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QU-Placer Math Sample Test No. 1 Section 1: Elementary Algebra
Answer the following questions:
1. The sum of two negative numbers is always a ______________________ .
(A) Negative number
(B) Positive number
(C) Even number
(D) Odd number
2. Which subset of real numbers contains 3β2 + 1 ?
(A) Irrational Numbers
(B) Rational Numbers
(C) Integers
(D) Whole Numbers
3. Perform the indicated operations and write the answer in the simplest form:
(βπ π2
125Γ·
12π3π
25) Γ β
75π
4π2= π€βπππ π β 0 , π β 0
(A) 5
16 π π
(B) π3
1125 π3
(C) β
9π5π
125
(D) β
5 π2π2
16 π3 π3
2
4. Evaluate 8 + 16 Γ· 4 Γ 5 β 3
(A) 31
(B) 27
(C) 25
(D) 16
5. Evaluate 4 β 5 Β· [5 β (42 β 2)]
(A) 9
(B) 13
(C) 49
(D) 69
6. The statement β81 is the product of a number and three times the same numberβ is
expressed by which of the following equations?
(A) 81 = π₯(π₯ + 3)
(B) 81 = π₯ β 3π₯
(C) 81 = 3π₯(π₯ + 3)
(D) 81 = 3π₯ β 3π₯
7. The solution of the equation 3(π₯ + 1) = π₯ + 2 is:
(A) 2
(B) 1
2
(C) β2
(D) β1
2
8. Which of the following represents the graph of the solution to the inequality
β12 β€ 2π₯ β 4 < 10 ?
(A)
(B)
(C)
(D)
3
9. What is the leading coefficient in the polynomial 1
9π₯3 β
3
2π₯ + 11 ?
(A) β 3
2
(B) 1
9
(C) 3
(D) 11
10. The quotient and the remainder of (π₯5 + π₯2 + π₯ + 1) Γ· (π₯2 β 1) are: _________________ .
(A) Quotient: π₯3 β π₯ + 1 Remainder: 2
(B) Quotient: π₯3 β 2 Remainder: 3
(C) Quotient: π₯3 + π₯ + 1 Remainder: 2π₯ + 2
(D) Quotient: π₯3 + 2π₯ Remainder: 3π₯ + 1
11. Expand the binomial (2π₯ β 3)3
(A) 6π₯3 β 36π₯2 β 54π₯ + 27
(B) 6π₯3 β 18π₯2 + 27π₯ β 27
(C) 8π₯3 β 36π₯2 + 54π₯ β 27
(D) 8π₯3 β 6π₯2 + 6π₯ β 27
12. π₯3 β π₯2 + π₯ β 1 is equivalent to: ______________________ .
(A) (1 β π₯)(π₯2 β 1)
(B) (π₯ β 1)(π₯2 β 1)
(C) (1 β π₯)(π₯2 + 1)
(D) (π₯ β 1)(π₯2 + 1)
13. 2π₯2 + π₯ β 3 = ______________________ .
(A) (2π₯ + 1)(π₯ β 3)
(B) (2π₯ β 1)(π₯ + 3)
(C) (2π₯ + 3)(π₯ β 1)
(D) (2π₯ β 3)(π₯ + 1)
4
14. Factor completely (4π₯2 β 2π₯)
(A) π₯(4π₯2 β 2)
(B) 2(2π₯2 β 2π₯)
(C) 2π₯(2π₯ β 1)
(D) 4π₯(π₯ β 1)
15. Given that π₯
π₯ + 4Γ· πΎ =
π₯ β 4
2 , which expression is equivalent to K ?
(A) 2π₯
π₯2 β 16
(B)
π₯2 β 16
2π₯
(C)
2π₯2
π₯ β 4
(D)
π₯ β 4
2π₯2
16. 8π₯+8π¦
4 Β·
42
48π₯+48π¦=
(A) 7
4(π₯ + π¦)
(B) 7(π₯ + π¦)
4
(C)
7
32
(D)
7
4
17. The LCM (Least Common Multiple) of the polynomials 8π₯2 β 6π₯ β 9 πππ 16π₯2 β 9 is:
(A) (2π₯ β 3)(4π₯ + 3)2(4π₯ β 3)
(B) (2π₯ β 3)(4π₯ + 3)(4π₯ β 3)
(C) (2π₯ β 3)(4π₯ β 3)2
(D) (2π₯ β 3)(4π₯ + 3)2
5
18. Which of the following expressions is equivalent to
2βπ₯
3βπ₯β2 ?
(A) 4π₯ + 4
9π₯ β 4
(B) 4π₯
9π₯ β 4
(C) 6π₯ + 4βπ₯
9π₯ β 4
(D) 6π₯ β 4βπ₯
9π₯ β 4
19. Simplify
(32π₯13π¦18)13
(π₯3π¦3)13
(A) 2π₯π¦ β2π₯π¦3
(B) 2π₯π¦ β2π₯3
(C) 2π₯3π¦5 β4π₯π¦3
(D) 2π₯3π¦5 β4π₯3
20. Simplify 5 β27 β 6 β3
(A) ββ30
(B) ββ24
(C) 9 β3
(D) 9 β6
21. What is the LCD (Least Common Denominator) of the equation
7
π₯ + 2 +
5
π₯ β 2 =
10π₯ β 2
π₯2 β 4 ?
(A) π₯2 β 4
(B) π₯2 β 16
(C) 10π₯ β 2
(D) 12π₯ β 2
6
22. The solution set of the inequality 2 β€ 4π₯ + 6 < 8 is: ______________________ .
(A) [β51
2, β4]
(B) [β4, 2]
(C) [β4, 2)
(D) [β1,1
2)
23. Which of the following equations has 2 and β10 as solutions?
(A) π₯2 β 40π₯ β 20 = 0
(B) π₯2 + 40π₯ β 20 = 0
(C) π₯2 + 8π₯ β 20 = 0
(D) π₯2 + 20 = 0
24. For which value(s) of π does the equation ββπ₯ + 4 β βπ = 0 has a solution.
(A) π = β4
(B) π = 0
(C) 0 < π < 4
(D) π β₯ 4
25. The solution set of the equation 022 234 =+ββ xxxx is ______________________.
(A) }3,1,0,1{ ββ
(B) }2,1,0,1{ ββ
(C) }3,1,0,1{β
(D) }2,1,0,1{β
26. The solution set of the equation 18
π₯β2= 1 +
20
π₯+2 is ______________________ .
(A) {β20, 10}
(B) {8, β10}
(C) {β8, 10}
(D) {20, β10}
7
27. The solution set of the equation |π₯2 + 3π₯ β 2| + |β5| = 7 is ______________________ .
(A) {β4, β3, β1, 0}
(B) {β4, β3, 0, 1}
(C) {β3, β2, 0, 2}
(D) {β3, β1, 0, 4}
28. What is the value of the perimeter of triangle CAR?
(A) 6 + 6β2
(B) 6 + 6β3
(C) 12 + 3β2
(D) 18
29. The midpoint between A(β1, 3) and B(2, a) is βΆ ______________________ .
(A) (β3, 3 β a)
(B) (1, 3 + a)
(C) (β
3
2,3 β a
2)
(D) (
1
2,3 + a
2)
30. For the line 10π₯ + 2π¦ = 6
(A) The slope = β10 and y-intercept = 6
(B) The slope = β5 and y-intercept = 3
(C) The slope = 3 and y-intercept = β5
(D) The slope = 5 and y-intercept = 3
8
Section 2: Pre-Calculus
Answer the following questions:
31. Which of the following is the correct graph of π(π₯) = πππ2(π₯ β 2) β 1 ?
(A)
(B)
(C)
(D)
9
32. Using the graph of the function π shown below, solve π(π₯) > 0.
(A) [β2, β1] βͺ [1,5]
(B) [β2, β1] βͺ (1,5)
(C) (β2, β1) βͺ (1,5]
(D) (β2, β1) βͺ (1,5)
33. If π ππ πΌ = πππ πΌ and πΌ is in the third quadrant, then πΌ is equal to: ______________________ .
(A) π
4
(B) 7π
6
(C) 4π
3
(D) 5π
4
34. The domain of π(π₯) =βπ₯+1
π₯β2 is ______________________ .
(A) [β1, β) (B) (ββ, 2) βͺ (2, β) (C) [β1,2) βͺ (2, β) (D) (ββ, β)
35. If 8π₯ = (
1
2)
2π₯β5 then π₯ = ______________________ .
(A) β5
(B) β1
(C) 1
(D) 5
10
36. If 2π₯ β 31βπ₯ = 0 then π₯ = ______________________ .
(A) π₯ = β
ln 3
ln 3+ln 2
(B) π₯ =
1
ln 3+ln 2
(C) π₯ = β
1
ln 3+ln 2
(D) π₯ =
ln 3
ln 3+ln 2
37. State the domain of the relation {(β10, 9), (6, 0), (β5, 0)}.
(A) Domain = {β10, β5, 0, 6, 9}
(B) Domain = {β10, β5, 0, 6}
(C) Domain = {β10, β5, 6}
(D) Domain = {0, 9}
38. Given the graph of function π(π₯), what is domain of π(π₯)?
(A) [β5,9)
(B) [β5,0) βͺ (0,9)
(C) [β5,0) βͺ (0,4) βͺ (4,9)
(D) [β5,1) βͺ (2,4) βͺ (4,9)
[
11
39. What is the range of the function π(π₯) = log3(π₯2 + 1)?
(A) (0, β)
(B) [0 , β)
(C) (1, β)
(D) [1 , β)
40. Find the inverse of the function ( ) β 8f x x=
(A) 1 2( ) + 8f x xβ = for 8x
(B) 1 2( ) + 8f x xβ = for 0x
(C) 1 2( ) + 8f x xβ = for any real number π₯
(D) 1 1( )
β 8f x
x
β = for 8x
41. If ln 2 = π and ln 3 = π‘ then ln β243
(A) π π‘
(B) π π‘
3
(C) π +
π‘
3
(D) None of the above
[
42. Select the possible graph for the function
π(π₯) = β(π₯ β π)(π₯ β π), if π > 0 and π > 0
(A)
(B)
(C)
(D)
β6 β5 β4 β3 β2 β1 1 2 3 4β1
1
2
3
4
5
6
7
8
9
10
x
y
β1 1 2 3 4 5 6 7 8 9 10
β4
β3
β2
β1
1
2
3
4
5
6
7
8
9
10
x
y
β5 β4 β3 β2 β1 1 2 3 4 5 6
β5
β4
β3
β2
β1
1
2
3
4
5
6
x
y
β3 β2 β1 1 2 3 4 5
β3
β2
β1
1
2
3
4
5
x
y
12
43. If logπ₯ π¦ = 1
2 then logπ₯ π₯ π¦2 = ______________________ .
(A) 1
(B) 2
(C) 3
(D) 4
44. β
cot2 π₯1βcsc π₯
= ______________________ .
(A)
1+cos π₯
cos π₯
(B)
1+sin π₯
sin π₯
(C) β1
(D) 1
45. The graph of the function π(π₯) =π₯3βπ₯
π₯2+4 ππ ______________________ .
(A) Symmetric with respect to the origin
(B) Symmetric with respect to the π₯ β axis
(C) Symmetric with respect to the π¦ β axis
(D) Symmetric with respect to the line π¦ = π₯
46. List all the intervals on which the graph of π(π₯) is decreasing.
(A) (β1,0), (1,2)
(B) (1,2)
(C) (1,0), (2,1)
(D) (1,0)
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
x-axis
y-axis
(-4,-3)
(-2,0)
(-1,1)
(0,0)
(1,2)
(2,1)
(3,4)
f(x)
13
47. If π₯ & π¦ angles are both in the third quadrant and π ππ π₯ = β3
5 and πππ π¦ = β
β3
2 .
Find cos( π₯ + π¦).
(A)
β5β3 β 10
10
(B)
4β3 β 3
10
(C)
β5β3 + 10
10
(D)
4β3 + 3
10
48. Given π(π₯) = 2(π₯ β 1) and π(π₯) = π₯2 + 1 , find the composite function defined by
(π β π)(π₯).
(A) 2π₯2
(B) 2π₯2 β 2
(C) 4π₯2 β 8π₯ + 5
(D) 4π₯2 + 8π₯ + 5
49. To obtain the graph of π(π₯) = (π₯ β 4)2 + 3 , the graph of π(π₯) = π₯2 must be shifted
(A) right 4 units, up 3 units
(B) right 4 units, down 3 units
(C) left 4 units, up 3 units
(D) left 4 units, down 3 units
50. Which angle is co-terminal with 300Β° angle?
(A) 660Β°
(B) 480Β°
(C) 390Β°
(D) 60Β°
51. The solution set to 1 β πππ 2 π₯ = 0 in interval [ 0, 2π] is ______________________.
(A) { π
2 , 2π }
(B) { π
2 , π }
(C) { π
2 , π ,
3π
2 }
(D) { 0 , π , 2π }
14
52. If π(π₯) = π₯2 β 2π₯ + 3 and π(π₯) = |π₯ β 3|, then π(0)
π(1)= ______________________ .
(A) β
3
2
(B) β1
(C)
2
3
(D)
3
2
23
53. The graph of the function π(π₯) = βπ₯3
is ______________________ .
(A)
(B)
(C)
(D)
15
54. The function representing the following graph is ______________________.
(A) π(π₯) = 2π₯ β 2
(B) π(π₯) = β
1
π₯+ 1
(C) π(π₯) = ln (π₯)
(D) π(π₯) =
1
π₯2
55. If π ππ(π₯) = β4
5 and πππ (π₯) < 0 then π ππ(2π₯) = ______________________ .
(A) β
24
25
(B) β
1
25
(C) 1
25
(D) 24
25
56. In which quadrants is π‘ππ π₯ = sin π₯
β1βπ ππ2 π₯ ?
(A) I, II
(B) I, III
(C) I, IV
(D) All Quadrants
57. Which of the following functions is one to one?
(A) π(π₯) = π₯3
(B) π(π₯) = |π₯ + 1| for π₯ β€ 0
(C) π(π₯) = ππ|π₯|
(D) π(π₯) = ππ₯2+ 1
16
58. Using the given graphs, which of the functions has two real zeros?
(A)
(B)
(C)
(D)
59. The graph of the inverse for the function graphed below is ______________________ .
(A)
(B)
(C)
(D)
17
60. The graph of function π is given below
Which of the following is the graph of (π₯) = 1 β π(π₯) ?
A)
B)
C)
D)
18
Answer Key
Section 1 1. A 2. A 3. A 4. C 5. C 6. B 7. D 8. A 9. B 10. C 11. C 12. D 13. C 14. C 15. A 16. D 17. B 18. C 19. D 20. C 21. A 22. D 23. C 24. D 25. D 26. B 27. B 28. A 29. D 30. B
Section 2 31. C 32. C 33. D 34. C 35. C 36. D 37. C 38. B 39. D 40. B 41. C 42. B 43. B 44. B 45. A 46. A 47. B 48. A 49. A 50. A 51. D 52. D 53. C 54. C 55. D 56. C 57. A 58. C 59. B 60. C