Download math 0310 review for test #3 (10.1 – 10.7)

MATH 0310
REVIEW FOR TEST #3 (10.1 – 10.7)
1. Find all square roots of the given numbers.
a) 324
b) 529
2. Simplify.
361
a) 
9
c) 8100
b)  5  3125
c)
d)
0.0064
3

64
125
3. Identify the radicand and the index for each expression.
a
a)  7 y 2  8
b) a 2 b 3 3 2
a b
4. Given pz   2 z 2  20 . Find the following values p(4), p(3), p(-5), p(0).
5. Simplify.
4 x 2  28x  49
a)
4
b)
5a 4
c)
e) 4 x  2
d)  3  216z 3 w18
8
6. Determine the domain of each function.
a) f  x   4 2 x  5
f)
5

y 22
32 10 25
a b
243
b) g h   3 7  3h
7. Write an equivalent expression using radical notation.
a) x 3 y 3 
1
b)  81
4
3
c) 125z 
2
2
3
8. Write an equivalent expression with positive exponents and, if possible, simplify.
a) 5 xy
5
1
b)  
 16 
6
3
4
c) 3
5
2
a 3b
7
3
9. Use the laws of exponents to simplify. Do not use negative exponents in any answers.
a) 13
2
3
 13
1
2
b)
7.8
3
14
7.8
1
2
c)  27 3 


7
3
2
10. Use rational exponents to simplify. Do not use fractional exponents in the final answer.
a)
4
a12
b)
 xy 
7
14
c)

8
2x

6
d)
5 4
z
e)
xy
3
2
4
18
11. Multiply.
a)
5
w  y  w  y  
b)
c)
81t 2 5 3t 
7
x  7 7 18

3
x4
12. Simplify by factoring.
a) 90
b)
4
64
c)
3
 81a 6 b 2
d)
5
243a11 z 8
13. Find the simplified form of f x   5 x 2  10 x  5 . Assume that x can be any real number.
14. Simplify. Assume that no radicands were formed by raising negative numbers to even powers.
a)
5
 32m 7 n11
b)
3
 80d 14
15. Multiply and simplify.
75a 9 75a 8
a)
b) 4 12 z 3 w7
c)
5
4
x 3 b  c 
4 z 2 w5
6 5
x 4 b  c 
4
16. Simplify. Assume all variables represent positive numbers.
49
y2
a)
b)
3
54a 5
b6
17. Divide and, if possible, simplify. Assume all variables represent positive numbers.
96a 4 b 2
3
a)
12a 2 b
3
75xy
b)
3 3
3
c)
x3  y3
x y
3
18. Perform the indicated operation. Simplify. Assume all variables represent nonnegative real numbers.
a) 5 12  16 27
b)
3
6 x 4  3 48x
c)
4x  4  x 3  x 2
d)
2 3 10  2 2
e)

3
a

3

a 2  3 24a 2



g)

y  3x
h)

m 4 n 2 m 3 n
i)

53 9
f) 3  2 7 3  2 7
3


2


3
25  3 3


19. Rationalize each denominator.
6
a)
4
3x 3
b)
3
10ab 2
72a 3 b
c)
7 3
d)
e)
9
3a
3 7
5 8
4 2
20. Given g  x  
 
a) g 5
2
, find each of the following. Express your answer in simplest form.
x 1
b) g 3 2
21. Solve.
a) 4 y  1  3  0
b) 3x
c)
d)
3
1
2
 12  9
y2  y  7  5  8
x  2  3x  4  2
 
22. Simplify.
a)   125
b)
c) 9  8i   (5  4i)
d) 5  6i 2  5i 
e)  7  2i 
2
23. Write in standard form.
3i
a)
3i
c)
 49  25
b)
3i
4  9i
1  3i
5  2i
24. Find the powers of i .
a) i 71
b) i 52
c) i 44
d) 5i 5  4i 3
25. The tallest structure in the United States is a TV tower in Blanchard, North Dakota. Its height is 2063 feet.
A 2382-foot length of wire is to be used as a guy wire attached to the top of the tower. Approximate to the
nearest foot how far from the base of the tower the guy wire must be anchored.
26. The formula v  2 gh gives the velocity v , in feet per second, of an object when it falls h feet accelerated
by gravity g , in feet per second squared. If g is approximately 32 feet per second squared, find how far an
object has fallen if its velocity is 80 feet per second.
27. Find the distance between each pair of points. Give an exact value.
a) ( - 3, 2) and ( 1, - 3)
b) (1.7, - 3.6) and (-8.6, 5.7)
28. Find the midpoint of the line segment whose endpoint are ( - 3, - 4) and (6, - 8).
REVIEW FOR TEST #3 – Answer Key
MATH 0310
1. a)  18
19
2. a) 
3
b)  23
c)  90
b) 5
c) .08
d) 
4
5
a
and the index is 3
a b
d) not a real number
2
2
d) 6zw6
e)  x  2 
f)  a 2b5
3
3. a) the radicand is y 2  8 and the index is 2 ;
4. a) 2 3
b) not a real number c)
5. a) 2 x  7
8. a)
1
 5xy 
5
b)  ,  
b) 8
7. a)
a3
c)
6
3
10. a) a 3
b) x 2 y 2
11. a) 3 5 t 3
b)
12. a) 3 10
c)
5
4
2
x2  a 2
f) -19
c)
b)
g) y  2 3xy  3x
22. a)  5i 5
1
23. a)  i
3
24. a)  i
b) -729
6
b)
1
7.8
d)
7
20
1
14
e) x12 y 24
z
6  x  7
x4
d) 3a 2 z 5 az 3
c) x  b  c 
2 5
b) 2d 4 3 10d 2
x2
3a 3 2a 2
b2
5 xy
3
3
b)  x  2  6 x
2 4 27 x
x
10  2
20. a)
4
21. a) y  82
2
3
b) 2 zw3 4 3 z
b)
19. a)
7
14. a) 2mn2 5 m2 n
7
y
18. a) 58 3
x3 y 3
7
c) 3a 2 3 3b2
b) 2 4 4
15. a) 75a 8 a
17. a) 2 3 a 2b
b
4
9. a) 13
8x3
13. x  1 5
16. a)
30
c) y11
b) 5a
6. a)  2.5, 
b) the radicand is
c)
3
x 2  xy  y 2
c)  2  x  x  1
d) 6 5  4
h) 2m  11 mn  12n
3 3 9a 2
a
6 2
b)
17
b) No solution
b)
c)
i) 2  3 15  3 225
5a
6a
d) – 1
c) y  5, y  4
b) – 35 c) 4  4i
d) 40  13i
27 12
11 13
b) 

i c)

i
97 97
29 29
25. 1191 ft
b) 1
26. 100 ft
27. a) 41
b) 192.58
c) 1
d)
e) a  2a 3 3
e)
d) x  1
e) 45  28i
i
3

28.  ,  6 
2

20 2  10
7
c) 25 3 z 2
c)
1
27