Texas instruments TI-30X PRO User Manual

TI-30X Pro MathPrint™

Scientific Calculator Guidebook

This guidebook applies to software version 1.0. To view the latest version of the documentation, go to education.ti.com/eguide.

Important Information

Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programmes or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental or consequential damages in connection with or arising from the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

MathPrint, APD, Automatic Power Down, and EOS are trademarks of Texas Instruments Incorporated.

Contents

Getting Started 1

Switching the Calculator On and Off Display Contrast Home Screen 2nd Functions Modes Multi-Tap Keys Menus Examples Scrolling Expressions and History Answer T oggle Last Answer Order of Operations Clearing and Correcting Memory and Stored Variables

Math Functions 13

Fractions Percentages Scientific Notation [EE] Powers, Roots and Inverses Pi (symbol Pi) Math Number Functions Angles Rectangular to Polar Trigonometry Hyperbolics Logarithm and Exponential Functions Numerical Derivative Numerical Integral Statistics, Regressions and Distributions Probability

13 15 16 17 17 18 19 21 23 24 26 26 27 28 30 40

1 1 1 2 2 4 5 5 6 6 7 7 9

Math Tools 43

Stored Operations Data Editor and List Formulas Function Table Matrices Vectors Solvers

43 44 48 50 53 55

iii

Number Bases Expression Evaluation Constants Conversions Complex Numbers

60 62 63 64 67

Reference Information 70

Errors and Messages Battery Information Troubleshooting

70 74 75

General Information 76

Online Help Contact TI Support Service and Warranty Information

76 76 76

Getting Started

This section contains information about basic calculator functions.

Switching the Calculator On and Off

& turns on the calculator. % ' turns it off. The display is cleared, but the history, settings, and memory are retained.

The APD™ (Automatic Power Down™) feature turns off the calculator automatically if no key is pressed for about 3 minutes. Press & after APD™. The display, pending operations, settings, and memory are retained.

Display Contrast

The brightness and contrast of the display depend on room lighting, battery freshness and viewing angle.

To adjust the contrast:

1. Press and release the % key.

2. Press ] (to darken the screen) or [ (to lighten the screen).

Note: This will adjust the contrast one level at a time. Repeat steps 1 and 2 as

needed.

Home Screen

On the Home screen, you can enter mathematical expressions and functions, along with other instructions. The answers are displayed on the Home screen.

The TI-30X Pro MathPrint™ screen can display a maximum of four lines with a maximum of 16 characters per line. For entries and expressions longer than the visible screen area, you can scroll left and right (! and ") to view the entire entry or expression.

In MathPrint™ mode, you can enter up to four levels of consecutive nested functions and expressions, which include fractions, square roots, exponents with ^, Ü, ex, and 10x.

When you calculate an entry on the Home screen, depending upon space, the answer is displayed either directly to the right of the entry or on the right side of the next line.

Special indicators and cursors may be displayed on the screen to provide additional information concerning functions or results.

Indicator Definition

2ND 2nd function.

FIX Fixed-decimal setting. (See Mode section.)

SCI, ENG Scientific or engineering notation. (See Mode

section.)

Getting Started 1

Indicator Definition

DEG, RAD, GRAD

L1, L2, L3 Displays above the lists in data editor.

H, B, O Indicates HEX, BIN, or OCT number-base mode. No

5 6 An entry is stored in memory before and/or after

Angle mode (degrees, radians, or gradians). (See Mode section.)

indicator displayed for default DEC mode.

The calculator is performing an operation. Use & to break the calculation.

the visible screen area. Press # and $ to scroll.

Indicates that the multi-tap key is active.

Normal cursor. Shows where the next item you type will appear. Replaces any current character.

Entry-limit cursor. No additional characters can be entered.

Insert cursor. A character is inserted in front of the cursor location.

Placeholder box for empty MathPrint™ template. Use the arrow keys to move into the box.

MathPrint™ cursor. Continue entering in the current MathPrint™ template, or press " to exit the template.

2nd Functions

Most keys can perform more than one function. The primary function is indicated on the key and the secondary function is displayed above it. Press % to enable the secondary function of a given key. Notice that 2ND appears as an indicator on the screen. To cancel before pressing the next key, press % again. For example, % b

25 < calculates the square root of 25 and returns the result, 5.

Modes

Use q to choose modes. Press $ # ! " to choose a mode, and < to select it. Press - or % s to return to the Home screen and perform your work using the chosen mode settings.

Default settings are highlighted in these sample screens.

2 Getting Started

DEGREE RADIAN GRADIAN - Sets the angle mode to degrees, radians, or gradians.

NORMAL SCI ENG - Sets the numeric notation mode. Numeric notation modes

affect only the display of results, and not the accuracy of the values stored in the unit, which remain maximal.

NORMAL displays results with digits to the left and right of the decimal, as in

123456.78.

SCI expresses numbers with one digit to the left of the decimal and the appropriate

power of 10, as in 1.2345678E5, which is the same as the value (1.2345678×105) including the brackets for correct order of operation.

ENG displays results as a number from 1 to 999 times 10 to an integer power. The

integer power is always a multiple of 3.

Note: E is a shortcut key to enter a number in scientific notation format. The

result displays in the numeric notation format selected in the mode menu.

FLOAT 0 1 2 3 4 5 6 7 8 9 - Sets the decimal notation mode.

Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal.

0 1 2 3 4 5 6 7 8 9 (fixed decimal point) specifies the number of digits (0 to 9) to

display to the right of the decimal.

REAL a+bi r±q - Sets the format of complex number results.

REAL real results

a+bi rectangular results

r±q polar results

DEC HEX BIN OCT - Sets the number base used for calculations.

DEC decimal

HEX hexadecimal (To enter hex digits A through F, use % §, % ¨, and so on.)

BIN binary

OCT octal

MATHPRINT CLASSIC

MATHPRINT mode displays most inputs and outputs in textbook format.

CLASSIC mode displays inputs and outputs in a single line.

Examples of MathPrint™ and Classic Modes

MathPrint™ Mode Classic Mode

Sci Sci

Getting Started 3

MathPrint™ Mode Classic Mode

Float mode and answer toggle key

Fix 2 and answer toggle key Fix 2

Un/d Un/d entry

Exponent example Exponent example

Square root example Square root example

Cube root example Cube root example

Float mode and answer toggle key.

Multi-Tap Keys

A multi-tap key is one that cycles through multiple functions when you press it. Press " to stop multi-tap.

For example, the X key contains the trigonometry functions sin and sin/ as well as the hyperbolic functions sinh and sinh/. Press the key repeatedly to display the function that you want to enter.

4 Getting Started

Multi-tap keys include z, X, Y, Z, C, D, H, and g. Applicable sections of this guidebook describe how to use the keys.

Menus

Menus give you access to a large number of calculator functions. Some menu keys, such as % h, display a single menu. Others, such as d, display multiple menus.

Press " and $ to scroll and select a menu item, or press the corresponding number next to the item. To return to the previous screen without selecting the item, press

-. To exit a menu and return to the Home screen, press % s.

% h (key with a single menu):

RECALL VAR

1:x = 0 2:y = 0 3:z = 0 4:t = 0 5:a = 0 6:b = 0 7:c = 0 8:d = 0

d (key with multiple menus):

MATHS NUM DMS R³´P

1:4n/d³´Un/d 2:lcm( 3:gcd( 4:4Pfactor 5:sum( 6:prod( 7:nDeriv( 8:fnInt(

1:abs( 2:round( 3:iPart( 4:fPart( 5:int( 6:min( 7:max( 8:mod(

1:¡ 2:¢ 3:£ 4:r 5:g 6:4DMS

1:P 4 Rx( 2:P 4 Ry( 3:R 4 Pr( 4:R 4 Pq(

Examples

Some sections are followed by instructions for keystroke examples that demonstrate the TI-30X Pro MathPrint™ functions.

Notes:

• Examples assume all default settings, as shown in the Modes section unless noted in the example.

• Use - to clear the home screen as needed.

Getting Started 5

• Some screen elements may differ from those shown in this document.

• Since wizards retain their memory, some keystrokes may be different.

Scrolling Expressions and History

! " # $

Press ! or " to move the cursor within an expression that you are entering or editing. Press % ! or % " to move the cursor directly to the beginning or end of the expression.

From an expression or edit, # moves the cursor to the history. Press < from an input or output in history to paste that expression back to the cursor position on the edit line.

Press % # from the denominator of a fraction in the expressions edit to move the cursor to the history. Press < from an input or output in history to paste that expression back to the cursor position on the edit line.

Example

7 F U 4

( 3 ) ( 1 ) <

% b # # < <

Answer Toggle

Press the r key to toggle the display result (when possible) between fraction and decimal answers, exact square root and decimal, and exact pi and decimal.

Example

Answer toggle

6 Getting Started

% b 8 <

Note: r is also available to toggle number formats for values in cells in the Function

Table and in the Data Editor. Editors such as in matrix, vector and system solver will display toggled cell values.

Last Answer

% i

The last entry performed on the home screen is stored to the variable ans. This variable is retained in memory, even after the calculator is turned off. To recall the value of ans:

• Press % i (ans displays on the screen), or

• Press any operations key (T, U, and so forth) in most edit lines as the first part of an entry. ans and the operator are both displayed.

Examples

ans 3 V 3 <

V 3 <

3 % c % i

Note: The variable ans is stored and pastes in full precision which is 13 digits.

Order of Operations

The TI-30X Pro MathPrint™ calculator uses Equation Operating System (EOS™) to evaluate expressions. Within a priority level, EOS™ evaluates functions from left to right and in the following order.

1st Expressions inside brackets.

2nd Functions that need a ) and precede the argument,

3rd Functions that are entered after the argument,

4th Exponentiation (^) and roots (x‡).

such as sin, log, and all R³´P menu items.

such as x2and angle unit modifiers.

Note: In Classic mode, exponentiation using the

G key is evaluated from left to right. The expression 2^3^2 is evaluated as (2^3)^2, with a result of 64.

Getting Started 7

In MathPrint™ mode, exponentiation using the G key is evaluated from right to left. The expression 2^3^2 is evaluated as 2^(3^2), with a result of

512.

The calculator evaluates expressions entered with F and a from left to right in both Classic and MathPrint™ modes. Pressing 3 F F is calculated as (32)2= 81.

5th Negation (M).

6th Fractions.

7th Permutations (nPr) and combinations (nCr).

8th Multiplication, implied multiplication, division, and

angle indicator ±.

9th Addition and subtraction.

10th Logic operators and, nand.

11th Logic operators or, xor, xnor.

12th Conversions such as 4n/d³´Un/d, F³´D, 4DMS.

13th

14th < evaluates the input expression.

Note: End of expression operators and Base n conversions such as 4Bin, angle

conversion 4DMS, 4Pfactor, and complex number conversions 4Polar and 4Rectangle, are only valid in the Home Screen. They are ignored in wizards, function table display and data editor features where the expression result, if valid, will display without a conversion. Editors such as in matrix, vector and system solver will also ignore these end of expression operators in the edit line.

Note: Use brackets to clearly indicate the operation order you expect for your

expression entry. If necessary, the brackets can be used to override the order of operations followed by the algorithms in the calculator. If the result is not as expected, check how the expression was entered and add brackets as needed.

Examples

+ Q P M 60 T 5 V M 12 <

8 Getting Started

(M) 1 T M 8 T 12 <

‡ and + % b 9 T 16 <

( ) 4 V ( 2 T 3 ) <

( ) and + 4 ( 2 T 3 ) <

^ and ‡ % b 3 G 2 " T 4

( ) and M ( M 3 ) F <

G 2 <

M 3 F <

Clearing and Correcting

% s Returns the cursor to the home screen.

Quickly dismisses these applications: Expression Evaluation, Set Operation, Function Table, Data Editor, Statistics, Distributions, Vector, Matrix, Numeric Solver, Polynomial Solver, and System Solver.

% f Inserts a character at the cursor.

% { 1 Clears variables x, y, z, t, a, b, c, and d to their

%  2 Resets the calculator.

Clears an error message. Clears characters on entry line.

Deletes the character at the cursor. When the cursor is at the end of an expression, it

will backspace and delete.

default value of 0. Any computed Stat Vars will no longer be available

in the Stat Vars menu. Recompute statistic features as needed.

Getting Started 9

Returns the calculator to default settings; clears memory variables, pending operations, all entries in history and statistical data; clears any stored operation and ans.

Memory and Stored Variables

z L % h % {

The TI-30X Pro MathPrint™ calculator has 8 memory variables—x, y, z, t, a, b, c, and d. You can store the following to a memory variable:

• real or complex numbers

• expression results

• calculations from various applications such as Distributions

• data editor cell values (stored from the edit line)

Features of the calculator that use variables will use the values that you store.

L lets you store values to variables. Press L to store a variable, and press z to select the variable to store. Press < to store the value in the selected variable. If this variable already has a value, that value is replaced by the new one.

z is a multi-tap key that cycles through the variable names x, y, z, t, a, b, c, and d. You can also use z to recall the stored values for these variables. The name of the variable is entered in the current entry, but the value assigned to the variable is used to evaluate the expression. To enter two or more variables in succession, press " after each.

% h recalls the values of variables. Press % h to display a menu of variables and their stored values. Select the variable you want to recall and press <. The value assigned to the variable is inserted into the current entry and used to evaluate the expression.

% { clears variable values. Press % { and select 1:Yes to clear all variable values. Any computed Stat Vars will no longer be available in the Stat Vars menu. Recompute statistic features as needed.

Examples

Start with clear screen

Clear Var % {

10 Getting Started

% s -

1 (Selects Yes)

Store 15 L z

Recall % h

< F <

L z z

z z

< W 4 <

³ Problem

In a gravel quarry, two new excavations have been opened. The first one measures 350 metres by 560 metres, the second one measures 340 metres by 610 metres. What volume of gravel does the company need to extract from each excavation to reach a depth of 150 metres? To reach 210 metres? Display the results in engineering notation.

q $ " " < -

350 V 560 L z <

Getting Started 11

340 V 610 L z z <

150 V % h

< <

210 V % h < <

For the first excavation, the company needs to extract 29.4 million cubic metres to reach a depth of 150 metres, and extract 41.16 million cubic metres to reach a depth of 210 metres.

150 V z z <

210 V z z <

For the second excavation, the company needs to extract 31.11 million cubic metres to reach a depth of 150 metres, and extract 43.554 million cubic metres to reach a depth of 210 metres.

12 Getting Started

Math Functions

This section contains information about using the calculator maths functions such as trigonometry, statistics and probability.

Fractions

P % @ d 1 % j

Fractions with P can include real and complex numbers, operation keys (T, V, etc.), and most function keys (F, % _, etc.).

In Classic mode or classic entries in MathPrint™ mode, the fraction bar P displays inline as a thick bar, for example . Use brackets to clearly indicate the arithmetic you expect. While the Order of Operations rules will apply, you are in control of the way an expression evaluates by placing the correct brackets in your inputs.

Fraction Results

• Fraction results are automatically simplified and output is in improper fraction format.

• When mixed number output is desired, use the 4n/d³´Un/d mixed number conversion at the end of the input expression. This feature is located in d 1: 4n/d³´Un/d.

• Fraction results are obtained when the calculated value can display within the limits of the fraction format supported by the calculator and no decimal value was entered in the input expression.

• If decimal numbers are used or calculated in a fraction numerator or denominator, the result will display as a decimal. Entering a decimal forces the result to display in decimal format.

• Use % j (above r) on results to attempt fraction to decimal conversions within the fraction display limits offered by this numeric calculator.

Mixed Numbers and Conversions

• % @ enters a mixed number. Press the arrow keys to cycle through the unit, numerator, and denominator.

• d 1 converts between simple fractions and mixed-number form (4n/d³´Un/d).

• % j converts results between fractions and decimals.

MathPrint™ Entry

• To enter numbers or expressions in the numerator and denominator in MathPrint™ mode, press P.

• Press $ or # to move the cursor between the numerator and denominator.

• Pressing P before or after numbers or functions may pre-populate the numerator with parts of your expression. Watch the screen as you press keys to ensure you enter the expression exactly as needed.

Math Functions 13

On the Home Screen

• To paste a previous entry from history in the numerator or mixed number unit, place the cursor in the numerator or unit, press # to scroll to the desired entry, and then press < to paste the entry to the numerator or unit.

• To paste a previous entry from history in the denominator, place the cursor in the denominator, press % # to jump into history. Press # to scroll to the desired entry, and then press < to paste the entry to the denominator.

Evaluation of Your Expression

• When < is pressed to evaluate your input expression, brackets may be displayed to clearly indicate how it was interpreted and calculated by the calculator. If it is not what you expected, copy the input expression and edit as needed.

Classic Mode or Classic Entry

• If the cursor is in a classic entry location, enter the numerator expression enclosed by brackets, then press P to display the thick fraction bar, and then enter the denominator expression also enclosed with brackets for the result to be calculated as you expect for your problem.

Examples in MathPrint™ Mode

n/d, Un/d P 3 $ 4 " T 1 %

@ 7 $ 12 <

Note: Brackets are added

automatically.

4n/d³´Un/d 9 P 2 " d 1 <

f³´d 4 % @ 1 $ 2 " %

j <

Example P 1.2 T 1.3 $ 4 <

Note: Result is decimal

since decimal numbers were used in the fraction.

Example P M 5 T % b 5

F U 4 ( 1 ) ( 6 ) $ 2 ( 1 ) <

14 Math Functions

Examples in Classic Mode

n/d, Un/d 3 P 4 T 1 % @ 7 P

12 <

4n/d³´Un/d 9 P 2 d 1 <

f³´d 4 % @ 1 P 2 %

j <

Brackets ( 2 F U 1 ) P ( 2

F T 1 ) <

Percentages

% _

To perform a calculation involving a percentage, press % _ after entering the value of the percentage.

Example

2 % _ V 150 <

³ Problem

A mining company extracts 5000 tonnes of ore with a concentration of metal of 3% and 7300 tonnes with a concentration of 2.3%. On the basis of these two extraction figures, what is the total quantity of metal obtained?

If one tonne of metal is worth 280 units of currency, what is the total value of the metal extracted?

3 % _ V 5000 <

T 2.3 % _ V 7300 <

Math Functions 15

V 280 <

The two extractions represent a total of 317.9 tonnes of metal for a total value of 89012 units of currency.

Scientific Notation [EE]

E is a shortcut key to enter a number in scientific notation format. A number such as

(1.2 x 10-4) is entered in the calculator as the number 1.2E-4.

Example

2 E 5 < Note: Enters (2 x 10

) using the

calculator E notation.

q $ " <

Note: The SCI mode setting displays

results in scientific notation.

- <

4 E 2 V 6 E M 1 <

P 5 E 3 $ 2 E 4 < % i % j

Example

Textbook Problem

( 5 V 10 G 3 " ) W ( 2 V 10 G

4 " ) <

Using E

5 E 3 W 2 E 4 <

16 Math Functions

Powers, Roots and Inverses

% b Calculates the square root of a non-negative value.

% c Calculates the xth root of any non-negative value

Examples

5 F T 4 G 2 T 1 "

10 G M 2 <

% b 49 <

% b 3 F T 2 G 4 <

Calculates the square of a value.

Raises a value to the power indicated. Use " to move the cursor out of the power in MathPrint™ mode.

In complex number modes, a+bi and r±q, calculates the square root of a negative real value.

and any odd integer root of a negative value.

Inverts the entered value as 1/x.

6 % c 64 <

3 < % a <

Pi (symbol Pi)

g (multi-tap key)

p ≈ 3.14159265359 for calculations.

p ≈ 3.141592654 for display in Float mode.

Math Functions 17

Example

2 V g <

³ Problem

What is the area of a circle if the radius is 12 cm?

Reminder: A = p×r

g V 12 F < r

The area of the circle is 144 p square cm. The area of the circle is approximately 452.4 square cm when rounded to one decimal place.

Math

d MATH

d displays the MATH menu:

1:4n/d³´Un/d Converts between simple fractions and mixed-

2:lcm( Least common multiple

3:gcd( Greatest common divisor

4:4Pfactor Prime factors

5:sum( Summation

6:prod( Product

7:nDeriv( Numerical derivative at a point with optional

number form.

Syntax: lcm(valueA,valueB)

Syntax: gcd(valueA,valueB)

Syntax: sum(expression,variable,lower,upper) (Classic mode syntax)

Syntax: prod(expression,variable,lower,upper) (Classic mode syntax)

tolerance argument, H, when command is used in Classic mode, classic entry, and in MathPrint™

18 Math Functions

mode. Syntax: nDeriv(expression,variable,point

[,tolerance]) (Classic mode syntax)

8:fnInt( Numerical integral over an interval with optional

tolerance argument, H, when command is used in Classic mode, classic entry, and in MathPrint™ mode.

Syntax: fnInt(expression,variable,lower,upper [,tolerance])

(Classic mode syntax)

Examples

4n/d³´Un/d 9 P 2 " d 1 <

lcm( d 2

6 % ` 9 ) <

gcd( d 3

18 % ` 33 ) <

4Pfactor 253 d 4 <

sum( d 5

1 " 4 " z V 2

prod( d 6

1 " 5 " 1 P z

" " <

Note: See Numerical Derivative, nDeriv(, and Numerical Integral, fnInt( in Maths

Functions for examples and more information.

Number Functions

d NUM

d " displays the NUM menu:

Math Functions 19

1:abs( Absolute value

Syntax: abs(value)

2:round( Rounded value

Syntax: round(value,#decimals)

3:iPart( Integer part of a number

Syntax: iPart(value)

4:fPart( Fractional part of a number

Syntax: fPart(value)

5:int( Greatest integer that is { the number

Syntax: int(value)

6:min( Minimum of two numbers

Syntax: min(valueA,valueB)

7:max( Maximum of two numbers

Syntax: max(valueA,valueB)

8:mod( Modulo (remainder of first number P second

number) Syntax: mod(dividend,divisor)

Examples

abs( d " 1

M % b 5 <

round( d " 2

1.245 % ` 1 ) <

# # < ! ! ! ! ! 5 <

iPart( fPart(

4.9 L z <

d " 3 z ) < d " 4 z ) <

int( d " 5

M 5.6 ) <

min( max(

20 Math Functions

d " 6

4 % ` M 5 ) <

d " 7

.6 % ` .7 ) <

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