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 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
7
8
9
10
7 8 9 10A = + + +
, we have the Pressing key process:
7 ( 7 8 ( 8 9 ( 9 10 10 ) ) )
x x x x
+ + + =
The calculator notified the result: 1.353494786.
To continue, we have:
3 ( 3 4 ( 4 5 ( 5 6 ( 6 ) ) ) )
x x x x
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
10
10
to variable A.
- Assign 10 to variable B.
- Do the process:
: 1; : ( )
B
B B A B A= − = +
Continuous pressing key process:
10 10 , 10
x
SHIFT SHIFT STO A SHIFT STO B
1 :
( )
x
ALPHA B ALPHA ALPHA B ALPHA
ALPHA A ALPHA ALPHA B ALPHA B ALPHA A
= −
= + =
Press key “=” until we have
1
3
B B= −
. 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:
53
20107519430
579
−
−+++
x
xxxx
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:
9 7 5
9 7 5
4 19
25 10 670
30 4 19 75 2010
3 3
5
3 5
3
x x x x
x x x x
x
x
+ + + −
+ + + −
=
−
−

.
Therefore, we only want calculate
9 7 5
4 19
25 10 670
3 3
x x x x+ + + −
at
5
3
.
* Use the function CALC of Vn - 570RS:
4 3 ^ 9 19 3 ^ 7
25 ^ 5 10 670 5 3
ALPHA X ALPHA X
ALPHA X ALPHA X CALC
÷ × + ÷ × +
× + × − ÷ =
We have 26,71628647.
We also can put whole expression into calculator and get a similar one.
Problem 3:
* Result:
359426628, 4
* Detail of solution and Pressing key process:
- With Vn – 570RS, we assign
33
2
51
2
51 −

+
+
=
α
to variable A and use function
CALC to calculate
)(
α
f
:
3 3
( ( 1 5 ) 2 ) ( ( 1 5 ) )
( ^ 3 2 2 ) ^ 20
SHIFT SHIFT
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
3
3 3 3
3 3
1 5 1 5 1 5 1 5 1 5 1 5
3 . . 1 3
2 2 2 2 2 2
3 1 0 2 2 3
α α α

α α α α α
 
+ − − + − +
 ÷
= + = + + = −
 ÷
 
⇒ + − = ⇒ + + = −
So
3 20 20 20
3 3
1 5 1 5
( ) ( 2 2) (3 ) (3 )
2 2
f
α α α α
+ −
= + + = − = − −
.
Pressing key process:
,
20
3 3
(3 ( ( ( 1 5 ) 2 ) ( ( 1 5 ) ) ))SHIFT SHIFT− + ÷ + −
.
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+
or
1
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
+ ≈
(VND).
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.
Problem 5:
* Result:
49863
* Detail of solution and Pressing key process:
Using the programming on the VietnamCalculator Vn - 500RS & Vn - 570RS scientific
calculator to calculate :
10987654321
23456789
+++++++++
.
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 , , 2 10
n
n n
u u u n n
−

−
= = + ≤ ≤
or
10 1 11
1 1
1 10 , ( (11 ) ), 2 5
n n
n n
u u u n n n
−
−
= + = + + − ≤ ≤
.
- Assign 0 to B.
- Assign 0 to A and add all of results that we have when value of B is increases.
0 , 0
1 :
^ ( 11 ( )
SHIFT STO A SHIFT STO B
ALPHA B ALPHA ALPHA B ALPHA
ALPHA A ALPHA ALPHA A ALPHA B ALPHA B
= +
= + −
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.
0 , 0
1 :
^ ( 11 ( )
( 11 ) ^
SHIFT STO A SHIFT STO B
ALPHA B ALPHA ALPHA B ALPHA
ALPHA A ALPHA ALPHA A ALPHA B ALPHA B
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
1 , ^ (11 ) ,
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.