bai bao cao khoa hoc tai bac kinh 2009 thescientificreportatcm 2009
TRANSCRIPT
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The 14th ASIAN TECHNOLOGYCONFERENCE IN MATHEMATICS,
BEIJING, CHINA 2009
BEIJING NORMAL UNIVERSITY
December 17-21, 2009
THE MINH TRAN
HCMC UNIVERSITY OF TECHNOLOGY
VIETNAM
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TITLE : USING SCIENTIFIC
CALCULATORS TO SOLVEMATHEMATICAL PROBLEMS
Authors : THE MINH TRAN
DEPARTMENT OF APPLIED MATHEMATICS
HCMC UNIVERSITY OF TECHNOLOGY (HCMUT)
VIETNAM
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Introduction
Using a calculator is an important skill forstudents. As they grow and progress throughtheir education.
They will learn advanced math skills that
certainly require them to use a calculator . A few quick steps can help anyone use the
device and solve mathematical problems .
I have organized exams : Excellent students use
scientific calculators to solve mathematicalproblems
Therefore, I have built math-calculator subjectand technology in mathematics
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WE CAN USE SCIENTIFICCALCULATORS :
1.VIETNAM CALCULATORVN- 570RS 3.CASIO FX-570MS
4.CASIO FX-570ES2.TEXAS INSTRUMENTS83 Plus
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A. ARITHMETIC
We calculate : 3281978 8791803
We input 3281978 8791803 on the screen
Press the = key. Answer : 2.885450403
We know that answer have 14 digits but the digit 3 canhave rounded
We delete the digit 3 at the first number and the digit 8 atthe second number then we multiply two numbers together
Press the = key. Answer : 2.232710263
We continue to delete the digit 2 at the first number andthe digit 7 at the second number then we multiply 81978and 91803 to get 7525826334
Result: 3281978 8791803 = 28854504026334
Note : when you multiply two numbers, you need tothoroughly check digits
1310
1.Multiply two numbers
1110
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2. Find x, know that :
We input 381978 382007 on the screen
Press the = key. Answer : 0.999924085
We continue to press : 3 - 8 then we press 9 timesthe = key. The final result have saved to the Ans key
Now,we have then we press : Ans - 1 =
Result : x = - 1.11963298
3
83
83
8 3
83
83
83
83
83
81
1 x
381978
382007
1
x
xAns
1
1 1x
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3. Find a natural number n , know that thenumber contains the first four digits and the
end four digits are digit 1
Step 1 :Find the number contains the end four digits are digit 1.
Solution :The number contains the end digit is digit 1
The number contains the end two digits are digit 1The number contains the end three digits are digit 1The number contains the end four digits are digit 1
Answer : the number contains the end four digits aredigit 1
n1 = 8471
3n
31
371
3471
38471
38471
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Step 2 : Find the number contains the first fourdigits are digit 1.
Solution :
We have ( we get the number 223 )
We try ( answer contains two digit
are digit 1 ) . we do not choose the number 223
The number contains the first two digit are digit 1We have ( we get the number 480 )We try ( answer contains four digits
are digit 1 )
We choose the number 480 . Answer : n2 = 480If we do not find n2, we can calculate
to find n2
Result: n = 4808471and
19310...1216.12238471
7.4801111011113 203
10...11178.14808471
11111000111;1111001111 33
14.223111111113
322308471
34808471 1111. . .1111
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4. Find natural number x,y, know that :( and y include a digit)
Solution : we guess : x is digit 2 or 3
When x = 2 : (we do not choose x = 2 )
We choose the digit 3 , we have :
2
2 25 541 1 ( )4481448( )
x
y y y x x y
2x
4 4(5 ) 59 12117361y
9 99
5410109448144809 5 541 1 94481448 9 5419199448144899y y y y
55, 99303467 5 56, 00348007 6y y
Result: x = 3 , y = 6 and 5416169448144896
Furthermore , we can find y by the SOLVE key.We input
9 13 12 11 10 9 2
50 541 10 10 1 10 10 9 10 4481448 10 90y y y y on the screen. We press SHIFT SOLVE key and press 1 key
6y
956
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5. Find the fourteenth digit after of thedecimal point of
We have : the digit 5 can have rounded
We try the digit 5 can not haverounded
We set :
The second power of two sides of equation :
We have :
(1)
We use function of calculator to solve equation :
We have roots :We only get root
12
12 3.464101615.. .Solution :10
12 3.464101615 1.4 10 0
12 3, 464101615 ( 0)x x
2 22 3.464101615 3.464101615 12 0 (1)x x
2 103.464101615 12 9,54391775 10
.
2 102 3.464101615 9,54391775 10 0x x
10
11, 37754 10x
2 6.92820323x
1x
12 3, 464101615137754...
Result : 5
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Exercise : Find the eighteenth digit after ofthe decimal point of
We use calculators :
VietnamCalculator Vn-570RS,Vn-500RS,CASIO fx 570MS,
fx 570ES , fx 991ES,fx-82ES,
HP- 10S,HP-300S
337
INTRODUCTION
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6.Calculate :
We press :
Input 1 for A , we press 1 SHIFT STO A
Input 7 for B ,we press 7 SHIFT STO BInput 7 for C ,we press 7 SHIFT STO C
We input letters on the screen : A = A +1:B = 10B + 7 : C =C + B
Press the = key until we have seen A = 17 on thescreen, then we press the = key two times
2
17 7
7 77 777 ... 77......77 293972367
digits are digit
P
B. PROGRAMMING ONVIETNAMCALCULATOR VN-570RS ;
CASIO FX- 570MS & ES , FX-991ES
Solution :
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168, 641975309 10C
We continue to press 2ALPHA C - 293972367
Answer : P = 526800000
Answer :
we continue to find the end five digits of P and we guess thatthe digit 8 can have rounded, so we only calculate
7 77 777 7777 77777 13 272367
=> The end five numerals of P are :
P = 1019739 - 82689 = 37050
Result : P = 526837050(we are sure that the digit 8 is true because theafter digit of thedigit 8 is the digit 3)
Answer : 1019739We calculate : Answer : 5236982689
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7. solve linear equations with four unknowns :
53605030702
4887465,0
100
tzyx
tzyx
tzyx
know that :tzyx ,,,
100,,,0 tzyx
We have
53605030702
4887465,0100
tzyx
tzyxtzyx
12901271787613711
tzytzy
4146 yt1000 t 8669 y
11 7 13 876y z t
7
1311876 tyz
Using the X ,Y key for x,y variable and the A, B key for z, tvariablePress 69 SHIFT STO YWe input letters on the screen :Y = Y + 1 : B = 6Y 414 :
A = ( 876
11Y
13B ) 7 : X=100
Y
B
A
Solution :
We have known :
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Press the = key until we have seen Y = 70 on the screen
We have seen :
B = 6 after we press the = keyA = 4 after we press the = keyX = 20 after we press the = keyResult : x = 20 ; y = 70 ; z = 4 ; t = 6
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C. INTRODUCE PROGRAMMING ON TI83,84,86,89 CALCULATORS
SOLVE UNLINEAR EQUATIONS WITH FOUR UNKNOWS
We use Jacobi theory
The expression in right side have solved with
The linear equation just is feature case
It can use for n roots
This program have run on TI calculators from 83 to 89 and
It can solve all equations
Cl H
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: ClrHome
: Lbl 2
: Input F(X, Y, Z, T) = 0 =, Str1
: Input G(X, Y, Z, T) = 0 =, Str2
: Input H(X, Y, Z, T) = 0 =, Str3
: Input K(X, Y, Z, T) = 0 =, Str4
: Lbl 1
: Input Xo = , A
: Input Yo = , B
: Input Zo = , C
: Input To = , D
: 1 N
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: String Equ(Str1, Y1): String Equ(Str2, Y2): String Equ(Str3, Y3): String Equ(Str4, Y4): While abs(X-A) > 1E-12 or abs(Y-B) > 1E
12 or abs(Z-C) > 1E 12 or abs(T-D) >1E-12
: Radian
: N+1 N: if (N
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: Disp CONTINUE
: Goto 1
: Else: A X: B Y: C Z: D T: nDeriv(Y1, X, X) E: nDeriv(Y1, Y, Y) F: nDeriv(Y1, Z, Z) G: nDeriv(Y1, T, T) H: nDeriv(Y2, X, X) I
: nDeriv(Y2, Y, Y)
K
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: nDeriv(Y2, Z, Z) L: nDeriv(Y2, T, T) M: nDeriv(Y3, X, X) O: nDeriv(Y3, Y, Y) P: nDeriv(Y3, Z, Z) Q: nDeriv(Y3, T, T) R: nDeriv(Y4, X, X) S: nDeriv(Y4, Y, Y) U: nDeriv(Y4, Z, Z) V: nDeriv(Y4, T, T) W: det([[E, F, G, H][I, K, L, M][O, P, Q, R][S,
U, V, W]]) J: if(J=0)
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: Then: Disp NO ROOT, MULTIPLICITY ROOT.
OR.XO, YO
: Goto 1: Else: X det ([[Y1, F, G, H][Y2, K, L, M][Y3, P,
Q, R][Y4, U, V, W]])/J A: Y det ([[E, Y1, G, H][I, Y2, L, M][O, Y3,
Q, R][S, Y4, V, W]])/J B: Z det ([[E, F, Y1, H][I, K, Y2, M][O, P,
Y3, R][S, U, Y4, W]])/J C: T det ([[E, F, G, Y1][I, K, L, Y2][O, P, Q,
Y3][S, U, V, Y4]])/J A
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: End
: End
: End: Disp X= ,X
: Disp Y =, Y
: Disp Z =,Z: Disp PRESS QUIT TO EXIT (1)
: Goto 1
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Ex : Solve the following unlinear equations :
Solution : The TI calculator will have result in 2 minutes
x=1.073805344; y=1.896586209; z=13.99719752;t=3.999983857
x=0.5624970866; y=1.514473157; z=17.34656344;t=3.995849184
x=0.2226617235 ; y=1.081330382; z=23.60485634 ;t=3.992903209
x=0.3465996175 ; y=1.267952118; z=20.3744967 ;t=3.994052946
x=2.130906063 ; y=0.6207813991 ; z=11.11177199 ;