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fx-991EX Quick Start Guide

43

POLYNOMIAL EQUATIONS 

The 

fx-991EX

 has the computing power to solve polynomial equations up to 4th degree.

To start solving polynomial equations, in the Equation/Func icon, 
press 

i

2

(Polynomial).

Select the degree of the polynomial. For this example, use a  
3rd degree polynomial. Press 

3

(Degree).  

 
 
 
Fill out the template for a 3rd degree polynomial. Type in each 
coefficient followed by the 

p 

key. 

 
x

3

 + 4x

2

 +x – 6 = 0 

 
Press 

p 

to solve the equation. 

 
 
 
 
Use the arrow keys (

ER

) to toggle through the solutions.

EQUATION/FUNC

Содержание ClassWiz fx-991EX

Страница 1: ...or on and press qC OFF to power the unit down The icon based menu accessible via the p key allows easy navigation of features using the arrow keys and the number keys or the Q shortcuts The o key can be used like Backspace in a word processor to delete the character s left of the cursor The symbols printed on the keys use Natural Textbook Display notation similar to that found in textbooks This ma...

Страница 2: ...s angles and unit vectors STATISTICS Calculate 13 different one variable statistics and apply linear quadratic logarithmic exponential and geometric power regressions DISTRIBUTION Investigate Normal Inverse Normal Binomial and Poisson probability and cumulative distributions SPREADSHEET Create spreadsheets with up to 5 columns and 45 rows Spreadsheet supports Fill Cut Copy Paste recursive formulas...

Страница 3: ...ions and mixed numbers can be entered using a and qaA respectively To enter the calculation to the left press a7 8 qaA2 3 11p To change the solution to a decimal format press n Press qnN to convert the result into a mixed number format When inputting radical expressions the radical bar automatically extends as additional characters are typed Press s24 The output will be displayed in simplest radic...

Страница 4: ...acked inside one another to allow input of complicated expressions such as this quotient of rational exponentials Press a3 a1 2 3 2 In a trigonometry setting arithmetic can be performed in terms of π Press a3qKC 4 2qKC Other useful Natural Textbook Display templates that help overcome typical calculator input frustrations include logarithms of any base ia1 2 16 Note the calculator does not generat...

Страница 5: ...te mode can be accessed by pressing qp SET UP Press R one or more times to reveal additional Setup options Solve x2 Ax Bx 0 for x when A 5 and B 6 Enter the equation by pressing xd Qz A x Qx B Qr 0 SOLVE The fx 991EX can elegantly solve an equation for any unknown using Newton s method with the SOLVE command To use SOLVE first input the equation to be solved then press qr SOLVE CALCULATE ...

Страница 6: ...same task and solve for A or B enter a value for x and a value for one of the other unknowns For example to solve for A when x 1 and B 4 press qr SOLVE 1p2p4p Arrow back up to A and SOLVE the equation by pressing p The solution also displays L R 0 This means that Newton s method of approximation is directly on 5 If L R is not 0 simply recalculate to get a better approximation CALCULATE ...

Страница 7: ...alculate icon and press p or press 1 There are many different types of unit conversions that can be accomplished on this menu To view the options press q8 CONV Use the down arrow key R to see all the possibilities Each one of the choices has a wide range of conversion options for many different types of unit conversion Use the arrow keys to locate the Length conversion and press 1 To convert 500 i...

Страница 8: ...US gallon 0 8326742321 UK gallons The same calculation can be accomplished using a string of conversions Press 1q8 CONV 3 Volume 1 gal US L q8 CONV 3 Volume 4 L gal UK p Start with a large number like 2 5 X 109 Press 2 5K9p The gap between digits at place value separation can be viewed by entering Set Up Press qp SET UP and use the arrow keys to navigate to the third menu ENGINEERING NOTATION Conv...

Страница 9: ...aration To convert this solution into engineering notation use the b key to change the solution into scientific notation To move the decimal to the right press b To turn on the engineering symbols in setup press qw SET UP Select 4 Engineer Symbol 1 On to turn on the Engineering Symbols Calculating with engineering symbols has never been easier To move the decimal to the left press qbX CALCULATE ...

Страница 10: ...tart Guide 10 To calculate 500k kilo 10M Mega press 500i3 Engineering Symbols 6 k 10i3 Engineering Symbols 7 M p The solution is displayed using the appropriate units Now use theb key to convert between units CALCULATE ...

Страница 11: ...ss p or press 2 In Complex Mode operations can be carried out using the imaginary unit U To add complex numbers press 2 3bU 5 7bUp Complex numbers that are multiplied are displayed in complex format Press 3 2bU 5 6bU p The argument of the complex number 1 2i can be found by taking the arctan y x 63 4349 or by using the Argument command Press i1 Argument 1 2bU p COMPLEX ...

Страница 12: ...onvert any polar form of a complex number use the r theta command or type in the angle in polar form Press C2qbZ330iR 2 a bi p Alternately simply type in the angle in polar form by pressing 2qbZ330p These calculations can also be accomplished in radian mode To change to radian mode press qp SET UP 2 Angle Unit 2 Radian COMPLEX ...

Страница 13: ...ain Menu use the arrow keys to highlight the Matrix icon and press p or press 4 To enter matrices first define the matrix Press 1 MatA 2 Rows 2 Columns 1p2pz3p4p To enter a second matrix press i From the resulting popup window press 1 Define Matrix 2 MatB Select the number of rows 2 Rows Select the number of columns 2 Columns MATRIX ...

Страница 14: ...name of a matrix press i To add A B press 3 MatA i4 MatB p The solution matrix is displayed in the window and can be viewed without scrolling To calculate the determinant of the matrix press iR2 Determinant i3 MatA p Matrices can be used to solve a system of equations Take the following equation with 3 unknowns Enter the coefficient matrix as Matrix A and the solution matrix as Matrix B MATRIX ...

Страница 15: ...cient matrix Select the number of rows 3 Rows Select the number of columns 3 Columns Enter the values of the coefficients pressing p after each one to move to the next value Now enter the 3 x 1 solution matrix as Matrix B Press i1 Define Matrix Define Matrix B 2 MatB as a 3 x 1 so select 3 Rows and 1 Columns from the next two windows MATRIX ...

Страница 16: ...g p after each one to move to the next value Press C to return to the Matrix Calculation screen The solution can be found by calculating A 1 x B Press i3 MatA uOi4 MatB p The solution represents the following This same system can also be solved using the Equation icon MATRIX ...

Страница 17: ...ector icon and press p or press 5 Let vectors u and v be defined in the 3 dimensional plane by the following u 2i 3j 2k and v 3i 4j 5k Define u as Vector A with dimension 3 Press 1 VctA 3 Dimension Enter the components of the vector and press p after each one to move to the next value Define v as Vector B with dimension 3 Press i1 Define Vector Press 2 VctB 3 Dimension VECTOR ...

Страница 18: ...lculation Recall the names of the vectors and execute the desired operation by pressing i Vector addition subtractions and multiplication are all available For subtraction press 3 VctA i4 VctB p For multiplication press i3 VctA Oi4 VctB p The sums of the product of the components of a vector are known as the vector s dot product So Press i3 VctA iR2 Dot Product i4 VctB p VECTOR ...

Страница 19: ...ome very complex vector operations like the angle between vectors which is defined as in which are easily accomplished on the fx 991EX To calculate vector cross product not vector multiplication press iR3 Angle i3 VctA q i 4 VctB p VECTOR ...

Страница 20: ...he Statistics icon then press p or press 6 On the resulting menu select 1 for 1 Variable statistics A data entry screen appears This example uses the following list of some students heights given in inches 70 5 74 67 71 71 72 73 5 72 69 71 Enter data by typing in each value one at a time with each followed by the p key 70 5p 74p etc To calculate the 1 Variable statistics for this data set press i3...

Страница 21: ...different categories of statistical variables For instance to calculate the interquartile range IQR press 3 Min Max 4 Q3 iR3 Min Max 2 Q1 p 13 different 1 variable statistics have been calculated 6 of which appear on the first screen Press R one or more times to reveal additional statistics These statistics have each been stored inside the fx 991EX as variables in case you should wish to use them ...

Страница 22: ...ess qp SET UP Press the down arrow R to reach the second page and 3 to select the Statistics settings Press 1 to turn the Frequency option On The Statistics Calculation area appears again Even though nothing appears to have happened the setting has indeed changed To access the Data entry area press i3 Data Notice a second column for frequencies now appears and the previous data set has been erased...

Страница 23: ...al to those previously found Enter the same 10 students height used previously making use of the Frequency column As each data point is inputted ClassWiz automatically assigns a default Frequency of 1 Edit a Frequency by using the arrow keys to highlight it then typing a new Frequency followed by p Once all of the data points x and frequencies Freq have been entered press i3 1 Variable Calc again ...

Страница 24: ... qp SET UP R3 Statistics 2 Off to remove it Input the ordered pairs 1 1 2 4 3 9 and 4 16 Use the arrow keys to navigate to the y column as necessary To view 2 Variable statistics or the linear regression results press i3 Other regressions including quadratic logarithmic exponential and geometric can be accessed via i1 Select Type Press Ci4 Regression Calc to display the linear regression results S...

Страница 25: ...ng Binomial Distribution problem A fair 6 sided die is rolled six times Find P 6 comes up at least twice After pressing p to input the value of p ClassWiz automatically converts the fraction into a decimal for its own purposes Press p again to calculate the probability To enter the values of x number of successes N number of trials and p probability of success press 2 Variable Input the values as ...

Страница 26: ...ls press i1 Select Type This time choose 4 Binomial PD Once the final value has been entered press p again to end the data entry process Notice the values of N and p are preserved from the cumulative probability calculation N and p are global calculator variables Enter the values 0 1 2 3 4 5 and 6 into the x column which represents number of successes Press p after each input Because the calculati...

Страница 27: ...tion press i1 Select Type Editor edits the previous PD s data list Select 3 Inverse Normal Input the values as shown to answer the question If the heights of U S males are normally distributed with a mean of 70 inches and a standard deviation of 4 inches what range defines the tallest 10 of U S males Press p once more to reveal the result To be in the top 10 of U S males by height a man must be ov...

Страница 28: ...liquid laundry detergent is 0 885 g mL Type 0 885p in cell A1 Use the arrow keys to move over to cell B1 and input 40p to represent a 40 fl oz bottle of laundry detergent Move to cell C1 and press Qr to create an equals sign Like in other spreadsheet programs this is the first step necessary when entering a formula To grab the value within a cell press i2 Grab The Spreadsheet mode is useful for st...

Страница 29: ...a has correctly calculated that a 40 fl oz bottle of laundry detergent has a volume of 1182 9 mL Formulas can also be typed directly without using the Grab command Navigate to cell D1 and input Qr Qz A 1OQu C 1p A 40 fl oz bottle of laundry detergent has a mass of 1046 9 grams Now let s use the power of relational formulas to check some other bottle sizes To populate many different cells with the ...

Страница 30: ...t the value 75 by pressing 75p To populate many different cells with the same formula press i1 Fill Formula Input the formula Qx B 2 25p Notice the cell Range is pre populated with the currently highlighted cell B3 Use the right arrow to edit only the end cell by pressing o6pp Scroll down to cell B6 to make sure that the formula has been adjusted relative to each cell s position so that cells B2 t...

Страница 31: ...his formula into cells C2 through C6 Column C now contains the volumes in milliliters of the different sizes of laundry detergent bottles To exit Copy Paste mode press C Time to practice Use the same technique to Copy Paste the mass calculation formula from cell D1 into cells D2 through D6 If done correctly Column D should show masses in grams as shown So for example a 175 fl oz bottle of laundry ...

Страница 32: ...igate to cell B7 and press i Scroll down three pages RRR and select 3 Mean Type in the cell range of the average Qx B 1Qy Qx B 6 p The average capacity is 110 83 fluid ounces If one of each of these bottles was purchased what is the total weight of laundry detergent purchased that would be placed in a car Navigate to cell D7 and press i Return again to the summary statistics calculation screen RRR...

Страница 33: ...nd Set it as the object to be Grabbed by pressing p Use Qy to type a colon Grab cell D6 as the ending cell in the cell range by pressing i2Ep Close the parentheses and press p to calculate the sum of the masses in cells D1 through D6 The bottles would have a total mass of 17404 grams or about 17 4 kilograms But this is a mass not a weight SPREADSHEET ...

Страница 34: ...u Select 4 Mass Choose mass conversion 4 kg lb This will convert the mass from cell D7 which is currently in kilograms into pounds Press p and Voila Even ClassWiz s powerful Conversion feature can be used within the Spreadsheet module But wait 38 thousand pounds 17404 grams needs to be converted into kilograms With cell D8 highlighted press i3 Edit Cell A cursor appears in the previously entered f...

Страница 35: ...o move within the formula inserting parentheses and a factor of 1000 adjustment as shown Press P1000 p Phew That s better The car is no longer carrying 19 tons of laundry detergent home The actual total weight is a much more reasonable 38 pounds SPREADSHEET ...

Страница 36: ...he down arrow key to view the menu option for Table it will be the 3rd screen Press 2 Table to choose the number of functions used in the table Press 1 f x to generate a table with only one function as an input The Table feature on the fx 991EX is a powerful way to solve a single function or two functions simultaneously The table range and step is easily customizable Consider the classic volume of...

Страница 37: ...the search enter a new value in any place in the table For example at line 8 press 6 5p To enter a value one step greater than the previous value press To enter a value one step less than the previous value press To change the step value or change the start and end values of the table press Cp Enter the new values and press p to view the table Use the arrow keys to scroll to the value that gives t...

Страница 38: ...ss qp SET UP and use the down arrow key to view the menu option for Table Press 2 Table to choose the number of functions used in the table Press 2 f x g x to generate a table with two function as inputs Enter the first function as f x by pressing x 3 7x 6p If there is already a function present press C to clear the previous function Enter the second function as g x by pressing xd 3x 2p Create a t...

Страница 39: ... to negative infinity to the left and g x goes to positive infinity to the left There appears to be roots of 1 and 2 for both functions To determine the behavior between roots type in a number between 1 and 2 like 1 5 The right end behavior for both functions appears to be increasing towards positive infinity TABLE ...

Страница 40: ...nd Polynomial Equations up to the 4th degree SIMULTANEOUS EQUATIONS From the Main Menu use the arrow keys to highlight the Equation Func icon and press p or press z A To solve the following system of simultaneous equations select 1 Simul Equation Choose the number of Unknowns For this example press 2 Unknowns A 2x2 system of equations template is displayed The template is in Ax BY C form in which ...

Страница 41: ...s press n To change the values in the system of equations without changing the type of equation or system press C The fx 991EX also solves inconsistent systems both independent and dependent Enter the displayed inconsistent and independent system Press p to see the solution To change the type of equation or system size press i and select from the on screen menus EQUATION FUNC ...

Страница 42: ...er the displayed inconsistent dependent system Press p to see the solution To input a larger system of simultaneous equation press i1 Simul Equation 3 Unknowns Enter the coefficents for each equation and press p to solve EQUATION FUNC ...

Страница 43: ...al equations in the Equation Func icon press i2 Polynomial Select the degree of the polynomial For this example use a 3rd degree polynomial Press 3 Degree Fill out the template for a 3rd degree polynomial Type in each coefficient followed by the p key x3 4x2 x 6 0 Press p to solve the equation Use the arrow keys ER to toggle through the solutions EQUATION FUNC ...

Страница 44: ... Press i and change the type of polynomial to quadratic 2 Enter the coefficients that appear in the displayed screen into the quadratic template and press p The solutions are displayed in simplified radical form including the imaginary unit Press R to see the second imaginary solution EQUATION FUNC ...

Страница 45: ... x B Enter the degree of the polynomial inequality in this case 3 Degree Choose the form of the inequality Press 2 Enter the coefficients of the polynomial as shown Press 1p4p1pz6p Press p to see the solutions Notice the form of the inequality is written as x a b x c If the solution runs off the screen use the left and right arrow keys to see the entire solution INEQUALITY ...

Страница 46: ...fx 991EX Quick Start Guide 46 NOTES ...

Страница 47: ...fx 991EX Quick Start Guide 47 NOTES ...

Страница 48: ...fx 991EX Quick Start Guide See the complete line of Casio calculators www casioeducation com ...

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