CALCULATOR
TECHNIQUES
ENGR. REX JASON H. AGUSTIN
THE MEMORY VARIABLES
MEMORY
A
B
C
D
E (ES PLUS only)
F (ES PLUS only)
X
Y
M
CALCULATOR BUTTONS
ALPHA (-)
ALPHA O ‘ “
ALPHA hyp
ALPHA sin
ALPHA cos
ALPHA tan
ALPHA )
ALPHA S D
ALPHA M+
HOW TO CLEAR MEMORY
• SHIFT 9 1 =
– This means you will automatically go to MODE 1
• SHIFT 9 2 =
– All values stored in the memory variables will be
erased
• SHIFT 9 3 =
– This means you will automatically go to MODE 1
and all values stored in the memory variables
will be erased.
MODE 1 :
GENERAL
CALCULATIONS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert 237.6150 to DMS (Degree Min Sec)
DISPLAY :
237.615O
237 036'54"
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert 210 47'12" to decimal degrees.
DISPLAY :
210 47 0120
21.78666667
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
Convert1200 to radians.
DISPLAY :
1200
2

3
BASICS
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
π
Convert radians to degrees.
2
DISPLAY :

r
2
90
BASICS
PAST CE BOARD EXAM
What is 1200 in centesimal system?
ENTER
DISPLAY :
0
120
400
3
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST CE BOARD EXAM
Find the polar coordinate of the point (4, - 6).
DISPLAY :
Pol (4,6)
r  7.211102551,  56.30993247
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST ECE BOARD EXAM
Find the value of cos if the terminal side
contains the point P(-3,-4)
Solution :
BASICS
HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
PAST ECE BOARD EXAM
DISPLAY :
Pol (3,4)
r  5,   126.8698976
NOTE : r is stored automatically to X and  to Y.
DISPLAY :
cos(Y )
3

5
BASICS
PAST ECE BOARD EXAM
Find the rectangula r coordinate of a point
whose polar coordinate is (3,1200 ).
DISPLAY :
Rec(3,120)
X  1.5, Y  2.59807621
BASICS
HOW TO SOLVE COMBINATION
AND PERMUTATION PROBLEMS.
PAST ECE BOARD EXAM
How many triangles are formed by 10 distinct
points no three of which are collinear?
Solution :
The number of triangles that can be formed from
10 non collinear points is 10C3.
DISPLAY :
10C 3
120
BASICS
PAST ECE BOARD EXAM
In how many different ways can the judges choose
the winner and the first runner up from among the
10 finalists in a student essay contest?
Solution :
There are 10 finalists taken 2 at a time.
Note : order is important here
DISPLAY :
10 P 2
90
BASICS
HOW TO EVALUATE FACTORIAL
NUMBERS
Find the value of 10!
DISPLAY :
10!
3628800
BASICS
HOW TO EVALUATE
FUNCTIONS
Evaluate f ( 6 ) if f(x)  3x 4  3x 2-5x  6
DISPLAY :
3x 4  3x 2  5 x  6
3972
BASICS
HOW TO EVALUATE
FUNCTIONS
Evaluate f ( 4,3 ) if f(x , y)  4 x3 y 2  3x 2 y-2 xy 2  y 3
BASICS
PAST ME BOARD EXAM
Find the remainder when 3x 4  2x 3 - 4x 2  x  4 is divided by x  2.
Solution:
f(x)  3x 4  2 x 3-4 x 2  x  4 , remainder  f(- 2 )
DISPLAY :
3x 4  2 x 3  4 x 2  x  4
Answer : Remainder  18
18
BASICS
HOW TO EVALUATE
FUNCTIONS
Is (x  3 ) a factor of x 6  6 x5  8x 4-6 x3-9 x 2?
Conclusion :Since f(-3)  0,
then x  3 is a factor of
x 6  6 x 5  8 x 4 -6 x 3-9 x 2
BASICS
HOW TO USE THE ∑ SIGN
Find the sum.1  2  3  ...  20
DISPLAY :
20
x
x1
210
BASICS
HOW TO SOLVE LINEAR
EQUATIONS
SOLVE 4(3  x)  5(4  x)
BASICS
HOW TO SOLVE A
SPECIFIC VARIABLE
D
(2 X  2Y ), X  4, D  2, and A  9,
7
what is the value of Y ?
If A 
BASICS
HOW TO USE MULTILINE FUNCTION
PAST EE BOARD EXAM
Find the area of a triangle whose sides are 6m, 8m, 12m.
Solution : Using Heron' s Formula :
A  s(s - a)(s - b)(s - c)
abc
s
2
ENTER :
BASICS
HOW TO USE MULTILINE FUNCTION
PAST EE BOARD EXAM
DISPLAY :
A BC
X
: X(X - A)(X - B)(X - C)
2
ENTER :
DISPLAY :
X
ABC
2
13
DISPLAY :
X ( X  A)( X  B)( X  C )
455
BASICS
HOW TO USE LOGARITHMIC EQUATIONS
PAST ME BOARD EXAM
Solve for x in log 2 x  log 2 (x  5)  10
ENTER :
DISPLAY :
log 2 x  log 2 (x  5)  10
X
L-R 
29.59750769
0
BASICS
HOW TO GET THE
DERIVATIVE AT A POINT
Find the derivative of x3  3x 2 when x  3.
ENTER :
DISPLAY :
d
( X 3  3X 2 )
dx
x 3
45
BASICS
PAST ECE BOARD EXAM
x2
Differentiate the equation y 
x 1
x2  2x
x
a.
b.
c.2 x
2
( x  1)
( x  1)
2x2
d.
( x  1)
Technique : Differentiate y at any value of x, say x  2 and compare this
value to the value of the choices when same value of x is substituted.
ENTER :
DISPLAY :
d  x2 


dx  x  1  x  2
0.8888888889
ADVANCE
PAST ECE BOARD EXAM
Note : Compare it to the choices as the value of x is being substituted.
x2  2x
a)
Substitute x  2
2
( x  1)
ENTER :
DISPLAY :
The values of the rest of the choices when x  2
x 2  2 x are summarized as follows :
( x  1) 2
x
2
b.
c.2 xx 2  4

0.8888888889
( x  1) x  2 3
x2
4
d .

( x  1) x  2 3
x2  2x
Answer : a.
( x  1) 2
ADVANCE
HOW TO GET THE LIMIT
OF A FUNCTION
1  cos x
lim
x 0 sin x
Answer : 0
ADVANCE
HOW TO GET THE LIMIT
OF A FUNCTION
3
lim
x 
3x  4x  2
3
7x  5
Answer : 3/7
ADVANCE
HOW TO INTEGRATE
2
Evaluate  ( x 5  3x  1)dx
1
ENTER :
DISPLAY :
2
x
5
 3x  1 dx
1
16
BASICS

1
4x
2
x
4x
2
C
C
xdx
4  x 
2
3
2
3
2 4x
2
1
2 4x
2
C
C
x
e
 ex  1dx
A.ln  e  1  C
C. ln  e  1  C
B.ln e x  1  C
D.ln  e x  1  C
x
x
2
MODE 2 :
COMPLEX NUMBER
CALCULATIONS
HOW TO SOLVE COMPLEX NUMBERS
For the complex number z  3 - 4i
a. Find the absolute value.
b. Find the argument.
DISPLAY :
3  4i  r
5  53.13010235
0
Answer : The absolute value is 5 and the argument is 53.13
BASICS
HOW TO SOLVE COMPLEX NUMBERS
Given : (2 - 3i)(5  2i), find the product.
ENTER :
DISPLAY :
(2  3i )(5  2i )
16  11i
BASICS
HOW TO SOLVE COMPLEX NUMBERS
4  3i
Simplify :
5 - 2i
ENTER :
DISPLAY :
4  3i
5  2i
14 23
 i
29 29
BASICS
HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
Find the x and y components of the force F  300N370
ENTER :
DISPLAY :
30037 0
239.590635  180.5445069i
Answer : The x component is 239.5 N and the y component is 180.54 N.
BASICS
PAST CE/ECE BOARD EXAM
Find the value of (1  i)5 where i is an imaginary number?
Technique : Rewrite as (1  i)3 (1  i) 2
ENTER :
ENTER :
DISPLAY :
(1  i ) 3 (1  i ) 2
 4  4i
ADVANCE
MODE 3 :
STATISTICAL AND
REGRESSION
CALCULATIONS
HOW TO FIND THE MEAN AND
STANDARD DEVIATION
Five light bulbs burned out after lasting 867,
859, 840, 852, and 888 hrs. Find the mean.
DISPLAY :
x
1
867
2
859
DISPLAY :
3
840
x
4
852
5
888
861.2
BASICS
PAST ME BOARD EXAM
Given the following statistical data, determine
the standard deviation.
Data :112 132 144 156 164 176 183 197
ENTER
DISPLAY :
x
1
2
112
132
3
144
4
156
5
164
6
176
7
183
8
197
DISPLAY :
x
26.21545346
BASICS
PAST CE/ECE BOARD EXAM
Find the 30th term of the arithmetic progression 4, 7, 10...
ENTER :
DISPLAY :
x
y
1 1
4
2 2 7
ENTER :
DISPLAY :
30 Ŷ
91
ADVANCE
If the first term of an arithmetic
progression is 3 and its tenth term is 39:
a. Find the fourth term
b. 23 is what term of the progression
PAST CE BOARD EXAM
The 4th term of the GP is 216 and the 6th term is 1944. Find the 8th term.
ENTER :
DISPLAY :
x
y
1 4
216
2 6
1944
ENTER :
DISPLAY :
8Ŷ
17496
ADVANCE
If the first term of a geometric
progression is 4 and its fifth term is 324:
a. Find the third term
b. 108 is what term of the progression
THANK YOU VERY
MUCH AND
GOD BLESS!!!