This document provides information on calculator techniques for mathematics and statistics. It discusses how to clear memory, convert between degrees, radians and gradian, evaluate functions and derivatives, solve equations, work with complex numbers, vectors and forces, and calculate mean and standard deviation. Instructions are given for common calculations as well as past exam questions.

1. MATHEMATICS
and
CALCULATOR
TECHNIQUES
ENGR. REYNILAN L. DIMAL

3. THE MEMORY VARIABLES
MEMORY CALCULATOR BUTTONS
A ALPHA (-)
B ALPHA O ‘ “
C ALPHA hyp
D ALPHA sin
E (ES PLUS only) ALPHA cos
F (ES PLUS only) ALPHA tan
X ALPHA )
Y ALPHA S D
M ALPHA M+

4. 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.

5. MODE 1 :
GENERAL
CALCULATIONS

6. Sec)Min(DegreeDMSto.Convert 0
615237
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
BASICS
"54'36237
237.615
:
0
O
DISPLAY

7. degrees.decimalto47'12"21Convert 0
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
BASICS
721.7866666
124721
:
000
DISPLAY

8. .1200
radianstoConvert
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
BASICS

3
2
120
:
0
DISPLAY

9. degrees.toradians
2
π
Convert
HOW TO CONVERT BETWEEN
DEGREES, RADIANS AND GRADIANS
BASICS
90
2
:
r

DISPLAY

10. system?centesimalin120isWhat 0
PAST CE BOARD EXAM
BASICS
ENTER
3
400
201
:
0
DISPLAY

11. HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
BASICS
30993247.56,211102551.7
)6,4(
:


r
Pol
DISPLAY
PAST CE BOARD EXAM
6).-(4,pointtheofcoordinatepolartheFind

12. HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
BASICS
PAST ECE BOARD EXAM
P(-3,-4)pointthecontains
sideterminaltheifcosofvaluetheFind 
:Solution

13. HOW TO GET THE POLAR AND
RECTANGULAR COORDINATE OF A
POINT IN THE CARTESIAN PLANE
BASICS
PAST ECE BOARD EXAM
8698976.126,5
)4,3(
:


r
Pol
DISPLAY
Y.toandXlly toautomaticastoredisr:NOTE 
5
3
)cos(
:

Y
DISPLAY

14. BASICS
).(3,120iscoordinatepolarwhose
pointaofcoordinaterrectangulatheFind
0
59807621.2,5.1
Rec(3,120)
:DISPLAY
 YX
PAST ECE BOARD EXAM

15. HOW TO SOLVE COMBINATION
AND PERMUTATION PROBLEMS.
BASICS
PAST ECE BOARD EXAM
collinear?arewhichofthreenopoints
distinct10byformedareglesmany trianHow
10C3.ispointscollinearnon10
fromformedbecanthattrianglesofnumberThe
:Solution
120
310
:DISPLAY
C

16. BASICS
contest?essaystudentainfinalists10
theamongfromuprunnerfirsttheandwinnerthe
choosejudgescan thewaysdifferentmanyhowIn
hereimportantisorder:Note
time.aat2takenfinalists10areThere
:Solution
90
210
:DISPLAY
P
PAST ECE BOARD EXAM

17. HOW TO EVALUATE FACTORIAL
NUMBERS
BASICS
10!ofvaluetheFind18.
3628800
!10
:DISPLAY

18. BASICS
I?MISSISSIPPlettersthefrom
madebecannspermutatiodifferentmanyHow
1!4!2!2!
11!
:isnspermutatiodifferentofnumberThe:Note
11.LettersofNumber
4;sS'2;sP'4;sI'1;MofNumber
:Solution


PAST EE BOARD EXAM

19. BASICS
PAST EE BOARD EXAM
34650
x4!x2!!4x!1
!11
:DISPLAY

20. 6533611 24
 x-xx) if f(x)f(. Evaluate
HOW TO EVALUATE
FUNCTIONS
BASICS

21. 32223
234,3,412 yxyy-xyxy)) if f(xf(. Evaluate 
HOW TO EVALUATE
FUNCTIONS
BASICS

22. 2.by xdividedis4x4x-2x3xwhenremaindertheFind 234

PAST ME BOARD EXAM
BASICS
)f(-remainder,xx-xxf(x)
Solution:
24423 234


23. ?x-x-xxof x) a factorIs (x. 23456
9686313 
HOW TO EVALUATE
FUNCTIONS
BASICS
23456
9686
offactorais3then x
0,f(-3)Since:
x-x-xxx
Conclusion




24. ADVANCE
PAST ECE BOARD EXAM
:ENTER
1.5-
Y0,32Y
:DISPLAY

3.2bydividedis48184whenremaindertheFind 23
 yyyy
y.forsolveandzerodivisor toSet the:Concept
:ENTER
11isremainderThe:Answer
11
4-8YY18Y4
:DISPLAY
23


25. HOW TO USE THE ∑ SIGN
BASICS
20...321sum.theFind 
210
:DISPLAY
20
1
x
x


26. )4(5)3(4 xxSOLVE 
HOW TO SOLVE LINEAR
EQUATIONS
BASICS

27. 1
9
2
6
1
12
3





 xxx
SOLVE
HOW TO SOLVE LINEAR
EQUATIONS
BASICS

28. ?
,9,2,4),22(
7
Yofvaluetheiswhat
AandDXYX
D
AIf 
HOW TO SOLVE A
SPECIFIC VARIABLE
BASICS

29. .57
.59
,53
numberthetimesthanlessFind
numberthetimesthanlessisresultthe
numberathanlessbymultipliedisWhen
PAST ECE BOARD EXAM
BASICS

30. PAST ECE BOARD EXAM
BASICS

31. HOW TO USE MULTILINE FUNCTION
BASICS
12m.8m,6m,aresideswhosetriangleaofareatheFind
:ENTER
PAST EE BOARD EXAM
2
cba
s
c)-b)(s-a)(s-s(sA
:FormulasHeron'Using:Solution




32. HOW TO USE MULTILINE FUNCTION
BASICS
:ENTER
C)-B)(X-A)(X-X(X:
2
CBA
X
:DISPLAY


PAST EE BOARD EXAM
13
2
CBA
X
:DISPLAY


455
))()((
:DISPLAY
CXBXAXX 

33. HOW TO SOLVE TRIGONOMETRIC
EQUATIONS
BASICS
3600:2tan3-5tanSolve  xxx
:ENTER
0R-L
30X
tan x23-tan x5
:DISPLAY



:ENTER
0R-L
210X
tan x23-tan x5
:DISPLAY



00
210and30X:Answer 

34. HOW TO USE LOGARITHMIC EQUATIONS
BASICS
105)(xlogxloginfor xSolve 22 
:ENTER
PAST ME BOARD EXAM
0R-L
929.5975076X
105)(xlogxlog
:DISPLAY
22




35. HOW TO USE LOGARITHMIC EQUATIONS
BASICS
100xin xfor xSolve x3log

PAST ECE BOARD EXAM
0R-L
10X
100
:DISPLAY
log3


 xx x

36. BASICS
HOW TO GET THE
DERIVATIVE AT A POINT
.3when3ofderivativetheFind 23
 xxx
:ENTER
45
)3(
:DISPLAY
3
23


x
XX
dx
d

37. PAST ECE BOARD EXAM
)1(
2
.2.
)1(
.
)1(
2
.
1
equationtheateDifferenti
2
2
2
2




x
x
dxc
x
x
b
x
xx
a
x
x
y
d.substituteisxofvaluesamewhenchoicestheofvaluethetovalue
thiscompareand2say xx,ofany valueatyateDifferenti:Technique 
:ENTER
8888888889.0
21
:DISPLAY
2






 xx
x
dx
d
ADVANCE

38. PAST ECE BOARD EXAM
d.substitutebeingisxofvaluetheaschoicestheit toCompare:Note
2xSubstitute
)1(
2
) 2
2



x
xx
a
:ENTER
8888888889.0
)1(
2
:DISPLAY
2
2


x
xx
     
3
4
)1(
.42.
3
2
)1(
.
:followsassummarizedare
2when xchoicestheofresttheofvaluesThe
2
2
2
2







 x
x
x x
x
dxc
x
x
b
  2
2
)1(
2
a.:Answer


x
xx
ADVANCE

39. BASICS
HOW TO INTEGRATE
 
2
1
5
)13(Evaluate dxxx
:ENTER
16
13
:DISPLAY
2
1
5
dxxx 

40. MODE 2 :
COMPLEX NUMBER
CALCULATIONS

41. HOW TO SOLVE COMPLEX NUMBERS
BASICS
argument.theFindb.
value.absolutetheFinda.
4i-3znumbercomplexFor the 
0
53.13isargumenttheand5isvalueabsoluteThe:Answer
13010235.535
43
:DISPLAY

 ri 

42. HOW TO SOLVE COMPLEX NUMBERS
BASICS
product.thefind2i),3i)(5-(2:Given 
i
ii
1116
)25)(32(
:DISPLAY


:ENTER

43. HOW TO SOLVE COMPLEX NUMBERS
BASICS
2i-5
2i4
:Simplify

i
i
i
29
23
29
14
25
34
:DISPLAY



:ENTER

44. HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
BASICS
0
37300NFforcetheofcomponentsyandxtheFind 
i5445069.180590635.239
37300
:DISPLAY
0


:ENTER
N.180.54iscomponentytheandN239.5iscomponentxThe:Answer

45. HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
BASICS
.40008F
forcetheofcomponentsyandxtheFind
0
QuadrantIIIatanglewithlbs
i51423008778355545.612
220800
:DISPLAY
0


:ENTER
514.23lbs.-iscomponentythe
and612.84lbs-iscomponentxThe:Answer
0
22080040)(180800FasforcetheExpress:Solution 

46. HOW TO GET THE COMPONENT OF A
FORCE AND RESULTANT OF FORCES
BASICS
.140angleofanwith400NFand
60at350NFforces,theofresultunttheFind
0
2
0
1


2017875.1034315683.575
14040060350
:DISPLAY
00


:ENTER
e)erclockwisaxis(count-xwith the
103.20with575.43Nisresultant
theofmagnitudeThe:Answer
0

14040060350numbers
complextheofsumtheisresultantThe:Solution


47. ADVANCE
number.imaginaryaniswhereexpressionheSimplify t 19991997
iii 
:ENTER
PAST EE/ECE BOARD EXAM
remainder.get theand4toexponentstheDivide:Technique
4
1
499
41997
:DISPLAY

:ENTER
4
3
499
41999
:DISPLAY

1)(i1toscorrespond
remainder)(0numberwhole
i)-(ii-toscorrespond3/4
i)(i1-toscorrespond2/4
i)(iitoscorrespond1/4:Note
4
3
2
1



 :ENTER
Answer)(0
:DISPLAY
ii 

48. ADVANCE
number?imaginaryaniswhere)1(ofvaluetheFind 5
ii
:ENTER
PAST CE/ECE BOARD EXAM
23
)1()1(asRewrite:Technique ii 
:ENTER
i
ii
44
)1()1(
:DISPLAY
23



49. MODE 3 :
STATISTICAL AND
REGRESSION
CALCULATIONS

50. HOW TO FIND THE MEAN AND
STANDARD DEVIATION
BASICS
mean.theFindhrs.888and852,840,859,
867,lastingafteroutburnedbulbslightFive
2.861
:DISPLAY
x
8885
8524
8403
8592
8671
:DISPLAY
x

51. BASICS
PAST ME BOARD EXAM
197183176164156144132112:Data
deviation.standardthe
determinedata,lstatisticafollowingGiven the
ENTER
1978
1837
1766
1645
1564
1443
1322
1121
:DISPLAY
x
21545346.26
x
:DISPLAY


52. HOW TO GET THE MEAN, VARIANCE
AND STANDARD DEVIATION OF
GROUPED DATA
BASICS
3807
5776
8745
15714
12683
5652
2621
:DISPLAY
FREQx

53. HOW TO GET THE MEAN, VARIANCE
AND STANDARD DEVIATION OF
GROUPED DATA
BASICS
50
:DISPLAY
n
94.70
:DISPLAY
x
391132065.4
:DISPLAY
sx
28204082.19
:DISPLAY
2
Ans

54. HOW TO FIND AREAS IN THE
NORMAL CURVE
BASICS
azto0zfromareameansQ(a)
ztoazfromareameansR(a)
azto-zfromareameansP(a)




55. HOW TO FIND AREAS IN THE
NORMAL CURVE
BASICS
1.64.zof
leftthetocurvenormalunder theareatheFind

:ENTER
9495.0
P(1.64)
:DISPLAY

56. HOW TO FIND AREAS IN THE
NORMAL CURVE
BASICS
1.58.-pointtheand0zbetween
curvenormalstandardabeneathareatheFind

:ENTER
44295.0
Q(-1.58)
:DISPLAY

57. HOW TO FIND AREAS IN THE
NORMAL CURVE
BASICS
mean.theofdeviationstandard1zwithinbewillvariable
randomondistributinormalay thatprobabilittheFind

:ENTER
68268.0
Q(1)Q(-1)
:DISPLAY

1.zto1-zfromareafor thelookingareWe:Solution 

58. HOW TO FIND AREAS IN THE
NORMAL CURVE
BASICS
mean.theabovedeviationstandard1.5thanmoreliewill
variablerandomddistributenormallyay thatprobabilittheFind
:ENTER
0.066807
R(1.5)
:DISPLAY
.zto1.5zfromareafor thelookingareWe:Solution 

59. HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
BASICS

60. HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
BASICS
:ENTER
2010
529
648
467
886
7105
6144
11163
10182
12201
:DISPLAY
yx
1359045.3
A
:DISPLAY
4090.40449955
B
:DISPLAY

61. HOW TO SOLVE LINEAR REGRESSION
PROBLEMS
BASICS
09X0.404499543.1359045Y
BXAYisequationsregressionThe:Therefore


:tcoefficienncorrelatiothedetermineTo.b
8854825905.0
r
:DISPLAY
:23XwhenYofvalueepredict thTo.c 
43939394.12
23
:DISPLAY
y

62. HOW TO GET THE EQUATION OF A
LINE GIVEN 2 POINTS
BASICS
(-3,8).and(2,5)
throughpassesthatlinetheofequationtheFind
531
A
:DISPLAY
:ENTER
PAST ECE BOARD EXAM
832
521
:DISPLAY

yx
53
B
:DISPLAY


63. HOW TO GET THE EQUATION OF A
LINE GIVEN 2 POINTS
BASICS
3153
3315:
5
3
5
31
Y
BXAY:islinetheofequationthe:Therefore




YX
XYor
X
PAST ECE BOARD EXAM

64. HOW TO GET A POINT ON THE LINE
GIVEN TWO POINTS
BASICS
y)?(-5,inyofvaluethe
and(x,4)inxofvaluetheiswhatline,on theis
y)(x,and(3,-7)and(4,1)throughpasseslineaIf
835
ˆ4
:DISPLAY
x 8
35
y4,When x:Answer 

65. HOW TO GET A POINT ON THE LINE
GIVEN TWO POINTS
BASICS
71
ˆ5
:DISPLAY

 y
71-x5,-yWhen:Answer 

66. ADVANCE
PAST ME BOARD EXAM
6
0
0
4
x
2
1
:DISPLAY

y
:is6-yataxis-ythe
and4at xaxis-xtheinterceptsthatlinetheofequationThe


:ENTER
6-
A
:DISPLAY
:ENTER
:ENTER
3/2or1.5
B
:DISPLAY
012-2Y-3X
:asrewrittenbecanichwh
3/2X6-Y
BXAY:Answer




67. ADVANCE
10...7,4,nprogressioarithmetictheofterm30theFind th
:ENTER
PAST CE/ECE BOARD EXAM
:ENTER
722
411
yx
:DISPLAY
91
Yˆ03
:DISPLAY

68. ADVANCE
term?20thetoup14...9,4,nprogressiotheofsumtheisWhat th
:ENTER
PAST CE/ECE BOARD EXAM
:ENTER
922
411
yx
:DISPLAY
1
A
:DISPLAY

:ENTER
1
AAns
:DISPLAY


:ENTER
5
B
:DISPLAY :ENTER
5
BAns
:DISPLAY


69. ADVANCE
term?20thetoup14...9,4,nprogressiotheofsumtheisWhat th
PAST CE/ECE BOARD EXAM
:ENTER
1030
BXA
:DISPLAY
20
1


x

70. ADVANCE
term.8theFind1944.is6th termtheand216isGPtheofterm4The thth
PAST CE BOARD EXAM
:ENTER
17496
Yˆ8
:DISPLAY
194462
21641
yx
:DISPLAY
:ENTER

71. MODE 4 :
SPECIFIC NUMBER
SYSTEMS
CALCULATIONS

72. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
2).(basebinaryto234Convert 10
:ENTER
234
ec
234
:DISPLAY
D
:ENTER
1010100000000011
Bin
234
:DISPLAY
210 11101010234: Thus

73. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
system.LHEXADECIMAto1234Convert 10
:ENTER
:ENTER
000004D2
Hex
1234
:DISPLAY
1610 20000401234: DThus 

74. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
system.OCTALtoABC12Convert 16
:ENTER
:ENTER
20000253602
Oct
ABC12
:DISPLAY
816 00025360220ABC12: Thus

75. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
).)(3F(ABEvaluate 1616
:ENTER
:ENTER
00002A15
Hex
3FxAB
:DISPLAY

76. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
10.basetovaluesallConvert:Solution
10)base(in.77AB24511Evaluate 816102 
211For 3:Result
16AB2For 2738:Result
877For 63:Result
2849:Answer
632738453:Add 

77. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
)110and101(ANDlogicaltheFind 22
0001000000000000
Bin
110and101
:DISPLAY
:ENTER

78. HOW TO DO BASE NUMBER
CALCULATIONS
BASICS
)110and101(XORlogicaltheFind 22
0001100000000000
Bin
11xor101
:DISPLAY
:ENTER

79. MODE 5 :
EQUATION
SOLUTION

80. 12
472


yx
yxSOLVE
HOW TO SOLVE EQUATIONS
IN 2 UNKNOWNS
BASICS

81. ..
,.
',5
agespresenttheirFindfriendhisasoldastimes
threewassheagoyearsFiveJunfriendher
ofagetheastwicebewillagesAnayearsIn
PAST ME BOARD EXAM
BASICS

82. PAST ME BOARD EXAM
BASICS

83. .investmenteachofamounttheFind
P1800.bewouldincometotaltheed,interchang
wereratesinteresttheIfP1700.issinvestmentthe
fromincometotalTheinterest.4%atothertheand
interestannual3%payingonesinvestment2hasmanA
PAST EE BOARD EXAM
BASICS

84. PAST EE BOARD EXAM
BASICS

85. needed?is
eachofmuchHownickel.6%containinganother
withnickel14%containingsteelmixingbymade
betoisnickel8%containingsteelofkg2000
PAST ECE BOARD EXAM
BASICS
nickel6%containingsteelofamountY
nickel14%containingsteelofamountX:Let
:


Solution

86. PAST ECE BOARD EXAM
BASICS

87. 0576 2
 xxequationquadraticSolve the
HOW TO SOLVE
QUADRATIC EQUATIONS
BASICS

88. 0522
 xin xalues of xFind the v
HOW TO SOLVE
QUADRATIC EQUATIONS
BASICS

89. 0925 2
 xxequationquadraticSolve the
HOW TO SOLVE
QUADRATIC EQUATIONS
rootsirrationalgivecanIt-ESOLDover the
PLUSESCASIOofadvantagetheisThis:NOTE
BASICS

90. 146
1629
433
z- yx
zyx
- zy-x
if:, y and zalues of xFind the v



HOW TO SOLVE EQUATIONS
IN 3 UNKNOWNS
BASICS

91. HOW TO SOLVE EQUATIONS
IN 3 UNKNOWNS
BASICS

92. 0652 23
x --xtion xcubic equaSolve the 
HOW TO SOLVE CUBIC
EQUATIONS
BASICS

93. 013
-Solve x 
HOW TO SOLVE CUBIC
EQUATIONS
BASICS

94. MODE 6 :
MATRIX
CALCULATIONS

95. HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
BASICS
:ENTER
PAST ECE BOARD EXAM

















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98
17
19
2
94
17
53
3Simplify AMATto
94
17
53
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BMATto
98
17
19
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96. HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
BASICS
PAST ECE BOARD EXAM
:ENTER
BMAT2AMAT3
:DISPLAY

:ENTER
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4528
535
1727
Ans
:DISPLAY

97. HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
BASICS
A.matrixto
231-
873
1-23
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281-
372
1-33
Ans
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231-
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1-23
AifAmatrixoftransposetheFind
:ENTER

98. HOW TO SOLVE PROBLEMS
INVOLVING MATRICES
BASICS
A.matrixto
273
416
312
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0.061-0.169-0.6
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Ans
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
273
416
312
AifAmatrixofinversetheFind
:ENTER

99. HOW TO COMPUTE THE
DETERMINANT OF A 3X3 MATRIX
BASICS
218
712
5-42:tdeterminantheFind
228
det(MatA)
:DISPLAY
:ENTER

100. ADVANCE
area?theisWhat(3,3).and(4,0)(-2,0),pointsfollowingthe
bydefinedaretriangleaofverticesthes,coordinateCartesianaIn
PAST CE BOARD EXAM
:ENTER
133
104
102-
:DISPLAY
133
104
102
det
2
1
A
1
1
1
2
1
A
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33
22
11
332211


yx
yx
yx
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9
A)0.5det(Mat
:DISPLAY

101. MODE 7 :
GENERATING TABLE
FROM A FUNCTION

102. HOW TO TABULATE VALUES OF A
FUNCTION
BASICS
11971011
888910
63789
43878
28567
17256
9345
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1323
012
301
F(X)X
:DISPLAY

step.unitevery10xto0x
from32xxf(x)ofvaluesTabulate 23


:ENTER

103. MODE 8 :
VECTOR
CALCULATIONS

104. HOW TO DO VECTOR CALCULATIONS
BASICS
B.andAvectorsofproductcrosstheFindc.
B.andAvectorofproductdottheFindb.
B.andAvectorsofresultanttheofmagnitudetheFinda.
9k.5j3iBand7kj-4iA:vectors2Given the 
]71-4[
A
:DISPLAY
:ENTER
:ENTER
]953[
B
:DISPLAY

105. HOW TO DO VECTOR CALCULATIONS
BASICS
717.9164728
VctB)Abs(VctA
:DISPLAY

:ENTER
:ENTERb.
70
VctBVctA
:DISPLAY

:ENTERc.
23]15-44-[
Ans
VctBVctA
:DISPLAY


106. HOW TO DO VECTOR CALCULATIONS
BASICS
vector.cosinedirectionitsgiveand
7k2j4iAvectortheofmagnitudetheisWhat 
:ENTER
PAST ME/CE BOARD EXAM
:ENTER
:magnitudeget theTo
:ENTER

107. HOW TO DO VECTOR CALCULATIONS
BASICS
PAST ME/CE BOARD EXAM
Ans)instoredis(This:Note
38.30662386
(VctA)Abs
:DISPLAY
:cosinedirectionget theTo
0.8427]0.2407[0.4815
Ans
:DISPLAY

108. THANK YOU VERY
MUCH AND
GOD BLESS!!!