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Mathematics
What time after 3 o'clock will the hands of the clock be together for the first time?
A. 3:02.
B. 3:17.
C. 3:14.
D. 3:16.
Ten liters of 25% salt solution and 15 liters of 35 % salt solution are poured into a drum
originally containing 30 liters of 10% salt solution. What is the per cent concentration of
salt in the mixture?*
A. 19.55%
B. 22.15%
C. 27.05%
D. 25.72%
An airplane flying with the wind, took 2 hours to travel 1000 km and 2.5 hours in flying
back. What was the wind velocity in kph?*
A. 50
B. 60
C. 70
D. 40
If the azimuth is 260°, the compass quadrant bearing is?
A. N 10 deg E B. S 10 deg W C. N 80 deg E D. S 80 deg W
The product of 1/4 and 1/5 of a number is 500. What is the number?
A. 50
B. 75
C. 100
D. 125
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. 6
B. 8
C. 10
D. 12
Mary is 24 years old. Mary is twice as old as Ann was when Mary was as old as Ann is
now. How old is Ann now?
A. 16
B. 18
C. 12
D. 15
Find the values of x in the equation 24x^2+5x-1=0.*
A. (1/6, 1)
B. (1/6, 1/5)
C. (1/2, 1/5)
D. (1/8, -1/3)
Solve for the value of x:
A. 379.
B. 365.
C. 397.
D. 356.
Evaluate the log 845 to the base 6 = x.
A. 3.
B. 5.
C. 4.
D. 2.
Solve for x: 10x^2+10x + 1 = 0
A. -0.113, -0.
B. -0.331, -0.
C. -0.113, -0.
D. -0.311, -0.
A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more
than the equal sides, what is the length of the third side?
c. 6. d. 5.
The two legs of a triangle measure 300 meters and 150 meters. The angle opposite the
150-meter side is 28.89 grads. How long is the third side(meters)?*
A. 341.
B. 340.
C. 341.
D. 339.
If the compass quadrant bearing is S 65 deg W, the azimuth is?
A. 245 deg B. 235 deg C. 225 deg D. 215 deg
Five different mathematics books, 4 different electronics books and 2 different
communications books are to be placed in a shelf with the books of the same subject
together. Find the number of ways in which the books can be placed.
A. 292
B. 5760
C. 34560
D. 12870
The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the
inscribed circle.
A. 2.43 cm B. 2.44 cm C. 2.45 cm d. 2.46 cm
The standard acceleration due to gravity is
A. 32.2 ft/s^ B: 980 ft/s^ C. 58.3 ft/s^ D. 35.3 ft/s^
If 1/3 and -3/2 are the roots of a quadratic equation, then the equation is
A. 6x^2+7x-3= B. 6x^2+7x+3= C. 6x^2-7x-3= D. 6x^2+7x+1=
What is the discriminant of the equation 4x2 = 8x-5?
A. 8
B. -
C. 16
D. -
Find the derivative of f(x) = 6x^3 - 9x + 4*
A. 19x^2 - 8 B. 18x^3 - 9 C. 19x^3 - 8 D. 18x^2 - 9
If the bearing of A from B is S 40deg W, then the bearing of B from A is
A. S 40 deg E B. N 40 deg E C. N 40 deg S D. S 40 deg W
How many horsepower is 746 kilowatts?
A. 500
B. 74.
C. 100
D. 1000
The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are
removed, what is the arithmetic mean of the remaining numbers?
A. 42.
B. 50
C. 38.
D. 57.
Solve for the value of x and y.
a) 5/3 or -½
- 4x + 2y =
- 13x - 3y =
- a. y = 1/2 , x = 3/
- c. y = 2 , x = b. y = 3/2 , x = ½
- d. y = 3 , x =
- Find the quotient when x^3 - 3x^2 - 4x + 12 is divided by x -
- a. x^2 – x –
- b. x^2 + x –
- c. x^2 – 5x +
- d. x^2 + 5x –
- a. - The polynomial 2x^3 - 5x^2 - x + 3 is divided by x + 3, then the remainder is
- b. -
- c. -
- d. -
- Solve for x that satisfies the equation 6x^2 – 7x –
- c) 7/5 or -7/ b) 3/2 or ⅜
- d) 3/5 or 3/
- What is the discriminant of the equation 4x^2 = 8x –
- a) Find the 30th term of the arithmetic progression 4, 7, 10…
- b)
- c)
- d)
- a. What is the sum of the progression 4,9,14,19, up to the 20th term?
- b.
- c.
- d.
- a. 7, -7/ Determine x so that: x, 2x + 7, 10x – 7 will be a geometric progression.
- c. 7, -14/ b. 7, -⅚
- d. 7, -7/
- a) 16) How many diagonals are there in a polygon of 20 sides
- b)
- c)
- d)
- a) 34.19 cm Find the area of a triangle whose sides are 12 cm, 6 cm and 15 cm.
- b) 33.19 cm
- c) 19.33 cm
- d) 19.34 cm
- a) 360 in A rhombus has diagonals of 32 and 20 inches. Determine its area
- b) 280 in
- c) 320 in
- d) 400 in
A and B are 100m apart and are at the same elevation as the foot of the building. The
angles of elevation of the top of the building are 21º and 32º from A to B respectively.
What is the height of the building?
a. 327 b. 235 c. 277 d. 452
If eccentricity is less than one, then the curve is
a) parabola b) ellipse c) hyperbola d) circle
What is the center of the ellipse 25x2 + 16y2 – 150x + 128y + 81 = 0?
a. (3,-4) b. (3,-5) c. (3, -6) d. (3, -7)
Triangle with no two sides are equal.
a. Scalene b. Equilateral c. Isosceles d. Obtuse
Find the area of a spherical triangle of whose angles are 123°, 84°, and 73°. The radius
of the sphere is 30 m.
A. 1863.3 square meter B. 1570.8 square meter C. 1958.6 square meter D. 1480.2 square meter
Find the derivative of y=
a. 0 b. 1 c. 5 d. 10
Find the derivative of f(x)= 8x^
a. 7x^ b. 16x^ c. 136x^ d. 16x^
__________ is a general method of evaluating indeterminate forms.
a. L’Hospital rule b. Trapezoid rule c. Simpson’s rule d. Chain rule a. 1 b. 8 c. 0 d. Does not exist
What is the derivative with respect to x of (x+1)^3-x^
a. (x+1)/3+2x^ b. 3(x+1)+3x^ c. 3x+ d. 6x+
If y= tanhx, find dy/dx
a. sech2 x b. -sech2 x c. sech x tanh x d. -sech x tanh x
A particle’s position is given by: s = t^3 – 6t^2 + 9t. What is its acceleration at time t=5?
a. 16 b. 17 c. 18 d. 19
Find the partial derivative with respect to the x of the function xy^2 – 5x + 6.
a. Xy-5x b. y^2 – 5 c. xy- d. y^2 + 6
Evaluate the integral of (2x^2 + 3x – 4) dx
a. (2x^3)/3 + (3x^2)/2 – 4x + C b. (2x^3)/2 + (3x^2)/3 – 4x + C c. (2x^2)/3 + (3x)/2 – 4x + C d. (2x)/2 + (3x^2)/3 – 4x + C
A collective term for maxima or minima, whether absolute of relative is called
a. Infinitium b. Extrema c. Domain d. none of the above
Determine the value of x on the interval [-1 , 4] to find the minimum value of of f(x) = x^
- 12x + 5. a. - b. 1 c. 2 d. 3 a. 0. b. 0. c. 0. d. 0.
Evaluate:*
a. -⅚ b. ⅚ c. 5/ d. 1/
