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TI-36X Pro Calculator
Important information............................................................. 2
Examples ............................................................................... 3
Switching the calculator on and off ........................................ 3
Display contrast ..................................................................... 3
Home screen ......................................................................... 3
2nd functions ......................................................................... 5
Modes .................................................................................... 5
Multi-tap keys......................................................................... 8
Menus .................................................................................... 8
Scrolling expressions and history .......................................... 9
Answer toggle...................................................................... 10
Last answer ......................................................................... 10
Order of operations.............................................................. 11
Clearing and correcting........................................................ 13
Fractions.............................................................................. 13
Percentages......................................................................... 15
EE key ................................................................................. 16
Powers, roots and inverses ................................................. 17
Pi.......................................................................................... 18
Math..................................................................................... 19
Number functions................................................................. 20
Angles.................................................................................. 21
Rectangular to polar ............................................................ 23
Trigonometry........................................................................ 24
Hyperbolics .......................................................................... 26
Logarithm and exponential functions ................................... 27
Numeric derivative ............................................................... 27
Numeric integral................................................................... 29
Stored operations ................................................................ 30
Memory and stored variables .............................................. 31
Data editor and list formulas ................................................ 34
1

Statistics, regressions, and distributions.............................. 36
Probability ............................................................................ 48
Function table ...................................................................... 49
Matrices ............................................................................... 52
Vectors................................................................................. 54
Solvers................................................................................. 56
Number bases ..................................................................... 61
Expression evaluation.......................................................... 63
Constants............................................................................. 64
Conversions......................................................................... 66
Complex numbers................................................................ 69
Errors................................................................................... 71
Battery information............................................................... 76
In case of difficulty ............................................................... 77
Texas Instruments Support and Service.............................. 78

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 programs 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 out of 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.
Copyright © 2010 Texas Instruments Incorporated

2

Examples
Each section is followed by instructions for keystroke
examples that demonstrate the TI-36X Pro functions.
Examples assume all default settings, as shown in the Modes
section.
Some screen elements may differ from those shown in this
document.

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 5
minutes. Press & after APD. The display, pending
operations, settings, and memory are retained.

Display contrast
The brightness and contrast of the display can depend on
room lighting, battery freshness, and viewing angle.
To adjust the contrast:
1. Press and release the % key.
2. Press T (to darken the screen) or U (to lighten the
screen).

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-36X Pro
screen can display a maximum of four lines with a maximum
of 16 characters per line. For entries and expressions of more
than 16 characters, you can scroll left and right (!and ") to
view the entire entry or expression.
In the 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.
3

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 display 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.)

DEG, RAD,
GRAD

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

L1, L2, L3

Displays above the lists in data
editor.

H, B, O

Indicates HEX, BIN, or OCT
number-base mode. No indicator
displayed for default DEC mode.
The calculator is performing an
operation.

56

An entry is stored in memory before
and/or after the active screen. Press
# and $ to scroll.

³´

An entry or menu displays beyond
16 digits. Press ! or " to scroll.
Normal cursor. Shows where the
next item you type will appear.
Entry-limit cursor. No additional
characters can be entered.
Placeholder box for empty
MathPrint™ element. Use arrow
keys to move into the box.

4

Indicator

Definition
MathPrint™ cursor. Continue
entering the current MathPrint™
element, or press an arrow key to
exit the element.

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 activate the secondary
function of a given key. Notice that 2ND appears as an
indicator on the screen. To cancel it before entering data,
press % again. For example, % b 25 < calculates
the square root of 25 and returns the result, 5.

Modes
q
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.

DEG RAD GRAD Sets the angle mode to degrees,
radians, or gradians.
NORM 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.
NORM displays results with digits to the left and right of the
decimal, as in 123456.78.

5

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 1.2345678×105).
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 point) 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 through 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
CLASSIC MATHPRINT
CLASSIC mode displays inputs and outputs in a single
line.
MATHPRINT mode displays most inputs and outputs in
textbook format.

6

Examples of Classic and MathPrint™ modes
Classic mode

MathPrint™ mode

Sci

Sci

Float mode and answer
toggle key.

Float mode and answer toggle
key.

Fix 2

Fix 2 and answer toggle key.

U n/d

U n/d

Exponent example

Exponent example

Square root example

Square root example

Cube root example

Cube root example

7

Multi-tap keys
A multi-tap key is one that cycles through multiple functions
when you press it.
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.
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 (with values set to default of 0)
1: x = 0
2: y = 0
3: z = 0
4: t = 0
5: a = 0
6: b = 0
7: c = 0
8: d = 0

8

d (key with multiple menus):
MATH
1:4n/d³´Un/d
2: lcm(
3: gcd(
4: 4Pfactor
5: sum(
6: prod(

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

DMS
1: ¡
2: ¢
3: £
4: r
5: g
6: ´DMS

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

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.
After you evaluate an expression, the expression and its
result are added automatically to the history. Use # and $
to scroll through the history. You can reuse a previous entry
by pressing < to paste it on the bottom line, where you
can edit it and evaluate a new expression.
Example
Scroll

7FU4
(3 ) (1 ) <
% b ## <
<
r

9

Answer toggle
r
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.
Pressing r displays the last result in the full precision of its
stored value, which may not match the rounded value.
Example
Answer
toggle

%b8<

r

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) as the first
part of an entry. ans and the operator are both displayed.
Examples
ans

3V3<

V3<

10

3%c%i
<

Order of operations
The TI-36X Pro 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 parentheses.

2nd

Functions that need a ) and precede the
argument, such as sin, log, and all R³´P menu
items.

3rd

Fractions.

4th

Functions that are entered after the argument,
such as x2 and angle unit modifiers.

5th

Exponentiation (^) and roots (x‡).
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.

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.
6th

Negation (M).
11

7th

Permutations (nPr) and combinations (nCr).

8th

Multiplication, implied multiplication, division.

9th

Addition and subtraction.

10th

Conversions (n/d³´Un/d, F³´D, 4DMS).

11th

< completes all operations and closes all
open parentheses.

Examples
+QPM

6 0 T 5 V M1 2 <

(M)

1TM8T12<

% b 9 T 16 <

()

4V(2T3)<

4(2T3)<

^ and ‡

%b3G2"T4
G2<

12

Clearing and correcting
%s

Returns to the Home screen.

-

Clears an error message.
Clears characters on entry line.
Moves the cursor to last entry in history
once display is clear.

J

Deletes the character at the cursor.

%f

Inserts a character at the cursor.

%{

Clears variables x, y, z, t, a, b, c, and d
to their default value of 0.

%

2

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

Fractions
P
%@
d1
%˜
In the MathPrint™ mode, fractions with P can include real
and complex numbers, operation keys (T, V, etc.), and
most function keys (F, % _, etc.).
In Classic mode, fractions with P do not allow operation
keys, functions, or complex fractions in the numerator or
denominator.
Note: In Classic mode, only number entries are supported
when using P. Fractions in Classic mode are shown with a
double-thick fraction bar (for example,
). The numerator
must be an integer, and the denominator must be a positive
integer. To compute more complex expressions (functions,
variables, complex numbers, etc.), use W along with ( and
).
The calculator defaults output to improper fractions. Results
are automatically simplified.

13

• P enters a simple fraction. Pressing P before or after a
number can result in different behavior. Entering a number
before pressing P makes that number the numerator.
To enter fractions with operators or radicals, press P
before you enter a number (in MathPrint™ mode only).
• In MathPrint™ mode, press $ between the entry of the
numerator and the denominator.
• In Classic mode, press P between the entry of the
numerator and the denominator. The fraction bar will
appear thicker than the division bar.
• Pressing % # from any MathPrint™ level, including the
denominator or a lower limit, places the cursor in the
history. Pressing enter will then paste the expression back
to that MathPrint™ level.
– To paste a previous entry in the denominator, place the
cursor in the denominator, press % # to scroll to the
desired entry, and then press < to paste the entry to
the denominator.
– To paste a previous entry in the numerator or unit, place
the cursor in the numerator or unit, press # or % #
to scroll to the desired entry, and then press < to
paste the entry to the numerator or unit.
• % @ enters a mixed number. Press the arrow keys to
cycle through the unit, numerator, and denominator.
• d 1 converts between simple fractions and mixednumber form (4n/d³´Un/d).
• % ˜ converts results between fractions and
decimals.
Examples Classic mode
n/

n
d, U /d

3P4 T1%@7
P 12 <

n/

n
d ³´U /d

9P2d1<

14

F³´D

4%@1P2
%˜<

Examples MathPrint™ mode
n/d, U n/d

P3 $ 4 " T 1
% @ 7 $12 <

n/

9P2"d1<

n
d ³´U /d

F³´D

4%@1$2"
%˜<

Examples
P1.2 T 1.3 $ 4 <
(MathPrint™
mode only)
(MathPrint™ P M 5 T % b 5
mode only) F U 4 ( 1 ) ( 6
)$2(1)<

Percentages
%_
To perform a calculation involving a percentage, press
% _ after entering the value of the percentage.
Example
2 % _ V 150 <

15

³ Problem
A mining company extracts 5000 tons of ore with a
concentration of metal of 3% and 7300 tons with a
concentration of 2.3%. On the basis of these two extraction
figures, what is the total quantity of metal obtained?
If one ton of metal is worth 280 dollars, what is the total value
of the metal extracted?
3 % _ V 5000 <

T 2.3 % _ V 7300 <

V 280 <

The two extractions represent a total of 317.9 tons of metal for
a total value of 89012 dollars.

EE key
E
E is a shortcut key to enter a number in scientific notation
format.
Example
2E5<

q$"<

-<

16

Powers, roots and inverses
F

Calculates the square of a value. The
TI-36X Pro calculator evaluates expressions
entered with F and a from left to right in
both Classic and MathPrint™ modes.

G

Raises a value to the power indicated. Use "
to move the cursor out of the power.

%b

Calculates the square root of a non-negative
value.

%c

Calculates the nth root of any non-negative
value and any odd integer root of a negative
value.

a

Gives the inverse of a value: 1/x. The calculator
evaluates expressions entered with F and a
from left to right in both Classic and
MathPrint™ modes.

Examples
q$<5FT4G2T1"
<
10 G M 2 <

%b 49 <

%b 3 F T 2 G 4 <

6 %c 64 <

17

2%a<

Pi
g (multi-tap key)
p = 3.141592653590 for calculations.
p = 3.141592654 for display.
Example
p

2Vg<

r

³ Problem
What is the area of a circle if the radius is 12 cm?
Reminder: A = p×r2
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.

18

Math
d MATH
d displays the MATH menu:
1:4n/d³´Un/d
2: lcm(
3: gcd(
4: 4Pfactor
5: sum(
6: prod(

Converts between simple fractions and
mixed-number form.
Least common multiple
Greatest common divisor
Prime factors
Summation
Product

Examples
n/

n
d³´U /d

9P2"d1<

lcm(

d2
6%`9)<

gcd(

d3
18 % ` 33 ) <

4Pfactor

253 d 4 <

sum(

d5
1"4"zV2
<

prod(S

d6
1"5"1Pz
""<

19

Number functions
d NUM
d " displays the NUM menu:
1: abs(
2: round(
3: iPart(
4: fPart(
5: int(
6: min(
7: max(
8: mod(

Absolute value
Rounded value
Integer part of a number
Fractional part of a number
Greatest integer that is  the number
Minimum of two numbers
Maximum of two numbers
Modulo (remainder of first number P second
number)

Examples
abs(

d"1
M%b5<

round(

d"2
1.245 % ` 1 ) <
## <
!!!!! 5 <

iPart(
fPart(

4.9 L z <
d "3 z ) <
d "4 z )
V3<

int(

d "5
M 5.6 ) <

min(
max(

d "6
4 % `M5 ) <
d "7
.6 % ` .7 ) <

20

mod(

d "8
17 % ` 12 ) <
## < !! 6 <

Angles
d DMS
d " " displays the DMS menu:
1: ¡
2: ¢
3: £
4: r
5: g
6: ´DMS

Specifies the angle unit modifier as degrees (º).
Specifies the angle unit modifier as minutes (').
Specifies the angle unit modifier as seconds (").
Specifies a radian angle.
Specifies a gradian angle.
Converts angle from decimal degrees to
degrees, minutes, and seconds.

You can also convert between rectangular coordinate form
(R) and polar coordinate form (P). (See Rectangular to polar
for more information.)
Choose an angle mode from the mode screen. You can
choose from DEG (default), RAD, or GRAD. Entries are
interpreted and results displayed according to the angle mode
setting without needing to enter an angle unit modifier.
Examples
RAD

q"<

X 30 d " "
1)<

21

DEG

q<

2gd""4
<
4DMSS

1.5 d " " 6 <

³ Problem
Two adjacent angles measure 12¡ 31¢ 45£ and 26¡ 54¢ 38£
respectively. Add the two angles and display the result in
DMS format. Round the results to two decimal places.
-q$$"""<

-12 d " "

1
31 d " "2
45 d " " 3
T 26 d " "1
54 d " " 2
38 d " " 3 <
d""6<

The result is 39 degrees, 26 minutes and 23 seconds.
³ Problem
It is known that 30¡ = p / 6 radians. In the default mode,
degrees, find the sine of 30¡. Then set the calculator to radian
mode and calculate the sine of p / 6 radians.
22

Note: Press - to clear the screen between problems.
- X 30 ) <

q" 0. x
can be an non-negative integer (SINGLE) or
a list of integers (LIST). The probability
density function (pdf) is:
Computes a cumulative probability at x for
the discrete Poisson distribution with the
specified mean mu, which must be a real
number > 0. x can be an non-negative
integer (SINGLE) or a list of integers (LIST).

Note: The default value for mu (m) is 0. For Poissonpdf and
Poissoncdf, you must change it to a value > 0.
1-Var Stats and 2-Var Stats results
Important note about results: Many of the regression
equations share the same variables a, b, c, and d. If you
perform any regression calculation, the regression calculation
and the 2-Var statistics for that data are stored in the StatVars
menu until the next statistics or regression calculation. The
results must be interpreted based on which type of statistics
or regression calculation was last performed. To help you
interpret correctly, the title bar reminds you of which
calculation was last performed.
Variables

Definition

n

Number of x or (x,y) data points.

v or w

Mean of all x or y values.

Sx or Sy

Sample standard deviation of x or y.
39

sx or sy

Population standard deviation of x or y.

Gx or Gy

Sum of all x or y values.

Gx2 or Gy2

Sum of all x2 or y2 values.

Gxy

Sum of (x…y) for all xy pairs.

a (2-Var)

Linear regression slope.

b (2-Var)

Linear regression y-intercept.

r (2-Var)

Correlation coefficient.

x¢ (2-Var)

Uses a and b to calculate predicted x value
when you input a y value.

y¢ (2-Var)

Uses a and b to calculate predicted y value
when you input an x value.

MinX

Minimum of x values.

Q1 (1-Var)

Median of the elements between MinX and
Med (1st quartile).

Med

Median of all data points (1-Var stats only).

Q3 (1-Var)

Median of the elements between Med and
MaxX (3rd quartile).

MaxX

Maximum of x values.

To define statistical data points:
1. Enter data in L1, L2, or L3. (See Data editor.)
Note: Non-integer frequency elements are valid. This is
useful when entering frequencies expressed as
percentages or parts that add up to 1. However, the
sample standard deviation, Sx, is undefined for non-integer
frequencies, and Sx = Error is displayed for that value. All
other statistics are displayed.
2. Press % u. Select 1-Var or 2-Var and press
<.
3. Select L1, L2, or L3, and the frequency.
4. Press < to display the menu of variables.
5. To clear data, press v v, select a list to clear, and
press <.
40

1-Var Example
Find the mean of {45, 55, 55, 55}
Clear all
data

vv$$$

Data

<
45 $ 55 $ 55 $ 55
<

Stat

%s
%u
2 (Selects 1-Var Stats)
$$
<

Stat Var

2<

V2<

2-Var Example
Data: (45,30); (55,25). Find: x¢(45)
Clear all
data

vv$$$

Data

< 45 $ 55 $ " 30
$ 25 $

41

Stat

%u

3 (Selects 2-Var Stats)
$$$
<%s
%u1
######
< 45 ) <

³ Problem
For his last four tests, Anthony obtained the following scores.
Tests 2 and 4 were given a weight of 0.5, and tests 1 and 3
were given a weight of 1.
Test No.

1

2

3

4

Score

12

13

10

11

Coefficient

1

0.5

1

0.5

1. Find Anthony’s average grade (weighted average).
2. What does the value of n given by the calculator
represent? What does the value of Gx given by the
calculator represent?
Reminder: The weighed average is
Σx
( 12 ) ( 1 ) + ( 13 ) ( 0.5 ) + ( 10 ) ( 1 ) + ( 11 ) ( 0.5 )
------ = -------------------------------------------------------------------------------------------------------n
1 + 0.5 + 1 + 0.5
3. The teacher gave Anthony 4 more points on test 4 due to a
grading error. Find Anthony’s new average grade.
vv$$$

42

<
v"$$$$
<
12 $ 13 $ 10 $ 11 $
" 1 $ .5 $ 1 $ .5 <
%u

2 (Selects 1-Var Stats)
$""<
<

Anthony has an average (v) of 11.33 (to the nearest
hundredth).
On the calculator, n represents the total sum of the weights.
n = 1 + 0.5 + 1 + 0.5.
Gx represents the weighted sum of his scores.
(12)(1) + (13)(0.5) + (10)(1) + (11)(0.5) = 34.
Change Anthony’s last score from 11 to 15.
v $ $ $ 15 <

%u2
$""<<
If the teacher adds 4 points to Test 4, Anthony’s average
grade is 12.

43

³ Problem
The table below gives the results of a braking test.
Test No.

1

2

3

4

Speed
(kph)

33

49

65

79

5.30

14.45

20.21

38.45

Braking
distance
(m)

Use the relationship between speed and braking distance to
estimate the braking distance required for a vehicle traveling
at 55 kph.
A hand-drawn scatter plot of these data points suggest a
linear relationship. The calculator uses the least squares
method to find the line of best fit, y'=ax'+b, for data entered in
lists.
vv$$$

<
33 $ 49 $ 65 $ 79 $ " 5.3
$ 14.45 $ 20.21 $ 38.45 <
%s
%u
3 (Selects 2-Var Stats)
$$$
<

Press $ as necessary to view
a and b.

44

This line of best fit, y'=0.67732519x'N18.66637321 models
the linear trend of the data.
Press $ until y' is highlighted.

< 55 ) <

The linear model gives an estimated braking distance of
18.59 meters for a vehicle traveling at 55 kph.
Regression example 1
Calculate an ax+b linear regression for the following data:
{1,2,3,4,5}; {5,8,11,14,17}.
Clear all data v v $ $ $

Data

<
1$2$3$4$
5$"
5 $ 8 $ 11 $ 14 $
17 <

Regression

%s
%u
$$$
<

$$$$ <
Press $ to examine all
the result variables.
Regression example 2
Calculate the exponential regression for the following data:
45

L1 = {0, 1, 2, 3, 4}; L2 = {10, 14, 23, 35, 48}
Find the average value of the data in L2.
Compare the exponential regression values to L2.
Clear all data v v 4

Data

0 $1 $ 2 $ 3 $ 4 $
"10 $ 14 $ 23 $ 35
$ 48 <

Regression

%u
#

Save the
<$$$ " <
regression
equation to
f(x) in the
I menu.
Regression
Equation

<

Find the
average
value (y) of
the data in
L2 using
StatVars.

%u
1 (Selects StatVars)
$$$
$$$
$$$

Examine the I 2
table of
values of the
regression
equation.

46

Notice that the title
bar reminds you of
your last statistical
or regression
calculation.

<
0<
1<
<<

Warning: If you now calculate 2-Var Stats on your data, the
variables a and b (along with r and r2) will be calculated as a
linear regression. Do not recalculate 2-Var Stats after any
other regression calculation if you want to preserve your
regression coefficients (a, b, c, d) and r values for your
particular problem in the StatVars menu.
Distribution example
Compute the binomial pdf distribution at x values {3,6,9} with
20 trials and a success probability of 0.6. Enter the x values in
list L1, and store the results in L2.
Clear all data v v $ $ $

Data

<
3$6$9<

DISTR

%u"
$$$
<"

<
20 $ 0.6
<$ $

47

<

Probability
H
%†
H is a multi-tap key that cycles through the following
options:
!

A factorial is the product of the positive integers
from 1 to n. n must be a positive whole number
{ 69.

nCr

Calculates the number of possible combinations
of n items taken r at a time, given n and r. The order
of objects is not important, as in a hand of cards.

nPr

Calculates the number of possible permutations of
n items taken r at a time, given n and r. The order of
objects is important, as in a race.

% † displays a menu with the following options:
rand
Generates a random real number between 0 and
1. To control a sequence of random numbers,
store an integer (seed value) | 0 to rand. The
seed value changes randomly every time a
random number is generated.
randint( Generates a random integer between 2 integers,
A and B, where A { randint { B. Separate the 2
integers with a comma.
Examples
!

4H<

nCr

52 H H 5
<

48

nPr

8HHH3<

STO 4 rand

5L%†

1 (Selects rand)
<
Rand

%†1<

Randint(

%†2
3%`5)<

³ Problem
An ice cream store advertises that it makes 25 flavors of
home made ice cream. You like to order three different flavors
in a dish. How many combinations of ice cream can you test
over a very hot summer?
25 H H 3 <
You can choose from 2300 dishes with different combinations
of flavors! If a long hot summer is about 90 days long, you will
need to eat about 25 ice cream dishes each day!

Function table
I displays a menu with the following options:
1: f(

Pastes the existing f(x) to an input area
such as the Home screen to evaluate the
function at a point (for example, f(2)).

49

2: Edit function Lets you define the function f(x) and
generates a table of values.
The function table allows you to display a defined function in a
tabular form. To set up a function table:
1. Press I and select Edit function.
2. Enter a function and press <.
3. Select the table start, table step, auto, or ask-x options and
press <.
The table is displayed using the specified values.
Start

Specifies the starting value for the independent
variable, x.

Step

Specifies the incremental value for the
independent variable, x. The step can be
positive or negative.

Auto

The calculator automatically generates a series
of values based on table start and table step.

Ask-x

Lets you build a table manually by entering
specific values for the independent variable, x.

³ Problem
Find the vertex of the parabola, y = x(36 - x) using a table of
values.
Reminder: The vertex of the parabola is the point on the
parabola that is also on the line of symmetry.
I2z ( 36 U z )
<

15 $ 3 $$

50

<

After searching close to x = 18, the point (18, 324) appears to
be the vertex of the parabola since it appears to be the turning
point of the set of points of this function. To search closer to
x = 18, change the Step value to smaller and smaller values
to see points closer to (18, 324).
³ Problem
A charity collected $3,600 to help support a local food kitchen.
$450 will be given to the food kitchen every month until the
funds run out. How many months will the charity support the
kitchen?
Reminder: If x = months and y = money left, then
y = 3600 N 450x.
I2
3600 U 450 z
< 0 $ 1 $" < $ <

Input each guess and press <.

Calculate the value of f(8) on the
Home screen.
%sI
1 Selects f(
8)<
The support of $450 per month will last for 8 months since
y(8) = 3600 - 450(8) = 0 as shown in the table of values.

51

Matrices
In addition to those in the Matrix MATH menu, the following
matrix operations are allowed. Dimensions must be correct:
• matrix + matrix
• matrix – matrix
• matrix × matrix
• Scalar multiplication (for example, 2 × matrix)
• matrix × vector (vector will be interpreted as a column
vector)
% t NAMES
% t displays the matrix NAMES menu, which shows
the dimensions of the matrices and lets you use them in
calculations.
1: [A]
2: [B]
3: [C]
4: [Ans]
5: [I2]
6: [I3]

Definable matrix A
Definable matrix B
Definable matrix C
Last matrix result (displayed as [Ans]=m×n) or
last vector result (displayed as [Ans] dim=n). Not
editable.
2×2 identity matrix (not editable)
3×3 identity matrix (not editable)

% t MATH
% t " displays the matrix MATH menu, which lets
you perform the following operations:
1: Determinant
2: T Transpose

Syntax: det(matrix)
Syntax: matrixT

3: Inverse
4: ref reduced
5: rref reduced

Syntax: squarematrix–1
Row echelon form, syntax: ref(matrix)
Reduced row echelon form,
syntax: rref(matrix)

% t EDIT
% t ! displays the matrix EDIT menu, which lets
you define or edit matrix [A], [B], or [C].
52

Matrix example
Define matrix [A] as 1 2
3 4
Calculate the determinant, transpose, inverse, and rref of [A].
Define [A] % t !

<

Set
"<"<
dimensions <
Enter
values

<
1$2$3$4$

det([A])

%t"
<
%t<)
<

Transpose % t <
% t "$ <
<

Inverse

%t<
% t "$$
<
53

<

rref

%t"#
<%t
<)
<
Notice that [A] has an
inverse and that [A] is
equivalent to the identity
matrix.

Vectors
In addition to those in the Vector MATH menu, the following
vector operations are allowed. Dimensions must be correct:
• vector + vector
• vector – vector
• Scalar multiplication (for example, 2 × vector)
• matrix × vector (vector will be interpreted as a column
vector)
% … NAMES
% … displays the vector NAMES menu, which shows
the dimensions of the vectors and lets you use them in
calculations.
1: [u]
2: [v]
3: [w]
4: [Ans]

Definable vector u
Definable vector v
Definable vector w
Last matrix result (displayed as [Ans]=m×n) or
last vector result (displayed as [Ans] dim=n). Not
editable.

54

% … MATH
% … " displays the vector MATH menu, which lets
you perform the following vector calculations:
1: DotProduct
2: CrossProduct
3: norm magnitude

Syntax: DotP(vector1, vector2)
Both vectors must be the same
dimension.
Syntax: CrossP(vector1, vector2)
Both vectors must be the same
dimension.
Syntax: norm(vector)

% … EDIT
% … ! displays the vector EDIT menu, which lets you
define or edit vector [u], [v], or [w].
Vector example
Define vector [u] = [ 0.5 8 ]. Define vector [v] = [ 2 3 ].
Calculate [u] + [v], DotP([u],[v]), and norm([v]).
Define [u] % … !

<

"<<
.5 < 8 <
Define [v] % … ! $ <

"<<
2<3<

55

Add
vectors

%…<
T
%…$<
<

DotP

%…"<
%…<
%`
%…$<
)<
.5 V 2 T 8 V 3 <
Note: DotP is calculated
here in two ways.

norm

% …" $$ <
% …$ < )
r<
% b 2 F T 3 F"
r<
Note: norm is calculated
here in two ways.

Solvers
Numeric equation solver
%‰
% ‰ prompts you for the equation and the values of
the variables. You then select which variable to solve for. The
equation is limited to a maximum of 40 characters.

56

Example
Reminder: If you have already defined variables, the solver
will assume those values.
Num-solv

%‰

Left side

1 P2 " zF
U5 z z z
z z ""

Right side 6 z U z z
zz z z
<

Variable
values

1P2$
2P3$
0.25 $ ""

Solve for b <
Note: Left-Right is the
difference between the
left- and right-hand sides
of the equation evaluated
at the solution. This
difference gives how close
the solution is to the exact
answer.
Polynomial solver
%Š
% Š prompts you to select either the quadratic or
the cubic equation solver. You then enter the coefficients of
the variables and solve.

57

Example of quadratic equation
Reminder: If you have already defined variables, the solver
will assume those values.
Poly-solv

%Š

Enter
<
coefficients 1
$
M2
$
2
<
Solutions

<

$

$
Note: If you choose to
store the polynomial to
f(x), you can use I to
study the table of values.
$$" <
Vertex form (quadratic
solver only)
On the solution screens of the polynomial solver, you can
press r to toggle the number format of the solutions x1, x2,
and x3.

58

System of linear equations solver
%‹
% ‹ solves systems of linear equations. You choose
from 2×2 or 3×3 systems.
Notes:
• x, y, and z results are automatically stored in the x, y, and z
variables.
• Use r to toggle the results (x, y and z) as needed.
• The 2x2 equation solver solves for a unique solution or
displays a message indicating an infinite number of
solutions or no solution.
• The 3x3 system solver solves for a unique solution or
infinite solutions in closed form, or it indicates no solution.
Example 2×2 system
Solve: 1x + 1y = 1
1x – 2y = 3
Sys-solv

%‹

2×2
system

<

Enter
1 < T1 < 1 <
equations
1 < U2 < 3 <

Solve

<

59

Toggle
r
result type
Example 3×3 system
Solve: 5x – 2y + 3z = -9
4x + 3y + 5z = 4
2x + 4y – 2z = 14
System
solve

%‹$

3×3
system

<

First
equation

5<
M2 <
3<
M9<

Second
equation

4<
3<
5<
4<

Third
equation

2<
4<
M2 <
14 <

Solutions

<
$
$

60

Example 3×3 system with infinite solutions
Enter the
system

%‹2
1 <2 <3 <4
<
2 <4 <6 <8
<
3 <6 <9 <12
<
<

<

<

Number bases
%—
Base conversion
% — displays the CONVR menu, which converts a
real number to the equivalent in a specified base.
1: ´Hex
2: ´Bin
3: ´Dec
4: ´Oct

Converts to hexadecimal (base 16).
Converts to binary (base 2).
Converts to decimal (base 10).
Converts to octal (base 8).

Base type
% — " displays the TYPE menu, which lets you
designate the base of a number regardless of the calculator’s
current number-base mode.
1: h
2: b

Designates a hexadecimal integer.
Specifies a binary integer.
61

3: d
4: o

Specifies a decimal number.
Specifies an octal integer.

Examples in DEC mode
Note: Mode can be set to DEC, BIN, OCT, or HEX. See the
Mode section.
d ´Hex

127 % — 1 <

h ´Bin

%¬%¬
%—"1
%—2<

b ´Oct

10000000 % — "
2
%—4<

o ´Dec

#<

Boolean logic
% — ! displays the LOGIC menu, which lets you
perform boolean logic.
1: and
2: or
3: xor
4: xnor
5: not(
6: 2’s(
7: nand

Bitwise AND of two integers
Bitwise OR of two integers
Bitwise XOR of two integers
Bitwise XNOR of two integers
Logical NOT of a number
2’s complement of a number
Bitwise NAND of two integers

62

Examples
BIN mode:
and, or

q $$$$
"" <
1111 % — ! 1
1010 <
1111 % — ! 2
1010 <

BIN mode:
xor, xnor

11111 % — ! 3
10101 <
11111 % — ! 4
10101 <

HEX mode: q $$$$
not, 2’s
"<
%—!6
%¬%¬)
<
%—!5
%i<
DEC mode: q $$$$ <
nand
192 % — ! 7
48 <

Expression evaluation
%‡
Press %‡ to input and calculate an expression
using numbers, functions, and variables/parameters.
Pressing %‡ from a populated home screen
expression pastes the content to Expr=. If the user is in an
input or output history line when %‡ is pressed, the
home screen expression pastes to Expr=.
Example
%‡

63

2zTzzz

<2

<5

<

%‡

<4<6<

Constants
Constants lets you access scientific constants to paste in
various areas of the TI-36X Pro calculator. Press %
Πto access, and ! oro" to select either the NAMES
or UNITS menus of the same 20 physical constants.Use #
and $ to scroll through the list of constants in the two
menus. The NAMES menu displays an abbreviated name
next to the character of the constant. The UNITS menu has
the same constants as NAMES but the units of the constant
show in the menu.

64

Note: Displayed constant values are rounded. The values
used for calculations are given in the following table.
Constant
speed of light
c
g
gravitational
acceleration
h
Planck’s constant
NA Avogadro’s number

R
me
mp
mn
mμ
G
F
a0
re
k
e
u
atm
H0
m0
Cc

Value used for calculations
299792458 meters per second
9.80665 meters per second2

6.62606896×10M34 Joule seconds
6.02214179×1023 molecules per
mole
ideal gas constant 8.314472 Joules per mole per
Kelvin
electron mass
9.109381215×10M31 kilograms
proton mass
1.672621637×10M27 kilograms
neutron mass
1.674927211×10M27 kilograms
muon mass
1.88353130×10M28 kilograms
universal gravitation 6.67428×10M11 meters3 per
kilogram per seconds2
Faraday constant 96485.3399 Coulombs per mole
Bohr radius
5.2917720859×10M11 meters
classical electron 2.8179402894×10M15 meters
radius
Boltzmann constant 1.3806504×10M23 Joules per
Kelvin
electron charge
1.602176487×10M19 Coulombs
atomic mass unit
1.660538782×10M27 kilograms
standard
101325 Pascals
atmosphere
permittivity of
8.854187817620×10M12 Farads
vacuum
per meter
permeability of
1.256637061436×10M6 Newtons
vacuum
per ampere2
Coulomb’s constant 8.987551787368×109 meters per
Farad
65

Conversions
The CONVERSIONS menu permits you to perform a total of
20 conversions (or 40 if converting both ways).
To access the CONVERSIONS menu, press % –.
Press one of the numbers (1-5) to select, or press # and $
to scroll through and select one of the CONVERSIONS
submenus. The submenus include the categories
English-Metric, Temperature, Speed and Length, Pressure,
and Power and Energy.

English³´Metric conversion
Conversion
in 4 cm

inches to centimeters

cm 4 in

centimeters to inches

ft 4 m

feet to meters

m 4 ft

meters to feet

yd 4 m

yards to meters

m 4 yd

meters to yards

mile 4 km miles to kilometers
km 4 mile kilometers to miles
acre 4 m2 acres to square meters
m2 4 acre

square meters to acres

gal US 4 L US gallons to liters
L 4 gal US liters to US gallons
gal UK 4 ltr UK gallons to liters
ltr 4 gal UK liters to UK gallons
oz 4 gm

ounces to grams

gm 4 oz

grams to ounces
66

lb 4 kg

pounds to kilograms

kg 4 lb

kilograms to pounds

Temperature conversion
Conversion
¡F 4 ¡C

Farenheit to Celsius

¡C 4 ¡F

Celsius to Farenheit

¡C 4 ¡K

Celsius to Kelvin

¡K 4 ¡C

Kelvin to Celsius

Speed and length conversion
Conversion
km/hr 4 m/s

kilometers/hour to meters/second

m/s 4 km/hr

meters/second to kilometers/hour

LtYr 4 m

light years per meter

m 4 LtYr

meters to light years

pc 4 m

parsecs to meters

m 4 pc

meters to parsecs

Ang 4 m

Angstrom to meters

m 4 Ang

meters to Angstrom

Power and energy conversion
Conversion
J 4 kkWh

joules to kilowatt hours

kWh 4 kJ

kilowatt hours to Joules

J 4 kcal

calories to Joules

cal 4 kJ

Joules to calories

hp 4 kkWh

horsepower to kilowatt hours

kkWh 4 hp

kilowatt hours to horsepower

67

Pressure conversion
Conversion
atm 4 kPa

atmospheres to Pascals

Pa 4 atm

Pascals to atmospheres

mmHg 4 kPa

millimeters of mercury to Pascals

Pa 4 mmHg

Pascals to millimeters of mercury

Examples
Temperature (M22)

%–2
<<
(Enclose negative
numbers/expressions in
parentheses.)

Speed,
Length

(60) %
–$$<
<<

Power,
Energy

(200) %
–$$$$
<"
<<

68

Complex numbers
%ˆ
The calculator performs the following complex number
calculations:
•
•
•
•

Addition, subtraction, multiplication, and division
Argument and absolute value calculations
Reciprocal, square, and cube calculations
Complex Conjugate number calculations

Setting the complex format:
Set the calculator to DEC mode when computing with
complex numbers.
q $ $ $ Selects the REAL menu. Use ! ando" to
scroll with in the REAL menu to highlight the desired complex
results format a+bi, or r±q, and press <.
REAL a+bi, or r±q set the format of complex number results.
a+bi rectangular complex results
r±q polar complex results
Notes:
• Complex results are not displayed unless complex
numbers are entered.
• To access i on the keypad, use the multi-tap key g.
• Variables x, y, z, t, a, b, c, and d are real or complex.
• Complex numbers can be stored.
• Complex numbers are not allowed in data, matrix, vector,
and some other input areas.
• For conj(, real(, and imag(, the argument can be in either
rectangular or polar form. The output for conj( is
determined by the mode setting.
• The output for real( and imag( are real numbers.
• Set mode to DEG or RAD depending on the angle
measure needed.

69

Complex menu Description
1:±
± (polar angle character)
Lets you paste the polar representation of
a complex number (such as 5±p).
2 :polar angle
angle(
Returns the polar angle of a complex
number.
3: magnitude
abs( (or |þ| in MathPrint™ mode)
Returns the magnitude (modulus) of a
complex number.
4: 4 r±p
Displays a complex result in polar form.
Valid only at the end of an expression.
Not valid if the result is real.
5: 4 a+bi
Displays a complex result in rectangular
form. Valid only at the end of an
expression. Not valid if the result is real.
6: conjugate
conj(
Returns the conjugate of a complex
number.
7: real
real(
Returns the real part of a complex
number.
8: imaginary
imag(
Returns the imaginary (nonreal) part of a
complex number.
Examples (set mode to RAD)

Polar angle -5 %ˆ
character:  1.
• For nCr or nPr: n or r are not integers | 0.
• For x!: x is not an integer between 0 and 69.
EQUATION LENGTH ERROR — An entry exceeds the digit
limits (80 for stat entries or 47 for constant entries); for
example, combining an entry with a constant that exceeds the
limit.
Exponent must be Integer — This error is returned if the
exponent is not an integer.
FORMULA — The formula does not contain a list name (L1,
L2, or L3), or the formula for a list contains its own list name.
For example, a formula for L1 contains L1.
FRQ DOMAIN — FRQ value (in 1-Var and 2-Var stats) < 0.
Highest Degree coefficient cannot be zero — This error is
displayed if a in a Polynomial solver calculation is prepopulated with zero, or if the you set a to zero and you move
the cursor to the next input line.
Infinite Solutions —The equation entered in the System of
linear equations solver has an infinite number of solutions.
Input must be Real —This error is displayed if a variable prepopulates with a non-real number where a real number is
required and you move the cursor just past that line. The
cursor is returned to the incorrect line and you must change
the input.
Input must be non-negative integer — This error is
displayed when an invalid value is input for x and n in the
DISTR menus.
INVALID EQUATION — This error is returned when:
• The calculation contains too many pending operations
(more than 23). If using the Stored operation feature (op),
you attempted to enter more than four levels of nested
functions using fractions, square roots, exponents with ^,
x y , ex, and 10x.
73

• You press < on a blank equation or an equation with
only numbers.
Invalid Data Type — In an editor, you entered a type that is
not allowed, such as a complex number, matrix, or vector, as
an element in the stat list editor, matrix editor and vector
editor.
Invalid domain — The Numeric equation solver did not
detect a sign change.
INVALID FUNCTION — An invalid function is entered in the
function definition in Function table.
Max Iterations Change guess — The Numeric equation
solver has exceeded the maximum number of permitted
iterations. Change the initial guess or check the equation.
Mean mu>0 — An invalid value is input for the mean
(mean = mu) in poissonpdf or poissoncdf.
No sign change Change guess — The Numeric equation
solver did not detect a sign change.
No Solution Found — The equation entered in System of
linear equations solver has no solution.
Number of trials 00 sigma Real — This error is returned when an
invalid value is input for sigma in the DISTR menus.
SINGULAR MAT — This error is displayed when:
• A singular matrix (determinant = 0) is not valid as the
argument for -1.
• The SinReg instruction or a polynomial regression
generated a singular matrix (determinant = 0) because it
could not find a solution, or a solution does not exist.

74

STAT — You attempted to calculate 1-var or 2-var stats with
no defined data points, or attempted to calculate 2-var stats
when the data lists are not of equal length.
SYNTAX — The command contains a syntax error: entering
more than 23 pending operations or 8 pending values; or
having misplaced functions, arguments, parentheses, or
commas. If using P, try using W and the appropriate
parentheses.
TOL NOT MET — You requested a tolerance to which the
algorithm cannot return an accurate result.
TOO COMPLEX — If you use too many levels of MathPrint™
complexity in a calculation, the TOO COMPLEX error is
displayed (this error is not referring to complex numbers).
LOW BATTERY — Replace the battery.
Note: This message displays briefly and then disappears.
Pressing - does not clear this message.

75

Battery information
Battery precautions
• Do not leave batteries within the reach of children.
• Do not mix new and used batteries. Do not mix brands (or
types within brands) of batteries.
• Do not mix rechargeable and non-rechargeable batteries.
• Install batteries according to polarity (+ and -) diagrams.
• Do not place non-rechargeable batteries in a battery
recharger.
• Properly dispose of used batteries immediately.
• Do not incinerate or dismantle batteries.
• Seek Medical Advice immediately if a cell or battery has
been swallowed. (In the USA, contact the National Capital
Poison Center at 1-800-222-1222.)
Battery disposal
Do not mutilate, puncture, or dispose of batteries in fire. The
batteries can burst or explode, releasing hazardous
chemicals. Discard used batteries according to local
regulations.
How to remove or replace the battery
The TI-36X Pro calculator uses one 3 volt CR2032 lithium
battery.
Remove the protective cover and turn the calculator face
downwards.
• With a small screwdriver, remove the screws from the back
of the case.
• From the bottom, carefully separate the front from the
back. Be careful not to damage any of the internal parts.
• With a small screwdriver (if required), remove the battery.
• To replace the battery, check the polarity (+ and -) and
slide in a new battery. Press firmly to snap the new battery
into place.
Important: When replacing the battery, avoid any contact
with the other components of the calculator.
76

Dispose of the dead battery immediately and in accordance
with local regulations.
Per CA Regulation 22 CCR 67384.4, the following applies to
the button cell battery in this unit:
Perchlorate Material - Special handling may apply.
See www.dtsc.ca.gov/hazardouswaste/perchlorate

In case of difficulty
Review instructions to be certain calculations were performed
properly.
Check the battery to ensure that it is fresh and properly
installed.
Change the battery when:
• & does not turn the unit on, or
• The screen goes blank, or
• You get unexpected results.

77

Texas Instruments Support and Service
For general information
Home Page:

education.ti.com

KnowledgeBase and education.ti.com/support
e-mail inquiries:
Phone:

(800) TI-CARES / (800) 842-2737
For U.S., Canada, Mexico, Puerto
Rico, and Virgin Islands only

International
information:

education.ti.com/international

For technical support
KnowledgeBase and education.ti.com/support
support by
e-mail:
Phone
(not toll-free):

(972) 917-8324

For product (hardware) service
Customers in the U.S., Canada, Mexico, Puerto Rico and
Virgin Islands: Always contact Texas Instruments Customer
Support before returning a product for service.
All other customers: Refer to the leaflet enclosed with this
product (hardware) or contact your local Texas Instruments
retailer/distributor.

78



---

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PDF Version                     : 1.7
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Author                          : Provided By MANUALSLIB.COM - http://www.manualslib.com/
Create Date                     : 2012:09:16 12:38:18Z
Keywords                        : manuals, instruction manuals, user manuals, service manuals, user guides, pdf manuals, owners manuals, installation guides
Modify Date                     : 2014:12:07 13:56:38+08:00
Subject                         : Search through 700.000 manuals online & and download pdf manuals.
Has XFA                         : No
XMP Toolkit                     : Adobe XMP Core 5.4-c005 78.147326, 2012/08/23-13:03:03
Format                          : application/pdf
Creator                         : Provided By MANUALSLIB.COM - http://www.manualslib.com/
Description                     : Search through 700.000 manuals online & and download pdf manuals.
Title                           : ManualsLib - Makes it easy to find manuals online!
Creator Tool                    : pdftk 1.44 - www.pdftk.com
Metadata Date                   : 2014:12:07 13:56:38+08:00
Producer                        : itext-paulo-155 (itextpdf.sf.net-lowagie.com)
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