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
x1
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) abc s 2
ENTER :
BASICS
HOW TO USE MULTILINE FUNCTION
PAST EE BOARD EXAM DISPLAY : A BC X : X(X - A)(X - B)(X - C) 2
ENTER : DISPLAY : X
ABC 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 4x
2
x 4x
2
C
C
xdx
4 x 2
3 2
3 2 4x
2
1 2 4x
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 300N370
ENTER :
DISPLAY : 30037 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 : ˆ 30 Y 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 : ˆ 8Y 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
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