Mathematics GE REVIEW Session 2

8/16/2019 Mathematics GE REVIEW Session 2

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MATHEMATICSWith Casio fx 991-ES plus Calculator

TechniquesSESSION 2

Engr. Broddett B. Abatayo, GE, REA


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Back SubstitutionExponential, Logarithmic and Trigonometric Equation


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Solve for x:

a.b.c.d.


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Laws of Logarithm


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136: ECE Board April 1993Solve for the value of x in the

follo in! equation:a. 1"b. #c. $%d.1%


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129: ECE Board o!"m#"r199$

&iven: . Which of thefollo in! is true'

a.b.c.d.


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13$: &iven: (ind x.

a. -1b. 9c. -1 and 9d. 1 and -9


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3%%: ECE Board April 1999is equal to ))))).

a. cos *+b. cos "+c. sin "+d. sin *+


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39&: EE Board April 1992(ind the value of + bet een",% and $ % if

a. -$%b. $"%c. $1%d. $$%


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'(9: ECE Board Mar)h 1996Solve for x in the !iven equation:

a. %.1*9b. %."#1c. %.*"1d. %.$1


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Solve for x:

a. %b. $%c.d. % /


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Plane Trigonometry

a b

-

a b

234E 5 1

ec 6/7 8


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'2': ECE Board April 199'+ pole cast a shado 15 lon!

hen the an!le of elevation of thesun is 1 . f the pole is leaned 15fro the vertical directl; to ardsthe sun/ deter ine the len!th ofthe pole.

a. 5*."$ b. *#."$ c. *".**

d. * ."1

61*

1$m

1$*


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'23: ECE Board April 199%+ an 0nds the an!le of elevationof the top of a to er to be $% .


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'2&: CE Board o!"m#"r 199&>oints + and ? are 1%% apart andare of the sa e elevation as thefoot of a buildin!. The an!les ofelevation of the top of the buildin!fro points + and ? are "1 and$" respectivel;.


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'29: ME Board April 199&+n observer ishes to deter inethe hei!ht of a to er.


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Maximum and Minimum Values


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$96: ECE Board April 1999(ind the ini u distance fro thepoint 6*/"7 to the parabola

a.b.c.d.

+',2-.

/


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$99: EE Board 0)to#"r 199&+ far er has enou!h one; to buildonl; 1%% eters of fence. What are

the di ensions of the 0eld he canenclose the axi u area'

a. "5 x "5b. 15 x $5c. "% x $%d. "".5 x ",.5


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6(2: EE Board April 199&+ poster is to contain $%% of printed

atter ith ar!ins of 1% c at the

top and botto and 5 c at eachside. (ind the overall di ensions ifthe total area of the poster is

ini u .

a. ",., c / *,.#cb. "%.*5c / $5. cc. ""."*c / **.5cd. "5.55c / * .,c


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6(&: +n open top rectan!ular tan=ith square bases is to have a

volu e of 1% . The aterials for its

botto are to cost >15 per . (ind theost econo ical di ensions for thetan=.

a. 1.5 x 1.5 x *.*b. " x " x ".5c. * x * x %.d. $ x $ x 1.1


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Time ates Problems


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$96: EE Board 0)to#"r 1993+ boat an is at + hich is *.5= fro thenearest point ? on a strai!ht shore.


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62': ECE Board o!"m#"r 1991+ balloon is released fro the !round 1%%

eters fro an observer. The balloon rises

directl; up ard at the rate of * eters persecond.


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62&: CE Board Ma/ 1996 T o railroad trac=s are perpendicular toeach other. +t 1":%% >.2. there is a train at

each trac= approachin! the crossin! at 5%=ph. 3ne bein! 1%% = and the other 15%= a a; fro the crossin!. .2.'

a. ,.%#b. #.%#c. 9.%#d % %#

5% =ph

15%=

1%%=


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61&: + an al=s across a brid!e at therate of 5 fps as a boat passes directl;beneath hi at 1% fps. f the brid!e is 1% ft.

above the boat/ ho fast are the an andthe boat separatin! 1 second later'

a. # fpsb. #."5 fpsc. #.$$ fpsd. #. , fps

1%ft.

5fps

1%fps


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9@s

* @s

1"

61%: +n T train above the !roundcrosses a street at 9 @s at the instant thata car approachin! at a speed of * @s is 1"

up the street. (ind the rate of the Ttrain and the car separatin! one secondlater.

a. $. * @sb. $.9* @sc. *."* @sd. *.* @s


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2 3$: ill"sa ia 4ol5 2+ he ispherical do e has a dia eter of 1%% . +searchli!ht as placed at a point + located at the

circu ference at the base. +t the iddle of thedo e at ?/ a balloon as released verticall; at avelocit; of * @s.

Mathematics GE REVIEW Session 2

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