ExamView - Algebra II Chapter 7 Practice Test.tst

Name: _____________________________________ Period: __________ Date: ______________ID: A

Algebra 2 Chapter 7 Practice Test - Show all work for full credit! 1. Find the real-number root.

8. A garden has width 10 and length 5 10 . What is the perimeter of the garden in simplest radical form?

125 − 343

3

9. Simplify. − 10 + 5 9 + 2 10

2. Multiply and simplify if possible. 12 ⋅ 2

3. Simplify positive.

3

10. Simplify. ÊÁ −1 5 ˆ˜ −3 ÁÁ m m ˜˜ ÁÁ −2 ˜˜ ÁÁ m ˜˜ Ë ¯

128a 13 b 6 . Assume that all variables are

4. Divide and simplify. 3

500 3

6

11. Write the exponential expression 6x 7 in radical form.

2

5. Rationalize the denominator of the expression. Assume that all variables are positive.

12. Write the radical expression

7x 10 y 10

2+ 3

3

8 in exponential x 15

form.

5x 4 y 3

6.

7

13. Divide

3

16 4x 3 ÷ 3. 2 3x y 3y

6 14. Simplify the expression variables are positive.

7. Simplify the radical expression. 4 81x 20 y 16

3 2

3

27z 9 . Assume that all

15. Write the expression 9 in radical form, and simplify. Round to the nearest whole number if necessary.

1

ID: A 22. Let f(x) = −2x − 7 and g(x) = −4x + 3 . Find (f û g)(−5).

16. Complete the equation, by supplying the missing exponent.

⋅ 3 −6 = 3 2

3

23. Find the inverse of y = 7x 2 − 3 .

17. Solve the equation. x + 10 − 7 = −5

24. For the function f(x) = (8 − 2x) 2 , find f −1 .

18. Solve the equation.

25. Let f(x) =

x−2 and g(x) = 2x 2 + 4 . 4 a. Find f(g(x)). b. Find g(f(x)).

2

(x − 7) 3 = 4 19. Solve. Check for extraneous solutions. 6x = 24 + 12x

26. Graph the function. y = x +1

20. Let f(x) = x 2 + 2x − 1 and g(x) = 2x − 4 . Find 2f(x) – 3g(x).

27. Find all the real cube roots of 0.000027.

21. Let f(x) = 3x + 2 and g(x) = 7x + 6 . Find f ⋅ g .

28. Multiply and simplify

4

29.

3

7x 7 ⋅

3

6x 8 . Assume that all variables are positive.

32. Multiply. ˆÊ ÊÁ ÁÁ 7 − 2 ˜˜˜ ÁÁÁ 8 + ¯Ë Ë

400 4

5

ˆ 2 ˜˜˜ ¯

30. Add if possible. 4 3 3x + 5 3 10x

33. Write (8a −6 )

31. Simplify.

34. Let f(x) = x 2 + 6 and g(x) =

4

−

2 3

in simplest form.

ÊÁ g û f ˆ˜ (−7) . Ë ¯

83

35. Graph the function. y = x+3 2

x+8 . Find x

ID: A

Algebra 2 Chapter 7 Practice Test - Show all work for full credit! Answer Section 1. ANS: 5 − 7 PTS: 1 DIF: L3 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STA: CA A2 15.0 TOP: 7-1 Example 2 KEY: real roots 2. ANS: 2 6 PTS: 1 DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions TOP: 7-2 Example 1 KEY: multiplying radical expressions | simplifying a radical expression 3. ANS: 4a 4 b 2 3 2a PTS: 1 DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions TOP: 7-2 Example 2 KEY: multiplying radical expressions | simplifying a radical expression 4. ANS: 53 2 PTS: 1 DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions TOP: 7-2 Example 4 KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator 5. ANS:

x3y3

35y 5

PTS: 1 DIF: L3 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions TOP: 7-2 Example 5 KEY: divide radical expressions | simplifying a radical expression 6. ANS:

2 3 36 + 3 3 4 6 PTS: OBJ: STA: KEY:

1 DIF: L3 REF: 7-3 Binomial Radical Expressions 7-3.2 Multiplying and Dividing Binomial Radical Expressions CA A2 15.0 TOP: 7-3 Example 6 binomial radical expressions | multiplying binomial radical expressions | rationalize the denominator

1

ID: A 7. ANS: 3 |x 5 |y 4 PTS: 1 DIF: L3 REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions STA: CA A2 15.0 TOP: 7-1 Example 3 KEY: simplifying a radical expression 8. ANS: 12 10 units PTS: 1 DIF: L2 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STA: CA A2 15.0 TOP: 7-3 Example 2 KEY: adding radical expressions | problem solving 9. ANS: 10 + 15 PTS: 1 DIF: L2 REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions STA: CA A2 15.0 TOP: 7-3 Example 3 KEY: like radicals | simplifying a radical expression 10. ANS: 1 m18 PTS: OBJ: TOP: KEY: 11. ANS: 67 x 6

1 DIF: L3 REF: 7-5 Division Properties of Exponents 7-5.2 Raising a Quotient to a Power STA: CA A1 2.0 | CA A1 10.0 7-5 Example 4 raising a quotient to a power | simplifying an exponential expression | exponential expression

PTS: 1 DIF: L2 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0 TOP: 7-4 Example 2 KEY: rational exponent | radical form 12. ANS:

8x

−

15 7

PTS: 1 DIF: L4 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0 TOP: 7-4 Example 2 KEY: rational exponent | radical form

2

ID: A 13. ANS: xy 2 4

4x 3 16 ÷ 3 2 3x y 3y

Rewrite as multiplication by the reciprocal.

3 4x 3 3y = 2 ⋅ 3x y 16

Simplify by canceling common factors.

xy 2 = 4 PTS: 1 DIF: Basic REF: Page 579 OBJ: 8-2.4 Dividing Rational Expressions NAT: 12.5.3.c STA: 2A7.0 TOP: 8-2 Multiplying and Dividing Rational Expressions KEY: divide rational expressions | simplify 14. ANS: 3z 3 3

27z 9 3

= 27 · z 3 · z 3 · z 3 = 3·z·z·z = 3z 3

Factor into perfect perfect cubes. Use the Product Property of Roots. Simplify.

PTS: 1 DIF: Basic NAT: 12.5.3.c STA: 2A12.0 KEY: simplify radical expressions 15. ANS: ( 9) 3 ; 27

REF: Page 611 OBJ: 8-6.2 Simplifying Radical Expressions TOP: 8-6 Radical Expressions and Rational Exponents

3 2

9 = ( 9 )3 = (3) 3 = 27 PTS: OBJ: STA: KEY: 16. ANS: 8

Write with a radical. Evaluate the root. Evaluate the power.

1 DIF: Average REF: Page 612 8-6.3 Writing Expressions in Radical Form NAT: 12.5.3.b 2A12.0 TOP: 8-6 Radical Expressions and Rational Exponents fractional exponents | rational exponents | radical form

PTS: 1 DIF: L3 REF: 7-3 Mulitplication Properties of Exponents OBJ: 7-3.1 Multiplying Powers STA: CA A1 2.0 | CA A1 10.0 KEY: multiplying powers with the same base | simplifying an exponential expression | exponential expression 3

ID: A 17. ANS: –6 PTS: 1 DIF: L2 OBJ: 7-5.1 Solving Radical Equations KEY: radical equation | 18. ANS: 15; –1

REF: 7-5 Solving Radical Equations STA: CA A2 8.0 TOP: 7-5 Example 1

PTS: 1 DIF: L2 REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations STA: CA A2 8.0 TOP: 7-5 Example 2 KEY: radical equation | rational exponent 19. ANS: 1 PTS: OBJ: KEY: 20. ANS: 2x 2 −

1 DIF: L2 REF: 7-5 Solving Radical Equations 7-5.1 Solving Radical Equations STA: CA A2 8.0 TOP: 7-5 Example 4 radical equation | extraneous solutions

2x + 10

PTS: 1 DIF: L3 REF: 7-6 Function Operations OBJ: 7-6.1 Operations with Functions STA: CA A2 24.0 | CA A2 25.0 TOP: 7-6 Example 2 KEY: addition and subtraction of functions | operations with functions 21. ANS: 21x 2 + 32x + 12; all real numbers PTS: OBJ: TOP: KEY: 22. ANS: –53

1 DIF: L2 REF: 7-6 Function Operations 7-6.1 Operations with Functions STA: CA A2 24.0 | CA A2 25.0 7-6 Example 2 operations with functions | multiplication and division of functions | domain

PTS: 1 DIF: L2 OBJ: 7-6.2 Composition of Functions TOP: 7-6 Example 3 23. ANS:

y = ±

REF: 7-6 Function Operations STA: CA A2 24.0 | CA A2 25.0 KEY: composition of functions | operations with functions

x+3 7

PTS: 1 DIF: L2 OBJ: 7-7.1 The Inverse of a Function TOP: 7-7 Example 2

REF: 7-7 Inverse Relations and Functions STA: CA A2 24.0 | CA A2 25.0 KEY: inverse relations and functions |

4

ID: A 24. ANS:

f −1 (x) =

8±

x 2

; f −1 is not a function.

PTS: 1 DIF: L2 OBJ: 7-7.1 The Inverse of a Function TOP: 7-7 Example 4 25. ANS: x2 + 1 a. f(g(x)) = 2 x 2 − 4x + 36 b. g(f(x)) = 8 PTS: OBJ: TOP: KEY: 26. ANS:

REF: 7-7 Inverse Relations and Functions STA: CA A2 24.0 | CA A2 25.0 KEY: domain | inverse relations and functions | range

1 DIF: L3 REF: 7-6 Function Operations 7-6.2 Composition of Functions STA: CA A2 24.0 | CA A2 25.0 7-6 Example 3 composition of functions | multi-part question | operations with functions

PTS: 1 DIF: L2 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions TOP: 7-8 Example 1 KEY: domain | graphing | range | radical function | translation 27. ANS: 0.03 PTS: OBJ: TOP: 28. ANS: x5 ⋅ 3

1 DIF: L2 REF: 7-1 Roots and Radical Expressions 7-1.1 Roots and Radical Expressions STA: CA A2 15.0 7-1 Example 1 KEY: real roots | cube root

42

PTS: 1 DIF: L2 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions TOP: 7-2 Example 3 KEY: multiplying radical expressions | simplifying a radical expression

5

ID: A 29. ANS: 24 5 PTS: 1 DIF: L3 REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions TOP: 7-2 Example 4 KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator 30. ANS: not possible to simplify PTS: OBJ: TOP: KEY: 31. ANS: 16

1 DIF: L2 REF: 7-3 Binomial Radical Expressions 7-3.1 Adding and Subtracting Radical Expressions STA: CA A2 15.0 7-3 Example 1 binomial radical expressions | adding radical expressions | like radicals

PTS: OBJ: TOP: 32. ANS: 54 −

1 DIF: L2 REF: 7-4 Rational Exponents 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0 7-4 Example 4 KEY: rational exponent

PTS: OBJ: STA: KEY: 33. ANS: a4 4

1 DIF: L2 REF: 7-3 Binomial Radical Expressions 7-3.2 Multiplying and Dividing Binomial Radical Expressions CA A2 15.0 TOP: 7-3 Example 4 binomial radical expressions | simplifying a radical expression | multiplying binomial radical expressions

2

PTS: 1 DIF: L2 REF: 7-4 Rational Exponents OBJ: 7-4.1 Simplifying Expressions with Rational Exponents STA: CA A2 12.0 TOP: 7-4 Example 5 KEY: rational exponent 34. ANS: 63 55 PTS: 1 DIF: L3 OBJ: 7-6.2 Composition of Functions TOP: 7-6 Example 3

REF: 7-6 Function Operations STA: CA A2 24.0 | CA A2 25.0 KEY: composition of functions | operations with functions

6

ID: A 35. ANS:

PTS: 1 DIF: L2 REF: 7-8 Graphing Radical Functions OBJ: 7-8.1 Radical Functions TOP: 7-8 Example 2 KEY: domain | graphing | range | radical function | translation

7