Download 1. Evaluate the expression without using a calculator. [A] [B] [C] [D] 2

1. Evaluate the expression without using a calculator.
1
3 
27
[A] 
1
81
[B] 
1
27
[C]
1
9
[D] 
1
3
2. Multiply or find the special product.
c3x  y h
5 3
[A] x 3  9 x 2 y 5  18xy10  3y15
[B] 27 x 3  27 x 2 y 5  9 xy10  y15
[C] 27 x 3  y15
[D] 27 x 3  9 x 2 y 5  3xy10  y15
3. Identify the number written in decimal form.
130
.  102
[A] 13
[B] 1300
[C] 0.013
[D] 130
4. Since 1993, Isabel Rueda has owned a franchise of take-out restaurants called Cookies Galore.
The number of customers C, in thousands, that Cookies Galore has served each year is
C  t 2  36t  600
where t is the number of years after 1993. Using this model, estimate the number of customers
served in 1999.
[A] 852
[B] 852,000
[C] 828,000
[D] 1,902,000
5. Find the distance between the points.
F
I and  5 0
G
H0 3J
K
d
[A]
i
34
[B] 8
[C] 34
[D] 2 2
6. Identify the polynomial written in standard form.
 6x 4  12 x 5  10x 5
[A] 10x 5  6x 4  12 x 5
[B] 
6 12
 5  10 x 5
4
x
x
[C] 10x 5  6x 4  12 x 5
[D] not a polynomial
7. Write the expression as a single radical. Then simplify your answer.
b g
72 x  1
b g
[A] 5 2 x  1
[B]
[C]
b g
6b
x  1g
 3
54 2 x  1
4
b g
[D] 6 x  1 3
8. Write the rational expression in simplest form.
 9x
x  x2
[A]
9
, x  0, x  1
x 1
[B] 
[C]
9
, x  0, x  1
x 1
9
, x  0, x  – 1
x 1
[D] 
9
, x  0, x  – 1
x 1
9. Which equation is correct?
[A]
 2  2x
 1 x
2
[B] 6 
x
1
 6
2x
x
[C]
 2  6x
 1  6x
2
[D]
6  6x
 6 x
6
10. Evaluate the expression for the given value of x.
x2  4
for x  11
8  x3
[A] 
[B]
1
9
13
3
[C] 
13
147
[D] None of these
11. Perform the operations and identify the result written in standard form.
2t 3 5t 4  6t 2  4t  1
c
h
[A] 10t 7  2t 5  4t 4  t 3
[B] 10t 12  12t 6  10t 3
[C] 7t 7  8t 5  2t 4  t 3
[D] 10t 7  12t 5  8t 4  2t 3
12. Identify which of the following is an example of the Commutative Property of
Multiplication.
[A] 93  39
[B] 93  39
b g
[D] 9 b
34gb
 93g
4
[C] 4  9  3 4  9  4  3
13. Find the domain of the expression.
5
11  x
[A] All real numbers x such that x  0
[B] All real numbers x such that x  5
[C] All real numbers x such that x  11
[D] All real numbers x such that x  – 11
14. Find the midpoint of DE .
y
10
D
–10
E
10 x
–10
b g
[B] b
– 1, 2g
[C] b
– 2, 1g
[D] b
2, – 1g
[A] 1, – 2
15. Perform the operation(s) and simplify.
x
2

2
x  4 4  x2
[A]
x2
x2
[B]
1
x2
[C]
1
x2
[D]
x2
x2
b g
16. Determine the quadrant in which x , y is located so that the conditions are satisfied.
x  0 and y  0
[A] Quadrant I
[B] Quadrant II
[C] Quadrant III
[D] Quadrant IV
17. Factor by grouping.
3x 3  5x 2  18x  30
b gb g
[B] b
x  6g
b3x  5g
[C] c
x  6h
b3x  5g
[D] c
x  6h
b3x  5g
[A] x  6 3x  5
2
2
18. Identify the verbal description of the interval.
2, 4
b g
[A] All real numbers greater than or equal to 2 and less than 4
[B] All real numbers greater than 2 and less than 4
[C] All real numbers greater than 2 and less than or equal to 4
[D] All real numbers greater than or equal to 2 and less than or equal to 4
19. Simplify the expression.
– 2 7  3 64  2 63
[A] – 20 7
[B] 4 7  24  2 63
[C] 4 7  24
[D] – 3 134
20. Find the domain of the expression.
2x2
[A] All real numbers x such that x  0
[B] All real numbers x such that x  2
[C] All real numbers
[D] All real numbers x such that x  0
21. Completely factor the expression.
9 x 2  16 y 2
b gb g
[B] b
3x  4 yg
b3x  4 yg
[C] b
3x  4 yg
b3x  4 yg
[D] b
3x  4 y g
[A] 3x  4 y 3x  4 y
2
b g b
g
22. Find the midpoint of the line segment connecting 13, 17 and – 12, – 18 .
b g
25 35I
[B] F
G
H2 , 2 JK
1
1I
[C] F
,  J
G
H2 2 K
[D] b
1, – 1g
[A] – 1, 1
23. On a street map, the side of each square represents 1 mile. The local Q-Mart is located at
1, 2 , and the Circle Cineplex is located at 9, 8 . A diagonal street runs directly between the
two locations. Approximately how far is it from Q-Mart to Circle Cineplex?
bg
b g

Circle Cineplex



Q-Mart




[A] 14 miles
[B] 100 miles
[C] 10 miles
[D] 20 miles
24. Find the length of the hypotenuse of the triangle.
y
10
10 x
–10
–10
[A] 12.04
[B] 6.4
[C] 4.12
[D] 13
25. Factor the trinomial.
2
8 x  2  12 x  2  4
b g b g
b gb g
[B] 4b
2 x  3g
bx  1g
[C] b
3x  3g
b3x  4g
[D] b
3x  3g
bx  1g
[A] 4 2 x  3 3x  4
26. Write the rational number as the ratio of two integers.
0.54
[A]
27
50
[B]
6
11
[C]
27
25
[D]
27
5
27. Perform the operation(s) and simplify.
12n 2  n  1 12n 2  4n

3n 2  8n  3 1  16n 2
[A]
[B]
[C]
b3n  1gb3n  1g
b1  4ngbn  3g
4nb
3n  1g
b1  4ngbn  3g
4n
1  4n n  3
b gb g
4nb
3n  1g
[D]
b1  4ngbn  3g
28. Factor the trinomial.
f  g w2  4 w f  g  21 f  g
b g
b g b g
bf  ggbw  3gbw  7g
[B]  b
f  gg
cw  4w  21h
[C] b
w  3g
bw  7g
[D] b
f  gg
bw  3gbw  7g
[A]
2
29. Perform the operation and simplify the expression.
4
ex j
4
3
[A] x 3
[B] x 12
[C] x 4 3
[D] x 16 3
30. Rationalize the denominator of the expression. Then simplify the answer.
6
9– 6
[A]
12
29
[B]
18 + 2 6
25
[C]
6 6
9 6 –6
[D]
54 + 6
75
31. Perform the operation and simplify.
x 1 5  x 1 2
[A]
1
x
7 10
[B]
1
x
1 10
[C] x1 10
[D] x 7 10
32. Leslie is on a mountain 11,224 feet above sea level. Jon is in a submarine 3703 feet below
sea level. Which of the following can be used to find the difference between Leslie’s elevation
and Jon’s elevation?
[A] 11,224  3703
b g
[B] 11,224  – 3703 
[C] – 3703  11,224
[D] 3703  11,224
33. Find the product written in scientific notation.
d3.7  10 id4.6  10 i
– 20
25
[A] 8.3  105
[B] 1702
.
 106
[C] 1702
.
 105
[D] 8.3  104
34. Simplify by removing all possible factors from each radical.
18
[A] 2 3
[B] 3 2
[C] 6 3
[D] 3 6
35. Multiply or find the special product.
b3x  2 yg
2
[A] 9 x 2  12 xy  4 y 2
[B] 9 x 2  4 y 2
[C] 9 x 2  6xy  4 y 2
[D] 9 x 2  10 xy  4 y 2
36. Identify the polynomial written in standard form.
[A]  2  2 x 2  4 x 6  5x
[B]  5x  2  4 x 6  2 x 2
[C] 4 x 6  2 x 2  5x  2
[D] 2 x 2  4 x 6  5x  2
37. A rectangular garden, with length three times its width, is being expanded so that the length
of each side is increased by 7 yards.
7
x
3x
7
Find a polynomial in standard form that could represent the area of the new garden.
b gyd
[B] b
8x  28gyd
[C] c
3x  14 x  49hyd
[D] c
3x  28 x  49hyd
[A] 4 x  14
2
2
2
2
2
2
38. Identify the missing factor which, if placed in the parentheses, would make the equation true.
b1  xg  3b1  xg  b1  xgb g
32
12
12
b g 3
[B] b
1  xg 3
[A] 1  x
32
3
[C]  x  2
[D]  x  2
Factor out the common factor.
39. 25x 3  35x 5
c
h
c
h
[A] x 3 25  35x 2
[B] 5x 2 5x  7 x 4
c
[C] 5 5x 3  7 x 5
c
[D] 5x 3 5  7 x 2
h
h
40.
1 8 1 7
2
4
x  x + x6  x4
5
5
5
5
[A]
1 4 4
x x  x3  2x2  4
5
c
1
1
2
4I
F
G
H5 x  5 x + 5 x  5J
K
x c
x  x  2 x  4h
[B] x 4
[C]
[D]
h
4
4
4
c
3
3
2
2
1 4 4
x x  x3  2x2  4
5
h
41. Identify which of the following numbers are natural numbers.
5
1
2, ,– 5,4 ,6,0.3, 7 ,
8
2
[A] 4,6
[B] 2, 7
[C] 2,6
[D]
1
7 ,6, ,2
2
42. Rationalize the numerator of the expression. Then simplify the answer.
8– 6
6
[A]
29
24 + 3 6
[B]
8 6–6
6 6
[C]
35
18
[D]
58
48 + 6
43. Simplify the expression.
F
5x I
G
H4 x J
K
3
–2
3
[A] 25x
[B]
25
16 x 12
[C] 16x12
[D]
16 x 12
25
44. Insert the required factor in the parentheses.
5x  3
1
=
10 x  6
2
2
x2  x  6
x2  x  6
c
h
bg
c
b
h
g
[A] x 2  x  6
[B]
1
2
[C] 2
[D] None of these
45. A highway map of Ohio has a coordinate grid superimposed on top of the state. Cincinnati is
at point – 3, 1 and Dayton is at point 7, 5 . The Cincinnati R.O.T.C. group is going to Dayton
to see Wright Patterson Air Force Base. The map shows a highway rest area halfway between the
cities. What are the coordinates of the rest area? What is the distance between Cincinnati and
Dayton? (one unit = 4.09 miles)
b g
bg
bg
[A] Rest area = 2, 3
Dayton = 44 miles
bg
[B] Rest area = 5, 2
Dayton = 18 miles
b g
[C] Rest area = 5, 2
Dayton = 29 miles
bg
[D] Rest area = 3, 2
Dayton = 37 miles
46. Identify the rule of algebra illustrated by the equation.
11  0  11
[A] Additive Identity Property
[B] Distributive Property
[C] Associative Property of Addition
[D] Commutative Property of Addition
47. Simplify the complex fraction.
3
2
 2
x  4 x  21 x  2 x  63
3
1
 2
2
x  12 x  27 x  x  42
2
[A]
[B]
[C]
[D]
b3x  2gb5x  1g
2b
x  2g
b2 x  7g
2b
x  2g
b2 x  7g
b3x  2gb5x  1g
b5x  33gbx  6g
4 x 2  9 x  99
4 x 2  9 x  99
5x  33 x  6
b
gb g
48. Insert the required factor in the parentheses.
x2
x2
25x 2 9 x 2
=


4
16
b gb g
[A]
16 4
,
9 25
[B]
4 16
,
25 9
[C]
1 1
,
25 9
[D]
1 1
,
4 16
49. Use inequality notation to describe the set.
Peter earned $51 or more.
[A] t  51
[B] t  51
[C] t  51
[D] t  51
50. Completely factor the expression.
25t 2  60t  36
b gb g
[B] b
5t  6g
b5t  6g
[C] b
5t  6g
[D] b
5t  6g
[A] 5t  36 5t  1
2
2
51. Evaluate the expression for the given value of x.
2
for x  2
– 3 x
3
IJ
b gF
G
HK
[A] 
1
4
[B] 1
[C] 4
[D] 2
52. Write the rational expression in simplest form.
x 2  2 x  24
5x 2  80
[A]
x4
, x6
5 x6
[B]
x6
, x4
5 x4
[C]
x4
, x6
5 x6
b g
b g
b g
[D]
x6
, x4
5 x4
b g
53. Identify the expression that corresponds to the distance shown by the bar.
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
x
bg
[B] 5  b
– 2g

[C] – 5  b
– 2g

[D] – 5  b
– 2g
[A] – 5  – 2
54. Simplify the complex fraction.
c9 – x h  7x c9 – x h
2 1/ 2
2
2 1/ 2
9 – x2
[A]
[B]
[C]
9  9x2
c9 – x h
2 3/ 2
1 7x2
c9 – x h
2 3/ 2
9  6x 2
c9 – x h
2 3/ 2
[D] None of these
b gb g
b g
55. Identify the graph of the points A 3, 0 , B 2, 3 , and C 0, 2 .
[A]
y

A

 x
C
B

[B]
y

A
B
C

 x

[C]
y

C
 B
 x
A

[D]
y

C
B
A

 x

56. Factor by grouping.
5x 7  15x 5  2 x 3  6x
c
hc h
xc
5x  2h
cx  3hbx  2g
[A] x 5x 4  2 x 2  3
[B]
4
2
c
hc h
xc
5x  2 h
cx  3hbx  2g
[C] x 5x 4  2 x 2  3
[D]
4
2
57. Perform the operations and identify the result written in standard form.
3x  5 2 x  4
b gb g
[A] 6x 2  22 x  21
[B] 6x 2  22 x  20
[C] 6x 2  2 x  21
[D] 6x 2  21x  20
58. Evaluate the expression.
2 – 2 – 5– 2
[A]
100
21
[B]
100
29
[C]
29
100
[D]
21
100
Reference: [2.3.30]
[1] [D]
Reference: [3.3.54]
[2] [B]
Reference: [2.2.25]
[3] [D]
Reference: [3.4.58]
[4] [B]
Reference: [7.2.106]
[5] [D]
Reference: [3.1.45]
[6] [D]
Reference: [2.6.42]
[7] [B]
Reference: [5.2.81]
[8] [A]
Reference: [6.1.94]
[9] [A]
Reference: [1.4.14]
[10] [C]
Reference: [3.2.49]
[11] [D]
Reference: [1.5.17]
[12] [B]
Reference: [5.1.77]
[13] [D]
Reference: [7.3.110]
[14] [D]
Reference: [5.3.85]
[15] [C]
Reference: [7.1.102]
[16] [C]
Reference: [4.4.73]
[17] [D]
Reference: [1.2.6]
[18] [B]
Reference: [2.4.34]
[19] [C]
Reference: [5.1.78]
[20] [C]
Reference: [4.2.66]
[21] [C]
Reference: [7.3.109]
[22] [C]
Reference: [7.4.114]
[23] [C]
Reference: [7.2.105]
[24] [D]
Reference: [4.3.70]
[25] [B]
Reference: [1.1.2]
[26] [B]
Reference: [5.3.86]
[27] [B]
Reference: [4.3.69]
[28] [A]
Reference: [2.3.29]
[29] [A]
Reference: [2.5.37]
[30] [B]
Reference: [2.6.41]
[31] [A]
Reference: [1.3.9]
[32] [B]
Reference: [2.2.26]
[33] [B]
Reference: [2.4.33]
[34] [B]
Reference: [3.3.53]
[35] [A]
Reference: [3.1.46]
[36] [C]
Reference: [3.4.57]
[37] [D]
Reference: [6.1.93]
[38] [C]
Reference: [4.1.62]
[39] [D]
Reference: [4.1.61]
[40] [A]
Reference: [1.1.1]
[41] [C]
Reference: [2.5.38]
[42] [A]
Reference: [2.1.21]
[43] [D]
Reference: [6.2.97]
[44] [B]
Reference: [7.4.113]
[45] [A]
Reference: [1.5.18]
[46] [A]
Reference: [5.4.89]
[47] [C]
Reference: [6.2.98]
[48] [B]
Reference: [1.2.5]
[49] [B]
Reference: [4.2.65]
[50] [C]
Reference: [1.4.13]
[51] [C]
Reference: [5.2.82]
[52] [D]
Reference: [1.3.10]
[53] [C]
Reference: [5.4.90]
[54] [C]
Reference: [7.1.101]
[55] [D]
Reference: [4.4.74]
[56] [A]
Reference: [3.2.50]
[57] [B]
Reference: [2.1.22]
[58] [D]