1. Find the value
of x in the
equation shown: 4x2 + 48x + 144 = 400
(a) 16, 4 (b) -16, 4 (c) -32, 8 (d) -4, 16
2. The age of a
crocodile at the Manila Zoo 13 years ago was
of its age 7 years from
now. How old is the crocodile at present?
(a) 15 (b) 21 (c) 23 (d) 27
3. An airplane
flying with the wind can cover a certain distance in 2 hours. The return trip
against the wind takes 2.5 hours. How fast is the plane and what is the speed
of the air, if the one-way distance is 600 miles? (NOTE: Let x be the speed
of the plane and y be the speed
of the wind.)
(a) x = 40, y = 260 (b) x = 30, y = 270 (c) x = 270, y = 30 (d) x = 230, y = 70
4. How many
gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9
gallons of 30% alcohol solution?
(a) 3 gallons of
20% solution and 6 gallons of 50% solution
(b) 6 gallons of
20% solution and 6 gallons of 50% solution
(c) 5 gallons of
20% solution and 3 gallons of 50% solution
(d) 6 gallons of 20%
solution and 3 gallons of 50% solution
5. How many
different second order determinant can be formed from four different numbers?
(a) 4 (b) 8 (c) 16 (d) 24
6. The angle of
elevation of the top of an incomplete vertical pillar at a horizontal distance
of 100 meters from its base is 450. If the angle of elevation of the
top of the complete pillar at the same point is to be 600, then the
height of the incomplete pillar is to be increased by how much?
(a) 73.21 m (b) 100 m (c) 173.21 m (d) 26.79 m
7. The function f is defined for
0 ≤ x ≤ 360, f(t) = 3sin(2t – 1). What is
the period of the wave formed?
(a)
(b)
2 (c)
π (d)
8. If an
equilateral triangle is circumscribed about a circle of radius 12 cm, determine
the side of the triangle.
(a) 34.64 cm (b) 41.57 cm (c) 83.14 cm (d) 20.78 cm
9. Solve for the
value of x: 2log5(x – 4) = 4
(a) 29 (b) 21 (c) 4 (d) 25
10. The two
vertices of a triangle are A(2, 4) and B(-2, 3). Find
the locus of the third vertex of the triangle if its area is 2 square units.
(a) 4x
– y = 12 (b) 4x + 4y = 10 (c) x + 4y = 12 (d) x – 4y = -10
11. What are the
coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?
(a) (-1, -1) (b) (-2, -2) (c) (1, 2) (d) (2, 1)
12. Find the
eccentricity of the curve 9x2 – 4y2 – 36x + 8y = 4.
(a) 1.76 (b) 1.80 (c) 1.86 (d) 1.92
13. If the edge of
a cube is increased by 30%, by how much is the surface area of one side of the
cube is increased?
(a) 30% (b) 33% (c) 60% (d) 69%
14. A conical
vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a
depth of 18 cm above its vertex. Find the volume (in cm3) of its
content.
(a) 188.40 cm3 (b) 298.40 cm3 (c) 381.70 cm3 (d) 412.60 cm3
15. A 10 m-diameter
hemispherical rubber ball is filled with liquid to a depth of 4 m. Determine
the surface area of the ball which is not in contact with the liquid.
(a) 5π (b) 10π (c) 20π (d) 120π
16. Find the value
of k such that the
function defined by f(x) =
is continuous at every real
number.
(a) 3 (b) 4 (c) 5 (d) 7
17. If f ‘(2) = g‘(2) = f(2) = g(2) = 2, then
what is the value of (fg)‘(2)?
(a) 8 (b) 12 (c) 16 (d) 20
18. Find the
equation of the tangent line to the curve y = x3 at the point (2, 8).
(a) 12x – y – 16 = 0 (b) x + 12y – 98 = 0 (c) 12x + y – 98 = 0 (d) x – 12y + 16 = 0
19. Find
in the equation tan x + tan y = xy.
(a)
=
(b)
=
(c)
=
(d)
=
20. Evaluate:
.
(a)
(b)
(c)
(d)
21. Evaluate:
.
(a)
(c)
(b)
(d)
22. The region
bounded by the lines y = 3 – 2x, y = 2 and the
coordinate axes is revolved about the y-axis. Find the
volume of the solid formed.
(a)
(b)
(c)
(d)
23. Find the area
of the region bounded by the curve y2 = 4x, the line y = 2 and the y-axis.
(a)
(b)
(c)
(d)
24. Find a vector
orthogonal to both of the vectors u = <2 -1="-1" 3="3"> and v = <-7 -1="-1" 2="2">.
(a) -5i – 19j – 3k (b) 5i + 19j + 3k (c) 5i – 19j + 3k (d) -5i + 19j – 3k
25. Evaluate:
.
(a)
(b)
11 (c)
(d)
12
BAKIT KASI WALA SAGOT
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