Brief Guide to

the Casio

fx-991ES Plus

Calculator

Allen Brown

Cambridge

Paperbacks

www.CambridgePaperbacks.com

© Allen Brown 2016

All rights reserves. This ebook is subject to conditions

that is shall not, by way of trade or otherwise be lent

sold, hired out or otherwise circulated in any form of

binding or cover other than that in which it

is published and without a similar conditions.

The rights of Allen Brown to be identified as the author

of this work has been asserted by him in accordance with

the Copyright Designs and Patents Act 1988.

1

Making Progress in Maths If you want to make really good progress in maths, then you will need to

know how to make effective use of a scientific calculator. In this booklet

you should gain a good understanding of how a Casio fx-991ES Plus

calculator can be used effectively. Also, you will learn how to use the

REPLAY feature and to set-up a fx calculator and perform common

functions. Keystrokes are provided to enable you to acquire a good

understanding of the features of the fx. The several books that have been

written for GCSE Key Stage 4 and A Level Maths that make extensive

use of the fx-991ES calculator and it will be worthwhile spending some

time reading through this booklet as it will serve as a valuable source of

information on the many powerful features the calculator possesses.

1 The Casio fx-991EX Plus Calculator The pocket calculator is one of the most underrated pieces of technology

in use today. Although almost everyone owns one, very few people are

able to use a calculator efficiently. Most people are familiar with the basic

four function calculator (+, , and ). These usually perform square

roots () as well and have a memory for storing a result. The so called

scientific calculators have an extensive range of functions and Casio is

major manufacturer of pocket scientific calculators. The series of maths

books sold by Cambridge Paperbacks use the fx-991ES PLUS.

The Casio fx-991ES PLUS calculator

2

It’s important for you use of this calculator as the keystroke sequences

for every problem and example in each of the maths book relate to the fx-

991ES Plus calculator.

2 User’s Guide When you buy one of these calculators the User’s Guide will probably

come as a small booklet as shown below.

This covers all the functions of the calculator and provides examples of

how each function is used. Like most people you probably find User’s

Guides difficult and, more often than not, boring to read. Just keep it

handy for future reference. What you’ll find, the more familiar you are

with the device, the more readable the User’s Guide becomes.

3 Learning to use your Calculator In each of the maths books in the Cambridge Paperbacks series extensive

use is make of the fx-991ES calculator and actual keystrokes for each

example is provided. In particular when keystrokes are given, you will

be expected to confirm the answers provided.

First of all, you’ve got to the various modes your fx calculator possesses.

There are two modes regarding the input and output formats (how the

numbers appear in the display). These are the Math and the Linear modes, we shall be using the calculator mainly in the Math mode

(MthIO) where you can input numbers as fractions as required. To see

the mode options enter qw and you will see,

3

You can see the options for MthIO and LineIO. To select MthIO press

1. Once in the MthIO mode you will be able to enter fractions directly.

For example to enter the expression,

3

4−

2

7+ 2

the keystrokes would be,

3a4$p2a7$+2=n and the result would be as shown here,

In the display shown above you will notice the precision has been limited

to four decimal places. To achieve this enter the following keystrokes,

qw64

You will also see Fix 09? in the display - where you will have chosen

4. Although the display only shows four decimal places, the calculator

retains a precision of 15 decimal places. Very often when you perform a

calculation the answer often appears as a fraction, by using the n key

will can switch between fraction or decimal form.

4 Key sequence When performing calculations it’s important to ensure you use the correct

key sequence. For example if you need to calculate the square root of

21.32 the sequence is,

s21.32=n

4

The display appears as,

Sometimes you need to use the n key to convert from a fractional

display √533

5 to a decimal display of 4.617. You will also need to know

about the power key ^ which is used to take a value to any power (or

index). For example 35 is equivalent to 33333 243. Let’s illustrate

with a more interesting example, evaluate 3.55.6. The keystrokes are,

3.5^5.6=

giving an answer of 1113.733 which appears as,

Calculating percentages also requires the correct sequence of keystrokes.

For example 32% of 245; the key strokes are,

32q(%)(245)=

giving an answer of 78.400 as shown in the display,

If you wanted to perform a slight more difficult calculation, such as, 1054 × 0.487

0.12 × 1.63√23.58

The keystrokes would be,

a1054O0.487R0.12O1.6q(x3)$s23.58=

5

The display will show,

5 Using the REPLAY Key A useful feature on the Casio fx calculator is the REPLAY function

which is the dark blue (or purple) button below the

display. The purpose of this feature is to move the

screen cursor and to ease corrections and repetitive

calculations where only one or two variables change

each time. The REPLAY function has four pointers

which are denoted by E, R, ! and $ for

moving the cursor around the display. Once a

calculation has been performed, pressing the REPLAY takes the cursor

back into the expression. To delete a number, place the cursor on the right

hand side of the number and press o. You then enter the new number

as normal. To illustrate the operation of the REPLAY key, consider the

example 3

4+

2

3. Now enter the following key strokes.

3a4$+2a3=n

which gives an answer of 1.417.

If you now wanted to calculate 1

4+

2

3, enter the following key strokes.

$$$o1=n

which gives an answer of 0.917. Each time you press $ the cursor

moves one place to the right. You will observe that you only need to

change one number instead of re-entering the whole expression. With a

little practice you will soon get the hang of using the REPLAY feature.

6

1.6 Memory The fx calculators have several memory locations for storing data. These

are labelled A, B, C, D, E, F, X, Y and M and can be used in a number

of different ways. When you look at the keypad on the fx-991ES

calculator you will observe the following area,

M is the general purpose memory, you can add or subtract to the data in

M. If you wanted to add several numbers together the m key can be

used. For example to add all the numbers from 1 to 10, the keystrokes

would be (first zero the contents of M),

0q(STO)(M)

1m2m3m4m5m6m7m8m9m10J(M)

The display would show,

which is the sum of the first 10 integers. For the other memories, to store

a number, for example 21 in A, use the following keystrokes,

21q(STO)(A)

and the display will show,

7

to indicate that 21 is stored in A. To recall the contents of A use the

keystrokes, J(A) and the contents of A will appear in the display. To

clear all the memories, use the keystrokes q(CLR) you will see,

Now enter 2 and you will see,

When you enter = , you will see

Enter C and all the memories will be set to zero.

7 Using the CALC Function

When there is need to perform repetitive calculations the r feature is

a great labour saving device. For example, given an equation,

𝑦(𝑥) = 2𝑥 + 3𝑥3 and you want to find the value of y(x) for several values of x. Let’s say

you want to find the value of y(1), y(1.5), y(5) and y(6). First enter the

following keystrokes,

Q(Y)Q(=)2Q(X)+3J(X)q(x3)r

When you see X?

Enter 1= giving an answer of 5.

Enter r1.5=n giving an answer of 13.125.

Enter r5= giving an answer of 385.000.

Enter r6= giving an answer of 660.000

8

So we have determined that

𝑦(1) = 5, 𝑦(1.5) = 13.125 𝑦(5) = 385.0, 𝑦(6) = 660.0

As you can see from this example the r key is very effective for

performing repetitive calculations. This is particularly useful when

compiling tables for graphs. There is however another way of creating a

table using the TABLE option.

8 Using the TABLE Option Instead of performing individual calculations for each function value, the

TABLE option lets you generate the entire table. For example if you

wanted to calculate values of the function

𝑦 = 𝑒2𝑥 − 2𝑥

in the range -2.5 ≤ x ≤ 1 with step sizes of 0.5, then you would use the

TABLE option. First set up the table mode, Ww

You will observe in the display the TABLE option is 7, enter 7. You

will next see in the display,

Now enter the keystrokes for the function,

qH2Q(X)$p2J(X)

The display will show,

9

Once you enter = you will see

Enter z2.5= and you will see,

Enter 1= and you will see,

The step size is the interval between each calculated value, enter

0.5= and you will see the start of the table,

As you use the down cursor R

the rest of the table will appear.

When you plot these data points

you should get a plot similar to

the one shown on the right. Also

shown in red is the actual

function. This is a very useful

feature for generating function

data values ready for plotting.

10

9 Using the SOLVE Function This is a powerful function and will allow you to find solutions to

equations. For example, what is the value of x that satisfies the equation,

sin(𝑥) = 𝑥2

A plot of sin(x) and x2 are shown in the plot below.

Where the functions intersect are the solutions to the equation. You can

see there are two values, one of the values is zero. First make sure the

calculator is in its radian mode, qw4. Now use the following

keystrokes to find the other value,

jQ(X))Q(=)J(X)dq(SOLVE)

You will see in the display,

Enter say 5, then you will see,

11

Showing the solution is 0.876 which can be confirmed from the graph on

the previous page. The L-R= in the display shows the difference between

the left hand side of the equation from the right hand side. The way the

fx-991EX works is that it calculates an approximate value for the left hand

side, but mostly the difference is zero.

10 Using Symbols as Variables It has already been mention the fx-991 has several memories, well the

letters A, B, C, D, E, F, M, X and Y can also serve as variables in

expressions. This was eluded to in the section on the r key. For

example if you have the equation,

𝑦 =𝑥3

2

and you want to know the value of y when x = 2.6, you can use the

following keystrokes,

Q(Y)Q(=)aQ(X)q(x3)R2r

You will see in the display,

Now enter 2.6= and you will see an improper fraction in the

display,

Now press n and you will see,

12

You will observe the actual equation appears in the display together with

the answer. Any letter that appears on the right hand side of the = will be

treated as a variable. For example,

𝑌 =𝐴+𝐵

𝐶

To calculate the value of Y when A = 3.2, B = 4.7 and C = 0.7, then

Q(Y)Q(=)aQ(A)+Q(B)RQ(C)r

You will see in the display,

Enter 3.2= and you will see,

Enter 4.7= and you will see,

After you enter 0.7= you will see the equation together with

the answer in the display,

13

Press n to see,

If a letter has already been used in an expression you can use the J

key. For example

𝑌 =ln(𝑋)

𝑋

The keystrokes for evaluating this expression are,

Q(Y)Q(=)ahQ(X))RJ(X)r

You will see in the display,

For example, to calculate the value of Y when X = 4.7, enter

4.7= and you will see,

11 Multiple Stage Calculations A very attractive feature of the fx-991ES is its ability to perform multiple

stage calculations using the Q(:) key. You can effectively pass on the

answer from one stage to the next using the M key (first clear the

memories). For example if you have two equations,

𝑌 = 3𝑋2.2 + 3 and 𝐴 = 2𝑌 − 1.4

14

Y is the answer to the first expression which is then passed to the second,

the keystrokes for these expressions are,

Q(Y)Q(=)3Q(X)^2.2$+3Q(:)

Q(A)=2Mp1.4r

You will see in the display,

To calculate the value of Y and A when X = 3.87, enter 3.87=

and you will see,

Press = again and you will see,

This is a very powerful feature of the fx-991ES calculator that will be

used throughout these series of books.

12 More Books on the Casio fx-991ES Plus Calculator This is a brief guide to the Casio fx-991ES Plus calculator and if you are

taking your GCSE in Maths or at A Level you will find the other books

published by Cambridge Paperbacks really useful. These books in the

maths series will really expand your knowledge of mathematics at both

GCSE Key Stage 4 and A level.

15

Books on GCSE Key Stage 4. This four part series on using a Casio fx calculator to solve problems for GCSE

Mathematics, has been designed to enable you to get better results at Key

Stage 4.

We all know Casio fx calculators are really powerful

and when used properly can make a big difference

in expanding your problem solving ability. This

book should be used together with your course text-

book in GCSE Maths. You will find many examples

showing you how the Casio fx calculator is used to

solve GCSE maths problems. The material in this

book is drawn from AQA, Edexcel and OCR sylla-

buses. The material covered includes,

● Fractions

● Percentages

● Basic Algebra

● Linear and Quadratic Functions

● Vectors

● Binary Numbers

● Essential Skills

Whether you are on a Linear or Modular scheme,

every week you can delve into this book to see how

problems are solved using the power of your fx

calculator. The learning is clear and precise as each

problem example shows all the fx keystrokes. By

following through every example you will expand

your problem solving skills that will being huge

benefits and positive results to you. Let your fx

calculator help you perform better, smarted and

sharpen your focus on problem solving. The

material covered includes, ● Calculating Areas

● Calculating Volumes

● Logarithms

● Powers and Indices ● Changing the Subject of an Equation

16

As you master its potential you will be able to

apply it to problem solving, at the same time you

will be developing your own person mathematical

skill set. This series will show you how to

configure your Casio fx calculator for a whole

range of problem solving activities - giving you a

bigger advantage in your maths learning. The

material covered includes, ● Functions

● Dealing with Numbers

● Scale Conversions

● Rounding and Decimal Numbers

● Ratios

● Dealing with Data

● Surds

This series of books will not only show you how

to realise the power of your Casio fx calculator,

but also show you how to develop your

mathematical skills for future success and raise

your game to the next level. If you are thinking of

taking A Level Maths, the skills you will gain

using your Casio fx calculator will put you in a

strong position to make really good progress in the

subject. This four part series of books will show

you how to master your Casio fx calculator and

give maximum advantage as you develop your

maths skill set. The material covered includes, ● Trigonometry

● Trigonometry of Irregular Triangles

● Simultaneous Equations

● Graph Transformations

● Quadrilaterals

● Trial and Improvement

● Inequalities

● Sequencing and Modelling

17

Here are the books from Cambridge Paperbacks on A Level Maths.

Algebra can be regarded as the fundamental skill of

all mathematicians and to make progress in your A

Level Maths you will need to enhance the algebra

skills you acquired at GCSE Level. This book pro-

vides you with many of the algebraic methods

you’ll need as you progress through your course.

You will be shown how to use your Casio fx-991ES

calculator to enhance your algebraic skill set The

material covered in this book includes, ● Multiplying Algebraic Functions

● Polynomials

● Identities

● Quadratic Functions

● Series and Series Expansions

● Asymptotic Equations

● Parametric Equations

● Numerical Methods

This is the first book on calculus for A Level

Mathematics and most of the material is on differ-

entiation. Emphasis is placed on using the Casio

fx-991ES Plus calculator for solving problems

and every example where appropriate, has the cal-

culator keystrokes for performing the calcula-

tions. This books should be used alongside your

recommended classroom textbooks, so you will

be able to recognise similar problems in both

books. The material includes. ● A Very Short History of Calculus

● Differentiation and Differentiation Rules

● Differentiating Trigonometric Functions

● Higher Order Differentiation

● Maxima and Minima

● Power and Logarithmic Functions

● Applications of Differentiation

18

Calculus is a major component in your A Level

Mathematics course and this is Part 2 of the

Calculus series and covers integration and the

various techniques you need to acquire in its

understanding. Your fx-991ES calculator will

prove to be an invaluable tool in helping you to

further your understanding. You will find the

material is drawn from AQA, Edexcel, NEC and

OCR syllabuses. The material covered in this book

includes, ● Elementary Integrations

● The Substitution Method

● Integration of Exponential Functions

● Integration Techniques

● Integration of Trigonometric Functions

● Integration by Parts

● Applications of Integration

● Harder Integration

As you progress through your A Level Mathematics

course you are likely to be introduced to matrices

and complex numbers. In both these topics a lot of

computation is expected and you will find the

Casio fx-991ES Plus will offer you a range of

options to enable you to perform these

calculations. This book will show you how to

access the features on the fx-991ES that are

specifically designed for matrix and complex

calculations. This will enhance your understanding

of both these topics and provide you with an insight

into their significance in the field of mathematics.

The material in this book includes, ● Vector Revision

● First Look at Matrices

● Determinants

● Solving Simultaneous Equations

● Transformations

● Introduction to Complex Numbers

● Trigonometry and Complex Numbers

19

● Quadratic Equations with Complex Roots

Mechanics forms an important part of the A Level

Maths syllabus and involves a considerable number

of calculations. The Casio fx-991ES PLUS can be

an important asset in furthering your understanding

of the subject. This book should be used together

with your course text books on mechanics. It will

offer an alternative insight into problem solving us-

ing the power of your fx-991ES PLUS calculator.

The material is drawn from the AQA, Edexcel,

NEC and OCR syllabuses and includes, Terms used in Mechanics

Using Vectors in Mechanics

Moving Particles

Static Particles

Newton’s Second Law of Motion

Appreciating Moments

Projectiles

This is the second book in the Cambridge Paper-

back series on Mechanics and as with Part 1, this is

best used together with your classroom text books

on mechanics. Most of the topics you will cover in

your classroom are discussed with special empha-

sis on how the Casio fx-991ES PLUS calculator

can be used to solve mechanics problems. It is as-

sumed that you have a reasonable working

knowledge of algebra and calculus. Many of the

examples in this book are derived from calculus

models. The material covered in this book in-

cludes, ○ Collisions and Impulse

○ Work, Energy and Power

○ Statics and Limited Equilibrium

○ Moments of Inertia

○ Rotation

○ Harmonic Motion

20

Statistics has long been regarded as an important

tool in the analysis of data and its inclusion in your

A Level Mathematics course is a reflection of its

significance. This is Part 1 in the series which em-

phasises the role your Casio fx-991ES calculator

can play in developing your skill set in statistical

techniques. This calculator is ideal for processing

small data sets and provides you with a convenient

way of finding answers to statistics problems. The

material covered includes,

● First Look at Probability

● Sets and Probability

● First Look at Statistics

● Normal Distribution

● Applying the Normal Distribution

● The Poisson Distribution

This is the second book on statistics for A Level

Mathematics and should be used together with

your classroom text books. As you progress

through your course you will learn the application

of statistics relies on methods and understanding

how the different methods are applied to various

types of data. Your Casio fx-991ES Plus calcula-

tor will prove to be particularly useful in perform-

ing statistical calculations and the many examples

will show you how this is achieved. You will find

the material in this book is drawn from AQA,

Edexcel, NEC and OCR syllabuses. The material

covered includes, ● The Binomial Distribution

● Continuous Random Variables

● Sampling theory

● Hypothesis Testing and Correlation

21

Understanding the significance of angles in geo-

metrical shapes has intrigued man since the days

of the ancient Egyptians. You have already been

introduced to trigonometry at GCSE level and at

A Level your understanding will be further devel-

oped. This book will show you how your Casio

fx-991ES calculator will enable you to gain a

greater understanding of the subject through nu-

merous examples. These show all the calcula-

tor’s keystrokes needed to solve many trigonom-

etry problems. The material includes, ● Angles and their Measurement

● The Pythagoras Theorem

● Sine, Cosine and Tangent

● Identities

● Triangle Calculations

● Secant, Cosecant and Cotangent

● Inverse Functions

● Hyperbolic Functions

● Graphs of Trigonometry Functions

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