Transcript Navigating Your Casio Calculator

Navigating Your Casio Calculator
Dr J Frost ([email protected])
www.drfrostmaths.com
Last modified: 30th August 2015
Click a button.
For details on statistical
calculations, press the
‘Mode’ button.
You didn’t press a button for which information is
provided. Click the button below to go back.
< Return
Mode Menu
< Return
1 COMP
Puts the calculator in normal ‘computation’ mode.
You would need to do this if you were previously using stats/table mode and
want to revert back to regular calculations.
2 STATS
> Go
Allows you to calculate various statistics based on a table of data, e.g. mean,
variance, standard deviation, the equation of the line of best fit, strength of
correlation, etc.
3 TABLE
> Go
Allows you to generate a table of values for a
given function, like the table on the right.
1
2
3
0
1
4
4 VERIF
Allows you to verify whether an equation or inequality is true.
Special Buttons
< Return
SHIFT
If you press a button after pressing SHIFT, it will use
the operation indicated by the gold text above that
button.
ALPHA
If you press a button after pressing ALPHA, it will use
the operation or letter indicated by the red text above
that button.
The letter X is particularly useful for entering a
function. Click the ‘MODE’ button then ‘TABLE’ for
more information.
Arrow Buttons
You can use the up and down arrow buttons to
retrieve previous calculations (a bit like your internet
browser’s ‘Back’ and ‘Forward buttons!)
You’ll need the left and right button for example when
entering a fraction, and want to switch between
numerator and denominator.
The arrow buttons are also used when navigating a
table (e.g. in Statistics mode)
< Return
On
On
< Return
Engineers are yet to discover the true nature of this
button, which has eluded mankind for centuries.
But some mathematicians have theorised that
pressing this button turns the calculator on.
Multi-Statements
:
x3
< Return
The semi-colon allows you to write multiple different
expressions, and evaluate them one at a time.
[2] [+] [3]
[ALPHA] [:]
[=]
 5
[=]
 28
[4] [x] [7]
The Absolute Function
< Return
Abs
It’s particularly useful for C3/C4 at A Level, if you want to check your
sketch for a function (involving the modulus function) is correct by
generating a table of values.
The Reciprocal Function
x-1
< Return
The Factorial Function
x!
x-1
< Return
The Logarithm Function
log
log
< Return
Just as the ‘square root’ function is the opposite of
‘squaring’, log2 for example is the opposite of finding 2 to
the power of something.
log2 32 = 5, because 25 = 32
log3 81 = 4, because 34 = 81
Use the arrow keys to move between the boxes after
pressing the button.
When you use the second log button with no ‘base’, it uses base 10.
Fractions


< Return
Root Functions
3√
√
√
< Return
Recurring Decimals
< Return
Powers
x
< Return
Natural Logarithm
ln
< Return
Euler’s Constant
e
e
< Return
Degrees, Minutes, Seconds
< Return
When you have some angle or time as a decimal,
press this key to convert it to degrees, minutes (a 60th
of a degree) and seconds (a 60th of a minute).
Fun fact: Whereas the ‘decimal’ system is base 10 (i.e. each digit can
have one of 10 values: 0 to 9), the ‘sexagesimal’ system is base 60.
Subdivisions of hours and degrees are in sexagesimal.
Factorise
FACT
< Return
This finds the prime factorisation of a number.
You need to enter the number first, then press =.
THEN use the FACT button.
[120] [=] [FACT]

23 x 3 x 5
Hyperbolic Functions
hyp
< Return
Trigonometric Functions
< Return
cos
Trigonometry allows you to find missing sides and
angles on triangle. For right-angled triangles, sin, cos
and tan give the ratio of different pairs of sides.
tan
For example, to solve the following problems...
sin
sin-1
x
4
3
y
60°
x = 3sin60
3
y = cos-1 (3/4)
Brackets
(
)
< Return
Brackets are hugely handy in ensuring operations in
your expression are evaluated in a certain order.
Recall that in ‘BIDMAS’, ‘Brackets’ comes first.
Storing values in variables
STO
< Return
In algebra we use variables to represent values. We
can use the letters A, B, C, D, E, F, X, Y on the
calculator for this purpose.
Store store 3 + 5 in memory as ‘A’:
(Note, don’t press the ALPHA button after pressing STO)
[3] [+] [5] [STO] [A]
To evaluate 10A:
[10] [x] [A] [=]
Engineering Notation

ENG
< Return
Engineering notation is similar to standard form,
except the power of 10 can only be a multiple of 3.
Percentages
%
< Return
The % button is of fairly limited usefulness. It converts
a percentage into its equivalent decimal (by dividing
by 100).
[90] [x] [40] [%] = 36
(this found 40% of 90)
Comma
,
< Return
The comma is used for used in generating random
integers, and converting between rectangular and
polar coordinates.
Click the RANDINT, REC or POL buttons for more
information.
Converting between decimal/surd/fraction
< Return
Improper Fractions and Mixed Numbers
< Return
Independent Memory
M+
M-
M
< Return
The independent memory is useful if you’re trying to
keep a running total of calculations.
Once entering an expression, press [M+] instead of [=] to add
your result from the running total.
To subtract the result, use [M-]
To display the currently stored total, use [RCL] [M]
(Your value will be preserved when the calculator is turned off.
See the [CLR] button to see how to wipe the value.)
Clear Memory
CLR
< Return
This allows you to delete the values you’ve stored for
variables and in independent memory.
Permutation Function
nPr
< Return
This function used in ‘Combinatorics’ (the study of
arrangements of items and structures), allows us to
find the number of ways of picking r objects from n,
and putting them in a line.
Example:
We have 5 cards with the letters A, B, C, D, E.
We want to put 3 in a line. This gives words such as
ABC, AEC, DEA, etc. How many possibilities are there?
[5] [nPr] [3]
 60
This function tends not to be used very often – the ‘choose’
function (nCr) is much more common.
Choose Function
nCr
< Return
This function used in ‘Combinatorics’ (the study of
arrangements of items and structures), allows us to find
the number of ways of choosing r objects from n, such
that the order of the items doesn’t matter.
Examples:
“How many different possible lottery tickets are there?”
You choose 6 numbers from 49. So:
[49] [nCr] [6] [=]

13983816
Polar and Rectangular (Catersian) Coords
Pol
Rec
< Return
Cartesian coordinates are represented by x and y values
(and any further dimensions).
Polar coordinates however are represented by the
distance of the origin, and the angle anticlockwise from
the x-axis.
y
In Cartesian coordinates:
(√3,1)
(√3,1)
30
In Polar coordinates:
(2, 30)
x
To convert Rectangular to Polar:
[POL] [√][3] [,] [1] [=]
To convert Polar to Rectangular:
[REC] [2] [,] [30] [=]
Statistic
STAT
< Return
Allows you to calculate a statistic (such as mean,
variance, correlation strength) based on a data set
you’ve entered. Click on the MODE button from the
calculator display and then ‘Stats’ for more information.
Rounding
Rnd
< Return
Rounds a number according to the current accuracy
set on he calculator.
Random Numbers
RAN#
RanInt
< Return
Pi
< Return

Pi is typically used in calculations to do with circles.
It is a constant with the value 3.1415...
3
Circumference
Area
Standard Form
x10x
< Return
The Answer Button
ANS
< Return
Stats Mode
< Return
This mode allows you to calculate various statistics based on a table of data,
e.g. mean, variance, standard deviation, the equation of the line of best fit,
strength of correlation, etc. You’ll be presented with various options:
Single Variable (X)
Two Variables (X, Y)
Use when you have just one variable, e.g.
height, weight, shoe size.
Use when you have a scatter diagram, e.g.
hours revised against test score.
1 - VAR
A + BX
For your single variable, calculates things like
mean, standard deviation, variance, etc.
Assumes your data points
roughly follow a straight
line, i.e. have a linear
relationship. e.g. will find a
straight line of best fit for
you. Use if you’re trying to
find the Product Moment
Correlation Coefficient
(which assumes a linear
relationship).
y = a + bx
y = a + bx + cx2
> Click to see how to enter your data.
_ + CX2
Assumes y has a quadratic
relationship to x, i.e. Your
points roughly fit onto a
parabola.
ln X
Assumes your data follows
the model y = a ln X + b
Stats Mode – Entering Data
< Back
A table should appear.
Enter each X value in your data, pressing [=]
after each one. If you have two variables,
your Y value will temporarily be set to 0.
If you have a second variable, use the
arrow keys to move to the top of the Y
column. Now enter your Y values using [=]
again.
Once you’ve finished entering your data, press the [AC] button to go back
to calculation entry mode, so that you can now calculate statistics based
on your table. You can modify your table again using SHIFT -> [1] and
selecting ‘Data’.
> Click to see how you now calculate
statistics based on your table.
AC
Stats Mode – Calculating Statistics
< Back
< Home
Presuming you have just pressed the [AC] button while in Stats mode:
|STAT|
1
Use the |STAT| button (SHIFT and 1). This will present a number of
options...
Sum
Finds the sum of the
values of your variables.
e.g. x, x2 (useful
when calculating
variance), y, xy, etc.
Var
Reg
MinMax
Allows you to calculate
the mean of x or y, the
number of items n, and
the population or
sample standard
deviations.
Will find the a, b (and c)
in your line or best fit,
whether a + bx (if a
straight line) or
otherwise.
Will also find your
correlation coefficient r
(known as the PMCC
for the linear case).
Unsurprisingly,
will find the
maximum or
minimum X or
Y value.
Once you’ve chosen a statistic to use, it’ll
appear in your calculation area. You can
always combine multiple together. Once done,
press [=]
> Practice
< Home
Stats Mode – Exercise
< Back
Use your calculator to directly calculate the following statistics.
Age of dwarf (x)
Orcs killed in battle (y)
46
1423
57
1203
26
697
105
1948
A formula for estimating the number of orcs
killed (y) using the age of the dwarf (x).
(Use Reg  a to find the y-intercept and Reg  b to
find the gradient of your line of best fit)
Click to Reveal
The Product Moment Correlation Coefficient.
(Use Reg  r. -1 means perfect negative correlation, 0
means no correlation, and 1 mean perfect positive
correlation)
Click to Reveal
Click to Reveal
< Home
Table Mode
< Back
In some exam questions you’re asked to calculate a table of values for a given function:
f(x) = x2 + 1/2
x
-1
-0.5
0
0.5
f(x)
1.5
0.75
0.5
0.75
Your calculator can do this for you. Once in table mode, your calculator display should
look like this:
Now input some expression in terms of X. You can use [ALPHA]  [X] to use X in your
expression.
> Next
Table Mode
< Back
Now press [=]. You will be asked for the ‘Start’ number.
In our table, the first value of x is -1. Type in -1 and press [=]
x
-1
-0.5
0
0.5
1
f(x)
1.5
0.75
0.5
0.75 1.5
You will now be asked for the ‘End’ number. In our table above, the last value of x is 1.
Type 1 then press [=].
Finally you’re asked for the step size. This is how much x is increasing by each time. In
our table, it’s 0.5.
Once you press equals, you’ll be presented with a nice looking table.
You can use the arrow keys to scroll through it.
< Return
Secret Menu!
7
< Return
Hold [SHIFT] and [7] and then press [ON].
Now press [9], then [SHIFT] 5 times.
After waiting for the messages to display, press [AC].
You can change the screen contrast, and pressing [AC]
again activates a button test – pressing each button
(in the correct order!) displays a different integer.