Mapua University
Civil Engineering Department
CE199L-1: Correlation Course 1
PRACTICE EXAM # 2
[Trigonometry, Analytic/Plane/Solid Geometry, Differential Calculus]
1. A pole cast a shadow of 15 meters long when the angle of elevation of the sun is 61°. If the
pole has leaned 15° from the vertical directly toward the sun, what is the length of the pole?
a. 52.43 c. 53.25
b. 54.23 d. 53.24
2. The corners of a 2-meter square are cut off to form a regular octagon. What is the length of
the sides of the resulting octagon?
a. 0.525 c. 0.727
b. 0.626 d. 0.828
3. Find the equation of the curve whose slope is 3x^4 – x^2 and passes through point (0,1).
a. 3𝑥 5 𝑥 3 c. 3𝑥 5 𝑥 3
𝑦= − +1 𝑦= + +1
5 3 5 3
b. 3𝑥 5 𝑥 3 d. 3𝑥 5 𝑥 3
𝑦= − −1 𝑦= + −1
5 3 5 3
4. A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in
diameter with a central angle of 150°. Find the volume of the cone in cc.
a. 7733 c. 7744
b. 7722 d. 7711
5. A hemispherical bowl of radius 10 cm is filled with water to such a depth that the water
surface area is equal to 75π cm^2. The volume of water is:
a. 625/3 c. 625π/2
b. 625π/3 d. 625π
6. A swimming pool is to be constructed in the shape of partially overlapping identical circles.
Each of the circles has a radius of 9 m., and each pass through the center of the other. Find the
area of the swimming pool.
a. 302.33 c. 398.99
b. 362.55 d. 409.44
7. The surface area of a sphere is 4πr^2. Find the percentage increase in its diameter when the
surface area increases by 21%.
a. 30.2 % c. 34.5 %
b. 33.1 % d. 30.9 %
8. Find the equation of the circle with center on x + y = 4 and 5x + 2y + 1 = 0 and having a
radius of 3.
a. x^2 + y^2 + 6x – 16y + 64 = 0 c. x^2 + y^2 + 6x – 14y + 49 = 0
b. x^2 + y^2 + 8x – 14y + 25 = 0 d. x^2 + y^2 + 6x – 14y + 36 = 0
9. Find the radius of curvature of the curve x = y^3 at the point (1, 1).
a. 2.56 c. 2.88
b. 1.76 d. 1.50
Mapua University
Civil Engineering Department
CE199L-1: Correlation Course 1
10. From a point A at the foot of the mountain, the angle of elevation of the top B is 60°. After
ascending the mountain one mile at an inclination of 30° to the horizon, and reaching a point
C, an observer finds that the angle ACB is 135°. The height of the mountain in feet is:
a. 14386 c. 11672
b. 12493 d. 11225
11. If the distance between the points (8, 7) and (3, y) is 13, what is the value of y?
a. 5 c. -19
b. 19 or -5 d. -19 or 5
12. A rectangle is inscribed in a parabola y^2 = 16x with the side of the rectangle along the latus
rectum of the parabola. If the area of the rectangle is maximized, compute its perimeter.
a. 24.63 c. 14.57
b. 13.69 d. 20.69
13. What is the distance between the vertices of the ellipse: 64x^2 + 25y^2 _ 16x – 16y – 648 =
0?
a. 6.324 c. 10.21
b. 12.54 d. 5.105
14. The angle of elevation of a point C from a point B is 29°42’; the angle of elevation of C from
another point A 31.2 m directly below B is 59°23’. How high is C from the horizontal line
through A?
a. 47.1 m. c. 35.1 m.
b. 52.3 m. d. 66.9 m.
15. A closed cylindrical tank of maximum volume is to be constructed. With only 381.7 m^2 of
material, what will be the tank’s height in meters?
a. 12.0 c. 6.0
b. 9.0 d. 4.5
