1 - ALGEBRA AND TRIGONOMETRY

Solve for x in: x = sqrt(1 - sqrt(1 - sqrt(1 - …)))

A. -1
B. 0.734
C. 1
D. 0.618

D. 0.618

What is the greatest common factor of 108 and 60?

A. 12
B. 18
C. 6
D. 24

A. 12

The orange bulbs of a light flash every 8 seconds, the red bulbs every 9 seconds and the green bulb flash every 10 seconds. If they all start flashing together, in every how many seconds will they flash simultaneously?

A. 300
B. 360
C. 270
D. 540

B. 360

The middle term in the expansion of (x^2 - 3)^8 is:

A. -70x^8
B. -5670x^8
C. 70x^8
D. 5670x^8

D. 5670x^8

What is the remainder if the polynomial 3x^4 + 2x^3 - 4x^2 + x + 4 is divided by (x-2)?

A. 60
B. 54
C. 3
D. 16

B. 54

The sum of Kim's and Kevin's ages is 18. In 3 years, Kim will be twice as old as Kevin. How old is Kevin now?

A. 13
B. 5
C. 9
D. 10

B. 5

Mary is 24 years old. Mary was twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

A. 16
B. 18
C. 20
D. 12

A. 16

The ages of Diophantus, a Greek mathematician, may be calculated from the epitaph which reads as follows: "Diophantus passed 1/6 of his life in childhood, 1/12 in youth, 1/7 as 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
B. 84
C. 76
D. 90

B. 84

Two thousand kg of steel containing 8% nickel is to be made by mixing steel containing 14% nickel with another 6% nickel. How much of the 14% nickel is needed?

A. 1500
B. 1305
C. 500
D. 1200

C. 500

A book is bought by a company for 200 pesos per copy. What will be the selling price if a discount of 20% and a profit of 30% is to be made?

A. 225
B. 300
C. 325
D. 200

C. 325

A painting job can be done by 72 men in 100 days. There were 80 men at the start of the project but after 40 days, 30 of them had to be transferred to another project. If the contract time is only for 80 days, how many men should be hired 20 days after the 30 men had to be transferred to complete the job on time?

A. 150
B. 100
C. 50
D. 120

B. 100

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?

A. 10
B. 12
C. 7
D. 9

A. 10

How many minutes after 5 o'clock will the hands of the clock be perpendicular for the first time?

A. 10.91
B. 43.63
C. 60
D. 27.27

A. 10.91

A boat takes 2/3 as much time to travel downstream as to return. If the rate of the river's current is 8kph, what is the speed of the boat in still water?

A. 38
B. 39
C. 40
D. 41

C. 40

If the 6th term of an AP is 11 and its 13th term is 123, then the 2nd term of this AP is:

A. -61
B. -53
C. -49
D. -33

B. -53

If 1/18 and -1/486 are respectively the 4th and the 7th terms of a GP, then the first term of this GP is:

A. -7/4
B. -3/2
C. -5/3
D. -11/6

B. -3/2

The 2nd term and the 4th terms of a HP are 4/5 and -4. Find the 5th term.

A. 1
B. -1
C. -2
D. 2

B. -1

There were two Calculus problems that came out in the latest licensure examinations. How many were able to solve both problems if 50% of them solve the integral problem and 75% of them solve the differential problem? The total number of examinees is 2000.

A. 250
B. 500
C. 750
D. 700

B. 500

If the supplement of an angle is 5/2 of its complement, find the value of the angle.

A. 30
B. 50
C. 25
D. 15

A. 30

What quadrant cotangent is positive but sine is negative?

A. QI
B. QII
C. QIII
D. QIV

C. QIII

A transit set up 40 m from the base of a vertical chimney reads 32 deg 30 min with the cross hairs set on the top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 2.1 m. Approximately, how tall is the chimney?

A. 15
B. 26
C. 28
D. 38

C. 28

A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower are 13 deg and 35 deg, respectively. The height of the tower is 50 m. Find the height of the monument.

A. 33.51
B. 47.3
C. 7.58
D. 30.57

A. 33.51

An engineer left a point walking at 6.5 kph in a direction E 20 N (bearing 70 deg). A cyclist leaves the same point at the same time in a direction E 40 S (bearing 130 deg) traveling at constant speed. Find the average speed of the cyclist if the engineer and the cyclist are 80 km apart after 5 hours.

A. 18.23 kph
B. 24.34 kph
C. 13.45 kph
D. 21.45 kph

A. 18.23 kph

Which is identically equal to (secA + tanA)?

A. 1 / (secA - tanA)
B. cscA - 1
C. 2 / (1 - tanA)
D. cscA + 1

A. 1 / (secA - tanA)

A pole cast a shadow 15 m long when the angle of elevation of the sun is 61 deg. If the pole is leaned 15 deg from the vertical directly towards the sun, determine the length of the pole.

A. 23.45
B. 5.67
C. 54.23
D. 34.56

C. 54.23

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed and circumscribing circle.

A. 2.45, 7.14
B. 2.45, 8.14
C. 3.43, 7.14
D. 5.43, 9.34

A. 2.45, 7.14

In the curve y = tan(3x) what is its period?

A. 3pi
B. pi/3
C. 2pi/3
D. pi

B. pi/3

Two cities 270 km apart lie on the same meridian. Find the difference in latitude if the earth's radius is 3960 km.

A. 15/44 rad
B. 3/44 rad
C. 9/44 rad
D. 21/44 rad

B. 3/44 rad

ln(7.18^(xy)) equals:

A. 1.97 xy
B. xy
C. 0.86 xy
D. 7.18 xy

A. 1.97 xy

The logarithm of the quotient and the logarithm of the product MN is equal to 1.55630251 and 0.352182518, respectively. Find the value of M.

A. 6
B. 7
C. 8
D. 9

D. 9

Given one right spherical triangle ABC in which C is 90 deg and sides a and b are 50 deg and 80 deg, respectively. Find the length of the other side in degrees.

A. 77.45
B. 54.55
C. 74.33
D. none of the above

D. none of the above

Manila is situated (14° 36' N, 121° 05' E) and San Francisco is at (37° 48' N, 122° 24' W). Compute the distance between them considering that 1 minute is equivalent to 1 nautical mile.

A. 6570 nautical miles
B. 7550 nautical miles
C. 6046 nautical miles
D. 5450 nautical miles

C. 6046 nautical m