ALGEBRA 1

REAL NUMBER SYSTEM 10. Find the 4, 388th digit to the right of the decimal when 218, 107 is
1. Which of the following is not an irrational number? divided by 333, 333.
a. e b.  c. 2 9 d.ALL a. 3 b. 4 c. 5 d. 6
SIGNIFICANT FIGURES
2. If x is odd and y is even and x is a factor of y, which of the
11. The number 3,032 has
following is false?
a. 1 SF b. 2 SF c. 3 SF d. 4 SF
a. y/x is even b. xy is even c. 2x + y is even d. x + 2y is even
12. The number 55, 100 has
3. A rational number divided by an irrational number is a/an
a. 3 SF b. 4 SF c. 5 SF d. 6 SF
a. fraction b. irrational c. rational d. complex
13. The number 0.000028040 has
4. When two fractions are added, which of the following is not
a. 4 SF b. 5 SF c. 9 SF d. 10 SF
possible?
14. The number 403,520.000 has
a. integer b. fraction c. mixed fraction d. surd
a. 6 SF b. 4 SF c. 5 SF d. 9 SF
5. A fraction is also a/an
15. Round off 3,429 to two significant figures.
a. integer b. irrational no. c. rational no.d. natural no.
a. 3,400 b. 3,400 c. 3,420 d. 3,500
6. Which of the following is not a real number?
a. surd b. complex number
MULITPLE AND DIVISOR
c. irrational number d. negative number
16. Which of the following is a prime number?
7. Given the following statements:
a. 51 b. 81 c. 71 d. 91
i) The sum of any two positive integers is a positive
17. Which of the following is a composite number?
integer.
a. 947 b. 1,039 c. 1, 007 d. 1, 151
ii) The sum of any two negative integers is a negative
18. Which of the following is the largest prime factor of 759?
integer.
a. 3 b. 29 c. 23 d. 11
iii) The product of any two negative integers is a
19. Find the greatest common factor of 36 and 64.
negative integer.
a. 4 b. 2 c. 8 d. 9
iv) The quotient of any two negative integers is a
20. Find the least common multiple of 32 and 68.
negative integer.
a. 1, 088 b. 2, 176 c. 272 d. 544
Which is correct?
21. Find the product of the GCF and LCM of 162 and 252.
a. one statement is true b. two statement is true
a. 20,412 b. 81,648 c. 40,824 d. 13,608
c. three statement is true d. four statement is true
22. The GCF and LCM of two numbers are 25 and 150 respectively. If
8. The number 0.38444… equals
one of the numbers is 75, find the other number.
a. 317/450 b. 371/450 c. 173/450 d. 137/450
23. What is the sum of the prime factors of 15, 351?
9. The fractional equivalent of 0.6383838…as a mixed fraction is
a. 69 b. 67 c. 70 d. 71
a. 613 b. 631 c. 316 d. 361
24. What is the sum of all factors of 192?
a. 507 b. 508 c. 316 d. 315
 25. What is the sum of all factors of 1,386? 41. Which of the following is equivalent to 5x+2 + 3(5x+1) – 40(5x)?
a. 2,357 b. 3,049 c. 3,744 d. 3,669 a. 3(5x) b. -2(5x) c. 0 d. 5x
2 2
26. A composite number is divided by a prime number. The quotient 42. If 5x = 7y, what is the value of 5x /7y ?
may be a. 25/49 b. 7/5 c. 5/7 d. 49/25
i) a composite number 43. Under certain conditions, the production of people informed
ii) a prime number through advertising after t weeks is
iii) an even integer 200 + 3−2t
iv) an odd integer P(t ) =
Which is correct? 50 − 3(6−25t )
a. one statement is true b. two statement is true What value does P(t) approach as t becomes larger and larger?
c. three statement is true d. four statement is true a. 2 b. 3 c. 4 d. 5
FUNCTIONS 44. The number of bacteria after t hours is 5.6(106)3t/5. How long will it
27. If f(x) = 3x – 2 and g(x) = x+ 1, find (f + g)(2). take for this number to triple?
28. If f(x) = 3x -2 and g(x) = x + 1, find (f – g)(1). a. 4 b. 5 c. 6 d. 7
29. If f(x) = 3x – 2 and g(x) = x + 1, find (fxg)(1). 45. Find the last digit of 3128 + 7535 + 14860.
30. If f(x) = x3– 8 and g(x) == x - 2, find (f/g)(2) RADICALS
31. If f(x) = 3x-2 and g(x) = x2 + 1, find (f o g)(3). 46. Find the principal root of 6
729 x18 y 12
32. If f(5) = 15 in the function f(n) = n + f(n – 1), find f(12).
33. If f(x – 1) = 1 + x2, then what is f(x)? a. 3xy2 b. 3x3y2 c. 3xy d. 3x2y
a. x2 + 2x + 1 b. x2 + 2x + 2 47. Solve for x in the given equation
3
2  4 16 8 x = 2 .
2
c. x -2x -1 d. x2 – 2x – 2
34. Which of the following functions is even? a. 32 b. 16 c. 64 d. 8
2 3 LOGARITHMS
a. f(x) = sin x c. f(x)=x +5x 48. The base of a common or Briggsian logarithm is
b. c. f(x)=sinx d. f(x)=tanx a. 2 b. 1 c. 10 d. e
35. Which of the following functions is odd? 49. The base of a natural, hyperbolic, or Napierian logarithm is
3
a. f(x)=x +3 c. f(x)=cosx a. 2 b. 1 c. 10 d. e
2 50. The whole number part of the logarithm is called
c. f(x)=sinhx d. f(x)=x +3
36. Which of the following functions is periodic? a. mantissa b. antilogarith
c.. cologarithm d. characteristics
a. x -x b. x +x c. cos(1/x) d. xsinx
51. The decimal part of the logarithm is called
37. Find the domain and range of the function f(x) = x−2. a. mantissa b. antilogarithm
38. Find the inverse of f(x)=2x-y. c. cologarithm d. characteristics
EXPONENTS 52. The characteristics of the logarithm of 3209.65 to the base 10 is
39. If 3x=6, what is the value of 34x-1? a. 2 b. -3 c. 3 d. -2
a. 72 b. 432 c. 216 d. 108 53. The characteristics of the logarithm of 0.0078807 to the base 10 is
40. Which of the following is equivalent to 128x32y? a. 3 b. -3 c. 4 d. -4
a. 25x+7y b. 26x+7y c. 27x+5y d. 27x+6y 54. The mantissa of the logarithm of 329.65 to the base 10 is
 a. -0.5181 b. -0.4819 c. -0.4819 d. -0.5181 a. 3 or 0 b. 1 or 2 c. 1 or 0 d. 3 or 1
55. The mantissa of the logarithm of 0.00078807 to the base 10 is 69. Find the sum and product of the roots of the equation 4x 5-
a. -0.8966b. -0.1034 c. 0.1034 d. 0.8966 12x4+5x3+6x2-7X+20=0.
56. The mantissa of the logarithm of 5.0932 to the base 10 is INEQUALITIES
a. 0.2930 b. 0.7070 c.-0.2930 d. -0.7070 70. Find the solution set of 3 − 4 x  2 x + 9
57. The equation ax = y in logarithmic form is 2
71. Solve the quadratic inequality x + 2x – 8 >0.
a. logx a = y b. logx y = a
a. (-  , -4 )  (2 ,  ) b. (-  , -4)  [ 2 ,  )
c. loga y = x d. loga x = y
58. Find the antilogarithm of 8.20189 – 10 b. ( -  , 4)  [-2 ,  ) d. [-  , -4]  [2 ,  ]
a. 0.913 b. -0.9139 c.0.0159 d. -0.0159 72. Solve for x in the compound inequality 3x + 2<14 and 2x-5>-11.
59. Which of the following is the cologarithm of 132 to the base 10? a. X<4 and x>-3 b. x>4 and x>-3
a. 7.8794b. 2.1206 c. -7.7794d. -2.1206 c. x<-3 and x>4 d. x<3 and x>4
60. If logab = 0.25, what is the value of logb a? 73. Solve the inequality 2x + 3<7 or 3x + 5>20.
a. 2 b. 4 c. 6 d. 5 a. (− ,2)  (,5) c. (− ,  )  (3,5)
(− ,2)  (,5) d. (− ,5)  (3,8)
..
x. b.
61. Solve for x in the equation x
xx
=5
62. If log 2 = p and log 3 = q, find the log 1.20. 74. Solve the absolute value inequality: x − 20 >5
a. 2p + q
POLYNOMIAL EQUATIONS
b. 2p c. 2p + q– 1 d. pq – 1 a. − ,15  25,  c. − ,15  25,  
63. Find a quadratic equation whose roots are 3 and -9. b. (− ,15)  (25,  ) d. − ,15  (25,  ]
a. x2 – 6x – 27 = 0 b. x2 + 6x – 27 = 0 75. Solve x − 3  4
2
c. x + 12x – 27 = 0 d. x2 – 12x – 27 = 0
64. If ¼ and -7/2 are the roots of the quadratic equation Ax2 + Bx + C = a. x  −1 and x  7 c. x  -1 or x  7
0, what is the value of B? c. x  −1 and x  7 d. x  −1 or x  7
a. -28 b. 4 c. -7 d. 26
65. Find the sum and product of the roots of the equation 15x 2 + 2x – 76. Solve the absolute value inequality x + 5  −2
8=0 a. -7 or 7 b.-3 or 9 c.-2 or 2 d. No solution
a. 2/15, -8/15 b. -2/15,-8/15 c. 2/15, 8/15 d. -3/2, 4/3 2x − 6
66. Find the value of k in the quadratic equation 7x 2 + (2k + 5)x – 5k + 77. Solve the rational inequality 0
1 = 0 so that the(a)roots are equal & (b) sum and the product of the
x+4
a. (-  , -4) and (3 ,  ) b. (-  , 4) and [3,  )
roots are equal.
c. (-  , -4] and (3,  ) d.(;  , -4] and [3,  )
a. 2 b. -3 c. -2 d. 3
67. In a quadratic equation problem, one student made a mistake in THEORY OF EQUATIONS
copying the coefficient of x2 and got the roots 5 and -3/2. Another 78. If 4x4 – 120x2 + 18 x – 720 is divided by x – 6, compute the
student also made a mistake in copying the constant term and got remainder.
the roots 2/3 and ¼. Find the correct quadratic equation. a. 252 b. 225 c. 525 d. 522
68. How many positive real solutions are there in the polynomial: x 4 – 79. Given f(x) = (x – 3)(x + 5) + 3. When f(x) is divided by (x – k), the
4x3 + 7x2 - 6x – 18 = 0 remainder is k. Find k.
 a. 5 b. 2 c. -3 d. -4 93. z varies directly as x and inversely as the square root of y. It is equal
80. When you divide 2x4 + ax3 – x2 + bx + 1 by x – 2, the remainder is to 3 when x is 13 and y is 16. Find the value of z when x is 52 and y
13. When you divide it by x + 3, the remainder is 223. Find the value is 9.
of a. a. 24 b. 20 c. 25 d. 16
a. 2 b. -1 c. -3 d. 4 94. If x : y : z = 4 : -3 : 2 and 2z + 4y – 3z = 20, find x,y,z
81. Determine the value of k so that (3x + 2) is a factor of (6x 3 – 5x2 – a. -8, 6, -4 b.-5, 4, -6 c.7, -5, 6 d. 9, -4, 5
12x + k). 95. Find the fourth proportional to 33, 22 and 27.
a. 4 b. 2 c. -2 d. -4 a. 21 b. 18 c. 15 d. 20
3 2 2 3
82. Find the remainder if 3x - 4x y + 5xy + 6y is divided by x - 2xy
2 96. Find the third proportional to 16 and 12.
2 a. 9 b. 10 c. 12 d. 15
+3y .
97. Find the mean proportional between 8 and 392.
0 b. 1 c. 2 d. 3
a. 80 b. 72 c. 60 d. 56
BINOMIAL THEOREM
98. The quality of water discharged over a rectangular weir is directly
83. Find the 6th term & middle term in the expansion of
proportional to the crest length and three-halves the power of the
(2x – 3y)6
head (height of water above the crest). If the rate of discharge over
12
 2 2 weir having a crest length of 3 m and a head of 0.70 m is 3.23
84. Find the constant term and term involving x in  x + 
9
m3/sec, find the rate of discharge over weir having a crest length of
 x
6 m and a head of 1.40 m.
85. Find the term in (x – y + z)11 that involves x3y5
a. 18.72 m3/s b. 17.82 m3/s c. 17.28 m3/s d. 18.27 m3/s
a. 9,240x3y5z2 b. 9,240x3y5z3
3 5 3 99. Coulomb’s Law states that the electrical force between two point
c. -9,240x y z d. -9,240x3y5z2
charges varies directly as the product of the charges and inversely
86. The middle term in the expansion of (a3 + 2b2)n is Camb12. Find m.
as the square of the distance between them. If the electrical force
a. 19 b. 20 c. 17 d. 18
between two point charges 25 x 10-9 coulombs and 75 x 10-9
87. Find the sum of the coefficients in the expansion of (2x – 3y)35.
coulombs and 0.03 meters apart is 0.019 N, find the electrical force
a. -1 b. 1 c. -2 d. 2
between two point charges 30 x 10-9 coulombs and 120 x 10-9
88. Find the sum of the coefficients in the expansion of (3x +1)4.
coulombs and 0.10 meters apart.
a. 256 b. 254 c. 255 d. 257
a. 0.0033 N b. 0.0044 N c. 0.0055 N d. 0.0066 N
89. Find the sum of the coefficients in the expansion of (x + y – z)8.
100. The relative of twist between the ends of a solid circular rod varies
a. 3 b. 2 c. 0 d. 1
directly as the product of the applied torque and the length, and
90. Find the sum of the exponents in the expansion of (x + y)3.
inversely as the fourth power of the diameter. If the angle of twist
a. 6 b. 10 c. 8 d. 12
of a circular rod is 2.23 radians, find the angle of twist on another
91. Find the sum of the exponents in the expansion of (2x3 – y5) 7.
rod of the same material when the length, diameter and the
a. 210 b. 224 c. 56
applied torque were halved.
PROPORTION AND VARIATION
a. 4.46 b. 1.12 c. 8.92 d. 0.56
92. If y varies directly as x and is equal to 36 when x is equal to 10, find
the value of y when x is equal to 25.
a. 80 b. 75 c. 60 d.90