Name:
Partners:
Honors Algebra II
Date:
Review 6 Version A
[A] Circle whether each statement is true or false.
T F 1. p 5/3 = (5√p)3
T F 2.m(m -1(h 3)) = h -3
T F 3. (b  n) (x) = b(n(x))
T F 4. (-64)3/2 • (-1)3/2 = 643/2
T F 5. (-64)2/3 • (-1)2/3 = 642/3
T F 6. 2(cos 210° + i sin 210°) is a 12th root of 4096.
T F 7. x 7 = -30 has 7 solutions, none of which are real.
T F 8. If f(g(x)) = g(f(x)) then f and g are inverses of each other.
[B] Simplify without a calculator.
1. 4√2x • 4√8x 3
2.32/3 • 92/3
3.9 3√5 – 6 3√40
4.
[C] Find all real solutions, if any.
1. 3√x = 5
2. 3 (2x – 9)5/3 + 100 = 4
3. 2 (4x + 6)4 + 33 = 1
4. 6x = √3 – 3x
( )
x8
16y 12
-3/2
[D] Find the inverse and simplify. Then identify whether or not the original function is one-to-one.
1. a(x) = x 32.
b(x) = x 3/5
3. c(x) = 3x + 6
4. d(x) = 100x 2
5. e(x) = the number of grams in x kilograms
6. f(x):
5
-5
0
5
-5
[E] Simplify or evaluate. Refer to the functions in part [D].
1. a(x) • b(x)2.
b(c(-10))
3. d(c(x))4.
b(b -1(5k))
[F] Do the following to organize your group’s reviews.
1. Make sure your name and your partners’ names are at the top of your review the first day.
2. Staple the reviews in order, all facing the same way, with the staple in the very top left corner.
Name:
Honors Algebra II
Date:
Review 6 Version B
[A] Circle whether each statement is true or false.
T F 1. p 5/3 = (5√p)3
T F 2.m(m -1(h 3)) = h -3
T F 3. (b  n) (x) = b(n(x))
T F 4. (-64)3/2 • (-1)3/2 = 643/2
T F 5. (-64)2/3 • (-1)2/3 = 642/3
T F 6. 2(cos 210° + i sin 210°) is a 12th root of 4096.
T F 7. x 7 = -30 has 7 solutions, none of which are real.
T F 8. If f(g(x)) = g(f(x)) then f and g are inverses of each other.
[B] Simplify without a calculator.
1. 4√5x • 4√125x 11
3.4 3√7 – 9 3√56
2.45/6 • 165/6
( )
4. x -8y 6
16y 12
-3/2
[C] Find all real solutions, if any.
1. 3√x = 8
2. 4 (2x – 9)5/3 + 77 = 53
3. 7 (5x + 6)4 + 36 = 1
4. 3x = √4 – 9x
[D] Find the inverse and simplify. Then identify whether or not the original function is one-to-one.
1. a(x) = x 102.
b(x) = 7√x 3
3. c(x) = 10x + 5
4. d(x) = 9x 2
5. e(x) = the value (in dollars) of x euros
6. f(x):
5
-5
0
5
-5
[E] Simplify or evaluate. Refer to the functions in part [D].
1. a(x) • b(x)2.
b(c(-10))
3. d(c(x))4.
a -1(a(5k))
[F] Bonus.
1. Use the calculator to find the following, given the inverse of f(x) = 10x is f -1(x) = log x.
a) 10x = 80
b) 102x + 30 = 840
Name:
Honors Algebra II
Date:
Review 6 Version C
[A] Circle whether each statement is true or false.
T F 1. p 5/3 = (5√p)3
T F 2.m(m -1(h 3)) = h -3
T F 3. (b  n) (x) = b(n(x))
T F 4. (-64)3/2 • (-1)3/2 = 643/2
T F 5. (-64)2/3 • (-1)2/3 = 642/3
T F 6. 2(cos 210° + i sin 210°) is a 12th root of 4096.
T F 7. x 7 = -30 has 7 solutions, none of which are real.
T F 8. If f(g(x)) = g(f(x)) then f and g are inverses of each other.
[B] Simplify without a calculator.
1. 4√27x 13 • 4√243x 7
3.7 3√2 – 5 3√54
2.163/5 • 643/5
( )
4. x -8y -1
16y 11
-3/4
[C] Find all real solutions, if any.
1. 3√x = 27
2. 3 (2x – 9)5/4 + 100 = 4
3. 7 (5x + 6)3 + 36 = 1
4. 5x = √18 – 15x
[D] Find the inverse and simplify. Then identify whether or not the original function is one-to-one.
1. a(x) = x -72.
b(x) = 7√x 9
3. c(x) = 3x + 5
4. d(x) = 5x 2
5. e(x) = how many marbles fit into x bags
6. f(x):
5
-5
0
5
-5
[E] Simplify or evaluate. Refer to the functions in part [D].
1. a(x) • b(x)2.
b(c(-10))
3. d(c(x))4.
d(b -1(b(5k)))
[F] Bonus.
1. Use the calculator to find the following, given the inverse of f(x) = 10x is f -1(x) = log x.
a) 10x = 6146
b) 102x – 1 + 30 = 840
Name:
Honors Algebra II
Date:
Review 6 Version D
[A] Circle whether each statement is true or false.
T F 1. p 5/3 = (5√p)3
T F 2.m(m -1(h 3)) = h -3
T F 3. (b  n) (x) = b(n(x))
T F 4. (-64)3/2 • (-1)3/2 = 643/2
T F 5. (-64)2/3 • (-1)2/3 = 642/3
T F 6. 2(cos 210° + i sin 210°) is a 12th root of 4096.
T F 7. x 7 = -30 has 7 solutions, none of which are real.
T F 8. If f(g(x)) = g(f(x)) then f and g are inverses of each other.
[B] Simplify without a calculator.
1. 4√32x 13 • 4√128x 51
3.4 3√108 – 5 3√32
2.169/7 • 89/7
( )
4. x -6y -5
27y 20
-4/3
[C] Find all real solutions, if any.
1. 3√x = -125
2. 4 (2x – 9)4/5 + 77 = 53
3. 7 (5x + 6)11 + 36 = 1
4. 4x = √22x + 3
[D] Find the inverse and simplify. Then identify whether or not the original function is one-to-one.
1. a(x) = x -42.
b(x) = 6√x 9
3. c(x) = 3x + 1/24.
d(x) = 8x 2
5. e(x) = the championship NFL team in year x6.
f(x):
5
-5
0
5
-5
[E] Simplify or evaluate. Refer to the functions in part [D].
1. a(x) • b(x)2.
b(c(-10))
3. d(c(x))4.
a -1(d(b -1(b(5k))))
[F] Bonus.
1. Use the calculator to find the following, given the inverse of f(x) = 10x is f -1(x) = log x.
a) 10x = .002
b) 102x – 1 + 30 = 24