Algebra 2 Chapter 5 Review

Name: ________________________ Class: ___________________ Date: __________

ID: A

Algebra 2 Chapter 5 Review Numeric Response Evaluate the expression without using a calculator.

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate.

1. 256 1 / 4 3. x 5  3125 2. 216 1 / 3 Short Answer 4. Find the indicated real nth root(s) of a. n  6, a  0

Write the expression in simplest form. 12.

5. Find the indicated real nth root(s) of a. n  2, a  9

7 6

2

Evaluate the expression without using a calculator. 6. 100 1 / 2

Simplify the expression.

7. 8 1 / 3

z6 81n 2

13. Use the properties of rational exponents to simplify the expression.

Write the expression in simplest form. Assume all variables are positive.

  5 / 2 8.  7 4 / 3  7 5 / 3     1/3 9.  7 4   

4

14.

w3 

w3

16w 24

Use the properties of radicals to simplify the expression. 10.

3

9  3 24

6

15. 3

11.

w5

100w 20

6 3 4 3

w5 

3

1

Name: ________________________

ID: A

Perform the indicated operation. Assume all variables are positive.

Graph the function. Identify the domain and range of the function.

16. 11y 7 / 4  6y 7 / 4

22. g x 

x 5

Write a rule for g described by the transformations of the graph of f. 17. Let g be a vertical stretch by a factor of 4, followed by a translation 1 unit left of the graph of f(x)  x  2.

18. Let g be a reflection in the x-axis, followed by a translation 3 units down of the graph of f(x)  2 3 x  1 .

23. g x  2 x  1

1/3

Solve the equation. Check your solution(s). 19. x  6 

20. x  33

21.

8x

1/2

 2x

5x  4  9

Describe the transformation of f represented by g. 24. f(x) 

.

2

3

x,

g(x)  2 3 x  1

ID: A

Algebra 2 Chapter 5 Review Answer Section NUMERIC RESPONSE 1. ANS: 4 PTS: NAT: NOT: 2. ANS:

1 DIF: Level 1 HSN-RN.A.1 | HSN-RN.A.2 Example 2 6

REF: Algebra 2 Sec. 5.1 KEY: evaluating expressions with rational exponents

PTS: NAT: NOT: 3. ANS:

1 DIF: Level 1 HSN-RN.A.1 | HSN-RN.A.2 Example 2 5

REF: Algebra 2 Sec. 5.1 KEY: evaluating expressions with rational exponents

PTS: 1 DIF: Level 1 NAT: HSN-RN.A.1 | HSN-RN.A.2 NOT: Example 4

REF: Algebra 2 Sec. 5.1 KEY: solving equations using nth roots

SHORT ANSWER 4. ANS: 0 PTS: 1 DIF: Level 1 NAT: HSN-RN.A.1 | HSN-RN.A.2 NOT: Example 1 5. ANS: 3

REF: Algebra 2 Sec. 5.1 KEY: nth root of a | finding nth roots

PTS: 1 DIF: Level 1 NAT: HSN-RN.A.1 | HSN-RN.A.2 NOT: Example 1 6. ANS: 1 10

REF: Algebra 2 Sec. 5.1 KEY: nth root of a | finding nth roots

PTS: 1 DIF: Level 1 NAT: HSN-RN.A.1 | HSN-RN.A.2 NOT: Example 2

REF: Algebra 2 Sec. 5.1 KEY: evaluating expressions with rational exponents

1

ID: A 7. ANS: 1 2 PTS: 1 DIF: Level 1 NAT: HSN-RN.A.1 | HSN-RN.A.2 NOT: Example 2 8. ANS: 7 15 / 2

REF: Algebra 2 Sec. 5.1 KEY: evaluating expressions with rational exponents

PTS: NAT: KEY: NOT: 9. ANS: 74 / 3

1 DIF: Level 1 REF: Algebra 2 Sec. 5.2 HSN-RN.A.2 properties of rational exponents | simplifying expressions with rational exponents Example 1

PTS: NAT: KEY: NOT: 10. ANS: 6

1 DIF: Level 1 REF: Algebra 2 Sec. 5.2 HSN-RN.A.2 properties of rational exponents | simplifying expressions with rational exponents Example 1

PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 2 11. ANS: 2

Level 1

REF: Algebra 2 Sec. 5.2 KEY: properties of radicals

PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 2 12. ANS:

Level 1

REF: Algebra 2 Sec. 5.2 KEY: properties of radicals

PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 4 13. ANS:  z3    9 n 

Level 1

REF: Algebra 2 Sec. 5.2 KEY: writing radical expressions in simplest form

PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 6

Level 1

REF: Algebra 2 Sec. 5.2 KEY: simplifying variable expressions

42  7 2 34

2

ID: A 14. ANS: 4

w 4w 10 PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 7 15. ANS:

Level 1

REF: Algebra 2 Sec. 5.2 KEY: simplifying variable expressions

PTS: 1 DIF: NAT: HSN-RN.A.2 NOT: Example 7 16. ANS: 17y 7 / 4

Level 1

REF: Algebra 2 Sec. 5.2 KEY: simplifying variable expressions

PTS: 1 DIF: NAT: HSN-RN.A.2 17. ANS: g(x)  4 x  1  8

Level 1

REF: Algebra 2 Sec. 5.2 KEY: like radicals NOT: Example 8

3

w 10w 7

PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 5.3 NAT: HSF-BF.B.3 KEY: writing transformations of radical functions | radical function NOT: Example 4 18. ANS: g(x)  2 3 x  1  3 PTS: 1 DIF: Level 2 REF: Algebra 2 Sec. 5.3 NAT: HSF-BF.B.3 KEY: writing transformations of radical functions | radical function NOT: Example 4 19. ANS: x  18 PTS: NAT: KEY: NOT: 20. ANS: x=3

1 DIF: Level 1 REF: Algebra 2 Sec. 5.4 HSA-REI.A.1 | HSA-REI.A.2 radical equation | solving radical equations | extraneous solutions Example 3

PTS: 1 DIF: Level 1 NAT: HSA-REI.A.1 | HSA-REI.A.2 NOT: Example 6

REF: Algebra 2 Sec. 5.4 KEY: solving equations with rational exponents

3

ID: A 21. ANS: x  17 PTS: 1 DIF: Level 1 NAT: HSA-REI.A.1 | HSA-REI.A.2 NOT: Example 1 22. ANS:

REF: Algebra 2 Sec. 5.4 KEY: radical equation | solving radical equations

domain: x  0, range: y  5 PTS: 1 DIF: Level 1 NAT: HSF-IF.C.7b | HSF-BF.B.3 NOT: Example 1 23. ANS:

REF: Algebra 2 Sec. 5.3 KEY: radical function | graphing radical functions | range | domain

The domain and range are all real numbers.

PTS: 1 DIF: Level 1 NAT: HSF-IF.C.7b | HSF-BF.B.3 NOT: Example 1

REF: Algebra 2 Sec. 5.3 KEY: radical function | graphing radical functions | range | domain

4

ID: A 24. ANS: The graph of g is a vertical stretch by a factor of 2 and a translation 1 unit down of the graph of f.

PTS: NAT: KEY: NOT:

1 DIF: Level 1 REF: Algebra 2 Sec. 5.3 HSF-IF.C.7b | HSF-BF.B.3 radical function | graphing radical functions | transformations of radical functions Example 2

5