Second Grading Examination in

Mathematics 9

Direction: Read and analyze the problem provided carefully, write the letter of your answer on the space provided for.
1. In the symbol n
a m, what does n indicates? a. radical b. Index/order c. radicand d. Power
2. (21/2)(21/3) equals. a. 6 2 5 b. 5 2 6 c.21/6 d. 41/6
2 0 1/2
3. Express 3 • 4 +1 • 5 . 0
a. 9 b.10 c. 11 d. 12
4. Time taken by the light to travel 1 meter is roughly 3 x 10-8.
a. 30 000 b. 30 000 000 c. 300 000 d. 3 000 000
5. Any real number a = 1 is _______. a. false
0
b. sometimes true c. always true d. sll of the above
6. Evaluate 6e0 + (11f)0 - 5/g0. a. 0 b.3 c. 2 d. 1
7. (-8) equals.
1/3
a. -2 b. 2 c. 4 d. -4
32
8. The following are examples of zero exponent EXCEPT. a. b.50 c. a0 = 1 d. y1/2
32
1
9. Simplify −1 . a. 32x3y5 b. -32x-3y-5 c. 32x-3y-5 d. -32x3y5
(32x3y5)
(𝑠2 )3 𝑟6
10. Which of the following is true? a. b5 x b3=b15 b. 3 =
(𝑠4 ) 𝑠12
𝑎𝑚
c. (ab)m = am + bm d. = am+n
𝑎𝑛
11. The r of moving object is inversely proportional to the time traveled is written as
a. t= kt b. r = k/t c. t = kr d. r/k = r
1 2+√5 √5−2 2−√5 −2−√5
12. Simplify . a. b. c. d.
2+√5 9 9 9 9
1
13. Perform the operation of the expression . a. x /x b. x /1 c. 1+ x d. x -1
√𝑥
14. An equation in which the variable appears in a radicand,
a. radical expression b. radical equation c. linear equation d. Quadratic Equation
15. Simplify
3
x  2 = 3. a. x=27 b. x=50 c. x=25 d. x=34

16. Solve for m in the equation 2m =4. a. m=8 b. m=12 c. m=16 d. m=24

17. Evaluate: x = 10. a. 100 b.50 c. 200 d. 150

18. Simplify a. 2 b. c. d.
3 3
16 . 2 2 23 2
19. Refer to symbol in item no. 10, if a is positive or negative real number and n is an odd, then
there exist one real nth root of a, the sign of the root being the same as the sign of the number.
a. true b. Sometimes true c. Always true d. none of the above
20. The following listed below are false EXCEPT,
a. 32/3 = 3 3 2 b. (2n)3/5 =
3
2n 5 c. 3
9=3 d.  16 = -4
21. An encoder can type n words in t hours. The formula that relates n to t is n = k/t. What kind of
variation is it? a. inverse b. direct c. joint d. combined
22. The cost c of mango varies directly as its weight w. This relationship is written as ______.
a. c =kw b. k =cw c. K/c =w d. c =k/w
23. If s varies directly as t and inversely as v, then which of the following equations describes the
relation among the three variables s, t, and v? a. s= k/tv b. s= kv/t c. 1/s= kt/v d. s= kt/v
24. If y varies directly as x and y= 12 when x=4, find y when x=12.
a. 3 b. 4 c. 36 d. 48
25. Which of the following describes an inverse variation?
a. x 2 3 4 5 b.
x 40 30 20 10
y 5 10/3 5/2 2
y 8 6 4 2

c. x 1 2 3 4 d. x 4 8 10 12

5 10 15 20 y 2 4 5 6
y
26. Y varies directly as x and y=32 when x=4. Find the constant of variation.
a. 8 b. 36 c. 28 d. 128
27. Which is an example of direct variation?
a. xy=10 b. y=2/x c. y=5x d. 2/y =x
28. Which of the following rational algebraic equation is equal to x -11x+24=0?
2

6 𝑥−3 6 2 6 2 6 𝑥−3
a. + =2 b. + 𝑥 − 3 = c. +𝑥−3= d. + =2
4 𝑥 4 𝑥 𝑥 4 𝑥 4
29. It is an equality that contains a polynomial function of degree 2,
a. linear Inequality b. quadratic Inequality c. quadratic Function d. quadratic quality
30. A taut rope starting from the top of a flag pole and tied to the ground is 15 meters long. If the
pole is 7 meters high, how far is the rope from the base? a. 2.83 m b. 4.69 m c. 13.27 m d. 16.55 m
31. Which of the following is the result when we simplify (2√8+3√5)(6√8+7√5)?
a. 12√64+14√40+18√40+21√25 b. 12√8+32√40+21√5 c. 201+64√10 d. 195√10
32. What is the result after simplifying 2√3+4√3-5√3? a.-√3 b. √3 c. 11√3 d. 21√3
33. Which of the following radical equations will have x=4 as the solution?
a. √𝑥 -2x+7=0 b. 2 x  3 = x-3 c. √𝑥=9 d. 3√𝑥=6
34. The amount of gasoline used by a car varies jointly as the distance traveled and the square root of
the speed. Suppose a car used 25 liters on a 100 km-trip at 100 kph, about how many liters will
be use on a 1000 km trip at 64 kph? a. 100 liters b. 200 liters c. 300 liters d. 400 liters
35. If p varies directly as q and inversely as r, then which of the following equations describes the
relation among the three variables p, q, r? a. p=kq/r b. p=kr/q c. 1/p=kr/q d. p=k/qr
36. Y varies inversely as x and y =50 when x =4, find y when x=40. a. 5 b. 10 c. 40 d. 50
1
22 1
37. Which of the following is true? a. 51/2+51/3=55 b. 1 =22/9 c. (31/3)2= 32/3 d. 4-2/3= 3
23 42
38. What is the simplified form 405-26-11/2-1? a. 1 b. 1/75 c. 1/150 d. 1/6000
39. If h varies jointly as j and i and inversely as g, and h=50 when j= 2, i=5, and g= 1/2, find h when j=4, i=10, and
2

g=1/4. a. 25 b. 100 c. 800 d. 805

40. If (x-4) varies inversely as (y+3) and x=8 when y=2, find x when y= -1.
a. 20 b. 18 c. 16 d. 14
41. What happen to t when h is doubled in the equation t=4h?
a. T is halved b. T is tripled c. T is doubled d. T becomes zero
42. If 3 men can do a portion of a job in 8 days, how many men can do the same job in 6 days?
a. 7 b. 6 c. 5 d. 4
43. In the equation x2=k, if k<0, how many real solution/s do/es it have?
a. 3 b. 2 c. 1 d. No real roots
44. The cost c varies directly as the number n of pencils is written _______.
a. c=kn b. k=cn c. n=k/c d. c=k/n
45. It takes Mary 3 hours more to do a job than it takes Jane. If they work together, they can finish the
same job in 2 hours. How long would it take Mary finish the job alone?
a. 3 hrs b. 5 hrs c. 6 hrs d. 8 hrs
46.A car travels 20 kph faster than a truck. The car covers 480 km in two hours less than the time it takes
the truck travel the same distance. How fast does the car travel? a. 44kph b. 60kph c. 80kph d. 140 kph
47. Teacher Linda charges 500.00 per hour tutorial service to a grade-9 students. If she spends 3 hours tutoring per
day, how much would she received in 20 days? a. 300 b. 3000 c.30000 d. 300000
48. Simplify (5a2b)(3a-3b4). a. 15ab b. 15a/b5 c. 15b5/a d. 15a5b
49. Luis walks 5 kilometers due to east and 8 kilometers due north, how far is he from the starting point?
a. √89 b. √64 c.√39 d. √25
50. Any real numbers that is raised to zero exponent is equal to 1_____.
a. Constant b. flexible c. theorem d. Postulate
51. Find the length of an edge of a cube whose area is 72 m 2. a.6√2 m b. 6√12 m c.2√3 m d. √2 m
52. What is the simplified form of √3 divided by 4
3? a. √3 b. 4
3 c. √27 d. 4
27
53. Simplify 2√3+8√3-5√3. a. -√3 b. 5√3 c.11√3 d. 21√3
54. What is the equivalent of 3 4 + 5 2 using exponential notation?
a. 41/3+21/5 b. 43+25 c. 68 d. 61/8
55. What is the equation of a relation s varies directly as the square of v, and inversely as square
root of t? a. s= kv2/t1/2 b. v= ks2/t1/2 c. t= kv2/s1/2 d. s= kt2/v1/2
2
56. What is the sum of the roots of the quadratic equation 2x +6x-14=0?
a. -7 b. -3 c. -6 d. -14
57. The length of the swimming pool is 8 cm longer than its width and the area is 105 m 2, what
mathematical phrase can represent the situation?
a. w(8-w)=105 b.(w+7)(w-5)=105 c. w(w+8)=105 d. (w+15)(w-7)=105
58. What number must be added to the expression t2 + 10t + ____ to make it a perfect square trinomial?
a. 10 b. 20 c. 25 d. 100
59. The graph of y= x +5 is obtained by sliding the graph of y= x2
2

a. 5 units downward b. 5 units upward c. 5 units to the right d. 5 units to the left
60.What are the dimensions of the largest rectangular field that can be enclosed with 100 m of
wire? a.24 m x 26 m b. 25 m x 25m c. 50 m x 50 m d. 50m x 25 m