mathematics with word and excel

8/9/2019 Mathematics With Word and Excel

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TO THE READER:

The author of this work to him will be recognized very if you to himpresent your opinion about this work that I offer to him, as well as itspresentation and impression.I also thank for any other suggestion to him.

My direction email is: [email protected]

FIRST EDITION 2009.

Copyright. 2006. copyright Javier Gonzlez Czares

Name of the publication house: GaussianRegistries N 03-2006-071115045600-01, SEP and N 03-2007-081615321700-01, SEP

Rights of Author Art. 184

Rights in proceeding no. 2693 17 of August of the 2009

* Translated of Spanish with the original title: Matemticas con Word y Excel, of

Javier Gonzalez Czares
mailto:[email protected]:[email protected]:[email protected]


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INDEX

INTRODUCTION...............................................................................................................5

PREFACE TO THE EDITION IN ENGLISH.6FIRST PART

I. EDIT OF EQUATIONS--------------------------------------------------------------------------------------------------------------7

PRACTICE # 1. HOW YOU WOULD WRITE FORMULAS And EQUATIONS IN The LEAF WORD? 8PRACTICE # 2. "TO EXPRESS A FRACTION IN WHOLE NUMBER And FRACTION 11PRACTICE # 3. "ARITHMETICAL OPERATIONS WITH EXCEL" 12PRACTICE # 4. "EQUATIONS OF FIRST DEGREE" (WITH A VARIABLE) 14PRACTICE # 5. "SOLUTION OF EQUATIONS OF FIRST DEGREE". (METHOD BY FORMULA) 16PRACTICE # 6. "BINARY SYSTEM" 18PRACTICE # 7. "THE ARITHMETICAL PROGRESSION" 19PRCT ICA # 8. "FACTORS OF DIVISION 21PRACTICE # 9. "DRAWING WITH EXCEL" 22PRACTICE # 10. "IT APPLIES YOUR KNOWLEDGE" 23

"PROBABILITY And STATISTIC" 23PRACTICE # 11PRACTICE # 12

SECOND PARTII. GENERAL CONCEPTS. -----------------------------------------------------------------------------------------------------------28PRACTICE 1 3: FRACTIONS REPRESENTED IN CIRCULAR GRAPHS 42PRACTICE 14: FRACTIONS IN GRAPH DE BARS 43PRACTICE 15: CIRCULAR GRAPH OF FRACTIONS 46PRACTICE 16: FRACTIONS 48PRACTICE 17: SUM And SUBTRACTION OF FRACTIONS 53PRACTICE 18: SECOND PART: EXTREME OF FRACTIONS 55PRACTICE 19: ARITHMETICAL MULTIPLICATION 57PRACTICE 20: FORTUNE-TELLER OF NUMBERS 60PRACTICE 21: TO DRAW FIGURES GEOMETRICS 63PRACTICE 22: AREA OF FIGURES IN EXCEL 66PRACTICE 23: AREA OF A TRIANGLE IN SPACE 68PRACTICE 24: AREA OF A TRIANGLE IN THE SPACE (THREE STRAIGHT LINES IN THE SPACE) 71PRACTICE 25:CHEMICAL BALANCE 73PRACTICE 26: VERIFICATION OF EQUATIONS 75PRACTICE 27: POLAR COORDINATES And RECTANGULAR COORDINATES 78PRACTICES 28: INEQUALITIES WITH INECUATIONS 81PRACTICE 29: SYSTEMS OF EQUATIONS BY RULE DE CRAMER. 85PRACTICE 30: RULE DE KRAMER 2 (CONTINUATION) 88PRACTICE 31: SYSTEMS OF LINEAR EQUATIONS (METHOD REGULATES DE CRAMER) 89PRACTICE 32: LINEAR EQUATIONS BY GAUSSIAN ELIMINATION 93PRACTICE 33: QUADRATIC EQUATION 97PRACTICE 34: EQUATIONS WITH AN INCOGNITO 99PRACTICE 35: EQUATIONS WITH AN INCOGNITO; SECOND PART (USING SCROLL BARS) 100

PRACTICE 36: EQUATIONS WITH AN INCOGNITO; THIRD PART (CONTINUATION) 102PRACTICE 37: EQUATIONS WITH AN INCOGNITO; FOURTH PART (IT MAKES HIS CALCULATION And ITVERIFIES) 104

PRACTICE 38: EQUATIONS BY RANDOM METHOD 105PRACTICE 39: STATISTIC 106PRACTICE 40: GRAPH OF TWO FUNCTIONS 109PRACTICE 41: CHARTS IN THREE DIMENSIONS 112PRCTICA 42: "INTERACTIVE PARBOLA".EXAMPLES 115PRACTICE 43: PARABOLA (MINIMUM And MAXIMUM) 118PRACTICE 44: GRAPH OF TWO FUNCTIONS (INTERSECTION OF TWO CURVES) 122PRACTICE 45: SLOPE OF A STRAIGHT LINE. 1RA. PART 124


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PRACTICE 46: SLOPE OF A STRAIGHT LINE. 2DA. PART 126PRACTICE 47: SLOPE OF A STRAIGHT LINE. 3RD. PART 129PRACTICE 48: REMARKABLE PRODUCTS 131PRACTICE 49: CIRCLE(With rectangular and polar coordinates) 135PRACTICE 50: CIRCLE OUTSIDE ORIGIN 137PRACTICE 51: INTERSECTION BETWEEN A STRAIGHT LINE And A CIRCLE 140PRACTICE 52: TRIGONOMETRICAL FUNCTIONS: "COSINE" 143

PRACTICE 53: SYSTEMS OF EQUATIONS TWO Xs TWO 148PRACTICE 54: FUNCTION SPECIFIES 152PRACTICE 55: EXPLICIT FUNCTION. CONTINUATION 154P RCTICA 56: EQUATION OF THE PARABOLA OUTSIDE ORIGIN 157PRACTICES 57: GENERAL EQUATION OF THE PARABOLA 160PRACTICE 58: CHART OF POLAR FUNCTIONS WITH ANIMATION 162PRACTICE 59: VECTOR (Using coordinated polar) 167

GLOSSARY ---------------------------------------------------------------------------------------------- 170


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INTRODUCTION

THIS WORK THAT APPEARS IN WRITTEN FORM, AT FIRST WAS A SERIES OF LOOSE AND DISORDEREDEXERCISES.

ALTHOUGH ORIGINALLY "NIOS HEROES" WERE DONE FOR THE STUDENTS OF THETELESECUNDARIA, OF THE COMMUNITY OF BUENAVISTA, FRESNILLO, ZAC., MEXICO; IN ORDER TOEVALUATE A WORK OF INVESTIGATION BUT OF EQUAL WAY THEM THE STUDENT OR STUDENT OFSECONDARY GENERAL OR TECHNIQUE CAN USE.

THEY GO OF THE SIMPLE THING, FROM LIKE WRITING FORMULAS IN THE WORD PROGRAM, NOTWITHOUT BEFORE PUTTING A PROBLEM SO THAT THEY MAKE IT IN HOME. IN EXCEL YOU WILL BEABLE TO APPLY FORMULAS OR TO DEDUCE THEM FOR DIFFERENT CASES.

CHILDBIRTH OF WHICH THE STUDENT MUST EXERCISE ITSELF FIRST IN THE HALL CLASS, THATINCLUDES/UNDERSTANDS WELL HOW TO SOLVE MATHEMATICAL PROBLEMS AND SOON TO VERIFYITS RESULTS IN THE HALL CALCULATION. ALL GOOD KNOWLEDGE MUST HAPPEN THROUGH ANAPPROPRIATE PRACTICAL REFLECTION.

THE IDEA IS THAT IT LEARNS TO EXERCISE AND TO COMMUNICATE BETWEEN HIS COMPANIONS ANDTEACHERS HIS RESULTS, OF HOW TO USE THE LEAF EXCEL IN THE LABORATORY OF MATHEMATICS,IN SOME CASES THERE IS MAS OF TWO WAYS TO FOLLOW FOR A SAME SOLUTION, MOST OPTIMAL ISTHE ONE THAN YOU CHOOSE.

IT IS CERTAIN THAT THERE IS AN ENDLESS NUMBER OF WAYS TO ARRIVE, THE JOKE IS TO KNOW ASHE IS BEST, THE LESS MOST TEDIOUS ONE, MORE BETTER IN THE KNOWLEDGE AND APPLICATION TOTHE GIVEN PROBLEM.

THE EXPERIENCE IN THE HALL SAMPLE THAT A MOTIVATION IN MATHEMATICAL SHOWS ONEBETTER TOLERANCE TO LEARN AND SEARCH OTHER WAYS.

THE DISCUSSION ON IF HE IS APPROPRIATE OR NOT THIS RESOURCE IS IN THE HALL CLASSES, WITHTHE OWN ONES INVOLVED: LIKE AUTHORITIES, TEACHERS, STUDENTS AND PARENTS OF FAMILY.

IN ORDER TO UNDERSTAND THIS BOOKLET IT IS NECESSARY TO SEAT AND TO USE THE COMPUTER, ISTO SAY ACTUALLY. THE LAST ADVANCES IN THE TECHNOLOGY OF THE INFORMATION ALLOW THATTHE MATHEMATICAL ONE IS MORE EXPERIMENTAL. THE STUDENT ALWAYS COMPLAINT OF THETEDIOUS THING THAT IS TO SOLVE OPERATIONS WITH VARIABLES. HE MATTERS, THAT THE STUDENTLEARNS AN ALGORITHM OR THAT IS ALL THE DAY SOLVING ONLY A PROBLEM? OR, NOT EVEN TO BEABLE TO SOLVE IT? ONCE LEARNED THE METHOD, HE CAN HAPPEN TO EXPERIMENT AND LOOK FOROTHER ALTERNATIVES, LIKE REPRESENTING NUMBERS WITH DRAWINGS, WHICH AMPLE THE FIELDOF REFLECTION OF APPLICATIONS AND KNOWLEDGE. THE USE OF OTHER METHODS ALTHOUGHDOES NOT KNOW THEM CAN CAUSE THAT IT HAS A AUTORREFLEXIN AND IT CAN PROPOSE OTHERROUTES OF SOLUTION. IT IS NOT SCARED TO KNOW, IT EXPERIMENTS, IT LOOKS FOR, DOES,ALTHOUGH IT IS MISTAKEN.

THESE WORDS THAT WILL FIND IN ALL THE TEXT, ARE A REFLECTION THAT THROUGHOUT THEYEARS I HAVE HAD, AND THAT I THANK FOR MY WIFE JOSEFINA, MY CHILDREN JAVIER ANTONIO

AND M. JOSEFINA ADRIANA SU UNDERSTANDING, PATIENCE AND ENTHUSIASM.TO PROFESSORS JOSE.ANGEL GUERRERO LOERA AND LUIS MANUEL AGUAYO RENDON TO BELIEVE INMY WORK, AND MY FRIEND AND COMPANION OF IN FIGHT FELIPE H. CORTEZ VZQUEZ.

J. G. C.JUNIO 2006


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PREFACE TO THE EDITION IN ENGLISH

This edition has in addition corrections to the edition in Spanish, as they are of style butbetter even of concept, improve in some cases the result and proposing are added.

The idea to update this work to Office 2007, has been with the idea to spread the

mathematical one between that they initiate in this field, to communicate the most complete

image of the mathematical field, to offer a greater interaction and participation. But mainly

to motivate to that the knowledge flow between creators and students.

Although the difficulty between the mathematicians of the emergent countries now called

is distrust towards everything what is technology that has an historical origin in theformation of colonial societies, does not have to be reason for not letting pass the

opportunity to provoke changes in the economy, sciences, industry and culture.

This work would have to be reviewed and although corrected errors them, as well as their

foundations exist to be verified and to be evaluated by the interested ones.

Many mathematical problems exist still that must be solved, and with the traditional

methods to do them by hand (a mano), time and loss of energy have been beside the

point very expensive in. With a technology like this one, John Neper (1550-1617) had

saved half of his life in constructing his famous tables of logarithms.

All the examples are resolute in the decimal system, reason why if it handles anothersystem makes the changes necessary.

J. G. C.OCTOBER 2009


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FIRST PART

I. EQUATIONS EDITORThe MathTypes translation facilities can be used as component of a more comprehensive

document conversion process

1

, is a very useful tool in Word, transfers formulas, equations,etc.In office 2007 we can accede to the publisher of equations in the card Insert, click

Equation

For example: The following you formulate writting in Word:

In order to begin to write, it writes within this image

a

acbb

xa

acbb

x 2

4

;2

42

2

2

1

08432 xx

1 TOPPING, Paul; Using MathType to Create TEX and MathML Equations; Design Science, Inc., 4028 Broadway, Long,Beach, CA 90803; USA; [email protected]; URL: www.mathtype.com

Note: MathTypes Word support is written in that products Visual Basic language. The source code is accessible and may be used as the basis for your own conversion scheme.

2

1

)2)(1(

3

)1)(1(

13

xxx

x

xx

x
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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For the first example, we opened and Editor of equations gives click inImmediately it appears.

In order to begin to write, it writes within this image

It begins to write the equation, as well as one appears:

In the end it is this way:

II. PRACTICE # 1

1. HOW YOU WOULD WRITE FORMULAS And EQUATIONS IN The LEAFWORD?

Objective:You will use your abilities to write mathematical formulas and equations in the computer.Order of steps:

dc

ddc

d

d

22

32

61 12232 xx


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You open a New Word Document, you write the title "HOW TO MAKE EQUATIONS",soon to center. Like subtitle "the life of Diofant".

In Insert + Table choose opened Insert Table click, Number of columns 2, Number ofarrows 9, click in OK

With your mouse, in the first column you write "LANGUAGE VERNCULA", with theright cursor, you write "LANGUAGE Of ALGEBRA", the pictures that we will fill arethose of the left side, those of the right you will fill you to them after the dictation.

Second picture, first column (next to be brief so on to third picture and), writes:

1. Traveller! Here the rest of Diofanto were buried. And the numbers can show, OH,miracle, how it releases was his life,

2. Whose sixth part constituted its beautiful childhood3. One twelfth part to its life had passed in addition, when with hair covered in its chin4. And the seventh part of its existence passed in a sterile marriage5. It spent a quinquennium more and it made the birth happy of his precious first-born,

(Note: between rows 6 and 7, column 1, you choose To divide to Cells give click.Again click)

6. that it gave his body, his beautiful existence, to the Earth, that lasted only half of the itsfather

7. And with deep pain it descended to the grave, having survived four years the decease ofhis son

8. (Note: you choose two columns in this last row, you go to Table + Dividir Cells

click, you select Negrita, click) Tell me how many years Diofanto had lived whenthe death arrived to him.

Once finalized all the dictation, you will put the appropriate variables and constants to eachstep that was indicated, when you have finished it compares your results with the teacherand solves in your house this incognito, that surely you will be surprised of the result.


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II To HOW TO MAKE EQUATIONS

This exercise to use the "MathType", you will make a dictation, takes care of errors ofmathematical spelling and handwriting.

Next the life of Diofant is related, in epitaphic of its tomb:THE DIOFANTO LIFE2

LANGUAGE VERNACULAR LANGUAGE Of ALGEBRA

Traveller! Here the rest of Diofanto wereburied. And the numbers can show, OH,miracle, how it releases was his life,

x

Whose sixth part constituted its beautifulchildhood

One twelfth part to its life had passed inaddition, when with hair covered in its

chin

And the seventh part of its existencepassed in a sterile marriage

It spent a quinquennium more and itmade the birth happy of its precious first-

born,that it gave its body, its beautifulexistence, to the Earth, that lasted onlyhalf of the its father

5

2

x

And with deep pain it descended to thegrave, having survived four years thedecease of its son.

It tell me how many years Diofant had lived when the death arrived to him

Obvious the result you will do it "by hand", since it beams of regular way or in your house,and your results you compare with your companions and teacher.

Exercises:It finds the variables and constants:

2PERELMAN, Y, "Algebra recreativa", Ed. Quinto Sol, Mexico, 1983, Pg. 46.

6

x

12

x

7

x

42

57126

xxxxx


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1. It is tried to surround a rectangular land and to divide it in three parts with two innerand parallel fences to one of his sides. Find the dimensions of the land if the lengthoverall of the fences has to be of 800 ms and the area of the land is 19.200 ms 2.

2. A page with 3 plg more of length than of width, has 80 plg 2 of impression. Find thedimensions of the page.

PRACTICE # 2

"TO EXPRESS A FRACTION IN WHOLE NUMBER AND FRACTION"

2. A FRACTION WRITES IN THE LEAF EXCEL, ITS SIMPLER FORM.It is easy in the Excel leaf only is to know how they are made by hand.

Objective:That the student can express the division as were taught to him in primary and expressesfractions improper in whole and remainder.

Order of steps:It opens a new leaf of Excel, writes the title "TO EXPRESS a FRACTION IN WHOLENUMBER and FRACTION", soon in the C6 cell writes the numerator of the fraction, inthe C7 cell writes the denominator of the fraction. Center and with Crtl + 1, Wild forthedivision ray.

In B9 it writes "EXPRESS:"In B11 the formula writes =IF(C7=0,"indeterminada",INT(C6/C7))In C11 it writes "WHOLE".

It selects cells from B11 to D11 (row) lowering a row (D12), choosesing personalize in

Home + Merge and center.

In the cell E11 the formula writes = MOD ( C6 , C7 ), it gives Crtl + 1, it down choosesline for the line of division.


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In the cell E12 the formula writes = C7 it gives ENTER.

NOTE: you can change to the numerator and denominator for different results.

EXERCISES:1. It applies the divisibilidad criterion to find the multiples of any number.

How to find if a number is splitter another number.

PRACTICE # 3

ARITHMETICAL OPERATIONS WITH EXCEL

3. IT CONDUCTS DIFFERENT ARITHMETICAL PENCIL OPERATIONS, SOONVERIFIES YOUR RESULTS IN THE SPREADSHEETEXCEL.

Objective: You will learn how to conduct arithmetical operations with computer.

Used expressions or symbols:You will use the following symbols in Excel, like ( + ), ( - ), ( * ), ( / ), ( ^ ), ( ABS),(COS), (SIN), (INT), (EXP), (FACT), (DEGREES), (PI), (POWER), (SQRT), (MOD).

Examples:It conducts the following operation by hand:

(4)*(-5)*(-2)

How much it is to you?Well, now it introduces these operations in a new Excel leaf:First you must write in the cell B7 soon the equal sign so that it is solved like a formula, theoperation

(4)*(-5)*(-2)


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In the end it gives ENTER.Your result is equal when introducing to Excel leaf?, if it is not thus it corrects.

Example: now it makes 4*9 + 50/10, by hand; soon in Excel, it remembers that first you

must introduce equal sign ( = ).

In the following exercises, first to solve by hand and later in Excel.

EXAMPLES BY HAND EXCEL(8+5)*(2)

8+5*2(8/2+5)*(1+8)

8^46*(8+9-(15/3)^2)

ABS(-789)COS(60)SINE (60)

WHOLE NUMBER(15.548888)

EXP(1)FACT(8)

DEGREES (1)PI()


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ab

x

POWER (4,3)RAIZ (144)

REMAINDER 43 FACTORIAL 88*2-5^3*(1/8)

8^2*5+3/1-88+2^(5-3)*3*1/8

8^(2+5)-3^1/88^(2*5)/3+1-8

It remembers that first you must do it by hand and soon in Excel, it compares your resultsand it concludes.

I recommend to you that the steps 3 to follow in an operation of Arithmetic can varyaccording to is the case, but first you must consider that first you conduct the operationsthat are within the parentheses, soon multiplications, divisions and powers, finally you

carry out the sums or subtractions.

PRACTICE # 4EQUATIONS OF FIRST DEGREE

(WITH A VARIABLE)

4. IT APPLIES YOUR KNOWLEDGE OF CLEARS OF EQUATIONS TO FIND A"FORMULA THAT SOLVES EQUATIONS OF FIRST DEGREE OF THE FORM:a x = b

An equation is a statement in which two amounts are equal, the equals sign is placed in themiddle of these two. The equations have one, two or more letters, variable or incognitocalls. By means of algorithms we can find the values of the variables, these they arereplaced in the equations, they make equal as well to both members of the equation, it is tosay satisfy to, or is a solution of. The total of the solutions is known him like set ofsolutions.It is as well as for the general formula of an equation to prioritize degree with a variableand a constant it will be:

Its solution, for when: if 0a

It is:--------------------- Formula (1)

3For more examples: http://homepage.cem.itesm.mx

ax b

axa


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Of equal way when, an equation with a variable is had and two constants, the rank of a isthe same one:

Si 0a The general formula is:

Reason why clearing it is had.

-------------------- Formula (2)

In both cases, the value ofa, will not be zero, by definition.

Objective: Find you the algorithm general or particular Excel, for equations of first degree.

Order of steps: It opens a new Excel document. The title writes "EQUATIONS OF FIRSTDEGREE (WITH a VARIABLE)", soon in the interjection to, "the case for a constant",

writes respectively in the cells B8 and B9 to and b, now the values of each one of them,those that you want.

Immediately, "the value of the variable is:", in the B12 cell, x writes "=", C12 cell thecorresponding formula.

As the formulas are defined based on which the denominator is not zero, since he wouldgive to a indetermination or an infinite number us, to solve them is necessary anothercourse advanced more, but so far we put a restriction to our formula.

= IF (C8=0," indeterminate ", C9/C8)

Why "indeterminate? Consultation to your teacher.

In summary it would be thus:

Once finished, you begin in the following cell writing: "b) the case for a variable and twoconstants". And you follow the same procedure that the previous one, only that now in theformula you will add the following thing:

=IF (C21=0, Indeterminate, (C23-C22)/C21)

c bx

a

ax b c

axa


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In summary:It verifies your values, changing the values of coefficients and constants, it by hand makesthese calculations and in the computer.

EXERCISES:1. For next equations to deduce the general formulas:

Once deduce the formulas; to aplicate now in the Excel program, soon head of cattle tosolver for different values.

PRACTICE # 5

SOLUTION OF EQUATIONS OF FIRST DEGREE(METHOD BY FORMULA)

5. IT APPLIES YOUR KNOWLEDGE OF CLEARS OF EQUATIONS TO FIND A"FORMULA, WHICH SOLVES EQUATIONS OF FIRST DEGREE OF THE FORM:

OBJECTIVE: That you determine the value of a variable from a formula that you deducein your hall or your house, to be able to solve equations of first degree in general forms.

Be the general formula, for an equation:

The solution will be:

ax b a x b

ax b c ax b c

ax b c ax b c

ax b cax b

ax b cx d

d bx

a c

ax b cx d


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This formula is applied when: 0ca

Ordered steps: Now, it opens a new document Excel. The problem to solve is:

The theory writes as it comes in the Excel presentation, soon in the cells B50, B51, B52 Y

B53, the letters of each constant or coefficient successively.

From C50 to C53, the values of each constant or coefficient

For example:The value which you introduce in the computer, by a = 8, it is in the cell C50, to add 8beams ENTER and it is added automatically, to do successively with the other constants.

Once finished, in the E52 cell we put x =, to say soon that the value of X is, in the F52

cell, we put what follows:

=IF (C50-C52 =0," infinitely, without real solution ", (C53-C51)/ (C50-C52))

It verifies your results, in the notebook. It voluntarily changes the values for differentproblems.

EXERCISES:1. On the basis of the proposed algorithm it solves for one of the following cases, it

bases your deductions on Word the Publishing leaf of equations, and soon to applyto Excel, for each case, it varies his values to verify your results:

ax b cx d ax b cx d ax b cx d ax b cx d

8 5 4x x

8

5

1

4

a

b

c

c


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ax b cx d ax b cx d

PRACTICE # 6BINARY SYSTEM

6. IT TURNS A NUMBER DECIMAL TO THE BINARY SYSTEM THESPREADSHEET.

Objective: You will use the binary algorithm to change to the decimal system.

Order of steps: You open a New Excel Document, you write the title "BINARY SYSTEMOF NUMERATION", point to aside and write "EXPRESSES the BINARY NUMBER ToNUMBER DECIMAL", aside you write "INTRODUCES ANY BINARY NUMBER INthe ROW OF the TABLE:.

We are going to form a table from B8 until J11, you tighten Crtl + 1, choose Format Cell+Border + Outline + Inside + OK, soon for each row choose a Color of different Filling.

In the row POSITION, you add in C8 number 8, D8 the 7 and so on until J8.

In the row POWER, you add in C9 the formula = (2) ^7,in, D9 the formula = (2) ^6, and so on until J9.

In the row BINARY NUMBER, put on the binary number that you look for. Well-takencare of Ten that you begin to put it of right to left.


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In the row POSITIONAL VALUE, in the C11 cell, put the formula = C10*C9, in cell D11,put on the formula = D10*D9, and so on until the J11 cell.

From the A14 cell, you write "THEREFORE the BINARY NUMBER TURNED ToNUMBER DECIMAL IS:. SUM

In the B15 cell, you write the formula = SUM(C11:J11). It is of this form:

It verifies that the values of the formulas well are reviewed.

Exercises: there are east exercise but in the quinary system this exercise in the system octal

PRACTICE # 7

"THE ARITHMETICAL PROGRESSION

7. IT INCREASES 0.5 TO THE VALUE OF 1, TO KNOW ITS BEHAVIOR, TO USETHE CONCEPT OF ARITHMETICAL PROGRESSION

Objective: To apply linear or progressive a succession of numbers.

You open a new Excel document, Beams just like this in the figure.


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Selects Home + fill + Series.

The Series, is Rows + Step value 0.5 + Stop value 5 next OK.

It is thus:

Exercises:1. It makes in progressive order of 2.0.2. It makes in order regressive (or decreasing) of the order of6.3. another one in order of - 12.

4. The following problem, is said that it solved the great mathematician Gaussian, ofboy when his teacher of School let to his students add all the consecutive numbersfrom the one to the one hundred.a)Resulvalo by hand, for it I propose to him writes down all the numbers to add

them, soon finds the relation among them.b) To contrast its result with the following formulas:

n = to + [ (N - 1) x r ]S = (to + n) x N/2


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to = first term of the progressionn = last term of the progressionr = reasonN = number of termsS = sum of the terms of a to n.

Which is the succession of the following formula? It calculates this by means ofsignificants, is to say very great to know the conjecture correct.

1 1n nn

a n n

PRACTICE # 8DIVISION FACTORS

8. IT FINDS THE FACTORS OF DIVISION OF ANY NUMBER USING THE

SPREADSHEETEXCEL.

Objective: You will remember it forms in how finding the splitter of any number and theuse of the splitters to solve examples.

Order of steps: It opens a new Excel document, pon the title with size 20, font Times,capital letters, "FACTORS OF DIVISION.

Next you will put the formulas, for example, in the C4 cell, pon any number, next in thecell D4, the number to which "you will guess" if it is division factor, in the E4 cell, you addthe formula = IF(MOD(C4,D4)=0, "is SPLITTER, CONGRATULATIONS!", "YOU

WERE MISTAKEN, TRIES Again"), in the H4 cell when is not the division you put =IF(C4=1, "YOU FINISHED, CONGRATULATIONS", "IT CONTINUES").

Once finished, you must put the formula from which you obtain the quotient, from the C5cell, this way: = C4 / D4.

For the other cells since you will find more splitters, copy.

EXERCISES: this same exercise but with two factors; same but with three or more factors


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PRACTICE # 9DRAWING WITH EXCEL

9. YOUR IMAGINATION TO DRAW FIGURES IN THE LEAF EXCEL

Objective: You will draw in the Excel leaf, having used your imagination.Order of steps: It opens a new Excel leaf, soon selects all the document. With the mouse itselects the number of rows that you wish, next, Home + Format + Rows height, selects 6.

Now, with the mouse it selects the number of columns that you wish, In the superior cornerof the leaf of I calculate gives to click and select all the cells, to continuation next in the

card Home + format + Column width. Select 3. Click, OK:

Soon there are drawings as if each picture was vectors or pixels of a figure, for it use thefilling color, selects Fill Color

that you wish and. The others run of your account. As you see in the example that is next:


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EXERCISES: it elaborates your own drawings.

PRACTICE # 10"IT APPLIES YOUR KNOWLEDGE"


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10. IN THE SPREADSHEET FIRST IN A COLUMN, THERE ARE A TABULATIONFROM -1,5 TO +2, SOON CALCULATES FOR EACH DATA WITH THE FUNCTION

xy

1, IT FORMS ONE SECOND COLUMN, WHEN YOU FINISH, CHARTS THESE

DATA.

Objective: You will apply your knowledge to find the behavior of a series of data, in agraph.Order of steps:When expressing values, magnitudes or other data by means of tables, we can intuit itsbehavior, but when they are many data is very difficult, reason why we will use a techniqueof Excel to be able to relate the numbers to figures is to say graphical Cartesians.

It opens a new Excel document, soon put the title "WONDERFUL FUNCTIONS", soon"to graphic the function and you put the formula:

It begins with the first column, you put X, later for down you put number 1,5, ENTER,in that cell Home + Fill + Series, click. Select column with Step value of o.3 and Stopvalue 2.

In the following column next to X, you put and, later ENTER, in that cell you add theformula = 1/A6, ENTER, select to that formula it copies, soon it selects downwards all thecells and it give ENTER to copy the formula and it alongside applies it according to thedata.

As time the column alongside collects all the previous data like ordered data, in D6, you

put = A6, in the F6 cell you put = B6, ENTER, copy and you select them for all the foundvalues.

You select the two columns, it gives click in Assistant for graphs, and you follow the stepsthat already you know, and in the end you have left of the following form:


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It answers the following questions:1. It explains the behavior of the graph.2. What happens in point x = 0?3. Can be modified the behavior of the graph?4. It explains as it is the division of a constant number between zero

EXERCISES:THERE ARE A GRAPH OF THE FOLLOWING DATA

X Y-3 -21.25

-2.5 -10-2 -1.25

-1.5 5-1 8.75

-0.5 100 8.75

0.5 51 -1.25

1.5 -102 -21.25

2.5 -35

IT EXPLAINS ITS BEHAVIOR.a) how it is its graph?b) it explains when the curve has an increase or diminutionc) this graph is followed in other matters and applications very. in which

matters? in which applications of the real life?


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d) The table shows the brake horsepower in H.P., at several speeds, of certain Peltonturbine, as it has been verified by means of a series of tests. Construct a graph thatshows to the relation between brake horsepower in H.P. and the number of RPM.

Power in H.P. RPM

0.625 11200.668 13600.673 15000.658 17500.640 19800.590 21000.530 23400.475 25000.390 2700

PRACTICE # 11

"PROBABILITY AND STATISTIC" I

11. STATISTIC: IN THE FOLLOWING TABLE THE TEMPERATURES OF THEYEAR OCCUR, CALCULATES THE TEMPERATURE AVERAGE.

MONTH TEMPERATURE,C

JANUARY 10FEBRUARY 14

MARCH 20APRIL 22MAY 24JUNE 25JULY 26

AUGUST 24SEPTEMBER 20

OCTOBER 18NOVEMBER 15DECEMBER 12

Objective: apply to the formulas of statistic and probability to solve simple examples.

Solution: It opens a new spreadsheet Excel, soon you add these data like table, and put onclick in B18 you put the formula:

= AVERAGE (B5:B16)


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PRACTICE 12"PROBABILITY AND STATISTIC" II

12. PROBABILITY: HOW MANY EXCHANGES CAN TAKE CONTROL OF THE 9LETTERS OF WORD FRESNILLO?

Solution: a letter F, a R, one E, a S, a N, an I, two Ls and one O:

The formula to calculate the number of exchanges with n objects,

1 2 3

!

! ! !...

nP

n n n

You open a new Excel document, you write down your results, with the previous formula:In the spreadsheet it is thus:=FACT(C3)/(FACT(C4)*FACT(C5)*FACT(C6)*FACT(C7)*FACT(C8)*FACT(C9)*FACT(C10)*FACT(C11))See as it is in the leaf:


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EXERCISES:1. Of how many ways four pairs can seat around a table if men and women have to

alternate themselves?2. In the statistic problem it finds the fashion, the maximum value by formula,

minimum value by formula; in addition it makes a graph de barras vertical.

SECOND PART

GENERAL CONCEPTS

Excel in the School is a didactic tool with a great potential, although we only use the basicoptions. It is a computer that allows us: to conduct heavy and complex operations betweenrows or columns, to order or to look for data and to present/display in graphical form the

obtained results, with mathematical formulas of a way fast and easy. Algorithms, models,visualizations, and mathematical uses in execution can be put naturally and witheffectiveness through interactive constructions of the leaf of balance and creative graphicalexhibitions. This paper demonstrates the techniques that allow educators to designexhibitions animated graphics in their constructions of the balance leaf to producedemonstrations in the hall class to heighten the mathematical understanding, whereas alsoit presents/displays to students with the new and attractive visual mechanisms in his tasksand mathematical projects.

This educative experience makes the development of skills and abilities efficient that allowobtaining better results in the handling of the algebraic language. The use of computerscience like attractive means reflects to deepen algebraic concepts using the creativity, the

knowledge and the mathematical reasoning.

It handles images designed by the user from algebraic expressions when those that thecreation of formulas allow their execution.

When this happens, algebraic language, algebraic expressions, graphics of functions and itsresults extend the level of conceptualization and understanding.

The abilities necessary to include/understand this text are: To use letters to representnumbers, to evaluate algebraic expressions, to identify algebraic expressions, to constructalgebraic expressions, to represent categories of numbers by means of algebraic

expressions, to use procedures to identify the parts of a term, to classify algebraicexpressions according to the number of terms.The author has interest in developing in the student or teacher: the creative, analogical andcritical thought, its interest and capacity to know the reality, to use the knowledge and toselect, to process, to organize and to synthesize information, the personal initiative, thecreativity, the work in equipment, to create attitudes of rigor, patience and fulfillment of thetasks, to use the software of intention like creative means in the conceptualization andunderstanding of algebraic expressions.


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What must use is its notebook, pencil, computer of the scholastic laboratory, this booklet,elementary book of mathematics and an average one to keep its tasks.

TYPES OR TEST EXERCISESThe Developer card helps us to insert Pictures of Controls and ActiveX, for it looks forInsert Controls and it selects some type of Form Controls or ActiveX click in them.

He is usual that the controls are formed mainly through Visual Basic (VBA).

The Properties dialog box for the scrollbar:

When inserting the control, we click with the right button of the Mouse on this control, this

so that it appears to us the picture of dialogue of properties of this control. This picture ofdialogue as well has in the superior end a picture combining or combobox, which willallow us to form the properties of some other control which we must in the present bookwith no need to be selecting this one previously.

There are two options for the visualization of the properties. First in alphabetical form andsecond by categories.


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The Mode Design, it can modify whichever times is necessary the differentcontrols from our book. The way design is activated when the attached icon is stood out, toactivate only makes it lack click on him. In order to leave the way design, it will be enoughwith returning has to click in this same icon. It is possible to clarify that when we are inthe way design the different controls will not be operative, reason why will be necessary toleave this way to be able to use these controls.

MAIN PROPERTIES OF THE CONTROL PANEL

LinkedCell

This property that will use more, is tie with the control at issue. In some cases it will serveso that the control shows the content of this cell, although in most of the cases the one willbe the control that conditions the content of this cell. In order to form the control, it willonly be necessary to introduce the value rather or the position of the cell that is desired totie. We recommended doing it in absolute terms, by ej. "A1 ". This is, the cell produced bythe concurrence of the column "To and Row "1 ".Value

This property denotes the Value that will have the control. According to it is the interactionthat has the control, the value of this one will change. For example in the case of a buttonof alternating, the property value takes the values "TRUE" (true) or "FALSE" (false)according to it treats. In the case of a control knob of number, the property value will takethe value of the respective sequence.

Name

This property denotes him name of the control, by Excel defect assigns to a name made upof the type of control but a corelative one to him, for example "CommandButton1". Thiswill serve later to identify this control and to form it for example through macros or VBA.

Min, Max, SmallChange

Corresponding they indicate the minimum value of the control, the maximum and the valuein which this one will be changing (increase or decrement, according to is the case)whenever click becomes on anyone of the arrows of this control. The value ofSmallChange property can be any whole number, although the interval of valuesrecommended is from -32767 to +32767. The predetermined value is 1.

In the Excel leaf, sometimes it must modify the presentation of graphs, cells, or anotherthing. Here recommendations.


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Source: In this card we can specify options about the source in which are going away tovisualize the selected data, or the style, the source itself, the size, the emphasized type of,color and several effects more. Also we can see like in all other cards it shows of whichwe are doing. Almost all the commands who are in this card, them we can find in the bar oftools Format.

Border: it defines the type of line and the color of all the edges (internal and external) thatthe selected rank has.

Fill: it defines the bottom of the cell or selected rank (generally a color).
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Protection: it has options with respect to the protection of the selected rank or cell.

The graphs now are more dynamic, since directly it inserts them: go to Insert + Charts andyou select the Chart that wishes.

BAR OF FORMULASBar located in the superior part of the window that shows to the constant value or formulaused in the active cell. In order to write or to modify values or formulas, it selects to a cellor a graph, writes the data and, next, it presses TO ENTER. Also it can make double clickin a cell to modify the data in her directly.

Like predetermined value, Excel calculates a formula of left to right, beginning by theequal sign (=).

The arguments can be logical numbers, text, values like TRUE or FALSE, matrix, valuesof error like # N/A or references of cell. The argument that is designated will have togenerate a valid value for the same one. The arguments also can be constant, formulas orother functions. The syntax of a function begins by the name of the function, followed ofan opening parenthesis, the separated arguments of the function by commas and aparenthesis of closing.

In order to introduce a formula that contains a function, it clicks in the cell in which itwishes to introduce the formula. Once it completes the formula, presses TO ENTER.

ABSOLUTE, RELATIVE AND MIXED REFERENCESExcel always uses relative references forthe directions of cells introduced in the formulas.This means that the used references will change of agreed way after copying the formulafrom a cell to another one. Very frequently this one is the wished behavior.

In certain cases it is necessary to avoid that the references to cells change when the formulato a new position is copied. For it it is necessary to use absolute references. It is possible touse absolute references for relative rows and for columns, or vice versa. The relativereferences become absolute introducing the character dollar ($) before the letter of thecolumn or the number of row, that is wanted to maintain invariable. If it is desired that itchanges neither the index of rows nor of columns, it is necessary to both put the character

dollar ($) in front of each one of indices.An absolute reference can be inserted of two different forms:1. According to the formula is introduced, keys in character $ in front of the row index,

back if it is column that is wanted to maintain constant.

2. Placing the point of insertion in the bar of references so that it is within the reference tothe cell, pressing the F4 key goes cyclical through relative, absolute references and by both


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mixed cases. In the cases in which only one of the two dimensions is tried that, row orcolumn, he remains constant is used a mixed reference, that is to say, a reference thatcontains absolute and relative references simultaneously. For example, the reference $A5avoids that it changes the column, whereas the row adapts whenever the formula is copied.With A$5 it happens the opposite: the column changes, whereas row 5 always remains

constant.REFERENCES AND NAMESThe references to cells are used to talk about to the content of a cell or group of cells. Theuse of references allows using values of different cells or groups from cells of a spreadsheetto make certain calculations. References to cells of another spreadsheet can be introducedalso, introducing the name of that leaf before the reference to the cells, and separating themby the admiration sign (), for example: (Sheet1! B5:C6).

It is important to know that in the references to cells or groups of cells, Excel does notdistinguish between capital and very small letters.

NAMES OF CELLS AND SETS OF CELLS

Sometimes it turns out annoying to have to repeatedly use references such as B2:B4 orB2:D3; C5:D6 in a spreadsheet, or to select such ranks time and time again. Excel solveseast problem allowing to define namesand to assign them to a cell or to a selection. Thesenames of cells or ranks can be used in the formulas, be created composed names, and evenbe assigned a more significant name to the constants of more frequent use.

The use of names in the spreadsheets diminishes the possibility of introducing errors andallows remembering with greater facility the references to cells. At the time of creating names, it agrees to consider certain rules:1 the names mustalways begin by a letter or the emphasized character(_); after this firstcharacter, any set of letters, numbers can be used and special characters.2 spaces in target cannot be used. Like alternative to the spaces in target, a character ofemphasized or a point can be used.3 Although names can have up to 256 characters, agrees that they are shorter. Since theformulas are limited 256 characters, the long namesleave less.

NAMES OF CELLS And RANKS Or GROUPS OF CELLS.

The form simplest to define names is by means of the commando to Formulas + DefineName + New Name. For it, the following steps can be followed:

1. To select the cell, the rank or the multiple rank to which it wishes to assign the name.2. To choose the card Formulas + Define Name, with which the shown one in the figure isopened to a dialogue picture as.


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3. To key in the name that wishes - in this case concept - in the picture Book Names ofWork.4. To click in Adding or OK. Another possibility - simpler it is to select to the cell orranks of cells to which it is desired to give a name, and soon click on the picture of namesof the reference bar. The reference to the active cell is replaced by the name keying. Whenpressing OK the selected cells they are registered with the name keying.

If what is desired it is to change a name to cells it must come from the following way:1. To select the cell, rank or multiple rank to which it wishes to change the name.2. To activate the picture of names in the reference bar.3. To change the name and to press To OK.

In order to erase a name the button can be used To eliminate of the dialogue picture

GRAFICSIf the values of a graph are made up of great numbers, change automatically, can bereduced or increase the text of the axis and make it more legible. For example, if thevalues oscillate between 1.000.000 and 50.000.000, it can show numbers 1 50 with in theaxis with a label that it indicates that the units are millions. Make the following thing:

Create a graph.Select with the right button of the mouse the axis of values that this constituted by

numbers of great magnitude.

Select to the option Format of axis.Choose the unit of more appropriate visualization to the data and give Close.

Define Name


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FORMULAS AUDITINGSometimes it is mistaken in the formula, when it passes this, in Card + Trace Precedents orTrace Dependents

This action determines if the elimination of a certain cell can have detrimental effects onthe leaf. Thus, if it is wanted to eliminate a cell, but security is not had on if the spreadsheet

it is affected by the elimination, can be resorted to the bar Audit finding the cells thatdepend on her (To track Employees) as well as the cells on which it depends (To trackPrecedents). Next are arrows that indicate the selected thing. The arrows remain in screenuntil the leaf keeps or until clica on the button To take off All the Arrows.


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In order to include new a series of data in a graph the new rank of data is copied and itsticks on the graph.

PROTECTION OF A LEAFThe cells by defect come blocked. If we wished to unblock some of them we must do thefollowing thing: First Home late Format, Cell, eyelash to protect, to clear the square ofverification that this putting by defect in Unlocked. If we markedHidden not it will see thecontent of the cell in the bar of formulas. This becomes when it is not desired thatsomebody sees the formula of a cell. Later the leaf is due to protect with: Tools, To protect,To protect leaf. Actions can be allowed him more or less the user. If we did not allow to

select the blocked and unblocked cells him it will not be able to be positioned with thecursor on them. If we solely let select the unblocked ones to him we will find withsomething similar to a form.

Some abbreviations of keyboard

Ctrl + C CopyCtrl + V PasteCtrl + X CutCtrl + Z Undo


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To protect cellsWith Format, Cell, Protects, to clear the square of Blocked verification in obtains that inthese cells it is possible to be written after executing Tools, Protecting, To protect leaf.

To hide formulates it in a cell

With Format, Cell, to protect, Hidden the cells are marked whose formulas or containedsight in the line of edition are desired to hide. Later it is had to protect the leaf, with Tools,to protect, to protect leaf.

INTERPOLATION and EXTRAPOLATION.The interpolation and the extrapolation are two concepts of modeled mathematical, are veryimportant to do predictions in the s natural, social, economic science s, etc.; specially, thestudents will begin to explore models linear or not linear. An introduction can be doneusing an interactive leaf of balance. "To interpolate or to extrapolate" the spreadsheetallows to discover the graphical difference re two or more terms with only oneunderstanding of the equation of a line.

In a leaf it selects with the mouse, the line to graphic, soon with the right button chooses ToAdd Trendline

To select TrendLine to its pleasure


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Soon in the graph, right click in some of the two lines and chooses Format of Lines ofDivision, discontinuous Plots, Customized, Lines, click in the color that you prefer, Toclick.

For the color of the layout area, it give click in this area and Format of layout area, chooseWild No, Area None, next OK.

Until now, to copy formulas from a cell to other(s), one takes control of Ctrl. + C, but areanother way to do it. When to is escri its formula underneath approaches the cursor theright of the picture. See that the cursor becomes an X, of click in the left button of themouse and maintaining it, to drag to where wishes, single to loosen.


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SOME USED FORMULAS

ABS (value): It gives back absolute value of the argument number. Examples: Thefunction Abs(-5) gives like result 5. The function ABS(10) gives like result 10. functionAbs(-2) gives like result 2.

RAND( ): This function gives back at random included/understood value between 0 and1. This function does not have arguments. Whenever it is generated a random valuedifferent from will be previously calculated.

CONCATENATE(): It unites several text elements in one single one. Their syntax is TOCONCATENATE (text1; text2; ); Text1, text2 they are of 1 to 30 text elements thatwill be united in a unique text element. The text elements can be text chains, numbers orreferences to unique cells.

COS(number): This function calculates the cosine of the argument number. The angle

comes expressed in radianes.INT (value): It gives back the whole part of the number, without concerning themagnitude of the part decimal. That is to say, it gives back to the number eliminating thepart decimal. For example: INT(3.1) it gives like result 3.

DEGREES (value): It turns the expressed argument radianes to degrees. For example,DEGREES (PI()) gives like result 180 degrees. DEGREES (PI()/2) it gives like result 90degrees.

MDETERM (matrix): It gives back the one determinant matrix. The argument matrix can

be a rank of cells or a constant. This function gives back an only value. It is generated errorcode # VALUE! if at least one cell of the matrix contains a nonnumerical value or if thecell is empty. The matrix must have the same number of rows and columns; If it is notfulfilled this restriction, the function gives back error code # VALUE!

MINVERSE (matrix): The result generated by this function is the inverse matrix of theargument that is of first type. In the example, it is explained how to calculate the inversematrix.

MMULT (matrix1, matrix2): The result of the function is matrix product of matrix1 andmatrix2. The number of columns of matriz1 must be the same number of rows that matrix2.

The matrix result has the same number of rows that matrix1 and the same number ofcolumns that matrix2. Remember that as one is a function that gives back a matrix,procedure is similar to the explained one for function MINVERSA.

RADIANS (): This function takes the argument angle that is expressed in degrees andgives back its equivalent one expressed in radians. For example: RADIANS (90) it giveslike result 1,571, is to say PI/2. RADIANS (180) it gives like result 3,142, is to say PI
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ROUND (number, num_digits): It gives back to the argument number, with the amountof decimal specified in the argument nm_decimals, making the approaches of I clearrespective. For example, ROUND (1.4545, 2) gives like result 1.45.

MOD (number, divisor): The function divides to the argument number between

num_divisor and gives back to the remainder or rest of this division. If the division is exact,the remainder gives like result zero. Example, MOD (20, 5) gives like result 0, MOD (9, 4)gives like result 1, MOD (12,8) gives like result 4.

SIN (number): This function gives back to the sine of the angle specified in the argumentnumber. The angle goes expressed in radians. For example, in figure no. 21 it is possible tobe observed that in each one of the cells of column B, the sine for the corresponding valueof each one of the cells of the column To A calculates the right is including the graph of thefunction sine.

IF (): it allows us to make a logical question, which can have two possible results True or

False and of acting of one or another form according to the obtained answer.Structure: Logical IF (Logical_test; Value_if_true; Value_if_false). Checks whether acondition is met, and returns one value if True, and another value if False. What we writewithin the second and third argument they will be the actions that will be made in case thatthe answer to the logical question is true that is false. Both first arguments are only theobligatory ones for this function. In order to make the logical question we will be able touse the following operators of comparison:

= in order to ask if two values are equal,

> to know if a value is greater than another one,< to ask for minor,> = with this we will be able to know if he is greater or equal,< = we asked for equal minor or,< > if they are different s

Example: It imagines that in the A1 cell we wrote the age of a person and in the A2 cellwe want that appears "the Greater" text in the case that the age is equal or superior to 18,whereas in it will to us appears "Smaller " in case the age is smaller of 18.

The function that we would have to write would be = ";"Minor "IF(A1>=18;" Greater ). Itobserves that in the first argument we asked for greater or just as 18, if the answer to thequestion is True will be made the second argument: "Greater", however if the answer isfalse, we made the third argument: "Smaller".

OR: This function also usually is used jointly with the function IF(). With her also we willbe able to make several questions within If and the part that is in the reserved argument forwhen the question she is true, will be only made in the case that anyone of the answers tothe questions within that is the true one. Structure: OR(Question 1; it asks 2; it asks 3;)
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Example: We will use the same previous example but we will let pass if the person isgreater of 16 years or measures more than 150. This way whereupon one of the two isfulfilled will appear the text "Can happen". The only case that will appear "cannot happen",will be when the two questions are not fulfilled. = IF (OR (A1>16; B1>150);" It canhappen";"Not can happen").

AND: This function usually is used jointly with the function IF(). It allows us to makeinstead of a question several. And the argument located in the true part will be only madeof If in the moment that all the answers are true. Structure: AND (Question 1; it asks 2; itasks 3 ;). Example: In the A1 cell, we will introduce the age and in the A2 the stature ofthe person measured in centimeters. In the A3 cell it will appear the text "Can happen" ifthe age is greater of 16 years and measures more than 150. In the case that some of thetwo conditions is not fulfilled, it will appear the text "cannot happen". =IF(Y(A1>16;B1>150);" It can happen ";"Not can happen") It observes that all the AND()function is written within the first argument of the function IF().

FRACTIONS REPRESENTED INCIRCULAR GRAPHS And

OF BARS

Several types of graphs in the Excel leaf exist, for our case we will use those of Circulartype and Bars, that is most appropriate.

PRACTICE 13FRACTIONS REPRESENTED IN

CIRCULAR GRAPHS

13. It explains as they are the steps to graphical a fraction in the leafExcel.

In order to begin, we will make that it varies the value of the denominator causing whoeach value in each cell is unitary, for it draws a bar of displacement of the bar of Forms,ties its value with the cell origin

Order of the steps:

It opens a new Spreadsheet Excel.

The fraction writes that you want to represent, now writes number 1 (one), in the E6 cell,the F6 cell is = IF($4>=2,1,0), in G6 is: = IF($4>=3,1,0), in the H6 cell is = IF($4>=4, 1,0), in I6 is = IF($4>=5, 1, 0), and so on until the X6 cell = IF($4>=20,1,0).

Grafics these results:In the Insert card it looks for Charts and it chooses Pie click in 2-D Pie selects first:
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Change the graph to represent it and modify its results.Put bars of sliding to the denominator.

It is important that you understand because the denominator is not equal to zero.

PRACTICE 14

FRACTIONS IN GRAPH DE BARS

14. CHART A FRACTION IN THE GRAPH DE BARS, VARIES THE DENOMINATOROF THE FRACTION, FOR IT DRAWS A BAR OF DISPLACEMENT OF THE BAR OFFORMS, TIES THEIR VALUE WITH THE CELL ORIGIN.

Objective: to include/understand the fraction from bars, using the Excel Leaf.

Order of the steps:


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It opens a new Excel leaf, and put the fraction that you want to represent. As wepresent/display to a fraction until tenth second part of a whole number, we will writetwelve formulas to represent it.For example in the cell, D7 the formula is: = 1/B$3, in the E7 cell is: = IF ($B$3>1, D7),in the F7 cell is: = IF ($B$3>2, E7), in G7 is: = IF ($B$3>2, f 7), in H7 is: = IF ($B$3>2,

G 7), in I7 is: = IF($B$3>2, H 7), in J7 is: = IF($B$3>2, H7), in K7 is: = IF($B$3>2, H7),in L7 is: = IF ($B$3>2, K7), in M7 is: = IF($B$3>2, L7), in N7 is: = IF ($B$3>2, M7), inO7 is: = IF ($B$3>2, N7).Select and graphs:

Select the cells to chart:

In Insert 2-D chooses Bar soon Bar + Stacked Bar to give click

It appears the graph that follows:

Unlike which we did in Excel 2003, we will do the following thing: it selects the chart,soon in Switch Row/Column click, surprise!


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Clear the axes, and lines:

Change the values of the axes to be able to visualize them better:


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Modify the values to see its representations, experiences its results.

PRACTICE 15

CIRCULAR GRAPH OF FRACTIONS

15. GRAFIQUE A FRACTION BUT VARIES The NUMERATOR And TheDENOMINATOR OF The FRACTION, FOR IT DRAWS TWO BARS OFDISPLACEMENT OF The BAR OF FORMS, TIES HIS VALUE WITH The CELL

ORIGIN.

Objective: that it represents fractions with a circular graph:

Order of the steps:Open a newExcel Leaf:In B7 and B8 it puts numbers and to express like fraction. Soon to tie with bars ofdisplacement, the picture of forms:


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Like note, the F7 cell ties the same with the cell B7. Make for the F8 cell; the valuesminimum are 1, and the maximum is 10.

In F7 the formula = B7, in the F8 cell the formula to be able to evaluate an average orfraction is: = B8-b7.It selects these values:

In order to graph, in Insert: choose Pie + 2-D Pie:


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Click in Finalizing. It changes the values as you wish, and experiences your results. Up tohere the related thing to the graphs of fractions, can do hers inventing others; for exampleas they would be if we united two fractions.

Exercise: this example can represent fractions smaller one, what happens when thefractions are greater to a whole number? Make the changes appropriate to be able torepresent them suitably

PRACTICE 16

FRACTIONS

16. MAKE THE METHODOLOGY FOR CHART A FRACTION BY MEANS OFBARRAS, BUT IT VARIES THE NUMERATOR LIKE DENOMINATOR, USES TWOBARRAS OF DISPLACEMENT.

Open a newExcel document

In the Excel leaf it puts the fraction that is going to graph:

In the cell D9 put on the formula = B3, in the E9 cell the formula = B4-B3 to graphic thefraction:


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In D11 = IF ($D$8


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In x-axis in Format Axis I number maximum is 7 and minimum 0:

To enlarge the values

Slipping in Gap Width until No Gap


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Again Select cells D11:J11, chart with Bar + 2-D Bar + Stocked Bar:

Now, Click in Switch Row/Column

So that he is transparent, it makes the following steps


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Click within each data in the chart to add edges

When finalizing its work will be thus:

EXERCISES:Design a spreadsheet to represent equivalent fractions, as one is:


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PRACTICE 17

SUM And SUBTRACTION OF FRACTIONS I

17. IT DESIGNS The ALGORITHM DE SUM Or IT REDUCES OF TWO Or MOREFRACTIONS IN The LEAF EXCEL.

Objective: that by means of the arithmetic algorithm of sum or it reduces of broken youadapt them to the formulas ofthe Excel Leaf.

Order of the steps:

The following formulas are applied to the Excel leaf, and they are loaded like part of theTools for analysis.

FIRST PARTCommon maximum divisor, it returns the common maximum two more whole number orsplitter. The Greatest Common divisor of two or more natural numbers, he is the greaterone of its common splitters. is the greater whole number by which number1 and number2are divisible without leaving remainder. GCD (number1;num ber2; ) Number1,number2 are of 1 to 29 values whose multiple common minimum wishes to obtain. If a

value is not a whole number, it is truncated.

The Least Common Multiple of two or more natural numbers, she is the minor of itscommon multiples, is the greater whole number by which number1 and number2 aredivisible without leaving remainder. LCD (number1; number2; ), they are of 1 to29 values. If a value is not a whole number, it is truncated.


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The Remainder Gives back to the remainder or rest of the division between number andnm_divisor. The result has the same sign that nm_divisor. MOD (number; divisor).Number is the number that wishes to divide and whose remainder or rest wishes to obtain.Nm_divisor is the number by which it wishes to divide to the argument number.

Open a new spreadsheet:In this, splitter of two numbers calculates the common maximum: the formula is =LCM(C5, D5).

In order to obtain the common maximum splitter with the formula = GCD(C7,D7).

The calculation of the remainder of a division with the formula: = MOD (D11,D12)

For the whole part of that division with: = INT (B11/B12)


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PRACTICE 18

EXTREME OF FRACTIONS II

18. IN The LEAF EXCEL, IT MAKES The SUM OF TWO FRACTIONS, WITH The

TRADITIONAL ALGORITHM (AS IF IT DID IT BY HAND).In a new spreadsheet this writes:

Now it calculates the multiple common minimum, = LCM(B10, D10), in the twoequivalent fractions:

Divide lcm between the denominator of each fraction and to multiply by its numerator:with the respective formula: = (G10/B10)*B9

Add/sink its results like a common fraction: in the K9 cell the formula = G9, and thusconsequently:


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In the N9 cell the formula is: = K9+M9, and in O10 is: =L10.

For it calculates the equivalent fractions and to obtain the final result, does the followingone.

In the Q9 cell the formula: = INT(O9/O10); in the R9 cell it is: = MOD(O9, O10), and inR10 is: = O10.

The final equivalent fraction is: In T9 put on =Q9; in U9 put =R9/D12, (where D12 is ==GCD(R9,R10) ) in U10 is: =Q10/C12:

EXERCISES:

a) With this same method, resolvable for a subtraction.

b). Design the method to add three fractions.

c). Design the method for four fractions.

d) It designs the method to multiply fractions.


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PRACTICE 19

ARITHMETICAL MULTIPLICATION

19. IT CARRIES OUT The MULTIPLICATION OF TWO NUMBERS IN EXCEL,

GREATER OF ONE HUNDRED, IN WHICH The MULTIPLICATION OF EACHFACTOR IS SEEN AS IF YOU CARRIED OUT IT By hand.

It opens a newExcel document, the multiplication two or more numbers, is possible to becarried out by different methods, for example on www.nrich.maths.org, its method is basedon divisions between 10, nevertheless we will do it with a called formula MID, this onegives back a specific number of characters of a text string, beginning in the position that itspecifies and based on the number of characters that it specifies. See in the aid of Excel.The followed method is as if we made the multiplication normally by hand.

By example: 344

Text is the chain that contains the characters that wish to extract.

Starting point is the position of the first character that wishes to extract of text. The startingpoint of the first text character is 1 and so on.

Number of characters specifies the number of characters that that wishes RETURNS givesback of the argument text.

If the starting point is greater than the text length, RETURNS gives back "" (empty text). Ifstarting point is minor who the text length, but starting point more number of charactersexceeds the length text, RETURNS gives back the characters until the end of text.


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We put two numbers in the new leaf, as it appears in the figure:

in the A3 cell, we put any number, for example 188, in B3, the formula: = MID(A3; 1; 1)to extract the first character of the number, in B4 he is = MID(A3; 2; 1), in B5 is =MID(A3; 3; 1), for the last character or digit, of equal way for the second number that thisin C3, if he is 521, in D3, the applied formula = MID(C3; 1; 1), in D4 is = MID(C3; 2; 1),

in D5 is = MID(C3; 3; 1).We put numbers both as we multiplied habitually:

We will fill a picture like this, to carry out the first multiplication, that is to say, 2 by 4, in

T6 the formula = $O$4*$K$4 will be applied, but in U6 and V6 we will extract its digitsrespectively as it follows: U6 = IF($T$6>=10;MID($T$6;1;1);0) ; V6 =IF($T$6>=10;MID($T$6;2;1);$O$4*$K$4). For effects to write the cells we will changethe nomenclature of the figure by the numbers of the example, changes 1 BY 1 to the oneof 2 BY 4.

As one sees, in U6 the precaution is taken if the multiplication is greater to ten since thiswould affect the position of the number. In K6 put the formula = V6.


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In order to multiply the first digit by the second digit of the second number, that is 2 by 6,the following thing is made: In T7 the formula is written: =$O$4*$J$4, soon to pass a U7,=IF($T$7>=10;MID($T$7;1;1);0) ; in V7 it writes=IF($T$7>=10;MID($T$7;2;1);$O$4*$J$4) ; in W7 it writes down =V7+ U6, in X7 it is=IF($W$7>=10;MID($W$7;2;1);0) ; in Y7 is =U6 +T7 ; and it stops Z7

=IF($Y$7>=10;MID($Y$7;1;1);0) . See the figure that follows:

We tied the results in the multiplication, in J6 we put the formula is the one that follows:=IF($W$7>=10;$X$7;$W$7),

The third number (2 by 1) is if in the T8 cell the formula is written =$O$4*$I$4 , in U8 itwrites =IF($T$8>=10;MID($T$8;1;1);0) ; in V8=IF($T$8>=10;MID($T$8;2;1);$O$4*$I$4) , in W8 the formula =Z7 +T8 , in X8 to put=IF($W$8>=10;MID($W$8;2;1);0) , in Y8 it writes down =W8 , and finally in Z8 is=IF($Y$8>=10;MID($Y$8;1;1);0) .

When tying these results with the cell I6 and H6, the formulas are=IF($W$8>=10;$X$8;$W$8) and in addition =Z8 respectively.

In order to carry out the other multiplications of the tens and hundreds it makes the sameprocedure above written.


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In the end it ties to the numbers with bars of displacement, 100 minimum values of andmaximum of 999.

EXERCISES.

1. how it would do so that one of the factors can change from values of 10 to 999?make the change in the spreadsheet.

2. What factors give like result an ascending value?3. design a spreadsheet to make the multiplication interactive, as next one is:

PRACTICE 20FORTUNE-TELLER OF NUMBERS

20. HE GUESSES THE NUMBER THAT I THINK USING SIMPLE ALGEBRAICEQUATIONS.

Objective: that you shape in equations the words of a given problem.

Order of steps:Open a new Excel leaf, and put on like title "the fortune-teller of Numbers", soon in theA10 cell writes: IT THINKS ABOUT a NUMBER, in A11 writes SUM, in A12 the


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RESULT BY, in A13 SUBTRACTION, A14 SUBTRACTION the THOUGHTNUMBER, in A15 MULTIPLIES BY, in A16 SUBTRACTION.

It sees the figure following so that you DES an idea of how it would be.

Now it adds numbers as one is in the cells, C11 even C16.

The problem considers thus:It is an equation of first degree with a variable:

cbax If we cleared, we have:

a

bcx

In order to raise the equation in Excel, they are only mechanical steps as you observe,reason why the constant coefficients of the variables and terms change according to thecase, for example:

In the G11 cell, put the formula = C11; in D12 cell, = C12; in G12 cell, = C12*G11, inG13, = G12 C13; in D14, = D13 1, in G14 put =G13; in D15, = C15*D14; in G15, =G14*C15; in D16 is =D15, but in G16, = G15-C16.

In any place this writes, for example in the cell H20, in the end it will say to you as it isthe result and your you will say to him as it was the number:


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But this cell put a name: goes Formulas in Define Name. It defines the name, in this case,Number: next To OK:

Or, you can write in the bar of you formulate its name, simply written in Name Box, and tocontinuation ENTER:

In A22 writte then the thought number is equal to.

In the K22 cell, put the formula: = (number-G16)/D16

With your friends or companions it makes east exercise changing of situations stops to

guess of which numbers you thought.


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PRACTICE 21

TO DRAW FIGURES GEOMETRICS

21. IT DRAWS A SQUARE And A TRIANGLE IN The CARTESIAN PLANE EXCEL,

USING The COORDINATES LIKE VERTICES OF The FIGURESObjective:To create geometric figures in the Cartesian plane, using the coordinates of its vertices. Sothat the points are united uses the Graphical "Dispersion with points"

Order of the steps:It draws a square: As a square has four points, tabulate those four points in the Cartesianplane but we repeated the first point for "closing" the figure.

We selected the points, en Insert choose Scatter + Scatter with Straight and Markers

(click):

We have left therefore the figure:


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We fit to colors of the area of layout and the appropriate scale for this example:Double click in Gridlines, next Layout + Primary Horizontal Gridlines + More PrimaryHorizontal:

Select Format Major Gridlines in Line Style, choose Dash type, to continuation Close:

Continue until you have l to figure that wishes


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The axis and, is obtained with; C7=ABS((B6-B5)*SIN(F5))+1

In order to close the triangle, point four is (1,1). Make now interactive adding Scroll Bar,linked Cell

EXERCISES:Create figures in the Excel Leaf, like pentagons rectangles, etc.

PRACTICE 22

AREA OF FIGURES IN EXCEL

22. IT CALCULATES IN The LEAF EXCEL, The AREA OF A SQUARE And ATRIANGLE, VARIES ITS VALUES USING A SCROLL BAR.

Objective:That you calculate areas of different figures applying Excel.


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In I11 cell that you choose, pon the formula = Abs((b6-b5)* sine (f5)) to calculate theheight of the triangle.

In the I13 cell = B6-b5 compute the range of the base.

For the area of the figure in I15 cell for any dimension it is =I11*I13/2.

EXERCISESCalculate the area of the triangle varying the dimensions but with next formula.

PRACTICE 23

"AREA OF A TRIANGLE IN THE SPACE"

23. IT CALCULATES THE AREA OF A TRIANGLE BUT IN THE CARTESIANPLANE VARYING THE COORDINATES IN THE LEAF EXCEL.

Objective: to calculate the area formed by three straight lines in the Cartesian space.

Order of steps: You will use the following formula to calculate the area formed by threestraight lines in the space4, using solely the coordinates of each straight line.

31213223312121 yxxyxyxyxyyxrea

The sign is selected according to which their result is not negative.

It opens a newExcel leaf, like EXAMPLE: to find the area included/understood in thefollowing points:

4Manual of Mathematical Formulas, Series Shawn,


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A ( 3 , 4 ) B ( -1 , 2 ) C ( 4 , 1 )

A ( x1 , y1 ) B ( x2 , y2 ) C ( x3 , y3 )The Cartesian space coordinateses are:

In order to graficar it, tabulamos the coordinates in a table:

We selected all the table, we go to Insert for graphs and we selected Charts + Scatter +Scatter with Stright Lines, with points of data connected by lines without markers of data,clicks in Following:

Of click in Accepting. Present its graph as it follows:


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For it calculates the area puts the formula in one of the Cells: for example in. J15

=(0.5)*(B7*C8+C7*B9+C9*B8-C8*B9-C7*B8-B7*C9)

In the end it is thus:

It can change the values of the coordinates to its pleasure


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PRACTICE 24

AREA OF A TRIANGLE IN THE SPACE "THREE STRAIGHT LINES IN THE SPACE

24. WITH THREE GIVEN POINTS, IT FINDS The AREA And The EQUATIONS OFEACH STRAIGHT LINE, AS WELL AS ITS REPRESENTATIONS IN The GRAPH.

In Geometry in the space we found generally straight that they are crossed in the Cartesianspace. We can find the equations for the given straight lines at least two points.

The general equation for a straight line with slope m, is:

Where:

x = independent variable

x1 = first point coordinate in xy = dependent variabley1 = first point coordinate in ym = slope

But equal slope a:

x2 = second coordinate axis xy2 = second coordinate axis y

In order to be able to apply these formulas in Excel , we will have to assign to differentvalues each point.Objective: to apply the general formula of a straight line with slope m, to Chart and tocalculate the area in Excel.

Order of the s steps:It opens a newExcel document, and writes down in a picture the coordinates of the threepoints.

In C8, E8, C10, E10, C12 and E12 put on any number, to be able to bind the values of thepoints in other cells.

Now put on the coordinates like Table of graphics.

)( 11 xxmyy

12

12

xx

yym


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In order to calculate the first slope we choose from the point To a B, in the G15 cell we putthe formula =(B16-B15)/(A16-A15).

In G16 the second slope is: =(B17-B16)/(A17-A16)

In G17 the third slope will be: =(B17-B15)/(A17-A15).

In order to consider the first equation of the first straight line, we took as it bases thegeneral equation of the straight line, reason why we have left thus: in the cell H15, we put"equation AB" and in the cell I15, the formula is = CONCATENATE ("y=",$G$15,"x+", (-1)*$G$15*A15+B15).

La segunda ecuacin en I16 es =CONCATENATE ("y=",$G$16,"x+",(-1)*$G$16*A16+B16).

The third equation in I17 is =CONCATENATE ("y=",$G$17,"x+",(-1)*$G$17*A17+B17).

As it is seen in the Excel figure, it calculates the data and they appear the equations foreach straight line:

TABULATION:The tabulation and graficacin of the straight lines take place as it follows:For the first straight line, in the A21 cell, we put -10, next Home + Fill, Series, andselects Series in columns, Type Linear, and Stop Value 10. To accept.

In the B21 cell it puts the formula =$G$15*A21-$G$15*$A$15+$B$15

Copy until the limit of 10.


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The second straight line, has the same procedure that previous the single one that in theG21 cell the formula is: =$G$16*F21-$G$16*$A$16+$B$16. Copy until limit of 10.

Third straight line, in the J21 cell the formula will be: =$G$17*I21+

(-1)*$G$17*$A$17+$B$17.Chart with the assistant for graphs, selecting Dispersion. Make the changes necessary:

Apply the formula to calculate the area between three points and apply:

So that they appear the equations of each straight line, click in each one of them with theright button and chooses "To add Line of Tendency", and in options it chooses "Topresent/display equation in the graph", next To accept.

EXERCISE: Chart and finds the area of a pentagon:

PRACTICE # 25

CHEMICAL BALANCE

25. IT BALANCES THE FOLLOWING CHEMICAL REACTIONS USING THE LEAFEXCEL.


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___Ca + O2 ____Ca O

_____Fe + ___H2O ___Fe3O4 + ____H2

___NH3 + ___O2 ___NO + ___H2O

Objective. To use the formulas of Excel, to make chemical balance.

Order of the steps:to 1er. Example: in the chemical balance of the carbon Monoxide, first we assigned thename to each coefficient of each element.

In the cells B4 and H4, in Box Name change the Name by A and C next Enter.

Assign a name to each coefficient of the substances:

ANOTHER EXAMPLEWE ASSIGNED A LETTER To EACH CELL

The balance equation is the one that follows: =IF(A=D, "correct", "incorrect"), we added itin the D8 cell.

2do. Example: in this example more complex is a little. In the following balance it assignsthe formula for his correct balance.


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The same procedure that in the first example, is to say assigns a name to each coefficient ofeach element or substance, in the B13 cell its name is E, in E13 is G, in H13 becomes is H,in K13 is I.

The formula in the D17 cell is =(E+2*G+G*1=(H*3+H*4+2*I)).

3rd. EXAMPLE:Since practical it makes the following example assigns the formula for the correct balance.

In such a way that if you are mistaken the equation notifies to you if it is thus:

PRACTICE 26

"VERIFICATION OF EQUATIONS"

26. SOLVE The FOLLOWING EQUATION By hand, FOR IT CLEARS The VALUE OFx:

17243

xxx

LATER IT VERIFIES ITS VALUE IN THE LEAF EXCEL.

In mathematics it is common to verify the results of a problem, in this section we will see

how verify some equations using Excel.

First we defined the equation to solve:

For example it is the equation:x/3+x/4=2x-17


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In order to verify your knowledge it elaborates the appropriate formulas in the Excel Leaf,for the following examples:

a) x+3x/4+9x/16=185 b)

c) d)

e) f)

POLAR COORDINATES

System of coordinates, system of identification of elements in a set of points marking themwith numbers. These numbers denominate coordinates and it is possible to be consideredthat they give the position of a point within the set.

In polar coordinates, to each point of the plane they assign to the coordinates (r,) withrespect to a fixed straight line in the denominated plane polar axisto him and to a point ofthis called line pole. For a point anyone of the plane, coordinate r is the distance of thepoint to the pole, and is the angle (measured in sense in opposition to the needles of theclock) between the polar axis and the line that unites the pole and the point, as it is in figure

2. For example, the point with polar coordinates (1, / 2) is located to a unit of the pole andforms a 2 angle of/ radians, or 90 degrees, with the axis. The cylindrical coordinates andthe space polar coordinates are two extensions different from the polar coordinates in threedimensions.

Normally the coordinates of a point or set of points in a system of coordinates can betransformed to another system of coordinates. For example, if the polar axis and the pole ofthe polar coordinates respectively correspond with x-axis and the Cartesian coordinateorigin, then the point with polar coordinates (1, / 2) is located a unit over the origin,reason why their Cartesian coordinates are (0,1). In the same way, the point of polar

304

)30(330

xx

603505 xx 306707 xx

1250

xx

83

)1(2

13

)2(2x

xx


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As you see, first tabulamos the data, into polar coordinates and soon we transformedthose data to rectangular coordinates, we began with the origin ( 0 , 0 ).

The degrees vary from 0 to 360 degrees. Soon we changed radianes. Finally we assignedformula to graficar.

In the B11 cell pon the formula, = RADIANS(A11). Copy and paste to the other cells (upto 360 degrees).

In the C11 cell put=$C$7*(1-COS(B11)) in order to evaluate the first point. Copy andpaste from this point to 360 degrees.

Well, now we will happen of polar coordinates to Cartesian coordinates, since only chartExcel on the basis of the coordinates X and Y.


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For this we do for coordinate x.In the E11 cell, the applied formula is: = C11*COS(B11), copy and paste from 0 to 360degrees.

In the F11 cell, the formula is = C11* SIN(B11) copy and paste to the other cells, from 0to 360 degrees. Finally we have the awaited tabulation.

It selects to the coordinates x,y. chooses assistant for graphs and choose Dispersion tografic. There are the necessary changes so that it is thus:


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dcxbax

dcxbax

PRACTICES 28

"INEQUALITIES WITH INECUACIONES"

28. WHAT METHODOLOGY YOU WOULD USE TO FIND THE SET OFSOLUTIONS OF AN INEQUALITY LIKE THE FOLLOWING ONE:

IN THE LEAF EXCEL?

Objective: to know that the methods applied in algebra normal are applied in the solutionof inequalities and like introducing them in the field of the formulas of the SpreadsheetExcel.

Order of the steps:It opens a newExcel leaf, and applies the formulas to solve inequalities, applying yourknowledge of grafica basic algebra and your results.

A first case is:

The solution is:

The second case:

ca

bdx


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In the C27 cell it adds: = SI((B24-I24)=0, "indeterminate",SI((B24-I24)>0, "the sense ofthe inequality are to left", "the sense of the inequality is to the right")).

FOR THE FIRST CASE: In order to chart the results it makes the following thing: add likecoordinate in and, a value zero. And it selects Insert for Graphs. To two results: Select cells

T20 and U20.

In order to modify this chart Select the coordinates in x and and for the result. For x he is= Sheet1!T$20, and for the axis and is =Sheet1!U$20. Click in Select Data:

Click in Edit and modify:

One is thus: Now the point to select so that it appears thus, since it is an inequality


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Select Format Data Series:

Erase the axis y:

Also the area of layout, Plots, None and in Area, None.

Erase the lines of division


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Modify the graph so that the scale in x is visible:

The solution of these cases considers thus, the lines can select them in the state bar:

Change to the values and chart.

Exercises:Raise with the same method, for the leaf excel, if the inequality considers as it follows:

02

cbxax Find its roots.

PRACTICE 29

SYSTEMS OF EQUATIONS BY RULE DE CRAMER

29. CONSIDER THE FOLLOWING SYSTEM OF LINEAR EQUATIONS WITH TWOINCOGNITS:

222

111

cybxa

cybxa


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FIND ALL The SOLUTIONS (IF THEY EXIST) To The GIVEN SYSTEMS.CALCULATE BY DETERMINANTS USING THE RULE OF CRAMER

Objective: to solve systems of equations by the method of the rule of Cramer, being usedthe spreadsheet Excel.

Order of the steps:Using the method of the Rule of Cramer, the found equation of the general for systems ofequations of

mathematics with word and excel

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