Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
1)
f(x) =8x –56
1)
A)
domain of f: [–7, )
B)
domain of f: ( , 7]
C)
domain of f: [7, )
D)
domain of f: ( , –7]
2)
f(x) =21 –3x
2)
A)
domain of f: [7, )
B)
domain of f: ( , –7]
C)
domain of f: [–7, )
D)
domain of f: ( , 7]
3)
f(x) =x +4
3)
A)
domain of f: ( , 4]
B)
domain of f: [4, )
C)
domain of f: [–4, )
D)
domain of f: ( , –4]
3
4)
f(x) =x –2
4)
A)
domain of f: [2, )
B)
domain of f: [–2, )
C)
domain of f: ( , 2]
D)
domain of f: ( , –2]
5)
f(x) =3– x
5)
A)
domain of f: [–3, )
B)
domain of f: ( , –3]
C)
domain of f: ( , 3]
D)
domain of f: [3, )
Simplify the expression. Include absolute value bars where necessary.
6)
3
–64(x – 1)3
6)
A)
–4x + 4
B)
–64x – 1
C)
–4x – 4
D)
–4x + 4
Find the indicated root, or state that the expression is not a real number.
7)
3
–64
7)
A)
4
B)
not a real number
C)
–
34
D)
–4
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
8)
(16x6y6)1/2
8)
A)
4x13/2y13/2
B)
4x11/2y11/2
C)
8x3y3
D)
4x3y3
D
Find the square root if it is a real number, or state that the expression is not a real number.
9)
196
625
9)
A)
49
156
B)
14
25
C)
3
5
D)
7
13
B
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
10)
881x4
10)
A)
3 3x
B)
1
9x
C)
3x
D)
43x
C
D
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
11)
x5/8·x3/8
11)
A)
1
x
B)
x15/64
C)
x
D)
x15/8
Multiply and simplify. Assume that all variables represent positive real numbers.
12)
7( 5 –3)
12)
A)
8 7
B)
35 –21
C)
7 5 + 7 3
D)
56
B
Find each product. Write the result in the form a +
bi.
13)
(5 – 4i)(5– 6i)
13)
A)
1+ 50i
B)
1– 50i
C)
49 + 10i
D)
24i2– 50i + 25
B
Rationalize the denominator.
14)
3
26 +5
14)
A)
326 +15
B)
326 –15
C)
326 +15
52
D)
326 –5
B
C
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
15)
34
54
15)
A)
543
B)
15 16
C)
4316
D)
15 4
Divide and, if possible, simplify.
16)
630x7
10x5
16)
A)
3x67
B)
3x 70
C)
x63
D)
3x 7
Rewrite the expression with a positive rational exponent. Simplify, if possible.
17)
27
64
–1/3
17)
A)
–3
4
B)
4
3
C)
–4
3
D)
3
4
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
18)
–332x+ 6 98x
18)
A)
30x 2
B)
54x 2
C)
30 2x
D)
–54 2x
8
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
19)
18 ·6
19)
A)
18 6
B)
6 3
C)
324
D)
3 6
Rationalize the denominator.
20)
3
7–2
20)
A)
21 + 3 2
47
B)
21 – 3 2
47
C)
3
7–3
2
D)
21 + 3 2
–5
A
Find the indicated root, or state that the expression is not a real number.
21)
5
–1
21)
A)
1
B)
not a real number
C)
–1
5
D)
–1
D
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
22)
Find the area of the trapezoid given that its height is 2 2 m and the lengths of its bases are 18 m
and 6 m.
22)
A)
12 sq m
B)
(36 +2 3) sq m
C)
(6 +2 3 ) sq m
D)
(6 +4 3) sq m
C
B
Simplify the expression.
23)
(x + 5)2
23)
A)
x2+ 10x + 25
B)
x + 5
C)
5 x
D)
x + 5
Perform the indicated operation. Write the result in the form a +
bi.
24)
7i + (–4– i)
24)
A)
–4+ 6i
B)
4– 8i
C)
4– 6i
D)
–4+ 8i
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
25)
Find the area of a rectangle whose length is 310 meters and whose width is 320 meters.
25)
A)
90 2 sq m
B)
900 2 sq m
C)
90 20 sq m
D)
9200 sq m
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
26)
4 x + 3 ·
4( x + 3)18
26)
A)
4(x + 3)4( x + 3)3
B)
(x + 3)44( x + 3)3
C)
(x + 3)54( x + 3)3
D)
(x + 3)44( x + 3)2
Divide and, if possible, simplify.
27)
3625a4b6
35a
27)
A)
5ab2
B)
5a2b4
C)
5ab235ab
D)
5ab435a2
28)
1440x7
10x
28)
A)
12x310
B)
12x6
C)
12 x7
D)
12x3
Rewrite the expression with a positive rational exponent. Simplify, if possible.
29)
9–1/2
29)
A)
–1
3
B)
1
9
C)
1
3
D)
–3
Solve the radical equation.
30)
5+3x – 5 = x
30)
A)
{10}
B)
{10, 3}
C)
{5}
D)
Simplify the expression. Assume that variables can represent any real number.
31)
x2– 10x + 25
31)
A)
x – 5
B)
–x + 5
C)
x – 5
D)
–x – 5
Solve the problem.
32)
The average height of a boy in the United States, from birth through 60 months, can be modeled by
y = 2.9 x+ 20.1 where y is the average height, in inches, of boys who are x months of age. What
would be the expected difference in height between a child 36 months of age and a child 16 months
of age?
32)
A)
17.4 in.
B)
7.8 in.
C)
46 in.
D)
5.8 in.
Find the indicated function value for the function.
33)
Evaluate f(x) =
3x +5 for f(59)
33)
A)
4
B)
9
C)
4, –4
D)
64
Add or subtract as indicated.
34)
11 14 –23x+ 6 14 – 3 3x
34)
A)
514 – 5 3x
B)
514 +3x
C)
17 14 –3x
D)
17 14 – 5 3x
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
35)
48 –108
35)
A)
–2 3
B)
–2 6
C)
–6
D)
10 3
Solve.
36)
The function T(x) =x
16 models the time, T(x), in seconds, that it takes an object to fall x feet. How
long will it take for a ball dropped from the top of 66–foot building to hit the ground? Leave the
solution in simplified radical form.
36)
A)
8+2
4 sec
B)
8 2
4 sec
C)
66
16 sec
D)
66
4 sec
Divide and, if possible, simplify.
37)
5486x21y17
52xy–3
37)
A)
3x15y15 5x2
B)
3x4y4
C)
3x20y20 52x2y3
D)
3x20y20
Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
38)
(b7)2/7
38)
A)
b1/2
B)
b9/7
C)
b2/9
D)
b2
D
Find each product. Write the result in the form a +
bi.
39)
(8 – 6i)(3+ 5i)
39)
A)
–6– 58i
B)
–30i2+ 22i + 24
C)
54 + 22i
D)
54 – 22i
C
Express the function, f, in simplified form. Assume that x can be any real number.
40)
f(x) =64(x – 1)8
40)
A)
f(x) =8(x – 1)(x – 1)7
B)
f(x) =8(x – 1)4
C)
f(x) =8(x – 1)4
x
D)
f(x) =8(x – 1)4
D
B
Rationalize the denominator and simplify.
41)
34
9x2
41)
A)
3324x2
9x
B)
336x
9x
C)
312x
3x
D)
3324x
81
Rewrite the expression with a rational exponent.
42)
(21xy)3
42)
A)
(21xy)2
3
B)
(21xy)3/2
C)
(21xy)3
2
D)
(21xy)2/3
Rationalize numerator.
43)
35
37
43)
A)
5
335
B)
3245
7
C)
335
7
D)
5
3175
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
44)
3y8
44)
A)
2y 3y2
B)
2y23y2
C)
y23y2
D)
y5
Solve the equation.
45)
x=6
45)
A)
{12}
B)
{–36}
C)
{36}
D)
{6}
Solve the problem.
46)
A manufacturer’s cost is given by C =300 n1/3 + 200, where C is the cost and n is the number of
parts produced. How many parts are produced when the cost is $4100?
46)
A)
2197 parts
B)
17,576 parts
C)
3900 parts
D)
169 parts
Simplify the expression. Assume that variables can represent any real number.
47)
252x2
47)
A)
6x 7
B)
7 x 6
C)
6 x 7
D)
6x27
Simplify the expression. Include absolute value bars where necessary.
48)
4(–2)4
48)
A)
–16
B)
–2
C)
2
D)
– – 2
Rationalize the denominator and simplify.
49)
3
7x
49)
A)
52x
B)
9 7x
7x
C)
3 7x
D)
3 7x
7x
Perform the indicated operation. Write the result in the form a +
bi.
50)
(3 + 4i) – (–4+ i)
50)
A)
–1+ 5i
B)
7+ 5i
C)
–1+ 3i
D)
7+ 3i
Find the square root if it is a real number, or state that the expression is not a real number.
51)
12 + 4
51)
A)
16
B)
4
C)
2 3 –2
D)
not a real number
B
Use the product rule to multiply.
52)
3 x
27 ·327
y
52)
A)
1
3
3 x
y
B)
3 x
y
C)
33 x
y
D)
6 x
y
B
Evaluate.
53)
i27 +i23
53)
A)
–2i
B)
2
C)
–2
D)
0
A
Divide and, if possible, simplify.
54)
340x6
35x2
54)
A)
x32x
B)
2x 3x
C)
2x
D)
2x 3x2
B
D
Use radical notation to rewrite the expression. Simplify, if possible.
55)
163/2 +275/3
55)
A)
69
B)
288
C)
307
D)
1361
6
Find the indicated root, or state that the expression is not a real number.
56)
31000
56)
A)
–10
B)
10
C)
310
D)
30
Provide an appropriate response.
57)
Let f(x) =2x – 9. Find f(17).
57)
A)
34
B)
25
C)
34
D)
5
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
58)
Find the area of the trapezoid.
2847 ft
611 ft
7 7 ft
58)
A)
87 77 sq ft
B)
87 11 sq ft
C)
406 77 sq ft
D)
174 77 sq ft
Perform the indicated operation. Write the result in the form a +
bi.
59)
–36 · – 4
59)
A)
12
B)
–12i
C)
–12
D)
12i2
Solve.
60)
The radius needed to create a sphere with a given volume V can be approximated by the equation r
= 0.62(V)1/3. Find the radius of a sphere with a volume of 64 cubic meters. Round the answer to the
nearest hundredth.
60)
A)
3.41 m
B)
13.23 m
C)
2.48 m
D)
4.96 m
C
Use the product rule to multiply.
61)
66x2y3·
66x3y2
61)
A)
636x5y3
B)
6x5y5
C)
66x5y5
D)
636x5y5
D
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
62)
x4y7
62)
A)
x2y2x2y5
B)
xy y3
C)
x2y3y
D)
x27y
C
Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a
real number and does not exist, state so.
63)
Evaluate g(x) = – x +13 for g(–4)
63)
A)
not a real number
B)
–3
C)
3
D)
–1.73
B
18
C
Solve the equation.
64)
2x + 1 =7
64)
A)
{–24}
B)
{48}
C)
{12}
D)
{24}
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
65)
12 32– 3 354
65)
A)
–332
B)
332
C)
932
D)
12 32– 3 354
66)
5 8 – 4 72 – 9 98
66)
A)
5 2
B)
16 2
C)
–77 2
D)
–16 2
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
67)
97xy
67)
A)
16 xy
B)
63 (xy)2
C)
2xy
D)
63 xy
Provide an appropriate response.
68)
Evaluate: 25–3/2
68)
A)
–125
2
B)
–1
125
C)
1
125
D)
–125
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
69)
7( 5 + 3 14)
69)
A)
35 – 21 2
B)
35 + 3 98
C)
35 – 3 98
D)
35 + 21 2
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
70)
3100 ·
3100
70)
A)
310,000
B)
310
C)
10 3100
D)
10 310
D)
Simplify the expression. Include absolute value bars where necessary.
71)
5
–100,000x5
71)
A)
10x
B)
–10 x
C)
– – 10 x
D)
–10x
D)
Solve the radical equation.
72)
(4x – 2)1/3 + 6 = – 4
72)
A)
– 7
B)
51
2
C)
D)
–499
2
D)
Solve.
73)
If a number is subtracted from 57, the principal square root of this difference is equal to the number
decreased by 1. Find the number(s).
73)
A)
8
B)
–7, 8
C)
–8
D)
–7
D)
20
D)