Texas TI-83 User manual

Contents:
A
B
C
D
E
F
G
Basic calculations
Basic functions
Secondary function and
alpha keys
Memory
Lists
Statistical graphs
Working with functions
Graphics calculator
instructions
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10 GRAPHICS CALCULATOR INSTRUCTIONS
In this course it is assumed that you have a graphics calculator. If you learn how to operate
your calculator successfully, you should experience little difficulty with future arithmetic
calculations.
There are many different brands (and types) of calculators. Different calculators do not have
exactly the same keys. It is therefore important that you have an instruction booklet for your
calculator, and use it whenever you need to.
However, to help get you started, we have included here some basic instructions for the Texas
Instruments TI-83 and the Casio fx-9860G calculators. Note that instructions given may
need to be modified slightly for other models.
GETTING STARTED
Texas Instruments TI-83
The screen which appears when the calculator is turned on is the home screen. This is where
most basic calculations are performed.
You can return to this screen from any menu by pressing 2nd MODE .
When you are on this screen you can type in an expression and evaluate it using the ENTER
key.
Casio fx-9860g
Press MENU to access the Main Menu, and select RUN¢MAT.
This is where most of the basic calculations are performed.
When you are on this screen you can type in an expression and evaluate it using the EXE
key.
Most modern calculators have the rules for Order of Operations built into them. This order
is sometimes referred to as BEDMAS.
This section explains how to enter different types of numbers such as negative numbers and
fractions, and how to perform calculations using grouping symbols (brackets), powers, and
square roots. It also explains how to round off using your calculator.
NEGATIVE NUMBERS
To enter negative numbers we use the sign change key. On both the TI-83 and Casio this
looks like (¡).
Simply press the sign change key and then type in the number.
For example, to enter ¡7, press (¡)7.
BASIC CALCULATIONS
A
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GRAPHICS CALCULATOR INSTRUCTIONS 11
FRACTIONS
On most scientific calculators and also the Casio graphics calculator there is a special key
for entering fractions. No such key exists for the TI-83, so we use a different method.
Texas Instruments TI-83
To enter common fractions, we enter the fraction as a division.
For example, we enter 3
4by typing 3¥4. If the fraction is part of a larger calculation,
it is generally wise to place this division in brackets, i.e., (3¥4).
To enter mixed numbers, either convert the mixed number to an improper fraction and enter
as a common fraction or enter the fraction as a sum.
For example, we can enter 23
4as (11 ¥4)or (2+3¥4).
Casio fx-9860g
To enter fractions we use the fraction key ab/c.
For example, we enter 3
4by typing 3ab/c4and 23 4by typing 2ab/c3ab/c4. Press
SHIFT a b/c(ab
c$d c)to convert between mixed numbers and improper fractions.
SIMPLIFYING FRACTIONS & RATIOS
Graphics calculators can sometimes be used to express fractions and ratios in simplest form.
Texas Instruments TI-83
To express the fraction 35
56 in simplest form, press 35 ¥56
MATH 1ENTER . The result is 5
8.
To express the ratio 2
3:1
1
4in simplest form, press (2
¥3)¥(1+1¥4)MATH 1ENTER .
The ratio is 8:15.
Casio fx-9860g
To express the fraction 35
56 in simplest form, press 35 ab/c56
EXE . The result is 5
8.
To express the ratio 2
3:1
1
4in simplest form, press 2ab/c
3¥1ab/c1ab/c4EXE . The ratio is 8:15.
ENTERING TIMES
In questions involving time, it is often necessary to be able to express time in terms of hours,
minutes and seconds.
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12 GRAPHICS CALCULATOR INSTRUCTIONS
Texas Instruments TI-83
To enter 2hours 27 minutes, press 22nd MATRX (ANGLE)
1:o27 2nd MATRX 2:0. This is equivalent to 2:45 hours.
To express 8:17 hours in terms of hours, minutes and seconds,
press 8:17 2nd MATRX 4:IDMS ENTER .
Casio fx-9860g
To express 8:17 hours in terms of hours, minutes and seconds,
press 8:17 OPTN F6 F5 (ANGL) F6 F3 (IDMS)EXE .
This is equivalent to 8hours, 10 minutes and 12 seconds.
GROUPING SYMBOLS (BRACKETS)
Both the TI-83 and Casio have bracket keys that look like (and ).
Brackets are regularly used in mathematics to indicate an expression which needs to be
evaluated before other operations are carried out.
For example, to enter 2£(4 + 1) we type 2£(4+1).
We also use brackets to make sure the calculator understands the expression we are typing in.
For example, to enter 2
4+1 we type 2¥(4+1). If we typed 2¥4+1
the calculator would think we meant 2
4+1.
In general, it is a good idea to place brackets around any complicated expressions which need
to be evaluated separately.
POWER KEYS
Both the TI-83 and Casio also have power keys that look like ^. We type the base first,
press the power key, then enter the index or exponent.
For example, to enter 253we type 25 ^3.
Note that there are special keys which allow us to quickly evaluate squares.
Numbers can be squared on both TI-83 and Casio using the special key x2.
For example, to enter 252we type 25 x2.
BASIC FUNCTIONS
B
To enter 2hours 27 minutes, press OPTN F6 F5 (ANGL)2
F4 (o000)27 F4 (o000)EXE . This is equivalent to 2:45 hours.
This is equivalent to 8hours, 10 minutes and 12 seconds.
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GRAPHICS CALCULATOR INSTRUCTIONS 13
SQUARE ROOTS
Texas Instruments TI-83
The TI-83 uses a secondary function key 2nd .
To enter p36 we press 2nd x236 ).
The end bracket is used to tell the calculator we have finished entering terms under the square
root sign.
Casio fx-9860g
The Casio uses a shift key SHIFT to get to its second functions.
To enter p36 we press SHIFT x236.
If there is a more complicated expression under the square root sign you should enter it in
brackets.
For example, to enter p18 ¥2we press SHIFT x2(18 ¥2).
ROUNDING OFF
You can use your calculator to round off answers to a fixed number of decimal places.
Texas Instruments TI-83
To round to 2decimal places, press MODE then Hto scroll
down to Float.
Use the Ibutton to move the cursor over the 2and press
ENTER . Press 2nd MODE to return to the home screen.
If you want to unfix the number of decimal places, press MODE
HENTER to highlight Float.
Casio fx-9860g
To round to 2decimal places, select RUN¢MAT from the Main
Menu, and press SHIFT MENU to enter the setup screen. Scroll
down to Display, and press F1 (Fix). Press 2EXE to select
the number of decimal places. Press EXIT to return to the home
screen.
To unfix the number of decimal places, press SHIFT MENU to return to the setup screen,
scroll down to Display, and press F3 (Norm).
To enter square roots on either calculator we need to use a secondary function (see the
).Secondary Function and Alpha Keys
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Texas Instruments TI-83
To evaluate 23003, press 2300 ^3ENTER . The answer
displayed is 1:2167e10, which means 1:2167 £1010.
To evaluate 3
20 000 , press 3¥20 000 ENTER . The answer
displayed is 1:5e¡4, which means 1:5£10¡4.
You can enter values in scientific notation using the EE function,
which is accessed by pressing 2nd ,.
For example, to evaluate 2:6£1014
13 , press 2:62nd ,14 ¥
13 ENTER . The answer is 2£1013.
14 GRAPHICS CALCULATOR INSTRUCTIONS
INVERSE TRIGONOMETRIC FUNCTIONS
Texas Instruments TI-83
The inverse trigonometric functions sin¡1,cos¡1and tan¡1are the secondary functions of
SIN ,COS and TAN respectively. They are accessed by using the secondary function key
2nd .
For example, if cos x=3
5, then x= cos¡1¡3 5¢.
To calculate this, press 2nd COS 3¥5)ENTER .
Casio fx-9860g
The inverse trigonometric functions sin¡1,cos¡1and tan¡1are the secondary functions of
sin ,cos and tan respectively. They are accessed by using the secondary function key
SHIFT .
For example, if cos x=3
5, then x= cos¡1¡3 5¢.
To calculate this, press SHIFT cos (3¥5)EXE .
SCIENTIFIC NOTATION
To enter inverse trigonometric functions, you will need to use a secondary function (see the
).Secondary Function and Alpha Keys
If a number is too large or too small to be displayed neatly on the screen, it will be expressed
in scientific notation, that is, in the form a£10kwhere 16a610 and kis an integer.
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GRAPHICS CALCULATOR INSTRUCTIONS 15
Casio fx-9860g
To evaluate 3
20 000 , press 3¥20 000 EXE . The answer
displayed is 1:5e¡04, which means 1:5£10¡4.
You can enter values in scientific notation using the EXP key.
For example, to evaluate 2:6£1014
13 , press 2:6EXP 14 ¥13
EXE . The answer is 2£1013.
Texas Instruments TI-83
The secondary function of each key is displayed in yellow above the key. It is accessed by
pressing the 2nd key, followed by the key corresponding to the desired secondary function.
For example, to calculate p36, press 2nd x236 )ENTER .
The alpha function of each key is displayed in green above the key. It is accessed by pressing
the ALPHA key followed by the key corresponding to the desired letter. The main purpose
of the alpha keys is to store values into memory which can be recalled later. Refer to the
Memory section.
Casio fx-9860g
The shift function of each key is displayed in yellow above the key. It is accessed by pressing
the SHIFT key followed by the key corresponding to the desired shift function.
For example, to calculate p36, press SHIFT x236 EXE .
The alpha function of each key is displayed in red above the key. It is accessed by pressing
the ALPHA key followed by the key corresponding to the desired letter. The main purpose
of the alpha keys is to store values which can be recalled later.
MEMORY
D
CSECONDARY FUNCTION AND
ALPHA KEYS
To evaluate 23003, press 2300 ^3EXE . The answer
displayed is 1:2167e+10, which means 1:2167 £1010.
Utilising the memory features of your calculator allows you to recall calculations you have
performed previously. This not only saves time, but also enables you to maintain accuracy
in your calculations.
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16 GRAPHICS CALCULATOR INSTRUCTIONS
SPECIFIC STORAGE TO MEMORY
Values can be stored into the variable letters A, B, ..., Z using either calculator. Storing a
value in memory is useful if you need that value multiple times.
Texas Instruments TI-83
We can now add 10 to this value by pressing ALPHA MATH
+10 ENTER , or cube this value by pressing ALPHA MATH
^3ENTER .
Casio fx-9860g
Suppose we wish to store the number 15:4829 for use in a number
of calculations. Type in the number then press IALPHA
X,µ,T (A) EXE .
We can now add 10 to this value by pressing ALPHA X,µ,T +
10 EXE , or cube this value by pressing ALPHA X,µ,T ^3
EXE .
ANS VARIABLE
Texas Instruments TI-83
The variable Ans holds the most recent evaluated expression,
and can be used in calculations by pressing 2nd (¡).
If you start an expression with an operator such as +,¡,
etc, the previous answer Ans is automatically inserted ahead of
the operator. For example, the previous answer can be halved
simply by pressing ¥2ENTER .
If you wish to view the answer in fractional form, press MATH
1ENTER .
Suppose we wish to store the number 15:4829 for use in a
number of calculations. Type in the number then press STOI
ALPHA MATH (A) ENTER .
For example, suppose you evaluate 3£4, and then wish to
subtract this from 17. This can be done by pressing 17 ¡
2nd (¡)ENTER .
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GRAPHICS CALCULATOR INSTRUCTIONS 17
Casio fx-9860g
The variable Ans holds the most recent evaluated expression,
and can be used in calculations by pressing SHIFT (¡). For
example, suppose you evaluate 3£4, and then wish to subtract
this from 17. This can be done by pressing 17 ¡SHIFT (¡)
EXE .
If you start an expression with an operator such as +,¡,
etc, the previous answer Ans is automatically inserted ahead of
the operator. For example, the previous answer can be halved
simply by pressing ¥2EXE .
If you wish to view the answer in fractional form, press FJ ID.
RECALLING PREVIOUS EXPRESSIONS
Texas Instruments TI-83
The ENTRY function recalls previously evaluated expressions, and is used by pressing 2nd
ENTER .
This function is useful if you wish to repeat a calculation with a minor change, or if you have
made an error in typing.
Suppose you have evaluated 100 + p132. If you now want to evaluate 100 + p142, instead
of retyping the command, it can be recalled by pressing 2nd ENTER .
The change can then be made by moving the cursor over the 3and changing it to a 4, then
pressing ENTER .
If you have made an error in your original calculation, and intended to calculate 1500+p132,
again you can recall the previous command by pressing 2nd ENTER .
Move the cursor to the first 0.
You can insert the digit 5, rather than overwriting the 0, by pressing 2nd DEL 5ENTER .
Casio fx-9860g
Pressing the left cursor key allows you to edit the most recently evaluated expression, and is
useful if you wish to repeat a calculation with a minor change, or if you have made an error
in typing.
Suppose you have evaluated 100 + p132.
If you now want to evaluate 100 + p142, instead of retyping the command, it can be recalled
by pressing the left cursor key.
Move the cursor between the 3and the 2, then press DEL 4to remove the 3and change it
to a 4. Press EXE to re-evaluate the expression.
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18 GRAPHICS CALCULATOR INSTRUCTIONS
LISTS
E
Lists are used for a number of purposes on the calculator. They enable us to enter sets of
numbers, and we use them to generate number sequences using algebraic rules.
CREATING A LIST
Texas Instruments TI-83
Press STAT 1to take you to the list editor screen.
To enter the data f2,5,1,6,0,8ginto List1, start by moving
the cursor to the first entry of L1. Press 2ENTER 5ENTER
...... and so on until all the data is entered.
Casio fx-9860g
Selecting STAT from the Main Menu takes you to the list editor
screen.
To enter the data f2,5,1,6,0,8ginto List 1, start by moving
the cursor to the first entry of List 1. Press 2EXE 5EXE ......
and so on until all the data is entered.
DELETING LIST DATA
Texas Instruments TI-83
Pressing STAT 1takes you to the list editor screen.
Move the cursor to the heading of the list you want to delete then press CLEAR ENTER .
Casio fx-9860g
Selecting STAT from the Main Menu takes you to the list editor screen.
Move the cursor to anywhere on the list you wish to delete, then press F6 (B)F4 (DEL-A)
F1 (Yes).
REFERENCING LISTS
Texas Instruments TI-83
Lists can be referenced by using the secondary functions of the keypad numbers 1–6.
For example, suppose you want to add 2to each element of List1 and display the results in
List2. To do this, move the cursor to the heading of L2and press 2nd 1+2ENTER .
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