THE SOLUTION OF EXAMINATION PAPER IN APRIL, 2010

THE SOLUTION OF THE EXAMINATION PAPER EXCELLENT STUDENTS USE SCIENTIFIC CALCULATORS TO SOLVE MATHEMATICAL PROBLEMS IN APRIL, 2010 Chairman of Organization : The Minh Tran Mathematics Sp

THE SOLUTION OF THE EXAMINATION PAPER EXCELLENT STUDENTS USE SCIENTIFIC CALCULATORS TO SOLVE

MATHEMATICAL PROBLEMS

IN APRIL, 2010

Chairman of Organization : The Minh Tran

Mathematics Specialist – VietnamCalculator Company

Problem 1:

*Result: 1.654364493

*Detail of solution and Pressing key process:

- Way 1: As we know, if we put all of this expression into calculator, it’ll notify us a

problem: “Stack ERROR” So we should divide it into 2 parts and calculate each one

First, to calculate A 7 788991010 , we have the Pressing key process:

7 x ( 7 8 x ( 8 9 x ( 9 10 x 10 ) ) )

The calculator notified the result: 1.353494786.

To continue, we have: 3 x ( 3  4 x ( 4  5 x ( 5  6 x ( 6  Ans ) ) ) ) 

The calculator notified the result: 1.654364493.

That is the value of given - expression.

- Way 2:

Base on the structure of this expression, we can create a “Continuous pressing key process”:

- Assign 1010to variable A.

- Assign 10 to variable B.

- Do the process: B: B 1; :A B(B A )

Continuous pressing key process:

10 SHIFT x 10 SHIFT STO A, 10 SHIFT STO B

x

ALPHA B ALPHA ALPHA B ALPHA

ALPHA A ALPHA ALPHA B ALPHA B ALPHA A

Press key “=” until we have

3 Press key “=” one more time to get the result.

Problem 2:

* Result: 26.71628647

* Detail of solution and Pressing key process:

To find the following remainder of expression:

5 3

2010 75

19 4











x

x x

x x

Base on one Theorem about Algebra, the remainder of division polynomial P(x) and binomial

x – a exactly is P(a), we can solve this problem easier than calculate it with the normal way Other hand, we have:

25 10 670

30 4 19 75 2010 3 3

5

3 5

3







Therefore, we only want calculate 4 9 19 7 5

25 10 670

3x  3 x  x  x at

5

3

* Use the function CALC of Vn - 570RS:

We have 26,71628647.

We also can put whole expression into calculator and get a similar one.

* Result: 359426628, 4

* Detail of solution and Pressing key process:

- With Vn – 570RS, we assign 3 3

2

5 1 2

5







 to variable A and use function CALC

to calculate f( ) :

3 ( ( 1 5 ) 2 ) 3 ( ( 1 5 ) )

SHIFT STO A ALPHA A ALPHA A

Because we rounded the expression two times, the result may be not correct So we should direct calculate after some changes:

Easy to have:

3

1 5 1 5 1 5 1 5 1 5 1 5

3 1 0 2 2 3

        

Pressing key process:

,(3 ( SHIFT 3 ( ( 1  5 ) 2 )  SHIFT 3 ( ( 1  5 ) ) ))20

We have 359 426 628,4.

Problem 4 :

* Result: 88.507.100 VND

* Detail of solution and Pressing key process:

- Make the general function:

Let U 0 is the value of deposit at first (VND), a is the interest rates every month (%), n is amount of months (months), U n is the value of deposit after n months (VND):

The interest rates per month is a% so after n month, the value of deposit increase (100a)%

or1

100

a

 So, after n months, we have: 0.(1 )

100

n n

a

U U  (VND).

- Apply to calculate:

With U 0 = 60 000 000, a = 0,65; n = 60 (5 years = 60 months), we have:

60

0,65 60000000.(1 ) 88507100

100

Pressing key process: 60000000 ( 1  0.65 100 ) ^ 60 .

We have 88 507 078.17, round this result, we have the value of deposit 88 507 100 VND.

* Result: 49863

* Detail of solution and Pressing key process:

Using the programming on the VietnamCalculator Vn - 500RS & Vn - 570RS scientific

calculator to calculate : 1  2 9  3 8  4 7  5 6  6 5  7 4  8 3  9 2  10

With Vn – 570RS: it’s easy to use variables to calculate the expression base on

one of two recursive formula: 10 11

1 1 , 1 n, 2 10

n n



1 1 10 , 1 ( n (11 ) ), 2n 5

n n



- Assign 0 to B

- Assign 0 to A and add all of results that we have when value of B is increases

^ ( 11 ( )

SHIFT STO A SHIFT STO B

ALPHA B ALPHA ALPHA B ALPHA

Press key “=” until we see 1

10

B B 

Press key “=” one more time to get the result.

That’s 49 863

We also can cut down that Pressing key process by using the second fomula:

- Assign 0 to B

- Assign 0 to A and add all of results that we have when value of B is increases

^ ( 11 ( )

SHIFT STO A SHIFT STO B

ALPHA B ALPHA ALPHA B ALPHA

ALPHA B ALPHA B

 

Press key “=” until we see 1

5

B B 

Press key “=” one more time to get the result.

That’s 49 863

With VN – 500RS: we use key “REPLAY” to calculate:

Way 1 : We have algothihm:

- Assign 0 to A, assign 0 to B

- Assign A + 1 to A, assign B + A(11 – A) to B

- Press  to return A + 1  A

- Press SHIFT  to Copy express, we have: A + 1  A : B + A(11 – A)  B

Press “=” until we see 1

10

A  A

and press key “=” one more time to get the result

0 , 0

SHIFT STO A SHIFT STO B

ALPHA A SHIFT STO A ALPHA B ALPHA A ALPHA A SHIFT STO A SHIFT

Way 2 : We also have a difference algothihm but use combination key  = :

- Assign 1 to A, assign 0 to B

- Assign B + A(11 – A) to B

- Assign A + 1 to A

- Press combination key  = several times until we see on the screen 1

10

A  A

, press  = one more time to get the result