Name: ______________________ Class: _________________ Date: _________ ID: A

1

Alg 1B Chapter 11 Final Exam Review

Match the correct graph with the appropriate function type

a. c.

b. d.____ 1. Linear Function

____ 2. Quadratic Function

Name: ______________________ ID: A

2

____ 3. Exponential Function

____ 4. Square Root Function

Please answer all questions on a seperate sheet of paper

5. Graph y = 3 2( ) x .

x -2 -1 0 1 2

y

Name: ______________________ ID: A

3

6. Graph y = 3( ) x .

x -2 -1 0 1 2

y

7. The value of a gold coin picturing the head of the Roman Emperor Marcus Aurelius is increasing at the rate of 7% per year. If the coin is worth $110 now, what will it be worth in 14 years?

8. The value of a gold coin picturing the head of the Roman Emperor Marcus Aurelius is increasing at the rate of 5% per year. If the coin is worth $145 now, what will it be worth in 13 years?

9. A radioactive isotope has a half-life of 15 hours. Find the amount of the isotope left from a 80-milligram sample after 90 hours. If necessary, round your answer to the nearest thousandth.

Name: ______________________ ID: A

4

10. A radioactive isotope has a half-life of 9 hours. Find the amount of the isotope left from a 280-milligram sample after 27 hours. If necessary, round your answer to the nearest thousandth.

11. Graph the data set {(–1, 0.5), (0, 1), (2, 4), (3, 8), (4, 16)}. Which kind of model best describes the data?

12. Graph the data set {(0, 0), (2, 2), (4, 4), (6, 6), (8, 8)}. Which kind of model best describes the data?

13. Look for a pattern in the data set. Which kind of model best describes the data?

Population Growth of BacteriaTime (hours) Number of

Bacteria0 2,0001 5,0002 12,5003 31,2504 78,125

14. Find the domain of the square-root function f(x) = 8(x + 2) − 6x.

15. Find the domain of the square-root function f(x) = 3(x − 3) .

Name: ______________________ ID: A

5

16. Simplify the expression 9w4 z5 . All variables represent nonnegative numbers.

17. Simplify the expression 4a 4b 3 . All variables represent nonnegative numbers.

18. Simplify y9

4y. The variable represents a nonnegative number.

19. Simplify x11

81x. The variable represents a nonnegative number.

20. Subtract.14 2 − 11 2

21. Add.18 2 + 14 2

Name: ______________________ ID: A

6

22. Multiply. Write the product in simplest form.

6b 4b

23. Multiply. Write the product in simplest form.

9h 6h

24. Simplify the quotient 52

.

25. Simplify the quotient 103

.

26. Solve the equation x + 8 = 19. Check your answer.

27. Solve the equation z + 5 = 7. Check your answer.

28. Solve the equation 4m + 8 − m + 5 = 0. Check your answer.

Name: ______________________ ID: A

7

29. Solve the equation 2z+ 4 − z+ 8 = 0. Check your answer.

30. Write in the inverse of the relation below:x -1 1 3 5 7y 4 2 1 0 1

xy

31. Write in the inverse of the relation below:x 1 2 3 4 5y 3 4 5 6 7

xy

ID: A

1

Alg 1B Chapter 11 Final Exam ReviewAnswer Section

MATCHING

1. ANS: B PTS: 1 2. ANS: A PTS: 1 3. ANS: D PTS: 1 4. ANS: C PTS: 1

SHORT ANSWER

5. ANS:

Choose several values of x and generate ordered pairs. Then, graph the ordered pairs and connect with a smooth curve.

PTS: 1 DIF: Basic REF: Page 773 OBJ: 11-2.3 Graphing y = ab^x with a > 0 and b > 1 NAT: 12.5.1.hTOP: 11-2 Exponential Functions KEY: exponential function | graph

ID: A

2

6. ANS:

Choose several values of x and generate ordered pairs. Then, graph the ordered pairs and connect with a smooth curve.

PTS: 1 DIF: Basic REF: Page 773 OBJ: 11-2.3 Graphing y = ab^x with a > 0 and b > 1 NAT: 12.5.1.hTOP: 11-2 Exponential Functions KEY: exponential function | graph

7. ANS: $283.64y = a 1 + r( ) t Use the exponential growth equation.

y = 110 1 + 0.07( ) 14 Substitute 110 for a, 0.07 for r, and 14 for t.

y = 110(1.07 14 ) Simplify.y = 283.64

PTS: 1 DIF: Average REF: Page 781 OBJ: 11-3.1 Exponential Growth NAT: 12.5.1.h TOP: 11-3 Exponential Growth and Decay

8. ANS: $273.42y = a 1 + r( ) t Use the exponential growth equation.

y = 145 1 + 0.05( ) 13 Substitute 145 for a, 0.05 for r, and 13 for t.

y = 145(1.05 13 ) Simplify.y = 273.42

PTS: 1 DIF: Average REF: Page 781 OBJ: 11-3.1 Exponential Growth NAT: 12.5.1.h TOP: 11-3 Exponential Growth and Decay

ID: A

3

9. ANS: 1.25 mg

First calculate t: 9015

= 6.

A = P(0.5) tWrite the half-life formula. A represents the final amount, P represents the original amount, and t represents the number of half-lives in a given time period.

A = 80(0.5) 6 Substitute 80 for P and 6 for t.

A = 1.25 Use a calculator.

PTS: 1 DIF: Average REF: Page 784 OBJ: 11-3.4 ApplicationNAT: 12.5.1.h TOP: 11-3 Exponential Growth and Decay KEY: exponential function | decay | half-life

10. ANS: 35 mg

First calculate t: 279

= 3.

A = P(0.5) tWrite the half-life formula. A represents the final amount, P represents the original amount, and t represents the number of half-lives in a given time period.

A = 280(0.5) 3 Substitute 280 for P and 3 for t.

A = 35 Use a calculator.

PTS: 1 DIF: Average REF: Page 784 OBJ: 11-3.4 ApplicationNAT: 12.5.1.h TOP: 11-3 Exponential Growth and Decay KEY: exponential function | decay | half-life

ID: A

4

11. ANS: exponentialPlot the data points and connect them. See whether a line, a parabola, or an exponential curve is the best fit.

This function is exponential.

PTS: 1 DIF: Basic REF: Page 789 OBJ: 11-4.1 Graphing Data to Choose a Model NAT: 12.5.2.gTOP: 11-4 Linear Quadratic and Exponential Models KEY: model | data | linear | exponential | quadratic

ID: A

5

12. ANS: linearPlot the data points and connect them. See whether a line, a parabola, or an exponential curve is the best fit.

This function is linear.

PTS: 1 DIF: Basic REF: Page 789 OBJ: 11-4.1 Graphing Data to Choose a Model NAT: 12.5.2.gTOP: 11-4 Linear Quadratic and Exponential Models KEY: model | data | linear | exponential | quadratic

ID: A

6

13. ANS: exponentialCheck for a pattern in the differences and the ratios of the y-terms.A linear function has constant first differences.A quadratic function has constant second differences.A cubic function has constant third differences.An exponential function has constant ratios.

Population Growth of Bacteria

Change in Time

Time (hours

)

Number of Bacteria

First Differenc

e

Second Differenc

e

Ratio

0 2,0001 1 5,000 3,000 2.51 2 12,500 7,500 4,500 2.51 3 31,250 18,750 11,250 2.51 4 78,125 46,875 28,125 2.5

For each change in time of 1 hour, only the ratios of the y-terms remain constant.The best model for the data is an exponential function.

PTS: 1 DIF: Average REF: Page 790 OBJ: 11-4.2 Using Patterns to Choose a Model NAT: 12.5.2.gTOP: 11-4 Linear Quadratic and Exponential Models

14. ANS: x ≥ –2The expression under the radical sign must be greater than or equal to 0, so 8(x + 2) ≥ 0. Solve the inequality for x to find the domain of the function.

PTS: 1 DIF: Advanced REF: Page 799 OBJ: 11-5.2 Finding the Domain of Square Root Functions TOP: 11-5 Square-Root Functions

15. ANS: x ≥ 3The expression under the radical sign must be greater than or equal to 0, so 3(x − 3) ≥ 0. Solve the inequality for x to find the domain of the function.

PTS: 1 DIF: Advanced REF: Page 799 OBJ: 11-5.2 Finding the Domain of Square Root Functions TOP: 11-5 Square-Root Functions

ID: A

7

16. ANS: 3w2 z2 zFactor perfect squares out of the radicand. Use the Product Property of Square Roots to take the square root of each factor separately. Simplify.

PTS: 1 DIF: Average REF: Page 806 OBJ: 11-6.2 Using the Product Property of Square Roots NAT: 12.5.3.cTOP: 11-6 Radical Expressions

17. ANS: 2a 2b bFactor perfect squares out of the radicand. Use the Product Property of Square Roots to take the square root of each factor separately. Simplify.

PTS: 1 DIF: Average REF: Page 806 OBJ: 11-6.2 Using the Product Property of Square Roots NAT: 12.5.3.cTOP: 11-6 Radical Expressions

18. ANS: y4

2

y9

4y

= y8

4Simplify the radicand.

= y4

2

Use the Quotient Property of Square Roots.

always indicates a nonnegative square root.

PTS: 1 DIF: Average REF: Page 806 OBJ: 11-6.3 Using the Quotient Property of Square Roots NAT: 12.5.3.cTOP: 11-6 Radical Expressions

ID: A

8

19. ANS: x5

9

x11

81x

= x10

81Simplify the radicand.

= x5

9

Use the Quotient Property of Square Roots.

always indicates a nonnegative square root.

PTS: 1 DIF: Average REF: Page 806 OBJ: 11-6.3 Using the Quotient Property of Square Roots NAT: 12.5.3.cTOP: 11-6 Radical Expressions

20. ANS: 3 214 2 − 11 2= 3 2 Combine the like radicals.

PTS: 1 DIF: Basic REF: Page 811 OBJ: 11-7.1 Adding and Subtracting Square-Root Expressions NAT: 12.5.3.cTOP: 11-7 Adding and Subtracting Radical Expressions

21. ANS: 32 218 2 + 14 2= 32 2 Combine the like radicals.

PTS: 1 DIF: Basic REF: Page 811 OBJ: 11-7.1 Adding and Subtracting Square-Root Expressions NAT: 12.5.3.cTOP: 11-7 Adding and Subtracting Radical Expressions

ID: A

9

22. ANS: 2 6Ê

ËÁÁÁÁ

ˆ

˜̃̃˜b

6b 4b = 24b 2 Product Property of Square Roots.

= 4 6( )b 2 Factor 24 using a perfect-square factor.

= 4 6 b 2 Product Property of Square Roots.

= 2 6Ê

ËÁÁÁÁ

ˆ

˜̃̃˜b

Simplify.

PTS: 1 DIF: Advanced REF: Page 816 OBJ: 11-8.1 Multiplying Square Roots NAT: 12.5.3.c TOP: 11-8 Multiplying and Dividing Radical Expressions

23. ANS: 3 6Ê

ËÁÁÁÁ

ˆ

˜̃̃˜h

9h 6h = 54h 2 Product Property of Square Roots.

= 9 6( )h 2 Factor 54 using a perfect-square factor.

= 9 6 h 2 Product Property of Square Roots.

= 3 6Ê

ËÁÁÁÁ

ˆ

˜̃̃˜h

Simplify.

PTS: 1 DIF: Advanced REF: Page 816 OBJ: 11-8.1 Multiplying Square Roots NAT: 12.5.3.c TOP: 11-8 Multiplying and Dividing Radical Expressions

24. ANS: 102

52

=52

22

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃˜̃̃˜

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

=104

Simplify the denominator.

=102

PTS: 1 DIF: Basic REF: Page 818 OBJ: 11-8.4 Rationalizing the Denominator NAT: 12.5.3.cTOP: 11-8 Multiplying and Dividing Radical Expressions

ID: A

10

25. ANS: 303

103

=103

33

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

˜̃̃˜̃̃˜̃̃˜

Multiply by a form of 1 to get a perfect-square radicand in the denominator.

=309

Simplify the denominator.

=303

PTS: 1 DIF: Basic REF: Page 818 OBJ: 11-8.4 Rationalizing the Denominator NAT: 12.5.3.cTOP: 11-8 Multiplying and Dividing Radical Expressions

26. ANS: x = 121x + 8 = 19x = 11 Subtract 8 from both sides.

( x ) 2 = 11( ) 2 Square both sides.

x = 121

PTS: 1 DIF: Basic REF: Page 823 OBJ: 11-9.2 Solving Radical Equations by Adding or Subtracting TOP: 11-9 Solving Radical Equations

27. ANS: z = 4z + 5 = 7z = 2 Subtract 5 from both sides.

( z ) 2 = 2( ) 2 Square both sides.

z = 4

PTS: 1 DIF: Basic REF: Page 823 OBJ: 11-9.2 Solving Radical Equations by Adding or Subtracting TOP: 11-9 Solving Radical Equations

ID: A

11

28. ANS: m = –1

4m + 8 − m + 5 = 04m + 8 = m + 5 Add m + 5 to both sides.

4m + 8Ê

ËÁÁÁÁ

ˆ

˜̃̃˜

2= m + 5Ê

ËÁÁÁÁ

ˆ

˜̃̃˜

2Square both sides.

4m + 8 = m + 5 Simplify.m = –1 Solve.

PTS: 1 DIF: Average REF: Page 824 OBJ: 11-9.4 Solving Equations with Square Roots on Both Sides TOP: 11-9 Solving Radical Equations

29. ANS: z = 4

2z+ 4 − z+ 8 = 02z+ 4 = z+ 8 Add z+ 8 to both sides.

2z+ 4Ê

ËÁÁÁÁ

ˆ

˜̃̃˜

2= z+ 8Ê

ËÁÁÁÁ

ˆ

˜̃̃˜

2Square both sides.

2z+ 4 = z+ 8 Simplify.z = 4 Solve.

PTS: 1 DIF: Average REF: Page 824 OBJ: 11-9.4 Solving Equations with Square Roots on Both Sides TOP: 11-9 Solving Radical Equations

30. ANS: w

PTS: 1 31. ANS:

w

PTS: 1