in a Program kUsing Solve Calculation Function in a Program Solve( f(x), n, a, b) Upper limit Lower limit Initial estimated value Page kPerforming Statistical Calculations Page 8-7PRGM Mode Command List [VARS] key [SHIFT] key BASE Program [SHIFT][MENU](SET UP) key 8-8Program Library Page Program Name Arithmetic-GeometricSequence Differentiation Example 1 5, 10, 15, ... Arithmetic sequence Example 2 5, 10, 20, ... Geometric sequence Page Ellipse Page Rotation Important Page Program Name Interior Angles and Surface Area of a Triangle Page Spreadsheet 9-1Spreadsheet Overview kS • SHT Mode Function Menu •{FILE} … {displays the FILE submenu} •{NEW} … {creates a new spreadsheet ﬁle} OPEN •{SV • AS} … {saves the displayed spreadsheet under a new name (Save As)} SEQ FILL SRT ROW COL •{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} 9-2File Operations and Re-calculation uTo open a ﬁle uTo delete a ﬁle uTo 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 kAbout Auto Save 9-3Basic Spreadsheet Screen Operations Basic Spreadsheet Screen Operations uTo move the cell cursor using the JUMP command To move the cell cursor to Do this: here: uTo select an entire line uTo select an entire column uTo select all of the cells in a spreadsheet uTo select a range of cells 1.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 9-4Inputting and Editing Cell Data uTo replace a cell’s current contents with new input 1.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 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 uFormula Input Example uTo input formulas kUsing Cell References Relative Cell References Absolute Cell References This cell reference: Does this: kReferencing a Particular Cell uTo 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: kReferencing a Range of Cells uTo reference a range of cells 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 kInputting the Absolute Reference Symbol ($) uTo input the absolute reference symbol Example To input =$A$1 into cell C1 kInputting a Constant Constant Displayed Result 7+3 sin kInputting Text kGenerating a Numeric Sequence in a Spreadsheet uTo generate a numeric sequence in a spreadsheet following parameters 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 kFilling a Range of Cells with the Same Content uTo ﬁll a range of cells with the same content 4. Press w 5.Press 6(EXE) or the w key =A1+1 =B1+1 =A2+1 kCut and Paste uHow 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) A1: 4, B1: =A1+1, C1: = $B$1+2 uTo 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) 4.Press 1(PASTE) kCopy and Paste uTo copy and paste spreadsheet data 1.Select the cell(s) you want to copy 2.Press 2(EDIT)2(COPY) After you are ﬁnish pasting the data where you want, press kSorting Spreadsheet Data uTo sort spreadsheet data kDeleting and Inserting Cells uTo delete an entire line or column of cells uTo delete the contents of all the cells in a spreadsheet uTo insert lines or columns of blank cells 2.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 9-5S • SHT Mode Commands kS • SHT Mode Command Reference uCellIf uCellMin uCellMax uCellMean uCellMedian uCellSum uCellProd 9-6Statistical Graphs kConﬁguring Graph Parameter Settings uXCellRange (range x-axisdata cells) Cell uYCellRange (range y-axisdata cells) uFrequency (number of times a value occurs) kGraphing Statistical Data uTo graph statistical data Example: Input the following data into a spreadsheet, and then draw a scatter diagram Page kConﬁguring Range Settings for Graph Data Cells uTo 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 kConﬁguring the Frequency Setting uTo specify the frequency of each data item 9-7Using the CALC Function kConﬁguring Statistical Calculation Data Settings u1Var XCell (x-variablecell range for single-variablestatistical calculations) u1Var Freq (value frequency) u2Var XCell (x-variablecell range for paired-variablestatistical calculations) u2Var YCell (y-variablecell range for paired-variablestatistical calculations) kExecuting a Statistical Calculation uTo execute a statistical calculation Page 9-8Using Memory in the S • SHT Mode kSaving Spreadsheet Data to List Memory uTo 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 uTo save the contents of a range of cells to File Memory 1. 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 kRecalling Data from Memory kRecalling Data from List Memory uTo recall data from a List Memory to a spreadsheet uTo recall data from a File Memory to a spreadsheet uTo recall data from a Mat Memory to a spreadsheet uTo use a variable in a spreadsheet eActivity 10-1eActivity Overview kWorkspace Screen Function Menu kText Line Function Menu SAVE OPT CAPA STRP kMath Line and Stop Line Function Menu kStrip Function Menu SIZE GUIDE kBasic eActivity File Operations 1.From the main menu, enter the e • ACT mode 2.Create a new eActivity ﬁle 4.Use math lines to enter the expression (2x2 + x – 3 = 0) and solve it 5.Now to draw a graph, insert a Graph strip into the eActivity 6.Graph the expression using the Graph strip 7.Use G-SLVto extract the roots on the graph screen 8.Save the eActivity ﬁle 10-2Working with eActivity Files If the ﬁle you want to open is in a folder, use •This will open the ﬁle If the ﬁle you want to delete is in a folder, use 2.Use f and c to highlight the ﬁle you want to delete, and then press 3(DEL) uTo search for a ﬁle 10-3Inputting and Editing eActivity File Data kNavigating around the eActivity Workspace Screen uTo 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 uTo change the current line into a text line uTo insert a text line Perform this key operation: located here: uInputting and Editing Text Line Contents You can input a carriage return into a text line by pressing If the text is wrapped into multiple lines, pressing the kUsing Math Lines •You can input stop lines in an eActivity uTo 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 uTo insert a math line To insert a math line while the cursor is 5(INS)2(CALC) 6(g)3(INS)2(CALC) 3(INS)2(CALC) These math lines are not required to test various values for Substituting a value will produce a result of If we wanted to test various values for and press kInserting a Strip Title Field Screen Name Field You can input a strip title up to 16 characters long uTo insert a strip When you want to embed this type of data: Select this type of strip: DYNA mode Dynamic Graph screen Dynamic Graph TVM mode Financial screen Financial S • SHT mode Spreadsheet screen uTo change the title of a strip uTo call up an application from a strip 2.Press w •Also see “Practical Strip Examples” (page 10-3-13)for more information Press !a(') 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 3.Press w to call up the graph screen 4.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(') uTable Editor Strip Example uTo create a Table Editor strip 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 uTo use copy and paste to draw a graph Perform 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 kUsing Notes You can perform the following operations on a Notes screen u Input and edit text u Copy and paste text uNotes Screen Function Menu kDeleting an eActivity Line or Strip uTo delete a line or strip 2.Press 6(g)2(DEL • L) kSaving an eActivity File uTo 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 10-4Using Matrix Editor and List Editor kCalling Up List Editor uTo call up List Editor To call up List Editor while the cursor is 6(g)6(g)2('LIST) 6(g)4('LIST) 10-5eActivity File Memory Usage Screen 10-6eActivity Guide kCreating a Guide uTo enter the guide creation mode On the eActivity workspace screen, select a strip and then press • In this example we will select a Graph Editor strip 2.Press 5(GUIDE) uTo create an n-keyoperation Page uTo create a 1-keyoperation uTo create an AUTO operation uTo change the position of the comment box HIDE uTo exit the guide creation mode 1.While creating a guide, press 4(END) • This will display the dialog box shown to the right 2.Press 1(Yes) or 6(No) kEditing a Guide kEditing the Guide You Are Creating uTo display the key editing screen Input a value to specify the number of keys you want to jump and then press • Here we want to jump to the b key, so we will input hw •{nKEYS} ... {inserts an n-keyoperation at the display position} •{1-KEY} ...{inserts a 1-keyoperation at the display position} •{EDIT} ... {starts editing of the key at the current position} kEditing Example uTo change −X2 + 1 to −2X2 + 1 (by inserting a c key before the v key) uTo change −2X2 + 1 to −2X2 + 2 (by overwriting the b key with the c key) uTo edit an n-keyoperation comment uTo change −2X2 + 2 to 2X2 + 2 (by deleting the - key) uTo exit a editing operation uTo edit the guide of an existing strip from the eActivity workspace screen uRunning a Guide 4.If exit strip is turned on, press w •1(Yes) ... Exits the strip and returns to the eActivity workspace screen •6(No) ... Returns to the screen in step keActivity Guide Editing Techniques uTo edit a guide from the end uTo insert SETUP or V-Windowsetting changes into a key operation sequence uTo create a guide that starts with list data input System Settings Menu 11-1Using the System Settings Menu 11-2System Settings kPower Properties Settings uTo specify the Auto Power Off trigger time While the initial 2.Use f and c to select “Auto Power Off” •1(10) ... {10 minutes} (initial default setting) kSystem Language Setting uTo select the message language uTo select the menu language 11-3Version List uTo register a user name 11-4Reset Page Data Communications 12-1Connecting Two Units 12-2Connecting the Unit to a Personal Computer 12-3Performing a Data Communication Operation kPerforming a Data Transfer Operation Receiving unit Sending unit MAIN SMEM When 1(MAIN) is pressed When 2(SMEM) is pressed •{SEL} ... {selects new data} •{CRNT} ... {automatically selects previously selected data*1} uTo send selected data items (Example: To send user data) uTo execute a send operation Sending Unit kSpecifying the Cable Type USB 3PIN kConﬁguring the Receiver’s Wakeup Feature 12-4Data Communications Precautions <CAPTURE Capture memory group CAPT n Capture memory (1 to 20) data SETUP kExchanging Data with another Model Calculator 12-5Image Transfer kAuto Image Transfer to an OHP Unit (OH-9860*1) kConnecting to a Projector uConnectable Projectors (As of July 2007) (As of July 2007) uTo project calculator screen contents from a projector uPrecautions when Connecting 12-6 Add-ins kInstalling an Add-inApplication and Message Language Data Using FA-124 PROGRAM-LINK 6.Select the add-inthat you want to install If you are installing an 7.Click [Open] •This should cause the imported add-inﬁle to appear in the Computer window On the calculator, enter the Page Page 12-7MEMORY Mode kMemory Information Screen Main Memory Data Name Storage Memory*1 kCreating a Folder in Storage Memory uTo create a new folder uTo rename a folder kSelecting Data Page kCopying Data uTo copy from main memory to storage memory kError Checks During Data Copy Low battery check Available memory check A “Memory Full” error occurs if there is not enough memory available A “Too Many Data” error occurs when the number of data items is too great Type mismatch error check kDeleting Files uTo delete a main memory ﬁle uTo delete a storage memory ﬁle uTo search for a ﬁle in the main memory letter “R” uTo search for a ﬁle in the storage memory •Input the letter “S” for the keyword kBacking Up Main Memory Data uTo back up main memory data uTo restore backup data to the main memory 2.Press 2(LOAD) This displays the folder selection screen 3.Use f and c to select a folder 4.Press w.*1 kOptimizing the Storage Memory uTo optimize the storage memory 1. On the initial MEMORY mode screen press 5(OPT) to optimize the storage memory The message “Complete!” appears when the optimize operation is complete Appendix 1 Error Message Table Page Page Page 2 Input Ranges α-2-2 x2 + y2 < 1 ⋅ |r| < 1 ⋅ However, for tanθ : (DEG) |θ| < 9 ⋅ (109)° Input range