BATAC NATIONAL HIGH SCHOOL City of Batac, Ilocos Norte DIAGNOSTICS TEST MATHEMATICS IV (Special Science Class) Direction : Write the letter that best and adequately ans wers each item. 0
0
0
0
1. In a 30 – 60 60 – 90 90 triangle, the ratio of the hypotenuse to the side opposite the 30 angle is always equal to ___________. a. 2. If
√
b. ½
c. 2
and
, then
a. I
is in quadrant: b. II
d.
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 makes 24 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/s 4. If
lies on the line segment joining the points (0, 0) and (12, -5), find the value v alue of a. 1 b. – 1 c. 0 d. undefined
.
0
5. The coordinates of P(-450 ) are a. (0, 1) 6. If
b. (0, -1)
, then
a.
7. Find the value: a. 1
= _________ b. x
b. -1
c. (1,0)
d. (-1, 0)
c. 2x
d. 4x
c. 0
d. undefined
0
8. What is the exact value of sin 75 ? a. 9.
√ √
√
√ √
c.
√ √
d.
√ √
b.
√
c.
√
d.
√
c.
d.
= ________________
a.
10. If
b.
, then
a.
= _____________. b.
11. A 60 – meter meter 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. meters
√ √
√ √
12. 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. miles
√ √
√
√ √
√ √
13. Find the radius of the inscribed circle of a triangle if the measures of the sides 32, 18 and 48. a.
b.
√
c.
√ √
14. A pole 45 meters high casts a shadow a. 300 b. 600
meters long. Find the angle of elevation of the sun? c. 450 d. 900
15. Solve for x and y: a.
b.
d.
c.
d.
√ (√ )
16. A man on top of the light tower meters above the ground has spotted 2 boats. One boat has an angle of depression of 450 while the other has an angle of depression equal to 600. Find the distance between the two boats? a. 8 meters b. meters c. meters d. meters
√
√
17. 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
19. What is the restriction of b for the function a. b> 0 b.
20. Evaluate:
a.
c. 3
d. 10
c.
d. has no restriction
and
[ * + ]
b. 81
c.
d.
21. Given the function F(x) = 5 – 2x, evaluate F(x + 1). a. 7 – 2x 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. 5x – 4y +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 its equation. a. b. c. d.
25. Find the distance between the parallel lines 15x – 8y – 51 = 0 and 15x – 8y + 68 = 0. a. 7 b. 6 c. 8 d. 8.5
and a vertex at (0,6).
26. Find the equation of the ellipse with foci at a.
√ b.
c.
.
d
27. Evaluate: a. ½
b. ¼
c. 1/8
d. – 1/6
b. 2
c. -1
d. 0
28. Evaluate: a. 1
29. Differentiate: a.
c.
b.
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 2 the maximum area (in m ) that can be enclosed this way? a. 60 000 b. 70 000 c. 80 000 d. 90 000
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 330 32. 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 80 33. 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 2
34. Find the area of a triangle whose sides are 13 cm, 14 cm, and 15 cm (in cm ). 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 + 4y – 38 =0 b. 4x – 3y + 38 =0
?
. d. 4x – 3y = -38
c. 3x – 4y = 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. 2x – 7y = 0 c. 5x + 2y = 0 d. 2x – 5y – 3 = 0
√ {} {} {} {}
38. What is the domain of a.
39. What is the range of a.
b.
c.
d.
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
{} {} { } √
41. What is the amplitude of a. 3x 42. The domain of a.
?
b. -2
is_________________. b. all real numbers
43. How many triangles are formed given: a. 1 b. 2 44. Solve the point of intersection of a. (-5, - 7/2) b. (5, 7/2)
c. 2
d. -6
c.
d.
?
and
c. none
d. infinitely many
. c. (5, - 7/2)
d. (-7/2, 5)
45. Which of the following is the derivative of the function, a.
d. -13/6
b.
?
c.
d.
46. The midpoint of (x, 4) and (-5,8) is (8, 6). Determine the value o f 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.
to degrees. a. 45 b. 315 50. If , then x = _____________. a. b.
d.
49. Convert
0
0
0
c. 225
c.
0
d. 135
d.
