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BATAC NATIONAL HIGH SCHOOL

City of Batac, Ilocos Norte

DIAGNOSTICS TEST

MATHEMATICS IV

(Special Science Class)

Direction: Write the letter that best and adequately answers each item.

1. In a 30060

090

0triangle, the ratio of the hypotenuse to the side opposite the 30

0angle is always equal to

___________.

a. b. c. 2 d.

2. If and , then is in quadrant:a. I b. II c. III d. IV

3. A waterwheel with radius 2 meters is used to determine the speed of the water in river B. If the wheel makes24 revolutions per second, what is the speed of the river in meters per second?

a. 96 m/s b. 48 m/s c. 24 m/s d. 192 m/s4. If lies on the line segment joining the points (0,0) and (12, -5), find the value of .

a. 1 b.1 c. 0 d. undefined

5. The coordinates of P(-4500) are

a. (0, 1) b. (0, -1) c. (1,0) d. (-1, 0)

6. If , then = _________a.

b. x c. 2x d. 4x

7. Find the value:

a. 1 b. -1 c. 0 d. undefined8. What is the exact value of sin 75

0?

a. b.

c. d.

9. = ________________a.

b.

c.

d.

10. If , then = _____________.a. b. c. d. 11. A 60meter ladder leans against a window sill at an angel of inclination of 300. Find the height of the

window sill from the ground.

a. 30 meters b. meters c. 60 meters d. meters12. Two planes leave an airport at the same time. Plane A flies in the direction of 2450 at 5 mph, and the other

follows a course of 1850 at 3 mph. How far are they from each other after 2 hours?

a.miles b. miles c. miles d. miles13. Find the radius of the inscribed circle of a triangle if the measures of the sides 32, 18 and 48.

a. b. c. d.

14. A pole 45 meters high casts a shadow meters long. Find the angle of elevation of the sun?a. 300 b. 600 c. 450 d. 900

15. Solve for x and y: a. b. c. d.

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16. A man on top of the light tower meters above the ground has spotted 2 boats. One boat has an angle ofdepression of 450 while the other has an angle of depression equal to 600. Find the distance between the twoboats?

a. 8 meters b. ( )meters c. meters d. meters17. About 4 200 bacteria are initially present in a colony. It was observed that this grew to 16 800 after 40

minutes. How many bacteria will there be at the end of one hour?

a. 33 600 b. 67 200 c. 60 000 d. 10 000

18. Express as a single logarithm and simplify a. 0 b. 1 c. 3 d. 10

19. What is the restriction of b for the function and a. b> 0 b. c. d. has no restriction

20. Evaluate: [ *+]

a. b. 81 c. d. 21. Given the function F(x) = 52x, evaluate F(x + 1).

a. 72x b. 3 + 2 c. -2x + 3 d. 2x 7

22. What is the zero of the linear function f(x) = 3x + 7

a. 7 b. 3 c. -3/7 d. -7/3

23. Find the equation of the line passing (-5, 2) and is perpendicular to the line 5x 4y = 1.a. 4x + 5y + 10 = 1 b. 4x + 5y = 10 c. 5x4y +10 = 0 d. 5x 4y = 10

24. A parabola has its vertex at the origin, its axis along the x-axis, and passes through the point (3,6). Find itsequation.

a. b. c. d. 25. Find the distance between the parallel lines 15x 8y51 = 0 and 15x 8y + 68 = 0.

a. 7 b. 6 c. 8 d. 8.5

26. Find the equation of the ellipse with foci at and a vertex at (0,6).a.

b.

c.

d.

27. Evaluate: a. b. c. 1/8 d.1/6

28. Evaluate: a. 1 b. 2 c. -1 d. 0

29. Differentiate: a.

b.

()

c. d. () 30. A farmer has 800 m of fencing material to enclose a rectangular pen adjacent to a long existing wall. He will

use the wall for one side of the pen and the available fencing material for the remaining three sides. What is

the maximum area (in m2) that can be enclosed this way?

a. 60 000 b. 70 000 c. 80 000 d. 90 000

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31. Find two numbers whose sum is 640 and whose product is as large as possible.

a. 520 and 120 b. 320 and 320 c. 230 and 410 d. 310 and 33032. A commuter train carries 600 passengers each day from a town to a city. A one-way trip costs Php 100 per

person. Market research reveals that 10 fewer people would ride the train with every Php 1 increase in fare.

What fare should be charged to get the largest possible revenue?

a. Php 90 b. Php 70 c. Php 60 d. Php 8033. A man 6-ft tall walks with a speed of 5 fps away from a street light that is top a 24 ft pole. How fast is the

tip of his shadow moving along the ground when he is 50 ft from the pole?

a. 6.24 fps b. 5.67 fps c. 7.56 fps d. 6.67 fps

34. Find the area of a triangle whose sides are 13 cm, 14 cm, and 15 cm (in cm2).

a. 84 b. 68 c. 48 d. 42

35. The point (12, 5) is on the terminal side of angle in standard position. What is the value of ?a. 5/12 b. 5/13 c. 13/5 d. 12/5

36. Find an equation of the tangent line to the circle .a. 3x + 4y38 =0 b. 4x3y + 38 =0 c. 3x4y = 38 d. 4x 3y = -38

37. Find the equation of the line through the origin and perpendicular to the line 2x

5y + 7 = 0.a. 5x + 2y +3 = 0 b. 2x7y = 0 c. 5x + 2y = 0 d. 2x 5y3 = 0

38. What is the domain of a. b. c. d.

39. What is the range of a. { } b. { } c. . { } d. . { }

40. What is the slope of the line containing the points (3, 8) and (-3, -5) ?

a. -6/13 b. 13/6 c. 6/13 d. -13/6

41. What is the amplitude of ?a. 3x b. -2 c. 2 d. -6

42. The domain of is_________________.a. { } b. all real numbers c. { } d. { }

43. How many triangles are formed given: ?a. 1 b. 2 c. none d. infinitely many

44. Solve the point of intersection of

and

.

a. (-5, - 7/2) b. (5, 7/2) c. (5, - 7/2) d. (-7/2, 5)

45. Which of the following is the derivative of the function, ?a.

b. c. d.

46. The midpoint of (x, 4) and (-5,8) is (8, 6). Determine the value of x.a. 21 b. -21 c. 22 d. -22

47. A flower garden is a 270-degree sector with a 6-m radius. Find the area of the garden in terms of a. b. c. d.

48. Find the distance travelled by the tip of a 4-cm minute hand of a clock in 20 minutes.

a. b.

c.

d.

49. Convert to degrees.

a. 450 b. 315

0 c. 225

0 d. 135

0

50. If , then x = _____________.a.

b.

c.

d.