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# Description

Preface

#### Over 40 years,

the scientific calculator has evolved from being a computational device for scientists and engineers to becoming an important educational tool

#### What began as an instrument to answer numerical questions has evolved to become an affordable,

powerful and flexible environment for students and their teachers to explore mathematical ideas and relationships

# The significant calculator developments of recent years,

together with advice from experienced teachers,

have culminated in the advanced scientific calculator,

• the CASIO fx-991 ES PLUS,

with substantial mathematical capabilities and extensive use of natural displays of mathematical notation

This publication comprises a series of modules to help make best use of the opportunities for mathematics education afforded by these developments

The focus of the modules is on the use of the calculator in the development of students’ understanding of mathematical concepts and relationships,

as an integral part of the development of mathematical meaning for the students

The calculator is not only a device to be used to undertake or to check computations,

once the mathematics has been understood

The mathematics involved in the modules spans a wide range from the early years of secondary school to the early undergraduate years,

and we leave it to the reader to decide which modules suit their purposes

## Although mathematics curricula vary across different countries,

we are confident that the mathematical ideas included in the modules will be of interest to mathematics teachers and their students across international boundaries

The modules are intended for use by both students and teachers

### Each module contains a set of Exercises,

focusing on calculator skills relevant to the mathematics associated with the module

a set of exploratory Activities is provided for each module,

to illustrate some of the ways in which the calculator can be used to explore mathematical ideas through the use of the calculator

these are not intended to be exhaustive,

and we expect that teachers will develop further activities of these kinds to suit their students

### The Notes for Teachers in each module provide answers to exercises,

Permission is given for the reproduction of any of the materials for educational purposes

We are grateful to CASIO for supporting the development of these materials,

and appreciate in particular the assistance of Mr Yoshino throughout the developmental process

We were also pleased to receive feedback from mathematics teachers in several countries during the writing,

which helped to shape the materials

We hope that users of these materials enjoy working with the calculator as much as we have enjoyed developing the materials and we wish both teachers and their students a productive engagement with mathematics through the use of the calculator

### Barry Kissane and Marian Kemp Murdoch University,

#### Western Australia

Table of Contents ································································································································ 1 Module 1: Introduction to the calculator························································································ 5 Entering and editing commands·································································································· 5 Mathematical commands ············································································································ 6 Recalling commands ··················································································································· 8 Scientific and engineering notation····························································································· 9 Calculator modes······················································································································· 10 SET UP ····································································································································· 11 Memories ·································································································································· 14 Initialising the calculator··········································································································· 15 Exercises and Notes for teachers ······························································································ 16 Module 2: Representing numbers ································································································· 18 Representing decimals ·············································································································· 18 Representing fractions··············································································································· 19 Representing percentages·········································································································· 20 Recurring decimals ··················································································································· 21 Powers······································································································································· 22 Scientific notation ····················································································································· 24 Roots ········································································································································· 25 Reciprocals································································································································ 26 Exercises,

Activities and Notes for teachers············································································· 27 Module 3: Functions ······················································································································· 30 Evaluating expressions and functions ······················································································· 30 Table of values ·························································································································· 31 Linear and quadratic functions·································································································· 32 Cubic functions ························································································································· 34 Reciprocal functions ················································································································· 35 Maximum and minimum values ······························································································· 36 Intersection of two graphs········································································································· 37 Exercises,

Activities and Notes for teachers············································································· 39

Module 4: Equations······················································································································· 42 Equations and tables·················································································································· 42 Automatic solving ····················································································································· 43 Solving quadratic equations ······································································································ 44 Systems of linear equations······································································································· 45 Using the solver ························································································································ 47 Exercises,

Activities and Notes for teachers············································································· 50 Module 5: Trigonometry ················································································································ 53 Trigonometry and right triangles ······························································································ 53 Tables of values ························································································································ 55 Exact values ······························································································································ 56 Radian measure ························································································································· 57 Gradian measure ······················································································································· 57 Solving triangles with the Sine Rule························································································· 58 Solving triangles with the Cosine Rule····················································································· 59 The Pythagorean Identity ·········································································································· 60 Coordinate systems ··················································································································· 61 Exercises,

Activities and Notes for teachers············································································· 62 Module 6: Exponential and logarithmic functions······································································· 65 Exponents and roots ·················································································································· 65 Exploring exponential functions ······························································································· 66 Using exponential models········································································································· 68 Logarithms ································································································································ 69 Properties of logarithms ············································································································ 70 Logarithms to other bases ········································································································· 71 e and natural logarithms ··········································································································· 73 Exercises,

Activities and Notes for teachers············································································· 75 Module 7: Matrices ························································································································· 78 Defining matrices······················································································································ 78 Matrix arithmetic······················································································································· 79 Matrix inversion························································································································ 80 Transformation matrices ··········································································································· 82 Matrices and equations·············································································································· 83 Exercises,

Activities and Notes for teachers············································································· 84

Module 8: Vectors ··························································································································· 87 Representing vectors ················································································································· 87 Vector magnitude and direction································································································ 88 Vector arithmetic······················································································································· 90 An example from sailing··········································································································· 92 Dot product ······························································································································· 93 Three-dimensional vectors········································································································ 94 Cross product ···························································································································· 95 Exercises,

Activities and Notes for teachers············································································· 96 Module 9: Further numbers··········································································································· 99 Scientific constants ··················································································································· 99 Measurement conversions······································································································· 100 Numbers to other bases ··········································································································· 100 Binary logical operations ········································································································ 102 Complex numbers ··················································································································· 103 Argand diagrams ····················································································································· 104 Polar form ······························································································································· 105 Powers and roots of complex numbers ··················································································· 105 Exercises,

Activities and Notes for teachers··········································································· 107 Module 10: Univariate statistics ·································································································· 110 Getting started with statistics ·································································································· 110 Entering,

editing and checking data························································································ 110 Retrieving statistics ················································································································· 112 Determining normal probabilities ··························································································· 113 Frequency data ························································································································ 115 Inferential statistics ················································································································· 117 Exercises,

Activities and Notes for teachers··········································································· 119 Module 11: Bivariate statistics····································································································· 122 Getting started with bivariate statistics ··················································································· 122 Entering,

editing and checking data························································································ 122 Retrieving statistics ················································································································· 123 Using a linear model ··············································································································· 124 Other regression models·········································································································· 126 An exponential model ············································································································· 129 A note about curve fitting ······································································································· 130 Exercises,

Activities and Notes for teachers··········································································· 131

Module 12: Probability················································································································· 134 Probability of an event ············································································································ 134 Simulating events···················································································································· 134 Simulating integers ················································································································· 136 Combinatorics ························································································································· 137 The Normal probability distribution ······················································································· 139 Exercises,

Activities and Notes for teachers··········································································· 142 Module 13: Recursion,

sequences and series ·············································································· 145 Recursion ································································································································ 145 Clever counting ······················································································································· 146 Recursion and multiplication ·································································································· 147 Sequences································································································································ 148 Arithmetic sequences ·············································································································· 150 Geometric sequences··············································································································· 151 Series······································································································································· 153 Exercises,

Activities and Notes for teachers··········································································· 154 Module 14: Calculus ····················································································································· 157 Continuity and discontinuity··································································································· 157 Exploring the gradient of a curve···························································································· 158 The derivative of a function ···································································································· 159 Properties of derivatives·········································································································· 160 Two special derivatives··········································································································· 161 Exploring limits······················································································································· 162 Integration as area under a curve ···························································································· 164 Exercises,

Activities and Notes for teachers··········································································· 167

Barry Kissane & Marian Kemp

Module 1 Introduction to the calculator The CASIO fx-991 ES PLUS calculator has many capabilities helpful for doing and learning mathematics

In this module,

the general operations of the calculator will be explained and illustrated,

### After tapping the W key,

tap w1 to enter COMPutation mode

### The screen will be blank and ready for calculations,

• as shown below

### Notice the two small symbols showing on the top line of the screen,

even before you enter any calculations

The D'symbol shows you that the calculator assumes that angles are measured in degrees

The Math symbol shows you that the calculator has been set to accept and display calculations in natural mathematical notation

### Each of these settings can be changed,

• as we will explain below

# Here are two examples:

### You can change this to a decimal if you wish by tapping the n key

An alternative is to tap q before tapping =,

which will produce a decimal result immediately

Notice that no unnecessary decimal places are shown: the result is shown as 5

• 4 and not 5

which students sometimes obtain with hand methods of calculation

You should use the z key to enter negative numbers,

• as in the screen above

# The p key is for subtraction

## Look carefully at the screen below to see that a subtraction sign is longer than a negative sign

#### If a command is too long to fit on the screen,

it is still acceptable for entry,

• as the screens below show

# Module 1: Introduction to the calculator

As you can see,

the calculator automatically shows arrows on the display when a command is longer than the display

If you need to check or edit what has already been entered,

you can move backwards and forwards with the two cursor keys

! and \$ (These keys are on opposite sides of the large oval REPLAY key at the top of the keyboard

### Note especially that if you tap \$ when the cursor is at the right end of the display,

• similarly,
• if you tap

! when the cursor is at the left end of the display,

### As shown above,

it is not necessary to return the cursor to the end of the display before tapping =

#### Notice that only the first part of the command is shown,

although the clear arrow indicates that there is more to be seen

# If you make an error when entering a command,

you can erase it and start again using the C key or you can edit it using the o key

### Position the cursor to the write of a character and tap o to delete a single character

You can then add another character by entering it from the keyboard

Characters can also be inserted using qo,

but it is generally not necessary to do this

Try this for yourself by entering the above command and then editing it to replace the 8 with a 3 before you tap =

Mathematical commands Many special mathematical operations are available on the calculator

## These will be explored in some detail in later modules,

so only a brief look at a few of the keyboard commands is provided here

#### When in Math mode,

you can usually enter a mathematical command in the same way in which you would write it,

as the calculator uses natural display

In some cases,

the keyboard command is the first one you need to use,

• while in other cases,

a command is entered after the number concerned

#### Here are three examples for which the command key is entered first:

The square root key s'is discussed in more detail in the next module

### Notice that in the example above,

q= was used to get a numerical approximation in the form of a decimal

# Learning Mathematics with ES PLUS Series Scientific Calculator

### Barry Kissane & Marian Kemp

Notice that the sine command j has been completed with a right parenthesis

although this is not strictly necessary here,

as the calculator will compute the value without it

It is a good practice to close parentheses,

rather than trust the calculator to do it for you

#### As the calculator is set to degrees,

the command gives an approximation to sin 52o

## This and other trigonometry keys are discussed in more detail in the Module 4

#### The absolute value command requires two keys,

• q and c,

and is represented on the calculator keyboard with Abs (written above the c'key)

## The example above shows that the distance between 3 and 9 is 6,

ignoring the direction or sign of the difference

#### Here are three examples for which the command key is used after the number has been entered:

Tapping the d'key after entering a number will give the square of the number

• in the example shown above,
• 123 x 123 = 15 129

# Most powers require the use of the ^ key,

as shown to find the fourth power of 137 above

## The factorial key % is used above to calculate 12 factorial,

which is 12 x 11 x 10 x … x 1

This is the number of different orders in which twelve things can be arranged in line: 479 001 600

## The mathematics associated with factorials is important in probability,

and so is discussed in detail in the Probability module

## Some mathematical commands require more than one input

In general,

when using natural display mode,

you should enter these commands in the calculator in the same way in which you would write them by hand

# Here are three examples for which more than one input is needed:

The first example above shows a fraction being entered

# You can either tap the a key first and enter the numerator and the denominator,

using the cursor keys such as R and E to move between these,

or you can start by entering 26 and then tap the a key

# Notice that mixed fractions A are accessible with qa

The second example above shows the use of the calculator to find the logarithm to base 2 of 32: that is,

the power of 2 that is needed to obtain 32

Tap the i key first and then enter both 2 and 32 as shown,

• using the \$ and
• ! keys to move between these

### The third example above shows the number of combinations of 52 objects taken five at a time,

represented in mathematics by 52C5

#### The best way to enter this into the calculator is to first enter 52,

then use the nCr command with qP and then enter the 5

The result in this case shows that there are 2 598 960 different five-card hands available from a complete deck of 52 playing cards

Calculations of these kinds are discussed in more detail in Module 12

#### © 2013 CASIO COMPUTER CO

Module 1: Introduction to the calculator

When using mathematical commands in calculations,

it is often necessary to use the cursor key \$ to exit from a command before continuing

### To illustrate this idea,

study the following two screens carefully

In the first case,

• after tapping s,

we entered 9+16 and then tapped =

# The cursor remained within the square root sign

## In the second case,

• after entering s9,

we tapped \$ to move the cursor out of the square root before tapping +s16 to complete the command and then = to get the result

# Try this for yourself to see how it works

### Here is another example of the same idea,

• using fractions:

### In the second of these screens,

\$ was used to exit the fraction before adding 4

## Of course,

it is always possible to use parentheses to clarify meanings in a mathematical expression,

but it is not always necessary

# For example,

• in the three screens below,

the parentheses are necessary in the first case,

• but not in the second,

as the third screen makes clear

## As it takes longer to enter expressions with parentheses,

it is a good idea to develop expertise in constructing expressions without them,

• when possible

Recalling commands You may have noticed a small upward arrow (next to Math) at the top of your calculator display

# This indicates that you can use the E cursor key to recall earlier commands

When you are at the top of the list,

the arrow points downwards to show this

### When between top and bottom of the list of recent commands,

both up and down arrows will show,

to indicate that you can recall commands in either direction

These three possibilities are shown below

If you move the cursor key to a previous command,

you can enter the command again by tapping =,

or can edit it first (using o) and then tap =

### This is a good way of performing several similar calculations in succession,

without having to enter each complete command again

### If you want to edit only the most recent command,

there is an even easier approach

## You need merely tap the

! key and then edit the command directly

For example,

the following screen shows an estimate of almost 113 million for the 2020 population of the Philippines,

which had a Learning Mathematics with ES PLUS Series Scientific Calculator

Barry Kissane & Marian Kemp

population of 92 337 852 in the 2010 census,

and a population growth rate of 2% per annum

# Notice that a growth rate of 2% can be calculated by multiplying a number by 1

The easiest way to obtain an estimate for later years,

assuming the annual population growth rate stays the same,

• is to tap

! and edit the command to change the exponent of 10 to a different number each time

The screens below show the results for 2030 and 2040

The very high growth rate of the Philippines in 2010 will lead to a population of more than 167 million in 2040

The same calculator process could be used to predict the population if the growth rate was assumed to be reduced drastically from 2% to 1%,

• as shown below,

where the number of years as well as the growth rate have both been edited

# As you can see the population of the Philippines is estimated to be almost 102 million in 2020,

if the growth rate were to be reduced to 1%,

a figure around 10 million fewer than predicted for a growth rate of 2%

Successive predictions of these kinds can be made efficiently in this way,

without needing to enter long and complicated expressions more then once

# The list of commands will be erased when you turn the calculator off,

or change modes (as described below) but will not be erased when you tap the C key,

so it is wise to keep the calculator in the same mode and switched on if you think it likely that you will need some of the same sorts of calculations repeatedly

Scientific and engineering notation Scientific notation When numbers become too large or too small to fit the screen,

they will automatically be described in scientific notation,

which involves a number between 1 and 10 and a power of 10

# The precise way in which this happens depends on the decimal number format,

which is described later in this module

#### To illustrate,

the screen below shows two powers of 2 that require scientific notation to be expressed

## The precise value of the first result is 1 099 511 627 776,

which does not fit on the screen,

so it has been approximated using scientific notation

## Similarly,

the second result has been approximated from 0

• 000000000931322574615479… to fit the screen

# Module 1: Introduction to the calculator

### Numbers can be entered directly into the calculator using scientific notation

tap the K key and then immediately enter the power of 10

For example,

the average distance from the Earth to the Sun is 1

• 495978875 x 108 km,

which can be entered in scientific notation as shown on the screen below

Notice that the exponent of 8 is not shown as raised on the screen,

although it is interpreted by the calculator as a power

# In the present mode used for display of results,

notice that he calculator does not regard this number as large enough to require scientific notation,

and so it is represented as a number,

indicating that the sun is on average about 149 597 887

• 5 km from the earth – an average distance of almost 150 million kilometres

# Scientific notation requires the first number to be between 1 and 10

if you use the K key to enter a number in scientific notation incorrectly (i

using a number that is not between 1 and 10),

the calculator will represent it correctly,

• as the screen below shows

Engineering notation Engineering notation is a different way of interpreting large and small numbers,

using scientific notation with powers of 10 that are multiples of 3

### This is convenient in many practical applications involving measurement,

since units often have different names with such powers

For example,

a distance of 56 789 m can be interpreted as 56

• 789 km or as 56 789 000 mm,
• as shown on the screen below,

by converting numbers through successively tapping the b key

The number itself is not changed by these steps,

but its representation is changed to make it easier to interpret

## Calculator Modes So far,

we have used the calculator only for computations

### However,

the calculator can be used to explore many other aspects of mathematics,

which are accessed in various modes

To see the choices,

• tap the w key,
• to get the screen shown below

# The mode we have used so far has been COMP (computation)

### The other modes will be explored in detail in later modules

For now,

note the following brief overview of the other modes

## Learning Mathematics with ES PLUS Series Scientific Calculator

Barry Kissane & Marian Kemp

### Mode 2: Complex mode deals with complex numbers,

An example of a complex number is i = -1

#### When in Complex mode,

the number i can be entered into the calculator and used for calculations via qb,

but this command will have no effect in other modes

### In Complex mode,

special complex number operations are also available with q2(CMPLX)

### Mode 3: Statistics mode is for various statistics,

both univariate and bivariate,

which are dealt with in the two respective Statistics modules

In this mode,

• q1 (STAT) provides various statistics calculations

Mode 4: Base N mode allows you to undertake computations in different number bases as well as the usual decimal number base

Both the calculator keyboard and the q3 (BASE) menu provide suitable commands for converting numbers between binary,

These are especially important for computer science,

as these bases are commonly used in computers

# Mode 5: Equation mode is for solving equations of various kinds

In particular,

both quadratic and cubic equations can be solved,

as well as systems of either two or three linear equations

# You can define and use matrices up to 3 x 3 in dimensions and perform arithmetic with them

### Mode 7: Table mode is for making a table of values of a function,

which is useful for various purposes including sketching graphs and solving equations

### We will use this mode in both the Module 6 and in other modules concerned with functions

Mode 8: Vector mode allows you to define and use up to three vectors with dimensions 2 or 3

# When the calculator is set in some modes,

this is indicated in the display

For example,

the two screens below show the calculator in Statistics and Matrix modes respectively

### Computations can still be performed in these modes,

but you will not have the benefits of natural display notation on the screen,

so it is better to use Computation mode if you intend to do some calculations

# In this Introductory Module,

we suggest that you keep your calculator in COMP mode

Notice that the calculator screen memory is cleared whenever you shift modes

SET UP We suggest that you now change back to Computation mode by tapping w1

In any mode,

the calculator can be set up in various ways by accessing T (via qw)

When you do this,

you will notice that there are two screens in the SET UP menu,

and you can move from one to the other using the R and E cursor keys

Here are the two screens:

# © 2013 CASIO COMPUTER CO

### Module 1: Introduction to the calculator

Display format The calculator display can be set up to either natural display (Math) mode or single line (Line) mode by tapping 1 or 2 respectively

#### Math mode allows for various mathematical expressions to be shown in the conventional way,

and it is usually better to use this

# In Line mode,

exact results will not usually be shown and the symbols will look a little different

It will also be more difficult to enter commands

# For example,

these two screens show the same information,

the first in Math mode and the second in Line mode:

# As well as looking different,

it is slightly more difficult to enter the fractions in Line mode,

as the numbers need to be entered in precisely the same order as they are written

## We suggest that you use Math mode for almost all purposes

### After selecting Math mode (with 1),

you will be presented with the choice of Output mode

## Sometimes,

people like results of some calculations in Math mode to be represented as decimal approximations rather than exact numbers (although this is always possible using q= or the n key)

If you prefer to do this,

you should choose the Line out (LineO) format for results after choosing Math Input and Output (MathIO),

• as shown on the screen below

### To illustrate the difference,

the screens below are both in Math mode,

but the first shows the result as an exact number with Math output and the second as an approximate number with Line output:

#### Angles The calculator can accept angles in degrees,

and the choice made in T is shown in the screen display with a small D,

## We will discuss the differences between these and their respective uses in the Trigonometry module

Your choices can always be over-ridden in practice using qM (i

which is also explained in the Module 4

Most people leave their calculator in degrees if they are generally concerned with practical problems or radians if they are generally concerned with theoretical problems

## Decimal format As the first Set Up screen above shows,

there are a few choices for the way that numbers are displayed as decimals

### You can select Fix (6) to specify the same number of decimal places for all results,

• select Scientific notation,

### Norm (8) for all results

It can sometimes be a useful idea to choose Fix or Sci (e

to ensure that all results are given in similar ways,

especially if all results are money values),

but we think it is generally Learning Mathematics with ES PLUS Series Scientific Calculator

#### Barry Kissane & Marian Kemp

best to choose Normal decimal formats,

allowing the calculator to display as many decimal places as are appropriate

When Normal is chosen,

there are two choices available,

• called Norm1 and Norm2

These are almost the same,

except that using Norm1 will result in scientific notation being used routinely for small numbers before Norm2 will do so

# For example,

two screens below show the same calculation as a decimal after selecting Norm1 and Norm2 respectively,

and using q= to force a decimal result

### We suggest that it is generally better to choose Norm2,

but you should decide this for yourself,

as it is mostly a matter of personal preference and also depends on the kinds of calculations you generally wish to complete

Here is the same number (134÷5) represented in the three formats Fix,

Sci and Norm respectively

Notice that both Fix and Sci are shown in the display when they have been set up as the chosen format

### When you select Fix,

you need also to select the number of decimal places to be used (five are shown in the first screen above)

### When you select Sci,

you need also to select the number of digits to be displayed (five are shown in the screen above,

so there are four decimal places showing and one digit to the left of the decimal point)

Fraction format The second Set Up screen shown below shows a choice of two ways of giving fraction results: as mixed fractions (using 1 ab/c) or proper fractions (using 2 d/c)

As shown in the next module,

results can easily be converted with N from one of these to the other (via qn),

so the decision is not very important

# To illustrate the effects of the choices,

the same calculation has been completed in each of these two formats above

Decimal point display You can select 5 Disp to choose between a dot or a comma for a decimal point in the calculator display

### Make the choice appropriate for your country

Here are the two choices:

# © 2013 CASIO COMPUTER CO

#### Module 1: Introduction to the calculator

Contrast You can select 6CONT to adjust the contrast of the screen to suit your lighting conditions

Hold down,

• or tap repeatedly,

! or \$ cursor keys until the contrast is suitable

### It is generally best to be somewhere between too light and too dark,

but this is also a personal preference

### Memories Calculator results can be stored in memories and retrieved later

This is convenient for recording values that you wish to use several times or for intermediate results

Both variable memories (labelled A to F as well as X and Y) and an independent memory (labelled M) are available

# To store a result that is already showing on the calculator into a variable memory,

• tap qJ(STO)

## Finally,

tap the memory key for the variable concerned,

shown with pink letters above the keys on the keyboard

### For example,

the memory key for B is x and that for X is )

The screens below show the process of storing a value of 7 into memory B

Notice that neither the Q key nor the = key is used here

## You can now regard B as a variable,

• with a present value of 7

#### To recall the present value of a variable,

• tap the Q key,
• followed by the variable key

Variables are used on the calculator in the same way that they are in algebra,

• as shown below,

after storing a value of 8 to memory A

To change the value of a memory variable,

you need to store a different number into the memory,

as storing replaces any existing value

### You can clear the memories with q9,

but it is not necessary to do so,

since storing a number replaces the existing number

## The Independent memory (M) works a little differently from the variable memories,

although you can use it as a variable memory if you wish

#### The difference is that you can add or subtract numbers to or from the memory,

• using m or qm (M-)

### The first two screens below show M being used to store (2 + 3) + (7 + 8),

while the third screen shows the result being recalled

#### It is not necessary to tap the = key at any stage here

Notice that whenever M contains a non-zero number,

the screen display shows an M to alert you to this

# You should do this before starting a new series of additions to M

### A very useful calculator memory is M,

which recalls the most recent calculator result

You might have seen this appearing when doing a succession of calculations

# For example,

the first screen below shows the calculator being used to find 7

When +5

• 1= is then pressed,

the calculator assumes that the value of 5

• 1 is to be added to the previous result,
• which it refers to as Ans,

since there is no number before the + sign

(Ans was not entered by the user

When a previous result is not to be used immediately,

• as it is in the above case,

then the Ans memory can be recalled with M,

as shown below to find 265 – (7

• 3) after first calculating the value in parentheses:

#### We will use the M key extensively in Module 13,

• where it is especially useful

## Initialising the calculator Finally,

while it is not necessary to initialise the calculator before use,

this is the easiest way to reset a number of settings at once

After turning the calculator on with the W key,

tap q and 9 to show the Clear menu,

shown in the first screen below

### Tap 3 to select All and then tap the = key to complete the process

The middle screen above shows the resulting message,

while the third screen shows that the default settings involve Math Set Up and Degrees for angle measures

As the screen above shows,

you can choose to clear only the Set Up or the memories,

• if you wish

# Exercises The main purpose of the exercises is to help you to develop your calculator skills

### Use the calculator to find 73 + 74 + 75 + 760 + 77 + 78

You should get a result of 1137

### Then edit the previous command,

• changing the 760 to 76,

and check that the resulting sum is now 453

## Express the square root of 32 as an exact number and as a decimal number

Find cos 52o

The hypotenuse of a right triangle with shorter sides 7 and 11 can be found by calculating 7 2 + 112

## Give this length as a decimal

22 14 ÷

### Then express the result as a mixed fraction

Use the calculator to evaluate

# Find log381

#### When each person in a room of n people shakes hands with each other person in the room,

• there are nC2 handshakes

## How many handshakes will there be if there are 38 students in a room and one teacher

Evaluate 38

which is the number of different orders in which the students in the previous question could line up outside their classroom

Find the absolute value of 3

4 – 7

which is represented in standard mathematical notation as 3

Use the calculator to evaluate 2 + 3

### As noted in the module,

the population of the Philippines was 92 337 852 in the 2010 census

## If the population keeps growing at 2%,

use the calculator to find out approximately when the population will reach 150 million

• (Hint: To do this,

enter a command and edit it successively until you get the desired result

Change the Mode of the calculator to use natural display but to give answers always as decimals in Line mode

4 x 1017

## Give memory variables A,

B and C the values of 7,

• 8 and 9 respectively

# Calculate the square of 34

but do not write down the result

## Learning Mathematics with ES PLUS Series Scientific Calculator

#### Barry Kissane & Marian Kemp

Notes for teachers This module is important for new users of the calculator,

as it deals with many aspects of calculator use that are assumed (and so are not repeated) in other modules

The text of the module is intended to be read by students and will h