Rte-m1 Algebra & Trigonometry

=reeEa=EE.

RTE-MI: AJ.gebra & Trigonomdtry 1.

Three numbers are in A.p. such that the sum of the first and third is 12 and the product of the first and second is 24. Find the largest of the three numbers.

4.4

2.

8.8

c.6

A.

'4.I

4.

5.

throws with a pair of

-1

D.25,536

21.

6.

The speed of tr,"

cm

aer

cEn oorrr

@re b

A

10

dtr

7- h h

D.6

8.

flt

ni,tr

120 mi/rrr in a carm. with the wind it

C.

Zl

milhr

D. 40 mi/hr

23.

dbHG"[Eotg-

{g,rs,-rz

D- t2,-18

D

12, lf sinxcosx+sin2x A.

32.2,69.3

A.46

1Sth

A. B.

ks

15,000

c.30,000

25,ooo

,'b.,zojooo

,.._Q.

ZO.g, Ot.g D. 20.9, -61.9

27. A boat going across a lake 8 km wide proceeds 2 km at a.certain speed and then completesthe kip at a speed otlzkmlhr faster. By doing this, the boat arrives 10 ' minutes earlier than if the original speed had been maintained. Find the original speed of the boat.

term of the progrBsqion 1!4Jn,1fiA,... B. i D. 56

1/56

C:'1t46

i c.i+

B. 16

D.6

extend in opposite directions for the first time? A. 2: 43min & 0.636 C.2:43 min & 38 sec B. 2: 48.636 sec D.2:48 min & 30 sec

sec

16. Vvhicfi of the following is a factor of xa-+f-lf+2}x+24.

,

A.5 kmlhr B. + rWnr

15. ln how manyminutes after 2 o'clock will the hands of the clock

Q.8 km/hr

D.6 km/hr

f. c.2.5

28. z varies direc;tly as x and inversely as tt x = 1 and y = 2, then z = 2. Find zwhen x = 3 and y = 4.

A:1.5

B.3

D.3.5

29. An audience of 540 people is seated in rows having the same number of persons in each row. lf 3 more'peisons seai in each row, it would require 2 rows less to seat

1of 4 h,,

kg

28. A machine costs PS0,000.00 and depreciates 20% of the original costduripg the first year,160/o during the second year,12% during the third year, and so on, for 5 years. What is the value at thi end of 5 years?

14. Find the geometric mean betwgen -2 and -g.

4.4

D. 11,291

ks

=1 , what are the values of x in degrees?

B. -32.2,69.3

13. Find the

.32oa?

150

25. Determine how much wat0r should be evaporqted from 50kg of 30% satt solution to produce a OO* sait solution. All"percentages are by weight. B.35 C. 15 D. 18 kg !,25

12

11. Find the_term containing x' in the expansion of [x3+(a/g110 A.12lat.f C. tioa?

&17o

c.21,435

8."10,912

minutes, respectively. If they start at the same instant from ihe same place, in fiow many minutes will they pass each other if they jog around the track in the same aireition? A,24min. B.20 min. C. 15 min. D.25 min.

210

D.270&

A.12,219

iges be 3:4i D,7 ..c.'.

B.21oa6*

c.

and requesting each to copy the letter and send it to four other friends. lf the chain was unbroken until the sth -' set of letters was mailed, how much was spent for postage at P8.00 per letter?

how many years will the ratio of their

10. Roy and RR can jog around a circular park in g and

n ftom

24. Alady started a chain lefter by writing to four ftiends

Two friends A and B are respectively S and g years old. ln

8.6

ZO

Serren carpefiters and 5 masons eam a total of 2,300 per day. At tre sarne rate of pay 3 carpenters and g masons earn 2,0rl0. $Jtra( are the wages per day of a carpenter ,and a mason?

B.3m&210

A caper(er and his helper together can repair a house in 10 days. h takes the helper E days longer than the carpenter to do the repair wften each works alone. How many days would [{ake the helper to do the repair if he is to work alone? ' A. 22.8 days B. 7.2 days C. 17.8 days D. 12.2 days

4.5

D. _3

A_wheel, 5 ft in diameter, rolls up an incline of 1g"20'.

h.:no a tao

8.

L

c.2

with the ground and the top ofthe tree is now its base, how tall was the tree? A.55fi c.45 ft B.&+fi D.36 fi

ery.-m&2a(m+Ilx+24:O. ftid m if sre of the

A-!9"17 B.-tar8

3

.

22. A tree broken over by the wind forms a right triangle w!!fr tle ground. tf the broken part makejan angle of b0"

a certain dbErce in 4 hours, but against the wind it or*y 3rE d tlrd distance in the same time. Find the

Ehcfydtuphd.

D.0.751

What is the height of the center of the wheelabove the base of the incline when the wheel has rolled up S ft up the incline? 4.3ft B.5ff c.4 ft D.6ft

numbers.

16

c.0.862

20. lf coversed Sin0 = 0.134 , find the value of versed Sin0 . A. 0.8 B. 0.3 c. 0 5 D. 0.2

sum of the three numbers is 54, find the largest of the three

c.

dicef

(x-4) = gx+{g is an identity. A. B.

The first of the three numbers exceeds twice the second number by 4, while the third number is twice the first. lf the

8.32

D.16

19. Find the value of A for which the equation A(2x+l)_

Two workers A and B tqgether can complete a job in 7 days. A works twice as fast as B. How many days woutO it take B to do the job wgrking alone? A. 10.Sdays: B.21days C. 9 days D. 18 days

4.12

D. (x+3)

c.32

8.12

A.0.033 B.0.263

Find the sum of the first 100 positive integers exacfly divisibre

c.53,350

(x-1)

18- What is the probabitity of getting a g exacily once in 3

bv .7.

8.2,053

C.

.greater part is divided by the smaller, the quotient is 3 and the remainder is S. Find the smaller number if the sum of the two numbers is 37.

ln a potato race, 8 potatoes are placed 6 feet apail on a straight line, the first being 6 ft frorn the basket. A iontestani starts from the basket and puts one potato at a time into the basket. Find the total distance he must run in order to finistr the race: A. 532 ft. iB. 432 ft c.342fl D.222ff.

A.35,350

B. (x-2)

_ _ _ _ _ _ -:'.

17. A number is divided into two parts such that when the

D.10

1"-

3.

(x-3)

-e-ffiL

3411g(rsBm

REE-MI: Algebra & Trigonometry the audience. How many persons were in each row originally?

4.17

c.27

B. 30

8.86.7

D.31

everyone else, it was found that 66 handshakes Were exchanged. How many were at the meeting? B. D.24 .A.

10

engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. 4.80 B.110 c.55 D. 100

B.

C.21Yo

5? A.0.03

D. 11yo

between the sides of each square.

c.4

B.5

distance of a point 36"N latitude from the equalor.

3a.

B- z+ag mi

D.4288 mi

4.55ft 8.64ft

[ow many ways can 10 different books be divided among A, B, and C so that A gets 5 books, B 3 books, and C 2

c.45ft D.36ft

47. Which is identically equalto secx(cok+tanx)?

11

A. cso< B. sinx

C. cosx D. -secx

books?

4.2,520

c.

B. so40

D.263

1360800

35. From the eguation 12f-af+U+18=0, find the value of k if one root is the negalive of the"ofrrer.

A

B.-12

-18

36- tf ore rod vafue

AB 8.5

ofk

c-a7

d $f2€I+k=O exceeds

D. -31

the ortrer by 2, find the

h-)

48. Woodz was four times as old as LC ten years ago. lf she is now twice as old as LC, how old is Woodz? 4.15 B.20 c.30 D.25 49. A boat propelled to move at 25 miftrr in still water. trauets 4.2 miles upstream in the same time that lt c n tra** SE roiles downstream. Find the speed dthe stsn

iA 4

equation

A.

37. The arithmeti! rnean of two numbers is 5, and their harmonic mean is 2415. Find the numbers.

.8:4&6

*

c.2&6

D.4&4

38. A man has P100,000, part of which he invested al 12% interest,and the rest at 18%. He received a total annual interest of P15;300. How much did he invest at 18% interest

39. Simplify the equation A.

sin'x

i,qj

D. 12

Ji-zlJi =t.

1

c.4

B. 1,4

D.0,4

that B can solve it is 2/3 and that C can solve it is 3/7. tf all three try, compute the probability that the problem will be

55,000

solved.

A.0.64 8.0.52

Sin2x(1+cot2x).

.b. o.go D. 0.81

1

53. ln how many ways can g different books be arranged on a shelf so that 3 of the books are never all 3 together?

40. A vertical pole consists of two parts, each one half of the whole pole. At a point in the horizontal plane which passes through the fqot of the pole and 36 m frorn it, the upper half of the pole subtend an angle whose tangent is 1/3. How high is the pole? 8.25 D. 16

4.72

c.8

52. The probability that A can solve a given problem is 4/5,

D.75,000 C.

10

51. Find the sum and product of roots qf the equation x3 +2x2 -23x -60 = 0. A.:2,60 G. 17,-60 8.2,17 D.2,60

rate?

4.45,000 B.60,000

B,

50. Find the value of x which will satisfy the

D. -6

&3&5

ternt

the ground and the top of the tree is now 20 ft from its base, how tallwas the tree?

33. Assuming the earth to be a sphere of radius 3g60 mi, find the C.2484mi

6th

46. A tree broken over by the wind forms a right triangle with the ground. lf the broken part makes an ingle of 50. with

D.9

4.2844mi.

l

45. ln the series 1, 1, 1t2, 1t6, 1t24,,..., determine the 4.1t28 o. 1t32 a. u64 D.1t120

32. A piece of wire of length E2 cm. is cut into two unequal.parts. Each part is then bent to form a square. lt is found tfrit ttre total area of the two sguares is g7'cm2. Find the difference

4.3

c.12

selected. What is the probabitity that it wiil be divisibti by4 and .8. 0.05 c.0.04 D.0.06

PedrO and pedro is 10% taller than

18o/o

20

44. A number between 1 and 1000 (inclusive) is randomly

Maria, then Juan is taller than Maria by how many percent?

A.2Oo/o

D.55.9 m

43. At a meeting, after everyone had shaken hands with

30. A group consists of n engineers and n nurses. If two of the

31. lf Juan is 1070 taller than

m

c.46

A. 130,240

'9.

ggZ,O+O

c.

160,490

D.260,354

54. Find the equation whose roots are numerically eqqal but qpposite in sign to the roots of the equation t'+7f+11x+S-O | C. x3+7f+11x-S=0

$,ixl-l{1llx-5=0 B. x"+7x2-11x+5=0

D. x3-7f-1 1x+S=0

41. ABDE is a square section and BDC is an equilateraltriangle pitfr C outside the sguare. Compute the value of angle ACE.

i"

deg. 8.60 deg.

A. 30

55. Determine the sum of the first 10 terms of the sequence

C. 50 deg. D. 20 deg.

whose general term is given by

4.88225 8t88552

42. The angle of elevation of the top of a tower from a point A is

'

23o30'. From another point B, the angle of elevation of the top of the tower is 55"30' . The points A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of$e tower is 90 degrees. Find the height of the tower. ,A.90.6 c. 89.s m

m

3n

-2

.

C.88255 D.88522

56. lf.3logx

-logy = 0, express y in terms of x. ,h: Y=x" c'Y=x B. Y =x2 D.Y=3x

57. Mark has nickels, dimes, and quarters amounting to $1.6,

2 of4

,Io:1uJr-

RTE-M1: Algebra & frigonometry 4.27t56

lf he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have?

c.6

8,8

A:3

D.31'l

59. Sotve for x in the following equation: x

x

'.

rebound it rises 2/3 of the height from which it last fe[. What distance has it traveledlt the instant it strikes the grognd for the 7th time? A.27.89 m C.2A.87 m B. 19.86 m D.24.27 m

D.3t2

!'.2 = 4: -3'.2 and 2x + 4y -32 = 20 , find x,y,2.

A. 4, -5,

2

B. -8, 6,

-4

C. 5, -6,

I

D. 2,

-7,4

61. A Caf6 Mocha Grande contains 16oz of a mixture of coffee

73, A wheel,

5 fi in diameter, rolls up an incline of 18"20'. What is the height of the center of the wheel above the base of the incline when the wheel has rolled up 5 ff up the incline?

and Chocolate which is 40% coffee by volume. How much of the mixture should be removed .and replaced by an equal volume oJ chocolate so that the resulting Caf6 Mocha will be

A.3ft

25o/o cofiee by volume?

A. 7,5 liters 8.4

oz

D.6oz

C.2.4 oz

C:120 deg.

B. 130 deg.

D. 110 deg

A:240 km. 90

desees and g) degrees, respedively. lf the side opposite the sr# angle b Z) crn., fird Ute area of the tsiangle. A:t46_4 c.289-6

75. ln a racing contest, there are 240 cars which will have provisions that will last for 15 hours. Assuming constant hourfi consumption for eacfr car, how long will the fuel prwisions last if I cars withdraw from the race every hour

D- 268.4

afier the first?

64. kr tiaqte ABG, angb A=80 deg. and point D is inside the Eiangb, lf BD and CD are bisectors of angle B and C, solve turthe angle BDC.

4.16

t:,lPoo"n'

by 1.5 workers. How many radios were produced in

one

2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle,

c.5000 D.4200

B: seoo

4.45.74 8.63.62,

66. A class of 40 students took examination in Etectronics and Communications. lf 30 passed in Electronics, 36 passed in Communication and 2 failed in both subjects, how many

A.28

c.26

B.30

,,in.opposite directions for the first time?

D.32

67. The excess of the sum of the fourth and fifih parts over the difference of the half and third parts of a number is 119. Find the number,

4.240 8.320

\.c..420 D.430

79.

4,6

B.

I

C.8

A2:43.64

C.2:34.64

B.2:43.46

.D.2:34.46

270 mi apart lie on the same meridian. Find ther difference in latitude.

Tvrlo cities

4.3144 rad

C.4/33 rad

3le+ rad

D- 4143rad

a

80. lt is a set of ordered pairs of numbers. A. function B. domain

68. How many terms of the progression 4, 7, 10, 13,. . . must be taken so that the sum will be 69.

G.95.43

',D.57.67

78. What time after 2 o'clock will the hands of the clock extend

students passed in both subjects? ,.

D.25

77. The sides of a triangular field which contains an area of

rronth by 30 men working 200 hrs during the month?

A.4000

c.20

a triangle is equal to 100 cm. lf the angles of the triangle are in the continued proportions of 1:2:4. Compule the shortest side of the triangle. A. 17.545 c. 18.525 D. 14.507 '8.19.806

65. A statistical clert submitted the following reports. The average rate of production of radios is 1.5 units for every 1.5 hrs work

8.18

76. The sum of the sides of

C. 120 deg. D. 140 deg.

-!00 deg.

C.320 km. D.200 km

B. 180 km

ffi. Tte sum and dftrence of turo angles in a triangle are

A.

D.6ft

c..4 fi

air is 125 kph. The velocity.of the wind due east is 25 kph. If the ptane travels dast and returns back to its base again in 4 hours, at what distance does the plane travel due east?

the grcatest angle.

A. 100 deg.

B.5ft

74. The velocity of an airplane in still

62. lf the sides of the triangle are 2x+3,1+3x+3, and x2+2x, find

g_?31.5

t

72. A golf ball is dropped from a height of 6 meters. On each

+3x +5x +7x +... +49x = 625 B. 1 c.112

4.1t4 60. lf

of work in

hours working together. Working alone, A can do the work in 6 hours more, B in t hour more, and C in twice the time if all working together. How long would it take to finish the work if att working,together? A.20 mins, I C.40 mins. 'D. 50 mins 8.30 mins.

how many ways c;ln a committee of 3 be formed so as to include at leastone ECE?

.,4. ttOO C.970

G. 29/56 D.5t14

71. Three friends A, B, and C can do a piece

D.10

58. An organization has 25 members, 5 of whom are ECE's. ln

A.540

B. 9/56

C. range D. relation

.

in a plane such that the difference of the distances of each point of the set from two fixed points (foci) in the plane is constant. C, Circle A. Parabola D. Ellipse .8. Hyperbola

81. The set of points

D.12

69. What is the angle measured in degrees clockwise from the north to the direction in which the carier is traveling. , C, direction A. bearing D. course B. azimuth

82. ln how many ways can a party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each other? C. 180 ways A. 240 ways D. 320 ways B: 480 ways

70. An urn contains 4 white balls and 3 black balls. Another urn contains 3 white balls and 5 black balls. lf one ball is drawn from each urn, determine the probability that the balls drawn will be 1 white and 1 black. 3

of4

_rE lrrvlauq:,rlrv,

Algebra & Trigonometry 83. Find the real vatues of'x and y satisfiing the given

95. The vibration frequency of a string varjes as the square

equation:(2x+3y)+ i(3x-5y) = 8-i7 . A. x=1 , y=-2 C. x=2,y=1 B. x=-2, y=-1 D,"x=2,y=-1

84. Missy goes to a bake shop to buy some pastries for resale

at Booklatte. She spends half her money for Revel Bars, and one-third of what remains for Triple Chocolate Brownies. She spends 150 for other pastries and still has 200 left from the amount she originally had. How much money did shq have

atthe start?

i*",tosa *9.5100

1500 D. 1250

,"C,2 mins "ii.

liters of acid? A. 160

a

40o/o

L

must be added to g0 acid solution tci have a solution that is 30%

c.

100 L

spends 15 minutes less time on the LRT than walking, and the distance fiom her house to work is 29 miles, wtrat is the disEnce fro{n her house to the LRT station?

3

.8.1

c.5

'.-_j

D.6

fienG A, B, and C are in a rztce. The odds trat A will win ale 7 to 5, and the odds that B willwin'are 1 to 3. What are the odds in favor of C?

88. Three

A.1to4 B.3to2

'Q,

1,to5

D.2to5

89. Two numbers differ by 40 and their arithmetic mean exceeds their geometric mean by 2. Whalare these numbers? A. 75 & 115 B. 45 & C.8.1 D. 88 &128

85

&121

90. Which of the following is a prime number?

A.437

8.483

c.417

,iD.4g7

91. A and B working together can do a job in 3 days, B and

C

together can do the same job in 4 days, and A and C in 2.5 days. ln how many days can all of them finish the job working together? A. 1.07 days C. 3.1 days " B. 2.8 days D.f.03 days , Find the mean, median and mode respectiv.ely of the following numbers; 13,13, 14,12,11,10,9, 11,8,11,5, and 15.

A. 10, 10,

11

B; 10,11 , 12

c.

10, 11, 11

, D: 1.1, 11, 11

93. The age of Diophantus, a Greek mathematician may be calculated from the epitaph which reads as follows: 'Diophantus passed 1/6 of his life in ohildhood, 1112 in youth, 117 as a bachelor. Five years after his marriage was born a son who died 4 years before his father at half his father's final age.'How old was,Diophantus when he died?

A.80

.c.78

8.82

'.D"'84

94. Your father told you "[ was your age now when you were bom'. lf you are 21 years old today, how old is your father?

k

A50

c.48

Br42 i-,.

D.44

97. A compound statement that says one sentence is true and only if the other sentence is true.

dependent statement f. B.biconditionalstatement

if

C. independent statement

D.conditionalstaiement

4.349,800

c.469,500

ts.549,600

o.369,600

99. The distance passed over by a certain pendulum bob

D. 120 L

87. Engr. RR walks at the rate of 6 mph to the LRT station. She then takes the LRT to work, averaging at 60 mph. if she

A

C. condition . D. theorem

different ways can they be arranged on a shelf?

a 25o/o acid solution

8.90 L

96. The hypothesis of conditionalstatement. The "if part of

98. T_here are 3 copies each of 4 different books. ln how many

1 min

86. How many liters of

D.5645

B. postulate

the rate of 0.5 m/s. afler how many minutes will the distance between them be 250 m?

mins mins

c.6830

8.7514

{'antecedent

85. Roy met Mark and RR walking hand in hand in Trinoma, and because of jealousy he decided to walk northward away from the two at the rate of 2 m/s while the two went to the east at

8.60

A.6210

an "if-then" statement.

c.

A. 121

length and diameter of ihe string. lf the itring is 3 feet long and 0.03 inch in diameter vibrates at 7i0 times per second under g0 lbs tension, at what frequencv will a 2 feet long, 0.025 inch string vibrate under 2500 tbs tension.

4ot4

in

succeeding swings form the geometric progression 16, 12,9,... feet respectively. Calculate the totai distance traversed by the bob before coming to rest.

4.64ft

B.75ft

c.54ft

D.96ft

100.At what price should Book Latte mark a book that costs F30O in order that it may ofier a disount of 20yo on tfre marked price and still make a profit ol 21o/o on the selling price?

A.400 . B.5@

C.450

D.70O

UIIU

. AIIU t tr. VgV

-----r----

I

!ola!@p@s

gc$\t

Algebra & Erigonometry 101. This states that every integral rational equation has at least one root. A. Fundamental p. Fundamental ,C. Fundamental D. Fundamental

8.250 m

D.25 m

115. A flagpole 3 m high stands at the top of a pedestat 2 m hii:rh

Theorem of Arithmetic Theorem of Counling Theorem of Algebra

located at one side of a pathway. At the opposite side of tire pathway directly facing the flagpole, the flagpole subten:ls the same angle as the pedestal. \A/hat is the width of il e

Theorem of Eq-uations

pathway? 102. The logarithm of the reciprocal of a numberis called A. lnverse Logarithm C. lndex B. Cologarithm D. Briggsian Logarithm

B. 5.25 m

103. How many differenl signals, each consisting of 8 flags hung in a vertical line, can be formed from 4 identical white flags and 4 identical blue flags?

&.70

B. 1680

c.

140

116. Two sides of a triangle measure 18 cm and 6 cm. The third side may be: A. 12 cm C. 10 cnr B. 13 cm D. 11 cm

D.3360

104. Find lhe mean deviation for the following set of data: {10, 20,

A. Unary matrix

301

Ef Unit matrix

A.6.67

c.60

8.20

D. 3.33

are functions which can be expressed using arithmelic operations and vrrhose values are either rational or a root 01 a rational number.

A.Transcedentalfunctions C. lnationalfunctions B. Algebraic 'l 19.

106. Find the quadratic mean of {2, 4, 6, 8, 10}

c.4.83 D.6.63

107. Find the probability of obtaining an ace on three draws frcm a

dd of cards when there is no replacement befiore the next one is draam.

A. 1/525 '8. 115525

c.3t26 D.1t2197

108. The probability of throwing at least 4 aces in 5 throvra of a die.

4.23t648

c.

B.5t1944

D.25t7776

A.5

A. 1.15 hrs

123. A man left his home at pasl3:00 PM as indicated in his wllll

'

of,a die.

11

c.

B. 0.161

D.0.238

clock. Between two to three hours after, he retumed horile and noticed that the hands of the clock interchanged. At wl.rat time did he left his home?

0.051

4.3:27.27

1. Two cards are drawn at random from a standard deck of E2 cards. What is the probability that both are diamonds?

4.13t52 8.7t13

c.7t26

124. A group consist of n boys and n girls. If two of the boys *re

replaced by two other girls, then 49olo of the group memh#r will be boys. Find the value of n.

A. will have at leasl 3 men?

c.84/14s D.37t425

each number having four choices, What is the probability that exactly hatf of the'answers arc correct?

c.0.0584 D.0.0093

114. A line map was drawn at a scale of 1:50,000. An enor of 0.05 mm in the drawing is equivalent to how many rneters in _ac{ual?

,A. p.s m

100

8.49

c.50

D.51

125. On his Christmas sale, a merchant marked a pair of slipp,r*n P180.00, which is 2oolo olf the normal retail price. lf the retall price is 500/o higher than the wholesale price, what is fl,le wholesale price of the slipper?

113. Billie guesses on all 10 questions on multiple choice quiz, 4.0.0385 8.0.0835

Q.3:22.22 D.3:44.44

d.s:gl.lz

1,.p."1t17

1'12. A committee of 5 people is to be selecded from a group of 6 men and 7 women. VUhat is the probability that the committee

A.59/143 8.14At292

C. 1.325 hrs D. 1.525 hrs

B. 1.125 hrs

110. Find the probability of throwing at least one ace in 10 throws

4.0.838

10

the pipe runs with the drain open for one hour and then trre drain is closed, it will take 45 more minutes for the pipe to iill the tank, if the drain will be closed at the start of filling, h