Download 1) Simplify the expression. -36 · -11 A) -6 11 B) 6 11 D) 6

Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
A)
2)
1)
Simplify the expression.
-36 -11
-6 11
B) 6
C)
11
D)
-66
6 -11
Evaluate the root without using a calculator or note that root is not a real number.
2)
4
0.0081
A) 81
C) 0.3
3)
4)
5)
D)
Not a real number
Evaluate the root without using a calculator or note that root is not a real number.
3 64
125
A)
-
C)
4
5
4
5
B)
5
4
D)
Not a real number
3)
4)
Identify the pair of like radicals.
A)
- 20 and 8 5
B)
C)
3
D)
7 and 7
8 and 16
-3 32 and 5 48
5)
Simplify the expression.
(-14 - 8x)2
A) 14 + 8x
6)
B) 3
B) 196
C)
- 64x
-14 - 8x
D)
Identify the real and imaginary parts of the complex number.
1
+i
9
A)
Real: 0; imaginary:
1
9
B) Real:
1
; imaginary: 1
9
C)
Real: 1; imaginary:
1
9
D)
1
; imaginary: 0
9
1
Real:
–14 - 8x
6)
7)
7)
Rationalize the denominator.
16
5
8)
A)
16 5
5
B)
256
5
C)
5 5
16
D)
Already rationalized
x+
3
A) y =
9)
(m - x)3
3
m 3 - x3
z
B) y =
z
C) y =
3m - 3x
z
D) y =
(m - x)3
z
10 in.
B) 12
C)
in.
14 in.
D)
D)
81
9)
28 in.
10)
Convert the expression to radical form and simplify.
91/2
9
A) 3
B)
2
C)
11)
yz = m
Find the length of the third side of the triangle by using the Pythagorean theorem.
A)
10)
8)
Solve for y.
Not a real number
11)
Simplify the radical expression.
x 2 y8
A) x2 y8
12)
C)
± xy4
D)
xy4
Simplify the expression. Assume that all variables represent positive real numbers.
3
A)
13)
B) |x|y4
64a15b6
61a12b3
B) 4a5 b2
C)
-4a5 b2
D)
2a3b3
13)
Simplify the expression in terms of i.
-200
A)
12)
10 2i
B) 100i
C)
2
2
10i 2
D)
-10i 2
14)
15)
14)
Simplify.
i42
A) 1
B) –i
D)
–1
15)
x
A) x-1/5
17)
i
Write the expression by using rational exponents rather than radical notation.
5
16)
C)
B) x5
Solve the equation.
3 5x - 2 = x + 26
A) { }
C) x-5
D) x1/5
16)
B) {1}
C)
{1, 7}
D)
{7}
Simplify the expression by using the properties of rational exponents. Write the final
answer using positive exponents only. Assume all variables represent positive real
numbers.
q27/7
17)
q6/7
A) q3
18)
19)
20)
B) q21
C)
q
D) q33/7
18)
Multiply the radical expressions.
(4 6 + 2)(2 10 - 3 8)
A) 32 15 + 8 5 - 192 3 - 12
C) 16 15 - 12
B) –16
D)
16 15 + 4 5 - 48 3 - 12
19)
Simplify the expression in terms of i.
-21
A) i 21
B) 21i
C)
-i 21
D)
–21i
Simplify the expression. Assume all variables represent positive real numbers.
4
4
( 14xy)
A)
4
14xy
B) 14
4
C)
xy
3
14xy
D)
14xy
20)
21)
Simplify the expression by using the properties of rational exponents. Write the final
answer using positive exponents only. Assume all variables represent positive real
numbers.
81s12r-4
21)
3/4
16s-4r4
A)
22)
3s16r8
2
B)
3s12
C)
2r6
27s12
8r6
D)
27s6
8
The amount of time it takes an object dropped from an initial height of h0 feet to reach a
22)
height of h feet is given by the formula
h0 - h
t=
16
An object dropped from the top of the Sears Tower in Chicago takes 9.5 seconds to reach
the ground. Use the above equation to approximate the height of the Sears Tower.
A) 990 feet
B) 1,170 feet
C) 1,520 feet
D) 1,444 feet
23)
24)
23)
Simplify the radical.
132
A)
4 33
B) 2
C)
2 66
D)
33
Cannot be simplified
Simplify the radical. Assume that all variables represent positive real numbers.
24)
99zt 13
A)
25)
B) 9t6
C)
11zt
3t 11zt 11
D)
3t6 11zt
25)
Multiply the radical expressions.
3 24
A)
26)
3zt6 33t
36 2
B) 2
C)
6
6 2
125y7
C)
3 3
26)
Rationalize the denominator.
7
A)
D)
B)
Already rationalized
7 5y
D)
25y4
4
7 125y7
125y7
7 5y
5y3
27)
28)
Multiply. Write the answer in the form a + bi.
(-4 – 9i) (7 + 3i)
A) -1 – 75i
B) -28 – 27i
27)
C)
-55 – 75i
D)
-1
28)
Multiply the radical expressions and simplify your answer.
3
3
3
( 5ab2 )( 2a3 b)( 50a7b10)
3
A) a3b4
29)
B) 5a3 b4
3
4a2 b
C)
3
5a7b6 4b2
3
D) a7b6
4b2
29)
Simplify the expression.
369 369
A)
30)
4a2 b
738
B) 369
C)
38
D)
136,161
On a certain youth league baseball diamond, the bases are 50 ft apart. Assuming home
plate and the three bases form a perfect square, find the exact distance from home plate
to second base. Then round to the nearest tenth of a foot.
A) The distance is 10 3 ft or approximately 17.3 ft.
30)
B) The
distance is 50 2 ft or approximately 70.7 ft.
C) The distance is 5 2 ft or approximately 7.1 ft.
D)
31)
The distance is 10 2 ft or approximately 14.1 ft.
31)
Solve the equation by using substitution.
z4 – 16 = 0
A) {2}
B) {2, -2, 2i, -2i}
C)
{2, -2, 4i, -4i}
D)
{2, -2}
32)
Write the coordinates of the vertex and determine if the vertex is a maximum point or a
minimum point.
f (x) = 15 - (x + 13)2
A) (-15, 13); maximum
B) (13, -15); minimum
C) (-13, 15); minimum
D) (-13, 15); maximum
32)
33)
The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana.
If the distance from Beckett to Vining is 2 miles less than 3 times the distance from
Beckett to Morgana, how far apart are Beckett and Morgana? Round to 1 decimal place.
A) 7.8 miles
B) 5.3 miles
C) 6.9 miles
D) 11.2 miles
33)
34)
Use the discriminant to determine the type and number of solutions.
5x2 + 5x + 2 = 0
A) One rational solution
B) Two rational solutions
C) Two irrational solutions
D) Two imaginary solutions
34)
5
35)
Find the vertex of g(x) =
A)
36)
37)
38)
5 6
,
6 5
6 5
,5 6
C)
-
6 5
,5 6
D)
-
5 6
,6 5
36)
B) {±3,
C)
±4i}
{±3i, ±4}
D)
{± 3, ±4i}
37)
C)
{1, -125}
D)
{1, 25}
38)
Find the x-intercepts of the function.
C)
4x2
– 16x + 16
B) (2,
(2, 0)
1
1
, 0 and - , 0
2
2
D)
0) and (–2, 0)
None.
Find the value of n so that the expression is a perfect square trinomial and then factor the
trinomial.
x2 + 12x + n
A)
n = 36; (x + 6)2
B) n
C)
n = 36; (x + 6)(x - 6)
D)
D)
{1 + 2i 19, 1 - 2i 19}
n = 36; (x - 6)2
40)
{-2 + 2 19, -2 - 2 19)
A catapult is designed to launch circus performers from a raised platform. After launch,
the height of the performer in feet is given by
h(t) = –16t2 + 80t + 32
where t is seconds after launch. After how many seconds is the performer exactly 100
feet above the ground? Round to the nearest tenth of a second.
A) –0.4 and 5.4 seconds
B) 5 seconds
C) 0.5 and 2.8 seconds
D) 1.1 and 3.9 seconds
6
39)
= 144; (x + 12)2
Solve the equation by using the quadratic formula.
w(w - 2) = -20
A) {1 + 19, 1 - 19}
B) {1 + i 19, 1 - i 19}
C)
41)
35)
Solve the equation by using substitution.
z2/3 + 4z1/3 – 5 = 0
A) {1, 125}
B) {4, -4}
A)
40)
B)
Solve the equation.
x4 + 13x2 - 48 = 0
A) {±3, ±4}
h(x) =
39)
62 5
1
x+
- .
3
5
6
41)
42)
43)
44)
Solve the equation by using the square root property.
5y2 + 17 = 3y2 - 179
A) {7 2}
B) {7i, -7i}
C) {7, -7}
42)
D)
{7i 2, -7i 2}
43)
Graph the function.
1
g(x) = (x - 2)2 - 4
4
A)
B)
C)
D)
44)
Solve the equation by using substitution.
(t + 10)2 – (t + 10) – 12 = 0
A) {-6, -13}
B) {6, 13}
C)
7
{4, –3}
D)
{-14, -7}
45)
Graph the parabola. Use the graph to write the domain and range in interval notation.
f (x) = -3(x - 2)2
A) Domain: (- , ); Range: (- , 0]
B) Domain: [- , 2); Range: (- , )
C)
46)
D)
Domain: (- , ); Range: [0, )
45)
Domain: (- , 0]; Range: (- , )
Simplify the radical. Assume that all variables represent positive real numbers.
46)
270z15
3z4
A)
47)
48)
9z5 10z
B) 3z
Solve the equation.
-6 = -2 + (q – 6)1/3
A) {70}
10z9
C)
3 10z11
D)
47)
B) {58}
C)
D)
{-58}
{}
48)
Identify the pair of like radicals.
A)
m m and 5 m
3
B)
C)
4 3
x
4 2
x
D)
and
3z5 10z
8
5t and 3 8t
-5
3 2
y
3
and 2 y2
49)
49)
Rationalize the denominator.
2-4 2
2+1
2 2-8
3
A)
50)
51)
6 2 - 10
D)
6 2 - 10
3
50)
A)
5
B) 125
C)
1
125
D)
Not a real number
51)
Simplify the radical expression.
A)
53)
C)
-5 2
Simplify the expression, if possible.
625-3/4
3
52)
B) 2
(-19)3
-19
Solve the equation.
2x - 5 = 2x - 2
32
A)
81
Solve the equation.
x2 (x2 - 1) = 90
A) {±10, ±3i}
B) -6859
C)
19
D)
6859
52)
B) {
C)
}
{0}
D)
81
32
53)
B) {±
C)
10, ±3i}
{±10, ±3}
D)
{±10i, ±3}
54)
Solve the equation by using the square root property.
3y2 = –120
A) {2i 10, -2i 10}
B) {2 10, -2 10}
C) {2 10}
D) {2i 30, -2i 30}
54)
55)
Solve the inequality.
-x2 – 8x – 16 < 0
A) (- , -4) (4, )
C) (- , )
55)
56)
B) {
D)
}
(- , -4) (-4, )
Write the equation of the axis of symmetry of the parabola.
f (x) = -10(x + 2)2 + 5
A) x = -2
B) x = 5
C) y = 5
9
56)
D)
x=2
57)
A)
58)
57)
Multiply the radical expressions.
-5 y ( y + 10)
–5y + 10
B) -5y2
C)
- 50 y
-55 y
D)
-5y - 50 y
Simplify the radical. Assume that all variables represent positive real numbers.
58)
12x7
A)
59)
2 3x7
C)
3x
2x 3x5
D)
4x6 3x
The formula for the area of a circle is A = r2, where r is the radius. Solve the formula
for r, and use your answer to find the radius of a circle with area 25 feet. Use 3.14 for
and round the answer to the nearest tenth of a foot.
A
A
,r=; 2.8 feet or –2.8 feet
A) r =
B) r =
60)
B) 2x3
A
; 4.0 feet
2
A
C)
r=
D)
r = A - ; 4.7 feet
; 2.8 feet
60)
Simplify the radical.
6 50
35
A)
59)
6 2
B)
6 2
7
C)
10
6 10
7
D)
12
35
Answer Key
Testname: TEST4
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Answer Key
Testname: TEST4
51)
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60)
A
D
B
A
D
A
D
B
C
B
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