School of Engineering IMP-A Exam 3

School of Engineering
IMP-A Exam 3
Name:_____________________________ Rating:___
Section:____________________________
Instructions:
1. Using of gadgets are not allowed during the examination.

2. No talking while the examination is ongoing.
3. A final grade of 0.0 will be given to those students who will be caught cheating during the examination.
4. Use the answer sheet provided. Answer sheets will be collected after the examination.
5. Calculators are allowed for computations.
6. Follow the instructions carefully.
7. No Erasures.
Answer Sheet
1. A B C D 16. A B C D
2. A B C D 17. A B C D
3. A B C D 18. A B C D
4. A B C D 19. A B C D
5. A B C D 20. A B C D
6. A B C D 21. A B C D
7. A B C D 22. A B C D
8. A B C D 23. A B C D
9. A B C D 24. A B C D
10. A B C D 25. A B C D
11. A B C D 26. A B C D
12. A B C D 27. A B C D
13. A B C D 28. A B C D
14. A B C D 29. A B C D
15. A B C D 30. A B C D
Multiple Choices. Shade the letter of your answer on the answer sheet provided.
1. Find the inclination of the line passing through (- B. 3r cos Ѳ + 4r sin Ѳ = -2

5, 3) and (10, 7).
C. 3r cos Ѳ + 4r sin Ѳ = 2
A. 14.73° B. 14.93°
D. 3r sin Ѳ + 4r tan Ѳ = -2
C. 14.83° D. 14.63°
10. The parabola y = –x2 + x + 1 opens:
2. If the distance between points (3, y) and (8, 7) is
13, then y is equal to A. To the right B. To the left
A. 5 or –5 B. 5 or 19 C. Upward D. Downward
C. 19 D. –5 or 19 11. The center of the ellipse 4×2 + y2 – 16x – 6y –

43 = 0 is at:
3. The segment from (-1, 4) to (2, -2) is extended
three times its own length. The terminal point is A. (2, 3) B. (4, -6)
A. (11, -24) B. (-11, -20) C. (1, 9) D. (-2, -5)
C. (11, -18) D. (11, -20) 12. An ellipse has the equation 16×2 + 9y2 + 32x –
128 = 0. Its eccentricity is:
4. Which of the following lines is parallel to the line
3x – 2y + 6 = 0? A. 0.531 B. 0.66 C. 0.824 D. 0.93
A. 3x + 2y – 12 = 0 B. 4x – 9y = 6 13. The equation of the line through (-3, -5) parallel

to 7x + 2y – 4 = 0 is
C. 12x + 18y = 15D. 15 x – 10y – 9 = 0
A. 7x + 2y + 31 = 0 B. 7x – 2y + 30 = 0
5. What is the radius of the circle with the following
equation? C. 7x – 2y – 4 = 0 D. 2x + 7y + 30 = 0
x2 – 6x + y2 – 4y – 12 = 0 14. The semi-conjugate axis of the hyperbola (x2/9)

– (y2/4) = 1 is:
A. 3.46 B. 5 C. 7 D. 6
A. 2 B. -2 C. 3 D. -3
6. Find the area of the triangle which the line 2x –
3y + 6 = 0 forms with the coordinate axis. 15. What is the equation of the asymptote of the
hyperbola (x2/9) – (y2/4) = 1.
A. 3 B. 4 C. 5 D.2
A. 2x – 3y = 0 B. 3x – 2y = 0
7. Given the equation of a parabola 3x + 2y2 – 4y +
7 = 0. Locate its vertex. C. 2x – y = 0 D. 2x + y = 0
A. (5/3, 1) B. (5/3, -1) 16. The angle subtended by an arc is 24o. If the
radius of the circle is 45 cm, find the length of arc
C. -(5/3, -1) D. (-5/3, 1)
A. 16.85 cm B. 17.85 cm
8. Find the location of the focus of the parabola y2
+ 4x – 4y – 8 = 0. C. 18.85 cm D. 19.85 cm
A. (2.5, -2) B. (3, 1)
17. A certain angle has as supplement 5 times its
C. (2, 2) D. (-2.5, -2) complement. What is the angle?
9. The polar form of the equation 3x + 4y – 2 = 0 is:
A. 67.5° B. 58.5° C. 30° D. 27°
A. 3r sin Ѳ + 4r cos Ѳ = 2
18. How many sides has a polygon if the sum of the 25. One side of a parallelogram is 10 m and its
interior angles is 1080°? diagonals are 16 m and 24 m, respectively. Its area
is:
A. 5 B. 6 C. 7 D. 8
A. 156.8 sq. m. B. 185.6 sq. m.
19. How many diagonals are there in a polygon of
20 sides? C. 158.7 sq. m. D. 142.3 sq. m.
A. 200 B. 170 C. 100 D. 158 26. The area of a rhombus is 132 square cm. if its
shorter diagonal is 12 cm, the length of the longer
20. In triangle ABC, angle A = 45° and C = 70°. The diagonal is:
side opposite angle C is 40 m long. What is the
length of the side opposite angle A? A. 20 centimeter B. 21 centimeter
A. 26.1 m B. 27.1 m C. 22 centimeter D. 23 centimeter
C. 29.1 m D. 30.1 m 27. Determine the area of the quadrilateral having

(8, -2), (5, 6), (4, 1), and (-7, 4) as consecutive
21. The sides of a triangle are 8 cm, 10 cm and 14 vertices.
cm. Determine the radius of the inscribed circle.
A. 22 sq. units B. 44 sq. units
A. 2.25 cm B. 2.35 cm
C. 32 sq. units D. 48 sq. units
C. 2.45 cm D. 2.55 cm
28. The area of a regular hexagon inscribed in a
22. Find the difference of the area of the square circle of radius 1 is:
inscribe in a semi-circle having a radius of 15 cmc.
The base of the square lies on the diameter of the A. 2.698 sq. units B. 2.598 sq. units
semi-circle.
C. 3.698 sq. units D. 3.598 sq. units
A. 171.5 cm2 B. 172.5 cm2
29. The area of a circle is 89.4 square inches. What
C. 173.5 cm2 D. 174.5 cm2 is the circumference?
23. The interior angles of a triangle measures 2x, x A. 35.33 inches B. 32.25 inches
+ 15, and 2x + 15. What is the value of x?
C. 33.52 inches D. 35.55 inches
A. 30° B. 66° C. 42° D. 54°
30. Given a cyclic quadrilateral whose sides are 4
24. A goat is tied to a corner of a 30 ft by 35 ft cm, 5 cm, 8 cm, and 11 cm. Its area is:
building. If the rope is 40 ft long and the goat can
reach 1 ft farther than the rope length, what is the A. 40.25 sq. cm. B. 48.65 sq. cm.
maximum area the goat can cover? C. 50.25 sq. cm. D. 60.25 sq. cm
A. 5281 ft2 B. 4084 ft2
C. 3961 ft2 D. 3970 ft2

1. b
2. d
3. d
4. d
5. b
6. a
7. d
8. c
9. c
10. d
11. a
12. b
13. a
14. a
15. a
16. c
17. a
18. d
19. b
20. d
21. c
22. c
23. a
24. b
25. c
26. c
27. a
28. b
29. c
30. A

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School of Engineering

1. Using of gadgets are not allowed during the examination.

1. Find the inclination of the line passing through (- B. 3r cos Ѳ + 4r sin Ѳ = -2

C. 19 D. –5 or 19 11. The center of the ellipse 4×2 + y2 – 16x – 6y –

A. (11, -24) B. (-11, -20) C. (1, 9) D. (-2, -5)

A. 3x + 2y – 12 = 0 B. 4x – 9y = 6 13. The equation of the line through (-3, -5) parallel

x2 – 6x + y2 – 4y – 12 = 0 14. The semi-conjugate axis of the hyperbola (x2/9)

A. 26.1 m B. 27.1 m C. 22 centimeter D. 23 centimeter

C. 29.1 m D. 30.1 m 27. Determine the area of the quadrilateral having

C. 3961 ft2 D. 3970 ft2

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