Sample Problems
1. Multiply (2x + 5y)(5x - 2y)
a. 10x² - 21xy + 10y²
b. 10x² + 21xy + 10y²
c. 10x² + 21xy - 10y²
d. 10x² - 21xy - 10y²
2. The value of (3^2.5) squared is equal to:
a. 729
b. 140
c. 243
d. 81
3. If 3 people can complete a task in 4 hours, how long will it take 5 people to complete the same task?
a. 2 hours and 24 minutes
b. 2 hours and 40 minutes
c. 2 hours and 30 minutes
d. 5 hours and 2 minutes
4. Edgar drives 231 km in the same time as Erwin drives 308 km. Erwin's rate exceeded Edgar's by 13 kph. What is Erwin's rate?
a. 39 kph
b. 44 kph
c. 48 kph
d. 52 kph
5. How many horsepower is 746 kilowatts?
a. 500
b. 74.6
c. 100
d. 1000
6. Express 45 degrees in mils.
a. 80 mils
b. 800 mils
c. 8000 mils
d. 800000 mils
7. What is the Fahrenheit equivalent of 100°C?
a. 200
b. 180
c. 212
d. 100
8. What is the temperature 45°C in Fahrenheit?
a. 45°F
b. 113°F
c. 57°F
d. 81°F
9. 3200 mils is equal to how many degrees?
a. 45
b. 90
c. 180
d. 270
10. Solve the simultaneous equations: (1) 2x² - 3y² = 6, (2) 3x² + 2y² = 35.
a. x = ±3; y = ±2
b. x = ±3; y = -2 or 1
c. x = ±3; y = -2 or -1
d. x = ±3; y = 2 or -3
11. Solve for y: x/(b-c) = y/(a-c) = z/(a-b)
a. x-z
b. x+z
c. a+b
d. a-b
12. Jacob's father's age is three times Jacob's. After 5 years, their ages sum to 70. Find Jacob's age.
a. 15
b. 20
c. 18
d. 21
13. What is the value in degrees of 1 radian?
a. 90
b. 57.3
c. 100
d. 45
14. A boatman rows 4.8 miles with the stream and back in 14 hours; he can row 14 miles with the stream in the same time as 3 miles against. What is the rate of the stream?
a. 1.5 mph
b. 1 mph
c. 0.8 mph
d. 0.6 mph
15. Find the 50th term of an arithmetic progression 7, 10, 13, ...
a. 154
b. 102
c. 178
d. 220
16. The number 0.123123123... is:
a. irrational
b. surd
c. rational
d. transcendental
17. If a man mails 10 chain letters to 10 friends, and the chain continues for 6 sets, with all replying and postage at P4 per letter, how much does the Phil. Postal Office earn?
a. 6 million
b. 60 thousand
c. 2.22 million
d. 4.44 million
18. 7 + 0i is:
a. irrational number
b. real number
c. imaginary number
d. a variable
19. A boat travels downstream in 2/3 the time as upstream. The river's velocity is 8 kph. Find the velocity of the boat in still water.
a. 40 kph
b. 50 kph
c. 30 kph
d. 60 kph
20. Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.
a. 1075 sq m
b. 1085 sq m
c. 1080 sq m
d. 1095 sq m
21. A wire supporting a pole is fastened 20 ft from the ground and to the ground 15 ft from the pole. Find the wire length and angle with the pole.
a. 24 ft, 53.13
b. 24 ft, 36.87
c. 25 ft, 53.13
d. 25 ft, 36.87
22. The area of a circle is 89.42 sq in. What is the side length of a regular hexagon inscribed in it?
a. 5.533
b. 5.3335
c. 6.3335
d. 7.3335
23. If w varies directly as the product of x and y and inversely as the square of z, w = 4 when x = 2, y = 6, z = 3. Find w when x = 1, y = 4, z = 2.
a. 3
b. 4
c. 5
d. 9
24. Given a right spherical triangle: a = 82°, b = 62°, C = 90°. What is the side opposite the right angle?
a. 83° 30'
b. 84° 45'
c. 86° 15'
d. 85° 15'
25. From a point outside an equilateral triangle, the distances to vertices are 10 m, 18 m, and 10 m. Find the side length of the triangle.
a. 17.75
b. 18.5
c. 19.95
d. 20.5
26. One number is 5 less than another. Their sum is 135. Find the two numbers.
a. 85, 50
b. 80, 55
c. 70, 65
d. 75, 60
27. Find the inclination of the line passing through (-5, 3) and (10, 7).
a. 14.73
b. 14.93
c. 14.83
d. 14.63
28. Jojo bought a Betamax VCR, sold to Rudy at 40% profit. Rudy sold to Noel at 20% profit. Noel paid P2856 more than Jojo. How much did Jojo pay?
a. 4000
b. 4100
c. 4200
d. 4300
29. The triangle sides are 8, 15, and 17 units. If sides are doubled, what is the new area?
a. 240
b. 420
c. 320
d. 199.98
30. A conical vessel is 24 cm high, base diameter 12 cm, holds water to 18 cm depth. Find the water volume in cm³.
a. 188.4
b. 298.4
c. 381.7
d. 412.6
31. Find the slope of the line y - x = 5.
a. 1
b. 0.25
c. -0.25
d. 5+x
32. A PLDT tower and a monument on level plane: angles of depression are 13° and 35°. Tower is 50 m high. Find the monument's height.
a. 29.13
b. 30.11
c. 32.22
d. 33.51
33. Find the distance from the origin to the line 3x + 4y = 5.
a. 4
b. 3
c. 2
d. 1
34. Find the eccentricity of the curve 9x² - 4y² - 36x + 8y = 4.
a. 1.8
b. 1.92
c. 1.86
d. 1.76
35. 4x² - y² = 16 is the equation of a/an:
a. Parabola
b. Hyperbola
c. Ellipse
d. Circle
36. What is the distance from A(4, -3) to B(1, -7)?
a. 3
b. 4
c. 5
d. 9
37. Find the equation of a straight line with a slope of 3 and a y-intercept of 1.
a. 3x + y - 1 = 0
b. 3x - y + 1 = 0
c. x + 3y + 1 = 0
d. x - 3y - 1 = 0
38. An airplane pilot left A and flew 200 miles S 20°20' W; then 148 miles S 69°40' E. Now he heads back to A. In what direction should he fly?
a. N 16°10' W
b. N 30°53' W
c. S 37°30' W
d. E 44° S
39. For equation y² = -4ax, the parabola opens to the:
a. Right
b. Up
c. Down
d. Left
40. Convert azimuth 232°31'18" to bearings:
a. S 52°31'18" W
b. S 52°31'18" E
c. N 37°28'42" W
d. E 37°28'42" W
41. An airplane can fly at 300 mph. Wind east at 50 mph. Compass reading for 30° course:
a. 21.55
b. 8.3
c. 30
d. 44
42. A boat sails N 30° W from a port for 20 km. How far is it west of the port?
a. 15
b. 20
c. 10
d. 25
43. What is the slope of the line 3x + 2y + 1 = 0?
a. 3/2
b. 2/3
c. -3/2
d. -2/3
44. Find the distance between centers of circles: x² + y² + 2x + 4y - 3 = 0 and x² + y² - 8x - 6y + 7 = 0.
a. 7.07
b. 7.777
c. 8.07
d. 7.87
45. Find the angle between the lines 3x + 2y = 6 and x + y = 6.
a. 12°20'
b. 11°19'
c. 14°25'
d. 13°06'
46. Find the distance between foci of the conic 8x² + 9y² = 288.
a. 8
b. 6
c. 4
d. 2
47. It is the fixed point of a conic.
a. Center
b. Focus
c. Directrix
d. Eccentricity