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Portrait 4: User`s Guide ()

1. 2 In the given date the month is 2 February Day of the Month Input monthDay date Description Finds the day of the month a given date lands on Example monthDay makeDate 5 2 2005 10 30 0 5 In the given date the day of the month is the 5 Current Date and Time Input now Description Returns the current local date and time Example Click on the Show Result button to find the current date and time Find the Seconds Input seconds date Description Finds the seconds in a given date time Example seconds makeDate 5 2 2005 10 30 12 12 In the given date and time there are 12 seconds Find the Time Input time date Description Finds the time in a given date time Example time makeDate 5 2 2005 10 30 12 10 30 12 In the given date the time is 10 30 12 am Day of the Week Input weekDay date Description Finds the day of the week that a given date lands on Example weekDay makeDate 5 2 2015 10 30 12 Thursday The date February 5 2015 falls on a Thursday Find the Year Input year date Description Finds the year in a given date Example year makeDate 5 2 2015 10 30 12 2015 The year is 2015 Equations To solve equations tap the following Functions gt Equations The equation solving functions available are as follows Solving a Single Equation Input fsolve equation variable lower bound upper bound Description Finds a value for the
2. 2 Function Plot etx 10 33 ES Se Insert Column Adds a column so data for another graph on the same set of axes can be entered and plotted This option 1s on bar graphs box and whisker plots curves of best fit normal probability plots and point plots Delete Column Removes a column that has been added If several columns have been added highlight the column you want to remove and tap on Delete Columns If a column is not highlighted the last column added is deleted This command will not remove the original column This option is on bar graphs box and whisker plots curves of best fit normal probability plots and point plots Tools Menu The Tools menu allows you to gather more specific information about the graphs With these tools you can find specific points on a graph as well as zoom in and out on a particular portion of a graph These tools are not available for all graphs to xfrom mn If a tool is in use it is shown in the bottom right corner of the graphing window To switch to another tool select it from the Tools menu To turn off a tool select it again Track points Zoom in Zoom out Derivative Integral File Edit Tools F E Ba 65 Track points This tool provides a E and crosshairs that can be placed anywhere on the graph It shows the y Function Plot a qx 10 05 ES specific x and or y coordinates in the bottom left corner of the frame as it is m
3. Cut py Equal Scaling Unequal Style Draw Grid Thickness E Equal Uses the same scale on the x and y axes preserving the true proportions of the graph Unequal Assigns different scales to the x and y axes so the graph fills the available space A check mark indicates your selection Box and whisker plots pie graphs and bar graphs do not have a scaling option Line Draws the graph with a line Point Draws the graph with points Line Style Choose between Dashed and Solid lines Thickness Choose between Thin Medium and Thick Symbol Choose between Circle Cross Diamond Point and Square Pie graphs and bar graphs do not have these style options Graphs of inequalities can only have the line thickness altered Point plots have an additional symbol type None which indicates that the points themselves are not to be plotted This can be useful if you set the Style to Line instead of point The Style menu for histograms is very different from that of the other graphs It includes being able to show the histogram with Cumulative Frequencies and or a Frequency Polygon If you choose the dashed line option and then change the thickness of the dashed line to either medium or thick the line no longer appears to be dashed 64 Options Draw Grid This option adds a graph paper background to a graph when selected Function Plot a dx 1032 ES
4. Input tpdf x degrees of freedom Description Finds the value of the probability density function for the Student t distribution at a specified value of x The degrees of freedom must be greater than 0 The Student distribution is defined as the ratio of a normal distribution to the square root of the quotient of a chi squared distribution by its degrees of freedom The f distribution is a bell shaped symmetrical distribution with a mean of zero It is flatter in shape than the normal distribution and the area under the tails 1s greater It is named after William Sealy Gosset 1876 1937 the Englishman who first published the result under the pseudonym Student Example tpdf 5 3 0 0042 Cumulative Student Distribution Input tcdf lower bound upper bound degrees of freedom Description Finds the cumulative Student distribution probability between a lower bound and an upper bound for the specified degrees of freedom The degrees of freedom must be greater than O Example tcdf 0 5 1 3 0 1302 51 Graphing Probability Distributions To graph any of the probability distributions open the Plot menu and select the Plot y f x window The type of information to be entered in the column under the header f x is probably best explained with the use of an example Let s say that you want to graph a normal distribution To calculate a probability value from the normal distribution you need the following information in
5. User s Guide www mathresources com MathResources Inc 5516 Spring Garden Road Suite 312 Halifax Nova Scotia Canada B3J 1G6 1 902 429 1323 Phone 1 800 720 1323 Toll Free in North America 1 902 492 7101 Fax support mathresources com Email http www mathresources com Portrait 4 for Pocket PC User s Guide Copyright 2005 MathResources Inc All rights reserved No part of this publication may be reproduced or distributed in any form or by any means or stored in a database or retrieval system without the prior written consent of the copyright holder MathResources Inc acknowledges all trademarks and registered trademarks in this document Printed in Canada ISBN _ 1 896977 20 0 06 06 2005 TABLE OF CONTENTS OT Veco d AAE Ee certain led ee ore ne mere 3 BUTTONS ON THe CALCULATOR Sacacasa nacos 3 SYNBOLRC GONS TANTO ea a A T aaa 4 EMENGO Dala reenn a A A 4 DATAY PE i aa a ocio 4 CONVERTING BETWEEN DATA TYPES CASTING o c 0 0 c ccccscccesssosseesosesssocccecccerscatuccuosevscovesevscsecceessectsnsecevesesssessseeeees 5 BOOLEANIO PER AMOR Score AEA E A E O EN EIA RES EE EEEE 5 RELA TON eaea eee ee ATA 6 ea arsa AOE GS N E E E A ES IEE AO E S EE EE ESE EE TEE ETAS TEE T OE 6 FONCTIONS MENE aa EE AE A dido A TOA 7 SH EO EO T ear T E A A AA O E AE AA 8 ERRORE S SAC E S aa E A A A AEO E AE TOASA 8 OPOR MEN e aaa A E A A atada ess 9 FUNCION PENELA fl Shc romana cantantes 9 PEEP MODE me
6. 26 29 32 147 Adding 17 20 23 26 29 32 147 Input 2 Parameter Form Sum equation variable first in range last in range Description Finds the sum of a list of results for a variable evaluated under a given equation for a given range of values The first value in the range must be less than or equal to the last value in the range and they must be integers Also between the first value in the range and the final value in the range there are only two dots between the commas Example sum 3 x 2 x 5 10 147 The result is the sum of the results of 3 x 2 evaluated for x ranging from 5 to 10 that is 17 20 23 26 29 32 147 Input 3 Sequence Form sum function variable list Description Finds the sum of a list of results for a variable evaluated under a given function for a given sequence Example sum x22 x 1 2 5 1 31 Statistical Functions Statistics is the area of mathematics that deals with collecting analyzing interpreting and presenting numerical data Statistics can summarize a set of known data in a clear concise manner such as in terms of its mean median or standard deviation Tip When entering data to calculate statistical functions be sure to separate the data by commas To get to the statistical functions tap the following Functions gt Statistics Confidence Intervals The following abbreviations are used to indicate the information to
7. 3 4 5 1 3 6 10 15 In this example 1 is the first element in the list but is not added to another element the second element 2 is added to the first to get 3 the third element is added to 3 to get 6 and so on until all elements have been added together List Differences Input diffList list A Description Returns a list containing the differences between consecutive elements in the original list Example diffList 1 2 3 4 5 1 1 1 1 In the example 2 1 1 3 2 1 4 3 1 and 5 4 1 Filla List Input fill element length of list Description Returns a list or matrix containing copies of a value Example fill 5 4 5 5 5 5 In the example the result is 4 copies of the value 5 Maximum Value Input max list Aj Description Finds the largest entry of a list or matrix Example 1 max 1 2 4 5 0 5 Five is the largest value in this set of data Example 2 max primeSet 12 3 The largest prime number dividing 12 is 3 Minimum Value Input min list A Description Finds the smallest entry of a list or matrix Example 1 min 1 2 4 5 0 4 Negative 4 is the smallest value in this list of data Example 2 min primeSet 12 2 The smallest prime number dividing 12 is 2 Ascending Sort Input sortA list Aj Description Sorts a list of numbers into ascending increasing order Example sortA 1 2 3 4 5 5 1 2 3 4 37 Descending Sort Input sort
8. Description Returns the net present value of the list of cash flows Example cfNPV 10 5000 4000 3000 2000 2618 33 The net present value is 2 618 33 Net Uniform Series Input cfNUS interest rate list Description Returns the net uniform series of the list of cash flows Example cfNUS 10 5000 4000 3000 2000 1052 87 Payback Period Input cfPbk list Description Returns the period when the initial investment of a given cash flow will be paid back Example cfPBK 5000 3000 3000 5000 1 666667 The initial investment will be paid back in 1 67 periods Profitability Index Input cfProf interest rate list Description Returns the profitability index of the given list of cash flows Example cfProf 10 5000 4000 3000 2000 1 523666 The profitability index of this list is 1 32 Cash Flow Total Input cfT otal list Description Returns the sum of the given cash flow Example cfTotal 1000 1500 2000 2500 3000 10000 The total of the cash flows in this list is 10 000 Finance Interest Bonds and Net Present Future Values Compound Interest Input compound principal interest compounding periods term Description Finds the accumulated amount that is the sum of the principal plus the earned interest compounded c y times a year over a given period of time the term Example compound 100 6 2 5 134 39 Starting with a principal of 100 and an interest rate of
9. Note If you do not enter x limits you will get a syntax error when you try to plot the function Entering the range of y values is optional but including them can improve the graph s appearance If you are graphing several functions the x and y limits do not have to be the same However the largest set of limits will be used for all functions so they all fit in the window on the same axes The equations you want evaluated can be comprised of integers symbolic constants decimal numbers or any functions or operations with numeric results 76 Polar Plots Polar plots are a useful way of investigating plane curves particularly circles ellipses spirals and other curves with similar symmetries The set of ordered pairs that make up a polar plot are r t where r is the distance from the origin and is the angle measure around the origin increasing counterclockwise where zero represents the positive x axis Polar Plot ir qx 12 50 S Assignment S3 Entering Data T CI 1 Tap on one of the cells in the column labeled r t Enter your function Use for exponents and for multiplication 3 Enter the values that you want your function evaluated from and to Tab over to these spaces or tap in them with your stylus This step is not optional for polar plots 4 Tap on the pencil to draw the graph of the function Note Ifyou do not enter t limits you will get a syntax error when
10. To draw the graph tap on the pencil icon 19 The Tools menu provides the option of graphing the derivative or the integral of the function In this example we Selected Derivative and then tapped on the point on the graph that we wanted to see the derivative of The graph is drawn and the equation provided in the bottom left corner Track points Zoom in Zoom out v Derivative Integral Function Plot et ia amp A function plot Complex Numbers Complex numbers z are numbers in the form a b I where I 1 and a and b are real numbers To get to the complex number functions tap the following Functions gt Complex Numbers Argument Input arg z Description Finds the argument of a complex number Example arg I 1 570796 The argument of I is equal to 1 570796 Conjugate Input conj z Description Finds the conjugate of a complex number Example conj I I The conjugate of I is equal to I Imaginary Part Input imag z Description Finds the imaginary part of a complex number Example imag l 1 The imaginary part of I is 1 20 Modulus Input modulus z Description Finds the modulus of a complex number Example modulus I 1 The modulus of I is 1 Real Part Input real z Description Finds the real part of a complex number Example real I 0 The real part of I is 0 Convert from Rectangular Form to Polar Form Input toPolar z Description Converts
11. Transpose of a Matrix Input transpose matrix A Description Finds the transpose of a given matrix Interchanging the rows and columns of a given matrix so that Matrix m X n is altered to Matrix n X m transposes a matrix Example transpose matrix 2 3 1 2 3 4 5 6 matrix 3 2 1 4 2 5 3 6 Tip To perform an additional function on a matrix highlight the matrix in the Input window and select the function from the Matrices menu This wraps the selected function around the existing matrix Tap the Show Result button in the template or tap or Enter and the matrix operation is performed Number Theory Functions Number Theory is the field of mathematics that studies the properties and relations of integers Some of the topics studied include divisibility primality and factorization In the descriptions below the term proper factors indicates all factors of a number except the number itself To get to the number theory functions tap the following Functions Number Theory Combinations Input choose m n Description Finds the number of combinations of m objects chosen n at a time The order of selection is not important The integers m and n must be nonnegative with n less than or equal to m Example choose 6 4 15 42 Factor Set Input factorSet n Description Finds a list of all the factors of n Factors of a number are any numbers that divide exactly into that given number Example factorSet
12. calculations in the history list go to the Edit menu and com pou nd 5 000 0 35 12 see select Clear History Error Messages Error messages appear in the result window if the expression you input cannot be evaluated There are many potential error messages and they are self explanatory For example e error syntax error You made a typing mistake or input a nonsensical expression The expression 1s then highlighted approximately where the error has been made e error division by zero The expression you want to evaluate includes division by zero e error input is too large You entered an integer or decimal number that is too large See the section on Data Types for the limits on the size of integers and decimal numbers that can be input e error wrong number of arguments You have not entered the proper number of arguments to evaluate the expression e error unassigned variable You have not given a value to a variable you have used e error floating point overflow error interger overflow An intermediate or final result is too large for the range of its data type see the section on DataTypes e error fsolve requires at least 4 arguments To remove an error message simply tap the Clear button This clears the Input window as well Options Menu Function Templates The simplest most efficient way to do calculations with Portrait 4 is by using the Function Templates especially if you are uncertain
13. method of depreciation It is expressed as a fraction where the denominator is the sum of digits from to the number of useful years of life and the numerator is the number of years in reverse order Depreciation Method 27 Once you have selected the method of depreciation you want to use open the Options menu Here you will enter information about the asset you are depreciating like the original cost the salvage value and the life of the asset When all of the appropriate information is entered open the Schedule menu to see the schedule of depreciation This information can be copied and pasted in to an Excel or word document 768 25 968 256 15 744 _ Finance Time Value of Money TVM Template Money has different values at different points in time and calculating the time value of money can be an effective way to analyze a variety of financial instruments like mortgages loans leases and annuities The difference in the value of money at different times is a result of the accumulation of interest Use the TVM Template to calculate the number of payments interest rate present value payment amount and future value To get to the TVM functions tap the following Functions gt Finance TVM Template Cash to be received must be entered as a positive number Cash to be paid must be entered as a negative number To use the TVM Template select the term that you want to solve for For example 1f you want to det
14. where x 0 Example coth e 1 009 Inverse Hyperbolic Functions To get to the inverse hyperbolic functions tap the following Functions gt Hyperbolic 34 Inverse Hyperbolic of Sine Input asinh x or arcsinh x Description Denotes the inverse of the hyperbolic sine function The inverse of the hyperbolic sine function is defined as y In x sqrt x 1 for all real numbers x Example arcsinh e 1 725 Inverse Hyperbolic of Cosine Input acosh x or arccosh x Description Denotes the inverse of the hyperbolic cosine function The inverse of the hyperbolic cosine function is defined as y In x sqrt 1 for x gt 1 Example arccosh e 1 657 Inverse Hyperbolic of Tangent Input atanh x or arctanh x Description Denotes the inverse of the hyperbolic tangent function The inverse of the hyperbolic tangent function is defined as y 1 2In 1 x 1 x for x lt 1 Example arctanh 0 5 0 549 Inverse Hyperbolic of Cosecant Input acsch x or arccsch x Description Denotes the inverse of the hyperbolic cosecant function The inverse of the hyperbolic cosecant function is defined as y In 1 x sqrt 1 x x for x 0 This function can also be typed in or you can use the mathematical equivalent arcsinh 1 x Example arccsch 0 5 1 444 Inverse Hyperbolic of Secant Input asech x or arcsech x Description Denotes the inverse of the hyperbolic secant function The inverse of
15. x y Description Finds the minimum value of a function under the given constraints and the x and y values at this minimum Remember to use braces around the constraints and the variables The constraints must be written as inequalities Use commas appropriately Example minimize 2 x y 3 x y gt 10 5 x 2 y gt 6 x y 6 67 x 3 33 y 0 The minimum value of the function under the given constraints is 6 67 This value occurs when x is equal to 3 33 and y is equal to 0 35 Maximization Problems Input maximize function constraints variables Description Finds the maximum value of the function under the given constraints and the x and y values at this maximum Remember to use braces around the constraints and the variables The constraints must be written as inequalities Use commas appropriately Example maximize 2 x y 3 x y lt 10 5 x 2 y lt 6 x y 3 x 0 y 3 The maximum value of the function under the given constraints is 3 This value occurs when x is equal to 0 and y is equal to 3 Graphing Linear Inequalities Linear functions are subject to restrictions imposed by a system of linear inequalities and equations This system of inequalities defines a feasible region for the function to be optimized Problems in two variables can be easily visualized and solved by considering only the vertices of the feasible region One of the theorems of linear programming states that if a linea
16. 12 1 2 3 4 6 12 The factors of 12 are 1 2 3 4 6 and 12 Fibonacci Number Input fibonacci n Description Finds the n th Fibonacci number Fibonacci numbers are numbers in the sequence 1 1 2 3 5 8 13 21 34 Each number in the sequence after the second number is the sum of the previous two numbers Example 1 fibonacci 2 1 Example 2 fibonacci 15 610 Greatest Common Divisor Input gcd m n or gcf m n or hcf m n Description Finds the greatest common divisor of m and n This is also referred to as the greatest common factor gcf or highest common factor hcf The greatest common divisor is the number that exactly divides into both of the numbers given Example gcd 56 46 2 The largest number that exactly divides into both 56 and 46 is 2 Abundant Number Input isAbundant 7 Description Finds whether n is an abundant number An abundant number is a number for which the sum of its proper factors is greater than the number itself This function returns a Boolean true or false value If n is abundant isAbundant returns true otherwise it returns false Example isAbundant 28 false The number twenty eight is not an abundant number Amicable Numbers Input isAmicable m n Description Finds whether m and n are amicable numbers Two numbers are amicable if the sum of the proper factors of one number is equal to the other number This function returns a Boolean true or false val
17. 2 2 1 2 3 4 matrix 2 2 4 3 2 1 matrix 2 2 5 5 5 5 Subtracting Matrices The difference between two matrices 1s obtained by subtracting the corresponding elements of two matrices Matrices have to be the same size to be subtracted Subtracting matrices of different SIZES gives an error message Example matrix 2 2 1 2 3 4 matrix 2 2 4 3 2 1 matrix 2 3 1 1 3 Scalar Product The scalar product is obtained by multiplying each element in a matrix by a given real number Example 3 matrix 2 2 1 2 3 4 matrix 2 2 3 6 9 12 Multiplying Matrices To multiply matrices the number of columns in the first matrix must equal the number of rows in the second matrix Example matrix 2 3 1 2 3 4 5 6 matrix 3 2 6 5 4 3 2 1 matrix 2 2 20 14 56 41 38 Matrix Exponentiation Exponentiation can only be done on square matrices The power must be a non negative integer Example matrix 2 2 1 2 3 42 matrix 2 2 7 10 15 22 Dividing Matrices Dividing one matrix by another matrix is not supported Adding and Multiplying Rows Input addrow matrix A destination row source row factor Description This operation replaces row i of a matrix with c row iz row i Example addrow matrix 2 2 1 2 3 4 1 2 3 matrix 2 2 10 14 3 4 In this example multiply row 2 by 3 and add the result to row 1 Multiplying a ro
18. Additional Information Additional information about the normal probability plot is available by opening the Tools menu and selecting Key This key will give you the equation of the line you have graphed It will also give you the mean squared error MSE and the correlation coefficient r for the data The information in this key can be copied and pasted into a word processing document or Plot Window like the Function Plot by using the Ctrl C copy and Ctrl V paste shortcuts on your keyboard Highlight the information you want to copy Use Ctrl C to copy it and then Ctrl V to paste it in the location you want Graphs of Functions The graph of a function is a graph of the equation y f x where f represents any function and the value of y is dependent on the value of x The graph is the set of all points where the x and y coordinates are x f x Function Plot ato zas ES Sine and Cosine y Entering Data a atom TERM 1 Tap in one of the cells in the column labeled f x Enter your function Use for exponents and for multiplication 3 Enter the domain x from and x to that you want your equation evaluated from and to Use the Tab key to move over to these spaces or tap in them with your stylus Entering the y limits is optional but you will build a better graph if appropriate y from and y to values are included 4 Tap on the pencil icon to draw the graph of the equation
19. Enter a new expression at the top of the new column Tap the Build Sequence button again to fill in the new column nfs DY 20 1 5 0 833333 gl File Edit Samples Help E Note Sequences can be saved and retrieved using the File menu in the Sequence Editor Use the Edit menu in the Sequence Editor to copy and clear cells You can also insert and delete columns using this menu as well as send the data to the graphing template listed 15 Table Editor With the Table Editor you can build a table of values Portrait4 BTS To build a table of values 1 Tap the Edit menu 2 Open the Table Editor 3 Enter a variable in the cell provided This step is not optional 4 Enter the range you want the variable to be evaluated From and To in the appropriate cells 5 Enter the Increment you want the variable to increase by for each row 6 Below the cell where the increment is entered there are two gray cells Tap on the 2 cell and enter the expression that you want the variable evaluated under 7 When you have input the expression tap the Build Table button to build a table of values 8 To add a column to the table tap on the Edit menu and select Insert Column Enter a new expression at the Build table button top of the new column Tap the Build Table button E Eal again to fill in the new column Note Tables can be saved and retrieved using the File menu in the Table Editor Use the E
20. SPS Or EGUAN eea E A aaa 79 POMERIO a A 0 E nerd isu A nnersoned baci amtdeatatlare 80 SKAPAS OT INEdUaA IO Strand 81 dot Soo e AAA o PE PEO PE RE A ae een ene 82 Contacimo MANRESOULCOS NC nia aaa 82 CODY WGI SAG MademarkS sat bronca eco dba 82 Using Portrait 4 Portrait 4 is a powerful piece of graphing and calculating software that is also very easy to use This User s Guide 1s written in an easy to understand style and covers basic functionality of the software Help is also available from the main menu of your handheld computer The software 1s designed to have you up and running very quickly The Screen Interface i we oa O The basic operating window of Portrait 4 is very simple Input When the program is open there is a calculator screen with three menus at the bottom From these menus the Edit menu the Functions menu and the Options menu you can access all of the graphing and calculating power of E ET T R Portrait 4 To open a menu tap on the menu name and messages appear here then tap on a specific command to open it Some menus have submenus to choose from Result The screen also contains number and function buttons that are standard on most handheld calculators To use any of these buttons simply tap on them The Plots menu is a part of the Functions menu The trigonometric hyperbolic exponential and log functions are also found in the Functions menu Buttons on the Calculator The buttons on Portrait 4 p
21. Tap on the scissors to cut the highlighted selection and put 1t on the clipboard Tap on the double pages to copy the highlighted selection and put 1t on the clipboard i Tap on the clipboard to insert or paste text from the clipboard E Tap on this icon to open the keyboard To close the keyboard tap on the icon again Helpful Hints for Graphing The following tips apply to all of the graphing templates It will be helpful to keep them in mind as you begin to explore each of the graphing templates 68 If you make a mistake entering data tap on a cell so that it is selected and delete or re enter the data properly If you enter inappropriate data or a nonsensical operation and plot 1t an error message appears If you require additional rows for data tap in a cell that accepts data and tap Enter An empty row appears below the row the selected cell is in If you want to graph more than one set of data go to the Edit menu Tap Insert Columns To change the width of columns in the data entry window place the cursor at the edge of the gray cell at the top of the column Drag the edge of the cell left or right to make the column smaller or larger Bar Graphs Bar Graph Er dx 11 25 3 A bar graph is a graph in which data values are shown by Pretest vs Posttest Scores means of the length of rectangular bars The graph to the left uses a bar graph to compare the scores from a pretest 20 and a posttest taken by four diff
22. Use the Functions menu on the calculator The functions listed in the menu are organized into categories Each of these categories expands to display the available functions Tap on a function to open a template Enter data in the appropriate fields Portrait4 a EN ok Calculus Complex Numbers Consumer Applications Date Equations Exponential Finance Hyperbolic Linear Programming Lists Matrices Number Theory Real Numbers Sequences File Edit Samples Help E T F E E F OS O E F F F F 2 Tap ona button Some of the functions have a button assigned to them on the calculator Examples of these are x4y sqrt and 1 x When you select one of these functions it appears in the Input window Enter your data inside the brackets in the input window 3 Enter the function you want directly in the Input window as a string of data Any command including those assigned to a button and those listed in the Functions menu can be entered as a string of data Tap in the Input window Enter the expression you want to evaluate as in the example below Portrait4 at E E3 Input An asterisk must be used to indicate multiplication Implicit multiplication by placing two factors side by side is not supported A caret must be used to indicate an exponent Tips Expressions can be combined in the input window If you are entering more than one expression semicolons must separate the expressions For e
23. alternate hypothesis Description Tests the null hypothesis for one population mean with an unknown population standard deviation The null hypothesis is tested against one of the alternatives specified by the alt hyp value that the actual population mean is less than 1 greater than 1 or not equal to 0 the hypothesized population mean Example ttest 25 21 23 26 30 17 0 t 0 725775 p 0 508165 Input 2 ttest population mean mean Sx n alternate hypothesis Description See description for Input 1 Example ttest 25 23 4 4 9294 5 0 t 0 72579 p 0 508157 Z Test Input 1 ztest population mean standard dey list alternate hypothesis Description Tests the null hypothesis for one population mean with a known population standard deviation The null hypothesis is tested against one of the alternatives specified by the alt hyp value that the actual population mean is less than 1 greater than 1 or not equal to 0 the hypothesized population mean Example ztest 25 4 9294 21 23 26 30 17 1 z 0 72579 p 0 766016 Input 2 ztest population mean standard dev mean n alternate hypothesis Description See description for Input 1 Example ztest 25 4 9294 23 4 5 1 z 0 72579 p 0 766016 Additional Statistical Functions One Way Analysis of Variance Input anova list 13 list 2 list A3 Description Finds a one way analysis of variance for comparing
24. alternate hypothesis Description Tests the null hypothesis that the means of two populations based on independent samples are equal when both population standard deviations are unknown against one of three alternatives specified by the alt hyp value Option 1 If one population mean is less than the other input 1 Option 2 If one population mean is greater than the other input 1 Option 3 If one population mean 1s not equal to the other input 0 Example samp2ttest 23 4 4 9294 5 21 4 8989 5 1 t 0 772202 p 0 231098 Two Sample Z Test Input 1 samp2ztest standard dev 1 standard dev 2 list 1 list 2 alternate hypothesis Description Tests the null hypothesis that the means of two populations based on independent are equal when both population standard deviations are known against one of three alternatives specified by the alt hyp value Option 1 If one population mean is less than the other input 1 Option 2 If one population mean is greater than the other input 1 Option 3 If one population mean is not equal to the other input 0 Example samp2ztest 4 9294 4 8989 21 23 26 30 17 24 18 14 26 13 0 z 1 415703 p 0 156862 Input 2 samp2ztest stan dev 1 stan dev 2 mean 1 71 mean 2 n2 alternate hypothesis Description See description for Input 1 Example samp2ztest 4 9294 4 8989 23 4 5 19 5 0 z 1 415703 p 0 156862 t Test Input 1 ttest population mean list
25. be useful to learn about the properties of the different probability distribution functions ee w normalcdf 0 gt 52 Statistical Tests Statistical tests are used to test the validity of hypotheses Statistical hypotheses are statements regarding the value of population parameters The hypothesis to be tested is called the null hypothesis and it represents the hypothesis or statement that you hope to reject The null hypothesis 1s tested against an alternative hypothesis the hypothesis or statement that you hope to support The null hypothesis is a contradiction of the alternative hypothesis The alternative hypothesis 1s defined as the statement we hope to show to be the case It contains a lt gt or The three possible alternatives that can be entered are Alternative 1 If the alternative hypothesis is less than lt input 1 Alternative 2 If the alternative hypothesis is greater than gt input 1 Alternative 3 If the alternative hypothesis is not equal to input 0 The statistical tests assume that the variances are to be pooled If the variances are not pooled input false after the alternative hypothesis parameter Chi Square Test Input chi2test matrix A Description Calculates a chi square test for association on the row and column variables in the specified matrix It tests the null hypothesis that no association exists between the row and column variables against the alternative that ther
26. by its number of characters The length of a string can be zero or any positive integer Strings are always contained in quotation marks like the string abcdef Substrings are any adjacent sequence of characters in a string To get to the string functions tap the following Functions gt String Find First Input findFirst string A string B position Description Finds the first occurrence after the indicated position pos of the string B in the string A or 1 if none exists Example findFirst abcabcdeb b 1 2 The string b first occurs after position 1 in position 2 Find Last Input findLast string A string B position Description Finds the last occurrence of the string B before the indicated position pos in the string A or 1 if none exists Example findLast abcabcdeb b 6 5 The string b last occurs before position 6 in position 5 Length of a String Input length string A Description Finds the length of a string Example length January 7 The string January is 7 elements long Replace Substring Input replace string A string B position length Description Replaces the substring of A starting at an indicated position pos of indicated length len with B Example replace abcdef xyz 1 3 xyzdef The substring abc is replaced with xyz 57 Find the Substring Input substring string A position
27. default setting for ee the functions or other data that you want to graph in these cells pencil icon to draw a graph the number of points drawn for a graph is 100 If you do not change this setting the table of values will also contain 1 00 points Tap on the colored cell in front of the function to change properties 61 File Menu The File menu enables you to open previously saved data or to save data This menu also enables you to copy and or export any graph images you create You can also close the graphing window from this menu Open Opens a plot It recalls the data from a previously saved plot When you tap Open the Open window template is brought forward Select your data by double tapping on your choice from the list of files This restores the data Tap on the pencil icon to redraw the graph Save Saves the plot data When the Save window opens name your file and save it You can save it using All Files If you save it this way tap on All Files to open it Copy Graphs can be copied and pasted into a word processing document or graphical display software Tap on copy open up your word document and then paste the graph into the document Export Allows for saving the graphical image as a bitmap file which can be moved onto a desktop computer for printing viewing or other uses Close This closes the plotting window Any unsaved data will be lost Edi
28. distribution is always positive always skewed to the right and unimodal The shape of the distribution depends on the degrees of freedom Example chi2paf 5 3 0 0732 Cumulative Chi Square Distribution Input chi2cdf lower bound upper bound degrees of freedom Description Finds the area under the chi square probability distribution between a lower bound and an upper bound where the degree of freedom is specified The degree of freedom must be greater than 0 Example chi2cdf 0 5 1 3 0 1176 F Distribution Input fpdf x numerator degrees of freedom denominator degrees of freedom Description Finds the value of the probability density function for the F distribution at a specified value of x The F distribution is used when independent random samples are drawn from two normal populations with equal variances It is a continuous distribution that is obtained from the ratio of two chi square distributions each of which is divided by the number of degrees of freedom It is used to test the equality of variances of two normally distributed variables and the significance of possible causal variables in a regression Example fpdf 5 10 15 0 0027 Cumulative F Distribution Input fcdf low bound up bound numerator deg of freedom denominator deg of freedom Description Finds the area under the F distribution probability between a lower bound and an upper bound for specified numerator degrees of freedom and denominator degr
29. elements in column 1 to 5 and 15 Frobenius Norm Input norm matrix A Description Finds the Frobenius norm of a matrix The Frobenius norm of a matrix is the square root of the sum of the absolute squares of its elements Example norm matrix 1 3 1 2 3 3 741657 Random Integer Matrix Input randintMatrix m n A B Description Generates an m X n matrix whose entries are random integers between 4 and B Example randIntMatrix 2 2 1 10 matrix 2 2 1 3 6 1 Random Matrix Input randMatrix m n Description Generates an m X n matrix whose entries are random integers between 0 and 1 Example randMatrix 2 2 matrix 2 2 0 27 241 0 360027 0 255287 0 98529 Rank of a Matrix Input rank matrix A Description Finds the rank of a square matrix The rank is the maximum number of linearly independent rows Example rank matrix 2 2 1 2 3 4 2 The number of linearly independent rows is 2 Resize a Matrix Input redim matrix A m n Description Resizes a matrix to the specified dimensions Example redim matrix 1 3 1 2 3 2 4 matrix 4 1 2 3 0 0 0 0 OJ Row Norm Input rNorm matrix A Description Finds the row norm of a matrix Example rNorm matrix 3 3 1 2 3 4 5 6 7 8 9 24 Row Reduction Input rowReduce matrix A Description Finds the row echelon form of a given matrix A matrix is said to be in reduced row echelon form if the following cond
30. enter to calculate Confidence Intervals X number of successes in a sample Xi number of successes in sample 1 X2 number of successes in sample 2 n total number of observations in a sample n total number of observations in sample 1 Ny total number of observations in sample 2 mean mean of the data 47 Sx or std dev standard deviation Conf Lev or CL confidence level list list of data in braces separated by commas Pooled indicates if variances are to be pooled Input true if the variances are to be pooled Input false if the variances are not to be pooled The default setting is false 48 Confidence Interval for One Proportion Input propizint x n ConfLev prop1zint 3000 5000 0 95 Description Finds a confidence level for an unknown proportion of successes in a binomial experiment Example prop1zint 3000 5000 0 95 0 5864 0 6136 Given 3000 successes out of 5000 observations and a confidence level of 95 the confidence interval is 0 5864 lt p lt 0 6136 Confidence Interval for the Difference of Two Proportions Input prop2zint x n x n2 Conf Lev Description Finds a confidence level for the difference between the proportions of successes in two populations Example prop2zint 75 100 50 100 0 99 0 0796 0 4204 Given 75 successes out of 100 observations in the first population and 50 successes out of 100 observations in the second population and
31. factors 1 and the number itself This function returns a Boolean true or false value Ifn is a prime number isPrime returns true otherwise it returns false Example isPrime 7 true Seven is a prime number Square Number Input isSquare n Description Finds whether n is a square number that 1s the square of some integer This function returns a Boolean true or false value If n is a square number isSquare returns true otherwise 1t returns false Example 1 isSquare 7 false Example 2 isSquare 4 true because 4 equals 2 Square Free Input isSquareFree n Description Finds whether n is divisible by the square of a number This function returns a Boolean true or false value If n is divisible by the square of a number isSquareFree returns false otherwise it returns true Example 1 isSquareFree 8 false because 8 is divisible by 4 and 4 is a square of 2 Example 2 isSquareFree 70 true because 70 is not divisible by the square of a number Least Common Multiple Input Icm m n Description Finds the least or lowest common multiple of m and n The least common multiple 1s the least number that is a multiple of both numbers Example lcm 56 46 1288 The least common multiple of 56 and 46 is 1288 Nines Excess Input ninesExcess r Description Finds the nines excess of n To find the nines excess add the digits of a number and repeat with the sum if necessary until you arrive at a single di
32. function to pass the vertical line test Ifa vertical line intersects a graph at most once it is the graph of a function To get to the trigonometric functions tap the following Functions gt Trigonometric Sine Input sin x Description Denotes the trigonometric sine function Sine is the ratio of the length of the side that is opposite the angle to the length of the hypotenuse Example sin pi 4 0 7071 using Radians mode Cosine Input cos x Description Denotes the trigonometric cosine function Cosine is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse Example cos pi 4 0 7071 using Radians mode 58 Tip Tangent Input tan x Description Denotes the trigonometric tangent function Tangent is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle Example tan pi 4 1 00 using Radians mode Cosecant Input csc x Description Denotes the trigonometric cosecant function Cosecant is the ratio of the hypotenuse to the length of the side opposite the angle Example csc pi 4 1 4142 using Radians mode Secant Input sec x Description Denotes the trigonometric secant function Secant is the ratio of the hypotenuse to the length of the side adjacent to the angle Example sec pi 4 1 4142 using Radians mode Cotangent Input cot x Description Denotes the trigonometric cotangent function Cotangent
33. is 2 Answers generated are approximate Local Maximum of a Function Input fmax function variable lower limit upper limit Description Finds the value at which a local maximum of the function occurs with respect to the variable and the lower and upper limits given A local maximum is any vertex of a function that is higher than its neighboring points It is not necessarily the absolute maximum Example fmax x43 12 x 1 x 3 1 2 A local maximum of this function in the interval 3 1 is 2 Answers generated are approximate Graphing Calculus Functions Graphing functions will in most cases provide a deeper understanding of the functions being explored To graph a function select the Plot menu on the calculator and choose the Plot y f x option Enter or copy and paste the function you want graphed under the f x header You must enter the domain of the function under the x from and x to headers The range is optional Portrait4 iaa Input derid x 3 12 x 1 x 4 Enter Cor copy and paste this function into the Plot y fix graphing window The boxed portion of the template and the input window above represents the function that can be graphed The y or f x part of the function is assumed Copy this portion of the input and then open a Plot y f x graphing window Paste the function under the f x header Enter the domain you want the function graphed over The range is optional
34. is the ratio of the length of the side adjacent to the angle to the length of the side opposite the angle Example cot 1 0 64029 using Radians mode For all of the trigonometric functions the default setting is radians If your input is in degrees select Degrees from the Mode section of the Options menu of your device Inverse Trigonometric Functions Inverse of Sine Input arcsin x or asin x Description Denotes the inverse of the trigonometric sine function The inverse of the sine function is defined by y arcsin x only if x sin y for 1 lt x lt 1 and pi 2 lt y lt pi 2 radians Example 1 arcsin 1 1 5708 radians Example 2 arcsin 2 1 5708 1 3170 I Inverse of Cosine Input acos x or arccos x Description Denotes the inverse of the trigonometric cosine function The inverse of the cosine function is defined by y arccos x only if x cos y for 1 lt x lt 1 and 0 lt y lt pi radians Example arccos 1 0 radians Inverse of Tangent Input atan x or arctan x Description Denotes the inverse of the trigonometric tangent function The inverse of the tangent function is defined by y arctan x only if x tan y for every x and pi 2 lt y lt pi 2 radians Example arctan 1 0 7854 radians 59 60 Inverse of Cosecant Input acsc x or arccsc x Description Denotes the inverse of the trigonometric cosecant function The inverse of the cosecant function is defined by y arccsc x only if
35. menu open and select the operation you want e Unassign If you select this unassign appears in the Input window Enter the variable you want unassigned Tap the equal sign to remove the assigned variable from the memory e Unassign All If you select this unassign all appears in the Input window Tap the equal sign to remove all of the assigned variables from the memory The result of assigning a value to a variable or unassigning one or more variables is the Boolean value true 17 Generating a Graph from the List Matrix Sequence or Table Editor The data in each of the List Matrix Sequence and Table Editors can be used to create graphs The data in these editors can be sent to one of the graphing templates listed to make a visual representation of the data To generate a graph from an Editor 1 Enter the data in the List Matrix Sequence or Table Editor 2 Tap the Edit menu open 3 Open Send To in the Edit menu Send To provides a list of graphing templates available for the Editor you are using Each Editor has different graphing templates available The List Editor has the choices shown here 4 Select the type of graph you want by tapping on your choice This opens the chosen graphing template with the data from the Editor already entered 9 Tap the pencil icon to draw the graph Bar Graph Box and Whisker Plot Histogram Pie Graph Tip If you only want a portion of the data graphed you m
36. on the pencil icon to redraw the graph with the new selections The Properties window for the Curves of Best Fit graphing window has an additional feature called Curves Use this property to indicate the type of curve you want to fit to your data For more information see the section on Curves of Best Fit on page 71 67 The Properties window for the function plots Plot y PALTA ixi f x graphing window has an additional feature called Shading Use this property to shade portions of the adin Pattern graph that are less than less than or equal to greater a than or greater than or equal to the function The feature UW O eee O also lets you select from six different patterns of shading HH I C Xoll o Other Graphing Icons There are icons on the task bar of each graphing window The icons to the right of the File Edit and Tools menus perform the following functions _ Draw the plot when new data is entered or any of the options have been changed Tap on this button to send the information in the data entry window to the Table Editor to see a table of values To return to the data entry window tap on this button again Remember the number of points plotted has an impact on the table of values Each point plotted is represented in the table of values To change the number of points plotted open Properties window by double tapping on a colored cell in a column or row header in a data entry window de
37. that is less than or equal to x Integers are positive and negative whole numbers and 0 Example floor 2 56 2 The largest integer that is less than or equal to 2 56 is 2 Fractional Part Input fracPart x Description Finds the fractional part of a real number Example fracPart 37 75 0 75 The fractional part of 37 75 is 0 75 Integer Part Input intPart x Description Finds the integer part of a real number Example intPart 37 75 37 The integer part of 37 75 is 37 Sequences A sequence is a list of elements or numbers that succeed or follow each other in a specific order or pattern To get to the sequence functions tap the following Functions gt Sequences 46 Product of a List Input prod list of values Input 1 List Form prod 1 2 3 4 Description Finds the product of a list of values Note The list of values to be multiplied must be contained within braces within the brackets This will differentiate this product from the product of the results obtained by evaluating an expression for a given range of values Example prod 1 2 3 4 24 Multiplying 1 x 2 x 3 x 4 24 Input 2 Parameter Form prod equation variable first in range last in range Description Finds the product of a list of results for a variable evaluated under a given expression for a given range The first value in the range must be less than or equal to the last value in the range and th
38. the Input window normalpdf x mean standard deviation To calculate a probability value from the normal distribution enter a value of 2 for x a mean of 10 and a standard deviation of 3 For example normalpdf 2 10 3 0 003799 Function Plot etx 5 42 ES This is the same information that must be entered in the column under the header f x in the Plot y f x window Enter the function description in this case it is normalpdf and within the brackets enter the variable x followed by the values for the mean and the standard deviation It is important that a domain x from and x to is also entered otherwise a syntax error occurs The graph to the left shows the normal distribution of x with a mean of 10 anda standard deviation of 3 Normal Distribution pp pp There must always be an x variable as part of the input For all the probability distributions that contain pdf the x variable is a part of the function Some of the cdf distributions do not include a variable To graph these distributions you must decide which value to make the x variable Typically the upper bound 1s designated as the x variable For example for cumulative normal distributions make the upper bound the x variable and enter normalcdf 0 x 10 3 See the graph to the right Cumulative Normal You can also plot many probability distributions or pdf and cdf versions of distributions on the same graph for comparison purposes This can
39. the changes are automatically applied to your graph Function Plot Er dx 4 31 ok Plot title Enter a title The default title for each graph 1s beis the name of the type of graph ss dl Al x axis label Label the x axis The default label is x y axis label y axis label Label the y axis The default label is y x axis ticks x axis ticks Put tick marks on the x axis The default is 4 y axis ticks Alion ticks above y axis ticks Put tick marks on the y axis The default is 4 L the X axi5 e e e Align ticks to right Align ticks above the x axis Place tick marks and values E of y axis above the x axis Align ticks to the right of the y axis Place tick marks and values to the right of the y axis Options Mode Samples Hoc Labels AXES md p Degrees Interprets or reports angle measures in degrees Radians Interprets or reports angle measures in radians Paste Delete Clear Erase All A check mark indicates your selection 63 Options Axes Samples Options Normal The x and y axes intersect at the origin The normal view of a box plot is a number line Framed The x and y axes intersect at the lowest x and y coordinates Boxed Places a box around the framed view of the graph None Removes all of the axes A check mark indicates your selection Pie graphs and histograms do not have these options Options Scaling Samples Options
40. the means of 2 to 20 populations The null hypothesis that the population means are equal is tested against the alternative hypothesis that they are not equal Example anova 3 4 2 7 5 6 3 8 15 7 9 4 F 1 131737 p 0 364389 df 2 SS 10 5 MS 5 25 df 9 SSE 41 75 MSE 4 638889 Geometric Mean Input geomMean x y Z Description Finds the geometric mean of a list of data The geometric mean of a list of n numbers is the n root of the product of these numbers Example geomMean 1 5 9 7 2 4 243 The product of this list of numbers is 324 and the fourth root of 324 1s approximately 4 243 Lower Quartile Input lowerQ x y Z y Description Finds the lower quartile of a list of data The lower quartile 1s the median of the lower half of a set of data Example lowerQ 5 6 7 8 9 5 5 The median of the lower half of this set of data is 5 5 55 56 Maximum Input max x y Z Description Finds the maximum of a list of numbers The maximum is the largest value in a set of data Example 1 max 1 2 4 5 0 5 Five is the largest value in this set of data Example 2 max primeSet 12 3 The largest number in the prime set of 12 is 3 Arithmetic Mean Input mean x y Z Description Finds the arithmetic mean of a list of numbers Also called the average the mean 1s the sum of the values divided by the number of values used in computing
41. value The future value 1s the value an investment will have at a future time if it earns compound interest at a specified rate Example tvm_fv 36 18 0 145 12 12 pmt_end 6855 02 The future value of the annuity is 6 855 02 Finance Cash Flow Analysis To get to the Cash Flow Analysis functions tap the following 30 Functions Finance Cash Flow Analysis Number of Cash Flow Periods Input cfCount list Description Returns the number of periods in the given cash flow list excluding the initial cash flow Example cfCount 1000 1500 2000 2500 30001 4 Excluding the initial cash flow period there are 4 cash flow periods in this list Internal Rate of return Input cfIRR list Description Returns the internal rate of return of the list of cash flows Example cfIRR 3000 1500 2000 2500 30004 54 8 The internal rate of return of this list of cash flow is 54 8 Modified Internal Rate of Return Input cfMIRR interest rate list Description Returns the modified internal rate of return of the list of cash flows Example cfMIRR 10 5000 4000 3000 2000 26 5773 The modified internal rate of return 1s 26 5773 Net Future Value Input cfNFV interest rate list Description Returns the net future value of the list of cash flows Example cfNFV 10 5000 4000 3000 2000 3485 00 The net future value is 3 485 Net Present Value Input cfNPV interest rate list
42. variable between the lower and the upper bounds given making the function equal to zero When solving for a variable in an equation it is assumed that the equation is equal to 0 You can however also enter equations in the form x x 1 Example fsolve x43 3 x 2 10 x x 10 10 5 The solution of x for this equation between the upper and lower bounds given is 5 Graphing a Single Equation Graphing an equation can help you in determining the lower and upper bounds that you want to evaluate the equation between A graph shows you how many roots an equation has Remember that each time a graph crosses the x axis there is a different root of the equation For example the graph of the equation x 3 3 x 2 10 x crosses the x axis three times indicating three roots To graph the equation open a Plot y f x window Type or copy and paste the equation you want graphed under the f x header You must enter the domain of the function under the x from and x to headers The range is optional but may be helpful in getting a clearer picture of the graph 23 To find all three roots of this equation evaluate fsolve three times using different lower and upper bounds each time To approximate the appropriate lower and upper xo S43 Fc 2 10 x bounds for each root look at the graph and estimate the d value where the graph crosses the x axis Choose a lower bound less than this value and an upper bound greater than this value making sure th
43. x csc y for x 1 and pi 2 lt y lt pi 2 radians y 0 Example arccsc 1 1 5708 radians Inverse of Secant Input asec x or arcsec x Description Denotes the inverse of the trigonometric secant function The inverse of the secant function is defined by y arcsec x only if x sec y for x gt 1 and y in 0 pi 2 or in pi 2 pil Example arcsec 1 0 radians Inverse of Cotangent Input acot x or arccot x Description Denotes the inverse of the trigonometric cotangent function The inverse of the cotangent function is defined by y arccot x only if x cot y for x 0 and pi 2 lt y lt pi 2 radians Example arccot 1 0 7854 radians Arctan2 Input arctan2 y x Description Finds the angle counterclockwise from the x axis to the vector x y position It equals arctan y x when x 0 and returns the appropriate angle measure if x 0 Example arctan2 1 1 0 7854 radians Convert Radians to Degress Input rad2deg angle Description Converts an angle measure in radians to degrees Example rad2deg 1 57 29578 Convert Degrees to Radians Input deg2rad angle Description Converts an angle measure in degrees to radians Example deg2rad 57 29578 1 Plots Menu and Graphing Portrait 4 has twelve different graphing templates including bar graphs box and whisker plots best fit or regression curve plots histograms pie graphs normal probability plots functions plots polar plots param
44. 0 Interest Rate of an Annuity Input tvm_int of payments present value payment future value payment periods compounding periods pmt_due Description Finds the annual interest rate Example tvm_int 60 12000 300 0 12 12 pmt_end 17 2734 An annuity with a present value of 12 000 provides 60 300 payments twelve times a year The interest rate the annuity earns is 17 2734 Present Value of an Annuity PV Input tvm_pv of payments interest payment future value payment periods compounding periods pmt_due Description Finds the present value of an annuity Example tvm_pv 24 7 5 100 0 12 4 pmt_end 2223 28 To receive 24 equal payments of 100 twelve times a year the present value of the annuity earning 7 5 interest compounded four times a year is 2 223 28 Amount of Each Payment in an Annuity Input tvm_pmt of payments interest present value future value payment periods compounding periods pmt_due Description Finds the amount of each payment Example tvm_pmt 36 18 5000 0 12 12 pmt_end 180 76 Given an annuity with a present value of 5 000 that earns 18 interest compounded 12 times a year you receive 36 equal payments 12 times a year until the future value is equal to 0 Each payment is 180 76 29 Future Value of an Annuity FV Input tvm_fv of payments interest present value payment payment periods compounding periods pmt_due Description Finds the future
45. 2 10 10 30 00 am Saturday April 8 1995 Three days and two months were added to the original date and 10 years were subtracted Adjust a Time Input adj Time date hours minutes seconds Description Adds or subtracts a number of hours minutes and seconds from a given date Example adj lime makeDate 5 2 2005 10 30 0 4 10 45 02 40 45 pm Saturday February 5 2005 Four hours 10 minutes and 45 seconds were added to the original time Difference Between Two Dates Input diffDates date 1 date 2 Description Finds the difference in days between two dates Example diffDates makeDate 5 2 2005 0 0 0 makeDate 9 6 2014 0 0 0 3411 The difference between the two dates is 3411 days Find the Hours Input hours date Description Finds the hours in a given date time Example hours makeDate 5 2 2005 10 30 0 10 In the given date and time there are 10 hours Create a Date Object Input makeDate day month years hours minutes seconds Description Creates a date time object Example makeDate 4 3 1975 4 16 32 4 16 32 am Tuesday March 4 1975 Find the Minutes Input minutes date Description Finds the minutes in a given date time Example minutes makeDate 5 2 2005 10 30 0 30 In the given date and time there are 30 minutes Find the Month Input month date Description Finds the month in a given date Example month makeDate 5 2 2005 10 30 0
46. 2 and 3 Shift Left Input shiftl m n Description Shifts the integer m left by n bit positions Example shiftl 15 4 240 The integer 15 is converted to a binary number and is shifted 4 bits to the left The binary number after the shift is then converted back to an integer 240 Shift Right Input shiftr m n Description Shifts the integer m right by n bit positions Example shiftr 64 2 16 The integer 64 is converted to a binary number and is shifted 2 bits to the right The binary number after the shift is then converted back to an integer 16 Sum of the Factors Input sigma n Description Finds the sum of all the factors of n A factor of a number is a number that divides exactly into it Example sigma 12 28 The sum of the factors of 12 is equal to 1 2 3 4 06 12 28 Real Numbers To get to the real number functions tap the following Functions Real Numbers Absolute Value Input abs x Description Finds the absolute value of x The absolute value of a number is its distance from zero on a number line Example abs 12 12 The absolute value of 12 is 12 Smallest Integer Input ceil x Description Finds the smallest integer that 1s greater than or equal to x Integers are positive and negative whole numbers and 0 Example ceil 2 56 3 The smallest integer that is greater than or equal to 2 56 is 3 45 Largest Integer Input floor x Description Finds the largest integer
47. 492 7101 Copyrights and Trademarks Portrait 4 1s a registered trademark pending of MathResources Inc Windows and WindowsCE are registered trademarks of Microsoft Corporation The User s Guide to Portrait 4 and Portrait 4 are copyright of MathResources Inc No part of this manual or Portrait 4 may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying and recording for any purpose without the express written permission of MathResources Incorporated 82
48. 6 compounded twice a year over a term of 5 years the accumulated amount is 134 39 Bond Accrued Interest Input bondA settlement date maturity date compounding periods coupon rate par value Description Returns the accrued interest of a bond Example bondA makeDate 1 1 2003 makeDate 15 12 2015 2 8 1000 36 67 The interest that has accrued on the bond since the last interest payment is 36 67 Bond Price Input bondP settlement date maturity date compounding periods coupon rate residual value annual yield Description Returns the price of a bond Example bondP makeDate 1 1 2003 makeDate 1 1 2015 2 6 5 100 5 524 108 48 The price of the bond is 108 48 Bond Yield Input bondY settlement date maturity date compounding periods coupon rate residual value price Description Returns the yield of a bond Example bondY makeDate 1 1 2003 makeDate 1 1 2015 2 6 5 100 108 48 5 524053 The bond yield is 5 524 31 32 Effective Rate of Interest Input eff nominal rate compounding periods Description Finds the effective rate of interest that is the simple interest rate that would produce the same accumulated amount in one year as the nominal or stated rate compounded c y times a year The effective rate of interest 1s often used to compare compound rates of interest Example eff 6 2 6 09 Given a nominal rate of interest of 6 compounded twice a year the simple interes
49. D list A Description Sorts a list of numbers into descending decreasing order Example sortD 1 2 3 4 5 5 4 3 2 1 Sort Indices Input sortindices list A true ascending false descending Description Sorts a list and returns the indices locations of the sorted elements within the original list Example sortindices f 1 8 6 0 4 true 1 4 5 3 2 Matrices Matrices are rectangular arrays of numbers The numbers that comprise the array are called elements or entries The elements are arranged in rows and columns and the size of the matrix is then stated as the number of rows by the number of columns See the section on the Matrix Editor on page 14 for information on inputting matrices To get to the matrix functions tap the following Functions gt Matrices Arithmetic with Matrices Simple arithmetic operations on matrices are not part of the Matrices function menu These calculations are very easy to perform Simply enter the matrices you want to add subtract or multiply making sure the proper operation symbol separates them An asterisk must be used to indicate multiplication A caret must be used to indicate an exponent Tap on the equal sign or press Enter for the result Adding Matrices The sum of matrices is obtained by adding corresponding elements in two or more matrices Matrices must be the same size to be added Adding matrices of different sizes gives an error Example matrix
50. Example 9 lt 4 false e gt greater than x gt y tests whether x is greater than y It is true if x is greater than y and false if x is less than or equal to y Example 9 gt 4 true e lt less than or equal to x lt y tests whether x is less than or equal to y It is true if x is less than or equal to y and false if x is greater than y Example 12 lt 16 true e gt greater than or equal to x gt y tests whether x is greater than or equal to y It is true if x is greater than or equal to y and false if x is less than y Example 12 gt 16 false e 1s equal to x y tests whether x is equal to y It is true if x is equal to y otherwise it is false Example 3 4 7 true e lt gt not equal to x lt gt y tests whether x is not equal to y It is true if x is not equal to y and false if x is equal to y Example 3 4 lt gt 7 false Order of Operations When evaluating expressions the calculator does so in a particular order The order from highest precedence to lowest precedence 1s as follows Casting integer boolean double Factorial 1 Exponentiation Multiplicative mod Additive Relational lt gt lt gt lt gt Boolean amp xor If you are uncertain about the order simply use brackets Functions Menu Portrait 4 has over 200 functions The three ways to access the functions are 1
51. The determinant of this 2 x 2 matrix is 2 Dimension Input dim matrix A Description Returns the dimensions of a matrix Example dim matrix 2 3 1 2 3 4 5 6 2 3 39 40 Dot Product Input dotProd matrix A matrix B Description Finds the dot product of two n vectors 1 X n matrices Example dotProd matrix 1 3 1 2 3 matrix 1 3 1 2 3 14 Fill a List or Matrix Input fill matrix A n Description Returns a list or matrix containing copies of a value Example fill matrix 2 2 1 2 3 4 6 matrix 2 2 6 6 6 6 Identity Matrix Input ident Description Returns the Identity matrix of a given size The Identity matrix is a square matrix of size n having 1s along the main diagonal and zeros everywhere else Example ident 2 matrix 2 2 1 0 0 1 Inverse of a Matrix Input inverse matrix A Description Finds the inverse of a square matrix The inverse of a matrix 1s that matrix that when multiplied by the given matrix returns the identity matrix A matrix multiplied by its inverse will give you the identity matrix Not all matrices have inverses Example inverse matrix 2 2 1 2 3 4 matrix 2 2 2 1 1 5 0 5 Singular Input isSingular matrix A Description Finds whether or not a matrix has an inverse A matrix that does not have an inverse is singular This function returns a Boolean true or false value If the matrix is singular that is i
52. a 99 confidence level the confidence interval is 0 0796 lt p lt 0 4204 Two Sample Interval Input 1 samp2tint list 1 list 2 Conf Lev Description Finds the confidence interval for the difference between two population means when standard deviations of the two populations are unknown Example samp2tint 20 29 30 26 21 28 21 27 21 20 0 99 7 1645 10 7645 Input 2 samp2tint mean 1 Sx n mean 2 Sx n2 Conf Lev Description Finds the confidence interval for the difference between two population means when standard deviations of the two populations are unknown Example samp2tint 25 2 4 5497 5 23 4 3 7815 5 0 99 7 1644 10 7644 Two Sample Z Interval Input 1 samp2zint std dev 1 std dev 2 list 1 list 2 Conf Lev Description Finds a confidence interval for the difference between two population means when the standard deviations of the two populations are known Example samp2zint 4 5497 3 7815 20 29 30 26 21 28 21 27 21 20 0 99 5 0150 8 6150 Input 2 samp2zint std dev 1 std dev 2 mean 1 n mean 2 n Conf Lev Description Finds a confidence interval for the difference between two population means when both standard deviations are known Example samp2zint 4 5497 3 7815 25 2 5 23 4 5 0 99 5 0150 8 6150 t Interval Input 1 tinterval list Conf Lev Description Finds a confidence interval for an unknown po
53. a complex number in rectangular form to polar form Example toPolar 3 I 3 162278 0 321751 r 0 Covert from Polar Form to Rectangular Form Input toRect list The list is equal to r 0 Description Converts a complex in polar form to rectangular form Example toRect 2 pi 2 0 I Consumer Applications As well as many plotting and calculation functions Portrait 4 includes helpful templates for everyday calculations These are found in the Functions menu under Consumer Applications When you select an application a template opens similar to the Function templates Enter any value or expression appropriate to the application in the entry cells Tap on the Show Result button to display the result Close the window by tapping ok in the top right corner Portrait4 Fa SN Plots Calculus Complex Numbers Car Loan Credit Card Debt General Loan Investment Return Finance Mortgage Hyperbolij Tip Calculator Linear Programming Show Result Lists Matrices Number Theory Real Numbers Sequences ke ai 21 Date The date functions use a 24 hour clock One am is entered as 1 while 1 pm is entered as 13 Dates are entered as day month and year To get to the date functions tap the following Functions Date 22 Adjust a Date Input adjDate date day months years Description Adds or subtracts a number of days months and years from a given date Example adjDate makeDate 5 2 2005 10 30 0 3
54. about entering strings of data in the Input window When a Function is selected from the menu a template opens for that function The template indicates the order and nature of the function s arguments that must be entered to obtain a result Results are obtained by tapping on the Show Result button Function Templates on is the default setting as indicated by the check mark If you want to turn this option off go to the Options menu and deselect Functions Templates If you now select Options a second time Function Templates no longer has a check mark beside it Most function arguments have an entry field followed by a brief description In most entry fields you can enter any expression involving values operators and functions Some entry fields require a variable or a list the description indicates if this is the case If you are required to enter a list the list must be contained within braces Some arguments are represented by a group of buttons You can select any of the buttons to indicate your choice for that argument The results displayed in the Show Result window are followed by the parameters used to obtain that result If you are experimenting with different values for a specific parameter this will help you compare results Portrait4 a 2957 ok Portrait4 Page EEN ok _ less than 4 not equal to greater than List Form Parameter Form Sequence Form Matrix Form Some functions have multiple forms that is
55. acters in a string Converting between Data Types Casting To convert a value to a different data type insert the desired type in parentheses before the value to be converted Casting takes effect before any other operation Converting to an Integer To convert either a Boolean or a decimal number to an integer integer va ue converts the true or false value to an integer The conversion rules are e The Boolean value true is converted to 1 Example integer true 1 e The Boolean value false is converted to 0 Example integer false 0 e Decimal number values are truncated to the largest integer less than the decimal number Example integer 5 75 5 Converting to a Decimal To convert either a Boolean or integer type to a decimal number double va ue converts the true or false value to a decimal number The conversion rules are e The Boolean value true is converted to 1 0 Example double true 1 0 This is displayed on the calculator as 1 but it is stored as 1 0 in the calculator e The Boolean value false is converted to 0 0 Example double false 0 0 This is displayed on the calculator as 0 but it is stored as 0 0 in the calculator e Integers are converted to the same value but are stored internally as decimal numbers This is convenient when using integers in an expression that might overflow the range of integer values Example double 5 5 0 Example 5 1000 1000 1000 overflows the in
56. alternative hypothesis is that one population standard deviation is less than the other input 1 If the alternative hypothesis is that one population standard deviation is greater than the other input 1 If the alternative hypothesis is that one population standard deviation is not equal to the other input 0 Example samp2ftest 21 23 26 30 17 24 18 14 26 23 1 F 1 0125 p 0 495342 Input 2 samp2ftest Sx1 n1 Sx2 n2 alternate hypothesis Description See description for Input 1 Example samp2ftest 4 9294 5 4 8989 5 1 F 1 012491 p 0 495345 Two Sample Test Input 1 samp2ttest list 1 list 2 alternate hypothesis Description Calculates an f test to compare two normal population standard deviations where the population means and standard deviations are all unknown The ratio of sample variances Sx Sx is used to test the null hypothesis that the ratios are equal against one of the three alternatives specified by the alt hyp value If the alternative hypothesis is that one population standard deviation is less than the other input 1 If the alternative hypothesis is that one population standard deviation is greater than the other input 1 If the alternative hypothesis is that one population standard deviation is not equal to the other input 0 Example samp2ttest 21 23 26 30 17 24 18 14 26 23 1 t 0 772187 p 0 231102 Input 2 samp2ttest mean 1 Sx1 nl mean 2 Sx2 n2
57. ard deviation of a list of numbers The standard deviation is equal to the square root of the variance Example stdP 1 4 0 7 7 2 93 The standard deviation is the square root of the variance Sample Standard Deviation Input stdS x y z Description Finds the sample standard deviation of a list of numbers The standard deviation 1s equal to the square root of the variance Example stdS 1 4 0 7 7 3 27 The standard deviation is the square root of the variance Upper Quartile Input upperQ x y Z Description Finds the upper quartile of a list of data The upper quartile is the median of the upper half of a set of data Example upperQ 5 6 7 8 9 8 5 The median of the upper half of this set of data is 8 5 Population Variance Input varP x y z Description Finds the population variance of a list of numbers The variance 1s the mean value of the squares of the deviations from the mean of the data Example varP 1 4 0 7 7 8 56 The variance of this set of data is 8 56 Sample Variance Input varS x y z Description Finds the sample variance of a list of numbers The variance is the mean value of the squares of the deviations from the mean of the data Example varS 1 4 0 7 7 10 70 The variance of this set of data is 10 70 String A string 1s a finite sequence of characters like numerals letters and symbols The length of a string 1s determined
58. at the graph crosses the x axis only once between these two bounds Function Plot ir x520 ES In the graph of x 3 3 x 2 10 x the graph crosses the x axis between 6 and 4 These are appropriate choices for lower and upper bounds to determine the value of x at this point The graph also crosses the x axis between 1 and 1 and again between 1 and 3 Calculating fsolve with these three sets of lower and upper bounds gives you the three correct roots of the function The tracking tool which is available on the graph is helpful in determining suitable bounds and the approximate root locations Solving Systems of Linear Equations Input solve equation 1 equation 2 list of variables Example solve x y 1 x y 0 x y finds the common solution for x and y in the two given equations In this example x 0 5 and y 0 5 Tips When solving systems of linear equations you can enter as many equations as you want Remember to use braces around the list of equations Equations must also be separated by commas or you get an error The system of equations must be followed by a complete list of the variables in the equations A comma must separate the list of equations from the list of variables The list of variables must be in braces and the variables must be separated by commas If not a syntax error occurs The equations entered must be linear equations If you enter a non linear equation you get an error m
59. ay highlight the information to be sent to the graphing template otherwise the entire set of data will be sent You can select any rectangular region of cells by tapping in one corner of the region and dragging the stylus to the other corner Calculus Calculus is a branch of mathematics that was developed by Gottfried Leibniz and Isaac Newton during the 17 century as a way of solving measurement problems in physics and geometry Today calculus has far reaching applications in many fields that study the dynamics of change Using calculus you can measure and describe rates of change and their impact The word calculus is derived from the Latin for pebble The ancient Romans and Greeks making the first calculators used pebbles as counters on counting tables There are two branches of calculus differential calculus and integral calculus Differential calculus deals with measuring the instantaneous rate of change of one quantity relative to the change in another quantity and finding the slope of the tangent to a curve at a certain point Integral calculus involves finding the area under a curve These two branches of calculus are inverses of one another To get to the calculus functions tap the following Functions Calculus Derivative of a Function Input deriv function variable value delta Delta is optional Description Finds the derivative of the function with respect to the variable You must provide the value at which to fin
60. be the graphs Using one of these reserved words as a variable name Portrait4 a EE ok Variable Value g Co generates a syntax error If an error is generated the window will not close and the row containing the error Paste is highlighted Delete Clear A variable can hold a value of any type including a list or matrix or even an expression to be evaluated later The name of a variable must start with a letter and contain only letters numbers or underscores Insert Row Delete Row E To Assign a Value to a Variable in the Input Window e x x 5 assigns x the value of 5 You can also assign any expression to x and evaluate it later Example 1 x 5 6 The expression remains unevaluated If you then use x in an expression the calculator looks up the expression evaluates it and returns the answer You can assign values or expressions to more than one variable Example 2 x 2 y y 2 Evaluating x now returns the answer 4 If you now set y 3 and evaluate x the result is 6 Remember you can also assign matrices or lists to a variable Example 3 x 1 2 3 4 sum x 10 e If you are using the List Matrix or Sequence Editor there is a field available to enter a variable that you want to assign to the list sequence or matrix To Unassign a Variable The Edit menu includes two operations that allow you to unassign a variable or unassign all variables if more than one is assigned Tap the Edit
61. cconcconnccononons 31 Y PEFDOMNE FUNCION SS Sii 33 INVERSE HYPERBOLIC FUNCTION ado 34 LIME ar Programming dido 35 GRAPHING LINEAR INEQUAL MES dai tii 36 ES Oe E re ee 36 E E pete ee 37 DVS Shih woos win tent O iaa 38 Number TNEOry FUNCIONS dias 42 FSI A AN 45 e A A A A A A 46 statistical Funcion Start it Mees oz 47 CONFIDENCE INTERVAES artesa reactor iio ne ada 47 aaa RAE so AS A yh tacard setennta 49 GRAPHING PROBABILITY DISTRIBUTIONS ccsecccssecccseccccssccnsecccescccnsscccescccusscceeesceussceceeceusncceueecensnceeaseceusceeasess 52 a SS AA AI O A AS 53 ADDITIONAL STATISTICAL FUNCTIONS a a LS eiiie 55 A A o are tec ate Belted table tN cite Sl ct Netra sl seb ts lbh sida Ad a ws at ara T 58 TAMOS TING F ACTIONS icra satan a a sit nn citing alone rere este ena Sa ao ela es eta a etme 58 INVERSE TRIGONOMETRIC FUNG TIONS 55g ss acl tstua ies ER ee 59 PLOT Menu and e219 a1 A A AAA A E 61 FEE MENU a o o a O 62 FILE MEN Didi 62 EDIPMEN dio 62 POOLS MEN dao 65 CHANGING COLORS POINTS AND OTHER PROPERTIES occcccnnnnnnnnninocccccncccnonnnnnnnnnnnnnnonononnncncnnnnnnnnnnnnnnnnnnnnnnnorncnnnnnnos 66 OTHER GRAPHING ICONS dida 68 A saben AE E AE E ETN 69 BOX and WDISKEr at 70 CUIN eS OP BOSE Filia dba 71 A 73 PESETAS aaa 74 elo str ODOUR eaa a 0 SE E E EEEE EE E E TE E ENE 75 Grabis o UM CUO sara T tabs taeda 76 BON Ae AA A A A A aera ote Paniee bad donne AS TI SEMI AAA a E rd isu A nneisoned berate 78
62. ctions and their inverses can be used to solve a variety of problems in engineering and the physical sciences They are a group of functions of an angle originally defined in terms of trigonometric or exponential functions All of the hyperbolic functions are defined for complex numbers To get to the hyperbolic functions tap the following Functions gt Hyperbolic Hyperbolic Sine Input sinh x Description Denotes the hyperbolic sine function The hyperbolic sine function is defined as e e 2 for every real number x Example sinh e 7 544 Hyperbolic Cosine Input cosh x Description Denotes the hyperbolic cosine function The hyperbolic cosine function 1s defined as e e 2 for every real number x Example cosh e 7 610 33 Hyperbolic Tangent Input tanh x Description Denotes the hyperbolic tangent function The hyperbolic tangent function is defined as sinh x cosh x Example tanh e 0 991 Hyperbolic Cosecant Input csch x Description Denotes the hyperbolic cosecant function The hyperbolic cosecant function is defined as 1 sinh x where x 0 Example csch e 0 133 Hyperbolic Secant Input sech x Description Denotes the hyperbolic secant function The hyperbolic secant function is defined as l cosh x Example sech e 0 131 Hyperbolic Cotangent Input coth x Description Denotes the hyperbolic cotangent function The hyperbolic cotangent function is defined as cosh x sinh x
63. ctions that are not algebraic Exponential and logarithmic functions are inverses of one another They have a wide variety of applications in mathematics and science All of the exponential and logarithmic functions are defined for complex numbers John Napier 1550 1617 originally developed the natural logarithm as an aid for multiplication and division Henry Briggs 1561 1630 who proposed that base 10 logarithms would be more useful later developed the common logarithm To get to the exponential logarithmic functions tap the following Functions gt Exponential Exponential Function Input exp x Description Denotes the exponential function e This is equivalent to the calculator expression e x Exponential functions have a constant base and a variable exponent They are continuous Example exp 2 7 389 25 Logarithm Input In x or log x Description Denotes the natural logarithm function The natural logarithm has an irrational base the constant e which is named for Leonard Euler Example 1 In e 2 2 Example 2 log 1 3 1415 I Base 10 Logarithm Input log10 x Description Denotes the base 10 logarithm It is also called the common logarithm Example log10 100 2 Base a Logarithm of x Input log a x Description Finds the logarithm to base a of x This function must be entered in the Input window Place square brackets around the first number and curved brackets around
64. d the derivative The derivative of a function is a function whose value at x 1s the slope of the tangent to the graph of the original function The derivative can also be thought of as a function whose value at x is the instantaneous rate of change of the original function with respect to x at point x Example deriv 2 x 3 1 x 1 6 0000 The derivative of 2x 1 with respect to x at x 1 is 6 18 Integral of a Function Input fint function variable lower limit upper limit Description Finds the numerical integral of the function with respect to the variable A lower and an upper limit must be given The integral of a function equals the area of the region between the graph of the function and the x axis with sections below the x axis counting as negative areas Example fint 2 x 3 x 1 4 24 The integral of the expression from 1 to 4 is 24 The signed area of the region between the graph of the function within the specified limits and the x axis 1s equal to 24 Local Minimum of a Function Input fmin function variable lower limit upper limit Description Finds the value at which a local minimum of the function occurs with respect to the variable The lower and upper limits must be given A local minimum is any vertex of a graph of a function that is lower than its neighboring points It is not necessarily the absolute minimum Example fmin x3 12 x 1 x 3 3 2 A local minimum of this function in the interval 3 3
65. ded This step is optional If you do enter a variable name it automatically assigns the list to the variable before the window closes If there are any errors a message will appear and the window will not close 4 Enter the elements of the list in Column 1 To adda row to the list place the cursor in a cell that takes data and press Enter or select Insert Row from the Edit menu 9 When you finish entering the list tap ok and it will appear in the Input window Sample data is available File Edit Samples Help E 13 Note Lists can be saved and retrieved using the File menu in the List Editor Use the Edit menu in the List Editor to cut copy and paste the elements of a list You can also insert and delete rows using this menu as well as send the data to one of four graphing templates listed When you enter a list in the List Editor and tap ok the list appears in the Input window The input window below shows the list entered from the List Editor above You can also enter lists directly into the Input window by typing in a similar expression ir d 1038 Input x 3 y 3 y 2 3 y 24 7 Matrix Editor With the Matrix Editor you can build a two dimensional matrix of any size The data input can be saved for use at a later time which may be useful for very large matrices The information can also be copied and pasted using the appropriate menus Portrait4 a 42 10 41 ok To enter a matrix 1 Tap the E
66. dit menu 2 Open the Matrix Editor 3 Enter the number of rows and columns you want the matrix to have Assigning the matrix to a variable is optional Enter the variable in the cell provided 4 To build a matrix tap on the Build matrix button to create an empty grid of the desired size 5 Enter the matrix elements in the grid cells and tap ok The matrix appears in the Input window Sample data is available Important Note If you do enter a variable name it automatically assigns the matrix to the variable before the window closes If there are any errors a message will appear and the window will not close File Edit Samples Help E When you have entered a matrix in the Matrix Editor and tapped ok the matrix appears in the Input window The input window below shows the matrix generated from the Matrix Editor in the figure above Matrices can also be entered directly into the Input window by typing in a similar expression Portrait4 i ioa amp matrix 5 3 76 70 87 89 81 14 Note If you do enter a variable name it automatically assigns the matrix to the variable before the window closes If there are any errors a message will appear and the window will not close If you make an error entering the elements of a matrix or if you simply want to make changes to the matrix you have input you can Highlight the matrix expression in the input window and select Matrix Editor again from the Edit menu to re ope
67. dit menu in the Table Editor to copy and clear cells You can also insert and delete columns using this menu as well as send the data to one of the graphing templates listed Unit Converter The Unit Converter is a measurement unit converter for area length and distance temperature volume and capacity and weight and mass Choose a conversion category and units of measurement to convert from and to Enter a number in the Convert From cell The result appears in the Convert To cell If you are working with very large or very small numbers you can enter numbers and see the results in Scientific notation If using scientific notation you must use the format 3 25e 6 For example to convert 458990 m to ft using Scientific notation gives a result of 4 940527e 6 which is equal to 4 940527 x 10 Tap on the Normal or Scientific button to switch between the two views Portrait4 a q 1o22 ok a 42 10 23 ok 16 Variable Editor A variable represents a value or other mathematical a concept The Variable Editor lists all of the assigned variables Assigned variables can be added or deleted using the Edit menu Deleting a row will unassign a variable When entering variables certain keywords and symbols cannot be used Symbols indicating operations relations or symbolic constants cannot be used as variables The names of functions or certain abbreviations cannot be used Nor can specific words used in the graphing package to descri
68. e Make sure that each of the fields contains data and tap Show Result for the answer There 1s sample data available for each of the terms that the Amortization Template can solve for in the Sample menu Amortization Schedule Balance Input amort_bal number of payments interest present value payment amount payment periods compounding periods Description Finds the balance for an amortization schedule that is the outstanding balance still to be paid Example amort_bal 24 7 5 65000 500 12 4 62516 90 With a present value of 65 000 an interest rate of 7 5 compounded quarterly making monthly payments of 500 at the end of 24 payments the balance remaining is 62 516 90 Amortization Schedule Interest Sum Input amort_int range of payments interest present value payment payment periods per year compounding periods per year Description Finds the sum of the interest for a given range of payment periods that is the amount of interest that has been paid over a specified range of payments Example amort_int 1 24 7 5 65000 500 12 4 9516 90 Starting with a present value of 65 000 an interest rate of 7 5 compounded quarterly and making monthly payments of 500 at the end of 24 payments 9 516 90 in interest will have been paid Amortization Schedule Principal Sum Input amort_prn range of payments interest present value payment payment periods per year compounding periods per year Descriptio
69. e is an association between the variables Example chi2test matrix 2 2 1 2 3 4 chi2 0 079365 p 0 77816 Linear Regression Test Input linregttest list 1 list 2 alternate hypothesis Description Calculates a linear regression on the given data and a f test on the value of the slope B and the correlation coefficient p for the equation y Bx a It tests the null hypothesis that the slopes of the lines of the two sets of data are equal against one of three alternatives specified by the alt hyp value If the alternative hypothesis is that one slope is less than the other slope input 1 If the alternative hypothesis is that one slope is greater than the other input 1 If the alternative hypothesis 1s that one slope is not equal to the other input 0 Example linregttest 20 29 30 26 21 28 21 27 21 20 0 t 0 085676 p 0 937122 y 0 041063 x 24 434783 s 4 361207 r 0 049404 One Proportion Z Test Input prop1ztest P x n alternate hypothesis Description Calculates a test for an unknown proportion of successes The input is the count of successes in the sample x and the count of observations in the sample n It tests the null hypothesis that the expected proportion is equal to the actual proportion against one of three alternatives specified by the alt hyp value If the alternative hypothesis is that the expected proportion is less than the actual proportion input 1 If the alternat
70. e second interval This continues until all 25 households in the survey are accounted for in the final Number of liters week interval 15 Show Frequency Polygon The frequency polygon draws a line graph over the bars of the histogram connecting the midpoints of each bar This histogram also shows the frequency polygon related to the data This may be useful for emphasizing trends in the data Pie Graphs A pie or circle graph is a graph in which parts or sections of a circle represent data The area of each section of the circle is drawn so that it represents the percentage with which a piece of data occurs relative to the whole it qx 1235 ES Daily Activities Homework Tu Class Meals Soccer Sleep Entering Data 1 Tap on one of the spaces in the column labeled Data 2 Enter each piece of data 3 Move to the second row in the column Enter the next piece of data Continue entering data in this way so that each row in the column contains a piece of data 4 Type in labels for your data This is optional but labels help to produce a more informative graph 9 Tap on the pencil icon to draw the graph 74 Note Each piece of data must be an expression that results in a positive whole number or a positive decimal number Negative numbers zero and unassigned variables cannot be represented on a pie graph Additional Information Additional information about the pie graph is availab
71. east squares fit The x and y values in your data must be positive or you will get an error message unable to fit a power regression to the data Logistic Regression Select logistic Fits the equation y c 1 e to the data using an iterative least squares fit Sinusoidal Regression Select Sinusoidal Fits the equation y a COS wx b sin wx c to the data using an iterative least squares fit You should have at least four points in your data set to fit a sinusoidal curve with at least two points per cycle Polynomials of degree n Select polynomial of degree then enter the number of the degree of the polynomial you want It fits the appropriate n degree polynomial equation to the data For example 6 will fit a polynomial of degree 6 Only a portion of the equations of the curves for these large degree polynomials will be visible in the key that displays the equations You can tap in the equation cell and use the cursor keys to view the rest of the equation Additional Information Additional information about the curves of best fit is available by opening the Tools menu and selecting Key This key will give you the equations of the lines you have graphed It will also give you the mean squared error MSE and the correlation coefficient r for the transformed data certain fit types may not provide this information If the data you have entered does not lend itself to the type of curve you want to fit to it you will get a
72. ees of freedom Example fcdf 0 5 1 10 15 0 3801 Discrete Geometric Distribution Input geompdf probability of success x Description Finds a probability at a given x which is the number of the trial on which the first success occurs for a geometric distribution with a specified probability of success In a series of independent trials the geometric distribution determines the number of the trial on which the first success will occur For example a geometric distribution could determine the number of customers that must be contacted before the first sale success is made or the number of cars that must go through a radar check before the first speeder 1s detected Example geompdf 0 3 10 0 0121 Cumulative Discrete Geometric Distribution Input geomcdf probability of success x Description Finds a cumulative probability at the number of the trial on which the first success occurs x for a geometric distribution with a specified probability of success Example geomcdf 0 3 10 0 9718 Inverse Cumulative Normal Distribution Input invnorm area mean standard deviation Description Calculates the inverse cumulative normal distribution function for a given area under a normal distribution curve for a specified mean and standard deviation Example invnorm 0 5 10 3 10 Normal Distribution Input normalpdf x mean std dev Description Finds the value of the probability density function for the normal distr
73. erent students BO 20 Sara Jon Jose Amita Entering Data 1 Tap in a cell in a column labeled Data Data 2 Enter your data in the cell E 3 Enter a label for your data This is optional but proper 76 70 labels make a graph more informative 80 4 Move to the next empty cell Enter the next piece of PHE a data Continue until all of your data is entered 82 5 From Graph type in the Options menu under Edit 7i tap on the type of bar graph you want 6 Tap on the pencil icon to graph the data Note The data must be an expression whose result is a positive or negative whole number or decimal Zero can be input however a bar representing zero may not appear on the graph if your Axes are set to Normal Unassigned variables cannot be represented on a bar graph Bar Graph Types Clustered column When you are graphing two or more sets of data you can Stacked column select the type of bar graph that you want to use to 100 Stacked column compare the sets of data The bar graph window has six choices available They are found in the Edit menu in Clustered bar Options under Graph type Stacked bar 100 Stacked bar Clustered Column A clustered column groups or Insert Column clusters comparisons among individuals or categories For Delete Column example in the bar graph above the pretest and posttest scores for each student are clustered together It is easy to see if a student s sc
74. ermine the number of payments select Number of Payments n in the template by tapping on the toggle button in front of number of payments This action grays out the field preventing you from entering data in it Fill in the other fields with the information you have and tap Show Result for the answer To now do another calculation simply tap on the toggle button in front of the new term you want to solve for Again this action grays out that specific field preventing you from entering data Make sure that each of the other fields contains data and tap Show Result for the answer There 1s sample data available for each of the five terms that the TVM Template solves for in the Sample menu 28 a qg a The default setting for Payment due at is the end of the period If you are entering strings of data pmt ban is the beginning of the period and pmt end is the end of the period Both pmt bhgn and pmt end are keywords File Edit Samples Help E Number of Payment Periods in an Annuity n Input tvm_n interest present value payment future value payment periods compounding periods pmt due Description Finds the number of payment periods Example tvm_n 9 5 10000 500 0 4 4 pmt_end 27 45 An annuity with a present value of 10 000 with an interest rate of 9 5 compounded 4 times a year provides equal payments of 500 four times a year There are 27 45 payment periods until the future value is equal to
75. essage This function does not solve systems of inequalities If the system of equations you enter is inconsistent or has no common solution you get a message in the Result window indicating this For example solve x y 1 x y 2 x y produces the following result error inconsistent system of equations You can assign a list of equations to a variable Example L x y 1 x y 0 so solve L x y x 0 5 y 0 5 If you enter only one equation instead of a system of equations the calculator solves for one variable in terms of the other Example solve 2 x y 2 x y solves for x in terms of y producing the result x 1 0 5 y To solve this same equation for y in terms of x enter the equation the same way but reverse the order of the variables Example solve 2 x y 2 y x produces the result y 2 2 x 24 Graphing a System of Linear Equations When solving systems of linear equations you may find it helpful to graph the equations To graph equations go to the Plot menu and open the Plot Equations window Simply enter the equations and the appropriate domain and range Tap on the pencil icon to see the graph Equation Plot et dx 5 24 ES Graph of x y 1 and x y 0 E Tip You can use the tracking tool on the graph to locate the approximate solution Exponential and Logarithmic Functions Exponential and logarithmic functions are examples of transcendental functions that 1s fun
76. est to have from 5 to 20 classes The larger the amount of data the more intervals can be used 6 Tap on the pencil icon to draw the graph Note Each piece of data must be an expression whose result is a positive or negative whole number or a positive or negative decimal number Unassigned variables cannot be represented on a histogram The number of classes must be a positive integer Frequencies must be positive integers Style Option w Cumulative Frequencies The Style menu for histograms is very different from that Show Frequency Polygon of the other graphs It includes being able to show the histogram with Cumulative Frequencies and or a Frequency Polygon Cumulative Frequencies A graph displaying the cumulative frequencies of the data takes each interval after the first and adds the frequencies of the intervals Histogram Er x 12 19 x ousehold Milk Consumption together The second interval is now an accumulation of gt the frequencies of the first and second interval The third interval is an accumulation of the frequencies of the el first second and third intervals In the histogram to the right the first interval shows that 2 households consume 0 to 1 liters of milk per week The second interval adds 10 the 2 households from the first interval to the 5 households that drink 1 to 2 liters of milk per week to get a cumulative frequency of 7 which is displayed in i th
77. etric plots graphs of equations f x y g x y point plots and graphs of inequality regions The plots are accessed from the Functions menu Bar Graph Box and Whisker Plot Curves of Best Fit Histogram Pie Graph Normal Probability Plot Plot y f x Polar Plot r r t Parametric Plot f t y g t Plot Equations Point Plot Inequality Plot Real Numbers Sequences e ai Selecting any plot from the menu opens a graphing template Each of graphing templates allows you to input your own data and at the tap of a button draw new graphs All of the graphs have many features in common The appearance of each graph can be altered in many ways using the menus available The Plots are found at the top of the Functions menu when it is opened Tap open Plots and select the graph of your choice There is no limit other than the memory limits of your device to the number of functions equations or the amount of data you can graph The screen shot below provides an overview of a typical graphing window 2 Function Plot atdxoso ES Change the size of the sraphing or the data entry window by sliding this horizontal bar up and down Tap the up arrow to maximize the data entry window Tap the down arrow to maximize the staph window The graph of the data entered below is drawn in this space Use the File Edit and Tools menus to make changes to a raph Tap this icon to see a table of values Keep in mind that the
78. ey must be integers Also between the first value in the range and the final value in the range there are only two dots between the commas Example prod x 2 x 1 4 360 Multiplying 1 2 x 2 2 x 3 2 x 4 2 360 Input 3 Sequence Form prod function variable list Description Finds the product of a list of results for a variable evaluated under a given function for a given sequence Example prod x 2 x 1 2 5 1 100 Generate a Sequence Description Finds a list of results for a variable evaluated under a given expression for a given range of values Note The first value in the range must be less than or equal to the last value in the range and they must be integers Also between the first value in the range and the final value in the range there are only two dots between the commas Input seq equation variable first in range last in range Example seq 3 x 2 x 5 10 17 20 23 26 29 32 In this example 3 x 2 is evaluated for x ranging from 5 to 10 giving us the sequence 17 20 23 26 29 32 Sum ofa List Input 1 List Form sum list of values Description Finds the sum of a list of values given Note The list of values to be summed must be contained within braces y within the brackets This will differentiate this sum from the sum of the results obtained by evaluating an expression for a given range of values Example sum 17 20 23
79. f a single 1 00 payment Example sppv 15 10 0 247 Uniform Series Future Value Input usfv interest rate number of payments Description Returns the future value of a series of 1 00 payments Example usfv 15 10 20 3037 Uniform Series Present Value Input uspv interest rate number of payments Description Returns the present value of a series of 1 00 payments Example uspv 15 10 5 0188 Graphing Finance Functions Each of the templates in the Finance menu include a Graph by button Tap on this button to see a list of the variables available for graphing that particular function For example if you tap on the Graph by button in the Compound Interest template you are presented with four options P principal ZR interest rate CP compounding periods per year and T term If you tap on T term a graph of the data is drawn with the term along the x axis and the compound interest along the y axis Portrait4 Fade EEEN oki Tap on the Function Plot i E amp Compound Interest Graph By button to see a list of available options If you tap on T you will see the graph to the right Remember there must be data entered In 1921 863198 P 100 IR R 0 the cells before a graph can be drawn In this graph the Term 7 is running along the axis Once the graph is drawn you can use all of the tools available in the graphing template Edit and Tools menus Hyperbolic Functions Hyperbolic fun
80. f its type generates an error message Integers numbers like 1 0 5 etc There is a limit to the size of integer you can use in an expression The largest or smallest integer you can use is 2 147 483 647 or 2 1 Entering an integer that 1s too large results in error integer overflow If the integer you input is too large you may want to put it in decimal form For example 2732 gives an error message but 2 032 does not Fractions The numerators and denominators of fractions are stored as integers Any fraction whose numerator or denominator exceeds the integer range generates an integer overflow error Decimal numbers numbers with a decimal place like 1 5 3 0 and 2 1 Scientific notation is also allowed For example 1 1290 and 3 2e 5 There is a limit to the size of decimal number you can use in an expression The largest or smallest decimal allowed is approximately 1 79e308 Any decimal number that is too large results in error floating point overflow Boolean true false values A Boolean variable function or operator takes either of the values true or false To manipulate Boolean values in expressions you must use Boolean operators Lists list of expressions Any function that takes a single argument can also handle a list of arguments For example 1 2 3 4 5 or 1 2 1 2 3 4 Lists must be enclosed within braces with each element separated by commas Each list element can be a value of any type but m
81. git This single digit is the nines excess To check an answer in basic arithmetic operations find the nines excess of each number and the nines excess of the answer Take addition for example If the nines excess of the answer does not equal the nines excess of the sum of the nines excesses of the addends then the answer is wrong however if they are the same they may or may not be correct Example 1 ninesExcess 56 2 Add 5 6 to get 11 Add 1 1 to get 2 The nines excess is 2 Example 2 Assume you want to check whether 2 3 33 Since the product of the nines excesses of 2 and 3 1s 6 and the nines excess of the answer is also 6 you cannot assume that the answer 1s correct If the nines excesses had been different you would know that the answer is wrong Permutations Input perm m n Description Finds the number of permutations of m objects taken n at a time The order of selection is important The integers m and n must be nonnegative with n less than or equal to m Example perm 6 4 360 There are 360 different permutations of 6 objects taken 4 at a time Prime Factors Input primeSet n Description Finds a list of the prime factors of n A prime factor of a number is a factor that is a prime number Note The prime set function does not count multiplicities It only provides the distinct primes and does not indicate if they occur more than once Example primeSet 24 2 3 The number 24 has two prime factors
82. helpful to change the number of points plotted as the default value of 100 points may not provide a true representation of the function For example open the Plot y f x graphing window and enter the function sin 1 x Enter a domain from 0 05 to 0 05 and tap the pencil icon Enter this information again in the next row but this time open the Properties window Change the color of the graph and Color Thicknej 4 change the number of points plotted to 500 Once you have a a Y made your changes tap ok and tap on the pencil icon to see a much more accurate representation of sin 1 x Remember the number of points plotted also has an impact on the table of values Each point plotted is represented in the table of values If your plot 500 points the table of values will provide a value for each of the 500 points Function Plot etedxii07 ES 7 Function Plot atomos S Sin 1 fx 100 points Sin 1 f x S00 points a LA A The Style features can also be changed from the Properties window The default settings for the style features are the same as the Edit menu on the graph To change the Line Style of a graph open the Properties box select either Solid or Dashed To change the Thickness of a graph open the Properties box select Thin Medium or Thick To change the Symbol of a graph open the Properties box select Circle Cross Diamond Point or Square After a choice is made always tap
83. ibution at a specified value of x The normal distribution is a distribution that is continuous and symmetric about the mean Example normalpdf 2 10 3 0 0038 Cumulative Normal Distribution Input normalcdf lower bound upper bound mean standard deviation Description Calculates the inverse cumulative normal distribution function for a given area under a normal distribution curve for a specified mean and standard deviation Example normalcdf 0 5 1 10 3 0 0006 Discrete Poisson Distribution Input poissonpdf mean x Description Finds a probability for a specified x for a Poisson distribution with a specific mean The Poisson probability distribution provides a good approximation to binomial probabilities when the sample size is large and the population mean is small In a Poisson distribution limiting arguments or parameters are applied to other distributions The Poisson distribution could be used to determine distribution if you were restricted or limited by time volume or area For example the Poisson distribution would be useful in modeling the number of flaws in a square meter of fabric or the number of bacteria in a limited sample of water Example poissonpdf 5 10 0 0181 Cumulative Discrete Poisson Distribution Input poissoncdf mean x Description Finds the cumulative probability at x for a discrete Poisson distribution with the specified mean Example poissoncdf 5 10 0 9863 Student Distribution
84. ied by the upper and lower bounds To get to the probability functions tap the following Functions Statistics gt Probability Discrete Binomial Distribution Input binompdf of trials probability of success x Description Finds the probability at a given x for a binomial distribution with a specified number of trials and a specified probability of success on each trial It counts the number of successes in a fixed number of independent events where each event has the same probability of success For example the number of defective items in a sample of n items can be represented by a binomial distribution Example binompdf 10 0 5 3 0 1172 Cumulative Discrete Binomial Distribution Input binomcdf of trials probability of success x Description Finds a cumulative probability at a given x for a binomial distribution with a specified number of trials and a specified probability of success on each trial Example binomcdf 10 0 5 3 0 1719 49 50 Chi Square Distribution Input chi2pdf x degrees of freedom Description Finds the value of the chi square probability distribution of a specific value of x The chi square distribution is used to measure goodness of fit and to test hypotheses and obtain confidence intervals for the variance of a normally distributed random variable The chi square distribution is the distribution of the sum of squares of the independent standard normal variables The chi square
85. ine to the function at that point The equation of the derivative is displayed in the bottom left corner of the graphing window Integral This tool is available for the function plots Plot y f x only With Integral selected tap on a point on the graph and drag the stylus to a second point The integral of the function between these two points is displayed in the bottom left corner of the graphing window Key Provides pertinent information about the graph Not all graphs have a key Changing Colors Points and Other Properties A double tap on a colored cell in a column or row 8 3 lt _Zx header in a data entry window opens a Properties ania o i pi The Properties window allows you to make changes to cos x pi pi a specific graph For example if two functions are plotted on the same set of axes opening the Properties of one of the functions changes the properties of the graph for that function only The properties of the other function remain unchanged 66 Function Plot un dx 4 45 ok To change the color of a graph or portion of a graph select the color you want the graph to be and tap OK The graph appears in the new color after you tap on the pencil icon If you want to change the color of the graph after it has been drawn change the color the same way Always tap the pencil icon E The number of Points plotted can be changed in many of the graphing windows In some cases it may be
86. itions exist The first nonzero entry in each row is 1 Each successive row has its first nonzero entry in a later column All entries above and below the first nonzero entry of each row are 0 All full rows of zeros are the final rows of the matrix Example rowReduce matrix 2 3 1 2 3 4 5 6 matrix 2 3 1 0 1 0 1 2 Sum of a Matrix Input sum matrix A Description Finds the sum of a list of numbers Example sum matrix 2 2 1 2 3 4 10 41 Swap Two Rows of a Matrix Input swaprows matrix A source row destination row Description This operation swaps the position of row i and row i in matrix A Example swaprows matrix 3 2 1 2 3 4 5 6 1 3 matrix 3 2 5 6 3 4 1 2 Row 1 in the given matrix was swapped or changed positions with row 3 in the matrix Swap Two Columns of a Matrix Input swapcols matrix A source column destination column Description This operation swaps the position of column j and column jz in matrix A Example swapcols matrix 2 3 1 2 3 4 5 6 2 3 matrix 2 3 1 3 2 4 6 5 Column 2 1n the given matrix changed positions or was swapped with column 3 Trace of a Matrix Input trace matrix A Description Finds the trace of a matrix The trace is the sum of the entries along the main diagonal in a square matrix of any size Example trace matrix 2 2 1 2 3 4 5 The entries along the main diagonal of this matrix are land4 1 4 5
87. ive hypothesis is that the expected proportion is greater than the actual proportion input 1 If the alternative hypothesis is that the expected proportion is not equal to the actual proportion input 0 Example prop1ztest 0 75 3000 5000 0 z 24 494897 p 0 q 0 6 Two Proportion Z Test Input prop2ztest x1 1 x2 n2 alternate hypothesis Description Calculates a test to compare the proportion of successes from two populations The input is the count of successes and the count of observations in each sample It tests the null hypothesis that the two proportions are equal against one of three alternatives specified by the alt hyp value If the alternative hypothesis is that one proportion is less than the other input 1 If the alternative hypothesis is that one proportion is greater than the other input 1 If the alternative hypothesis is that one proportion is not equal to the other input 0 53 54 Example prop2ztest 75 100 50 100 0 z 3 651484 p 0 000261 q1 0 75 q2 0 5 q 0 625 Two Sample F Test Input 1 samp2ftest list 1 list 2 alternate hypothesis Description Calculates an f test to compare two normal population standard deviations where the population means and standard deviations are all unknown The ratio of sample variances Sx Sx is used to test the null hypothesis that the ratios are equal against one of the three alternatives specified by the alt hyp value If the
88. l icon to draw the graph of the points 5 To draw the line connecting the points go to the Options menu under the Edit menu and tap on Style and Line Note Data may take the form of integers decimal numbers symbolic constants or calculations If you do enter inappropriate data and try to plot it a syntax error message appears 80 Graphs of Inequalities An inequality is a mathematical sentence that contains one of the following relations gt greater than lt less than gt greater than or equal to lt less than or equal to A graph of inequalities shows the region of intersection of two or more inequalities Shading indicates the region of intersection If there is no shaded region in an inequality graph then there is no set of points that satisfies all the inequalities Entering Data 1 Inequality Plot EN 3 Intersection of 4 Equations Tap in one of the cells in the column labeled Inequalities 2 Enter your inequalities Use for exponents and for multiplication 3 Enter the x and the y limits that you want your inequality evaluated from and to 4 Tap on the pencil icon to draw the graph of the inequality Note The equation must contain an inequality sign and only linear inequalities can be evaluated You must enter the x limits and the y limits that you want the equation evaluated under If you do not enter them you will get a syntax error when you try to plot
89. le by opening the Tools menu and selecting Key Tapping on this opens a window that will give you the percentages that each section of the pie represents If you have input incorrect data in the data boxes and try to graph it you get a message saying empty plot in this area The information in this key can be copied and pasted into a word processing document by using the Ctrl C copy and Ctrl V paste shortcuts on your keyboard Highlight the information you want to copy and use Ctrl C to copy it and then Ctrl V to paste it in the location you want The column headers do not copy and paste Normal Probability Plot A normal probability plot assesses whether or not a data set is normally distributed When plotted against a theoretical normal distribution the points should form a straight line Points not on this straight line indicate a deviation from the normal distribution Normal Probability x 1 28 ES Scores Entering Data Tap in a cell in the column labeled Data Enter your data set Row 1 is the first point row 2 is the second point and these points represent the x coordinate If you have more than one set of data add more columns by opening the Edit menu and selecting Insert Columns Once the data set has been entered tap the pencil icon The z values for each point are automatically calculated and these represent the y coordinates The graph will be drawn 7 i Pa els S 75
90. length Description Finds the substring of A starting at an indicated position pos of an indicated length len Example substring abcdef 3 2 cd The substring starting at position 3 that is 2 elements in length is ed Test To get to the test functions tap the following Functions Test Test a Condition Input if condition x y Description Returns the value of x if the condition is true otherwise it returns the value of y Example if true Wednesday Friday Wednesday The value of b is true so the result is the value of x Wednesday Select a Value Input select m list Description Returns the value at position m of the list Example select 10 a b c d e P g h 1 1 yj The letter in the tenth 66599 position of the list is J Trigonometric Functions Trigonometric functions are defined in terms of an angle The magnitude or size of an angle can be expressed in either radians or degrees An angle that has a radian measure of 1 is equal to 1 27 of a complete revolution An angle that has a degree measure of is equal to 1 360 of a complete revolution All of the trigonometric functions are defined for complex numbers Remember to find the inverse of a trigonometric function the domain and or range are restricted to obtain a one to one correspondence between input and output This allows the graph of the
91. n Finds the sum of the principal for a given range of payment periods that is the amount of the principal that has been paid back over a specified range of payments Example amort_prn 1 24 7 5 65000 500 12 4 2483 10 Starting with a present value of 65 000 an interest rate of 7 5 compounded quarterly and making monthly payments of 500 at the end of 24 payments 2 483 10 of the principal will have been paid back Finance Depreciation Template Depreciation 1s a way of measuring the loss in value of an asset due to general wear and tear over a given period of time To get to the depreciation template tap the following Functions gt Finance Depreciation Template The Depreciation Template provides the choice of four different methods of depreciation They are e Declining Balance This method assumes that the asset declines in value or depreciates more at the Deciining Balance beginning of the life of the asset Declining Balance Crossover e Declining Balance Crossover This method begins with the declining balance method and then O Straight Line crosses over to the straight line method when the 5 Sum of Years Digits annual depreciation using the declining balance method becomes less than the annual depreciation using the straight line method e Straight Line This method assumes that the asset depreciates by an equal amount over the life of the asset e Sum of Years Digits This is an accelerated
92. n error message the curve cannot be fit to the data 12 The information in this key can be copied and pasted into a word processing document or Plot Window like the Function Plot by using the Ctrl C copy and Ctrl V paste shortcuts on your keyboard Highlight the information you want to copy Use Ctrl C to copy it and then Ctrl V to paste 1t in the location you want Histograms A histogram is a graph that is similar to a bar graph except that it indicates the frequency distribution of data Also there are no spaces between the bars It is used to display continuous data that can be organized into intervals The intervals are placed on the horizontal axis and the frequencies are on the vertical axis The height of a bar or rectangle that is drawn corresponds to the frequency of data within that interval Histogram i 12 17 ES ousehold Milk Consumption Humber of liters week Entering Data Tap on one of the cells in a column labeled Data Enter your data in the cells available Tap in the Frequency column and record the number of times that piece of data occurs in the set of data The data in row 3 indicates that 2 occurs in the entire set of data 9 times The frequency is 9 Continue entering the data and frequencies in this manner until all of your data has been entered Determine the number of classes or intervals that you want the data divided into Enter this number in the cell beside of classes It is b
93. n the Editor When the Matrix Editor is re opened make your changes Re enter the matrix by tapping ok again Matrices can be saved using the File menu in the Matrix Editor Use the Edit menu in the Matrix Editor to cut copy and paste cells You can also insert and delete columns using this menu as well as send the data to one of the graphing templates listed Results in the Matrix Editor Any expression whose result is a matrix automatically opens the Matrix Editor displaying the result of the calculation as an array Sequence Editor A sequence is a list of elements or numbers that succeed or follow each other in a specific order or pattern With the Sequence Editor you can build a sequence of any size Sequences can be saved for use at a later time which may be useful for very large sequences The data can also be copied and pasted using the appropriate menus Portrait a q oa ok To build a sequence 1 Tap the Edit menu 2 Open the Sequence Editor 3 Enter a variable in the cell provided This step is not optional 4 Enter the range you want the variable evaluated From and To in the appropriate cells 5 Below the cell where the range is entered there are two gray cells Tap on the 2 cell and enter the expression that you want the variable evaluated under 6 When you have input the expression tap the Build Sequence button to build the sequence 7 To add a column tap on the Edit menu and select Insert Column
94. ns Each Help window contains information on what is required in the input window and how to input the information for immediate results A complete example is also included Each individual function template also has its own Help menu a a dx 5 02 ES i me n Templates solve Form solve equation 1 equation 2 variable 1 variable 2 Description Finds the solution for the variables in a system of linear equations Example sove aty 1 y 07 i vt fx 0 5 y 0 5 finds the common solution for xand yin the two gwen equations amp As long as Help Mode is selected you are provided with assistance on all computation and plotting functions When learning how to use the calculator it may be useful to keep this feature on Accessing Help from Start When Portrait 4 is open on your handheld Help can E Today be accessed by tapping on the Start menu Tap on t ActiveSync Help to see a Table of Contents for Graphing Ea Calendar Calculator Help Each item in the table of contents IE Contacts expands to show all of the items in that list For Home example tap on Plots to see a complete list of all of Internet Explorer the plots available in Portrait 4 From this list tap on Messaging a specific plot to see detailed help for that plot a Each Help window includes information on what is CECI required in the input window how to input the n Portrait information for immediate results plus a comple
95. ore improved from the pretest to the posttest Stacked Column Stacked bar graphs show the relationship of individual items or categories to the whole The heights of the individual columns vary accordingly 69 100 Stacked Column These stacked columns show the relationship of individual items or categories to 100 The heights of the columns are all the same They all go to 100 Each item in a column represents a portion of the 100 This type of graph is only appropriate for positive data Clustered Bar Like the clustered column a clustered bar groups or clusters comparisons among individuals or categories Categories are organized vertically and values horizontally Stacked Bar Similar to the stacked column except that the categories are organized vertically and values horizontally 100 Stacked Bar Similar to the 100 stacked column except that the categories are organized vertically and values horizontally This type of graph is only appropriate for positive data Box and Whisker Plots Box and Whisker E x 11 37 ES A box and whisker plot is a graphic way of showing a summary of data using the median quartiles and extremes Scores of the data The whiskers or lines on the graph represent the range of the data the box represents the quartiles and the line in the box represents the median Entering Data 1 Tap on the first cell in the column labeled Data 2 Enter your first piece of data in
96. ost functions that use lists expect numeric elements only For example sin 1 2 3 fsin 1 sin 2 sin 3 0 84 0 91 0 14 Similarly arithmetic operations with lists and numbers are also possible For example 1 2 3 4 5 5 10 15 20 and 1 2 3 42 1 4 9 An empty list cannot be entered but can be generated by certain functions Matrices rectangular arrays of numbers that are arranged in rows and columns Matrices can be inserted into other expressions using the matrix function Only two dimensional matrices are supported and only numeric types are allowed in matrices Complex Numbers Arithmetic operations and operations using real numbers are supported with complex numbers Complex numbers z are numbers in the form a b I where F 1 For example 2 5 3 5 0 24 705 I Capital I is used for complex numbers Dates Dates can be entered as a type of data The following function can be used to create a date makeDate day month year hour minute second For example makeDate 2 4 2000 11 16 15 returns the time and date 11 16 15 am Sunday April 2 2000 Strings A string is a finite sequence of characters like numerals letters and symbols The length of a string 1s determined by its number of characters The length of a string can be zero or any positive integer Strings are always contained in quotation marks like the string abcdef Substrings are any adjacent sequence of char
97. oved along the graph The values are shown to five decimal ae If this is too many round up or down appropriately The Track points tool is activated only if there is a plot in the graphing window Snap to Intersections Snap to Intercepts If you have two or more functions that intersect you can find the precise coordinates of the intersections When the tracking crosshairs are close to an intersection they snap to the intersection A small box pops up near the intersection displaying the coordinates in a shortened form More precise values are displayed in the lower left corner of the graph window The tacking tool will also snap to the x and y intercepts on a graph Zoom in When Zoom in is selected place your stylus on the screen and draw a box around the portion of the graph that you want to zoom in on When you remove your stylus 1t automatically zooms in on the selected area To return to the original view tap the pencil icon The Zoom in tool can be activated only if there 1s a plot in the graphing window Zoom out When Zoom out is selected each tap on the screen returns you to a previously zoomed view of the graph To return to the original view tap the pencil icon The Zoom out tool can be activated only if there is a plot in the graphing window Derivative This tool is available for the function plots Plot y f x only With Derivative selected tap on a point on the graph to see the tangent l
98. pulation mean u when the population standard deviation s is also unknown Example tinterval 20 29 30 26 21 0 99 15 8321 34 5679 Input 2 tinterval x Sx n Conf Lev Description Finds a confidence interval for an unknown population mean u when the population standard deviation s is also unknown Example tinterval 25 2 4 5497 5 0 99 15 8321 34 5679 Z Interval Input 1 zinterval std dev list Conf Lev Description Finds a confidence level for an unknown population mean u when the population standard deviation s is known Example zinterval 3 7815 28 21 27 21 20 0 99 19 0439 27 7561 Input 2 zinterval std dev x n Conf Lev Description Finds a confidence level for an unknown population mean u when the population standard deviation s is known Example zinterval 3 7815 23 4 5 0 99 19 0439 27 7561 Tip The calculated confidence interval will vary according to the confidence level that you input Probability Distributions Portrait 4 calculates both probability density functions pdf and cumulative density functions cdf for several distributions The probability density function is a function of a discrete or continuous random variable that determines the probability or the chance that a specified value x will occur The cumulative density function calculates the probability that the value of the random variable will fall within a range specif
99. r function has a maximum or minimum value over a feasible region then it must occur at one of the vertices of the feasible region The inequalities underlined in the entry below define the feasible region To graph these select Inequality Plot from the Plots menu on the calculator Enter these constraints inequalities in the cells in the column labeled Inequalities maximize 3 x 5 y x y lt 10 x y gt 5 y x lt 3 y x gt 4 x y Inequality Plot it x529 ES Maximize 3x HOY 10 The constraints were entered and the feasible region graphed If we calculate the optimization furiction we get aresult of 45 whens 5 5 andy 6 5 How does this result compare to the graph of the feasible region Is the ordered pair 3 5 6 2 one of the vertices of the feasible region 36 Lists To get to the list functions tap the following Functions Lists Augment Input augment list A list B Description This operation joins two lists or joins matrix B to matrix A as new columns the two matrices must have the same number of rows Example augment 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 Length of a List Input card list A Description Finds the cardinal number of elements in a list Example card 1 4 0 7 7 5 This list contains 5 elements Cumulative Sum Input cumSum list A Description Returns the cumulative sums of the elements in a list Example cumSum 1 2
100. rear ee naaa AE O A AA 10 ACCESSING HELP FROM STAR aan ala 10 SOC AEC OEA RONIEO Ceata e E ana cta 11 FIX NUMBER OF DECIMAL PLACES Dat AA a cla 12 MODE NORMAL OR SCIENTIFIC DECIMALS OR FRACTIONS DEGREES OR RADIANS occcnoccnnnoccnnnccnnnoccnnnccnnnacononicnnns 12 Edna Mentir TODIS tati da 13 Ma o SI eee ge ac es sant ene are nega 13 VATRI EDITOR mra cheatin oe el al o 14 SEQUENCE EDITO Rasa ctas tacita 15 A ante to to lo 16 NITO ONVER TE seen tt cotas 16 VARIABLE E Rs TE 17 GENERATING A GRAPH FROM THE LIST MATRIX SEQUENCE OR TABLE EDITOR oocoocccncccnnccnnnccnnoconnccnnocnnncconiccnnccnns 18 5 PP A E nis teasers act eaea 18 GRAPHING CALCULUS FUNCTION Slds 19 Complex NUDE Scout tits 20 CONSUME FAO IC AE ONS ad LA AAA AA A AAA A AA 21 Data A A A AA A A eee eae deat ee 22 EUA Sta A AR A ada 23 GRAPHINGA SINGLE EQUATION at A A da eel total lala eshte cea NA fata eae daletecradl dato 23 GRAPHING A SYSTEM OF LINEAR EQUATIONS vic cree weitere ota AA E A AA TA 25 EXxponenual and EG AN UU ANT UNS I WI CLI INS esenee a aaa Pe AA A a isd vnc 25 Finance AMOZaU ON aislante diodo alitas 26 Finance Depreciation empate tic diia 2 Finance Time Value of Money TVM Template occcccccccccnnnnnnnnnnnnnonoccccononononnnononononananonoconoccnnnnnnnnnnnns 28 Finance Cash FlOW Analy SIS italia oia 30 Finance Interest Bonds and Net Present Future Values ooooccoocccoccconcccnccconcccnncconoconnccnnocnonccon
101. rovide standard calculator operations Clear Tapping on Clear removes all information in the Input and Result windows Left Arrow Tapping on the left arrow moves the cursor to the left Right Arrow Tapping on the right arrow moves the cursor to the right Backspace Tapping on the backspace arrow moves the cursor to the left deleting input mod m mod n finds m modulo n that is the remainder when m is divided by n Example 5 mod 2 1 Reciprocal 1 x read one over x Example 1 3 0 3333 Exponentiation A caret must be used to indicate an exponent Example 2 5 2 2 2 2 2 32 Square root Finds the square root of a non negative number Example sqrt 16 4 Other roots can be calculated using the following format x 1 n Example 274 1 3 3 Factorial n Example 5 5 4 3 2 1 120 Symbolic Constants There are two symbolic constants on the calculator They are velo pi The constant n is denoted by pi It is approximately equal to 3 14159265359 HEM e The constant e It is approximately equal to 2 71828182846 Entering Data There are some basic rules to keep in mind when entering data in Portrait 4 These are covered in the following sections on Data Types Converting between Data Types Boolean Operators Relations and Order of Operations Data Types All values in the calculator must be one of the following types Any value or expression that exceeds the range o
102. t does not have an inverse the answer is true otherwise it is false Example isSingular matrix 2 2 1 2 3 4 false This matrix has an inverse Maximum Value Input max matrix A Description Finds the largest entry of a list or matrix Example max matrix 2 2 1 2 3 4 4 Minimum Value Input min matrix A Description Finds the smallest entry of a list or matrix Example min matrix 2 2 1 2 3 4 1 Minor Input minor matrix A row 7 column Description Finds the i 7 th minor of the matrix A that is the determinant of the matrix obtained by removing row i and column j from 4 Example minor matrix 3 3 1 2 3 4 5 6 7 8 9 1 3 3 The determinant is 3 Multiplying Rows by a Scalar Input mulrow matrix A row i factor Description This operation multiples row of a given matrix by a scalar value c and stores the result in the row i Example mulrow matrix 2 2 1 2 3 4 2 3 matrix 2 2 1 2 9 12 The elements of row 2 of the matrix were each multiplied by 3 changing the elements in row 2 to 9 and 12 Multiplying Columns by a Scalar Input mulcol matrix B column j factor Description This operation multiplies column j of a given matrix by a scalar value c and stores the result in the column Example mulcol matrix 2 2 1 2 3 4 1 5 matrix 2 2 5 2 15 4 The elements of column 1 of the matrix were each multiplied by 5 changing the
103. t Menu The Edit menu provides access to the cut copy paste delete clear and erase all operations The standard keyboard shortcuts Ctrl x Ctrl c and Ctrl v can also be used for cut copy and paste operations The Edit menu also provides sample data and options for changing graph features comple 1 Samples Provides sample data to graph Cut Cuts the selection in the data entry window and puts it on the clipboard Copy Copy Copies the selection in the data entry window and Paste puts it on the clipboard Delete Clear Paste Inserts clipboard contents into the data entry Erase All 7 window at the selection point Delete Deletes the selected data only If no data is selected nothing is deleted If all of the data is selected all the data is deleted Delete rows by selecting the row header Clear Erases the current data but leaves the graph Erase All Removes all of the data as well as the graph Options The Options menu lets you change the features of the graphs The title the number of tick marks on the axes and the type of axes used can all be altered using the choices in Options Not all options are available for all graphs 62 Scaling Style Draw Grid Options Labels Tap on Labels to open the Plot Labels window In this window you edit the labels on the graph To enter new information delete the default labels and enter the new ones Once changes have been made tap ok and
104. t rate that would produce the same accumulated amount in one year 1s 6 09 Net Present Value Input net_pv interest initial cash flow list of cash flows Description Finds the net present value for a series of cash inflows and outflows The list of cash flow items must be in braces Cash inflows must be entered as positive numbers while cash outflows must be entered as negative numbers Example net_pv 8 1000 500 2000 1500 3442 46 Given an interest rate of 8 an initial cash flow of 1000 and the three cash flow amounts the net present value is 3442 46 Nominal Rate of Interest Input nom effective rate compounding periods Description Finds the nominal or stated rate of interest Example nom 16 25 8 15 19988 The nominal rate of interest is 15 19988 Simple Interest Input simple principal interest term Description Finds the accumulated amount that is the sum of the principal and the simple interest earned on the principal over a given period of time the term Example simple 100 6 5 130 00 Given a principal of 100 and an interest rate of 6 the accumulated amount over a term of 5 years is 130 00 Single Payment Future Value Input spfv interest rate number of payments Description Returns the future value of a single 1 00 payment Example spfv 15 10 4 05 Single Payment Present Value Input sppv interest rate number of payments Description Returns the present value o
105. t squares fit Quadratic Regression Select quadratic Fits the equation y ax bx c to the data using a least squares fit This equation is a second degree polynomial Cubic Regression Select cubic Fits the equation y ax bx cx d to the data using a least squares fit This equation is a third degree polynomial Quartic Regression Select quartic Fits the equation y ax bx cx dx e to the data using a least squares fit This equation 1s a fourth degree polynomial Median line Select median median Fits the equation y ax b to the data using the resistant line technique Exponential Regression Select exponential Fits the equation y a b by transforming the data to x and In y and then fits a straight line to the transformed data using a least squares fit The y values in your data must be positive or you will get an error message stating 1t was unable to fit an exponential regression to the data Logarithmic Regression Select logarithmic Fits the equation y a b by transforming the data to In x and y and then fits a straight line to the transformed data using a least squares fit The x values in your data must be positive or you will get an error message stating it was unable to fit a logarithmic regression to the data Power Regression Select power Fits the equation y a b by transforming the data to In x and In y and then fits a straight line to the transformed data using a l
106. te LOM example Help 10 a a 42 10 12 ES Graphing Calculator Help Edit Menu Plots e Functions Keypad Bar Graph Histogram Point Plot Show Calculation Log The Calculation Log provides a record of the calculations Plot Eq uations Inequality Plot TT Ld Box and Whisker Plot Curves of Best Fit you have performed using the function templates The data in the Calculation Log can be saved It can also be copied and pasted to a new location like a word file The log can be cleared as well 10 13 ES Help Er 10 13 x Function Plots Description The graph of a function is a graph of the equation y A2 where f represents any function and the value of vis dependent on the value of x The graph is the set of all coordinates where the and coordinates are Ux Fx Entering Data Enter the function you want evaluated in the space under Ax The x values that you want the function evaluated from and to must also be entered The values are optional If you are graphing more than one function these values do not have to be the same View Find lt a E Portrait4 a 42 10 22 fsolvelx 1 1 x x 1 1 gt 0 618054 fsolve x 3 3 x 2 10 x x 10 10 gt 5 compound 1000 7 0 12 25 gt 5 725 418209 derw x3 12 x 1 x 3 gt 15 000001 dim matrx 3 1 4 1 7 3 1 gt ta 1 11 Fix Number of Decimal Places Yo
107. teger range but double 5 1000 1000 1000 does not Converting to Boolean To convert either an integer or decimal number to a Boolean value boolean value converts any value to a Boolean If the value is non zero the result is true and otherwise the result is false Example 1 boolean 0 false Example 2 boolean 5 true Converting to other data types fractions lists matrices 1s not supported by this method Boolean Operators e amp or and p g tests if both p and q are true Example 9 gt 5 amp 4 lt 3 tests if both of these expressions are true One of them is not so the result is false e or or pl g tests if p or q is true Example 9 gt 5 4 lt 3 tests if one of these expressions is true One of them is true so the result is true e or not p tests if p is not true Example 9 gt 5 tests if the expression is not true The expression is true so the result is false e xor p xorg tests if p or q is true but not both The result is true if exactly one of the two is true and false if both are true or if both are false Example 9 gt 5 xor 9 gt 6 tests if exactly one of these expressions 1s true They are both true so the result is false Relations Relational comparisons between numeric expressions can be evaluated They return a Boolean value e lt less than x lt y tests whether x is less than y It is true if x is less than y and false if x is greater than or equal to y
108. the first row of the column 3 Move to the second row in the column and enter your data 4 Continue entering data in this way so that each row in the column contains a separate piece of data 9 Once your data is entered tap on the pencil icon to draw a graph of the data Note Data may be entered in the form of integers decimal numbers symbolic constants and or calculations or other numeric expressions Additional Information Additional information about the box and whisker plots is available by opening the Tools menu and selecting Key This opens a key window that will give you the minimum value Min and maximum value Max of the data as well as the upper quartile U Q the lower quartile L Q and the median Med If you have input incorrect data and tried to graph it you will get a message saying empty plot in this area The information in this key can be copied and pasted into a word processing document by using the Ctrl C copy and Ctrl V paste shortcuts on your keyboard Highlight the information you want to copy and use Ctrl C to copy it and then Ctrl V to paste it in the location you want The column headers do not copy and paste 70 Curves of Best Fit Curves of best fit plots a set of points and draws a curve that comes closest to fitting that set of points Curves of Best Fit 2 x 11 58 ES P Linear Fit 2 5 Entering Data Tap in one of the spaces in the column labeled x or y Enter
109. the hyperbolic secant function is defined as y In 1 sqrt 1 x x where 0 lt x lt 1 This function can be typed in or you can use the equivalent arccosh 1 x Example asech 0 5 1 317 Inverse Hyperbolic of Cotangent Input acoth x or arccoth x Description Denotes the inverse of the hyperbolic cotangent function The inverse of the hyperbolic cotangent function is defined as y 1 2In x 1 x 1 for x lt 1 or x gt 1 This function can also be typed in or you can use the mathematical equivalent arccoth 1 x Example acoth e 0 386 Linear Programming Portrait 4 provides functions for solving linear programming problems Generally speaking linear programming problems deal with the optimization either minimization or maximization of linear functions subject to certain constraints imposed by a system of linear inequalities that are placed on that function The system of inequalities defines a feasible region for the function to be optimized In the graphing calculator the constraints must be written as inequalities but the inequalities must not be strict The implicit constraints that the variables be non negative do not need to be included The variables to be solved for do have to be indicated To get to the linear programming functions tap Functions gt Linear Programming Minimization Problems minimize function constraints variables minimize 2 x y 3 x y gt 10 5 x 2 y gt 6
110. the inequalities The equations you want evaluated can be comprised of integers symbolic constants decimal numbers or any functions or operations with numeric results When evaluating graphs of inequalities a dashed line indicates that the boundary does not belong to the solution set However if you set the line thickness to medium or thick dashed lines cannot be distinguished from solid lines A solid line indicates that the line itself does belong to the solution set 81 Trouble Shooting Problems with Portrait 4 If you experience any difficulties with Portrait 4 with the installation or the running of any part of the program please contact our web site immediately As we are made aware of any problems users of Portrait 4 are experiencing we will put this information on our web site along with our solution You can find our web site at www mathresources com Contacting MathResources Inc We would love to hear from you If you have any comments and or suggestions about Portrait 4 or this User s Guide or if you have some great ideas about other products that you would like to see please let us know Your feedback will help us improve on our current products and help us create better ones in the future You can reach us in the following ways e Email support mathresources com e Visit our web site at www mathresources com e Call us at 1 800 720 1323 within North America OR 1 902 429 1323 e Fax us at 1 902
111. the second number Example log 2 10 3 32 Finance Amortization Amortization 1s a gradual reduction of an amount over time The following amortization functions calculate the outstanding balance the sum of interest and the sum of the principal for an amortization schedule Generally speaking an amortization schedule shows the retiring of debt over time including the portion of interest and principal that each payment represents and the outstanding balance on the debt after each payment is made To get to the amortization functions tap the following Functions gt Finance Amortization Template Cash to be received must be entered as a positive number Cash to be paid must be entered as a negative number et EE ole Portrait4 fa Principal File Edit Form Samples 26 Select the term you want to solve for from the Form Menu To use the Amortization Template determine the term you want to solve for and select that term from the Form menu For example if you want to calculate the interest paid select Interest from the Form menu at the bottom of the template This calls up the proper version of the template Fill in the fields with the appropriate information and tap Show Result for the answer To now do another calculation simply tap on the Form menu again and make your selection from the available list Again this will call up the proper version of the Amortization Templat
112. the sum Example mean 1 4 0 7 7 3 8 The sum of the list is 19 the mean is19 5 3 8 Median Input median x y z Description Finds the median of a list of data For an odd number of data arranged in order the median is the middle number For an even number of data arranged in order the median 1s the average of the two middle numbers Example median 1 4 0 7 7 4 When the data is arranged in order the middle number is 4 Minimum Input min x y Z Description Finds the minimum of a list of numbers The minimum is the smallest value in a set of data Example 1 min 1 2 4 5 0 4 Negative 4 is the smallest value in this list of data Example 2 min primeSet 12 2 The smallest number in the prime set of 12 is 2 Mode Input mode x y z Description Finds the mode or modes of a list of data The mode is the number or numbers that occurs most frequently in a set of data If no number occurs more often than any other number the set of data has no mode Example mode 1 4 0 7 7 7 In this set of data 7 occurs most frequently It is the mode Random Number Input rand m n Description Finds a random integer k in the range m lt k lt n or n lt k lt m if n lt m Example rand 56 12 49 The number forty nine is a random integer between 56 and 12 Population Standard Deviation Input stdP x y Z Description Finds the population stand
113. they can take different lists of arguments These functions have a Form menu Once you select the form of the function that you want the template changes to show the list of arguments for that form All templates have several useful menus The File menu allows you to Open or Save the data in a template The Edit menu allows you to perform normal editing operations The Samples menu contains one or more sets of sample data Selecting an item from the Samples menu copies the sample data into the template Tap on the Show Result button to obtain the result of the sample data Tap ok in the corner of the template to close it It is important to remember when you are entering functions and or equations in the Function Template An asterisk must be used to indicate multiplication Implicit multiplication by placing two factors side by side is not supported A caret must be used to indicate an exponent Help Mode Under the Options menu select Help Mode If you select Options a second time you see that Help Mode has a check mark beside it The check mark indicates that the Help Mode has been activated Now when a Function with Function Templates deactivated or Plot is selected from the menu bar the Help file for that command opens For example if you open the Function menu and then select solve from the Equations section of the menu the help file will open a separate window containing the section on solving a system of linear equatio
114. u can select the number of decimal places that you would like results to show You can have as few as 2 digits after the decimal place and as many as 9 To change the number of decimal places 1 Tap on the Options menu 2 Select Fix to see the numbers of decimal places available 3 Select the number of decimal places you want the results to have by tapping on your choice A check mark indicates your selection The default setting is 6 Mode Normal or Scientific Decimals or Fractions Degrees or Radians You can choose to see numeric results as Normal or Scientific and Decimals or Fractions The Mode option also includes a choice between Degrees and Radians To change between normal and scientific mode 1 Tap on the Options menu 2 Select Mode to display the choices 3 Choose either Normal or Scientific from the menu A check mark indicates your selection The default Tf setting is Normal Fractions To change between decimal and fraction form CE Degrees 1 Tap on the Options menu i 1 Radians 2 Select Mode to display the choices 3 Choose either Decimals or Fractions from the menu A check mark indicates your selection The default setting is Decimals To change between degrees and radians 1 Tap on the Options menu 2 Select Mode to display the choices 3 Choose either Degrees or Radians from the menu A check mark indicates your selection The default setting is Degrees If the input
115. ue If m and n are amicable isAmicable returns true otherwise it returns false Example isAmicable 6 28 false The numbers 6 and 28 are not amicable Composite Number Input isComposite n Description Finds whether n is a composite number A composite number is a number that has more than two factors This function returns a Boolean true or false value If n 1s a composite number isComposite returns true otherwise it returns false Example isComposite 7 false Seven is not a composite number Deficient Number Input isDeficient n Description Finds whether n is a deficient number A deficient number is a number where the sum of its proper factors is less than the number itself This function returns a Boolean true or false value If n is deficient isDeficient returns true otherwise it returns false Example isDeficient 28 false The number twenty eight is not a deficient number 43 44 Perfect Number Input isPerfect 7 Description Finds whether n is a perfect number A perfect number is a number for which the sum of its proper factors is equal to the number itself This function returns a Boolean true or false value If n is perfect isPerfect returns true otherwise it returns false Example isPerfect 28 true Twenty eight is a perfect number because 1 2 4 7 14 28 Prime Number Input isPrime n Description Finds whether n is a prime number A prime number is a number that has exactly two
116. umbers or any functions or operations with numeric results 78 Graphs of Equations An equation is a mathematical sentence with an equal sign Equation Plot etx 5 26 ES Folium of Descartes Entering Data 1 Ba er w of the cells in the column labeled 2 Enter your equation Use for exponents and x 3 y 3 x y i for multiplication x S y 3 x Fy Enter the x and the y limits that you want your law ASE OC equation evaluated from and to KMS tyA sa TOY 4 Tap on the pencil icon to draw the graph of the equation Note The x and y limits that you want the equation evaluated from and to must be entered If you do not enter them you will get a syntax error when you try to plot the equations If you are graphing more than one equation the x and y limits do not have to be the same However the largest set of limits is used for all equations so they fit on the same set of axes The equations you want evaluated can be comprised of integers symbolic constants decimal numbers or any functions or operations with numeric results 79 Point Plots A point plot is a graph that connects all of the points of data with a straight line Point Plot EN amp Stock Prices Week Z Entering Data 1 Tap in one of the spaces in the column labeled x 2 Enter a value for x 3 Enter ina value for y Use the Tab key to move the cursor over to these spaces or tap in them with your stylus 4 Tap on the penci
117. uses fractions and decimals the result appears in decimal form regardless of the Decimals Fractions mode For example if the input is Y 5 0 the result is 2 5 even if the fraction mode is selected If the input is 2 5 the result is 5 2 if the fraction mode is selected otherwise the result will display as 2 5 Tip Keep in mind that some calculations can be more accurate if done in fraction mode For example you get an exact answer calculating determinants of matrices with integer entries in fraction mode In decimal mode there are always round off errors and you can get misleading answers 12 Editing Menu amp Tools The Edit menu includes the cut copy paste and undo operations The Edit menu also provides access to the List Editor the Matrix Editor the Sequence Editor the Table Editor the Unit Converter and the Variable Editor The Clear History and Unassign commands are also found here Cut Copy Paste Select All List Editor Matrix Editor Sequence Editor Table Editor Unit Converter Variable Editor Clear History Unassign Unassign All List Editor With the List Editor you can create a list of values or expressions using a spreadsheet like editor It is also possible to type lists directly into the Input window You have the option of assigning your list to a variable Portrait4 a 421033 ok To enter a list 1 Tap the Edit menu 2 Open the List Editor 3 Enter a variable in the space provi
118. w by 1 simply adds the source row to the destination row Adding and Multiplying Columns Input addcol matrix A destination column source column factor Description This operation replaces column of a matrix with c column j column ji Example addcol matrix 2 2 1 2 3 4 2 1 2 matrix 2 2 1 4 3 10 In this example multiply column 1 by 2 and add the result to column 2 Multiplying a column by 1 simply adds the source column to the destination column Augment Input augment matrix A matrix B Description This operation joins matrix B to matrix A as new columns You can only augment a matrix with another matrix that has the same number of rows Example augment matrix 2 2 1 2 3 4 matrix 2 2 1 0 0 1 matrix 2 4 1 2 1 0 3 4 0 1 Column Norm Input cNorm matrix A Description Finds the column norm of a matrix Example cNorm matrix 3 3 1 2 3 4 5 6 7 8 9 18 Cross Product Input crossProd matrix A matrix B Description Finds the cross product of two 3 vectors 1 x 3 matrices Example crossProd matrix 1 3 1 2 3 matrix 1 3 4 5 6 matrix 1 3 3 6 3 Determinant Input det matrix A Description Finds the determinant of a square matrix A determinant is a scalar quantity that represents a defined alternating sum of products of elements of a square matrix one from each row and column Example det matrix 2 2 1 2 3 4 2
119. xample input x 2 y y 3 x Here a value is assigned to x and to y and then the calculator solves for x the solution is 6 You can combine any number of expressions but only the result of the last expression is displayed in the Result window To wrap a function around information already entered in the input window highlight the text and then choose the function you want to enclose it in This inserts the function in the correct position with its brackets appropriately placed This can be a helpful time saving feature If you are inputting strings of data in the Input window answers or error messages are displayed in the Result window Once you input your data tap on the equal sign button on the calculator or press Enter on the keyboard to view a solution If the solution is longer than the result window a scroll bar will appear so the complete solution can be viewed To remove a result simply tap on the Clear button This clears the Input window as well History List ir 9 53 Ey At the far right of the Input window is a down arrow If you are inputting strings of data in the Input window tap on the arrow to view a list of the most recent calculations compound 5000 0 35 4 10 It stores up to 25 previous calculations you can use the compound 5000 0 35 4 10 scroll bar to view them all Tap on any entry in the list to Acompound 5000 0 35 4 20 copy it into the Input window To remove all the compound 5000 0 35 12 10
120. you try to plot the functions Ifyou are graphing more than one function the limits do not have to be the same This can be useful for graphing different sections of the same function in different colors The functions you want evaluated can be comprised of integers symbolic constants decimal numbers or any functions or operations with numeric results 77 Parametric Plots A parametric plot is a graph of two functions on an xy plane The set of ordered pairs that make up the graph are f t g t where f and g are functions of another variable t Parametric Plot e a x 12 58 x Path of 2 Objects Entering Data 1 Tap in one of the cells in the column labeled x f t Enter your function Use for exponents and for x f t y a t t from multiplication o 2 cos t 3 sin t 3 Enter a second function in the y g t column o 4 Enter the values that you want your functions evaluated ji sin t from and to This step is not optional for parametric plots 9 Tap on the pencil icon to draw the graph of the functions Note Ifyou do not enter t from and t to values you will get a syntax error when you plot the functions Ifyou are graphing more than one function the t values do not have to be the same This can be useful for graphing different sections of the same function in different colors The functions you want evaluated can be comprised of integers symbolic constants decimal n
121. your x and y values Row 1 is the first point row 2 1s the second point etc If you have more than one set of data add more columns by opening the Edit menu and selecting Insert Columns 3 Enter the x from x to domain y from and y to range values that you want your data plotted within This step 1s optional but you will build a better graph 1f you include appropriate limits 4 Once your x and y values and the limits have been entered tap on the pencil icon This opens the Curves property window N 5 Choose the type of curve that you want to fit to the PAUSA BES ok data To fit an n degree polynomial you must also Select a curve to fit to your data enter the degree in the box provided ea E tial 6 Tap ok and the graph will be drawn 2 No regression E oro ogai _ Polynomial of degree _ Sinusoidal Note The x and y values may be integers decimal numbers symbolic constants or calculations Ifyou select No Regression in the Curves section of the Properties window the points are graphed without a best fit line Entering the domain and range to plot the data within is optional but you will build a better graph if you include this If you do enter this information it has to be entered for both x and y 71 Types of Curves No Regression Select no regression A curve will not be fit to the data Linear Regression Select linear Fits the equation y ax b to the data using a leas

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